Prediction of structures and properties

Prediction of structures and properties for organic superconductors - CaltechTHESIS
CaltechTHESIS
A Caltech Library Service
About
Browse
Deposit an Item
Instructions for Students
Prediction of structures and properties for organic superconductors
Citation
Demiralp, Ersan
(1996)
Prediction of structures and properties for organic superconductors.
Dissertation (Ph.D.), California Institute of Technology.
doi:10.7907/7p7g-sm17.
Abstract
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
The main contributions of this thesis to the field of organic superconductors are basically (a) the band structure calculations for the investigations of the conduction properties of [...] using 2-D Hubbard Model with Unrestricted Hartree-Fock (UHF) theory, (b) ab initio quantum mechanical calculations for the structural characterizations and the properties of the donors of the organic superconductors, (c) electron-transfer boat-vibration (ET-BV) mechanism for the superconductivity of these materials, (d) developing force fields for BEDT-TTF and BEDT-TTF+.
To provide a basis for understanding the puzzling electronic properties of the organic superconductor [...] (with Tc=10.4K), we carried out band calculations using the 2-D Hubbard Model with Unrestricted Hartree-Fock (UHF) theory. The electron transfer hopping interactions are from ab initio calculations and the Hubbard parameter (Uopt=0.678950 eV) is adjusted to fit Shubnikov-de Haas and magnetic breakdown experiments. The calculations lead to a two-band semi-metal with a momentum gap separating the electron and the hole bands. The anomalous experimental observations are explained in terms of BEDT-TTF related phonons coupling these two bands (lower temperature) and by anion related phonons (higher temperature). These results also provide a framework for describing the conduction properties of other such complexes.
The donors of all known one- or two-dimensional organic superconductors, X, are based on a core organic molecule that is either tetrathiafulvalene (denoted as TTF) or tetraselenafulvalene (denoted as TSeF) or some mixture of these two molecules. Coupling X, with appropriate acceptors, Y, leads to superconductivity. The oxidized form of X may be X+ or X2+ species in the crystal. Using ab initio Hartree-Fock (HF) calculations (6-31G** basis set), we show that BEDT-TTF deforms to a boat structure (C2 symmetry) with an energy 28 meV (0.65 kcal/mol) lower than planar BEDT-TTF (D2 Symmetry). On the other hand BEDT-TTF+ is planar. Performing ab initio quantum mechanical calculations (HF/6-31G**) also on the other donors of organic superconductors, we find that all known organic superconductors involve an X that deforms to a boat structure while X+ is planar. This leads to a coupling between charge transfer and the boat deformation phonon modes. We propose that this electron-phonon coupling is responsible for the superconductivity and predict the isotope shifts [...] for experimental tests of the electron-transfer boat-vibration (ET-BV) mechanism. We suggest that new higher temperature organic donors can be sought by finding modifications that change the frequency and stability of this boat distortion mode. Based on this idea we have developed similar organic donors having the same properties and have suggested that with appropriate electron acceptors they will also lead to superconductivity.
The highest transition temperature Tc organic superconductors all involve molecule BEDT-TTF coupled with an appropriate acceptor. The experimental structures exhibit considerable disorder in the outer rings and concomitant uncertainty in the structures of BEDT-TTF. We find that Hartree-Fock (6-31G** basis set) calculations leads to results within 0.01Å and 1° of experiment for the ordered regions allowing us to predict to composite structures expected to have this accuracy. We report optimized geometries and atomic charges for BEDT-TTF, BEDT-TTF+, and BEDT-TTF+1/2 that should be useful for atomistic simulations.
The vibrational levels of BEDT-TTF and BEDT-TTF+ have been only partially observed and assigned. In order to provide a complete consistent description of all levels, we carried out HF calculations for all fundamental vibrational frequencies of BEDT-TTF and BEDT-TTF+ and obtained the Hessians for these structures. With these Hessians and available experimental frequencies, we developed the force fields for the neutral and cation BEDT-TTF molecules by using Hessian-biased method.
Item Type:
Thesis (Dissertation (Ph.D.))
Degree Grantor:
California Institute of Technology
Division:
Engineering and Applied Science
Major Option:
Applied Physics
Thesis Availability:
Public (worldwide access)
Research Advisor(s):
Goddard, William A., III
Thesis Committee:
Goddard, William A., III (chair)
Defense Date:
12 December 1995
Record Number:
CaltechETD:etd-09082006-140314
Persistent URL:
DOI:
10.7907/7p7g-sm17
Default Usage Policy:
No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:
3387
Collection:
CaltechTHESIS
Deposited By:
Imported from ETD-db
Deposited On:
26 Sep 2006
Last Modified:
16 Apr 2021 22:20
Thesis Files
Preview
PDF (Demiralp_e_1996.pdf)
- Final Version
See Usage Policy.
9MB
Repository Staff Only:
item control page
CaltechTHESIS is powered by
EPrints 3.3
which is developed by the
School of Electronics and Computer Science
at the University of Southampton.
More information and software credits
Prediction of Structures and Properties for

Organic Superconductors

Thesis by

Ersan Demiralp

In Partial Fulfillment of the Requirements
for the Degree of
Doctor of Philosophy

California Institute of Technology

Pasadena, California

1996
(Submitted 12 December 1995)

Ersan Demiralp

ill

To my parents

Acknowledgements

I am indebted to many generous people for their help and support during my stay at
Caltech. My deepest debt of gratitude is to my advisor, Bill Goddard. His intellec-
tual influence is evident throughout this thesis. Of all the members of the Goddard
group, I would especially like to thank Siddharth Dasgupta, Tahir Cagin, Naoki
Karasawa, Guanhua Chen, Francesco Faglioni, Xinlei Hua, Jean-Marc Langlois, Jim
Gerdy, Charles Musgrave, Xiaojie Chen, Ken Brameld for their friendship and sup-
port. I thank Terumasa Yamasaki of Asahi Chemical, a friend and a colleague for his
enjoyable friendship. My thanks also go to Kiirgad Kiziloglu for his “eski dostlugu.”

Mine’m has been a constant inspiration for me: “So oft have I invoked thee for
my Muse.” Finally, I would like to thank my family, in particular my parents who

have been my deepest source of support.

Abstract

The main contributions of this thesis to the field of organic superconductors are ba-
sically (a) the band structure calculations for the investigations of the conduction
properties of k — (BEDT —TTF).Cu(NCS)> using 2-D Hubbard Model with Unre-
stricted Hartree-Fock (UHF) theory, (b) ab initio quantum mechanical calculations
for the structural characterizations and the properties of the donors of the organic
superconductors, (c) electron-transfer boat-vibration (ET-BV) mechanism for the
superconductivity of these materials, (d) developing force fields for BEDT-TTF and
BEDT-TTF*.

To provide a basis for understanding the puzzling electronic properties of the or-
ganic superconductor «-—(BEDT —TTF)2.Cu(NCS)» (with T, = 10.4 K), we carried
out band calculations using the 2-D Hubbard Model with Unrestricted Hartree-Fock
(UHF) theory. The electron transfer hopping interactions are from ab initio calcula-
tions and the Hubbard parameter (U,p: = 0.678950 eV) is adjusted to fit Shubnikov-
de Haas and magnetic breakdown experiments. The calculations lead to a two-band
semi-metal with a momentum gap separating the electron and the hole bands. The
anomalous experimental observations are explained in terms of BEDT-TTF related
phonons coupling these two bands (lower temperature) and by anion related phonons
(higher temperature). These results also provide a framework for describing the con-
duction properties of other such complexes.

The donors of all known one- or two-dimensional organic superconductors, X, are
based on a core organic molecule that is either tetrathiafulvalene (denoted as TTF)
or tetraselenafulvalene (denoted as TSeF) or some mixture of these two molecules.
Coupling X, with appropriate acceptors, Y, leads to superconductivity. The oxi-
dized form of X may be X* or Xj species in the crystal. Using ab initio Hartree-
Fock (HF) calculations (6-31G** basis set), we show that BEDT-TTF deforms to

a boat structure (C2 symmetry) with an energy 28 meV (0.65 kcal/mol) lower than

planar BEDT-TTF (D2 symmetry). On the other hand BEDT-TTF* is planar. Per-
forming ab initio quantum mechanical calculations (HF /6-31G**) also on the other
donors of organic superconductors, we find that all known organic superconductors
involve an X that deforms to a boat structure while Xt is planar. This leads to
a coupling between charge transfer and the boat deformation phonon modes. We
propose that this electron-phonon coupling is responsible for the superconductivity
and predict the isotope shifts (67.) for experimental tests of the electron-transfer
boat-vibration (ET-BV) mechanism. We suggest that new higher temperature or-
ganic donors can be sought by finding modifications that change the frequency and
stability of this boat distortion mode. Based on this idea we have developed similar
organic donors having the same properties and have suggested that with appropriate
electron acceptors they will also lead to superconductivity.

The highest transition temperature 7’, organic superconductors all involve molecule
BEDT-TTF coupled with an appropriate acceptor. The experimental structures ex-
hibit considerable disorder in the outer rings and concomitant uncertainty in the
structures of BEDT-TTF. We find that Hartree-Fock (6-31G** basis set) calcula-
tions leads to results within 0.01A and 1° of experiment for the ordered regions
allowing us to predict to composite structures expected to have this accuracy. We
report optimized geometries and atomic charges for BEDT-TTF, BEDT-TTF*, and
BEDT-TTF*? that should be useful for atomistic simulations.

The vibrational levels of BEDT-TTF and BEDT-TTF* have been only partially
observed and assigned. In order to provide a complete consistent description of all
levels, we carried out HF calculations for all fundamental vibrational frequencies of
BEDT-TTF and BEDT-TTF* and obtained the Hessians for these structures. With
these Hessians and available experimental frequencies, we developed the force fields

for the neutral and cation BEDT-TTF molecules by using Hessian-biased method.

vil

Contents

Acknowledgements iv
Abstract Vv
1 Introduction 1
2 Band Structure Calculations for « — (BEDT — TTF),Cu(NCS)> 13
3 Structural Calculations for Organic Superconductors 58

3.1 Ab Initio and Semi-empirical Electronic Structural Studies
on BEDT-TTF ...... 0.0.0.0... 0000 es 59
3.2 The Electron-Transfer Boat-Vibration Mechanism For Organic
Superconductors ..........0. 0000000 cee eee, 80
3.3 Prediction of New Donors for Organic Superconductors ... 103
3.4 Ab Initio Studies of TTF-based Donors of Organic Supercon-

ductors .. 0... ek 115

4 Molecular Mechanical Calculations for BEDT — TTF and BEDT —
TT Ft 127

Chapter 1 Introduction

Organic molecular solids are commonly regarded as insulators. They usually have
few charged species and poor overlap between orbitals of neighboring molecules. In
the last fifteen years, new organic solids were found to exhibit metallic and even
superconducting behavior. These organic metals (also called synthetic metals) contain
only non-metallic elements such as carbon, hydrogen, sulfur, etc. in their conduction
frameworks. They also show interesting low dimensional behaviors. In this thesis, we
study the structures and the properties of the organic superconductors, except Cg
systems. Development of new organic materials is still in progress and very promising
for making higher transition temperature superconductors. Organic materials are
one of the best candidates for new superconductors since organic species can be
systemically modified.

In 1979, Bechgaard made (TMTSF).Y (now known as Bechgaard salts) which
consist of chains of TMTSF cations alternating with chains of inorganics anions,
Y (See Figure 1 in Section 3.3 for the nomenclature of organic donors).! For the
first Bechgaard salts, Y was PFs, AsF¢, SbF¢, etc. In 1980, (TMTSF),PFs was
shown to become superconductor at 1.4 K under an applied pressure of 6.5 kbar.?
Other Bechgaard salts were also shown to be superconducting under similar pres-
sures. Later, Bechgaard synthesized an ambient pressure organic superconductor
(ITMTSF),ClO, (T. = 1.4 K) with smaller spacing along chain of TMTSF stack.®
These successes opened the field of quasi one- or two-dimensional organic super-
conductors. The superconducting temperatures of Bechgaard salts are very low (1
to 3 K). However, several new donors of organic superconductors, such as BEDT-
TTF, BEDO-TTF, MDT-TTF, were synthesized to increase T, during the last. fif-
teen years. The highest transition temperature organic superconductors all involve
molecule BEDT-TTF (also denoted as ET) coupled with an appropriate acceptor.
In 1983, first ET superconductor, (ET)2ReO, was shown to be superconducting at

2 K under 4 kbar.* Since that time, more than twenty ET salts were found to be
superconducting.” The highest T, of these materials is 11.6 K at ambient pressure
for K — (ET),Cu[N(CN)2|Br (12.8 K at 0.3 kbar for k — (ET).Cu[N(CN),|CIl. See
Figure 1 for « — (ET),Cu|N(CN).|Br). The number of organic superconductors is
growing by synthesizing both new electron-donor molecules as well as new species.
There could be many substitutions to obtain higher T,, but it is not totally clear which
system would be best. The mechanism of the superconductivity in these materials
should be clarified for rational design of higher T, organic superconductors.

Most of the organic superconductors are of the form Dj{A~ with two donor
molecules sharing one charge. Different ways of stacking of the donor molecules
lead to many polymorphic phases. ET sometimes give many phases with one anion.
For example, (ET)2/3 have nine phases denoted by a, 6, y, 6, €, 7, €, K, 0.° Four
of these phases, a, k, 0, @ show superconductivity with T, between 1.5 K to 8.1 Kk.
These materials show a variety of electronic behaviors, i.e. semiconducting, metallic,
superconducting, etc.

The isotopic shift experiments °7°9!9) show that the mechanism of supercon-
ductivity involves the electron-phonon coupling and Bardeen-Cooper-Schrieffer (BCS)
theory. The electron-phonon matrix elements should be calculated to estimate T, for
a BCS system. To this end, one should obtain the electronic and the vibrational struc-
tures of these materials. Full quantum mechanical calculations are not practical for
these systems which contain on the order of hundred atoms in their unit cells. Thus,
one can employ the model Hamiltonians for the electronic structure calculations and
the force field methods for the phonon calculations. In Chapter 2, we performed elec-
tronic band structure calculations using the 2-D Hubbard Model with Unrestricted
Hartree-Fock (UHF) theory for the organic superconductor kt — (ET).Cu(NCS),
(with T, = 10.4K) to provide a basis for understanding the conduction properties of
this material (See Figure 2 and 3). The problem of electron-electron interactions and
their effects on the properties of physical systems are very important in solid state
physics. Hubbard proposed a model for the problem of electron correlations in the

d-electrons of the transition metals.!*13 In recent years, there have been many studies

on high J, superconducting materials using Hubbard Model. The Hubbard Model

has a simple Hamiltonian:

H® = SO (tyalaje + tiyalaic) HUY nioni-e (1)

where al, Gig, and nj, are the creation, annihilation, and number operators, respec-
tively, for the electron with spin o at site 7 and ¢,; are the hopping matrix elements
and U is the on-site Coulomb interaction. Here, < ij > indicates that the sum
is taken over nearest neighbor atoms. Despite the simplicity of this Hamiltonian,
Hubbard Model could not be solved exactly except in one dimension.'* The organic
superconductor « —(ET).Cu(NC'S)» possesses a number of puzzling electronic prop-
erties, including the temperature dependence of resistivity, magnetic susceptibility,
and Hall coefficient. Each unit cell of k-(ET)2Cu(NCS), has two Cu(NCS)>; units
and two (ET)} dimers packed perpendicular to each other in a parallel planar layer.
Since a plane of (ET)} dimers is sandwiched between the insulating Cu(NCS);
planes and two-dimensional electronic conduction behavior is observed, we describe
the electronic structure with a two-dimensional (2-D) Hamiltonian. There is no exact

solution for the 2-D Hubbard Model, hence we use Unrestricted Hartree-Fock (UHF)

approximation to describe electron-electron interaction terms,
NigNi-g © Nig < Ng > + < Nig > Nig-— < Nig >< Mg >. (2)

The UHF wavefunction is a Slater determinant of spin orbitals,

Noee
v= |] Alen9 (VAC >, (3)
kbo

where the spatial orbitals for up-spin are allowed to be different from those with
down-spin. Here, b, k denote the band index and k-point in the Brillouin Zone (BZ)

respectively. The variational equations have the form

HUHF,,
A Vkbo = EkboVkbs (4)

which must be solved self-consistently. Each UHF orbital is expanded in terms of
the basis set {xy} consisting of the Highest Occupied Molecular Orbital (HOMO) on
each ET
Vkoo = y XoCkbo(Q) — - (5)

The results of our band structure calculations are encouraging for the understanding
of several different electronic behaviors of ET salts.

The conducting molecular solid are charge-transfer (CT) salts with donor (D) and
acceptor (A) molecules. The charge transfer between donor and acceptor molecules

of the solid can be written as:
An + Dm — AZ’ + DP ;

where p is the amount of charge transferred. Several important issues related to
the molecular and the crystal properties should be considered to create a conducting
molecular solid. First, the solid should be stable with the charged building blocks.
Then, these charges should overcome Coulomb repulsions and delocalize to form
metallic bands. The electronic structure and the properties of the molecule (such
as ionization potential, electron affinity, polarizability, etc.) affect the nature and the
magnitude of the molecular interaction forces. The shape of the molecule is crucial for
the crystal packing due to van der Waals interactions. This leads to the interrelations
between the molecular arrangement and the molecular interactions. The stability
and the conduction properties of the molecular solid depend on these relations. In
Chapter 3, we present ab initio quantum chemical Hartree-Fock (HF) calculations
for the structures and the properties of the donors of the organic superconductors.
These organic materials show anisotropic conduction with high conductivity in the
plane (mostly for ET salts) or along chain (mostly for TMTSF salts) of the donors.
Thus, the changes in the properties of these molecules upon chemical modification
(structure, ionization potential, shape and energy of the molecular orbitals) are im-
portant for understanding the electronic and crystal structures of materials containing

these organic donors. We have performed ab initio quantum mechanical geometry op-

timizations for a number of donors in both the oxidized (Xt) and neutral (X) states.
We find that all known donors for superconductors lead to a distorted boat conforma-
tion and a planar conformation X*. As an electron hops from X to X7, the original
X distorts from boat to planar. This leads to a coupling between conduction electrons
and vibration (phonons) that is, we believe, the salient coupling for superconductivity.
With this insight, we have modeled electron-transfer boat-vibration (ET-BV) mech-
anism for the superconductivity of these materials. Using this model, we estimated
the isotope effects and found that our estimations are consistent with the available
experimental results.

In principle, one can perform quantum chemical calculations to obtain any prop-
erty for an isolated molecule. Recent developments of the computer hardware and
the software make it possible to do ab initio quantum mechanical calculations for
the donors of the organic superconductors. Despite this progress, ab initio quantum
mechanical calculations are still not practical for large systems such as molecules with
more than 100 atoms and crystals. Molecular mechanics or force field method is suit-
able for calculations on large systems. In general, the electrons are much faster than
nuclei, thus the electronic and nuclear motions are treated separately in the Born-
Oppenheimer approximation. Starting from the Born-Oppenheimer approximation,
the electronic states are averaged out to obtain atomic interaction potentials. In
molecular mechanics or force field method, each atom is a classical particle interact-
ing with atomic interaction potentials. Force fields are usually described in terms of

the sum of short-range valence interactions and long-range nonbond interactions:

The valence interactions are typically written as

om"
“I
Ne

vat = Boond + angle + E, + torsion + inversion

to include bond stretch Epona, angle bend Eangie, angle-bond and bond-bond cross E,,

dihedral torsion Ejorsion, inversion Ejnyersion terms. The nonbond interactions are

typically written as
Enp = Evaw + Eg (8)

to include van der Waals E,,aw and electrostatic Eg terms. The main advantage of the
force field approach is the reduction of the computational cost for large systems. The
amount of computer memory and time is drastically reduced by using the molecular
mechanics. For example, the quantum chemical frequency calculation (HF 6-31G*™*
basis set) took 14 hours 10 minutes 65 seconds on JPL Cray and molecular mechanical
frequency calculation took ~ 3.5 seconds on SGI Indigo workstation for neutral ET.

On the other hand, the force field approach can not be applied to the problems where

development of the reliable force field which will lead to reliable results. Hence, it is
very important to use some experimental or accurate quantum mechanical information
when one develops a force field. The Biased Hessian method uses the experimental or
accurate quantum mechanical frequencies to develop a force field. However, this is an
involved optimization process and can be very time consuming. But once a reliable
force field is obtained for a system, all kinds of molecular mechanical or molecular
dynamical calculations can be performed. In Chapter 4, we present the calculated
vibrational spectra for the equilibrium structures of ET (boat) and ET? (planar).
Using calculated structures, Hessians and available experimental frequencies we have
developed the force fields for the neutral and cation ET molecules. These results
should be helpful for the assignments of the modes and for the calculations of the
phonon structures of the crystals containing ET molecules.

Although most of our calculations are performed on ET systems, the applica-
tions of the models that are presented in this thesis on the other donors of organic

superconductors are straightforward.

References

10.

11.

12.

Bechgaard K., Jacobsen C. §., Mortensen K., Pedersen H. J., Thorup N., Solid
State Commun. 33, (1980) 1119.

Jerome D., Mazaud A., Ribault M., Bechgaard K., J. Phys. Lett. 41, (1980)
L95.

Bechgaard K., Carneiro K., Olsen M., Rasmussen F. B., Jacobsen C. S., Phys.
Rev. Lett., 46, (1981) 852.

Parkin S$. S., Engler E. M., Schumaker R. R., Lagier R., Lee V. Y., Scott J. C.,
Greene R. L., Phys. Rev. Lett., 50, (1983) 270.

Mori H., Int. J. of Modern Physics B, 8 (1994) 1-45.

Tokumoto M., Konishito N., Tanaka Y., Anzai H., Journal of the Physical
Society of Japan, 60, (1991) 1426.

Oshima K., Urayama H., Yamochi H., Saito G., Synthetic Metals, 27 (1988)
A473.

Schirber J. E., Overmyer D. L., Carlson K. D., Williams J.M., Kini A. M.,
Wang H. H., Charlier H. A., Love B. J., Watkins D. M., Yaconi G. A., Phys
Rev B 44, (1991), 4666.

Mori H., Hirabayashi I., Tanaka S., Mori T., Maruyama Y., Inokuchi H., Syn-
thetic Metals, 55-57 (1993)2437.

Heidmann C. P., Andres K., Schweitzer D., Physica 143B, (1986), 357.

Saito G., Yamochi H., Nakamura T., Komatsu T., Matsukawa N., Inoue T., Ito
H.,Ishiguro T., Kusunoki M., Sakaguchi k., Mori T., Synthetic Metals, 55-57
(1991) 2883.

Hubbard J., Proc. Roy. Soc., A276 (1963) 238-257

13. Hubbard J., Proc. Roy. Soc., A277 (1964) 237-259

14. Lieb E.H., Wu F.Y., Phys. Rev. Lett., 20, (1968) 1445-1448

Figure Captions

Figure 1. The crystal structure of « — ET,Cu[N(CN).|Br

Figure 2. The crystal structure of « — (ET)2.Cu(NCS).

Figure 3. Top view of the crystal structure of « — (ET).Cu(NC'S)>,

SES 34/ SES
= i] rae 1} Peo

i vt tT v

S- wt SS wh

js Fe

WN TS DY Ee

ear

way
See

oer,

Ear Grae as en

Chapter 2 Band Structure Calculations for
« —(BEDT — TT F)2Cu(NCS)»

The Conduction Properties of the Organic
Superconductor, « — (BEDT — TTF),Cu(NCS)2, Based on
the Hubbard Unrestricted Hartree-Fock Band Model

Abstract

The organic superconductor « — (BE DT —TTF).Cu(NCS), (with T, = 10.4k)
possesses a number of puzzling electronic properties, including the temperature de-
pendence of resistivity, magnetic susceptibility, and Hall coefficient. To provide a
basis for understanding these properties, we carried out band structure calculations

using the 2-D Hubbard Model with Unrestricted Hartree-Fock (UHF) theory. The

parameter (Ujp: = 0.678950 eV) is adjusted to fit Shubnikov-de Haas and magnetic
breakdown experiments. The calculations lead to a two-band semi-metal with a mo-
mentum gap separating the electron and hole bands. The anomalous experimental
observations are explained in terms of ET related phonons coupling these two bands
(lower temperature) and by anion related phonons (higher temperature). These re-
sults also provide a framework for describing the conduction properties of other such

complexes.

15
1.0 Introduction

Since 1980 the superconducting transition temperature, T,, of quasi one- and
two-dimensional organic superconductors has improved from 1.4 K! to 12.8 K.? The
best systems involve bis(ethylenedithio)tetrathiafulvalene (denoted as BEDT-TTF or
ET, shown in the Figure 1). Depending upon the acceptor and the packing, these
systems exhibit a variety of electronic behaviors, including semiconducting, metallic,
and superconducting.

One of the most interesting systems is « — (ET),Cu(NCS)o, which exhibits T, =
10.4 K at ambient pressure (See Figure 2 and 3 in Chapter 1). In k-(E'T)2Cu(NCS)o,
a layer of ET molecules paired into (ET)} dimers is sandwiched between insulating
Cu(NCS)5 planes. [The oxidation states are based on the ESR results? for Cu plus
charge neutrality.] This leads to conduction anisotropy along a, b and c directions
of?” Oge 1 0h 1 Oe = 5 : 1: 1.2. These systems can be considered as 2-D electronic
conductors (be plane). Each unit cell of k-(ET)2Cu(NCS)» has two Cu(NCS)>
units and two (ET)} dimers packed perpendicular to each other in a parallel planar
layer.

The electronic behavior of this salt is complex. As indicated in Figure 2a, the
resistivity, p, is a maximum around 100 K. p increases as T” below 100 K but decreases
as e?/T for above 100 K. As indicated in Figure 2b, the Hall coefficient, Ry, is positive
(hole-like) and both decreases rapidly and linearly as temperature increases to T =
60K; above 60 IK Ry decreases very slowly with T. As indicated in Figure 2c, the
magnetic susceptibility, x, is positive and almost constant (Pauli paramagnetism)
between 100 K and 300 K. Below 100 K, y decreases monotonically about 15% until
T = T, where it plummets to near zero. The superconducting T, is higher by 0.5
to 0.6 K when the hydrogens in ET are replaced by deuteriums (an inverse isotope
effect).

Shubnikov-de Haas’ (SdH) (Figure 2d), magnetic breakdown’ (Figure 2e) and
thermopower™* (Figure 2f) experiments on « —(ET)2Cu(NC'S), have been explained
qualitatively in terms of a two-band model derived from tight-binding band structure

calculations reported by Oshima et al.° and by LeBlanc et al.® However explana-

tions for the puzzling anomalies in the resistivity, susceptibility, and Hall effect have
not been provided. Several different mechanisms, (e.g. band gap opening,® polaron
formation®) have been offered to explain the anomaly of the resistivity around 100K.
However, no consistent explanation has been given for all these phenomena.

In this paper we develop a model for explaining these electronic properties. It
is based on the band structure (Section 2) of « — (ET)»Cu(NCS)> calculated using
a Hubbard model combined with Unrestricted Hartree-Fock (H-UHF) theory. The

predictions are compared with experiment in Section 3.

2.0 UHF Calculations Using the 2-D Hubbard Model

Since a plane of (ET)} dimers is sandwiched between the insulating Cu(NCS);
planes and since two-dimensional electronic conduction behavior is observed, we will
describe the electronic structure with a two-dimensional (2-D) Hamiltonian. The
highest two occupied molecular orbitals (MO) of ET are separated by 1.068 eV (HF
calculations with the 6-31G** basis set); hence we will consider only the Highest Occu-
pied Molecular Orbital (HOMO) on each ET molecule. The hopping matrix elements
(t;;) for HOMO’s on neighboring ET molecules are small compared to the Coulomb
interaction between two electrons in the same MO. Thus, electron correlation effects

are important, requiring a Hubbard model.

2.1 The Hubbard-UHF Calculations
We describe the electronic structure in terms of a 2-D Hubbard model with the

Hamiltonian (1):

HY = » (tijat,00 + ti; \,Qic) +U » NioNiio ’ (1)

<1j>,0

where a! Gig, and nig are the creation, annihilation, and number operators, respec-

wo?
tively, for the electron with spin o at site 7. Here, < 77 > indicates that the sum
is taken over the six nearest neighbors of each molecule. For the electron transfer
integrals t;;, we use the values (Table 1) of LeBlanc et al.® obtained from ab initio

generalized valence bond (GVB) calculations (on dimers corresponding to nearest-

neighbor ET molecules, using a minimal basis set). For the Hubbard parameter U
we estimate in Section 2.2 that U ~ 0.80 eV. Consequently, we calculated the band
structure using values of U in the range of 0 to 1.0 eV.

We find the following results:

1. U < Uz = 0.6780 eV leads to metallic behavior, with a nearly filled third band
(17% hole states) and a partially filled fourth band (17% electron states). |

ia. U < U, leads to an equal probability of up-spin and down-spin at each site!®
while U > U, leads to antiferromagnetic behavior.

iu. U, < U < U; = 0.698960 eV leads to semi-metallic behavior (nonoverlapping
third and fourth bands)

ww. U < Uaosea = 0.685195 eV leads to open orbits for electrons and closed orbits
for holes, but U > Ucipsea leads to closed orbits for both

v. U > U; leads to semiconducting or insulating behavior (a gap between the
third and the fourth bands).

vt. Usp: = 0.678950 eV leads to results in agreement with current experiments on
K — ET.Cu(NCS)o.

There is no exact solution for the 2-D Hubbard model, and hence we use the UHF

approximation to describe electron-electron interaction terms,
NigNi-¢ & Nig < Ning > + < Nig > Njug— < Nig >< Ni-g > . (2)

The average < nj, > for finite temperature is defined as the sum over all four bands

(nic) >> Noo (t

of the occupation number

Nkbo ( 1)
mel = SDE @)

where k is summed over the Brillouin Zone for all four bands. Here 3 = iat ae Qisa

normalization factor, and pu is the chemical potential.

The UHF wavefunction is a Slater determinant of spin orbitals,

Noce
v=] al,|vac> , (4)
kbo

where the spatial orbitals for up-spin are allowed to be different from those with

down-spin. The variational equations have the form

HUHF
H Vkbe = €kboVkbc

which must be solved self-consistently. Each UHF orbital is expanded in terms of the

basis set {x,} consisting of the HOMO orbital on each ET
Vkbo = d_ XoCkbo (0)
(4
This leads to the multiband equation (5) for each spin

3 [uv < Np,-0 > bno + toe Pre] Ckbo (17) = EkboCkbo (0) ’ (5)

where 6, is the Kronecker delta function and R,» is the distance vector between
neighboring sites. For t,. we use the values obtained by Leblanc et al.° from GVB

calculations.

2.2 The Value of U
To estimate the value of U we carried out Hartree-Fock (6-31G** basis set)
calculations"! on the successive ionization potentials of isolated ET and ET*+ molecules.
This leads to
IP, = Epps — Epp = 5.80eV

and

IP, = Eer+ _ Epr+ = 9.938eV

Thus for a vacuum we obtain
Uvac = [Pp — ITP, = 4.13eV . (6)

In the crystal, Uae is reduced by screening. ET is nearly planar with a length of
~13.5A (from the hydrogen of one end to the hydrogen of the other end) and 6
nearest neighbors at an average distance of 3.80A from the middle.!? Adding 1.0 A
_for the radius of the hydrogen atoms, we take a ~ 15.5A as the effective length of
ET.

Taking each ET as a charged conducting ellipsoid with semiaxes a = 15.5 A and

> b=c= 38A, leads the potential

a2 — b?
q tanh7!

&(q) Ja ak 2 q 3.993 e (7)

on the surface of the ellipsoid, where q is the electric charge (in units of absolute
electron charge) on the ellipsoid. By bringing the charge from infinity, the IP’s in the

crystal are estimated as

O(1
and
o(2
This leads to
—]l
Use = (IP: — IP1) se = Uvac — . (1) . (8)

We use € = 6 based on the estimate by Vlasova et al.' for the static dielectric constant
of (ET),Cu(NCS), in the b direction (in the plane of ET molecules). Using ® from
(7) in (8) leads to (IP,)s¢ = 2.47 eV, (IP2)s¢ = 3.27 eV and U,. = 0.80 eV. Thus
we considered the range 0 < U < 1.0 eV for the band calculations. Comparing to

experiment (vide infra) we conclude that Uj», = 0.678950 eV.

2.3 The Band Structure

Since the unit cell of k — (ET),Cu( NCS), has four ET molecules, there are four
bands based on the HOMO orbitals. With two electrons transferred to the Cu( NCS);
units, there are six electrons (two holes) to be shared by the HOMO’s of the four ET
molecules. Thus, 3/4 of all states are occupied.

Figure 3 shows the band structures for various values of U from 0 eV to 1.0 eV
and Figure 4 shows the corresponding Fermi surfaces. The Fermi energy is taken
as the energy reference, leading to negative energies for occupied levels and positive
energies for empty levels.

With UHF the energies and eigenstates of up-spin and down-spin are allowed to
be different at the same k-point. However, we find that for U < U, = 0.6780 eV
the band structures for spin-up and spin-down electrons are the same.! This leads
to calculated spin densities that are nearly the same (< nig >&< nig > 0.75)
for all sites. Our calculations (Table 2) lead to slight deviations from the expected
spin density of 0.75. Thus with U = 0 two sites have 0.7511 while the other two have
0.7489. This indicates that the four ET molecules have slightly different environments.
Very slight differences between < nig > and < nig > occur for U < U, = 0.678 eV.
Thus we find a net spin density of S,-, = 0.0003 at U = 0.670, 0.0007 at U = 0.674
and Sree = 0.0050 at U = 0.678. Above U, = 0.6780 eV the net spin density rises
rapidly as shown in Figure 5b. The numerical calculations are carried to a point
where < nig > is converged to better than 0.001 so that these small differences are
part of the H-UHF model.

For U > U,, the on-site Coulomb repulsion causes a significant difference between
the up-spin and down-spin densities at the same site (< nai >#< ng; >), leading to
antiferromagnetic character. Thus the down-spin bands differ increasingly from the
up-spin bands. The band structures are almost identical except for small differences
in the second and third bands, especially along M —TI. This is shown in Figures 31
(up-spin) and 3j (down-spin) for U = 1.0 eV. We conclude below that the value of
Usp: = 0.678950 eV (Figure 3c) explains the electronic behavior of those systems.

Table 2 shows up-spin and down-spin densities for various values of U. A good

measure of spin unpairing is
Snet = 4 S| < Nig — Nij-o > | ; (9)

which is tabulated in Table 3 and shown in Figure 5b. We see that

t. Spee © 0.0 for U < U, = 0.6780 eV.

a. for U > Ua, Snet equals to 0.018 at Uop: = 0.678950 eV. Then, S;,.¢ increases
rapidly to S,~ = 0.123 at U = 0.679 eV, Sree = 0.322 at U = 0.690 eV, and
Snet = 0.362 at U; = 0.698960 eV. Above U; it increases more slowly, finally reaching
Snet — 0.500 as U > ov.

iit. Snet = 0.5 for a perfect antiferromagnetic (U = co); thus Sy-¢ can be consid-
ered as the average spin density on each ET.

The conduction band occupancy (see Table 3, and Figure 5a) is constant, N, =
0.1697, for U < U, = 0.6780 eV. It decreases rapidly to N, = 0 at U; = 0.698960 eV.

Figures 6(a), 6(b), 6(c) and 6(d) show the density of states per spin at U = 0,
U, = 0.678 eV U = 0.678950 eV and U = 0.679 eV. The effective mass is defined as

N,(Er)
No

Mk = Me (10)
where N, is the band density of states, No is the density of states for free electrons
and Ep is the Fermi energy. This leads to m* = 0.90, m* = 1.14 for U = 0 eV
and m* = 0.99, mz? = 1.08 for Usp: = 0.678950 eV, where v and c denote the third
(valence) and fourth (conduction) bands.

Applying Fermi-Dirac statistics to the calculated band structure leads to the tem-
perature dependence for the conduction band occupation (NV) shown in Figure 7.
The valence band occupation is given by N, = 1— N,. For both U = 0 eV and
Uope = 0.678950 eV, N, increases monotonically with temperature.

Table 4 lists various characteristic energies of the band structure (measured rela-
tive to the bottom of the lowest band).

The band picture is strongly affected by the splitting of the bands. For U <

22
U, = 0.6780 eV the third and fourth bands overlap along the M — Y and M — Z
directions in reciprocal space, leading to metallic character. For U < U; = 0.698960
eV, this leads to holes in the third band and electrons in the fourth. For U > U; the
fourth (conduction) band and third (valence) band are totally separated, leading to
a semiconductor or an insulator. For U, < U < U; the third and fourth bands do not
overlap at the same k points. Thus orbitals at the Fermi surface in the conduction

bands no longer connect to orbitals in the valence band, leading to semi-metallic

behavior.

2.4 Calculational Details

The « — ET,Cu(NCS), crystal is monoclinic with space group P2,, Z=2, and
lattice parameters a = 16.256A, b = 8.4564A, c = 13.143A and @ = 110.276° at
T = 298K."

This leads to reciprocal lattice vectors (1/A units) of

~ bxe 1
=? =? ——..0 11
Ba orl X% = 9 (0,50) (115)
= 47 V = 47 > h? ’
- bxe -1 1
=2 = 2 {—_,0,- ll
C= en V (= :) (11¢)

where V is the volume of the unit cell.

Leblanc et al.© performed GVB calculations on ET dimers to obtain the trans-
fer integrals, t;;, between ET molecules [using the experimental room temperature
structure’ of k- ET,Cu(NCS)>]. These t;; values are given in Table 1 using the no-
tation in Figure 8. We used these transfer integrals and corresponding experimental
room temperature crystal structure in our calculations.

Every conduction layer (be-plane) of ET molecules is sandwiched by the insulating
layers of anion C'u(NC'S), along the a-axis. Since the nonzero t;; are in the be-plane,
the relevant 2-D Brillouin zone is for the BC-plane. B and C are perpendicular to

each other with lengths B = 0.74300947A~! and C = 0.50971229A~!, leading to

a rectangular Brillouin zone. The point Y lies along B, Z lies along C, and M is
at the corner of the Brillouin zone (see Figure 4). Hence, Y = a (0,0.11825363, 0),
Z = 7 (0.02810889, 0, 0.07608613), M = 7 (0.02810889, 0.11825363, 0.07608613). The
distances between these points are d(T Z) = 0.25485614A~!, d(TY) = 0.37150473A~!,
and the ratio is a = 0.68601048. We used 150 points along B and 102 points along
C.

For each U, the eigenvalues and eigenvectors were solved at each k-point leading
to 4 x (150 x 102) = 61200 energies for up-spin electrons and 61200 energies for down-
spin electrons for the four bands of k — ET,Cu(NCS)». Since there are 3 up-spin
electrons and 3 down-spin electrons for each 4 ET molecules, the 45900 states with
lowest energies were occupied for each spin. The average densities were calculated
using (3) for both up-spin and down-spin electrons. This process was continued
iteratively by using the new densities in (5) to obtain new energies and eigenvectors
at each k-point for both up- and down-spins. The up and down energies at each
k-point were saved and compared with energies of previous iteration at the same k-
point for all k-points of the Brillouin zone. The process was considered converged
when the RMS error of the energies was less than 107° eV. This took ~15 iterations
for U = 0.3 eV, ~400 iterations for U = 0.678 eV, ~15 iterations for U = 1.0 eV. For

the converged wavefunctions, we calculated band occupancies, density of states, and

the Fermi surface.

3.0 Comparison with Experiment
3.1 Magnetic Experiments

Using the band structures from Section 2, we will examine the various experi-
mental results. In making the comparisons we should emphasize that the t;; values
are based on minimum basis GVB calculations using the room temperature crystal
structure. Thus exact quantitative agreement cannot be expected.

Thermopower*”’ and Hall effect measurements (vide infra) indicate that hole con-
duction dominates,’* that electronic conduction is parallel to the b axis and that hole

conduction is parallel to the c axis. This is consistent with U values between 0 and

Ustosed = 0.685195 eV, which give band structures with a Fermi surface that is closed
for holes and open sheets for electrons. As U increases above U, = 0.6780 eV the
closed hole orbits shrink toward Z while the open electrons orbits move toward Y.
The open electron orbits touch the BZ boundary at Y for Ugosea & 0.685195 eV, and
above this value? lead to closed orbits around the M point (this would disagree with
the SdH experiments discussed below). As U approaches U; the hole orbits shrink to
zero at Z while the electron orbits shrink to zero at M. At U; = 0.698960 eV the 3rd
and 4th band separate leading to a semiconductor for U > Uj.

At a temperature of 1 K and for magnetic fields above 8 T, Oshima et al.° observed
magnetoresistance [Shubnikov-de Haas (SdH)] oscillations related to the extremal area

A of the Fermi surface normal to the field direction. The relation is

1 27 e
\(a)=i (12)

where H is the magnitude of magnetic field. They concluded that the observed os-
cillations correspond to a cylindrical Fermi surface containing 18% of the Brillouin
zone. Sasaki et al.!® observed the SdH effect at 0.5 K and above 8 T (see Figure 2d)
and found that the observed oscillations correspond to 16.3% occupation of the Bril-
louin zone. From a band structure based on the extended Hiickel (EH) approximation
(with the room temperature crystal structure), Oshima et al.’ found a “closed region
of about 18%.” These results can be compared to our result of 16.9% for U = 0.678950
eV. The antiferromagnetic transition reduces the area of the closed part of the BZ.
This closed portion totally disappears for U > U;. Thus SdH experiments are in
reasonable agreement with our results for U = 0.678950 eV.

The occurrence of magnetic breakdown (jumping of electrons between the open
and closed orbits under the magnetic field) supports the topology of Fermi surface
found by us and others,*® namely a closed valence band orbit and an open conduction
band orbit (see Figure 2e).'° These jumps correspond to the interband (between the
third and the fourth bands) transitions. This suggests that U > U, = 0.6780 eV but
U < Usosead = 0.685195 eV.

25
For large gaps, the probability of magnetic breakdown electronic transitions is

very small. The estimate is that magnetic breakdown transitions do not occur if

hu. << E. , (13)

where w, is the cyclotron frequency and E, is the direct gap between the third and
the fourth band. Sasaki et al.1® observed magnetic breakdown at 0.5K for fields above
H = 227, obtaining a value of £2 = 0.3417 meV. We find £4 = 0.1291 meV, 0.3197
meV and 8.4913 meV for U = 0.678 eV, 0.678950 eV and 0.679 eV respectively. Thus

e is very sensitive to U for U > 0.678 eV.

These comparisons with experiment suggest that the band structure for Uj ~
0.678950 eV in Figures 3 and 4 best describes the « — ET,Cu(NCS)> salt. Both
Oshima et al.>, and LeBlanc et al.® also obtained overlapping bands and hence metallic
conductivity, leading to a similar qualitative picture of the band structure. However,
Extended Hiickel (EH) calculations do not describe®® the antiferromagnetic states,
and hence EH calculations cannot provide a quantitative explanation of the magnetic
breakdown experiments.

Our results (Uo): = 0.678950 eV) suggest a very small antiferromagnetic coupling
with a net spin density of about 0.018 spins on each ET. Such antiferromagnetic
behavior has not yet been detected for « — ET,Cu(NC'S),. However, for the related
(nonsuperconducting) compound « — (ET)2C'u[N(CN),|Cl, Miyagawa et al.'’ and
Welp et al.'® found such an antiferromagnetic state (it becomes superconducting with
T. = 12.8 K under pressure of 0.3 kbar). Miyagawa et al.!’ observed a moment of (0.4-
1.0) 2p/dimer for k—(ET).Cu[N(CN),|Cl. We believe that these results support our
conclusion that the normal state of k - ET,C'u( NCS)» is a weakly antiferromagnetic
conductor. These « — (ET) CuX salts are similar and expected to have similar band
structures. The dramatic differences in the conduction properties of these two crystals
could likely arise from small differences in t;; and U values due to the slight differences
in packing. Thus changing U to U; = 0.698960 eV for K— ET,Cu(NC'S)2, would lead

to an insulating antiferromagnetic ground state with a moment of 1.4 jz, /dimer (taking

26
g=2.0). The temperature dependence of the susceptibility . of Kk — ET,Cu( NCS)»
shown in Figure 2c could be due to this very weak antiferromagnetism with a net
spin density 0.04 per dimer for U,,, = 0.678950 eV. x decreases as temperature
decreases for T <100 K (antiferromagnetic behavior) and shows little temperature
dependence between 100 K and 300 K (Pauli paramagnetic behavior). The spin
unpairing could be reduced by small changes in the t;; and U values due to slight
changes in the packing (e.g., the observed change in the interlayer spacing, which
has a maximum around 100 K). In this case, the weak antiferromagnetic contribution
may decrease as temperature increases above 100 K, allowing Pauli paramagnetism
to become dominant. Thus, Hubbard model is able to describe the puzzling magnetic

properties of these x salts.

3.2 Resistivity Experiments

The lattice spacing dyg9 = a-sin@ shows a maximum around 100 K. This maximum
has been attributed! to structural changes in the hydrogen bonding between the
terminal -CH,C H)— group of ET and the anion layer -SCN-Cu-NCS-. The bond
length of Cu-N also shows an anomaly around 100 k.”°

The resistivity increase in Figure 2a is proportional to T? until it peaks at T = 100

K, and then decreases exponentially with 1/T like a semiconductor. The ratio of

R(100K)

» . . . . a1
RGR) imcreases when tensile stress is applied along b axis.** Where

resistivities
electron-electron scattering dominates, we expect the temperature dependence of the
conductivity to be proportional to 7 while if electron-phonon scattering dominates
we expect it to be proportional to 7 (for large T). Thus experiment implies that
electron-electron scattering dominates for low T.

One might attempt to explain the semiconducting behavior of the resistivity in
terms of polarons. Polaron formation is plausible for this salt, especially around the
central (TTF) part of ET molecule. Indeed, quantum chemistry calculations show
that the central part of ET molecule changes most upon ionization.?”?*?4 However,
the temperature dependence of the thermopower for T > 100K (see Figure 2f) argues

against polaron formation. For polarons in metallic systems, the thermopower should

be constant, 1.e.
Sx logo, (14a)
qd

where p is the electron density. For polarons in semiconductor systems, the ther-

mopower (see Figure 2f) behaves as”°

Svs

(14)

This second type temperature behavior is exhibited by «-(ET),Cu(NCS),2 for T >
100K, suggesting that the system is semiconductor-like. However, such semicon-
ducting behavior is not consistent with the constant Pauli susceptibility observed for
T > 100K, see Figure 2c.

Electron-phonon scattering has the same effect on both spins and hence does
not affect the magnetic susceptibility even though it may dramatically affect con-
ductivity. Hence, we conclude that electron-phonon scattering must be involved in
the anomalous resistivity. This can explain the semiconductor-like conductivity since
the relaxation time for electron-phonon scattering is proportional to r Thus only
electron-phonon scattering would avoid a thermally activated region.

Based on the UHF calculations and using these experimental results as a guide,
we propose the following model for this system:

a. Below 100K, this system is semi-metallic. This happens when U > U, = 0.6780
eV and U < U; = 0.698960 eV. At low temperatures, the phonon densities are
low, hence there are no transitions between valence and conduction bands. As the
temperature increases the electron-phonon couplings promote electronic transitions
between these bands.

b. Around 100K, the electrons begin coupling to phonons of the anion layer. Due
to this coupling, the resistivity has a peak.

The phonons of the anion layers may scatter the electrons between different ET
molecules. The anion layer is insulating, but electrons can be scattered from one ET
to a nearest-neighbor ET (on the same side of anion layer) by coupling to a phonon

of the anion layer. Hence, this interaction will depend on the vibrations of ET and

28
of the anion, the distance of ET molecules from the anion layer, and the electronic
structure. Changes in the ET-anion layer interaction will modify the electron-phonon
coupling. Thus this mechanism involving scattering of ET electrons by anion phonons
can also explain the interlayer spacing anomaly! and the tensile stress effects on the

resistance.”! Consequently this model suggests that the conductivity has the form
ar (15a)

for T < 100K (where a is a constant). For T > 100K the electrons begin to scatter

with the phonons of anion layer, leading to the form

—ég/kyT
Si. ~ ye

— (156)

where ¥ is a constant and ¢, is the gap between Fermi surface and the bottom of the

anion band. Thus we can understand the behavior of the resistivity in Figure 2a.

3.3 Hall Measurements
The Hall coefficient Ry is observed (see Figure 2b) to be positive, decreasing with

temperature as

but with a dramatic break in the slope at 60K. The magnitude of the slope is 33 times
larger below 60K than above! There is no discontinuity in Ry around 100K where
the resistivity exhibits a hump.”°

Figure 7 shows that the change in carrier density is negligible between T = 0 Ix
and 300 Kk for both U = 0 eV and U, = 0.678950 eV.

For the parabolic two-band model, the Hall coefficient. is given as

_ 1 Ply — MK,

7 ; l7a
(ele (oily + 40,9 (ara)

where n, p are the electron. hole carrier densities and pn, Wy are the corresponding

29
mobilities. Since n = p, this leads to

Le Lp — Mn (17)

Ry= _
plelc (Hp + bn)? — ple|c Mp + pn

Similarly, for the parabolic two-band model, the conductivity is given as:
S. = Sq + Sp = nlelpin + Pleldp = Plel(tin + Lp) - (17)

The relaxation times for electron-phonon and electron-electron scattering are pro-
portional to - and ae respectively. Thus we take the temperature dependence of the

mobilities, fn and up, to be

Lo Ly

nn (18a)
Ho , He

Lp = al + T2 . (18d)

This leads to

Hy + fe
and
1 fla — ba 20
Ry = _ T . 20
" Bele sia + wa fa + ba (20)
Comparing with (16) leads to
1 2
a= Po (21a)
plele’ fa + py
and
1 —
_ Ha — Mi (22a)
plelc’ 2 + bn

The dramatic change in the slope of Ry at T = 60K must arise from a large change
in Zo. This could arise from transitions between the third and fourth bands caused

by the increased electron-phonon scattering with increased T.

4.0 Discussion and Conclusions

We should emphasize that the band calculations presented here include significant

approximations. The Hubbard model is a crude model of the many-body electron
correlations and UHF is a simple mean field approximation to this model. We have
used first principles calculations’ to obtain the ¢;; matrix elements; however, these
calculations used a minimal basis set and the room temperature crystal structure.
In addition, we ignored the role of the anion layer and of deeper bands. Even so
there is only one adjustable parameter (U) in our theory and the optimum value
is close to a first principles estimate. Thus given the good agreement of the final
band properties with experiment, we believe that the resulting model is useful for
describing the electronic structure of this class of organic superconductors.

The Hubbard UHF calculations lead to the following conclusions for
K — (ET).Cu(NCS)>. We find that the system is semi-metallic and weakly anti-
ferromagnetic with a momentum gap between the third and fourth bands. As the
temperature is increased, the ET phonons couple the electrons in these two bands.
We believe that this explains the anomalous Hall effect and susceptibility. Above
100K, we believe that electron-phonon scattering by phonons of the anion layer scat-
ter the conduction electrons, leading to the anomalous temperature dependence in
the resistivity.

The calculated band structure is very sensitive to U. This may be partly an artifact
of the Hubbard-UHF approximation. However, it may also signify the frustration
between antiferromagnetic coupling, vibrations of the ET and electronic coupling

that is at the heart of the superconducting in these systems.”?

References

10.

11.

Jerome D., Mazaud A., Ribault M., Bechgaard K., J. Phys. Lett. 41, (1980)
L95.

Wang HH, Carlson KD, Geiser U, Kini AM, Schultz AJ, Williams JM, Mont-
gomery LK, Kwok WK, Welp U, Vandervoort, Schirber J.E., Overmyer D.L.,
Jung D., Novoa J. J., Whangbo MH, Synthetic Metals, 42 (1991) 1983.

Oshima K., Urayama H., Yamochi H., Saito G., Physica C 153-155 (1988) 1148.

Oshima K., Mori T., Inokuchi H., Urayama H., Yamochi H., Saito G., Phys.
Rev. B 38, (1988), 938.

Leblanc O.H., Blohm M. L., Messmer R. P., MRS Symp. Proc. 173, (1990),
119.

Urayama H., Yamochi H., Saito G., Sugano T., Kinoshita M., Inabe T., Mori
T., Maruyama Y., Inokuchi H., Chemistry Letters (1988), 1057.

Mori H., Yamochi H., Saito G., Oshima K., in The Physics and Chemistry of
Organic Superconductors, (Springer-Verlag 1990), 150.

Toyota N., Sasaki T., Synthetic Metals, 41-43, (1991) 2235.

Cariss C. S., Porter L. C., Thorn R. J., Solid State Communications 74, (1990)
1269.

We define U, as the U value leading to a net spin unpairing of 0.005 per site.

Gaussian 92, Revision B, M. J. Frisch, G. W. Trucks, M. Head-Gordon, P.
M. W. Gill, M. W. Wong, J. B. Foresman, B. G. Johnson, H. B. Schlegel, M.
A. Robb, E. S. Replogle, R. Gomperts, J. L. Andres, K. Raghavachari, J. S.
Binkley, C. Gonzalez, R. L. Martin, D. J. Fox, D. J. Defrees, J. Baker, J. J. P.
Stewart, and J. A. Pople, Gaussian, Inc., Pittsburgh PA, 1992.

12.

13.

14,

15.

16.

17.

18.

19.

20.

21.

22.

32
Carlson KD, Geiser U, Kini AM, Wang H. H., Schultz AJ, Montgomery LK,
Kwok WK, Beno M. A., Williams JM, Cariss C. S., Crabtree G. W., Whangbo
MH, Evain M., Inorganic Chemistry, 27 (1988) 967.

Vlasova, R.M., Priev, S. Ya., Semkin V. N., Lyubovskaya, R. N., Zhilyaeva, E.
IL, Yagubskii, E. B., Yartsev V. M., Synthetic Metals, 48 (1992) 129.

Murata K., Ishibashi M., Honda Y., Fortune N. A., Tokumoto M., Kinoshita
N., Anzai H., Solid State Communications 76, (1990) 377.

The Fermi surfaces for U = 0.685190 eV and U = 0.685200 eV are shown
in Figure 3 (e) and (f). For U = 0.685190 eV The Fermi surface is open
for electrons but for U = 0.685200 it is closed. Thus we consider Uvioseq =
0.685195 eV. With the 150 x 102 discrete k points describing the BZ used in
our calculations we cannot obtain a Fermi surface that exactly touches the BZ

boundary.
Sasaki T., Sato H., Toyota N., Solid State Communications 76, (1990) 507.

Miyagawa K., Kawamoto A., Nakazawa Y., Kanoda K., Phys. Rev. Lett. 75,
(1995) 1174.

Welp U., Fleshler S., Kwok W. K., Crabtree G.W., Carlson K. D., Wang H.H.,
Geiser U., Williams J. M., Hitsman V. M., Phys. Rev. Lett. 69, (1992) 862.

Watanabe Y., Sasaki T., Sato H., Toyota N., Journal of The Physical Society
of Japan 60, (1991)2118.

Doi T., Kokichi O., Yamazaki H., Muruyama H., Hironobu M., Koizumi A..
Kimura H., Fujita M., Yunoki Y., Mori H., Tanaka S., Yamochi H., Saito G.,
Journal of The Physical Society of Japan 60, (1991) 1441.

Kusuhara H., Sakata Y., Ueba Y., Tada K., Kaji M., Solid State Communica-
tions 74, (1990) 251.

Demiralp E., Goddard W. A. III, J. Phys. Chem., 98, (1994) 9781.

23.

24.

25.

26.

27.

33
Demiralp E., Goddard W. A. III, Synthetic Metals, 72, 297 (1995).

Demiralp E., Dasgupta S., Goddard W. A. III, Journal of American Chemical
Society 117, 8154 (1995).

Chaikin P. M., in Organic Superconductivity, (Plenum Press 1990), 101.

Murata et al.° used the lack of an anomaly in Ry around 100K (which could be
caused by a change in the number of effective carriers) as an argument against

the gap formation model of Toyota et al.’

Saito G., Physica C 162-164, (1989) 577-582.

Table 1: Electron transfer matrix elements
Electron transfer matrix elements (t;;) from GVB calculations on ET dimers (from
reference 5). The nomenclature is explained in Figure 8. The units are in meV.

ty tg t3 ta ts t6
—162.9 —93.6 —92.8 32.3 —73.1 37.6

U (eV

Table 3: Characteristics of the band structure as a function of U
Characteristics of the band structure as a function of U. S,¢ is the spin unpairing
(see equation 9). N, is the occupation of the conduction band (it is the same for
both up-spin and down-spin bands). 6k is the momentum gap between closed orbits
(valence band) and open orbits (conduction band) of the Fermi surface; it is in units
of B/2 (the grid over k space has 75 points for B/2).

U (eV) N,. SNet bk State
0.000 0.1697 0.0000 & Metallic
0.300 0.1697 0.0001 * Metallic
0.670 0.1697 0.0003 & Metallic
0.674 0.1697 0.0007 4 Metallic
0.678 0.1697 0.0050 * Metallic
0.678950 0.1692 0.0183 & Semi-metallic
0.679 0.1434 0.1227 = Semi-metallic
0.680 0.1431 0.1238 fe Semi-metallic
0.685190 0.0796 0.2493 i Semi-metallic
0.685200 0.0511 0.2911 - Semi-metallic
0.690 0.0294 0.3221 - Semi-metallic
0.698960 0.0000 0.3615 - Semiconductor
0.800 0.0000 0.3874 - Semiconductor
1.000 0.0000 0.4218 - Semiconductor

oe) 0.0000 0.5000 - Insulator

Table 4: Energies from the band calculation

Energies (in meV) from the Hubbard-UHF band calculation on ET. All energies are
relative to the bottom of the first (lowest) band E? = 0. E? is the top of the fourth
(highest) band; this gives the total width of the ET HOMO band structure. Ep is
the Fermi energy (the chemical potential y, for zero temperature), E® is the energy of
the bottom of conduction (fourth) band E! is the energy of at the top of the valence
(third) band. E, is the direct energy gap between the third (valence) band and the
fourth (conduction) band. All results are for T = 0°.

U(eV) Et P ES, Et, E, =

0.000 844.8029 522.6820 442.4582 648.2950 8.1867 0.1282
0.300 844.8038 522.6751 442.4612 648.4528 «7.9128 ~—S «(0.1198
0.670 844.8049 522.6541 442.5829 648.5633 «7.7226 =~ 0.1141
0.674 844.8050 522.6398 442.6855 648.5620 7.7274 = 0.1143
0.6782 844.8223 522.6239 444.1521 648.3963 «8.2140 ~—S 0.1291
0.678950 845.0467 522.8909 448.8468 646.6708 «12.9284 —= 0.3197
0.679 855.3908 534.4193 491.2927 628.7004 «67.3640 ~—S 8.49113
0.680 855.6176 534.5743 491.9001 «628.5299 «68.0719 —«8.6682

0.685190° 886.6236 571.1884 555.7679 619.9479 122.9906 26.4828
0.685200° 900.3870 088.9825 578.9809 620.1448 131.4241 29.3256

0.690 912.3507 603.6132 597.9936 621.2653 139.6652 32.3160

0.6989607 929.5836 624.0354 624.0368 624.0339 148.4373 35.2914

0.800 968.6776 657.1822 677.9939 636.3704 158.9976 38.4676

1.000 1052.1515 728.6382 784.9779 672.2984 168.9013 39.1520
°Us,.

Us»: providing the best fit to the magnetic properties of k — ET,;Cu(NCS)po.
“Usosed == 0.685195 is between these two values.
OF

38
Figure Captions
Figure 1. The bis(ethylenedithio)tetrathiafulvalene molecule. This is denoted as
BEDT-TTF or simply as ET.
Figure 2.Experimental properties of k —- ET,Cu(NCS)o.
(a)Electrical resistivity, p is in bc plane. The maximum is at ~100 K.?"
(b) Hall coefficient (Ry) in the c direction with current parallel to b and magnetic
field parallel to a*. The large slope is from 20 to 60 K.'4
(c) The magnetic susceptibility with the field in the a*direction. The superconductor
transition is at 10.4 K .?”
(d) The magnetoresistance oscillations when the current and field are parallel to a*.*
(e) High field magnetoresistance oscillations. The arrows show the peak positions of
the high frequency F oscillations due to magnetic breakdown superimposed on the
low frequency Fy, oscillations.'®
(f) The thermoelectric power with the thermal gradient (a) parallel to c and (b)
parallel to b.??
Figure 3. The calculated Hubbard-UHF band structure as a function of U. Figures
a-h show the bands for spin-up electrons. For large U there are very slight differences
with the spin-down bands. This is shown in Figure 3j for U = 1.0 eV where there are
very small differences between the second and third bands for up-spin and down-spin,
especially along M —T in Figures 3i and 3}.
Figure 4. The Fermi surface as a function of U. The conduction (fourth) band
(electron states) has its lowest energy at M, and for U < 0.685190 eV leads to an
open Fermi surface in the MY direction, leading to the highest mobility in the c
direction. The valence (third) band (holes states) leads to a closed Fermi surface
centered around Z, leading to the highest mobility in the b direction. For U > U, =
0.678 eV the momentum gap between the third and fourth bands increases rapidly.
For U > U; = 0.698960 eV the lowest fourth band (electron) states (at M) are above
the highest third band (hole) states (at Z). This leads to semiconducting behavior.
Figure 5. Various properties as a function of U. (a) The conduction band occupancy

(N.) (for up-spin); the experimental value is about 0.163. Above U; = 0.698960

39
eV, the system is nonmetallic. (b) The (antiferromagnetic) the net spin density
(Snet); above U, = 0.678 eV the system is antiferromagnetic. (c) The momentum gap
(6k) between the third and fourth bands. (d) The magnetic breakdown factor oe
(assuming N. 4 0.0).
X marks the data point point for U,,: = 0.678950 eV.
Figure 6. Density of States for (a) U = 0 eV (b) U, = 0.6780 eV (c) Usp: = 0.678950
eV (d) U = 0.679 eV.
The dash lines show the contributions of the valence and the conduction bands.
Figure 7. Temperature dependence of the conduction band occupation for (a) U = 0
eV (b) Uy = 0.6780 eV (c) Usp = 0.678950 eV (d) U = 0.679 eV.
Figure 8. Definition of electron transfer matrix elements (t;;) for the band calcula-

tions of k — (BEDT — TTF),Cu(NCS).. Here aa’ and bb’ refer to the two pairs of

donors in each unit cell. See reference 5 for more details.

Figure 1. bis(ethylenedithio)tetrathiafulvalene, ET

1 aor =
3 3
\* P| -
r ; | c
1 2
x E 4 &
x t 7
= : Ww
B-l & 7 bd
«< &
gf ; rf
be - >
2 3 -
ig 3 a
=<
; x
-3 r i 1 roe
10 30 100 300
t/K
: d)
° 9
A ie
- Hg=30 kG
> 3F
oe] be
¥, 4
ime
‘Pe
Oo fas a a re
“IE 1 ri J
0 100 200 200
TIK

Fa =625T
F,=3800T

Figure 2

THVT TITTY TET ELLE TLV IT TEL PTT PITT ITTY ITT

re) ae cae Cer Oe ee es Ge

20s 2 a oe ee a a

FENVESTIVEVESUCTOCLCUSUOLTSTNCEOISTUCSESUSECSTN!

100
TEMPERATURE (K)

Nn
fo]

MAGNETO RESISTANCE (orb. units)

6 5 10
MAGNETIC FIELD H(T)

-30¢

oO
o}
oO

Energy (meV)

-200 rT
-400 Oran
Tv if | i

-600

400

Yt 2
a) U=0 eV
_ /~
E,
oY

ELL

400
Cc) U = 0.678950 eV
200 L
E,
ot YL [NZ
aah TS =~ |
-400 PONS
-600 T T T TT
400
U=0.685190 eV
2004 [-

soi _/ SA!

Figure 3

"7 .

400

200

-200

-400

-600

400

200

a / ae
-200+ ;
“ a
600 T T T T +

40
U=0.685200 eV
200

~200;

CA NS

-60

MOY rz Mor

b) U=0.678 eV

PNT

T qT q T

| qd) JN. U=0.679 eV /)
WL FX /

Energy (meV)

ewok

-400 4

-600 +

-800

-2004

-400-

-600 +

-B00

400

200 -

400

2004

-800 ; I

40 i iL ii i

h) U =0.698960 eV
200 LN
oLY.

ed—_ / i
aod TNO

i a ae

-80
400 -—~
j) Lowe vs
200 LY Ee ed i
0 a7
-200 + r
eee a ees
-400 + L
-600 a Ae

U=0.0eV Z M
a) NL
| Y
U=0.678950eV Z M
r Y
U=0.685190eV Z M
e) NY”
AS

Figure 4

U=0.678eV

b) ~

U=0.679eV

ay 7 \

gal

U=0.685200eV Z

| — I}
jo — |
\ RK

Conduction Band Occupancy, N

0.20

0.05-

0.00

0.20

? @
0.60 0.80 1.00
U (eV)

Figure 5 (a)

Net

Net Spin Density, S

0.50

0.40-

0.30-

0.20-

0.10-

0.00 -
0.00

0.20 0.40 0.60 0.80 1.00

Figure 5 (b)

o 9

. (o>)

Momentum Gap ( 6 k)
(units of B/2)

0.20-

0.00 I

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70

Figure 5(c)

U (eV)

0.2

0.4

| “ [

0.6 0.8 1
U (eV)

Figure 5 (d)

Density of States per spin (eV"')

20 | l
U =0.0 eV
15- Z
10- 7
57 o
-600 -400 -200 0 200 400
Energy (meV)

Figure 6(a)

Density of States per spin (eV)

15~

10-

U= 0.678 eV

-600

-400

| I
-200 0 200 400
Energy (meV)

Figure 6(b)

Density of States per spin (eV)

20 | |
U =0.678950 eV
15~- LL
10- _
5 + lL.
0 1 I
-600 -400 -200 0 200 400
Energy (meV)

Figure 6(c)

Density of States per spin (eV”')

20 i | |
U =0.679 eV
15- -
10- L
5 - |
0 I T I I
-600 -400 -200 0 200 400
Energy (meV)

Figure 6(d)

Fourth (Conduction) Band Density

0.176

0.175 -

0.174 -

0.173 ~

0.172 -

0.171

0.17 -

U=0eV

0.1694

100 += 150

Figure 7 (a)

200 _250 300

Temperature (K)

0.176 l

2 0.175~- U = 0.678 eV L

2 0.174- L

= 0.173~ L

2 0.172 -

= 0.171- a

£ 017————< ° :

0.169 . |
0 50 100 150 200 250 300

Figure 7(b)

Temperature (K)

Fourth (Conduction) Band Density

0.175

0.174 +

0.173 -

0.172 -

0.1715

0.17 -

0.169

U = 0.678950 eV

100

150

Figure 7(c)

200

250 300

Temperature (K)

Fourth (Conduction) Band Density

0.146

0.145 -
0.144 -
0.143
0.142 -
0.141 ~

0.14

U = 0.679 eV

100

150

Figure 7(d)

200

250 300

Temperature (K)

8 amn317

ie)
o ad
eee +
I a ~~
m. or
We)

Chapter 3 Structural Calculations for Organic

Superconductors

59
3.1 Ab Initio and Semi-empirical Electronic Struc

tural Studies on BEDT —TTF

Abstract

We report electronic structure calculations for the organic molecule
bis(ethylenedithio)tetrathiafulvalene (BEDT-TTF or ET), associated with the high-
est T, organic superconductors. The experimental structures exhibit considerable
disorder in the outer rings and concomitant uncertainty in the structures. We find
that Hartree-Fock (6-31G** basis set) calculations lead to results within 0.01A and 1°
of experiment for the ordered regions allowing us to predict to composite structures
expected to have this accuracy. We report optimized geometries and atomic charges

for ET, ET*, and ET +3 that should be useful for atomistic simulations.

1.0 Introduction

The transition temperature of organic superconductors has been in-
creasing since the discovery of (TMTSF),PF,.'* The highest T, organic supercon-
ductors involve the electron donor bis (ethylenedithio) tetrathiafulvalene (denoted as
BEDT-TTF or ET, shown in the Figure 1 in Chapter 2) complexed to appropriate
electron acceptors. Such systems show a variety of electronic behaviors (semiconduct-
ing, metallic, superconducting), but it is not totally clear how the superconductivity
is related to the structure, composition, electronic states, or vibrational states.”° We
are carrying out a series of theoretical studies aimed at establishing a basis for such
an understanding. In carrying out these studies we found a disturbing variation in
experimental structures from various sources. Since structure is the starting point
for many of our studies, we optimized the structures for both neutral and cation
ET molecules using both the ab initio Hartree-Fock (HF) method (with the 6-31G**
basis set)* and the semi-empirical modified neglect of differential overlap (MNDO)
method.°

The best organic superconductors have the composition (ET),,X, where
X is an electron acceptor.*? In most such crystals there are ET>' dimers, but some
crystals have HT+. Consequently, we report properties (structure, HOMO, LUMO
levels, atomic charges) for ET, ET+, and ET+?. By comparing theory and experi-

ment we were able to extract composite best structures.

2.0 Calculations

Using the HF method with a 6-31G** basis set, we optimized the struc-
tures of ET (Cy symmetry) and ET+ (Dy symmetry).4 With MNDO? we also opti-
mized the structures of ET and ET*, but it was necessary to distort the molecule
to C,. This led to deviations from the strict D. symmetry (less than 0.001A for
distances and less than 0.05 degrees for angles for neutral case, less than 0.005A for

distances and less than 0.5 degrees for angles for cation case).

3.0 Structural Results
3.1 Neutral ET

The crystal structure of neutral ET was reported by Kobayashi et
al? (See Figure 1). The monoclinic unit cell has four molecules grouped into two
dimers. Such dimer structures are observed in most crystals containing ET molecules.
The structural studies show a planar geometry for the central C2S4-like region; how-
ever, the terminal —C'H, — CH2— groups are nonplanar, leading to distortion and
(probably) disorder.

Averaging out the small differences of the bond lengths and the angles
of the neutral ET with C, symmetry , we take 7 independent atoms (See Figure 1 in
Chapter 2 for notation): Cc (central double bonded carbon), S$; (S in 5 membered
ring), Cs (double bonded C in 5 membered ring), Sg (S in 6 membered ring), Ce
(single bonded C in 6 membered ring), H, (H bonded to Cs but out of plane, axial),
H; (H bond to Cg but nearly in the plane, equatorial). The other atoms are obtained
from rotations about the x, y, or z axes.

From Table 1 we see that HF bond distances are within about 0.015A
of experiment while MNDO is within about 0.06A. The bond angles also agree well,
errors of about 1° for HF and about 3° for MNDO. In these comparisons with ex-
periment, we do not use the experimental positions for the terminal -CH) — CH)—
groups since they are disordered (thus the experimental Cg — Cs bond distance of
1.46A is clearly low by 0.07A). As a result the experimental data on the out-of-plane
distortions are not reliable.

Both theory and experiment show the Sg — Cs bond to be significantly
longer than Sg — C; (by 0.04 to 0.06A), indicating partial double bond character for
bonding of Sg to Cs = Cs,.

3.2 ETT

There are two crystal structures®® with essentially a full positive charge
on ET, ¢ — (ET)PFs and 6 — (ET)PFe (See Figure 2). We carried out full self-
consistent optimization of the structure for ET+ with both HF(6-31G**) and MNDO.
The structural parameters are compared with experiment in Table 2. Again there is
excellent agreement between HF and experiment. Of the experimental results, the

structure for e— (ET) PFs seems less reliable since the value obtained for the Cs —Ce-

62
bond is 1.32A (rather than the expected value of 1.53A). The 6 — (ET)PFs crystal
leads to R(Cg—C¢,) = 1.484A, short but in agreement with the structural data for the
neutral. Thus we compare these to the 6 crystal results. Comparing ET and ET™*,
we see that the structure changes occur only within the TTF portion, as indicated
in Figure 3. This suggests that ionization involves primarily the central C = C bond
followed by some delocalization of the Ss; 2 orbital onto Cc and some delocalization

of the Cs = Cs, bond onto Ss.

3.3 ET*?

The best organic superconductors have an average charge of +0.5 on
each ET. Examples include two important « phase crystals {«—(ET),Cu(NCS)» (see
Figure 2 and 3 in Chapter 1) and & — (ET).Cu[N(CN).|Br (see Figure 1 in Chap-
ter 1) and @ — (ET)2I3}.°~!! In Table 3 we compare the average of the calculated
structures for ET and ET* with the average structural parameters. The 5-membered
rings from all three crystal structures agree well with the theory (error of 0.01A for
HF); however, the 6-membered rings disagree substantially. Thus the C; — S, dis-
tance of the two « states have values of 1.744A and 1.749A while 6 — (ET) Iy has
1.712A. The experimental studies of ET lead to 1.742A while ET* of 6 — (ET)PF¢
leads to 1.736A. Thus we assume that there is some problem with the value 1.712A for
B—(ET)oI3. Also for the Sg—C¢ distance, the value of 1.740A for K~-(ET).Cu(NCS)»
differs substantially from all others (1.811A for the other « structure, 1.810A for
GB(ET )oI3, 1.809A for 6—(ET)PFe, and 1.802A for neutral ET). As a result only the
k— ET,CulN(CN).|Br structure seems to be without problems and we will use it for
all comparisons. Comparing the crystal structure for ET+? and the average experi-
mental values for ET and ET* (see Table 3), we find excellent agreement (Co = Co,
longer by 0.01A, S; — C; longer by 0.08A). This justifies the use of the average values
from the theory.

Comparing the theoretical values with experiment for ET*?, we also
find excellent agreement: bonds distance within 0.02A for HF and 0.08A for MNDO,
bond angles within 0.9° for HF and 5.6° for MNDO.

4.0 Charges

There are two ways to evaluate charges from electronic wavefunction.
Mulliken charges are based on the MO coefficients. Potential derived charges (PDQ)
are based on the electric field derived from the HF density.!° A set of atomic charges
are obtained that reproduce the same electric field outside the vdW radii. Since
the charges are used to predict packing energies and geometries in the crystal, PDQ
charges should be more useful. In addition we have applied an empirical method,
charge equilibration’ (denoted as QEq), which is based only on atomic parameters.

The PDQ charges were calculated using both the CHELPG model of
GAUSSIAN 92 and the PDQ module of the PS-GVB"® program. (For the latter, the
point charges fit not only the potential but also the ab initio dipole and quadrupole
moments.) There seems to be a numerical problem with GAUSSIAN 92 since the
calculated charges do not reflect the symmetry of the molecule (C2 for neutral ET
and D, for ET*) and of the wavefunction. We symmetry averaged the GAUSSIAN
92 results to obtain the values in Figure 4 (top line for each atom). PS-GVB leads to
symmetry consistent results (Figure 4, second line for each atom).

The main charge density is around the central part of the molecule.
This result is consistent with the STM experiment of « — (ET),Cu(NCS)»."* The
change between ET and ET*t suggests that during the electron transfer between ET
molecules, the vibrational modes of the central part of ET (center carbons and sulfurs
on the pentagon ring) may couple with the electrons. However, recent isotope exper-
iments exclude the importance of these kind of couplings for the superconductivity

of organic superconductors.1”!8

5.0 Ionization Potential

The orbital energies from HF and MNDO calculations on ET and ET*
are shown in Figure 5, 6 and Table 4. The HOMO and LUMO orbitals from HF are
plotted in Figure 7 and 8. The experimental gas-phase ionization potential is 6.21
eV.'8 Comparing the total energies from the HF calculations on the ion and neutral

leads to JP = 5.80 eV whereas the orbital energy of the neutral (Koopmans theorem)

64
leads to IP = 7.07 eV. This is typical, the correlation error is smaller for the positive
ion leading to too small an JP. Koopmans theorem assumes that the orbitals do not
relax upon ionization, leading to too large a value. The average value of 6.44 eV is
in good agreement with the experiment. From MNDO, the total energies leads to an

IP of 7.42 eV, whereas the orbital energy leads to IP = 8.09 eV.

6.0 Conclusion

The structures from HF calculations (6-31G** basis) are in excellent
agreement (0.01A and 1°) with the experimental data on the ordered regions of ET,
ET*, and ET+2. Thus one may use the HF structures to obtain full structural

parameters. The atomic charges should be useful in molecular dynamics simulations.

References

1. Jerome D., Mazaud A., Ribault M., Bechgaard K., J. Phys. Lett. 41, (1980)
L95.

2. Williams J. M., Ferraro J. R., Carlson K. D., Geiser U., Wang H. H.,Kini A.
M., Whangbo M-H, Organic Superconductors (Including Fullerenes): synthesis,
structure, properties, and theory, (Prentice-Hall 1992).

3. Kobayashi H., Kobayashi A., Yukiyoshi S., Saito G., Inkuchi H., Bull. Chem.
Soc. Jpn., 59, (1986) 301.

4. Gaussian 92, Revision B, M. J. Frisch, G. W. Trucks, M. Head-Gordon, P.
M. W. Gill, M. W. Wong, J. B. Foresman, B. G. Johnson, H. B. Schlegel, M.
A. Robb, E. S. Replogle, R. Gomperts, J. L. Andres, K. Raghavachari, J. S.
Binkley, C. Gonzalez, R. L. Martin, D. J. Fox, D. J. Defrees, J. Baker, J. J. P.
Stewart, and J. A. Pople, Gaussian, Inc., Pittsburgh PA, 1992.

5. The MNDO calculations used Mopac, Version 6.00: M. J. S. Dewar, et al., Frank
J. Seiler Research Laboratories, U.S. Air Force Academy, Colorado Springs,
Colorado, 80840.

6. a) Bu, X., Cisarova I., Coppens P., Acta Cryst. C48 (1992) 1562.
b) Bu, X., Cisarova I., Coppens P., Acta Cryst. C48 1992) 1558.

7. Kozlov M. E., Pokhodnia K. I., Yurchencko A. A., Spectrochimica Acta 45A
(1989), 323.

8. Kozlov M. E., Pokhodnia K. I., Yurchencko A. A., Spectrochimica Acta 45A
(1989), 437.

9. Carlson, K. D, Geiser U., Kini A. M., Wang H. H., Montgomery L. Kk., Kwok
W. K., Beno M. A., Williams J. M., Cariss C. S., Crabtree G. W., Whangbo
M-H. Evain M. Inorg. Chem. 27, (1988), 967.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

66
Geiser U., Schultz A. J.. Wang H. H., Watkins D. M., Stupka D. L., Williams
J. M., Schirber J. E., Overmyer D. L., Jung D., Novoa J.J., Whangbo M-H.
Physica C 174, (1991), 475.

Mori T., Kobayashi A., Yukiyoshi S., Kobayashi H., Saito G., Inkuchi H., Chem.
Lett., (1984) 957.

Yoshimura M., Shigekawa H., Nejoh H., Saito G., Saito Y., Kawazu A. Phys.
Rev. B 16, (1991), 13590.

Sato N., Saito G., Inokuchi H., Chem. Phys., 76, (1983),79.
Rappé A. K.; Goddard III, W. A. J. Phys. Chem. 95, (1991), 3358.
Chirlian L. E., Francl M. M., J. Comp. Chem. 8 (1987), 894.

Wang H. H., Carlson K. D., Geiser U., Kini A. M., Schultz A. J., Williams J.
M., Montgomery L. K., Kwok W. K., Welp U., Vandervoort, Schirber J. E.,
Overmyer D. L., Jung D., Novoa J. J., Whangbo M. H., Synthetic Metals, 42
(1991) 1983. .

Carlson K. D., Kini A. M., Klemm R. A., Wang H. H., Williams J. M., Geiser
U., Kumar S. K., Ferraro J. R. , Flesher S., Dudek J. D., Eastman N. L., Mobley
P. R., Seaman J. M., Sutin J. D. B., Yaconi G. A., Inorg. Chem., 1992, 3346.

Carlson K. D., Kini A. M., Schlueter J. A., Geiser U., Klemm R. A., Williams
J. M., Dudek J. D., Caleca M. A., Lykke K. R., Wang H. H., Ferraro J. R..
Physica C' 215, (1993) 195.

M. N. Ringnalda, J-M. Langlois, B. H. Greeley, T. V. Russo, R. P. Muller,
B. Marten, Y. Won, R. E. Donnelly, Jr., W. T. Pollard, G. H. Miller, W. A.
Goddard II, and R. A. Freisner, PS-GVB v1.0, Schrédinger, Inc., Pasadena,
California, 1994.

67
Figure Captions

Figure 1. Crystal Structure of Neutral ET

Figure 2. Crystal Structure of 6 — (ET)PF,

Figure 3. Distance changes upon ionization: experiment and [theory (HF)].
Figure 4. Calculated charges for ET (right side) and ETT (left side). For each atom
the top entry is PDQ (Gaussian), the next is PDQ (PS-GVB), followed by Mulliken,
and QEq.

Figure 5. Molecular orbital energy levels for ET and ET* from HF/(6-31G**)
calculations.

Figure 6. Molecular orbital energy levels for ET and ET* from MNDO calculations.

positive lobes are dark gray and the negative lobes are light gray. The isosurfaces are
for an amplitude of 0.02 in atomic units.

Figure 8. The LUMO orbital of neutral ET molecule from HF calculations. The
positive lobes are dark gray and the negative lobes are light gray. The isosurfaces are

for an amplitude of 0.02 in atomic units.

Table 1: Structural Parameters for Neutral ET
From Theory (HF and MNDO) and Experiment (Reference 3) (See Figure 1 in Chap-
ter 2 for notation).

a. Bond distances (A) for neutral E.

Number Xtal HF/6-31G** =MNDO

Co = Coz l 1.319 1.326 1.356
Co — Ss 4 1.758 1.771 1.695
Ss — Cs 4 1.754 1.774 1.688
Cs = Cs, 2 1.332 1.323 1.367
Cs — Se 4 1.742 1.767 1.670
Se — Ce 4 1.802 1.814 1.737
Cs — Coz 2 (1.462)° 1.523 1.530
C. — A; 4 - 1.084 1.112
C. — Ho 4 - 1.081 1.112
RMS Error 0.00 0.017 0.063

b. Bond angles (degrees) for neutral ET .

Number Xtal HF /6-31G** MNDO

Co - Co — Ss 4 123.2 123.71 123.38
Co — Ss — Cs 4 94.5 94.55 97.66
Ss — Cs — Cs: 4 117.3 117.22 115.72
Cs, — Cs — S¢ 4 126.6 128.45 127.19
C's — Sg — Ce 4 100.8 100.81 106.35
Se - Ca — Coz 4 (116.8)? 113.17 115.91
Cg: ~ Ce — H; 4 - 109.75 109.43
Ce: — Cy — Hy 4 - 110.83 109.97
RMS Error 0.00 0.86 2.96

*Crystallographic value is not accurate and was not included in the RMS error cal-
culation.

Table 2: Structural Parameters for ET*
From Theory (HF and MNDO) and Experiment (« — (ET)PF, from Reference 6a
and 6 — (ET)PFe from reference 6b]. (See Figure 1 in Chapter 2 for notation).

a. Bond distances (A) for ETt.

Number ¢—(ET)PFs 6—(ET)PFs HF/6-31G** MNDO

Co = Coz 1 1.396 1.381 1.389 1.398
Co - Ss 4 1.715 1.721 1.721 1.672
Ss —C; 4 1.743 1.732 1.751 1.676
Cs = Cs, 2 1.353 1.351 1.336 1.389
Cs — Ss 4 1.727 1.736 1.765 1.663
Ss —Cz 2 1.761 1.809 1.816 1.741
Cy — Coz 4 (1.32)¢ (1.484)2 1.523 1.529
Cy — H; 4 - - 1.083 1.112
Cs — H, 4 - - 1.080 1.112
RMS Error 0.024 0.00 0.017 0.059

b.Bond angles (degrees) for ET*.

Number ¢—(ET)PFs 6-(ET)PFs HF/6-31G** MNDO

Co —-Co — Ss 4 122.1 122.5 122.76 122.65
Co — Ss — Cs 4 95.8 95.9 96.33 97.47
Ss ~ Cs — Cs, 4 116.3 116.6 116.42 115.17
Cs, — Cs — Se 4 127.3 126.9 128.83 126.95
C's — Sg — Cs 4 116.4 100.6 100.50 106.54
Se — Co — Coz 4 (126.9)° (115.0) 113.10 115.69
Cs. — Ce — H; 4 - - 109.74 109.54
Ce: — Ce — Ho 4 - - 111.46 110.34
RMS Error 2.5 0.0 0.9 2.8

“Crystallographic value is not accurate and was not included in the RMS error cal-
culation.

Table 3: Structural Parameters for ET?
The theory values (HF and MNDO) use the average from ET and ET+. The ex-
perimental structures (references 9,10 and 11) are Xl= « — (ET).Cu(NCS), X2=
K ~ (ET),Cu[N(CN).]Br and X3=6 — (ET)oI3. It appears that X2 is most consis-
tent (See Figure 1 in Chapter 2 for notation).

a. Bond distances (A) for ET?.

No. X1 X2 X3 Av. Exp* HF/6-31G*** MNDO*
Co=Coz 1 1.364 1.360 1.363 1.350 1.358 1.377
Co — Ss 4 1.742 1.741 1.733 1.740 1.746 1.684
Ss — Cs 4 1.758 1.751 1.770 1.743 1.762 1.682
Cs=Cs, 2 1.339 1.343 1.360 1.342 1.330 1.378
Cs — Se 4 1.744 1.749 1.712 1.739 1.766 1.666
Se — Ce 4 1.740 1.811 1.810 1.806 1.815 1.739
Ce — Coz 2 (1.522)? 1.485)’ (1.304) (1.473)° 1.523 1.530
Ce — H; 4 - - - - 1.084 1.112
Ce — H, 4 - - - - 1.081 1.112
RMS Error 0.033 0.0 0.020 0.007 0.011 0.066

b.Bond angles (degrees) for ET? .

No. Xl X2 X3 Av. Exp* HF/6-31G*** MNDO*

Co-—Co-Ss 4 123.00 122.41 122.39 122.8 123.24 123.02
Co-Ss-Cs 4 96.22 95.14 95.78 95.2 95.44 97.56
Ss—C3—-Cs, 4 116.75 117.13 116.36 117.0 116.82 115.46
Cs: -Cs—Se 4 127.66 128.85 128.93 126.8 128.64 127.07
Cs—Se-Ce 4 102.78 100.86 100.61 100.7 100.66 106.42
S6—Ce—Ce: 4 (115.56)? (115.10)® (123.46)® 115.9° 113.14 115.80
Co: -Ce—H; 4 - - - - 109.74 109.48
Ce: -Ce-H, 4 - - - - 111.14 110.16
RMS Error¢ 1.16 0.0 0.43 0.9 0.44 2.94

“From neutral ET and 6 — (ET)+(PF%)~ crystals.
’Crystallographic value is not accurate and not included in the RMS error

calculation.
“Average of the optimized ET and ET+ structures.

Table 4: Energies for ET and ET* from HF and MNDO calculations

ET ETt
HF /6-31G** §=MNDO? HF/6-31G** = MNDO?
Total Energy (Hartree) -3563.3607 -118.4398 -3563.1476 -118.1670
Orbital Energies (eV)
HOMO -7.073 -8.093 -10.929 -12.056
LUMO 2.748 -0.519 -4.540 -6.711

Ionization Potential (eV)

ET*-ET (total energy difference) 5.80 7.42
Koopmans Theorem 7.07 8.09
Experiment? 6.21 6.21

“For MNDO, total energy is the sum of the electronic energy of valence elec-

trons and core-core repulsions.
’Reference 13.

Hoo N Sw SNH

iH
CL UL —/' Ne Cw Zs

0-023] (0.002

0.019

[0.013] [0.000]

[0.002]

Figure 3. Distance changes (in A) upon ionization: experiment and [theory (HF)]

BoC “5

C=C

0.037
0.058 Hu. 0.033 0.033 {0.094}
{0.120} "Cc {-0.022} {-0.020 mad w haart
fo201) F]~ 2.08 7~O Ome (-0.366) (-0.372) — CN Cs [0.164]
{-0.242} S {0.024} oi01 [0.219} [0.217] 0.068 {0.027} S {-0.177}4 Lo 193
0.152 (0.414) “9.982 (0.375) og 10.026) ©0398) (-0.400) (0.189)
(0.244) [0.146] }-9,9734 (0.238) \ oF | I 34) } [0.248] o 3 [-0.160] (0.172)
[-0.296]

Figure 4. Calculated charges for ET (right side) and ET™ (left side).

(QYStd) ,.LA pue (JOT) La J0y spore peg
IEINDG[OW JO suOTENILD »4O1E-9/TH “6 aNdiy

OV-

Energy ew)
Tn

oO
sab)
na

1 IIE
Mil

Ss
ce
S.

pet]
pane
17)

ao)

OWOH

OWN T——

(QUSH) LA pue (JOT) La JOJ spoasy yeugio

Je[Nsa[OW JO suoe[NITeD OGNIW ‘9 an8ry

Energy ev)
Mill VT MUU
I i NINGHIT
I il MG

Lite

Ne
SN

SS.

NSS
NIN

¥%,

ie
ie

Le,

YOO
yee

Les

Sed
Se
is

SINE

NSSN

SS
SASSO

LOOP BEE:

Be
CL fe A
a ifs LIL a Lipp
LED DRI PDI:
ITIP LELID BIEL, BAS
OPP A DST OD
POG! MIMI AIP DE

‘ei

SSG

Bee

DOLE Es LD:
AEG
ons g

wate,

SSS

Figure 8

80
3.2 The Electron-Transfer Boat-Vibration Mech-

anism For Organic Superconductors

Abstract

The highest T, organic superconductors all involve the organic molecule
bis(ethylenedithio)tetrathiafulvalene (denoted as BEDT-TTF or ET) coupled with an
appropriate acceptor. This leads to ET, ET*, or (ET)} species in the crystal. Using
ab initio Hartree-Fock calculations (6-31G** basis set), we show that ET deforms to
a boat structure with an energy 28 meV (0.65 kcal/mol) lower than planar ET (D»
symmetry). On the other hand ET* is planar. Thus conduction in this system leads
to a coupling between charge transfer and the boat deformation vibrational modes at
20 cm (ET) and 28 cm7! (ET*).

We suggest that this electron-phonon coupling is responsible for the
superconductivity and predict the isotope shifts (67,) for experimental tests of the
electron-transfer boat-vibration (ET-BV) mechanism. The low frequency of this boat
mode and its coupling to various lattice modes could explain the sensitivity of T, to
defects, impurities, and pressure. We suggest that new higher temperature organic
donors can be sought by finding modifications that change the frequency and stability

of this boat distortion mode.

[This section is based on the paper “The Electron-Transfer Boat-Vibration Mechanism
For Superconductivity In Organic Molecules Based on BEDT-TTF (ET)”, Ersan
Demiralp, Siddharth Dasgupta and William A. Goddard IT], published in Journal of
American Chemical Society 117, 8154 (1995).|

I. Introduction

Although the T,’s of the quasi one- and two-dimensional organic super-
conductors have gradually increased’, there is considerable uncertainty concerning
the mechanism of superconductivity. The most popular mechanisms involve phonons
and BCS theory. Yamaji? proposed that the mechanism of superconductivity in
organic conductors involves coupling between the Highest Occupied Molecular Or-
bital (HOMO) and totally symmetric intramolecular vibrational modes. However,
the pattern of isotope effects does not support for this view. %11:1819

We report here ab initio quantum chemical calculations (Hartree-Fock
with 6-31G** basis set) for the structure, vibrational frequencies, and isotope shifts
for the donor molecule bis(ethylenedithio)tetrathiafulvane (denoted as BEDT-TTF
or ET) shown in the Figure 1. Based on these calculations, we suggest a special role
for the low frequency boat modes ( at 19.5 em! for ET and 28.1 em~! for ET*) in

the superconductivity of these organic materials.

2.0 Results
2.1 Structures

The structure of ET is often discussed in terms of D» symmetry, which
assumes a planar structure for the central TTF moiety. The crystal structures of neu-
tral ET crystal are consistent with planarity but show a distinct boat-like distortion.‘
Some deviations from planarity are also suggested in crystals containing electron ac-
ceptors, (ET),Xm.*° Here the ET molecules often form dimers (ET,)*+ sharing a
single positive charge.

The terminal six membered-rings are nonplanar in order to avoid eclips-'
ing of the CH, — CH» groups at each end. This nonplanarity leads to two possible
conformations’: (1) The staggered conformation indicated in Figure la in which the
two Cg — Ce bonds are pointing in opposite directions; assuming a planar TTF cen-
tral region, this leads to D, symmetry. (2) The eclipsed conformation indicated in
Figure 1b in which the two Cg — Cg bonds are parallel; with planar TTF, this leads

to Co, symmetry. As discussed below these conformations are essentially degenerate,

82
differing by only 0.0000052 Hartrees = 0.00014 eV = 0.0032 kcal/mol, and we will
consider the higher symmetry staggered case.

To determine the structure and vibrational modes of ET, we carried
out ab initio Hartree-Fock calculations using the 6-31G** basis set.>° Restricting
the symmetry to D, leads to an optimized structure with two imaginary frequencies
vibrational modes (Table 2). We optimized the structure by relaxing the symmetry
leading to boat structure with C) symmetry. In this case, all vibration frequencies
are positive, indicating a stable (boat) structure. Figure 2 shows the side view of the
planar and boat structures.

Figure 3 shows the double well potentials along the reaction coordinate
of the boat deformation. The boat structure is calculated to be 28 meV (0.65 kcal/mol)
lower than planar ET.

In contrast, we find that ET*t leads to a stable planar D» structure
(see Figure 3).

Using the HF/6-31G** wavefunction, we calculated all 3N - 6 = 72
molecular vibrations for the boat and planar ET structures and for ET*+. Table 2
compares the lowest four vibrational modes and Figure 4 shows the boat vibrational
mode. This mode is the lowest frequency (19.5 cm~! [ET], 28.1 cm7! [ET+]) and also
is the mode converting ET structure to ET*. As the structure distorts from boat to
planar, the boat and chair deformation modes become imaginary while the other 70
modes (3N-8) of neutral ET change slightly. The biggest change is 7 %(21 cm7!) for
the 294 cm7! mode (and symmetry D2). These calculations were used to obtain the

vibrationally adiabatic potential curves.

Table 1: The total energy of the conformations of ET and ET+
All energies are in Hartree.

Conformation*® Staggered Staggered Staggered Eclipsed
Species Boat ET Planar ET Planar ETt Boat ET
Symmetry Co Do Do C;

-3563.360692 -3563.359652 -3563.147578 -3563.360697

Table 2: The lowest four vibrational modes of ET and ET*.
All frequencies are in cm7!,

Species Boat ET Planar ET Planar ETT
Mode C5 Do Do
First Boat 19.5 23.11 28.1
First Chair 37.8 24.2 j 36.4
Second Boat 42.6 36.7 42.6

Second Chair 43.8 41.3 49.0

For the lowest energy boat structure of ET, we optimized the neu-
tral molecules for both the eclipsed and staggered conformations of the terminal
—CH,—CH»,— groups. We found that the eclipsed and staggered conformations
have essentially the same energy (with eclipsed lower by 0.0032 kcal/mol, see Table
1), leading to the same bonds and angles. Hence, even at 10 K both forms of the
monomers would be nearly equally populated . In the crystals, packing interactions
(donor-donor and donor-anion) may lead to preferences for either conformation. For
the detailed structural and vibrational calculations of ET and ET* performed herein,
we focus on the staggered conformation which leads to Cy symmetry (the results for

the eclipsed conformation should be essentially the same).

2.2 Electron Transfer

The fact that ET is nonplanar whereas ET™ is planar leads to electron-
phonon coupling that we believe is critical to the superconductivity. After boat ET
loses the electron, ET* would relax toward the planar geometry. Simultaneously the
planar ET* upon accepting the electron would distort to the boat ET conformation.
Denoting the adiabatic ionization energy as J,, the vertical (fixed geometry) ioniza-
tion from the boat distorted ground state of neutral ET costs an energy of J, + 0.177
eV, while the electron affinity of ET* (at its optimum planar geometry) is J, — 0.028
eV. Thus isolated ET and ET* molecules with their optimum structures would lead to
a hopping barrier of 0.205 eV (ignoring polarization of the environment which might
increase the barrier). Figure 5 shows the corresponding Marcus-type electron transfer
diagram, using as the abscissa the simultaneous boat distortion in which the struc-
ture of boat ET changes to planar simultaneously with the structure of planar ET*
changing to the stable boat structure of ET. This leads to a net barrier of ~0.205/4

= 0.05 eV and a curvature corresponding to a frequency of w = \/5[w% + (w/)?] =

24.2 cm™!.

2.3 The ET Dimer
In the organic superconductors (ET),Xm, ET molecules donate elec-

trons to the anion layer. Thus, in (ET )2/3, each J; accepts one electron from a pair

of ET molecules, forming (ET)j and J;. Ignoring electronic interactions (orbital
overlap) and steric interactions, Figure 5 describes the charge transfer between the
two ET and ET* molecules of the dimer. If the overlap of the HOMO’s of this two
ET molecules is sufficiently large, the system will lead to a structure (denoted as
ET?) intermediate between ET and ET*. This requires interaction energies greater
than the barrier of 0.05 eV. |

The crystals of ET molecules exhibit a wide variety of phases and stack-
ings. Some lead to columnar stacking while others do not. Some lead to quasi-one
dimensional conductors, others lead to two-dimensional conductors. The best super-
conductors are generally two-dimensional. The S---S networks generally increase the
intercolumn interactions. Relative orientation of monomers in these dimers and the
dimers with respect to the other dimers will change the magnitude of transfer inte-
grals and determine the rate of the electron transfer. In addition, all these structural

effects can modify both vibrational and electronic modes which, in turn, may change

To.

2.4 The Electron-Transfer Boat-Vibration Mechanism For Electron- Phonon
Coupling

Figure 6a illustrates the electron transfer for a case in which one extra
electron is on one of the (ET). dimers (making it neutral). In the limit of slow
electron transfer, the system might go through the structures in Figure 6b (for strong
coupling within a dimer) or Figure 6c (weak coupling within a dimer). Thus there
1s a strong coupling between the boat vibrational distortion and electron transfer. For
a good conductor with rapid electron transfer, the molecules would all remain in
conformations close to that for ET2, but there would be a tendency towards a larger
boat distortion as the electron hops onto ET and then a smaller distortion as it
hops off. [This discussion implies that the hopping of electrons is directly between
the ET dimers; however, electron transfer between the (ET>)* and the acceptor (to
neutralize each) can also play a role in the conduction.] Thus we believe that it is this
coupling of the conduction electrons to the boat vibrational mode that is involved

in the BCS mechanism for these systems. We refer to this as the electron-transfer

86
boat-vibrational (ET-BV) mechanism for superconductivity.

We should emphasize that all vibrational energies are obtained from
Hessians involving self-consistent wavefunctions. Thus the frequencies include the
effect of changing the wavefunction upon distortion.

Some analyses of the superconductivity of ET molecules have assumed
that the molecule is planar and have used a formalism on which the MO’s of the equl-
librium molecule (assumed planar) are mixed by various symmetric (A,) intramolec-
ular vibrations.* The origins of the electron-phonon coupling responsible for super-
conductivity have been sought in terms of how the various intramolecular vibrations
might couple with the MO’s.

Our view is quite different. We find that the ET molecule is distorted
and that electron-phonon coupling arises from electron transfer between molecules.
The phonons that must couple strongly with electron transfer involve boat vibrations.
For the distorted (boat) geometry, the boat vibrational mode, the HOMO, and the
LUMO are all of A symmetry (for C,). However for the full planar geometry (ne-
glecting also the nonplanarity of six membered-rings) these will have By, , Bi, , and

A, symmetry (of Do), respectively.

3.0 Isotope Effects
3.1 Shifts in the Boat Frequency

The most direct test of the role of the ET-BV mechanism in super-
conductivity is the effect of isotope substitutions on the superconducting properties,
T.. Crystal effects such as donor-anion and donor-donor interactions can influence
the strength of the electron-phonon coupling, leading to substantial changes in T. for
different ET salts. For an accurate estimate of T., one should consider all such effects
and carry out calculations for the molecular crystals. However to provide a means for
rapid testing of the ET-BV model, we present estimates of isotopic shifts on T.. We
find cases where the isotopic shifts should be quite large, allowing direct experimental

test of the ET-BV model.

Table 3. : Frequency shifts for the lowest boat vibrational mode
Shifts are in % for the isolated ET and ET+ molecules. Also listed are the frequency
shifts for the coupled vibrational frequency, w = /}[w? + (wjt)?] = 24.2 cm™} (see
Figure 1 for nomenclature) for various isotopic substitutions.

Substitution ET (19.5 cm!) ETt (28.1 cm~?) w(24.2 cem7?)
D -4.10 -6.05 -5.41
130, -1.03 -1.07 -1.06
BC, 0.00 -0.36 -0.24
BO. +48 C, 0.00 -1.42 -0.96
34.5 -1.03 -1.07 -1.06
D+4+8C, -5.64 -6.76 -6.39
D+ Cy +45 -6.67 -7.47 -7.20

Using the Hessian (second derivative matrix) of the Hartree-Fock wave-
functions [6-31G** basis set], we calculated the isotopic shifts for the boat modes of
ET and ET*. Table 3 shows the frequency shifts for a number of isotope substitu-
tions. These results will be used to test of the role of the ET-BV mechanism in the
superconductivity.

In all cases, we find that an increase in the isotopic mass decreases
the frequency of the boat mode. We obtain the largest frequency shifts for H to
D substitutions {(5w,/w,) = —0.041[—0.060]} for ET [ET+]; smaller shifts for !2C,
to Ce {(Swe/w») = —0.010{[—0.011]} and 32S to 45 {(6uw,/u4) = —0.010{—0.011]};
and very small shifts for “C, + CO, {(duy/ws) = —0.000[—0.004]} and
%Cs — Cs {(6wy/us) = —0.000[—0.014]}. Table 4 shows that multiple isotopic

substitutions give almost additive frequency shifts for the boat mode.” These trends

88
that H, Cs, Sg atoms on the outer rings of ET provide the biggest shifts in w, are

consistent with the character of the boat mode in Figure 4.

3.2 Effect of 6w on 6T,

Assuming that the electron-phonon matrix elements are dominated by
the boat phonon mode and using the weak coupling formulation of BCS theory, leads

to *4 the equation (1) for Ty,

kT, = 1.14hw exp|[— ] = 1.14hw exp[—4] , (1)

(NoV)

where w is the frequency for the coupled boat phonon mode (w = 24.2 cm~1), No is the
density of states of the electrons at Fermi surface, and V is the attractive interaction
between electrons. However, using w = 24.2 cm~! and T, = 10 K in equation (1)

gives \ = 0.73. Thus we use the Kresin strong-coupling formulation?? (2):

9 ~1/2
exp (=) — 0] ; (2)

Assuming that an isotope substitution which changes w by éw also

T. = 0.25V < w? >

changes Aer» by 6A, equation (2) leads to

1+16—£
wd

(3)

6T. dw OX ( =
T- Ww re FF

The magnitude of A-¢ should be related to the boat frequency w and to the energy
barrier (0.05 eV) which in turn depends on w. In the crystal these quantities also
depend on the packing of the other molecules (particularly the dimer pairing) and on
the pressure.

In order to estimate the effect of the isotope substitutions on Aprs, we

write

Aes f (Ww) = Ap t+ A;dw + Ay (dw)? +.

This will likely lead to a linear dependence
bA=Abw, (4a)

but because of the double well nature of the boat mode, the net dependence might

be
bX =Az(6w)? (4b)

We will estimate A, or A, by using the experimental 67, for H to D substitutions.
Using 1 or Aq with the predicted w allows the prediction of 67, for other isotopic
substitutions.

Combining terms leads to

_ oT p
and
Te T, 6Tp ;
6T, = 7 bw + (bw) + mea} (dw) (5b)

for approximations (4a) and (4b), respectively. Here 6Tp and éwp are the shifts for

H to D substitution.

3.3 Observed 6T,. for H to D Substitutions

Recent isotopic shift experiments show the following results for replac-
ing the hydrogen atoms of ET with deuterium
(t.) K—- (ET)2CulN(CN).|Br (T, = 11.8 K’) leads to a normal isotope effect of
6T, = —0.09 K." In addition, Andres et al.’? found a “normal” isotope shift for the
“high T” phase of @* — (ET ).I3(T. = 8 A’); however, they considered the significance
uncertain because of the sensitivity of T, to pressure.
(iz.) On the other hand the following systems (1) Kk—(ET)2Cu(NCS)» (T, = 10.4 K),
(2) & — (ET).Cu[N(CN) |Cl (T, = 12.8 K), (3) & — (ET).Cu(CN)[N(CN)o](T. =
11.2K), (4) K-(ET).Ag(CN).H2,O(T, = 5.0 K), and (5) 6 — (ET )oI3(T. = 1.15 BK’)
all showed inverse isotope effects, with 67, ~ 0.7, 0.5-1.5, 1.1, 1.0, 0.28 Kk

respectively.2:142915,16

3.4 Predicted 6T, for Other Isotopic Substitutions

Using the experimental 67. (denoted 6Tp) and the calculated 6w (de-
noted 6wp) from Table 3, we estimated the parameters in (9). This leads to the
predicted isotopic effects in Table 4. These results are generally in agreement with
experiment. Thus
(i.) in K-(ET)2Cu(NCS)p, the substitution '*C¢g to ’C¢ leads to a T, “just between
those of H and D salts,”!’ This inverse effect is expected from (5) (see Table 4).
(ii.) Carlson et al.° checked the controversial “giant isotope effect” results of Merzhanov
et.al.° and found no isotopic shifts (within the standard deviations 6T, = 0.1 K) for
the substitutions of:

(1.) *?C, with 8C, in B* — (ET)oI3, & — (ET),Cu(NCS)., and « —
(ET)2Cu[N(CN).|Br
(2.) all ?C, and ?C; with 8C in 6* — (ET), 13.189

Indeed as shown in Table 4, we find very small shifts (67, less than
0.06 K) for all C, substitutions with °C. In addition, we find 5T, less than 0.20 K
for simultaneous !7C, and °C; substitutions with °C.
(iii.) Carlson et al.° found a very small isotopic shift, 67. = —0.08 + 0.07 K, upon
substituting all °°.S with 949 in k—-(ET).Cu[N(CN)»]Br. As shown in Table 4 we es-
timate that 67, = —0.18 to —0.13 K in reasonable agreement. In k—(ET).Cu(NC'S),
“less detailed” studies!’ indicate no isotope effect whereas we find +0.14 to —0.06 k.

From Table 4 we see that the largest isotope shifts are for H, Cs, and
Se. Indeed (a) simultaneously substituting for both H and Cg, should increase 6éT,
by ~ 18 to 57 % over that for H alone, while (b) simultaneously substituting H.C,
and Sg leads to an increase in 6T of ~ by 33 to 113 % over that for H only. Thus
multiple isotope substitution experiments should provide a clear cut test of the ET-

BV mechanism.

4.0 Summary

The stable structure of ET is boat-like whereas ET* is planar. The

91
energy of boat distortion is 28 meV (for ET) and the boat frequency is 19.5 em7!,
We propose that the mechanism for superconductivity of these materials involves the
coupling of charge transfer to the boat deformation mode. This boat mechanism can
be tested by measuring the isotopic shifts for specific simultaneous isotopic substitu-
tions.

This ET-BV mechanism provides some guidance for modifying ET to
obtain new higher T, materials. Thus, we require donor molecules that distort into
the boat form for the neutral form, but change significantly (becoming planar) upon
ionization. We expect T,, to be sensitive to the boat frequency w, and to the magnitude
of the distortion energy. Based on these ideas, one can postulate various modifications
of ET that would increase T... Consequently, we are carrying out quantum mechanical

calculations for some such cases.

Table 4. Predicted isotopic shifts (ST, ) based on the coupled boat phonon model for organic superconductors
(see Figure 1 for nomenclature). The experimental deuterium isotopic shift (6Tp)

éwp in equation (5a) to obtain the values listed while equation (5b)

was used with
was used for the values in

parentheses.
T, D BC, 13, BC. 418 Cs 345 D 418 Cs D 413 Or 434 Ss
K— (ET)2Cu[N(CN)2]Br 11.87 -0.90 -0.18(-0.13) -0.04(-0.03)" -0.16(-0.12) -0.18(-0.13)" -1.06(-1.12) -1.20(-1.32)
K— (ET )2Cu(NCS)> 10.42 +0.70 +0.14(-0.06)% 40.03(-0.02)" +0.12(-0.06) 40.14(-0.06)4 +0.83(41.10) +0.93(41.49)
A (ET)2Cu(CN)[N(CN)3] 11.26 +1.10 4+0.21(-0.05) +0.05(-0.02) +0.19(-0.05) 40.21(-0.05) — 41.30(41.68) +1.46(42.22)
k— (ET), Ag(CN)2H2O 5.04 +1.00 +40.20(+40.00) +0.04(-0.01) +0.18(-0.01) 40.20(4+0.00) = 41.18(41.45) +1.33(41.89)
B _- (ET )oIs 1.15° +0.28 = =+40.05(+0.00) 40.01(+0.00) +9.05(0.00) +0.05(4+0.00) 40.33(+40.40) +9.37(+4+0.52)
K— (ET)2Cu[N(CN)2]Cl 12.0/ of +0.20(-0.07) +0.04(-0.03) +0.18(-0.07) 4+0.20(-0.07) — 42.18(41.54) +1.33(+42.08)

Reference 7.
Reference 8.
° Reference 23.
Reference 15.
© Reference 16.

f Reference 14. The isotopic shifts were observed in the range 0.5-1.5K for different samples. We used 1.0 K.

9 For substitutions of !2Cg with 13Cy ink — (ET)2Cu(NCS)2 , T; was found “just between those of I] and D

salts.” See reference 17.

* 6T, = —0.08 + 0.07 was observed with 345 substitutions (see reference 12).

J No isotope effect (within standard deviations) was observed with *45 substitutions (
No isotope effect (within standard deviations 6T, = 0.1K) was observed with 13C, substitutions (see refer-

ences 9,11).

see reference 12).

References

10.

Jerome D., Mazaud A., Ribault M., Bechgaard K., J. Phys. Lett. 41, (1980)
L95.

Yamaji K., Solid State Communications, 61, (1987), 413.

. Kobayashi H., Kobayashi A., Yukiyoshi S., Saito G., Inkuchi H., Bull. Chem.

Soc. Jpn., 59, (1986) 301.

Demiralp E., Goddard W. A. III, Journal of Physical Chemistry, 98, (1994)
9781.

The quantum chemical calculations were carried out using Gaussian 92, Revision
B, M. J. Frisch, G. W. Trucks, M. Head-Gordon, P. M. W. Gill, M. W. Wong,
J. B. Foresman, B. G. Johnson, H. B. Schlegel, M. A. Robb, E. S. Replogle,
R. Gomperts, J. L. Andres, K. Raghavachari, J. S. Binkley, C. Gonzalez, R. L.
Martin, D. J. Fox, D. J. Defrees, J. Baker, J. J. P. Stewart, and J. A. Pople,
Gaussian, Inc., Pittsburgh PA, 1992.

Tokumoto M., Konishito N., Tanaka Y., Anzai H., Journal of the Physical
Society of Japan, 60, (1991) 1426.

Oshima K., Urayama H., Yamochi H., Saito G., Synthetic Metals, 27 (1988)
A473.

Carlson K. D., Williams J.M., Geiser U., Kini A. M., Wang H. H.. Klemm R.
A., Kumar S. K., Schlueter J. A., Ferraro J. R., Lykke K. R., Wurz P., Parker
H., Sutin J. D. B., Mol. Crsyt. Lig. Cryst. 284, (1993), 127.

Merzhanov V., Auban-Senzier P., Bourbonnais C., Jerome D., Lenoir C., Batail

P., Buisson J.P., Lefrant S$, C.R. Acad. Sci. Paris,314 (1992), 563.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

94
Carlson K. D., Kini A. M., Klemm R. A., Wang H. H., Williams J.M., Geiser
U., Kumar S. K., Ferraro J. R., Lykke K. R., Wurz P., Fleshler S., Dudek J.
D., Eastman N. L., Mobley P. R., Seaman J. M., Sutin J. D. B., Yaconi G. A.,
Inorg. Chem. 81, (1992), 3346.

Carlson K. D., Kini A. M., Schlueter J. A., Geiser U., Klemm R. A., Williams
J.M.,Dudek J. D., Caleca M. A., Lykke K. R., Wang H. H., Ferraro J. R.,
Physica C 215, (1993), 195.

Andres K., Schwenk H., Veith H., Physica 143B, (1986), 334.

Schirber J. E., Overmyer D. L., Carlson K. D., Williams J.M., Kini A. M.,

Rev B 44, (1991), 4666.

Mori H., Hirabayashi I., Tanaka S., Mori T., Maruyama Y., Inokuchi H., Syn-
thetic Metals, 55-57 (1993)2437.

Heidmann C. P., Andres K., Schweitzer D., Physica 148B, (1986), 357.

Saito G., Yamochi H., Komatsu T., Ishiguro T., Nogami Y., Ito Y., Mori H., Os-
hima K., Nakashima M., Takagi H., Kagoshima S., Osada T., Synthetic Metals,
41-48 (1991) 1993.

Carlson K. D., Kini A. M., Schlueter J. A., Wang H. H., Sutin J. D. B., Williams
J.M., Schirber J. E., Venturini E. L. , Bayless W. R., Physica C 227, (1994),
10.

Carlson K. D., Williams J.M., Geiser U., Kini A. M., Wang H. H., Klemm R.
A., Kumar S. K., Schlueter J. A., Ferraro J. R., Lyyke K. R., Wurz P., Parker
D.H., Sutin J. D. B. Mol. Cryst. Lig. Cryst. 234, (1993), 127.

Kozlov M.E., Pokhodnia K. I., Yurchencko A. A., Spectrochimica Acta 45A
(1989), 323.

21.

22.

23.

24.

25.

95
Ferraro J. R., Kini A. M., Williams J.M., Stout P., Applied Spectroscopy 48,
(1994) 531.

Kresin V. Z., Physics Letters A 122, (1987) 434

Saito G., Yamochi H., Nakamura T., Komatsu T., Matsukawa N., Inoue T., Ito
H.,Ishiguro T., Kusunoki M., Sakaguchi K., Mori T., Synthetic Metals, 55-57
(1991) 2883.

See for example , P. G. de Gennes, Superconductivity of Metals and Alloys,
(Addison-Wesley Pub. Co. Inc., 1989).

Williams J.M., Ferraro J. R., Carlson K. D., Geiser U., Wang H. H., Kini A.
M., Whangbo M-H, Organic Superconductors (Including Fullerenes): synthesis,
structure, properties, and theory, (Printice-Hall 1992)

96
Figure Captions
Figure 1. Bis(ethylenedithio)tetrathiafulvalene (denoted as BEDT-TTF or ET) (a)
Staggered (C) symmetry) (b) Eclipsed (C’, symmetry).
Figure 2. Side view of the optimized structure for ET. a) D, symmetry (planar).
(b) Cy symmetry (boat). Carbons are the solid circles, hydrogens are the open circles,
and sulfurs are the hatched circles. |
Figure 3. (a) Energy of the boat structure of ET as a function of the boat distortion.
The pathway for boat is obtained from a three point fit to the planar, + boat, and -
boat structures. (b) The energy for ET* using the boat structures of ET (based on
the Koopmans theorem).
Figure 4. Boat deformation mode of the boat structure (w) = 19.5cm~*).
Figure 5. The Marcus-type electron transfer diagram for ET ET*+ — ET*ET.
Electron transfer from ET ET* to ET* ET is couplied to simultaneous boat distor-
sions for both molecules, w = \/$[wj + (wy )?] = 24.2 cm~! = 0.0030eV.
Figure 6. Illustration of electron transfer in (ET) superconductors. (a) The case
of one extra electron. (b) The structural changes for fast transfer. (c) The structural

changes for slow transfer.

T ainsiq

LA ‘qua/eAInjelye.j9} (o1yypaue|AUye)siq

q \\ 8s |
° a" } > aN SN a Sin, 7 H
) p95
H~ 9 |
ae Ga \ ; ll ce,
| hy S97 0 \/ Go NN,
. pesdipoq (q
0 SoH > -\ “Sw a Si, An
H / 5 7
ty, . 0) S : 0
a Sg Sg— NA 4
'H

porssseys (e

(a) PLANAR ET (D, SYMMETRY)
(b) BOAT ET (C, SYMMETRY)

Figure 2

ENERGY(eV)

ENERGY (eV)

6.8 T T I ] I
“1, -4 -0.5 0 0.5 1 1.5
BOAT DISTORTION
0.05 ! :

q ET @
0.04-4 ~
0.035 Z
0.02 - —
0.01 5 -

wy
O ¢ T l ?
-1. - 1 -0.5 O 0.5 1 1.5

BOAT DISTORTION

100

BOAT VIBRATION MODE of ET

Figure 4

101

ETE],

0.05eV

J | ~ SIMULTANEOUS IL
. BOAT .
ET ET DISTORTION ET ET
(19.5¢m™!) (28.1cm"') - (2840m™) (19.5em")

Figure 5

102

(a)
ELECTRON
TRANSFER

—— (b)
STRONG

COUPLING
(FAST)

(oe)
WEAK
COUPLING

(SLOW)

pit

nol

i a

Oo 4 \
ror \ /
+ fN

IC + 30t

0 0

pro}

E=0 — E=0.05eV

Figure 6

VY.
/™N
oa VY
of nN

103
3.3. Prediction of New Donors for Organic Super-

conductors

Abstract

The donors of all known one or two dimensional organic superconduc-
tors are based on a core organic molecule that is either tetrathiafulvalene (denoted
as TTF) or tetraselenafulvalene (denoted as TSeF) or some mixture of these two
molecules. Coupling X, with appropriate acceptors, Y, leads to superconductivity.
The oxidized form of X may be X* or XJ species in the crystal. From ab initio
quantum mechanical calculations (HF /6-31G**), we find that all known organic su-
perconductors involve an X that deforms to a boat structure while X* is planar. This
leads to a coupling between charge transfer and the boat deformation phonon modes
that we believe is responsible for the superconductivity of these materials. Based on
this idea we have developed similar organic donors having the same properties and
suggest that with appropriate electron acceptors they will also lead to superconduc-

tivity.

104

A number of organic superconductors have been developed using the
donors in Figures 1b-d coupled with appropriate acceptors.1~* These are all based on S
or Se containing fulvalenes (tetrathiafulvalene, TTF, and related molecules in Figure
la). The superconducting transition temperatures, T,, range up to 12.8K and have
improved slowly over the years. Despite the advances in T,, progress in developing new
materials is impeded by the lack of an understanding of how the superconductivity
is related to fundamental structural quantities. Herein we identify what we believe
is the salient structural issue in the superconducting coupling mechanism and use
this insight to suggest a number of new donors, all of which are expected to show
superconductivity when coupled with appropriate acceptors. These donors are simpler
than the current ones and some may lead to higher T;,.

In most systems the donors form dimers X» so that there is one hole
per dimer. The holes on the dimers result in overlapping valence and conduction
bands, leading to electrical conduction involving both positive and negative charge
carriers.

We have used ab initio quantum mechanics*~® (Hartree-Fock, 6-31G**
basis) to examine the structures for a number of donors in both the oxidized (XT)
and neutral (X) states and find that all known donors for superconductors lead to
a distorted boat conformation (see Figure 2) for X and a planar conformation for
X*. The change in structure upon ionization from nonplanar X to planar X7+ leads
to electron-phonon coupling that we believe is critical for the electronic behavior of
molecular crystals based on these donors. After boat X loses the electron to form
X*, the structure would start to relax toward the planar geometry. Simultaneously
the planar X* upon accepting the electron would tend to distort toward the boat
conformation of X. The idea is illustrated in Figure 3 in this section. Thus this

charge transfers tends to couple the electrons to the boat deformation modes.

In analyzing these transfers, we define:

I, = the adiabatic ionization energy,

U = the relaxation energy for X*+ from the optimum boat structure of
X to the optimum structure of X7,

W = the relaxation energy for neutral X from the planar to the boat.
structure. |
Thus, the vertical (fixed geometry) ionization from the boat distorted ground state of
X costs an energy of J, +U, while the vertical electron affinity of X* (at its optimum
planar geometry) is J, — W.

Isolated neutral and cation donor molecules with their optimum struc-
tures would lead to a hopping barrier of U + W (ignoring polarization of the environ-
ment which might increase the barrier). Figure 5 shows the corresponding Marcus-
type electron transfer diagram, using as the abscissa the simultaneous boat distortion
in which the structure of the neutral boat molecule changes to planar simultaneously
’ with the structure of the planar cation molecule changing to the stable boat structure
of the neutral molecule. This leads to a net barrier of ene, and an approximate
curvature corresponding to w = ,/3[wj + (w# )?], where wy is the boat deformation
frequency for the neutral and w; is for X*. Of course in a metal, we do not have
such localized states. In this case the structure will tend to remain near that of X?
(in between X* and X). However the coupling between electrons and the boat de-
formation will remain. We believe that the coupling of conduction electrons to these
deformation modes is critical for the superconductivity of these organic materials.

Based on these considerations we hypothesize that TTF-like molecules
which lead to boat-distorted neutral donors (but a planar positive ion) will result in
superconductivity when combined with suitable acceptors. Here we use this idea to
suggest several new donors as candidates for forming superconductors. The simplicity
of these new donors might lead to improved properties.

The donors for the known superconductors Figures 1b-d (all based on
TTF, TSeF, or a mixture) are all expected have distorted neutral donors. However,

we find that the parent compounds of Figure la, are all planar in the neutral (and

106
oxidized) forms. Thus none of the donors in Figure la would lead to the coupling
such as in Figures 3 , responsible for superconductivity. Only upon replacing the
hydrogens of the TTF and TSeF molecules with bulky groups do we get distortions.

The results of calculations for several substitutions are summarized in
Table 1. We expect that the superconducting T, is related to the distortion angle 0,
boat stabilization AEjoat, and boat vibrational frequency, Vocar. Generally we expect
that larger ©, AF boar, and Vooat Will lead to higher T;, (as long as the positive ion is
planar and the system is a conductor).

Replacing the H in TTF with Cl or F leads to substantial distortions
(14° and 11°, respectively, see Figure 4). Cl-TSeF leads to a distortion larger by 1.2°
but Cl-TOF is planar. These results are consistent with the studies on BEDT-TTF
(i.e, ET) where S or O in the six membered ring (the same position as the Cl in
CI-TTF) leads to distortion. In addition, replacing the 5 in the five-membered ring
with Se leads to larger distortions, but replacing S with O in the five-membered ring
leads to no distortion. For TTF and TSeF replacing the H with CHz also leads to a
small distortion (6° and 8° respectively), but little energy lowering.

The origin of these distortions is found in the bond angle preferences
of the atoms involved. The bond angles in OH2, SH2, and SeH2 are 104.5°, 92.1%,
and 90.6°, respectively.’ On the other, hand the average angle in the five-membered
rings is 540/5=108°. Indeed for the molecules in Figure la, the optimum angles are
105.01° and 95.09° at O and S, respectively. Thus S and Se lead to a significant strain
energy. Although planar, these molecules (with 5 or Se) are spring loaded, needing
only additional steric interactions to tip the balance toward nonplanar. Although not
calculated, TTeF is expected to yield even larger distortions (probably ~ 17°) for Cl
substitution.

CI-TTF has a distortion 3° larger than F-TTF, and Br-TTF, I-TTF
should lead to even larger distortions. This is consistent with the results on BEDT-
TTF where replacing Sg with Og leads to much smaller distortions. Thus for BEDT-
TTF, replacing Sg with Seg or Teg should lead to increased distortions. Similarly
although CH; leads to only a small distortion for TTF and TSeF’, we expect that tBu

107
i.e., C(CH3)3] would lead to much larger distortions.

We have ignored packing issues. The ET based systems crystallize into
structures with two-dimensional layers of ET dimers separated by a two- dimensional
layer of acceptor molecules. The positive hydrogens of ET interacting with the neg-
ative acceptor layer probably play a role in stabilizing this structure. The modified
molecules such as CI-TTF are halogen terminated, leading to a net negative charge
in the region of the acceptor. This would likely require hydrogen on the acceptors to
electrostatically attract the negative halogens. Thus J; and Cu(NC'S)» would likely
not be good acceptors for CI-TTF. On the other hand with tBu groups the standard
acceptors might be satisfactory.

Summarizing,

(i.) We indicate a criterion for determining new classes of donors, namely that the
neutral molecule distort into a boat form while the cation species is planar.

(ii.) We suggest several new candidate donors for organic superconductors each in-
volving simple modifications of TTF and related molecules.

Tests of these suggestions should provide additional insights into the mechanism of

superconductivity and might lead to improved properties.

108

Table 1: The deformation angles, energy differences and the boat vibrational fre-
quency for various organic donors

The deformation angle is © (see Figure 2); energy difference between boat and planar
structures is APoa1, and the lowest boat deformation vibrational frequency is Vyoq¢.

Species Substitutions® e° A Ehboat Veoat
degrees (meV) (cm~?)

TOF - 0.0 POS? 76.1

Cl 0.0 POS? 29.7

TTF - 0.0 +14.39%¢ 17.7

F 11.3 NEG* 18.6

Cl 14.3 —5.87 18.1

CH3 5.8 —0.18 10.3

TSeF Cl 15.5 —5.74 nat

CH3 7.9 —0.40 nat

BEDT-TTF - 21.1 —28.36 19.5

Ses 24.4 NEG* nat

Og 8.5 NEG* 10.5

Os 0.0 POS# 21.5

“For TTF or TSeF, all substitutions replace H atoms with the corresponding substituents.
For BEDT-TTF, the subscripts show that the sulfurs in the five or six member rings are replaced
by Se or O.

“NEG indicates that starting with Co symmetry, the structure optimizes to a boat structure,
hence the energy of the boat structure is lower than planar structure. However, we did not separately
optimize the planar structure to obtain AE boat.

“POS indicates that starting with Cy symmetry, the optimized structure becomes planar
structure, hence the energy of the boat structure is higher than planar structure.

*To obtain the positive AByoat we started with the optimized planar and boat structures
containing Cl and replaced each Cl with H as the appropriate distance.

fFrequencies not yet calculated.

109

References

1. Jerome D., Mazaud A., Ribault M., Bechgaard K., J. Phys. Lett. 41 (1980)
L95.

2. Wang H. H., Carlson K. D., Geiser U., Kini A. M., Schultz A. J., Williams
J. M., Montgomery L.K., Kwok W. K., Welp U., Vandervoort, Schirber J.E.,
Overmyer D. L., Jung D., Novoa J. J., Whangbo M. H.,Synthetic Metals, 42
(1991) 1983.

3. Mori H., Int. J. of Modern Physics B, 8 (1994) 1-45.
4. Demiralp E., Goddard W. A. III, Journal of Physical Chemistry 98 (1994) 9781.
5. Demiralp E., Dasgupta S., Goddard W. A. III, submitted J. Am. Chem. Soc..

6. The quantum chemical calculations were carried out using Gaussian 92, Revision
B, M. J. Frisch, G. W. Trucks, M. Head-Gordon, P. M. W. Gill, M. W. Wong,
J. B. Foresman, B. G. Johnson, H. B. Schlegel, M. A. Robb, E. S. Replogle,
R. Gomperts, J. L. Andres, K. Raghavachari, J. S. Binkley, C. Gonzalez, R. L.
Martin, D. J. Fox, D. J. Defrees, J. Baker, J. J. P. Stewart, and J. A. Pople,
Gaussian, Inc., Pittsburgh PA, 1992.

7. Harmony M. D., et al. , Journal of Physical Chemistry Ref. Data, Vol. 8, No.
3, 1979.

110
Figure Captions
Figure 1. (a) Tetrathiafulvalene (TTF), tetraselenafulvalene (TSeF), and tetraoxa-
fulvalene (TOF).
(b) TTF based donors of organic superconductors.
(c) TSeF based donors of organic superconductors.
(d) TTF-TSeF mixed donors (DMET) of organic superconductors.
Figure 2. Side view of the boat structure for CI-TTF. The optimum angle is 0 =
14.3°.
Figure 3. The Marcus-type electron transfer diagram for X X*t — X*X. Electron
transfer from X X+ to X*X is couplied to simultaneous boat distorsions for both
molecules, w = 1/5 [w% + (w')?]
Figure 4. (a) Donors of organic superconductors.

(b) Donors with no superconducting structure.

(c)Predicted new donors for organic superconductors.

lil

(a)
a rx) OX

Serer S ° tor

(b)
Chr SIX re noe 05

(Cc) | |

Se a CH
IMTSE 3 BEDT-TSeF DMET-TSe $

(d)
Cc 1 aan

ape CH3

Fisure 1

112

Figure 2

os\

E=U +W

XXT

113

SIMULTANEOUS
BOAT
DISTORTION

Figure 3

‘IC

X*X

XTX

CoO

Creer

BEDO-TIF

BEDT-TSEr

O = 24.4°

Se S

e--CH3
Rae

CHs

TIMTSF
O = 7.9°

114

Crea

BEDT-TOF
© =0°

Figure 4

cl1~—S S Cl
ok osha

ieee

115

3.4 Ab Initio Studies of TTF-based Donors of Or-

ganic Superconductors

Abstract

We report the structures and properties of TTF-based organic donors
of organic superconductors. From ab initio quantum mechanical calculations (HF /6-
31G**) for the neutral (X) and cation (X7*), we find that X* is planar but that XY
deforms to a boat structure for all cases that are superconductors. Various charac-

teristics of these donors are also discussed.

116
I. Introduction

Most organic superconductors are based on the TTF-like donors in
Figure 1 in Section 3.3.1 The electronic structures of the molecular crystals involving
ET show a wide variety of electronic behavior leading to semiconductors, metals
or superconductors, etc. depending on the anion and the packing. For metallic
behavior of ET salts, the intermolecular S'---S contacts seem important. Hence, the
conformations and packing of these donors are very important for understanding the
electronic behavior of these materials.

Recently, we reported? that known donors for superconductors all lead
to a distorted boat conformation for X and a planar conformation for X*. We
indicated? that this is a criterion for determining new classes of donors and suggested
new TTF-based donors. As an electron hops from X to XT, the original X dis-
torts from boat to planar while the original Xt distorts from planar to boat. Thus
conduction in this system leads to a coupling between charge transfer and the boat
deformation phonon modes, which we suggest that is the electron-phonon coupling
responsible for the superconductivity.

In this paper, we report other structures and properties of the TTF-
based organic donors of organic superconductors. We used ab inztzo quantum
mechanics’ (Hartree-Fock, 6-31G** basis) to study the structures of these donors
in both the oxidized (X*) and neutral (X) states. The changes in the properties
of these molecules upon chemical modification (structure, ionization potential, shape
and energy of the molecular orbitals) are important for understanding the electronic

and crystal structures of materials containing these organic donors.

2.0 Results
2.1 Structures

It is often assumed that the TTF region of the TTF-related donors
for organic superconductors are flat.4 For neutral ET crystal? and for ET,PtClg -
C.H;CN,® some deviations from planarity are suggested in the X-ray structure. How-

ever there was no suggestion that these deviations from planarity are related to the in-

117

trinsic properties of the donor molecules. The crystal structure of ETyPtClg-CeHsCN
exhibits a first-order transition at 250 K. Doublet et al.° found that there are two
donor layers before the transition and only one donor layer after the transition. By
comparing with the neutral ET crystal for ET and with ET Ags(CN); for ETT, they
found that one of the layers (A) contains (ET*)) and (ET). dimers and the other
layer (B) contains two different (ET 2). dimers. After the transition, the (ET?)y
dimers of (B) disproportionate to form (ET*)2 and ET» dimers.

We determined the structures by carrying out ab initio Hartree-Fock
calculations using the 6-31G** basis set. We find that the parent TTF molecule is
planar but all the TTF-based neutral molecules deform to a boat conformation when
H in TTF is replaced with F, Cl or bulky (CH3) groups. Similarly, substituting S for
Se to form TSeF leads to a planar structure, but again neutral molecules with similar
substitutions for H are boat-like.? On the other hand, substituting S for O to form
TOF leads to planar structure for all similar substitutions of H.?

The propensity for distortion is easily understood. The average angles
are 105.0° for O on TOF, 95.1° for S in TTF and 93.2° for Se in TSeF. This is
related to the normal preferences in bond angles: thus, H,O has 104.5°, H2S has
92.1° and H»Se has 90.6°.’ However for a five membered ring, the average angle is
108°. Thus for S and Se, there are strains trying to obtain a smaller bond angle. By
going nonplanar, the angle at the S and Se is allowed to be ~ 95° without strain on
the rest of the five-membered ring. However it is only when an electronegative or
bulky ligand is attached that the TTF-like moiety snaps to a distortion structure.

Charge transfers from the TTF region to the end groups reduces the
strains in the pentagonal rings, leading to a positive center and negative ends for
these molecules. The neutral molecule deforms to the boat conformation. This charge
transfer is reversed upon ionization, leading to a planar molecule.

The energy difference between the stable boat mode and optimized
planar structure varies up to 0.65 kcal/mol (see Table 1), leading to a doubly well
potential along the boat coordinate. For ET molecules with the staggered ethylene

conformation, the deformation of the 6-membered rings lowers the symmetry to C,

118
leading to degenerate chiral molecules. There is also the eclipsed ethylene conforma-
tion leads to ET molecules with C’, symmetry. These ethylene conformations have
almost same energy (the eclipsed conformation has an energy 5 pHartree lower).® In
this section, we used the staggered conformation with Cy) symmetry for the detailed

structural calculations for neutral and cation ET molecule.

2.2 Ionization Potential

The total energy and orbital energies of from HF calculations are shown
in Table 3. The HOMO and LUMO orbitals of TTF-Cl from HF calculations are
plotted in Figure 1,2. Two ways of estimating ionization potentials (IP) are:

i. AE: using the total energy differences of neutral and cation molecules
because the correlation error is smaller for the positive ion than the neutral this usu-
ally leads to too small an IP, and

ii. Koopmans’ theorem (KT): using the orbital energy of the HOMO
level this assumes that the orbitals do not relax upon ionization and hence usually
leads to too large a value.

Table 2 shows that the available experimental gas-phase IP’s are in
between these estimates, as expected. The average of the AF and KT values, which
often gives a good estimate for the IP, leads to the order BEDT — TTF (6.44 eV)
> TTF(6.31 eV) > BEDO —TTF (6.26 eV). This is consistent with the gas-phase
experimental results BEDT — TTF = TTF(6.7 eV) > BEDO — TT F(6.46 eV).°
(The order from Ref. 10 is different, TTF (6.4 eV) > BEDT — TTF(6.21eV) (see
Table 2 in this section). The IP’s are very close so that the relative donor abilities
are affected by the molecular environment.’ Thus, the oxidation potentials in solution
are ordered BEDT —TTF > BEDO —TTF > TTF, which differs from the order
of the gas-phase first ionization potentials. Such polarization effects should also be
important in crystals. Hence, the structures and packing should influence the charge
transfer properties of the salts of TTF-based donors. This information should help
in understanding the wide variety of electronic properties of the molecular crystals

based on TTF donors.

119

4. Summary

The results of ab inztio HF calculations (6-31G** basis) show that TTF-
based molecules have boat conformations for X and planar conformation for X*.
This leads to coupling of charge transfer with the boat deformation modes of these
molecules. These results should be important for understanding the crystal and elec-
tronic properties of molecular crystals based on TTF-based molecules. The ionization
potentials should be useful for the comparisons of the relative electron donor abilities

these molecules in the synthesis of donor-acceptor systems.

120

References

10.

Mori H., Intl. J. of Modern Physics B, 8, 1 (1994).
Demiralp E. and Goddard W. A. III, Synthetic Metals, 72, (1995) 297.

Cowan D.O, Fortkort J. A., Metzger R. M., in Lower-Dimensional Systems and
Molecular Electronics, (Plenum Press 1991), 1.

Kobayashi H., Kobayashi A., Yukiyoshi S., Saito G., Inkuchi H., Bull. Chem.
Soc. Jpn., 59, (1986) 301.

Doublet, M-L., Canadell E., Shibaeva R. P., J. Phys. I France 4 (1994) 1479.

M. D. Harmony, V. W. Laurie, R. L. Kuczkowski, R. H. Schwendeman, D. A.
Ramsay, F. J. Lovas, W. J. Lafferty, A. G. Maki, J. Phys. Chem. Ref. Data, 8
(3) (1979) 619.

Demiralp E., Dasgupta S., Goddard W. A. III, Journal of American Chemical
Society 117, (1995) 8154.

Lichtenberger D. L., Johnston R. L., Hinkelmann K., Suzuki T., Wudl F., Jour-
nal of American Chemical Society, 112, (1990) 3302.

Sato N., Saito G., Inokuchi H., Chemical Physics 76, (1983) 79.

121
Figure Captions
Figure 1. The HOMO molecular orbital of the neutral TTF-Cl molecule. Results
are from HF calculations. The positive lobes are dark gray and the negative lobes
are light gray. The isosurfaces are for an amplitude of 0.02 in atomic units.
Figure 2. The HOMO molecular orbital of the neutral TTF-Cl molecule. Results
are from HF calculations. The positive lobes are dark gray and the negative lobes

are light gray. The isosurfaces are for an amplitude of 0.02 in atomic units.

122

Table 1: The deformation angles, energy differences and the boat vibrational fre-
quencies for various TTF-based organic donors
The deformation angle is © (see Figure 2 in Section 3.3); energy differ-
ence between boat and planar structures is AFoat, and the lowest boat deformation
vibrational frequency iS Vpoat-

TTF - 0.0 +0.332° 17.7
F 11.3 —0.046 18.6

Cl 14.3 —0.135 18.1

TMTTE - 5.8 —0.004 10.3
BEDT-TTF - 21.1 —0.654 19.5
BEDO-TTF - 8.5 —0.017 10.5
MDT-TTF - 21.5(7.6)4 NEG* 29.8

S,S-DMBEDT-TTF - 21.8(21.5)4 NEG* naf

TSeF - 0.0 POSS nal

Cl 15.5 -0.132 nal

TOF - 0.0 POS?’ 76.1
Cl 0.0 POS? 29.7

*For TTF, TSeF and TOF, all substitutions replace H atoms with the corresponding sub-
stituents.

°For ET-derived molecules with C2 symmetry, O is the average angle on both sides of central
plane.

°To obtain the positive AEsoat we started with the optimized planar and boat structures
containing Cl and replaced each Cl with H as the appropriate distance.

®NEG indicates that starting with Cz (or Co,) symmetry, the structure optimizes to a boat
structure, hence the energy of the boat structure is lower than planar structure. However, we did
not separately optimize the planar structure to obtain AE boat.

‘Frequencies not yet calculated.

9POS indicates that starting with Cy (or Co,) symmetry, the structure optimizes to a planar
structure with D2 (or Don) symmetry, hence the energy of the boat structure is higher than planar
structure.

123

Table 2: Ionization potentials (eV) for organic donors.

Species Substitutions? X*+—X Koopmans Theorem Experiment
(eV) (eV) (eV)

TTF - 5.821 6.806 6.7°, 6.4°

F 6.803 7.833 nat

Cl 6.599 7.807 nat
TMTTF - 5.491 6.579 6.03°
BEDT-TTF - 5.799 7.073 6.7°, 6.21°
BEDO-TTF - 5.725 6.791 6.46°
MDT-TTF - 5.954 7.055 naé
S,S-DMBEDT-TTF - na® 7.022 nat
TSeF 6.289 7.099 6.68°

Cl 7.005 8.024 nat
TOF 5.389 6.940 nat

Cl 6.249 7.952 na‘

“For TTF, TSeF and TOF, all substitutions replace H atoms with the corre-
sponding substituents.

'Data from Ref. 9

“Data from Ref. 10

4No experimental data available.

"Not yet calculated.

124

Table 3: Energies for various organic donors

x xt
Species Conformation Symmetry Total HOMO LUMO Total HOMO LUMO
@ VY) Vv) @® Vv) &y)
TTF planar Don -1819.5165 -6.806 3.070 -1819.3026 -11.641 -4.768
F9 boat Cay* -2214.8467 -7.833 1.853 ~2214.5967 -12.513 -5.752
Clg boat Cay? -3655.0704 -7.807 1.988 -3654.8279 -12.143 -5.397
TMTTF boat Cay* -1975.6844 -6.579 3.151 -1975.4826 -11.092 -4.342
BEDT-TTF® boat C2 -3563.3607 -7.073 2.748 -3563.1476 -10.929 -4.541
BEDO-TTF¢ boat Ce -2272.7063 -6.791 2.798 -2272.4959 -11.071 -4.612
MDT-TTF boat Cy? -2652.3944 -7.055 2.816 -2652.1756 -11.299 -4.833
S,S-DMBEDT-TTF boat C4 -3641.4361 -7.022 2.811 na® na® na®
TSeF9 planar Dan -265.4650 -7.099 2.060 -265.2339 -11.747 -5.330
clfig boat Coy -2098.1371 -8.024 1.034 -2097.8796 -12.210 -5.902
TOF planar Dan -528.8507 -6.940 5.278 ~528.6526 -12.948 -3.676
cls planar Doar -2364.4078 -7.953 4.329 -2364.1781 -13.160 -4.291

“There is only one negative curvature from the Hessian matrix for the planar conformation, indicating
that the only stable structure is boat.

> The staggered ethylene conformation is used. There is also an eclipsed ethylene conformation with
Cs; symmetry and an energy 5 wHartree lower than the staggered conformation (See Ref. 8).

© The staggered ethylene conformation is used. We did not do detailed conformation calculations for
BEDO-TTF, but we expect that the conformations of BEDO-TTF should be similar to BEDT-TTF.
“Molecule is asymmetric (See Figure 1 in Section 3.3).

“Not yet calculated.

fEffective Core Potential is used for Se atoms.

9For TIF, TSeF and TOF, all substitutions replace H atoms with the corresponding substituents.

125

igure

126

igure 2

127

Chapter 4 Molecular Mechanical Calculations
for BEDT —TTF and BEDT —TTFt

128
Force Field and Vibrational Frequency Calculations

for the Neutral and Cation BEDT-TTF

Abstract

BEDT-TTF is the donor of the best T. organic superconductors. Iso-
topic shift experiments support electron-phonon coupling mechanism for the super-
conductivity; however, the vibrational levels have been only partially observed and
assigned. In order to provide a complete consistent description of all levels, we car-
ried out Hartree-Fock calculations (6-31G** basis set) for all fundamental vibrational
frequencies of BEDT-TTF and BEDT-TTF* and obtained the Hessians for these

structures. With these Hessians and available experimental frequencies, we develop

the force fields for the neutral and cation BEDT-TTF molecules by using Hessian-
biased method. Calculated frequencies are compared with the available experimental

frequencies for the neutral and cation BEDT-TTF molecule.

129

1.0 Introduction

The organic superconductors all involve derivatives of the organic donor
molecules tetrathiafulvalene (denoted as TTF), tetraselenafulvalene (denoted at TSeF),
or some mixture of these two molecules, packed into quasi one- and two-dimensional
arrays and complexed to appropriate electron acceptors.! Figure 1 shows BEDT-
TTF (denoted also as ET) is the donor of the best organic superconductors. Using
ET, more than 20 organic superconductors have been synthesized with T, up to 12.8K.
Changes in T, for various isotope shifts indicate that electron-phonon coupling is im-
portant for the superconductivity of these materials. However, experimental data on
the vibrational modes is incomplete and does not supply clear evidence about the
vibrational modes that are important for superconductivity. Thus, we perform ab
initio HF and force field calculations to obtain all modes of neutral ET and of ET*.

With appropriate electron acceptors some modifications of ET show
superconductivity and some do not. The relation between superconductivity and
the molecular or crystal structures of these molecules is not yet clearly identified by
the experiments. Yamaji? proposed that the superconductivity in organic conduc-
tors involves coupling between the Highest Occupied Molecular Orbital (HOMO) and
total symmetric intramolecular vibrational modes. However, the pattern of isotope
effects does not support for this view. Isotopic shift experiments with deuterium
substitutions showed that the electron-phonon coupling plays a role in the super-
conductivity of these materials.?4°® We found that’ the neutral donor distorts into a
boat structure whereas the cation is planar for all known organic superconductors. We
suggested that the coupling between charge transfer and the lowest boat deformation
vibrational mode is responsible for the superconductivity and predicted the isotope
shifts (6T.) for experimental tests of this coupling.’ Although incomplete, current
experimental isotopic shifts are consistent with this charge transfer boat deformation
(ET-BV) coupling for the mechanism of the superconductivity.®

In this paper, we present the calculated vibrational spectra for the
equilibrium structures of ET (boat) and ET* (planar). Using calculated structures,

Hessians and available experimental frequencies we develop the force fields for the

130
neutral and cation ET molecules. These frequencies are compared with the available

experimental frequencies.*!°

2.0 Results
2.1 Structures

The structure of ET is often discussed in terms of Dz symmetry, which
assumes a planar structure for the central TTF moiety. The crystal structures of neu-
tral ET crystal are consistent with planarity but show a distinct boat-like distortion.!!
Some deviations from planarity are also suggested in crystals containing electron ac-
ceptors, (ET),Xm.'” Here the ET molecules often form dimers (ET))+ sharing a
single positive charge.
ly we reported ab initio quantum chemical calculations [Hartree-
Fock (HF) with 6-31G** basis set] for the structures of neutral and cation ET.”° These
results show that neutral ET is nonplanar. It deforms to boat conformation with a
well depth of 0.654 kcal/mol. However, the cation, ET*, is planar.

The terminal six membered-rings are nonplanar in order to avoid eclips-
ing of the CH — CH, groups at each end. This nonplanarity leads to two possible
conformations??:

1. The staggered conformation indicated in Figure 1a in Section 3.2 in which the two
Cs — Cg bonds are pointing in opposite directions; assuming a planar TTF central
region, this leads to D) symmetry.

2. The eclipsed conformation indicated in Figure 1b in Section 3.2 in which the two
Cs — Ce bonds are parallel; with planar TTF, this leads to Co, symmetry.

These conformations are essentially degenerate, differing by only 0.0000052 Hartrees(with
eclipsed lower). We will consider the higher symmetry staggered case.

To determine the structure and vibrational modes of ET, we carried
out ab initio Hartree-Fock calculations using the 6-31G** basis set.!° Restricting
the symmetry to D, leads to an optimized structure with two imaginary frequency

vibrational modes. The stable conformation is the boat structure with Cy symmetry.

The optimized boat structure has vibration frequencies positive, indicating a stable

131

structure.

2.2 Vibrational Analysis

Previously, assignments of the vibrational spectra of ET assumed pla-
nar molecule for both the neutral and cation cases. Planar ET would have D2 sym-
metry for the staggered conformation and C», for the eclipsed conformation. For the
staggered conformation this leads to fundamental modes with the following symme-

tries:

['(D2) =19A+17B; +18B,+18B; (1)

To simplify assignments, Kozlov et al.!” considered the ET to be totally flat leading
to Da, symmetries (they were aware that only the central C)S, group is planar). This

leads to the fundamental mode distribution
T(Do,) = 12A,+ 7A, + 6Big + 11 Biz + 7Bog + 11.Boy, + 11B39+7B3. . (2)

Thus Do, leads to g and u branching of the D. symmetry modes. However, the stable

boat structure of ET has Cy symmetry, leading to the mode distribution
(Cy) = 37A+35B. (3)

Consequently, some modes become both infrared and Raman active. Table 1 shows
that this is consistent with data of Kozlov et al. The two-fold axis of B; symmetry of
the planar molecule and C2 axis of the boat molecule are perpendicular to the central

plane of the molecule. The reduction of symmetry, is as follows:

and

Table 4 shows all calculated frequencies plus available experimental

frequencies for neutral ET. Calculated Raman and IR intensities are also given for all

132
the vibrational modes. We used the symmetry of the modes for assigning experimental
frequencies to the HF modes. The calculated IR and Raman intensities are in good
agreement with experimental intensities.

ETt molecules is planar (Dz symmetry) leading to the distribution of
fundamental mode in equation (1). Table 5 shows all the vibrational modes of ET*
compared to the available experimental frequencies. |
3.0 The Force Field

The ET molecules appear to be distorted in the crystal structures,
removing all symmetry. The assignment of frequencies for ET and ET* molecules by
Kozlov et al.?!° assumed Dy, symmetry. We used the optimized HF geometries of the
neutral and cation ET to develop the force fields. Neutral ET has Cy symmetry and
cation ET has D, symmetry. The optimized geometric parameters(distances, angles,
dihedrals) for the neutral and cation ET molecules are given in Table 1. We use
these structures when we optimize our force field (FF). (For the neutral molecule, the
optimized HF structure is minimized to reduce the total force by using FF. The rms
difference between HF and minimized structure (FF) are 0.002 A for bonds, 0.680°
for angles). We calculated the Hessian (second derivative of energy with respect to
the 3N coordinates) at the HF optimized geometry. This Hessian was used to develop
the force field by using Hessian-Biased (HBFF) approach.'*

The potential energy of the molecule is:

E=VBR+> A+ B+ DY Bt Ext+V w+ YS Eo ,
bonds angles torsions inversions cross vdW Charges

(5)

where the terms are defined below. In the HBFF approach, the potential energy is

expressed as a sum of valence, nonbonded interactions. We optimize the force field

terms by fitting the experimental frequencies and the calculated geometries.

a. Valence Interactions
We used the following valence terms:

2. the harmonic bond stretch

133

B,(R) = shal -R)?, (6)

where (R,) is the equilibrium bond distance and (ky) is the force constant.

ii. the harmonic angle bend

B4(0) = Sha(O— 60)? (7

where y is the equilibrium angle and kg is the force constant.

wt. angle-stretch cross terms
Ea =kre(P—%)(R-R,) , (8)

where kre is the force constant.

iv. stretch-stretch cross terms
Ew =krri(R- Ry)(R'- Ry), (9)

where kp, is the force constant for the bonds Ry and RF, that share a common atom.

v. the torsional potential
E.(¢) = Vicos@ + Voc0s2¢ + V3cos3¢@ (10)

where V;, Vo, V3 are in kcal/mol and the angle ¢ is defined as the angle between the
JKL plane and the IJK plane of the any two bonds IJ and KL attached to a common
bond JK.

vi. the inversion potential
E(w) = K(1—cosw) , (11)

with a minimum for planar structure (wp = 0°). w is the angle between the IL axis

and the IJK plane for an atom I with exactly three bonds IJ, IK and IL.

134
b. Charges

Partial atomic charges for the various atoms were obtained using the
Potential Derived Charge method(PDQ).! The electron density from Hartree-Fock
wavefunction is used to calculate the electrostatic potential around the molecule.
Then, a set of atomic point charges is obtained that reproduces the ab initio elec-
trostatic potential and dipole and quadrupole moments. Table 2 shows the atomic
charges for the neutral and cation molecules.

We write total electrostatic energy as

Ecouloms = Co ~ iQ (12)

where € is the dielectric constant, Rj; is the distance in A and the conversion factor

Cy = 332.0637 puts the energy in kcal/mol. We take e = 1 (i.e. vacuum value).

c. van der Waals Parameters
We used the van der Waals parameters '© previously determined from
empirical fits to lattice parameters. The exponential-6 potential is used for van der

Waals interactions:

Eyaw = Dyl( eae ® — (Say) (13)

¢-6 ¢-6
In Table 3 we give the bond strength (well depth) Do (in kcal/mol) and the bond
length Rp (in A) and ¢ are given for C, S and H.

The electrostatic and van der Waals interactions are excluded for 1-2,
1-3 and 1-4 interactions since they are considered to be already included in the bond

stretch, angle bend and torsion terms.

4.0 Hessian-biased Method"4

The potential energy can be expanded around the equilibrium geome-

try.
3N OE 1 3N OE
E= Fo+ Di ap, (ORs) + > &, Sran, )(6Ri)(SR;) + ... (14)

135

where
OE
F,=- 15
DR, (15)
is the force on the i** component and
CE
= 16
Ai = ROR, (16a)
is the Hessian. Using the mass weighting
Hi; = Hij(MiM;) (16d)
and diagonalizing (16b)
HU=UA _, (17)

where \ contains. the 3N vibrational frequencies(6 of which are zero for a free nonpla-

nar molecule).
In the Hessian-biased method, the theoretical Hessian (H;) is biased

with the experimental frequencies. From (17) the theoretical Hessian can be written

where U/ is the transpose of U;. We then modify \; by replacing A; with the

experimental A,. This leads to the experimental biased Hessian defined as

Ay = UA ,U . (19a)
The biased Hessian has the property that

HyU,= UtrAr (19b)

That is, it leads to the theoretical modes (U;) and the experimental frequencies (\,).
If the A, is not available from experiment, it can be obtained from the theory using

appropriate scaling rules.

136

We optimized the force field parameters that gave the best fit to Ay:
while leading to correct(theoretical) equilibrium geometry. The van der Waals pa-
rameters and charges were fixed during optimization of the valence parameters. The
charges (Table 2) were based on Potential Derived Charges (PDQ) by using quantum
mechanical potentials and the vdW parameters (Table 3) were from previous fits to
various crystals. The final force field parameters for the neutral and cation ET are
shown in the first two columns of Table 3.

Calculated frequencies for ET and ET* are compared with the available
experimental frequencies by Kozlov et al.?!° (frequencies for both neutral and cation
molecules) and Eldridge et al.!” (only frequencies for neutral molecule) in Table 4
and 5. Kozlov et al. reported more modes for neutral ET and Eldridge et al. did
not report for the frequencies of ET*, hence we use the experimental frequencies
by Kozlov et al.?!° for rms error calculations. The rms error between theory and
experiment frequencies are ~ 32 cm7! for ET and ~ 20 cm™! for ET*.

5.0 Summary

We develop force fields for the neutral, cation ET molecules including
the valence and nonbonded interactions. The Hessian-biased approach is used to
get the force field which reproduces experimental frequencies for the neutral and
cation ET. The calculated frequencies are compared with the available experimental
frequencies for the neutral, cation ET molecules. It is shown that. there is good

agreement between calculated and experimental frequencies.

137

References

10.

Jerome D., Mazaud A., Ribault M., Bechgaard K., J. Phys. Lett. 41, (1980)
L95.

Yamaji K., Solid State Communications, 61, (1987), 413.

Carlson K. D., Williams J.M., Geiser U., Kini A. M., Wang H. H., Klemm R.
A., Kumar S. K., Schlueter J. A., Ferraro J. R., Lykke K. R., Wurz P., Parker
H., Sutin J. D. B., Mol. Crsyt. Lig. Cryst. 234, (1993), 127.

Carlson K. D., Kini A. M., Klemm R. A., Wang H. H., Williams J.M., Geiser
U., Kumar S. K., Ferraro J. R., Lykke K. R., Wurz P., Fleshler S., Dudek J.
D., Eastman N. L., Mobley P. R., Seaman J. M., Sutin J. D. B., Yaconi G. A.,
Inorg. Chem. 31, (1992), 3346.

Carlson K. D., Kini A. M., Schlueter J. A., Wang H. H., Sutin J. D. B., Williams
J.M., Schirber J. E., Venturini E. L. , Bayless W. R., Physica C 227, (1994),
10.

Demiralp E. and Goddard III, W. A., Synthetic Metals, 72, (1995), 297.

Demiralp E.,Dasgupta S. and Goddard II, W. A., Journal of American Chem-
ical Society 117,(1995), 8154 .

Kozlov M.E., Pokhodnia Kk. I., Yurchencko A. A., Spectrochimica Acta 45A
(1989), 323.

Kozlov M.E., Pokhodnia K. I., Yurchencko A. A., Spectrochimica Acta 45A
(1989), 437.

11.

12.

13.

14.

15.

16.

17.

138
Kobayashi H., Kobayashi A., Yukiyoshi S., Saito G., Inkuchi H., Bull. Chem.
Soc. Jpn., 59, (1986) 301.

Dasgupta, S.; Goddard III, W. A.J. Phys. Chem. 95, (1989) 7207.

M. N. Ringnalda, J-M. Langlois, B. H. Greeley, T. V. Russo, R. P. Muller,
B. Marten, Y. Won, R. E. Donnelly, Jr., W. T. Pollard, G. H. Miller, W. A.
Goddard III, and R. A. Freisner, PS-GVB v1.0, Schrédinger, Inc., Pasadena,
California, 1994.

Mayo S.L, Olafson B. D., Goddard HI, W. A., , Journal of Physical Chemistry,
94, (1990) 8897.

Eldridge J. E., Homes C. C., Wang H. H., Kini A. M., Williams J.M., Synthetic
Metals, 70, (1995) 983.

139

H 32 S S32,
So a NN. _— SR R — a “On, ZA
H:-m &3 Cy Cy C3.
i 3 'H,
| | Crp=——Cpr | |
Hy Ninn,
C3, Cy J \ C, C3 Hi
Hinge Sh 5 NAN,

Figure 1 : Definition of the atomic types for the atoms of ET

140
Table la. Optimized distances(in A) for boat and planar ET conformations and

experimental distance (See Figure 1 for notation).

ET ETt

FF* HF FF HF
Cr—Cr 1 1.325 1.326 1.389 1.389
Sr- Cy 4 1.773 1.774 1.751 1.751
S32 — C3 4 1.812 1.814 1.816 1.816
Sr—Cr 4 1.769 1.771 1.721 1.721
Cy, —-C, 2 1.325 1.323 1.336 1.336
S32. — Cy 4 1.769 1.767 1.765 1.765
C3 — C3 2 1.523 1.523 1.523 1.523
C3;-H 8 1.083 1.082 1.082 1.082

Table 1b. Optimized angles (in degrees)

ET ET*

FF HF FF HF
128.68 128.45 128.83 128.83
113.80 114.29 114.75 114.75

S39 — Cy — C2 4

Sp—-C,—S3. 4

Sr-Cr-Sr 2 112.74 112.55 11449 114.49
Cr-Sp—-Cyp 4 9441 94.55 96.33 96.33
Sy —-C3-C; 4 112.87 113.17 113.10 113.10
Sp—C,-Cy 4 117.22 117.22 116.42 116.42
Sr-Cr-Cr 4 123.63 123.71 122.76 122.76
Cy—S32-C3 4 100.74 100.81 100.50 100.50
H-C,;-H 4
S32 —-C,; —H 8
C3—-C3;-—H 8

108.58 108.48 108.51 108.51
107.18 107.15 106.84 106.84
110.36 110.31 110.60 110.60

* For the neutral molecule, the optimized HF structure is minimized to reduce the

total force by using FF. The rms force is less than 0.1 (kcal/mol)/A for ET and ET*.

141
Table 2. Calculated charges by using Potential Derived Charge Method (See Figure

1 in this chapter for notation).

Number of Cases Neutral Cation
Cr 2 -0.0200 -0.0220
Sr 4 -0.0260 0.1390
on 4 0.0265 0.0240
S30 4 -0.0955 -0.0230
C3 4 -0.1770 -0.2420
Ai 4 0.1885 0.2440
H_o 4 0.0935 °* 0.1200

Net Charge 0.0 1.0

142
Table 3. Force-field parameters used in this calculations. Units are kcal/mol for

energies, A for length, and degrees for angles. Angular force constants use radians.

van der Waals Parameters

H Ro 3.19500

Dz 0.01520

¢ 12.38200

C Ro 3.89830
D, 0.09510

¢ 14.03400

S) Ro 4.03000
Dz 0.34400

¢ 12.00000

143
Table 3. (Continued) Force-field parameters used in this calculations. Units are
kcal/mol for energies, A for length, and degrees for angles. Angular force constants

use radians (See Figure 1 in this chapter for notation).

Neutral Cation
Bond Stretch
C; — H Ry 1.084 1.081
ke 636.386 636.530
C3 - C3 Ro 1.526 1.523
ky 613.257 606.042
Cy — Co R; 1.300 1.329
ky 1280.633 1073.148
Cr—-Cr Ro 1.319 1.399
kp 1120.168 995.272
S39 — C3 Ry 1.821 1.825
ko 312.535 304.720
S39 — C4 Ry 1.827 1.766
kp 361.172 479.499
Sp—Co R, 1.788 1.753
ko 836.525 674.396
Sr-~Cr Ro 1.736 1.721

ke 483.850 547.649

Table 3. (Continued)

144

Neutral Cation
Angle Bend
H-C;-H 9% 109.12 108.65
ko 92.818 72.886
C3; -—C3-— H 9 110.79 110.38
keg 80.057 109.365
S32 — C3 — H ey 107.44 105.85
ko 74.392 60.653
S32 — C3 — C3 o 114.35 113.57
kg 193.274 364.201
532 — Cy — Co Io 121.64 127.48
ko 96.121 77.349
Sp—Cy-—- Cy ey 113.62 115.72
ko 130.018 233.544
Spr — Cy — $32 Ao 108.09 114.96
ke 89.224 90.533
Srp—-Cr—-Cpr Ao 130.18 121.61
kg 98.621 129.464
Srp—Cr—- Sp Go 128.78 116.13
kg 154.837 148.992
Cy -- S39 — C3 G 100.03 160.67
kg 198.691 191.985
Cr—-—Sprp—-—Cy Oo 98.32 96.85
kg 250.173 322.658

145
Table 3. (Continued) |

Neutral Cation
Angle Cross Terms
H-C,;-H kre -75.260 -27.305
Kroo ~75.260 -27.305
Kr, Ro -38.305 -22.977
C3;-C3;-—H kre 7.847 6.245
kroo 3.295 86.784
KriR> 1.546 -0.226
S39 — C3 — H Krie 48.635 39.139
kro 18.933 -10.670
Kr, Ro -13.325 -0.371
S39 — C3 — C3 Krie -0.964 -6.689
Kroo -4.778 68.070

krik, 20.436 34.745
So — Cy — Cy kaye 96.007 119.264

kenge 47.517 --31.109
ky Ry 10.424 -2.801
Sp—C2—-Cy kre 178.792 162.888
roo 81.403 82.593

kripp 408.025: 264.133
Sp-C,-S3, kre 54.907 35.455
koe 113.414 135.257
KriRp 86.875 91.696
Sp-Cr—-Cr — kr 40.592 69.328
Kao 36.508 104.725
krikp 63.775 29.613
Srp-Cr-Sr kre 79.702 126.993
Koo 79.702 126.993
kr, Ry 60.025 19.556

C2 — S32 — C3

Cr—-Sr- Cy

kre
Kr.
Kr, Ro
Erie
Kr

Kr, Ro

49.887
46.465
-11.975
52.029
59.718
10.704

146
148.984
33.800
-69.191
124.512
43.796
25.593

Table 3. (Continued)

147

Neutral Cation
Torsion Terms
H-C;-C;-H V3 5.958 7.164
S3. -C3 —C; —H V3 19.558 9.641
S32 — C3 — C3 — S39 V3 73.125 -57.046
S39 — Cy — Cy — S39 Vp -25.759 -3.196
Sr - Cy — Cy — S32 V2 10.814 -13.975
Sp—Cy—Cy~-Sp Vo -44.726 0.876
Sre—-Cr-Cr—-Spr Vo -19.943 -0.217
Cy — S39 — C3 — H V3 1.531 0.684
Cy — S39 — C3 — C3 V3 -2.586 -2.605
C3 — S32 — Cy — Cy Vo 0.720 1.825
C3 — S32 — Cy — Sp Vo -0.020 0.170
Cr—-—Sr-Cy—-Cy Vo 2.764 -3.149
Cr — Spr — Cy — S3o Vo -0.774 -4.459
V3 1.845 0.000
Cy—- Srp—-Cr—-Cr Vi 6.756 12.840
Vp 0.844 0.263
V3 -0.350 0.000
Cy —Sp-Cr—Sp- Vo 1.175 -1.393
V3 2.127 0.000
Neutral Cation
Inversion Constant(K/,)
Cy — Sp — S32 — C2 5.738 4.917
Cy — Sp — Co — S39 85.778 155.854
Cy — S39 — C2 - Sp 6.745 1.651
Cr—-Sp—-Sr—Cr 10.713 16.128
Cr—-Sp—-Cr—- Spr 53.616 50.178

148

Table 4. Calculated (HF)and experimental frequencies and Raman and infrared

(IR) intensities for ET. The frequencies are in cm~!, IR intensities are in KM/Mole,

Raman intensities are in A*/AMU.

Sym. Modes HF Intensity Experiment FF
IR Raman IR Raman

A C-H str. 3302 11.60 71.75 - (2964) 2957.9
B C-H str. 3302 3.28 51.36 2958 w(2958) - 2957.9
A C-H str. 3290 0.01 256.30 - - 2915.0
B C-H str. 3290 0.37 9.60 - - 2915.0
A C-H str. 3237 0.20 606.22 - (2920) 2958.3
B C-H str. 3237 79.71 4.30 2958 w(2922) - 2958.3
A C-H str. 3229 10.24 161.39 - - 2909.8
B C-H str. 3228 2.68 6.80 - 2916 w 2909.8
A C=C str. 1815 0.57 354.11 - 1552 m(1551) 1546.9
B C=C str. 1790 1.48 0.26 1505 w(1509) 1511m 1519.5
A C=C str. 1772 0.35 509.60 - 1494 (1493) 1490.0
A CH, bend 1608 3.02 10.70 - (1408) 1424.3
B CH, bend 1608 1.11 14.73 1420 w(1409) - 1424.3
A CH, bend 1594 11.27 9.51 - 1406 m(1422) 1401.4
B CH, bend 1594 4.86 32.12 1409 vw(1422) - 1401.4
A CH, wag 1466 2.41 0.93 - 1285 vw(1283) 1295.0
B CH) wag 1466 63.72 1.71 1282 m(1284) - 1295.0

149

Sym. Modes HF Intensity Experiment FF
IR Raman IR Raman

A CH wag 1434 5.66 1.19 1259 w(1261) - 1247.4
B CH, wag 1434 0.90 0.57 - 1256 vw(1257) 1247.4
A CH, twist 1321 0.27 15.70 - 1175 vw 1164.2
B CH, twist 1321 0.06 2.33 1173 vw - 1164.2
A CH, twist 1260 248 0.29 1132 sh 1132 vw 1127.4
B CH, twist 1260 2.44 14.41 1125w 1126vw 1127.4
A Ring Def. (I.P.)> 1131 0.21 0.34 - 1016 vw(1000) 1029.5
B Ring Def. (I.P.) 1128 7.06 0.02 (997) - 1013.0
A Ring Def. (I.P.) 1125 0.01 0.59 - (1013) 1009.3
B C-C str. 1093 0.03 0.61 996 w(992) - 998.6
A C-C str. 1093 0.01 7.15 987 w - 998.6
A CHy rock. 1033 1.64 7.62 - - 948.1
B CHy rock. 1033 22.58 5.39 938 vw - 948.1
B CH, wag 996 12.99 1.83 917 s(906) - 915.5
A CH, wag — 990 5.72 0.04 - 919 vw(889) 915.5
B Ring Def. (I.P.) 967 28.10 0.77 905 m(919) - 900.0
A Ring Def. (I.P.) 967 3.50 1.81 - 911 vw(918) 899.6
B Ring Def. (I.P.) 951 2.29 0.28 890 m(890) 890 vw 854.1

150

Sym Modes HF Intensity Experiment FF
IR Raman IR Raman

B* Ring Def. (L.P.) 847 12.03 0.13 875 vw(687) 875 vw 758.6
B Ring Def. (1.P.) 846 42.37 0.02 772 s(771) - 761.6
A Ring Def. (1.P.) 842 0.17 1.96 860 vw - 824.4
A CH, rock. 759 0.10 15.90 - 687 w 726.8
B CH, rock. 759 2.47 1.86 687 Ww - 724.9
A CH rock. 716 0.02 44.08 - 653 m(625) 629.9
B CH rock. 716 6.70 0.62 653 w(625) - 628.9
B Ring Def. (O.P.)* 623 4.54 11.88 - - 724.9
B Ring Def. (O.P.) 606 0.06 4.15 - - 453.3
A Ring Def. (O.P.) 605 0.05 0.92 - - 449.6
A Ring Def. (O.P.) 539 1.50 15.60 - 486 m(487) 502.3
B Ring Def. (I.P.) 511 1.50 0.86 499 m(500) - 481.3
A* Ring Def. (1.P.) 510 0.03 1.73 - 625 w(654) 668.6
B* Ring Def. (1.P.) 496 6.24 0.43 624 w(654) - 667.8
A Ring Def. (I.P.) 483 0.01 14.54 450 w 440 m(440) 446.0
B Ring Def. (I.P.) 425 6.63 1.16 390 m(390) - (389.3
B Ring Def. (I.P.) 394. 0.04 0.80 - 334 m(335) 361.6
A Ring Def. (I.P.) 393 0.02 0.10 335 m(335) - 373.4
A Ring Def. (I.P.) 383 0.0.09 8.42 - 348 w(348) 347.3

151

Sym. Modes HF Intensity Experiment FF
IR Raman IR Raman

A Ring Def. (O.P.) 356 1.02 4.00 - 308 w(309) 303.0
B Ring Def. (O.P.) 327 3.16 0.17 278 m(277) _ 288.1
A Ring Def. (O.P.) 315 0.04 2.72 - - 361.9
B Ring Def. (O.P.) 309 0.28 0.05 - - 269.8
A Ring Def. (O.P.) 300 0.04 0.20 - - 261.4
B Ring Def. (I.P.) 286 3.72 0.02 257 m(258) 260w 264.9
A Ring Def. (O.P.) 270 0.01 0.75 - - 177.1
B* Ring Def. (O.P.) 262 4.45 0.61 - 127 vw 62.2
A Ring Def. (O.P.) 206 0.01 0.72 - 159 s(161) 183.5
A Ring Def. (I.P.) 173 0.03 14.86 - 151 8(161) 153.6
A Ring Def. (O.P.) 130 0.03 0.18 - - 177.0
B Ring Def. (O.P.) 129 0.00 0.28 96 m - 127.0
B Ring Def. (I.P.) 60 1.14 0.87 - - 98.1
A Ring Def. (O.P.) 53 0.16 0.19 - - 53.1

B Ring Def. (O.P.) 44 2.71 0.37 - - 46.7
A Ring Def. (O.P.) 43 7.24 0.26 30 w - 45.2
B Ring Def. (O.P.) 38 0.26 0.63 - - 36.9
A Ring Def. (O.P.) 20 2.21 = 1.28 - - 15.7
RMS Error 134 - - 0 0 32.1

°Relative intensities, vs: very strong, s: strong, m: medium, w: weak, vw: very weak,

sh: shoulder, br: broad.

‘In-plane ring deformation mode

“Out-of-plane ring deformation mode

* Experimental assignment of this mode is not consistent with the quantum chemical

calculation and not included in RMS error.

152
Table 5. Calculated and experimental frequencies and Raman and infrared (IR)
intensities for ET+. The frequencies are in cm~!, IR intensities are in KM/Mole,

Raman intensities are in A*/AMU.

Sym. Modes HF Intensity Experiment FF
IR Raman IR Raman

Bz C-H str. 3316 1.41 90.73 2936 w - 2935.9
Bo C-H str. 3316 0.21 86.51 - - 2935.9
A C-H str. 3305 0.00 251.75 ~ - 2916.5
B, C-H str. 3305 2.13 0.57 2914 vw - 2916.5
A C-H str. 3248 0.00 1086.34 - - 2871.1
By, C-H str. 3248 24.15 1.76 - 2847 vw 2871.1
Bo C-H str. 3242 0.29 13.57 2883 w - 2857.5
Bs C-H str. 3242 5.22 179.42 - - 2857.5
A C=C str. 1697 0.00 60707.55 - 1455 m 1496.0
B, C=C str. 1620 3060.40 1.32 1445 w - 1457.7
A CH» bend 1601 0.00 24.83 - - 1422.2
By, CHy bend 1601 5.04 4.97 1422 sh - 1422.2
Bs; CH, bend 1594 23.93 6.92 1411s - 1416.4
By CHy bend 1594 4,55 96.09 - - 1416.4
A C=C str 1565 0.00 34573.66 - 1431 vs 1385.1
A CH, wag 1469 0.00 279.93 - 1294 vw 1285.5
By, CHz wag 1467 209.74 1.47 1283 m - 1285.3
B3 CHa wag 1435 7.32 3.71 - 1274 vw 1263.6
Bz CHa wag 1435 0.00 0.72 1277 sh - 1263.6
A CH, twist 1325 0.00 16.62 - - 1173.5

By CH twist 1325 1.47 2.08 1180 w - 1173.5

153

Sym. Modes HF Intensity Experiment FF
IR Raman IR Raman

B3 C'He twist 1264 1.38 1.56 1125 sh - 1135.0
By C He twist 1264 2.21 18.511 - 1120 ws 1135.0
Bs Ring Def. (I.P.)® 1171 0.25 623.99 - 1056 w 1059.4
By Ring Def. (1.P.) 1141 16.86 0.06 1024 w - 1026.3
B3 Ring Def. (I.P.) 1138 0.10 5.88 - - 1025.6
A C-C str. 1093 0.00 31.22 - 976 mw 991.2
B, C-C str. 1093 0.30 0.61 1010 vw - 991.2
A C Hp rock. 1029 0.00 247.37 - 931 vw («952.3
By CH» rock. 1029 5.24 5.10 - - 936.4
B, CHy wag 997 0.04 2.42 915 w - 935.7
Bs CH, wag 991 8.04 0.00 - - 887.1
By Ring Def. (1.P.) 969 406 74.29 900 w - 895.7
A Ring Def. (1.P.) 963 0.00 7905.13 - 905 w 885.0
By Ring Def. (I.P.) 927 5.84 225.12 - - 950.9
By Ring Def. (I.P.) 881 5.86 956.10 812 w - 826.0
By Ring Def. (I1.P.) 857 6.11 0.09 886 w,br - 841.1
B; Ring Def. (1.P.) 853 0.29 3.72 - - 839.3
Bs CHy rock. 749 0.00 13.32 - - 691.6
By CH, rock. 749 = 4.23 2.77 640 vw - 691.6

154

Sym. Modes HF Intensity Experiment FF
IR Raman IR Raman

A CH rock. 707 0.00 339.78 - - 686.4
B, CH, rock. 706 36.60 0.04 672 vw - 684.9
B, Ring Def. (O.P.)° 610 0.01 3.23 - - 636.0
A Ring Def. (O.P.) 607 0.00 14.03 - - 636.0
By Ring Def. (O.P.) 596 0.02 6.19 - - 581.2
A Ring Def. (1.P.) 570 0.00 5148.20 - 5llmw 512.9
Bs Ring Def. (I.P.) 514 0.35 0.04 - - 487.1
B, Ring Def. (I.P.) 512 2.91 1.11 - - 476.5
B, Ring Def. (1.P.) 504 605.79 0.00 503 w - 512.0
A Ring Def. (I.P.) 492 0.00 2986.58 - 489m 453.9
By, Ring Def. (I.P.) 438 3.85 0.05 406 w - 397.6
B, Ring Def. (I.P.) 392 0.49 0.2 - - 344.6
Bs Ring Def. (I.P.) 387 0.06 4.84 - 355 vw 387.0
Bs Ring Def. (I.P.) 371 0.00 93.14 335 w - 349.4
B; Ring Def. (O.P.) 357 = 1.70 0.21 - - 340.3
A Ring Def. (I.P.) 348 0.00 4.39 - 320 w 335.2
B, Ring Def. (I.P.) 328 21.53 0.04 - - 339.7
By Ring Def. (O.P.) 309 0.52 3.29 265 w - 272.7

155

Sym. Modes HF Intensity Experiment FF
IR Raman IR Raman

By Ring Def. (I.P.) 295 4.79 0.01 - - 335.2
B; Ring Def. (O.P.) 294 0.07 0.32 - - 282.2
A CH, wag 294 0.00 0.32 - - 234.0
B, . CH, wag 283 0.00 0.07 - - 219.5
Bz Ring Def. (I.P.) 187 0.012 3.46 - - 179.8
A Ring Def. (1.P.) 175 0.00 185.20 - 169w 162.8
A Ring Def. (O.P.) 120 0.00 6.81 - - 83.6
By Ring Def. (O.P.) 120 0.48 0.57 - - 83.1
B Ring Def. (O.P.) 86 0.07 16.63 - - 70.3
B, Ring Def. (1.P.) 61 0.16 0.00 - - 53.6
Bs Ring Def. (O.P.) 49 893 0.29 - - 46.1
B, Ring Def. (O.P.) 43 0.02 0.17 - - 34.4
A Ring Def. (O.P.) 36 0.00 0.00 - - 19.8
B3 Ring Def. (O.P.) 28 2.04 0.02 ~~ - - 8.4

RMS Error 167 - - 0 0 20.0

* Relative intensities, vs: very strong, s: strong, m: medium, w: weak, vw:

very weak, sh: shoulder, br: broad.

> In-plane ring deformation mode.