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Molecular electronic structures : an introduction
The present book is an introduction to molecular electronic structural theory. It is aimed at students who have reasonable familiarity with differential and integral calculus and are beginning a study of the physical description of chemical systems. We have decided to concentrate on the description of ground state electronic structures, or, in other words, the principles of chemical bonding in molecules. In this important respect the present volume differs from our earlier book "Molecular Orbital Theory" (Benjamin, 1964), which included a strong emphasis on the description of electronic excited states.
In our treatment of molecular wave functions we make use of "symmetry operators", the latter being operators that leave the Hamiltonian unchanged. By using such symmetry operators, it is possible to characterize the electronic structures of molecules. In our opinion, this approach provides good preparation for later studies that may be undertaken in which formal group theory is employed.
The heart of the book is Chapter 4, where we discuss in some detail the bonding in several selected molecules. Examples from both organic and inorganic chemistry are included in an attempt to make the coverage as general as possible. Our objective here is to provide an introduction to molecular bonding that will serve as a foundation for more advanced study of electronic structures.
Suggested reading and problems are included in each chapter. Some of the problems are challenging, but working them will give the student a much better feeling for the principles involved. The suggested reading is of two types, books (and reviews) and original papers. And we urge students to examine at least some of the older papers in the field, as muck can be learned from them
Model for Triplet State Engineering in Organic Light Emitting Diodes
Engineering the position of the lowest triplet state (T1) relative to the
first excited singlet state (S1) is of great importance in improving the
efficiencies of organic light emitting diodes and organic photovoltaic cells.
We have carried out model exact calculations of substituted polyene chains to
understand the factors that affect the energy gap between S1 and T1. The
factors studied are backbone dimerisation, different donor-acceptor
substitutions and twisted geometry. The largest system studied is an eighteen
carbon polyene which spans a Hilbert space of about 991 million. We show that
for reverse intersystem crossing (RISC) process, the best system involves
substituting all carbon sites on one half of the polyene with donors and the
other half with acceptors.Comment: 7 Pages; 10 Figure
A multideterminant assessment of mean field methods for the description of electron transfer in the weak coupling regime
Multideterminant calculations have been performed on model systems to
emphasize the role of many-body effects in the general description of charge
quantization experiments. We show numerically and derive analytically that a
closed-shell ansatz, the usual ingredient of mean-field methods, does not
properly describe the step-like electron transfer characteristic in weakly
coupled systems. With the multideterminant results as a benchmark, we have
evaluated the performance of common ab initio mean field techniques, such as
Hartree Fock (HF) and Density Functional Theory (DFT) with local and hybrid
exchange correlation functionals, with a special focus on spin-polarization
effects. For HF and hybrid DFT, a qualitatively correct open-shell solution
with distinct steps in the electron transfer behaviour can be obtained with a
spin-unrestricted (i.e., spin-polarized) ansatz though this solution differs
quantitatively from the multideterminant reference. We also discuss the
relationship between the electronic eigenvalue gap and the onset of charge
transfer for both HF and DFT and relate our findings to recently proposed
practical schemes for calculating the addition energies in the Coulomb blockade
regime for single molecule junctions from closed-shell DFT within the local
density approximation
A model for orientation effects in electron‐transfer reactions
A method for solving the single‐particle Schrödinger equation with an oblate spheroidal potential of finite depth is presented. The wave functions are then used to calculate the matrix element T_BA which appears in theories of nonadiabatic electron transfer. The results illustrate the effects of mutual orientation and separation of the two centers on TBA. Trends in these results are discussed in terms of geometrical and nodal structure effects. Analytical expressions related to T_BA for states of spherical wells are presented and used to analyze the nodal structure effects for T_BA for the spheroidal wells
Undoing static correlation: Long-range charge transfer in time-dependent density functional theory
Long-range charge transfer excited states are notoriously badly
underestimated in time-dependent density functional theory (TDDFT). We resolve
how {\it exact} TDDFT captures charge transfer between open-shell species: in
particular the role of the step in the ground-state potential, and the severe
frequency-dependence of the exchange-correlation kernel. An expression for the
latter is derived, that becomes exact in the limit that the charge-transfer
excitations are well-separated from other excitations. The exchange-correlation
kernel has the task of undoing the static correlation in the ground state
introduced by the step, in order to accurately recover the physical
charge-transfer states.Comment: 2 figure
Ab initio derivation of multi-orbital extended Hubbard model for molecular crystals
From configuration interaction (CI) ab initio calculations, we derive an
effective two-orbital extended Hubbard model based on the gerade (g) and
ungerade (u) molecular orbitals (MOs) of the charge-transfer molecular
conductor (TTM-TTP)I_3 and the single-component molecular conductor
[Au(tmdt)_2]. First, by focusing on the isolated molecule, we determine the
parameters for the model Hamiltonian so as to reproduce the CI Hamiltonian
matrix. Next, we extend the analysis to two neighboring molecule pairs in the
crystal and we perform similar calculations to evaluate the inter-molecular
interactions. From the resulting tight-binding parameters, we analyze the band
structure to confirm that two bands overlap and mix in together, supporting the
multi-band feature. Furthermore, using a fragment decomposition, we derive the
effective model based on the fragment MOs and show that the staking TTM-TTP
molecules can be described by the zig-zag two-leg ladder with the
inter-molecular transfer integral being larger than the intra-fragment transfer
integral within the molecule. The inter-site interactions between the fragments
follow a Coulomb law, supporting the fragment decomposition strategy.Comment: 16 pages, 8 figures, published versio
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