Configuration-interaction methods, applied

Atextbook describing the theory associated with calculations of the electronic structure of molecular systems. While the book focuses on ab initio calculations, much of the information is also relevant to semi-empirical methods. The sections on the Hartree-Fock and Configuration Interactions methods, in particular, apply to HyperChem. The self-paced exercises are useful for the beginning computational chemist. 

Ab initio calculated geometrical parameters depend on the kind of applied basis sets (which is the main variable when using an ab initio computer programme like, for example, Pople s GAUSSIAN 90 ) and on the kind of calculational procedure The so-called Hartree-Fock limit is the theoretically best result obtainable with a single determinant MO basis. Because of the different weighting of inter-electron repulsion between electron pairs of like and unlike spin, Hartree-Fock calculations are in error. They may be improved by the use of configuration interaction methods (Cl) or by the use of perturbation theory, like the Moller-Plesset treatment of second, third or fourth order (MP2, MP3 or MP4). 

As the above narrative indicates, most of the ideas for the treatment of the many-electron problem were first developed by the nuclear and solid-state physicists. This is the case not only for perturbative methods, but also for variational ones, including the configuration interaction method, which nuclear physicists refer to as the shell model, or for the unitary group approach (see Ref. [90] for additional references see Refs. [23, 78-80]). The same applies to the CC approach [70]. For this reason, quantum chemists, who were involved in the development of post-Hartree-Fock methods, paid a close attention to these works. However, with Cizek s 1966 paper the tables were turned around, at least as far as the CC method is concerned, since a similar development of the explicit CC equations, due to Liihrmann and Kiimmel [91] had to wait till 1972, without noticing that by that time quantum chemists were busily trying to apply these equations in actual computations. 

The conceptual simplicity of the configuration interaction method is very appealing, and its variational nature is an important advantage, but its principal strength lies in its flexibility and generality. It can be applied straightforwardly to any electronic state, and can be spin- and symmetry-adapted relatively easily. 

The quantum theory of the electronic structure of infinite, periodic macromolecules is a well-developed and venerable topic which is reviewed often (1,12) and is well-known to the audience of this NATO school. The important aspect of this topic for our present purposes is the observation that ab initio (i.e., Hartree Fock plus configuration interaction) methods are simply too expensive to apply to the description of most of the large molecules (including polymers) of biological and technological interest. In addition, they fail to provide a quantitative description of UV absorption spectra without massive configuration-interaction analysis. Consequently, for quantum chemical calculations to be helpful in the design of polymeric materials of practical use in electronic applications (e.g., photoconductors (2,5), semiconductors (5), or battery electrodes (6)), some form of semiempirical model must be developed. 

Conjugated polymers have been studied theoretically since 1937. Quantum chemical calculations applied to conjugated chains include (i) Hiickel methods, for the rapid assessment of band structures " (ii) the Paiser-Parr-Pople configuration interaction method " (iii) complete neglect of differential overlap (CNDO) self-consistent field methods " (iv) ab initio Hartree-Fock calculations, which have given very close agreement with experimental results " " and (v) the valence effective Hamiltonian (VEH) method, which offers a considerable reduction in computational effort. ... 

In the RISM-SCF theory, the statistical solvent distribution around the solute is determined by the electronic structure of the solute, whereas the electronic strucmre of the solute is influenced by the surrounding solvent distribution. Therefore, the ab initio MO calculation and the RISM equation must be solved in a self-consistent manner. It is noted that SCF (self-consistent field) applies not only to the electronic structure calculation but to the whole system, e.g., a self-consistent treatment of electronic structure and solvent distribution. The MO part of the method can be readily extended to the more sophisticated levels beyond Hartree-Fock (HF), such as configuration interaction (Cl) and coupled cluster (CC). 

Among the most widely used ab initio methods are those referred to as Gl" and 02." These methods incorporate large basis sets including d and / orbitals, called 6-311. The calculations also have extensive configuration interaction terms at the Moller-Plesset fourth order (MP4) and fiirther terms referred to as quadratic configuration interaction (QCISD). ° Finally, there are systematically applied correction terms calibrated by exact energies from small molecules. 

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