Self-consistent-field approximation configuration interaction

Starting from the normal mode approximation, one can introduce anharmonicity in different ways. Anharmonic perturbation theory [206] and local mode models [204] may be useful in some cases, where anharmonic effects are small or mostly diagonal. Vibrational self-consistent-field and configuration-interaction treatments [207, 208] can also be powerful and offer a hierarchy of approximation levels. Even more rigorous multidimensional treatments include variational calculations [209], diffusion quantum Monte Carlo, and time-dependent Hartree approaches [210]. 

Chapter 4 discusses configuration interaction (Cl) and is the first of the four chapters that deal with approaches incorporating electron correlation. One-electron density matrices, natural orbitals, the multiconfiguration self-consistent-field approximation, and the generalized valence bond method are... 

One of the drawbacks of DFT is its inability to treat multiconfigurational problems properly. In these cases, some type of configuration interaction (Cl) method is needed [60], Ideally, one would like to carry out full Cl calculations, but this is generally not possible for practical reasons. Thus, some kind of approximation is needed and, in this respect, the so-called complete active self-consistent field (CASSCF) procedure is often used. 

Density-Functional Theory. Transition metals pose a problem for classical quantum chemical methods like self-consistent field (SCF), perturbation theory, configuration interaction (Cl), and variations on these methods, because of the very large electron correlation. SCF underestimates binding substantially, and post-SCF methods are so expensive for transition metals that one can do a calculation only on models with few atoms. DFT on the other hand is relatively cheap it is about as expensive as SCF. Moreover, with the development of the generalized-gradient approximations it is also reasonably accurate. A large majority of quantum chemical... 

In spite of these gross approximations, the method proved to be extremely useful and was extensively used to correlate the chemical properties of conjugated systems. Several attempts were subsequently made to introduce the repulsions between the n electrons in the calculations. These include the work of Goeppert-Mayer and Sklar 4> on benzene and that of Wheland and Mann 5> and of Streitwieser 6> with the a> technique. But the first general methods of wide application were developed only in 1953 by Pariser and Parr 7> (interaction of configuration) and by Pople 8> (SCF) following the publication by Roothaan of his self-consistent field formalism for solving the Hartree-Fock equation for... 

There are two ways to improve the accuracy in order to obtain solutions to almost any degree of accuracy. The first is via the so-called self-consistent field-Hartree-Fock (SCF-HF) method, which is a method based on the variational principle that gives the optimal one-electron wave functions of the Slater determinant. Electron correlation is, however, still neglected (due to the assumed product of one-electron wave functions). In order to obtain highly accurate results, this approximation must also be eliminated.6 This is done via the so-called configuration interaction (Cl) method. The Cl method is again a variational calculation that involves several Slater determinants. 

In the first place the Hiickel approximation for the tt electrons has been replaced by a self-consistent field (SCF) procedure, generally in a semiempirical approximation of the Pariser-Parr-Pople type completed with some limited configuration interaction (PPP-CI method).59 00 Second, the a skeleton of the molecules has been treated by the Del Re procedure61 for saturated systems (which is the counterpart for the a electrons of the Hiickel method for 77 electrons) as refined for the a skeletons of conjugated heterocycles by... 

Predictions can be made about the suitability of different system trajectories on the basis of orbital symmetry conservation rules (207). The most suitable trajectory is an approximation to the reaction path of the reaction under study. The rules can also yield information about the possible structure of the activated complex. The correlation diagram technique has been improved in a series of books by Epiotis et al. (214-216). The method is based on self-consistent field-configuration interaction or valence bond (SCF-CI or VB) (including ionic structures) wave functions. Applications on reactions in the ground states as well as in the excited electronic states are impressive however, the price to be paid for the predictions seems to be rather high. 

Werner and co-workers [2, 21, 34] used internally-contracted multi-reference configuration-interaction (IC-MRCI) calculations, based on state-averaged (three-state) multi-configuration, self-consistent-field (MCSCF) calculations with large atomic orbital basis sets, to determine the three electronically adiabatic C1(F)+H2 PESs in the reactant arrangement L4, 2A, and lA. These all correlate with X( P) + H2. These three adiabatic electronic states are the IC-MRCI approximations to the three lowest eigenfunctions of Hgi, namely... 

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