Post-Hartree-Fock models

Johnson, E. R., and Becke, A. D. (2006). A post-Hartree-Fock model of intermolecular interactions Inclusion of higher-order corrections, / Chem. Phys. 124, p. 174104, doi 10.1063/1.2190220. 

A variety of theoretical methods have been developed which include some effects of electron correlation. Traditionally, such methods are referred to as post-SCF methods because they add correlation corrections to the basic Hartree-Fock model. As of this writing, there are many correlation methods available in Gaussian, including the following ... 

Trioxane 210 has been used as a model system by Gu and coworkers to study the antimalarial drug artemisinin 211 (Scheme 137) [97CPL234, 99JST103]. It is the boat/twist form rather than the chair conformer of 210 that describes the subunit in 211. Moreover, geometric parameters and vibrational frequencies can only reliably be computed at the DFT level and by post-Hartree-Fock methods. B3-LYP/6-31G calculations on the conformers of 3,3,6,6-tetramethyl-1,2,4,5-tetroxane show that the chair conformer is stabilized with respect to the twisted conformer by about -2.8 kcal/mol [00JST85]. No corresponding boat conformer was found. 

The use of the Hartree-Fock model allows the perturbation-theory equations (1.2)-(1.5) to be conveniently recast in terms of underlying orbitals (,), orbital energies (e,), and orbital occupancies (n,). Such orbital perturbation equations will allow us to treat the complex electronic interactions of the actual many-electron system (described by Fock operator F) in terms of a simpler non-interacting system (described by unperturbed Fock operator We shall make use of such one-electron perturbation expressions throughout this book to elucidate the origin of chemical bonding effects within the Hartree-Fock model (which can be further refined with post-HF perturbative procedures, if desired). 

The set of atomic orbitals Xk is called a basis set, and the quality of the basis set will usually dictate the accuracy of the calculations. For example, the interaction energy between an active site and an adsorbate molecule might be seriously overestimated because of excessive basis set superposition error (BSSE) if the number of atomic orbitals taken in Eq. [4] is too small. Note that Hartree-Fock theory does not describe correlated electron motion. Models that go beyond the FiF approximation and take electron correlation into account are termed post-Flartree-Fock models. Extensive reviews of post-HF models based on configurational interaction (Cl) theory, Moller-Plesset (MP) perturbation theory, and coupled-cluster theory can be found in other chapters of this series. ... 

Advances in interpretation. Experimental KIEs are interpreted using quantum mechanical and/or bond order vibrational analysis (BOVA) approaches to yield the experimental transition state. In systems that are well understood, the accuracy of experimental TS structures derived using a BOVA unified model rivals X-ray crystallography of stable molecules. The largest advance in KIE interpretation since the description of BOVA by Sims and Lewis " has been the increase in computational power available to the average chemist. Previously, vibrational models were reduced to a minimal number of atoms to make them computationally tractable. Today, a desktop computer can perform BOVA calculations with hundreds of atoms. The accessibility of post-Hartree-Fock calculations to the average chemist has made ab initio calculations a routine part of TS analysis, and made possible the structure interpolation approach to BOVA. 

Presently, the widely used post-Hartree-Fock approaches to the correlation problem in molecular electronic structure calculations are basically of two kinds, namely, those of variational and those of perturbative nature. The former are typified by various configuration interaction (Cl) or shell-model methods, and employ the linear Ansatz for the wave function in the spirit of Ritz variation principle (c/, e.g. Ref. [21]). However, since the dimension of the Cl problem rapidly increases with increasing size of the system and size of the atomic orbital (AO) basis set employed (see, e.g. the so-called Paldus-Weyl dimension formula [22,23]), one has to rely in actual applications on truncated Cl expansions (referred to as a limited Cl), despite the fact that these expansions are slowly convergent, even when based on the optimal natural orbitals (NOs). Unfortunately, such limited Cl expansions (usually truncated at the doubly excited level relative to the IPM reference, resulting in the CISD method) are unable to properly describe the so-called dynamic correlation, which requires that higher than doubly excited configurations be taken into account. Moreover, the energies obtained with the limited Cl method are not size-extensive. 

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. 

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