Post-Hartree-Fock approaches

Barone, V. and C. Adamo. 1994. Theoretical study of direct and water-assisted isomerization of formaldehyde radical cation. A comparison between density functional and post-Hartree-Fock approaches. Chem. Phys. Lett. 224, 432. 

Isobe, H. Takano, Y. Kitagawa, Y. Kawakami, T. Yamanaka, S. Yamaguchi, K. Houk, K. N. Extended Hartree-Fock (EHF) theory of chemical reactions VI hybrid DFT and post-Hartree-Fock approaches for concofed and non-concerted transition structures of the Diels-Alder reaction, Mol. Phys. 2002,100, IVl-lH. 

We shall in this section give a historic overview of how the electronic structure theory for transition metal complexes in their ground state has evolved from the 1950s to the present time. The account will include a discussion of wave function methods based on Hartree Fock and post-Hartree Fock approaches as well as Kohn-Sham density functional theory (KS-DFT). 

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. 

Hartree-Fock and post-Hartree-Fock approaches... 

Again, there is a systematic error evident from the data, and the discrepancy between DFT and post-Hartree-Fock approaches scales almost linearly with the chain length (b). Similar DFT failures have been reported for questions of catalysis [355] and for conjugated hydrocarbons [356]. It is all due to the fact that no DFT parametrization whatsoever treats different bond or-... 

In a very recent study, Banerjee et al used different ab initio methods to study the properties of small Kjv clusters for even A with 2 < A < 20. They used both density-functional methods and post-Hartree-Fock approaches, where correlation is added either via Moller-Plesset perturbation theory or via the coupled-cluster approach (see, e.g., ref. 1). In order to determine the structures of the lowest total energy, they used as initial guesses structures from earlier studies on Nuat clusters that subsequently were allowed to relax to their closest total-energy minimum. Unfortunately, only the density-functional method was used in optimizing the structures, whereby a comparison between the two approaches is not made possible. 

Since about 1990, powerful post-Hartree-Fock approaches for the inclusion of electron correlation in chemical shift calculations have been developed and applied in main group chemistry (see NMR Chemical Shift Computation Ab Initio and NMR Chemical Shift Computation Structural Applications). Unfortunately, these correlated methods are computationally too demanding at present to be applied to transition metal complexes and clusters of chemically relevant size. In particular, the least expensive post-CHF method available, the MP2-GIAO approach, is expected to fail for systems with significant nondynamical correlation effects. 

In order to overcome the shortcommings of standard post-Hartree-Fock approaches in their handling of the dynamic and nondynamic correlations, we investigate the possibility of mutual enhancement between variational and perturbative approaches, as represented by various Cl and CC methods, respectively. This is achieved either via the amplitude-corrections to the one- and two-body CCSD cluster amplitudes based on some external source, in particular a modest size MR CISD wave function, in the so-called reduced multireference (RMR) CCSD method, or via the energy-corrections to the standard CCSD based on the same MR CISD wave function. The latter corrections are based on the asymmetric energy formula and may be interpreted either as the MR CISD corrections to CCSD or RMR CCSD, or as the CCSD corrections to MR CISD. This reciprocity is pointed out and a new perturbative correction within the MR CISD is also formulated. The earlier results are briefly summarized and compared with those introduced here for the first time using the exactly solvable double-zeta model of the HF and N2 molecules. 

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