Wave function basic ansatz

Regarding the problems of the electronic structure of molecular systems, we notice that in the past, the importance of the qualitative concepts and explanations has been stressed many times. In this context, V.A. Fock [3,4] discussed the (basically metaphysical) problem of interrelation between exact solution and approximate explanation . His point was that any approximation (more precisely, the general form of the trial electron wave function i.e. an Ansatz used for it) sets the system of qualitative concepts (restricted number of variables), which can only be used for interpreting the calculation results and for describing the experiments. A characteristic example... 

We assume that the reader is familiar with basic concepts of CC theory, such as the exponential wave function ansatz defining all single-reference CC methods. However, for the consistency of this presentation, let us recall that the ground-state wave function associated with the CC method A has the form... 

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. 

MOs first appear in the framework of the Hartree-Fock (HF) method, which is a mean-field treatment [17,22]. The basic idea is to start from an A-particle wave-function that is appropriate for a system of non-interacting electrons. Having fixed the Ansatz for the A-particle wavefunetion in this way, the variational principle is used in order to obtain the best possible approximation for the fully interacting system. Such independent particle wavefunctions are Slater-determinants, which consist of antisymmetrized products of single-particle wavefunctions (x)J (the antisymmetry brought about by the determinantal form is essential in order to satisfy die Pauh principle). Thus, the Slater-determinant is written as... 

Non-plane-wave solutions of the Klein-Gordon equation using unconventional basic functions and coupling ansatz ... 

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