Hartree-Fock method deficiencies

The original ab initio approach to calculating electronic properties of molecules was the Hartree-Fock method [31,32,33,34]. Its appeal is that it preserves the concept of atomic orbitals, one-electron functions, describing the movement of the electron in the mean field of all other electrons. Although there are some inherent deficiencies in the method, especially those referred to the absence of correlation effects. Improvements have included the introduction of many-body perturbation theory by Mollet and Plesset (MP) [35] (MP2 to second-order MP4 to fourth order). The computer power required for Hartree-Fock methods makes their use prohibitive for molecules containing more than very few atoms. 

The simplest type of MC-SCF wavefunction is one composed of just two configurations. It is often possible to choose the two configurations in such a way as to ensure that the dissociation products are correctly described. Das and Wahl first introduced this method119 arguing that it corrected the most important deficiency of the Hartree-Fock method. They called it the optimized double configuration (ODC) method. It has recently been used to study the system F + Li2 20 and was also used as a starting point in the Cl calculations on KrF2.33... 

We have used the terms SCF wave function and Hartree-Fock wave function interchangeably. In practice, the term SCF wave function is applied to any wave function obtained by iterative solution of the Roothaan equations, whether or not the basis set is large enough to give a really accurate approximation to the Hartree-Fock SCF wave function. There is only one true Hartree-Fock wave function, which is the best possible wave function that can be written as a Slater determinant of spin-orbitals. With current computer power, one can use very large basis sets for small molecules and obtain wave functions that differ negligibly from the true Hartree-Fock wave functions. Because of deficiencies in properties calculated from Hartree-Fock wave functions, several methods that go beyond the Hartree-Fock method are widely used (see Chapter 16). 

The electronic structure methods are based primarily on two basic approximations (1) Born-Oppenheimer approximation that separates the nuclear motion from the electronic motion, and (2) Independent Particle approximation that allows one to describe the total electronic wavefunction in the form of one electron wavefunc-tions i.e. a Slater determinant [26], Together with electron spin, this is known as the Hartree-Fock (HF) approximation. The HF method can be of three types restricted Hartree-Fock (RHF), unrestricted Hartree-Fock (UHF) and restricted open Hartree-Fock (ROHF). In the RHF method, which is used for the singlet spin system, the same orbital spatial function is used for both electronic spins (a and (3). In the UHF method, electrons with a and (3 spins have different orbital spatial functions. However, this kind of wavefunction treatment yields an error known as spin contamination. In the case of ROHF method, for an open shell system paired electron spins have the same orbital spatial function. One of the shortcomings of the HF method is neglect of explicit electron correlation. Electron correlation is mainly caused by the instantaneous interaction between electrons which is not treated in an explicit way in the HF method. Therefore, several physical phenomena can not be explained using the HF method, for example, the dissociation of molecules. The deficiency of the HF method (RHF) at the dissociation limit of molecules can be partly overcome in the UHF method. However, for a satisfactory result, a method with electron correlation is necessary. 

The few attempts at describing excited states in transition metal complexes within the Restricted Hartree Fock (RHF) formalism were rapidly abandoned due to the computational difficulties (convergence of the low-lying states in the open-shell formalism) and theoretical deficiencies (inherent lack of electronic correlation, inconsistent treatment of states of different multiplicities and d shell occupations). The simplest and most straightforward method to deal with correlation energy errors is the Configuration Interaction (Cl) approach where the single determinant HF wave function is extended to a wave function composed of a linear combination of many de-... 

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