Hartree-Fock method extended

The various methods used in quantum chemistry make it possible to compute equilibrium intermolecular distances, to describe intermolecular forces and chemical reactions too. The usual way to calculate these properties is based on the independent particle model this is the Hartree-Fock method. The expansion of one-electron wave-functions (molecular orbitals) in practice requires technical work on computers. It was believed for years and years that ab initio computations will become a routine task even for large molecules. In spite of the enormous increase and development in computer technique, however, this expectation has not been fulfilled. The treatment of large, extended molecular systems still needs special theoretical background. In other words, some approximations should be used in the methods which describe the properties of molecules of large size and/or interacting systems. The further approximations are to be chosen carefully this caution is especially important when going beyond the HF level. The inclusion of the electron correlation in the calculations in a convenient way is still one of the most significant tasks of quantum chemistry. 

M. M. Mestechkin, G. E. Vaiman, V. Klimo, et al., Extended Hartree-Fock Method and Its Application to Molecules, Naukova Dumka, Kiev, 1983. 

To solve the problem put by the Hartree-Fock method with ab initio qrproximation (non-empirical calculations) was chosen. All calculations have been done with the assistance of Gaussian 98/A7 software and use the extended valence-splitting basis, which included diffusive and polarized d- and p-functions — 6-31G(d,p). The correlation amendments were performed with use of Density Functional Theory (DFT) in B3LYP approximation. 

The UHF ansatz is necessary because in case of neutral solitons one has to deal with a doublet state. Thus a DODS (different orbitals for different spins) ansatz, as the UHF one, is necessary to describe the system. However, in the UHF method described so far, one Slater determinant with different spatial orbitals for electrons of different spins is applied, which is not an eigenfunction of S2, i.e. S(S+l)h2. The best way to overcome this difficulty would be to use the PHF (Projected Hartree Fock) method, also called EHF method (Extended Hartree Fock) where before the variation the correct spin eigenfunction is projected out of the DODS ansatz Slater determinant [66,67a]. Unfortunately numerical solution of the rather complicated EHF equations in each time step seems to be too tedious at present. Moreover for large systems the EHF wavefunction approaches the UHF one [68], however, this might be due to the approximations used in [67a]. Another possibility is to apply the projection after the variation using again Lowdin s projection operator [66]. Projection and annihilation techniques were... 

It is shown that the LCAO molecular Hartree-Fock equations for a closed-shell configuration can be reduced to a form identical with that of the Hoffmann extended Hiickel approximation if (i) we accept the Mulliken approximation for overlap charge distributions and (ii) we assume a uniform charge distribution in calculating two-electron integrals over molecular orbitals. Numerical comparisons indicate that this approximation leads to results which, while unsuitable for high accuracy calculations, should be reasonably satisfactory for molecules that cannot at present be handled with facility by standard LCAO molecular Hartree-Fock methods. 

In such intermediate cases it is a matter of convenience how extended a Hartree-Fock method is used and how much is left as correlation . This problem is discussed further in Sections XIX, XX, and XXI. 

A major weakness of the Hartree-Fock method is its failure to give accurate molecular dissociation energies. For example, an extended-basis-set calculation [P. E. Cade et al., /. Chem. Phys., 44,1973 (1966)] gives = 5.3 eV for N2, as compared with the true value 9.9 eV. (To calculate the Hartree-Fock D the molecular energy at the minimum in the U R) Hartree-Fock curve is subtracted from the sum of the Hartree-Fock energies of the separated atoms.) For F2 the true /) is 1.66 eV, while the Hartree-Fock is —1.4 eV. In other words, the Hartree-Fock calculation predicts the separated atoms to be more stable than the fluorine molecule. A related defect... 

Two types of theoretical and computational methods will be considered. The first one is the quantum-mechanical ab initio approach, in the particular version based on the Hartree-Fock approximation extended to periodic system[9]. This, as all first-principles theoretical schemes, is very attractive because does not require any kind of empirical knowledge. In the last years, it has proved to be able to account for the structural and electronic behaviour of a number of crystalline solids and minerals quite successfully[10, 11, 12]. The Hartree-Fock approach is particularly reliable and efficient, in this respect. The hypersurface of the ground-state total en-... 

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