Molecular Hartree-Fock calculations

A configuration interaction calculation uses molecular orbitals that have been optimized typically with a Hartree-Fock (FIF) calculation. Generalized valence bond (GVB) and multi-configuration self-consistent field (MCSCF) calculations can also be used as a starting point for a configuration interaction calculation. 

Besides the elementary properties of index permutational symmetry considered in eq. (7), and intrinsic point group symmetry of a given tensor accounted for in eqs. (8)-(14), much more powerful group-theoretical tools [6] can be developed to speed up coupled Hartree-Fock (CHF) calculations [7-11] of hyperpolarizabilities, which are nowadays almost routinely periformed in a number of studies dealing with non linear response of molecular systems [12-35], in particular at the self-consistent-field (SCF) level of accuracy. 

Baerends, E. J., Ellis, D. E., Ros, P., 1973, Self-Consistent Molecular Hartree-Fock-Slater Calculations I. The... 

One of the most conspicuous differences between computational results is in the degree to which a normal H—Si chemical bond is formed. In the local-density pseudopotential calculations, the Si—H separation is about 1.6 A. This is much larger than the predictions of MNDO, Hartree-Fock, or PRDDO calculations, which are much closer to the molecular Si—H distance. It is not clear at this point whether the H—Si bond is, in fact, weaker than a conventional bond when in this configuration and therefore is overestimated by the Hartree-Fock-like calculations, or whether the strength is being underestimated in the local-density calculations. 

In bridged metal-metal bonded dimeric complexes, the relative importance of metal-metal and bridging ligand effects are more difficult to unravel. Dahl and his co-workers have elegantly exploited systematic crystallographic analyses to detail the stereochemical consequences of valence-electron addition or removal in dimeric metal complexes (46, 47, 65, 230) and clusters (66, 88, 204, 205, 213, 216, 222). Their experimental work has been neatly underpinned by nonparameterized approximate Hartree-Fock molecular orbital calculations (217) on the phosphido-bridged dimers [Cr2(CO)80ti-PR2)2]n"2 and [Mn2(CO)g(/i.-PR2)2]n (rt = 0, + 1, or +2) ... 

In contrast to the semiempirical results, full optimization of the molecular geometry of 1-fluorosilatrane by restricted Hartree-Fock (RHF) calculations using the 3-21G, 3-21G and 6-31G basis sets did not find evidence for the existence of an endo minimum on the energy hypersurface193. Since the exo form was never found experimentally, the ab initio results support the view of the exclusive existence of silatranes in the endo form. As for the equilibrium Sk—N distance, the ab initio calculations using polarized basis sets overestimated its value (2.556 A) even more than the AMI and PM3 methods. 

Experimental trends in Si shielding observed experimentally arise from variations in the coordination number (i.e. the number of atoms in the 1st coordination sphere), the extent of polymerization of the silicate tetrahedra, the degree of replacement of one net-work forming cation by another (e.g. coupled Na+, Al+3 for Si+4 substitution), the size of the rings of tetrahedra present and the Si-O-Si angles (1,2). Similar trends are seen in gas-phase molecules, species in aqueous solution and in both crystalline and amorphous solids. Polarized double-zeta basis set Hartree-Fock level calculations using small molecular cluster models reproduce these trends semiquantitatively, as we will show. 

The simplest kind of ab initio calculation is a Hartree-Fock (HF) calculation. Modem molecular HF calculations grew out of calculations first performed on atoms by Hartree1 in 1928 [3]. The problem that Hartree addressed arises from the fact that for any atom (or molecule) with more than one electron an exact analytic solution of the Schrodinger equation (Section 4.3.2) is not possible, because of the electron-electron repulsion term(s). Thus for the helium atom the Schrodinger equation (cf. Section 4.3.4, Eqs. 4.36 and 4.37) is, in SI units... 

E.J. Baerends et al., Self-consistent molecular Hartree-Fock-Slater calculations I. The computational procedure. Chem. Phys. 2, 41-51 (1973)... 

The friction term has been evaluated for CO/Cu(l 00) by Hartree-Fock cluster calculations using single excitations [110]. A parametrized form of the Hartree-Fock results has been used for the molecular dynamics simulations. The interaction potential of CO/Cu(l 00) in the nuclear degrees of freedom, however, was derived empirically. 

One-electron picture of molecular electronic structure provides electronic wavefunction, electronic levels, and ionization potentials. The one-electron model gives a concept of chemical bonding and stimulates experimental tests and predictions. In this picture, orbital energies are equal to ionization potentials and electron affinities. The most systematic approach to calculate these quantities is based on the Hartree-Fock molecular orbital theory that includes many of necessary criteria but very often fails in qualitative and quantitative descriptions of experimental observations. 

The greater the number of functions 4 J, belonging to the orthonormal set, the more completely and in more detail the spectrum of the /(-decay-induced excitations of a molecule can be calculated. Consequently, the method for calculating the wave functions of the daughter ion must be such that at a reasonable volume of calculation we would be able to construct a sufficiently large number of multielectron wave functions of excited states. The Hartree Fock method allows one to construct the wave functions of excited states as the combinations of determinants symmetrized in a certain way. Within this method the excitation is considered to be a transition of an electron from an occupied Hartree-Fock molecular orbital into a vacant one. 

However, the vacant Hartree-Fock molecular orbital (MO) obtained as a by-product of the ground-state calculations are of little use for describing the excited states of a molecule. This is due to the fact that the vacant Hartree-Fock MOs correspond to the motion of an excited electron in the potential field of all N electrons rather than of N - 1 electrons, as must be the case (Slater, 1963). Hunt and Goddard (HG) (1963) have proposed modifying the Hartree-Fock operator in such a way that it would be possible to describe the motion of an excited electron in the potential VN 1 ... 

Optimizations of molecular geometries may be performed with a simpler basis set followed by a single-point Hartree-Fock (HF) calculation with a larger basis set for that derived geometry. This is indicated by double slashes, i.e. 6-31G //3-21G. 

The set of mathematical functions used to expand the molecular orbitals in a Hartree-Fock-Roothaan calculation... 

Hartree-Fock-Roothaan calculation in which each occupied atomic orbital of an atom is represented by one mathematical function with variable coefficient in the molecular orbitals... 

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