Hartree-Fock valence orbitals

Figure 7. Canonical Hartree-Fock valence orbitals of NO constructed in a minimal cartesian gausslan basis set (28). Values shown refer to a 6 by 16 plane, with N on the left 0 on the right.

In this article, we present an ab initio approach, suitable for condensed phase simulations, that combines Hartree-Fock molecular orbital theory and modem valence bond theory which is termed as MOVB to describe the potential energy surface (PES) for reactive systems. We first provide a briefreview of the block-localized wave function (BLW) method that is used to define diabatic electronic states. Then, the MOVB model is presented in association with combined QM/MM simulations. The method is demonstrated by model proton transfer reactions in the gas phase and solution as well as a model Sn2 reaction in water. 

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) ... 

PDDO PRDDO RHF SAMO SCF SOGI STO STO-nG UA UHF VB VIP Projectors of Diatomic Differential Overlap Partial Retention of Diatomic Differential Overlap Restricted Hartree-Fock Simulated ab initio Method Self Consistent Field Spin Optimized GVB method Slater Type Orbital Slater Type Orbital expanded in terms of nGTO United Atom Unrestricted Hartree-Fock Valence Bond Vertical Ionization Potential... 

In an effort to emphasize the valence structure of chemical bonds, valence electron density maps have been constructed.9 In these studies the core electron density (the spin restricted Hartree-Fock Is orbital product for a first row atom) is assumed invariant to chemical bonding and is the basis of the scattering factor that is incorporated in Eq. (11). 

Figure 2. Nonrdativistic Hartree-Fock (HF) and relativistic Dirac-Hartree-Fock (DHF) orbital energies e and orbital radius expectation values < r > for the valence shells of the group 4 elements (n = 2,3,4,5,6 for C, Si, Sn, Pb and Eka-Pb, respectively).

In a theoretical investigation of the electronic structure of diamond, its valence bands have been determined using a linear combination of bonding molecular orbitals formed from s—p hybridization of the 2s, 2p Hartree-Fock atomic orbitals of the isolated carbon atom. 

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. 

For planar unsaturated and aromatic molecules, many MO calculations have been made by treating the a and n electrons separately. It is assumed that the o orbitals can be treated as localized bonds and the calculations involve only the tt electrons. The first such calculations were made by Hiickel such calculations are often called Hiickel molecular orbital (HMO) calculations Because electron-electron repulsions are either neglected or averaged out in the HMO method, another approach, the self-consistent field (SCF), or Hartree-Fock (HF), method, was devised. Although these methods give many useful results for planar unsaturated and aromatic molecules, they are often unsuccessful for other molecules it would obviously be better if all electrons, both a and it, could be included in the calculations. The development of modem computers has now made this possible. Many such calculations have been made" using a number of methods, among them an extension of the Hiickel method (EHMO) and the application of the SCF method to all valence electrons. ... 

Figure 3. Comparison of the measured momentum distributions of the outermost valence orbital for wafer [6-8] with spherically averaged orbital densities from Hartree-Fock limit and correlated wave functions [6].

Ab initio calculations usually begin with a solution of the Hartree-Fock equations, which assumes the electronic wavefunction can be written as a single determinant of molecular orbitals. The orbitals are described in terms of a basis set of atomic functions and the reliability of the calculation depends on the quality of the basis set being used. Basis sets have been developed over the years to produce reliable results with a minimum of computational cost. For example, double zeta valence basis sets such as 3-21G [15] 4-31G [16] and 6-31G [17] describe each atom in the molecule with a single core Is function and two functions for the valence s and p functions. Such basis sets are commonly used, as there appears to be a cancellation of errors, which fortuitously allows them to predict quite accurate results. 

Most of the commonly used electronic-structure methods are based upon Hartree-Fock theory, with electron correlation sometimes included in various ways (Slater, 1974). Typically one begins with a many-electron wave function comprised of one or several Slater determinants and takes the one-electron wave functions to be molecular orbitals (MO s) in the form of linear combinations of atomic orbitals (LCAO s) (An alternative approach, the generalized valence-bond method (see, for example, Schultz and Messmer, 1986), has been used in a few cases but has not been widely applied to defect problems.)... 

---