Generalized valence bond orbitals

Figure 6-22 Generalized valence-bond orbitals calculated for ethene by the ab initio method. The nuclei are located in the x,y plane of the coordinate system at the positions indicated by crosses. The long dashes correspond to locations of change of phase. The dotted lines are contour lines of electron amplitude of opposite phase to the solid lines. Top shows both m-bonding carbon orbitals (almost sp2), middle-left is the carbon orbital and middle-right the hydrogen orbital of one of the C-H bonds, and bottom represents a side view of the ir orbitals in perpendicular section to the x,y plane. (Drawings furnished by Dr. W, A. Goddard, III.)...

Figure 3.3 Natural and generalized valence bond orbitals of SF/OF(X n, a L ) at the AVTZ level, (a) Natural orbitals for SF and OF states (b) Generalized Valence Bond orbitals for SF and OF states.

Figure 3.4 Natural and generalized valence bond orbitals of Sp2(X A, b Aj) at the...

Figure 3.5 Generalized valence bond orbitals for SF(a E ) + F( P) separations at the AVTZ level.

An MCSCF calculation in which all combinations of the active space orbitals are included is called a complete active space self-consistent held (CASSCF) calculation. This type of calculation is popular because it gives the maximum correlation in the valence region. The smallest MCSCF calculations are two-conhguration SCF (TCSCF) calculations. The generalized valence bond (GVB) method is a small MCSCF including a pair of orbitals for each molecular bond. 

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. 

Localized molecular orbital/generalized valence bond (LMO/GVB) method, direct molecular dynamics, ab initio multiple spawning (AIMS), 413-414 Longuet-Higgins phase-change rule conical intersections ... 

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.)... 

For the valence bond orbitals themselves, it is generally natural to specify a starting guess in the AO basis. Such a guess might, of course, not lie entirely inside the space spanned by the active space, and it must therefore be projected onto the space of the active MOs. This is achieved trivially in CASVB, by multiplication by the inverse of the matrix of MO coefficients. 

Figure 11-4 Generalized valence bond (GVB) orbitals for one hydrogen of ethyne (left) and of ethane (right) see Section 6-7. The hydrogen and carbon nuclei are located in the X, V plane of the coordinate system at the positions indicated by crosses, the hydrogen nucleus being on the left.

The generalized valence bond (GVB) method was the earliest important generalization of the Coulson—Fischer idea to polyatomic molecules (13,14). The method uses OEOs that are free to delocalize over the whole molecule during orbital optimization. Despite its general formulation, the GVB method is usually used in its restricted form, referred to as GVB SOPP, which introduces two simplifications. The first one is the perfect-pairing (PP) approximation, in which only one VB structure is generated in the calculation. The wave function may then be expressed in the simple form of Equation 9.1, as a product of so-called geminal two-electron functions ... 

GVB Generalized valence bond. A theory that employs CF orbitals to calculate electronic structure with wave functions in which the electrons are formally coupled in a covalent manner. The simplest level of the theory is GVB PP (PP-perfect pairing), in which all the electrons are paired into bonds, as in the Lewis structure of the molecule. 

Generalized Valence Bond method with one pair of correlated orbitals... 

Fig. 2. CASSCF, orthogonal localized, non-orthogonal localized, and generalized valence bond molecular orbitals for the hydrogen molecule.

J.H. van Lenthe and G.G. Balint-Kurti, VBSCF The optimisation of non-orthogonal orbitals in a general (Valence Bond) wavefunction, in 5th seminar on Computational Methods in Quantum Chemistry (Groningen, 1981). 

The recent developments in generalized Valence Bond (GVB) theory have been reviewed by Goddard and co-workers,13 and also the use of natural orbitals in theoretical chemistry,14 15 and the accuracy of computed one-electron properties.18 The Xa method has been reviewed by Johnson,17 and Hurley has discussed high-accuracy calculations on small molecules.18 Several other reviews of interest have appeared in Advances in Quantum Chemistry.17 Localized orbital theory has been reviewed by England, Salmon, and Ruedenberg,19 and the bonding in transition-metal complexes discussed by Brown et a/.20 Finally, the recent developments in computational quantum chemistry have been reviewed by Hall.21... 

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