Wave functions valence bonds

When the ionic terms are neglected, one gets the so-called valence-bond (VB) description. The (unnormalized) valence-bond wave function can also be written in the form... 

P. C. Hiberty, C. Leforestier, J. Am. Chem. Soc. 100, 2012 (1978). Expansion of Molecular Orbital Wave Functions into Valence Bond Wave Functions. A Simplified Procedure. 

WRITING AND REPRESENTING VALENCE BOND WAVE FUNCTIONS... 

Valence Bond Wave Functions with Semilocalized AOs... 

Writing Valence Bond Wave Functions Beyond the 2e/2c Case... 

Pictorial Representation of Valence Bond Wave Functions by Bond Diagrams... 

The Relationship between Molecular Orbital and Valence Bond Wave Functions... 

A.1 NORMALIZATION CONSTANTS, ENERGIES, OVERLAPS, AND MATRIX ELEMENTS OF VALENCE BOND WAVE FUNCTIONS... 

G. A. Gallup, J. M. Norbeck, Chem. Phys. Lett. 21, 495 (1973). Population Analyses of Valence-Bond Wave Functions and BeH2. 

MAPPING A MOLECULAR ORBITAL CONFIGURATION INTERACTION WAVE FUNCTION INTO A VALENCE BOND WAVE FUNCTION... 

F. W. Bobrowicz and W. A. Goddard III, Self-Consistent Field Equations for Open-Shell Hartree-Fock and Generalized Valence Bond Wave Functions, in Modem Theoretical Chemistry, vol. 3, H. F. Schaeffer III Ed., Plenum, New York, 1977... 

The BOVB method is aimed at combining the qualities of interpretability and compactness of valence bond wave functions with a quantitative accuracy of the energetics. The fundamental feature of the method is the freedom of the orbitals to be different for each VB structure during the optimization process. In this manner, the orbitals respond to the instantaneous field of the individual VB structure rather than to an average field of all the structures. As such, the BOVB method accounts for the differential dynamic correlation that is associated with elementary processes like bond forming/breaking, while leaving the wave function compact. The use of strictly localized orbitals ensures a maximum correspondence between the wave function and the concept of Lewis structure, and makes the method suitable for calculation of diabatic states. 

Goodgame, M. M., and W. A. Goddard III (1985). Modified generalized valence-bond method a simple correction for the electron correlation missing in generalized valence-bond wave functions prediction of double-well states for Crj and Moj. Phys. Rev. Lett. 54, 661-64. 

Regardless of preference, we are faced with three definitions of the term ionic character, in terms of electronegativity, molecular orbitals, or valence bond wave functions. Any paper on the nature of the H bond must be evaluated in the light of what the writer meant when he wrote that paper. 

Write simple valence bond wave functions for the diatomic molecules Li2 and C2. State the bond order predicted by the simple VB model and compare with the LCAO predictions in Table 6.3... 

Write simple valence bond wave functions for formation of bonds between B atoms and H atoms. What B—H compound does the VB model predict. What geometry does it predict for the molecules. ... 

Chemical Studies. Stretching force constants have been used in an investigation of the valence bond wave function from which an estimate has been made... 

Two necessary criteria for a theory of superconductivity are a phase coherence of the wave function and an attractive electron-electron interaction. We review how the BCS theory achieves these criteria and then show how a valence bond wave function can also meet these conditions. The energy scale of the latter approach has a larger range in principle than that possible via the electron-phonon interaction. 

Much remains to be done to implement the ideas outlined here about valence bond wave functions, in order to address the many questions about new high-Tc materials. However the fact that it is formulated in real space and is based on chemical bonds, should allow much more direct contact with the chemical aspects than has been previously possible. 

The valence bond wave function for the HF molecule (assuming that it is formed from Is orbital of H and 2pz orbital of F) in the following three cases ... 

Assuming that the ionic character in H Br bond is 11% the fraction of the contribution of ionic character to the valence bond wave function, calculated ... 

The valence-bond wave function for the bonding pair is y = YCl 3pzA (1) YCI 3pzB (2) + YCl 3pzA (2) YCl 3pzB (1)... 

Flo. 43-4.—Energy curves for the hydrogen molecule (in units es/2ao) A, for an extreme molecular-orbital wavo function B, for an extreme valence-bond wave function and C, for a valence-bond function with partial ionic character (Weinbaum). 

Let us now discuss the energy integral for a particular valence-bond wave function, in order to justify our correlation of valence-bond distribution and wave function as given in Equation 46-18. The superposition pattern for a structure with itself, as shown by 11 in Figure 46-1, consists of n islands, each consisting of two bonded orbitals. We see that... 

In certain cases, however, it is evident from symmetry or other considerations that more than one valence-bond wave function is important. For example, for six equivalent atoms arranged at the corners of a regular hexagon the two structures I and II of Figure 46-1 are equivalent and must contribute equally to the wave function representing the normal state of the system. It can be shown that, as an approximation, the benzene molecule can be treated as a six-electron system. Of the total of 30 valence electrons of the carbon and hydrogen atoms, 24 can be considered... 

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