Ab Initio VB Methods

AO undergoes when fragments assemble to a molecule. Accordingly, we shall restrict ourselves here to modern VB methods that perform orbital optimization. 

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VB correlation diagrams of this type have been computed for the other generic systems in Scheme 9 using ab initio VB methods.37 108-112 For 3-electron—... 

A spin-free approach for valence bond (VB) theory, based on symmetric group techniques, is introduced in this chapter. Bonded tableaux (BT) are adopted to represent VB structures, and a paired-permanent-determinant algorithm is developed to solve the so-called IV problem in the nonorthogonal VB method, followed by the introduction of our ab initio VB program, Xiamen-99. Furthermore, applications of ab initio VB method to the resonance effect, chemical reactions, and excited states are carried out by the Xiamen package. 

The arrangement of this chapter will be as following. Firstly, we discuss the construction of the bonded tableau basis and its properties. Secondly, the paired-permanent-determinant method is derived, followed by the introduction of our Xiamen-99 ab initio VB program. Then we show the applications of the ab initio VB method to the resonance effect, chemical reactions, as well as to excited states. Finally, we give a brief summary and an outlook for our future work. 

The only notable difference between classical ab initio VB and modem ab initio VB lies in the one-electron orbitals. As we already mentioned, in the classical ab initio VB method, all one-electron orbitals are strictly atomic orbitals. In contrast, in modem ab initio VB methods, one-electron orbitals are not restricted to atomic orbitals anymore and are allowed to extend over the whole molecule in the form of OEOs... 

Here we employed modem ab initio VB method to study several typical SN2 reactions including chloride, fluoride and hydrid exchanges with the three resonance structures a, b and c, whose VB wave functions are expressed as... 

We overview our valence bond (VB) approach to the ir-electron Pariser-Parr-Pople (PPP) model Hamiltonians referred to sis the PPP-VB method. It is based on the concept of overlap enhanced atomic orbitals (OEAOs) that characterizes modern ab initio VB methods and employs the techniques afforded by the Clifford algebra unitary group approach (CAUGA) to carry out actual computations. We present a sample of previous results, sis well sis some new ones, to illustrate the ability of the PPP-VB method to provide a highly correlated description of the ir-electron PPP model systems, while relying on conceptusilly very simple wave functions that involve only a few covalent structures. 

The classical VB method described in the last section uses AOs that are optimized for individual atoms. Several modem ab initio VB methods have been developed that use orbitals optimized for the molecule. Three such methods are described in this section. 

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