Principles of Biorthogonal Valence Bond Theory

PRINCIPLES OF BIORTHOGONAL VALENCE BOND THEORY 2.1. Theory 

In most modern valence bond calculations the wavefunction takes the form of a multiconfigurational expansion 

The main difficulty in performing calculations with an orbital set containing nonorthogonal orbitals is that of evaluating matrix elements over the hamiltonian. These matrix elements contain complicated products of orbital overlap integrals [14]. In the BOVB approach, the set vf/ is used in setting up the electronic Schrodinger equation 

The members of y have a one-to-one correspondence with the members of xf/ with respect to orbital occupancy and spin-coupling, except that the orbitals used in their construction belong to a dual set defined by 

The integrals over the one- and two-electron operators have the dual basis to the left of the operator and the primary basis to the right. The one- and two- 

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