The valence-bond self-consistent field method (VB–SCF): Theory and test calculations

A new and very general form of valence-bond theory is described. In this theory the molecular wave function is written as any desired linear combination of valence-bond structures, and the nonorthogonal orbitals used in the construction of the valence-bond structures are allowed to distort to their optimal shapes. The orbital optimization is achieved through successive transformations of an orbital basis. The theory of the method is based on an extension of the ‘‘generalized Brillouin theorem’’ which is presented in the text. The new VB–SCF method is a generalization of the molecular orbital MC–SCF method to permit the use of nonorthogonal orbitals. It, therefore, encompasses the MC–SCF method as a restricted subclass. Several different forms of restriction may be imposed on the orbitals and on the optimization procedures. One of these only allows orbitals centered on the same atom to mix during optimization and in this way generates optimal hybrid orbitals, which it is expected will prove to be of particular interest in providing simple qualitative descriptions of the chemical bond. Test calculations are presented for LiH, He+2, and for the ground-state potential energy curve of OH. The VB–SCF wave function and optimized orbitals may be used as a starting point for the construction of a larger multistructure valence-bond wave function which we term a VB-CI function. The VB–SCF and VB–CI results presented in the paper show that the method is capable of yielding very accurate molecular potential energy curves.