Perfect pairing GVB wave function

This strong orthogonality constraint, while seemingly a restriction, is usually not a serious one, since it applies to orbitals that are not expected to overlap significantly. On the other hand, the orbitals (

perfectly paired GVB wave function generated under the constraint of zero-overlap between the orbitals of different pairs. 

Amovilli et al. [20] presented a method to carry out VB analysis of complete active space-self consistent field wave functions in aqueous solution by using the DPCM approach [3], A Generalized Valence Bond perfect pairing (GVB-PP) level... 

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. 

Fig. 6. Average relativistic effective core potential and relativistic effective core potential energy curves for two states of Bi2. HF, Hartree-Fock GVB(pp), eight-configuration perfect-pairing generalized valence bond FVCI, full-valence Cl based on the GVB(pp) wave functions FV7R, full-valence Cl plus single and double promotions to virtual MOs relative to seven-dominant configurations. (The FVCI and FV7R calculations include the REP-based spin-orbit operator.)...

The perfect-pairing (PP) orbitals of this wave function clearly show the "lone-pairs" and "bond pairs" which are part of the language of the experimental chemist. This is in contrast to the molecular orbital description or to the GVB description with (7-7T restrictions where the lone pairs and "7T" bonds are not discernable from contour plots of the orbitals (2 ). It is somewhat reassuring that the wave function which gives the lowest variational energy (that of Figures 1 and 2a) also most closely coincides with the experimental chemist s traditional view of the bonding ( 3) ... 

The spin-coupled method of Gerratt and co-workers " differs from the GVB-PP method in that it removes any orthogonality and perfect-pairing restrictions. The method is still of the single-configuration type, but all the modes of spin-pairing are included in the wave functions and the orbitals are allowed to overlap freely with each other. The SC method has often been used to provide firm theoretical support to some basic concepts... 

---