Guidelines for VB Mixing

Derivation of matrix elements between polyelectronic VB determinants follows from the discussion in the text, and can be carried out by enumerating all the permutations of the respective diagonal terms, as in Eq. [A9]. Subsequently, one must define the reduced matrix element in Eq. [AlO].  

The first and foremost rule is that the entire matrix element between two 

VB determinants is signed as the corresponding determinant overlap and has the same power in AO overlap. For example, the overlap between the two determinants of an HL bond, ab and a b is S, and hence the matrix element is negatively signed, Since is proportional to 

Sabi both the matrix element and the determinant overlap involve AO overlap to the power 2. For the one-electron bond case (Eq. [51]), the overlap between the determinants is +Sab and the matrix element -hpafo, while for the three-electron bond situation (Eq. [52]) the overlap between the determinants aa b and bb a is —Sab and the matrix element is likewise — 

When the VB determinants differ by the occupancy of two spin-orbitals, the leading term of the matrix element will be the sum of the corresponding 

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