Simple Guidelines for Valence Bond Mixing

Derivation of matrix elements between polyelectronic VB determinants follows from the discussion in the text and the preceding appendix. This can be done by 

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 a HL bond, ab and ab is S lh. Hence, the matrix element is negatively signed and given as — 2(3ai,5 ai) since (3a/, is proportional to Sab, both the matrix element and the determinant-overlap involve AO overlap to the power of 2. For the one-electron bond case (Eq. 3.46), the overlap between the determinants is + Sah and the matrix element + (3afo. 

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 

The above considerations are the same whether the spin orbitals are AOs, CF orbitals, or FOs. 

Heitler, F. London, Z. Phys. 44, 455 (1927). Wechselwirkung neutraler Atome und homoopolare Bindung nach der Quantenmechanik. 

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