Investigating István Mayer's “improved” definitions of bond orders and free valence for correlated singlet‐state wave functions

Chosen from István Mayer's very impressive canon of important work on bond orders and related quantities, we explore a paper 2012 which introduced “pseudo spin density matrix” for correlated singlet-state wave functions, leading to “improved” definitions free valence. Examining such the singlet ground states H2, N2 CH+ find that all them exhibit sensible geometry dependences. valence index works well H2 N2; asymptotic behavior turns out be slightly more complicated but can easily explained. Using B2H6 examine three-center bonding, simple generalization approach produces numerical results close those based matrix.” As expected, various “correction” terms remain small, albeit some are larger multicenter indices excited benzene, S2N2 square (D4h) cyclobutadiene.