Investigating István Mayer's "improved" definitions of bond orders and free valence for correlated singlet‐state wave functions. Issue 8 (29th January 2021) - Cooper, David L.; Ponec, Robert; Karadakov, Peter B.
Abstract: Chosen from István Mayer's very impressive canon of important work on bond orders and related quantities, we explore a paper from 2012 which introduced a "pseudo spin density matrix" for correlated singlet‐state wave functions, leading to "improved" definitions of bond orders and free valence. Examining such "improved" bond orders for the singlet ground states of H2, N2 and CH + we find that all of them exhibit sensible geometry dependences. Mayer's free valence index works well for H2 and N2 ; the asymptotic behavior for CH + turns out to be slightly more complicated but can easily be explained. Using B2 H6 to examine three‐center bonding, a simple generalization of Mayer's approach produces numerical results close to those based on the "pseudo spin density matrix." As expected, the various "correction" terms remain small, albeit some of them are larger for the multicenter indices of ground and excited singlet states of benzene, S2 N2 and square (D4 h ) cyclobutadiene. Abstract : István Mayer's" improved" definitions of bond orders and free valence indices, F, for correlated singlet‐state wave functions are assessed for bond breaking processes and for three‐center and multicenter bonding situations.