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

David L Cooper,Robert Ponec,Peter B Karadakov

doi:10.1002/qua.26612

Abstract

AbstractChosen 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 B2H6 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, S2N2 and square (D4h) cyclobutadiene.

Highlights

As is well known, a central theme of István Mayer's distinguished scientific career was the extraction of useful chemical information from molecular wave functions
We look first at the hydrogen atoms in this molecule, for which we find FA values for the bridging (Hb) and terminal (Ht) domains of 0.061 and 0.044, respectively. We notice that these small values are comparable to the value of 0.059 that we found for H2 near its equilibrium geometry
We have explored in the present work a paper from 2012 [3], chosen from István Mayer's very impressive canon of important work on bond orders and related quantities

Summary

| INTRODUCTION

A central theme of István Mayer's distinguished scientific career was the extraction of useful chemical information from molecular wave functions. Mayer's “improved” bond order, which is obtained by substituting R for PS in Equation (3), takes the form [2, 3]: W~ Does this new definition solve the problem that Mayer had identified for the dissociation of ethene [2, 3] but it has the added advantage that the sum of all possible W~ RAB values for a system with N electrons is necessarily equal to 2N, as in the case of a single determinant closedshell RHF wave function. The same matrix R performs a role analogous to the spin density matrix in Mayer's related definition of a free valence index for correlated singlet-state wave functions This quantity, F~A, which takes the form [2, 3]: F~A. The QTAIM-generalized [9] “improved” Wiberg–Mayer index takes the following relatively simple form [10, 11]: W

D K jLiΩA iΩA ð11Þ

| RESULTS AND DISCUSSION

| CONCLUSIONS