CCL: crystal orbital Hamilton populations

Dear colleagues,

Recently, Taoyi Chen and I published a journal article studying the bond orders of 288 diatomic molecules and ions: T. Chen and T. A. Manz, "Bond orders of the diatomic molecules," RSC Advances, 9 (2019) 17072-17092 (open access).

While doing the literature review for that article, I was surprised to find there had been no prior studies of quantum-mechanically computed bond orders across a large set of diatomic molecules. Several prior studies did look at quantum-mechanically computed bond orders for a small set of diatomics, although the largest set appears to be my own prior study that included quantum-mechanically computed bond orders for 26 diatomics as part of a large study introducing a comprehensive method to compute bond orders: T. A. Manz, “Introducing DDEC6 atomic population analysis: part 3. Comprehensive method to compute bond orders,” RSC Advances, 7 (2017) 45552-45581 (open access).

Now, I'm trying to better understand the bonding, non-bonding, and anti-bonding contributions of individual occupied Kohn-Sham orbitals in period 2 homodiatomics and other molecules. Due to the s-p mixing in some of the period 2 homodiatomics, this problem is not as straightforward as often assumed. For example, the bond order of Be2 is around 0.65 which occurs because s-p mixing makes the 1 sigma u valence orbital only slightly anti-bonding. (Here, the core orbitals are not included in the numbering scheme, so 1 sigma g is the lowest energy molecular valence orbital.)

My question is to what extent approaches like Crystal Orbital Hamilton Populations (COHP or projected-COHP) or Crystal Orbital Overlap Populations (COOP) have been used to study diatomic molecules? Specifically, not just the integrated total COHP/pCOHP or COOP value, but the value of these descriptors plotted versus the orbital/band energy? These could be calculations on an isolated molecule using a localized basis set or periodic calculations using a single molecule placed in the center of a large periodic unit cell. In particular, has any prior literature investigated the claimed correlation between the sign of COHP/pCOHP and the bonding vs. anti-bonding orbital characteristics for molecules whose bonding, non-bonding, or anti-bonding contributions of individual orbitals/bands are independently assessed? For example, have any published studies demonstrated that the COHP/pCOHP or COOP approaches can accurately reproduce the bonding, non-bonding, and anti-bonding characteristics of individual orbitals/bands in period 2 homodiatomics (Li2, Be2, B2, C2, N2, O2, F2, and Ne2) or other small molecules? An even more pointed question: Does the COHP approach predict the 1 sigma u valence orbital in N2 is bonding, anti-bonding, or approximately non-bonding? How about the 2 sigma g valence orbital in N2?

Can anyone point me to COHP/pCOHP or COOP studies for isolated molecules that have tried to assess the reliability of the sign change of these descriptors for identifying orbitals/bands as bonding, anti-bonding, or non-bonding?

Sincerest thanks,

Tom Manz