Altered Terminology, Labelling, and Output Conventions of NBO 6

The NBO 6 program can analyze a broader spectrum of states and species than was possible in NBO 5 and its predecessors. Earlier NBO versions included algorithmic assumptions and labelling conventions that were adequate for near-equilibrium ground-state species but harbored implicit restrictions to that limit. Ambiguities or inconsistencies in labelling conventions become apparent in excited states and other cases exhibiting strong departures from conventional Lewis-structural depiction. This necessitates the changes in NBO 6 described below:

Altered Star(*)-Label Usage

In earlier NBO versions, a star(*)-label (as in BD*, LP*, RY*, 3C*) was taken to distinguish non-Lewis-type (NL) NBOs of low occupancy, which provide small delocalization corrections to the highly occupied "unstarred" Lewis-type (L) NBOs of the formal Natural Lewis Structure (NLS) configuration. Consistent with common chemical symbolism, however, a star-label was also taken to identify the out-of-phase ("antibonding") symmetry of an orbital about an inversion center or reflection plane. These dual usages of "*" to symbolize either "excited" (unoccupied) or "antibonding" (out-of-phase) are often consistent for near-equilibrium ground-state species, but lead to increasing conflicts for the exotic multi-center bonding scenarios of excited-state or metallic species, mandating more restricted usage of star-labels in NBO 6.

Severe inconsistencies arise whenever an out-of-phase "BD*" orbital is found to be of higher occupancy than the corresponding in-phase "BD" orbital, thereby forcing reversal of the usual assignments of L vs. NL character. In such cases, earlier NBO versions printed a warning message ("apparent excited-state configuration encountered...") and reassigned "BD" vs. "BD*" labels according to phase-pattern rather than occupancy order. This leads to superficially large NL-density and (often) to grossly sub-optimal NBOs and NLS assignments. Although rare for ground-state species, such cases become increasingly common in excited states.

NBO 6 corrects these notational conflicts by consistently identifying L/NL character without presumed relationship to "*" labelling. Star-labelling is now reserved for "antibonding" phase-symmetry (e.g., of 2c "BD*" or 3c "3C*" NBOs) and for the distinctive "LP*" (unfilled valence lone-pair) NBO of borane-like species. In common cases these labelling changes may pass unnoticed, but for highly delocalized or excited state species the advantages are significant.

Altered NBO Numbering and Listing in Printed Output

To clearly delineate high-occupancy L-type NBOs of the base NLS configuration, the NL-type "acceptor" NBOs are now separated by dashed lines from L-type donor NBOs in printed output. Certain details of NBO ordering are also altered within each L/NL section:

Within the Lewis section, NBOs are grouped consistently according to number of nuclear centers, with 1C NBOs (CR, LP) preceding 2C (BD) or higher multi-center (nC) NBOs. Within each nC group, NBOs are ordered according to the chosen atom numbering, and for a specific nC set, by occupancy within the set. As in previous versions, NBOs of a single-, double-, triple-... bond manifold are distinguished by the parenthesized integer (1), (2), (3),..., according to occupancy order.

Within the non-Lewis section, NBOs are also ordered by number of centers (LP*, BD*, 3C*,...) according to nC-groupings found in the L-type section. For each specific set of atoms, these NL groups arise from the same NAO manifold as the corresponding L-type manifold and are similarly ordered in occupancy, with each non-zero occupancy tending to incrementally saturate the unused valence-shell capacity of contributing atoms. The valence-type NL groupings are followed finally by residual 1C "RY" (extra-valent Rydberg-type) NBOs that complete the span of the basis space.

Altered Table of 2nd-Order E(2) Donor-Acceptor Interactions

Only donor-acceptor interactions of strongly occupied L-type donors and weakly occupied NL-type acceptors are now included in E(2) tables, consistent with the only reasonable "unperturbed" starting point for which the perturbative formulas are valid. This change eliminates the meaningless E(2) values that sometimes appeared for "BD* donors" or "BD acceptors", where the assumptions of perturbation theory are grossly violated.

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