Computer generation of nuclear spin species and nuclear spin statistical weights

Abstract

This article develops computer programs for computer generation of nuclear spin species and nuclear spin statistical weights of rovibronic levels. The programs developed here generate nuclear spin species and statistical weights from the group structures known as generalized character cycle indices (GCCIs) which are computed easily from the character table of the PI group of the molecule under consideration. Procedures are illustrated with examples.

Group theoretical treatment of Jahn–Teller versus spin-orbit effects on geometries, rovibronic levels and nuclear spin species of bismuth and antimony clusters

“…We will also consider correlation of the rotational levels and thus the rovibronic levels. The 209 Bi nuclear spin nuclear multiplets are obtained using a combinatorial multinomial generating function method previously proposed by the author [30].…”

“…The topic is continuing to generate interest over the decades, as outlined in the papers of Temme [18]. Although we have developed a code for nuclear spin statistics and spin multiplets before [29,30] and there are computer packages such as GAP [31], which can be adapted to yield total nuclear spin statistical weights, generating complete set of nuclear spin multiplets and symmetry-adapted nuclear spin functions for bismuth clusters is one of the most challenging problems, as there are up to 0.1 billion nuclear spin functions for a cluster like Bi 8 . Although the total statistical weights can be easily obtained by replacing every cycle in the permutation representation by 10 for 209 Bi, the process of generating all nuclear spin function symmetry-adaptations, that is, explicit constriction of the various nuclear spin multiplets and their frequencies is a combinatorially complex task, as each term in the combinatorial generating function becomes a decanomial.…”

“…Spectroscopic and other experimental studies concerning main group clusters including the very heavy bismuth clusters have received considerable attention over the years [4][5][6][7][8][9][10][11]. There have also been a number of graph theoretical, group theoretical, ab initio, and other studies on analogous clusters and aromatic species in view of recent interest in three-dimensional and other aromaticity concepts [23][24][25][26][27][28][29][30][31][32][33][34][35][36].…”

“…In order to seek the overall rovibronic level patterns and their nuclear spin populations, we have considered the method of generalized character cycle indices (GCCI) as generating functions for the nuclear spin species and nuclear spin statistics which were developed earlier by the author [29,33,34]. We use this formalism and the computer code developed before [30] to generate the nuclear spin species. The nuclear spin statistics then results in generating functions comprised of decanomials for the various terms in the generating functions.…”

Combinatorial Enumeration of Isomers of Superaromatic Polysubstituted Cycloarenes and Coronoid Hydrocarbons with Applications to NMR

“…Topological and graph theoretical techniques − have found extensive applications and use over the decades in enhancing our understanding of polycyclic aromatic compounds, fullerenes, large organic polymers, toxicity − ,, and other properties of heterocyclic aromatic compounds, periodic systems, and combinatorial chemistry of these species. Although fully ab initio quantum chemical studies are feasible, they are formidably difficult and consequently, graph-theoretical techniques have provided alternative platforms to gain new insight into especially larger circumscribed superaromatic compounds.…”