Rotation–vibration spectra of icosahedral molecules. I. Icosahedral symmetry analysis and fine structure

Abstract

Icosahedral symmetry analysis is developed for analyzing eigensolutions of rovibrational tensor Hamiltonians for molecules such as B12H12−2, C20H20, and C60. Simplified asymptotic formulas and procedures are developed for obtaining rotational spectral fine structure for high angular momentum. J=100 eigenlevels for sixth- and tenth-rank icosahedral tensors are discussed using different approximations and visualization schemes.

Molecular Eigensolution Symmetry Analysis and Fine Structure

“…The RES was introduced about thirty years ago [8] to analyze spectral fine structure of high resolution spectral bands in molecules of high symmetry including PH 3 [9] XDH 3 and XD 2 H molecules [10], tetrahedral ( P 4 ) [11], tetrafluorides ( CF 4 and SiF 4 ) [12], hexafluorides ( SF 6 , Mo ( CO ) 6 and UF 6 ) [13–16], cubane ( C 8 H 8 ), and buckyball ( C 60 ) [15,16] and predicted major mixing of Herzberg rovibronic species. Recently RES have been extended to help understand the dynamics and spectra of fluxional rotors [17] or “floppy” molecules such as methyl-complexes [18] and vibrational overtones [2].…”

Distinctive combinatorial aspects of NMR spin invariance for icosahedral exo-cage spin cluster problems: symmetry subduction and mapping for13C-fullerene and the analogous biclusters systems, [13C]6-60, [12CF]60, and [13CF]60

“…Further, we note that direct unitary-to-icosahedral subduction processes have been fruitful in other areas than MQ-NMR; Harter and Weekes [29] and Balasubramanian [12] have considered such processes from distinct viewpoints, namely, those associated with icosahedral Cartesian tensors, and that of cycle-index formalisms, respectively.…”

Frame Transformation Relations and Symmetry Analysis of Fluxional Symmetric Rotor Dimers

“…Longuet-Higgins points out that there are certain symmetry elements of non-rigid molecules; for example, the twisting of ethane which leads to configurations which cannot be brought into near-coincidence with the original one by a simple rotation of the whole molecule in space. The work of Hougen et al [16], Harter et al [17][18][19][20][21][22], and Bunker and Jensen [23] have allowed for an easier approach to compute spin weight, and rovibration wavefunctions, and to open new avenues to study large amplitude motions. In one approach, Groner [24] has tried to identify pinwheel rotations with crystal space groups, that is, point groups with translations.…”

“…In this paper, we will apply the techniques developed and used by Harter and Patterson [17][18][19][20][21][22]. The main goal is to attempt to answer the question of how molecular species come about due to some kind of coupling interactions in the strongly and weakly coupled regimes, which allows for insight into large amplitude motion of molecular systems.…”

“…Spin weights give spectral intensity ratios for different symmetry species. Here, we consider the permutation group along with Young tableau techniques [11,12,[17][18][19][20][21][22]29,30] for the symmetry of two coupled diatomic molecules. Lemus [31] applied the theory of Chen [29] to generate what is known as vibrational symmetry adapted bases.…”