Amore, Paolo; Fernández, Francisco M. Energy levels of a coupled-rotors model. (English) Zbl 1466.81016 J. Math. Chem. 59, No. 1, 161-167 (2021). Summary: We calculate the energy levels of a coupled-rotors model that has proved useful for the analysis of the multiple tunnelling peaks in the inelastic neutron scattering from 4-methylpyridine crystals. We resort to the Rayleigh-Ritz variational method with a basis set for each irreducible representation. The energy levels in terms of the rotor coupling strength exhibit a rich pattern of crossings between states of different symmetry and avoided crossings between states of the same symmetry. MSC: 81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis 81Q15 Perturbation theories for operators and differential equations in quantum theory 81R05 Finite-dimensional groups and algebras motivated by physics and their representations 81U26 Tunneling in quantum theory 81V35 Nuclear physics 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs Keywords:coupled rotors; 4-methylpyridine; avoided crossings; neutron scattering PDFBibTeX XMLCite \textit{P. Amore} and \textit{F. M. Fernández}, J. Math. Chem. 59, No. 1, 161--167 (2021; Zbl 1466.81016) Full Text: DOI References: [1] Clough, S.; Heidemann, A.; Horsewill, AH; Paley, MNJ, Z. Phys. B: Condens. Matter, 55, 1 (1984) · doi:10.1007/BF01307492 [2] Prager, M.; Heidemann, A., Chem. Rev., 87, 2933 (1997) · doi:10.1021/cr9500848 [3] Horsewill, AJ, Prog. Nucl. Mag. Reson. Spect., 35, 359 (1999) · doi:10.1016/S0079-6565(99)00016-3 [4] Häusler, W.; Hüller, A., Z. Phys. B: Condens. Matter, 59, 177 (1985) · doi:10.1007/BF01725534 [5] Khazaei, S.; Sebastiani, D., J. Chem. Phys., 145, 234506 (2016) · doi:10.1063/1.4971380 [6] Khazaei, S.; Sebastiani, D., J. Chem. Phys., 147, 194303 (2017) · doi:10.1063/1.5003081 [7] Amore, P.; Fernández, FM, J. Math. Chem., 57, 1840 (2019) · Zbl 1422.81178 · doi:10.1007/s10910-019-01041-0 [8] Znojil, M., J. Phys. A, 16, 293 (1983) · Zbl 0513.35028 · doi:10.1088/0305-4470/16/2/012 [9] Znojil, M., J. Phys. A, 17, 1603 (1984) · doi:10.1088/0305-4470/17/8/016 [10] Znojil, M.; Sandler, K.; Tater, M., J. Phys. A, 18, 2541 (1985) · Zbl 0574.34018 · doi:10.1088/0305-4470/18/13/029 [11] Fernández, FM; Ogilvie, JF; Tipping, RH, J. Chem. Phys., 85, 5850 (1986) · doi:10.1063/1.451547 [12] Teller, M., J. Phys. Chem., 41, 109 (1937) · doi:10.1021/j150379a010 [13] Naqvi, K. Razi; Brown, W. Byers, Int. J. Qunatum Chem., 6, 271 (1972) · doi:10.1002/qua.560060206 [14] Fernández, FM, J. Math. Chem., 52, 2322 (2014) · Zbl 1331.81094 · doi:10.1007/s10910-014-0386-1 [15] Cotton, FA, Chemical Applications of Group Theory, Third (1990), New York: Wiley, New York [16] Heiss, WD; Sannino, AL, J. Phys. A, 23, 1167 (1990) · doi:10.1088/0305-4470/23/7/022 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.