A nine-dimensional perturbative treatment of the vibrations of methane and its isotopomers

Abstract

The vibrations of methane isotopomers with Td, C3v, and C2v symmetry are studied by means of high order Van Vleck perturbation theory. The vibrational states up to 9000 cm−1 are investigated by combining the ab initio force field of Lee, Martin and Taylor [J. Chem. Phys. 95, 254 (1995)] with a fourth order perturbative treatment based on curvilinear normal coordinates. Implementation of the perturbation theory using both analytical and numerical expression of the kinetic energy operator is considered. The quadratic and select cubic and quartic force constants are refined via a nonlinear least squares fit to experimental data The fit force constants reproduce 130 experimental band centers with a root mean squares deviation of 0.70 cm−1. The choice of polyad quantum number is discussed with respect to different molecules. The convergence of the energy levels is discussed by carrying out the perturbation calculation up to eighth order.

Ab initio calculation of the rotational spectrum of methane vibrational ground state

“…So, bracketing the vibrational ground state, effective, dipole moment, D 0 (Y) of Eq. (19), between these k 's gives exact transition matrix elements, Section III C 2 explains how approximate D(Y) (dropping the ground state label "0") have been obtained.…”

“…16 The vibrational and/or rotational spectra of methane has been the topics of many theoretical studies, see Refs. [17][18][19][20][21][22][23][24][25][26][27][28][29][30] to quote a few. However, as far as we are aware, only Signorel et al 31 have investigated its effective rotational dipole moment coefficients.…”

Mode-specific reactivity ofCH4onPt(110)−(1Bisson1, Sacchi2, Beck3 2010Phys. Rev. B543310View full textAdd to dashboardCite

“…The states 2 2 + 4 , 1 + 4 , and 3 + 4 states are members of the octad, whereas 2 3 is part of the tetradecad. The zero-order normalmode labels 2 2 + 4 , 1 + 4 , and 3 + 4 are good descriptors of the octad states, 18 while the state labeled 2 3 contains about 15% 1 + 3 character both of which are pure stretching modes. Therefore, we consider the four eigenstates prepared in this study as pure bend ͑2 2 + 4 ͒, stretch/bend combinations ͑ 1 + 4 , 3 + 4 ͒ and pure stretch states ͑2 3 ͒.…”

Quantum-state-resolved reactivity of overtone excited CH4 on Ni(111): Comparing experiment and theory

“…Another complication is that anharmonicity mixes the normal mode states. In Table III we show the results of a 4th order perturbative calculation by Wang and Sibert, 27 who computed the vibrational eigenstates of methane using a dressed normal mode basis set with an accurate ab initio quartic force field. From now on, to distinguish between the true vibrational eigenstates and their normal mode components, we will include the symmetry label when we refer to the eigenstate, as we have already done with 2ν 3 -E, etc.…”