Internal Methyl Rotation in the CH Stretching Overtone Spectra of 2-, 3-, and 4-Methylpyridine

Abstract

A nonadiabatic model is presented to simulate the methyl regions of the overtone spectra of 2-, 3-, and 4-methylpyridine. The model incorporates harmonically coupled anharmonic oscillator local modes for CH stretching and rigid rotors for methyl internal rotation. Parameters for the model come from a series of ab initio calculations. The methyl regions of the overtone spectra are complex because of coupling between CH stretching and methyl torsion. Moreover there are differences between the similar spectra of 3-and 4-methylpyridine on one hand and the spectrum of 2-methylpyridine on the other. The simulation is successful in reproducing the methyl band profiles and in accounting for the spectral differences. Differences in the methyl band profiles are ascribed to differences in symmetry and magnitude of the frequency, anharmonicity, and torsional barrier and to differences in their dependence on the torsional angle. The success of the model and its ability to accommodate arbitrary functional forms of the frequency, anharmonicity, torsional barrier, and dipole moment function suggests its general applicability for the analysis of overtone spectra in a wide variety of molecules.

CH Stretching Overtone Spectra of Fluorine Substituted Toluenes

“…The In our previous work, we analyzed the similarities and differences of methyl band profiles between 2-, 3-, and 4-methylpyridines. 14 Differences in the methyl band profiles of 2-methylpyridine as compared to 3-and 4-methylpyridines arise from differences in the angular dependence of frequency and anharmonicity. The frequency changes, δω ˜, and anharmonicity changes, δω ˜x, for 3-and 4-methylpyridine are similar to each other but dissimilar to the changes for 2-methylpyridine.…”

“…For completeness we summarize the previously published model here. 13,14 The CH stretching methyl torsion model describes CH stretching modes within the HCAO local mode model and methyl torsion modes in a rigid rotor model. The Hamiltonian and the dipole moment function of the methyl group, including both CH stretching and methyl torsion, are described within a methyl coordinate system.…”

“…The Hamiltonian for a rotating methyl group is described in a stretching torsion basis set as products of Morse wave functions and rigid rotor wave functions. Thus, the Hamiltonian is given by 13,14 where F i ) [1, cos(θ i ), ..., cos(6θ i ), sin(θ i ), ..., sin(6θ i )] T are Fourier series components in a column with a dimension of 13, and V, Ω, and X are vectors consisting of the Fourier series expansion coefficients for the potential, frequency, and anharmonicity. γ′ is the effective CH stretch-stretch coupling constant.…”

“…13,14 The permanent dipole moment is not included, since it does not contribute to the vibrational transition intensities. Thus, the x component of the dipole moment vector becomes 13,14 where Q 1 ) [q 1 ,q 1 2 ,q 1 3 ,q 1 4 ,q 1 5 ,q 1 6 ,q 2 q 3 ,q 2 2 q 3 ,q 2 q 3 2 ]. The Q 2 and Q 3 vectors are obtained from Q 1 by permutation of the appropriate indices.…”

“…Coupling between CH stretching and methyl internal rotation was introduced to interpret methyl stretching overtone spectra. − We have formulated a CH stretching methyl torsion model and used it to explain successfully methyl overtone spectra for a series of molecules. − In this model, CH stretching modes are described by the HCAO local mode model, and methyl torsion is described by a rigid rotor model. The stretching torsion coupling affects all overtones if the torsional potential is sufficiently low.…”