Effect of an electric field on a methane molecule. II. Calculation of the degeneracy splitting of the ν3 band. Expression of the second derivatives of the CH4 dipole moment and evaluation of the second derivative of the C–H bond polarizability

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Abstract
In order to interpret infrared spectra of methane adsorbed in NaA at low temperature, we have calculated the frequencies of CH4 and CD4 perturbed by an electric field. This calculation needs the expressions of the second derivative of the dipole moment and the polarizability. These later were given by Montero and we have expressed the terms ∂2m/∂Si∂Sj using the same approximations: additivity of the CH bond dipole derivatives. We find for the CH bond derivatives: μ’=−0.7×10−10 esu, μ‘=+1.5×10−2 esu. The magnitude of the field (3×105 esu) has been determined by the intensity of the induced ν1 band. The orientation of the field deduced from the experiments, is along a C3 axis of the molecule. Adjusting theoretical and experimental results, we have calculated the parallel and perpendicular second derivatives of the CH bond polarizability 2β‘+δ‘=−6.4×10−8 cm, δ‘− β‘=+5.3×10−8 cm.