First-principles calculations on anharmonic vibrational frequencies of polyethylene and polyacetylene in the Γ approximation (original) (raw)

2010, The Journal of Chemical Physics

The frequencies of the infrared-and/or Raman-active ͑k =0͒ vibrations of polyethylene and polyacetylene are computed by taking account of the anharmonicity in the potential energy surfaces ͑PESs͒ and the resulting phonon-phonon couplings explicitly. The electronic part of the calculations is based on Gaussian-basis-set crystalline orbital theory at the Hartree-Fock and second-order Møller-Plesset ͑MP2͒ perturbation levels, providing one-, two-, and/or three-dimensional slices of the PES ͑namely, using the so-called n-mode coupling approximation with n =3͒, which are in turn expanded in the fourth-order Taylor series with respect to the normal coordinates. The vibrational part uses the vibrational self-consistent field, vibrational MP2, and vibrational truncated configuration-interaction ͑VCI͒ methods within the ⌫ approximation, which amounts to including only k = 0 phonons. It is shown that accounting for both electron correlation and anharmonicity is essential in achieving good agreement ͑the mean and maximum absolute deviations less than 50 and 90 cm −1 , respectively, for polyethylene and polyacetylene͒ between computed and observed frequencies. The corresponding values for the calculations including only one of such effects are in excess of 120 and 300 cm −1 , respectively. The VCI calculations also reproduce semiquantitatively the frequency separation and intensity ratio of the Fermi doublet involving the 2 ͑0͒ fundamental and 8 ͑͒ first overtone in polyethylene.