\textit{Ab initio} study of anharmonic vibrations for polymers

Energies of optically active $k=0$ phonons in extended systems of one-dimensional periodicity (polyethylene) are computed by taking account of the anharmonicity in the potential energy surfaces (PES) and the resulting phonon-phonon couplings explicitly. The electronic part of the calculations is based on Gaussian-basis-set crystalline orbital theory at the coupled-cluster singles and doubles, second-order M{\o}ller--Plesset perturbation (MP2), and Hartree--Fock levels, providing one-, two-, and three-dimensional slices of the PES, respectively, which are in turn expanded in the fourth-order Taylor series of normal coordinates. For the vibrational part, we employ the vibrational self-consistent-field, vibrational MP2 and vibrational truncated configuration-interaction (VCI) methods within the $\Gamma $ approximation that amounts to including only $k=0$ phonons. It is shown that inclusion of both electron correlation and anharmonicity is essential in achieving good agreement between computed and observed frequencies of optical phonons in polyethylene. The VCI calculations also identify quantitatively the frequency separation and intensity ratio of the Fermi doublets in the vibrational spectrum of polyethylene.