Density functional crystal orbital study on the normal vibrations and phonon dispersion curves of all-trans polyethylene

Abstract

Optimized structural parameters and frequencies of the infrared- and Raman-active vibrations are obtained for all-trans polyethylene by using the analytical energy gradient scheme in the density functional crystal orbital formalism. The Slater–Vosko–Wilk–Nusair (SVWN), the Becke–Lee–Yang–Parr (BLYP), and the Becke3–Lee–Yang–Parr (B3LYP) functionals are used with the 3-21G and 6-31G* basis sets. The frequencies calculated with the 6-31G* basis set are found to be in better agreement with the observed frequencies than those calculated with the 3-21G basis set regardless of the exchange-correlation functionals used. The root mean square errors between the calculated and observed frequencies are 21, 20, and 15 cm−1 for the SVWN/6-31G*, the BLYP/6-31G*, and the B3LYP/6-31G* calculations, respectively. Optical branches of the phonon dispersion curves are calculated at the SVWN/6-31G* level by adopting a C7H14 unit as a reference unit cell. The calculated phonon dispersion curves are in reasonable agreement with the curves experimentally determined and with the curves obtained with an empirical force field except for the skeletal stretching branches. Inelastic neutron scattering (INS) spectrum is also calculated by using the force field derived at the SVWN/6-31G* level. The overall intensity profile of the observed INS spectrum is well reproduced by the present calculations in which the effects of the Debye–Waller factors and the phonon wings are taken into account.