Analytic ab initio determination of the IR intensities in stereoregular polymers

An original scheme is developed to compute, fully analytically, the Hartree–Fock infrared intensities of stereoregular polymers. The infrared intensities are proportional to derivatives of the dipole moment with respect to atomic displacements. For the longitudinal component, the calculation of the infrared intensities requires a specific crystal-orbital treatment. Our approach is based upon the Bishop, Gu and Kirtman method for obtaining the undifferentiated dipole moment [J. Chem. Phys. 114, 7633 (2001)]. The implementation scheme is described in detail. The numerical stability of the methodology is tested on five polymers: (LiH)n, (FH)n, (H2O)n, polymethineimine (CH=N)n and polyacetylene (CH=CH)n. When a proper integration scheme is chosen, the values of the infrared intensities are in perfect agreement with the numerical derivatives of the dipole moment as well as with long oligomer calculations. We apply our approach to the analytical calculation of the vibrational polarizability of two systems.