Role of collective modes in vibrational polarizabilities and hyperpolarizabilities of polyacetylene and other quasilinear polymers

It is shown that the low frequency collective modes of quasilinear polymers can contribute to the vibrational polarizability and hyperpolarizability despite the fact that their infrared or Raman intensity vanishes in the infinite chain limit. The most significant of these modes are characterized and the dynamic vibrational nonlinear optical (NLO) properties are obtained, at the doubly harmonic Hartree-Fock level of approximation, from static field calculations on polyacetylene as well as polyyne, polysilane, and polyethylene. Comparison is made to a pair of unit cell modes, one Raman-active and the other infrared-active, that are expected to generate a large vibrational hyperpolarizability. The combined effect of the collective and unit cell vibrations is potentially of considerable importance for the enhancement of NLO properties. Further studies are suggested to exploit this potential.