Vibrational effects on the polarizability and second hyperpolarizability of ethylene

Static and dynamic polarizabilities and second hyperpolarizabilities are presented for ethylene, including electronic, pure vibrational and zero-point vibrational averaging (ZPVA) contributions. Static pure vibrational hyperpolarizabilities are of commensurate size with their electronic counterparts but show less dependence on basis set and (MP2) electron correlation. A Hartree–Fock estimate for the static ZPVA correction to γ is found to be 10% of the corresponding electronic contribution. The dynamic pure vibrational hyperpolarizability, despite being significant for the optical Kerr effect and intensity-dependent refractive index, reduces in magnitude for second and third harmonic generation, leaving ZPVA as the dominant vibrational effect.