# Hyperpolarizability contributions to the second Kerr-effect virial coefficients of non-dipolar molecules.

## Date

2020

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## Abstract

The molecular theory of the second Kerr-effect virial coeffcient, BK, describing the
effects of interacting pairs of molecules on the molecular Kerr constant for molecules
with non-linear symmetry is reviewed, and then extended to include second hyperpolarizability
contributions in the molecular interactions. The classical long-range
dipole{induced-dipole model is used to describe the interactions between pairs of
molecules.
This investigation has been limited to non-dipolar species, where the permanent
electric quadrupole moment is the leading multipole moment, since for dipolar
species, the hyperpolarizability contributions will likely be masked by the generally
much-larger contributions arising from the permanent electric dipole moment.
The resulting expressions for contributions to BK are evaluated numerically (using
Gaussian quadrature) for nitrogen (N2), carbon dioxide (CO2) and ethene (C2H4),
these molecules having measured data against which to assess the theoretical predictions.
N2 and CO2 are axially-symmetric molecules, while C2H4 is of lower symmetry, belonging
to the D2h point group. Previous attempts to approximate the molecular
properties of C2H4 to axial symmetry in calculations of BK have produced theoretical
results which signifi cantly underestimate the measured data. Inclusion of the full
molecular symmetry has been shown to be essential if the molecular-tensor theory
is to yield reasonable agreement with experimental data.
For CO2 the quadrupole{induced-dipole contribution dominates, and the interaction induced
hyperpolarizability contribution to BK is only 0.3% at 200 K rising to 1.5%
at 500 K. For the N2 and C2H4 molecules, the collision-induced hyperpolarizability
contributes just under 2% at 200 K, rising to 4% at 500 K for N2, and 5.5% for C2H4.
These contributions are non-negligible, and are hence worth refi ning in future work
through full ab initio quantum mechanical computation of the interaction-induced
hyperpolarizability contribution where dispersion force and electron cloud overlap
effects can be included.

## Description

Masters Degree. University of KwaZulu-Natal, Pietermaritzburg.