A second-order perturbation theory route to vibrational averages and transition properties of molecules: General formulation and application to infrared and vibrational circular dichroism spectroscopies

A general formulation to compute anharmonic vibrational averages and transition properties at the second-order of perturbation theory is derived from the Rayleigh-Schrödinger development. This approach is intended to be applicable to any property expanded as a Taylor series up to the third order with respect to normal coordinates or their associated momenta. The equations are straightforward to implement and can be easily adapted to various properties, as illustrated for the case of electric and magnetic dipole moments. From those, infrared and vibrational circular dichroism spectra can be readily obtained. This fully automatic procedure has been applied to several chiral molecules of small-to-medium sizes and compared to the standard double harmonic approximation and to experimental data.