An analytical derivative procedure for the calculation of vibrational Raman optical activity spectra

We present an analytical time-dependent Hartree-Fock algorithm for the calculation of the derivatives of the electric dipole-magnetic dipole polarizability with respect to atomic Cartesian coordinates. Combined with analogous procedures to determine the derivatives of the electric dipole-electric dipole and electric dipole-electric quadrupole polarizabilities, it enables a fully analytical evaluation of the three frequency-dependent vibrational Raman optical activity (VROA) invariants within the harmonic approximation. The procedure employs traditional non-London atomic orbitals, and the gauge-origin dependence of the VROA intensities has, therefore, been assessed for the commonly used aug-cc-pVDZ and rDPS:3-21G basis sets.