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.