Altogether, the expressions used in the complete VPT2 treatment involve the first-, second-, and third-order geometric derivatives of the molecular electric dipole moment and polarizability in the IR and Raman case, respectively, in addition to the cubic and quartic force constants, meaning that the highest-order property that must be calculated, i.e. the cubic force constants of the frequency-dependent polarizability, is a fifth-order energy derivative. The contributions to this property can be identified from eqn (23) and are shown here in order to demonstrate the complexity involved in the analytic calculations performed in this work and to justify the use of a recursive approach.