For closed-shell restricted Hartree-Fock reference states second-order properties for one-electron perturbation can be computed at the MP2 and the CC2 level. For MP2, second-order properties are computed as derivatives of the SCF+MP2 total energy. This approach include the relaxation of the SCF orbitals in the presence of the perturbation and is restricted to the static (i.e. frequency-independent) limit.
For coupled-cluster model CC2, second-order properties can, similar as the first-order properties, calculated in orbital-unrelaxed or orbital-relaxed approach as derivatives of the of the Lagrange functions in Eqs. 10.12 and 10.15. As for MP2, the orbital-relaxed calculations are restricted to the static limit. Frequency-dependent second-order properties as e.g. dipole polarizabilities can be computed with the orbital-unrelaxed approach.
Note that second-order properties are currently not yet available in the MPI parallel version or for spin-component scaled variants of MP2 and CC2. Furthermore, non-Abelian point groups are not implemented for second-order properties.
In addition to the standard input, second-order properties require that the data group for the numerical Laplace transformation $laplace and that the sops option in the data group $response is set. Frequency-dependent dipole polarizabilities with the CC2 model are obtained with the input:
The frequency has to be given in atomic units. Static orbital relaxed polarizabilities are obtained with