10.5 Ground State Second-order Properties with MP2 and CC2

Second-order properties for one-electron perturbations 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 includes the relaxation of the SCF orbitals in the presence of the perturbation and is restricted to the static (i.e. frequency-independent) limit.

For the coupled-cluster model CC2, second-order properties can, similar as the first-order properties, be computed in the orbital-unrelaxed or the orbital-relaxed approach as derivatives of the of the Lagrange functions in Eqs. 10.13 and 10.16. 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.

Second-order properties are available in the OMP and MPI parallel versions and for closed-shell and unrestricted high-spin open-shell Hartree-Fock refrences. Note, that second-order properties are not available for spin-component scaled variants of MP2 and CC2 or for restricted open-shell references. Furthermore, non-Abelian point groups and point groups with complex irreducible representations 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:

$ricc2
  cc2
$laplace
  conv=4
$response
  sop operators=(diplen,diplen) freq=0.077d0

The frequency has to be given in atomic units. Static orbital-relaxed polarizabilities are obtained with

$response
  sop operators=(diplen,diplen) relaxed

10.5.1 Damped Second-order Properties with CC2

Damped linear response is available at the CC2 level. In addition to the second-order property input, the flag cpp=on must be set along with a damping factor gamma, in atomic units. The following input will compute the damped polarizability with $\gamma=4.5563\cdot10^{-3}$ a.u.:

$response
  cpp=on gamma=4.5563d-3
  sop operators=(diplen,diplen) freq=0.077d0

using the symmetric expression for the linear response function. To compute a second-order property from the asymmetric expression, the keyword asym must be added to the sops option:

$response
  cpp=on gamma=4.5563d-3
  sop asym operators=(diplen,diplen) freq=0.077d0

Since damped response is often used to compute spectra in a frequency interval on an even-spaced grid. This can be done with the following simplified input for the interval $[0.4,0.5]$ with a step width of 0.005:

  cpp=on gamma=4.5563d-3
  sop operators=(diplen,diplen) frqscan=0.3d0, 0.4d0, 0.005d0

The options abscpp and ecdcpp can be used with the sop keyword as shortcuts to request the operator combinations that are needed to compute the isotropic avarages required for, respectively, absorption spectra in the length and ECD spectra in the velocity gauge.

  cpp=on gamma=4.5563d-3
  sop abscpp ecpcpp frqscan=0.3d0, 0.4d0, 0.005d0