L^{rel CC2, ex}(E,, t,, β) |
= | 〈HF| H| CC〉 + (t, β)E_{ν} |
(9.20) |

+ 〈μ_{1}| + [, T_{2}]| HF〉 |
|||

+ 〈μ_{2}| + [F, T_{2}]| HF〉 + F_{μ0} . |

Compared to unrelaxed properties, the calculation of relaxed properties needs in addition for each excited state the solution of a CPHF equations for the Lagrangian multipliers , for which the computational costs are similar to those of a Hartree-Fock calculation.

Orbital-relaxed properties are requested by adding the flag `relaxed`

to the input line for the `exprop`

option.
The following is an example for a CC2 single point calculation for
orbital-relaxed excited state properties:

$ricc2 cc2 $excitations irrep=a1 nexc=2 exprop states=all relaxed operators=diplen,qudlenNote that during the calculation of orbital-relaxed excited-state properties the corresponding unrelaxed properties are also automatically evaluated at essentially no additional costs. Therefore, the calculation of unrelaxed properties can not be switched off when relaxed properties have been requested.

Again the construction of gradients requires the same variational densities as needed for relaxed one-electron properties and the solution of the same equations. The construction of the gradient contributions from one- and two-electron densities and derivative integrals takes approximately the same time as for ground states gradients (approx. 3-4 SCF iterations) and only minor extra disk space. The implementation of the excited state gradients for the RI-CC2 approach is described in detail in Ref. [14]. There one can also find some information about the performance of CC2 for structures and vibrational frequencies of excited states.

For the calculation of an excited state gradient with CC2 at a single point
(without geometry optimization and if it is not a calculation with `NumForce`)
one can use the input:

$ricc2 cc2 $excitations irrep=a1 nexc=2 xgrad states=(a1 2)Note, that presently it is not possible to compute gradients for more than one excited state in one

For geometry optimizations or a numerical calculation of the Hessian
with `NumForce` the wavefunction model and the excited state for which
the geometry should be optimized have to be specified in
the data group `$ricc2`

with the keyword `geoopt`

:

$ricc2 geoopt model=cc2 state=(a1 2) $excitations irrep=a1 nexc=2If the geometry optimization should carried out for the lowest excited state (of those for which an excitation energy is requested in

`state=(s1)`

.
Since the calculation of unrelaxed and relaxed first-order properties
can be combined gradient calculations without significant extra costs,
a request for excited state gradients will automatically enforce the
calculation of the relaxed and unrelaxed dipole moments.
If the keyword `geoopt`

is used, the relaxed dipole moment
for the specified excited state and wavefunction model will be
written to the `control`

file and used in calculations with
`NumForce` for the evaluation of the IR intensities.