In response theory, transition strengths (and moments) are identified from the first residues of the response functions. Due to the non-variational structure of the coupled cluster models different expressions are obtained for ``left'' and ``right'' transitions moments and and the transition strengths are obtained as a symmetrized combinations of both:

Note, that only the transition strengths are a well-defined observables but not the transition moments and . For a review of the theory see refs. [93,96]. The transition strengths calculated by coupled-cluster response theory according to Eq. (9.23) have the same symmetry with respect to interchange of the operators and and with respect to complex conjugation as the exact transition moments. In difference to SCF (RPA), (TD)DFT, or FCI, transition strengths calculated by the coupled-cluster response models CCS, CC2, etc. do not become gauge-independent in the limit of a complete basis set, i.e., for example the dipole oscillator strength calculated in the length, velocity or acceleration gauge remain different until also the full coupled-cluster (equivalent to the full CI) limit is reached.

For a description of the implementation in the `ricc2` program see
refs. [89,13].
The calculation of transition moments for excitations out of the ground
state resembles the calculation of first-order properties for excited states:
In addition to the left and right eigenvectors, a set of
transition Lagrangian multipliers
has to be determined and
some transition density matrices have to be constructed.
Disk space, core memory and CPU time requirements are thus also similar.

The single-substitution parts of the transition Lagrangian
multipliers
are saved in files named
`CCME0-`

*s*`--`

*m*`-`

*xxx*.

To obtain the transition strengths for excitations out of the ground state the keyword
`spectrum`

must be added with appropriate options (see
Section 14.2.13) to the data group `$excitations`; else the input is same as for the
calculation of excitation energies and first-order properties:

$ricc2 cc2 $excitations irrep=a1 nexc=2 spectrum states=all operators=diplen,qudlen

To obtain the transition strengths for excitations between excited states the keyword
`tmexc`

must be added to the data group `$excitations`. Additionally, the initial and final states must be given in the same line; else the input is same as for the
calculation of excitation energies and first-order properties:

$ricc2 cc2 $excitations irrep=a1 nexc=2 irrep=a2 nexc=2 tmexc istates=(a1 1) fstates=all