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
*M*^{V}_{0←f} and
*M*^{V}_{f←0}
and the transition strengths
*S*^{0f}_{V1V2} are obtained as a symmetrized combinations of both:

Note, that only the transition strengths

For a description of the implementation in the `ricc2` program see
refs. [103,13].
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 15.2.13) 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

For the calculation of transition moments between excited states a set of Lagrangian multipliers
has to be determined instead of the
for the ground state transition moments. From these Lagrangian multipliers and the left and right eigenvectors one obtaines the ``right'' transition moment between two excited states *i* and *f* as

where are the matrix elements of the perturbing operator. A similar expression is obtained for the ``left'' transition moments. The ``left'' and ``right'' transition moments are then combined to yield the transition strength

As for the ground state transitions, only the transition strengths

The single-substitution parts of the transition Lagrangian
multipliers
are saved in files named
`CCNE0-`

*s*`--`

*m*`-`

*xxx*.

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 operators=diplen