The `ricc2` module therefore uses since release 6.5 an alternative double excitation diagnostic,
which is defined by
%_{1} = 100*_{1}/(_{1} + _{2})
with
_{1} = *E*_{ai}^{2}
and
_{2} = *E*_{aibj}^{2}
with
*E*_{ai}
and *E*_{aibj}
in the spin-orbital basis.
They are printed in the summaries for excitation energies under the headings `%t1`

and `%t2`

.
For spin-adapted excitation amplitudes
_{1}
and
_{2}
have to be computed
from respective linear combinations for the amplitudes which reproduce the values in the spin-orbital basis.
For ADC(2), which has a symmetric secular matrix with identical left and right normalized eigenvectors
_{1}
and
_{2}
are identical with the contributions
from the singles and doubles parts for the eigenvectors
to the trace of the occupied or virtual block of the (orbital unrelaxed) difference density between
the ground and the excited state, i.e. the criterium proposed in ref. [12].
Compared to the suggestion from ref. [12]
_{1}
and
_{2}
have the additional advantage of that they
are for all methods guaranteed to be postive and can be evaluated with the same insignificantly
low costs as *T*_{1}
and *T*_{2}
.
They are invariant with respect to unitary transformations of the occupied or the virtual
orbitals and give by construction identical results in spin-orbital and spin-free calculations.
For CC2 and CIS(D_{∞}
) the diagnostics
_{1}
and
_{2}
agree
for left and right eigenvectors usually with a few 0.01%
,
for CIS(D) and ADC(2) they are exactly identical.
For singlet excitations in spin-free calculations,
%_{2}
is
typically by a factors of 1.5-2 larger than %*T*_{2}
.
The second-order methods CC2, ADC(2), CIS(D_{∞}
) and CIS(D) can usually be trusted
for
%_{2}≤15%
.

For compatibility, the program can be switched to use of the old
%_{1}
and
%_{2}
diagnostics (printed with the headers `||T1||`

and `||T2||`

)
by setting the flag `oldnorm`

in the data group `$excitations`.
Note that the choice of the norm effects the individual results left and right
one- and two-photon transition moments, while transition strengths and all other observable
properties independent of the individual normalization of the right and left eigenvectors.

The
%_{2}
and %*T*_{2}
diagnostics can not be monitored
in the output of the (quasi-) linear solver.
But it is possible to do in advance a CIS(D) calculation.
The CIS(D) results for the
%_{2}
and %*T*_{2}
correlate usually
well with the results for this diagnostic from the iterativ second-order models,
as long as there is clear correspondence between the singles parts of the eigenvectors.
Else the DIIS solver will print the doubles diagnostics
in each iteration if the print level is set > 3
.
States with large double excitation contributions converge notoriously
slow (a consequence of the partitioned formulation used in the `ricc2` program).
However, the results obtained with second-order methods for
doubly excited states will anyway be poor. It is strongly recommended
to use in such situations a higher-level method.