I am trying to carry out CC3 calculations for an A1 excited state that has high contribution of the homo>lumo doubly excited configuration. Unfortunately, while iterating the root (that is supposed to be second in the A1 manifold of excited states is replaced by either the lowest one, or the third one.

My guess is that the initial guess contain insufficient contributions of the doubly excited configuration (which is too high in energy in the EOM-CCSD wavefunction) and therefore the identity of the state is lost in the CC3 iterations.

Is there any way to either manually put this configuration to contribute more to the initial vector, or (preferably) to modify the initial guess method to include such contribution. Otherwise I may never
pinpoint the desired state because of too poor the initial guess.

I think you should be able to follow even a bad guess using the FOLLOW_ROOT and PROP_ROOT keyword, as long as you can identify the actual root you want from the EOM-CCSD step.

Thank you! Currently I am trying the follow_root option (prop_root is
used to select different roots of a given symmetry), but the results are
slow to come (a large system).

Without this option, however, the root that I select (second of the A1
symmetry) is nicely projected onto the initial guess vectors:

Setting initial CC3 eigenvalue to 0.1873059615
Iter=1 L=3 Root EOM Energy Delta E Res. Norm Conv?
Overlaps of Rs with EOM CCSD eigenvector:
0 -0.008474
1 -0.972491
2 0.103157

As the wavefunction gets improved by allowing the triply excited
configurations to contribute, this changes to
sth like that:

Iter=5 L=7 Root EOM Energy Delta E Res. Norm Conv?
Overlaps of Rs with EOM CCSD eigenvector:
0 0.023720
1 0.694813
2 -0.217462
3 0.575534
4 0.111378
5 0.071792
6 0.073731
follow_root returning: 1
2 0.1266971003 -6.34e-03 5.62e-02 N
Iter=6 L=8 Root EOM Energy Delta E Res. Norm Conv?
Overlaps of Rs with EOM CCSD eigenvector:
0 -0.489920
1 0.400132
2 -0.655049
3 0.045113
4 0.120558
5 -0.086447
6 0.030661
7 -0.075826
follow_root returning: 2
3 0.1786808629 -2.47e-02 6.49e-02 N

It seems that the second root has negligible contribution in the
wavefunction that comes out of the calculations. I assume that the
initial guess must have been rather poor for the second A1 excited
state.

I hope that fixing the root as second in the A1 manifold of the excited
states will result in the correct wavefunction even if the initial guess
is inadequate. I will post the short report after the calculations have
completed (it may be only in several weeks, as one iteration takes over
30 hours) provided that there is sufficient memory in the node on which
the calculations run.