Trouble shooting:

For the iterative second-order methods CIS(D_∞), ADC(2), and CC2 the solution of the nonlinear partitioned eigenvalue problem proceeds usually in three steps:

1. solution of the CCS/CIS eigenvalue problem to generate reasonable start vectors; the eigenvectors are converged in this step only to a remaining residual norm < preopt
2. pre-optimization of the eigenvectors by a robust modified Davidson algorithm (see ref. [10]) using the LINEAR CC RESPONSE SOLVER until the norm of all residuals are below preopt, combined with a DIIS extrapolation for roots assumed to be converged below the threshold thrdiis.
3. solution of the nonlinear eigenvalue problem with a DIIS algorithm using the DIIS CC RESPONSE SOLVER until the norm of the residuals are below the required threshold conv

This procedure is usually fairly stable and efficient with the default values for the thresholds. But for difficult cases it can be necessary to select tighter thresholds. In case of convergence problems the first thing do is to verify that the ground state is not a multireference case by checking the D1 diagnostic. If this is not the case the following situations can cause problems in the calculation of excitation energies:

• almost degenerate roots in the same symmetry class
• complex roots (break down of the CC approximation close in the neighbourhood of conical intersections)
• large contributions from double excitations

The first two reasons can be identified by running the program with a print level ≤3. It will then print in each iteration the actual estimates for the eigenvalues. If some of these are very close or if complex roots appear, you should make sure that the DIIS procedure is not switched on before the residuals of the eigenvectors are small compared to the differences in the eigenvalues. For this, thrdiis (controlling the DIIS extrapolation in the linear solver) should be set about one order of magnitude smaller than the smallest difference between two eigenvalues and preopt (controlling the switch to the DIIS solver) again about one order of magnitude smaller then thrdiis.

Tighter thresholds or difficult situations can make it necessary to increase the limit for the number of iterations maxiter.

In rare cases complex roots might persist even with tight convergence thresholds. This can happen for CC2 and CIS(D_∞) close to conical intersections between two states of the same symmetry, where CC response can fail due to its non-symmetric Jacobian. In this case one can try to use instead the ADC(2) model. But the nonlinear partitioned form of the eigenvalue problem used in the ricc2 program is not well suited to deal with such situations.

Large contributions from double excitations 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 ||T2|| diagnostic correlate usually well with the CC2 results for this diagnostic. Else the DIIS solver will print the ||T2|| 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 double excited states will anyway be poor. It is strongly recommended to use in such situations a higher-level method.