Comments on the Output

• Most important output for ricc2, rimp2, and mpgrad are of course MP2(+HF) energies (written standard output and additionally to file energy) and MP2(+HF) gradients (written to file gradient).
• In case of MP2 gradient calculations the modules also calculate the MP2 dipole moment from the MP2 density matrix (note, that in case of mpgrad frozen core orbital specification is ignored for gradient calculations and thus for MP2 dipole moments).

Further output contains indications of the suitability of the (HF+MP2) treatment.

• As discussed above, reliable (HF+MP2) results are in line with small MP2 corrections. The size of the MP2 correction is characterised by the t-amplitudes, as evident from the above equations. mpgrad by default plots the five largest t-amplitudes as well as the five largest norms of t-amplitudes for fixed i and j, rimp2 does the same upon request, if $tplot is added to control file. More or less than five t-amplitudes will be plotted for $tplot n, where n denotes the number of largest amplitudes to be plotted. It is up to the user to decide from these quantities, whether the (SCF+MP2) treatment is suited for the present problem or not. Unfortunately, it is not possible to define a threshold, which distinguishes a "good" and a "bad" MP2-case, since the value of individual t-amplitudes are not orbital-invariant, but depend on the orbital basis (and thereby under certain circumstances even on the orientation). Example: the largest norm of t-amplitudes for the Cu-atom ( d¹⁰s¹, "good" MP2-case) amounts to ca. 0.06, that of the Ni-atom (d⁸s², "bad" MP2 case) is ca. 0.14.
• A more descriptive criterion may be derived from the MP2 density matrix. The eigenvalues of this matrix reflect the changes in occupation numbers resulting from the MP2 treatment, compared to the SCF density matrix, where occupation numbers are either one (two for RHF) or zero. Small changes mean small corrections to HF and thus suitability of the (HF+MP2) method for the given problem. In case of gradient calculations rimp2 displays by default the largest eigenvalue of the MP2 density matrix, i.e. the largest change in occupation numbers (in %). All eigenvalues are shown, if $mp2occ is added to the control file. For main group compounds largest changes in occupation numbers of ca. 5% or less are typical, for d¹⁰ metal compounds somewhat higher values are tolerable.
• A similar idea is pursued by the D₂ and D₁ diagnostics [86,87] which is implemented in ricc2. D₂ is a diagnostic for strong interactions of the HF reference state with doubly excited determinants, while D₁ is a diagnostic for strong interactions with singly excited determinants.