Diagnostics:

Together with the MP2 and/or CC2 ground state energy the program evaluates the D₁ diagnostic proposed by Janssen and Nielsen [86], which is defined as:

$$\sqrt{{\max\Big(\lambda_{\mathrm{max}}\Big[\sum_i t_{ai} t_{bi}\Big], \lambda_{\mathrm{max}}\Big[\sum_a t_{ai} t_{aj}\Big]\Big)}}$$ (9.7)

where λ_max[M] is the largest eigenvalue of a positive definite matrix M. (For CC2 the D₁ diagnostic will be computed automatically. For MP2 is must explictly be requested with the d1diag option in the $ricc2 data group, since for RI-MP2 the calculation of D₁ will contribute significantly to the computational costs.) Large values of D₁ indicate a multireference character of the ground-state introduced by strong orbital relaxation effects. In difference to the T₁ and S₂ diagnostics proposed earlier by Lee and coworkers, the D₁ diagnostic is strictly size-intensive and can thus be used also for large systems and to compare results for molecules of different size. MP2 and CC2 results for geometries and vibrational frequencies are, in general, in excellent agreement with those of higher-order correlation methods if, respectively, D₁(MP2)≤0.015 and D₁(CC2)≤0.030 [86,13]. For D₁(MP2)≤0.040 and D₁(CC2)≤0.050 MP2 and/or CC2 usually still perform well, but results should be carefully checked. Larger values of D₁ indicate that MP2 and CC2 are inadequate to describe the ground state of the system correctly!

The D₂ diagnostic proposed by Nielsen and Janssen [87] can also be evaluated. This analysis can be triggered, whenever a response property is calculated, e.g. dipole moment, with the keyword $D2-diagnostic. Note that the calculation of D₂ requires an additional O(N⁵) step! D₂(MP2/CC2)≤0.15 are in excellent agreement with those of higher-order correlation methods, for D₂(MP2/CC2)≥0.18 the results should be carefully checked.