Diagnostics:

Together with the MP2 and/or CC2 ground state energy the programm evaluates the $D_1$ diagnostic proposed by Janssen and Nielsen [72], which is defined as:

$$D_1 = \sqrt{\max\Big(\lambda_{\mathrm{max}}\Big[\sum_i t_{ai} t_{bi}\Big], \lambda_{\mathrm{max}}\Big[\sum_a t_{ai} t_{aj}\Big]\Big)}$$ (7.7)

where $\lambda_{\mathrm{max}}[{\mathbf{M}}]$ is the largest eigenvalue of a positive definite matrix $\mathbf{M}$. Large values of $D_1$ indicate a multireference character of the ground-state introduced by strong orbital relaxation effects. In difference to the $T_1$ and $S_2$ diagnostics proposed earlier by Lee and coworkers, the $D_1$ 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, $D_1(\mathrm{MP2}) \le 0.015$ and $D_1(\mathrm{CC2}) \le 0.030$ [72,13]. For $D_1(\mathrm{MP2}) \le 0.040$ and $D_1(\mathrm{CC2}) \le 0.050$ MP2 and/or CC2 usually still perform well, but results should be carefully checked. Larger values of $D_1$ indicate that MP2 and CC2 are inadequate to describe the ground state of the system correctly!