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Diagnostics:

Together with the MP2 and/or CC2 ground state energy the program evaluates the $ D_1$ diagnostic proposed by Janssen and Nielsen [90], which is defined as:

$\displaystyle D_1 = \sqrt{\max\Big(\lambda_{\mathrm{max}}\Big[\sum_i t_{ai} t_{bi}\Big], \lambda_{\mathrm{max}}\Big[\sum_a t_{ai} t_{aj}\Big]\Big)}$ (9.7)

where $ \lambda_{\mathrm{max}}[{\mathbf{M}}]$ is the largest eigenvalue of a positive definite matrix $ \mathbf{M}$. (For CC2 the $ D_1$ 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 $ D_1$ will contribute significantly to the computational costs.) 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$ [90,13]. 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!

The $ D_2$ diagnostic proposed by Nielsen and Janssen [91] 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 $ D_2$ requires an additional $ O(N^5)$ step! $ D_2(\mathrm{MP2/CC2}) \le 0.15$ are in excellent agreement with those of higher-order correlation methods, for $ D_2(\mathrm{MP2/CC2}) \ge 0.18$ the results should be carefully checked.


next up previous contents index
Next: Calculation of Excitation Energies Up: CC2 Ground-State Energy Calculations Previous: Fast RI-MP2 calculations with   Contents   Index
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