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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
[93], which is defined as:
*D*_{1} = |
(9.7) |

where
*λ*_{max}[**M**] is the largest eigenvalue of a positive
definite matrix
**M**.
(For CC2 the *D*_{1} diagnostic will be computed automatically.
For MP2 is must explictly be requested with the `d1diag`

option in
the `$ricc2` data group, since for RI-MP2 the calculation of *D*_{1}
will contribute significantly to the computational costs.)
Large values of *D*_{1} indicate a multireference character of the ground-state
introduced by strong orbital relaxation effects.
In difference to the *T*_{1} and *S*_{2} diagnostics
proposed earlier by Lee and coworkers, the *D*_{1} diagnostic is strictly
size-intensive and can thus be used also for large systems and to compare
results for molecules of different size.
MP2 and CC2 results for geometries and vibrational frequencies are, in general,
in excellent agreement with those of higher-order correlation methods if, respectively,
*D*_{1}(MP2)≤0.015 and
*D*_{1}(CC2)≤0.030 [93,13].
For
*D*_{1}(MP2)≤0.040 and
*D*_{1}(CC2)≤0.050 MP2 and/or CC2
usually still perform well, but results should be carefully checked.
*Larger values of **D*_{1} indicate that MP2 and CC2 are inadequate to describe
the ground state of the system correctly!
The *D*_{2} diagnostic proposed by Nielsen and Janssen [94]
can also be evaluated. This analysis can be triggered, whenever a response property
is calculated, e.g. dipole moment, with the keyword `$D2-diagnostic`

.
*Note that the calculation of **D*_{2} requires an additional *O*(*N*^{5}) step!
*D*_{2}(MP2/CC2)≤0.15 are in excellent agreement with those of
higher-order correlation methods, for
*D*_{2}(MP2/CC2)≥0.18
the results should be carefully checked.

** Next:** Calculation of Excitation Energies
** Up:** CC2 Ground-State Energy Calculations
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** Contents**
** Index**
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