Double corrections

To improve on the CCSD description, we go to the next level of coupled-cluster theory, including corrections from triple excitations -see the third row of Table 1.4, where we have listed the triples corrections to the energies as obtained at the CCSD(T) level. The triples corrections to the molecular and atomic energies are almost two orders of magnitude smaller than the singles and doubles corrections. However, for the triples, there is less cancellation between the corrections to the molecule and its atoms than for the doubles. The total triples correction to the AE is therefore only one order of magnitude smaller than the singles and doubles corrections. 

Configuration-interaction singles with a doubles correction Configuration-interaction singles with a third-order... 

The heat of solution of nickel chloride hexahydrate into l.OM HCl(aq) was measured, and (6.10 0.22) kJ moT was reported (2a uncertainties). The final solution was 0.02 M in Ni. A double correction to 0.0 M HCl(aq) and to / = 0 [95MAN/KOR] would be required to use the reported value to calculate the enthalpy of solution of the salt at infinite dilution in water. The corrections themselves have large uncertainties, and this heat of solution value is not used further in the present review. 

Head-Gordon, M., Rico, R. J., Oumi, M., Lee, T. J. [1994]. A Doubles Correction to Electronic Excited States from Configuration Interaction in the Space of Single Substitutions, Chem. Phys. Lett, 219, 21-29. 

In practice, only CO and the isonitrile ligand appear to require this type of stereochemical correction. For complexes containing both these ligands, a double correction must be imposed, viz ... 

The first result is quite satisfactory, while the second is not, but it must be remembered that it is always difiScult to separate the more volatile component of a mixture when present in relatively small quantity, and, in such a case, a second distillation is usually necessary. The first distillation was therefore continued until the temperature reached 100°, and the whole of the distillate, weighing 66 8 grams, was then redistilled and the double correction for loss by evaporation was applied. 

Doubles Correction to Electronic Excited States from Configuration Interaction in the Space of Single Substitutions. 

Head-Gordon M, Rico RJ, Oumi M, Lee TJ (1994) A doubles correction to electronic excited states from configuration interaction in the space of single substitutions. Chem Phys Lett 219 21... 

As an approximate alternative one does not directly include the doubles corrections in the principal propagator but corrects the RPA excitation energies, obtained by solving the RPA eigenvalue problem, with a non-iterative doubles correction. This approach is called doubles corrected random-phase approximation-RPA(D) (Christiansen et al, 1998a) and is based on pseudo-perturbation theory that was described in Section 3.13. 

Compared with the partitioned SOPPA eigenvalue problem in Eq. (10.49) we can see that only the RPA eigenvectors are necessary and that thus only the RPA eigenvalue problem has to be solved. The second-order and doubles correction, on the other hand, are evaluated only once, meaning that we have a non-iterative doubles correction in RPA(D). 

Christiansen, O., Bak, K. L., Koch, H., and Sauer, S. P. A. (1998a). A second-order doubles correction to excitation energies in the random phase approximation. Chem. 

The predicted dipole moments in Table 15.10 were obtained in the following manner. For each dipole moment calculated at the CCSD(T) level in the aug-cc-pVQZ basis, we first added a correction for the connected quadruples, obtained by assuming that the ratio between the quadruples and triples corrections is the same as the ratio between the triples and doubles corrections. Obviously, this procedure can give only a crude estimate of the quadruples correction, but it may at least serve as a rough indication of the error in the calculated dipole moments. 

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