Body Counterpoise Correction

So far we have described the CP correction for dimers that were well defined. When we have many monomers present, how best to do the CP is not so obvious because the BSSE is not additive, and thus ambiguities can result. Earlier workers such as Turi and Dannenberg addressed this problem, but their solution  

The expressions for a general n-mer are also in their paper. °° Results for the helium trimer and preliminary results for the tetramer appear to be well be- 

When we begin to calculate the interaction of systems in excited states, the problems will get much, much worse because present approaches are not up to the task. In addition, when geometries are sensitive to the BSSE, we need much better methods than are currently available, since geometry optimization must be done concurrently with the energy minimization (requiring better coupling of statistical mechanics and quantum mechanics, a problem many researchers are now exploring). 

We end by encouraging more research into cases where the BSSE is large. For small systems the FCP usually works well, but not always. 

APPENDIX. SAMPLE INPUT DECKS FOR COUNTERPOISE CORRECTIONS 

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The resulting quantities are reported in Table 5.8 where the cc superseript indicates counterpoise correction of basis set superposition error. The two-body terms in the first row underscore the greater H-bond interactions in oligomers of HF, as compared to HCl. When corrected for superposition error, MP2 adds little to the interactions between HF monomers, but is responsible for a 25% enhancement in HCl. It is important to mention that erroneous... 

The two- and three-body interaction energies in the water hexamer were decomposed via the Morokuma procedure, without counterpoise correction, and some of the results are listed in Table 5.13. Beginning with the two-body terms, the results for all adjacent molecules are identical to the data for the 1-2 pair in the first row of the table. This similarity is explained by the fact that all adjacent pairs constitute a single H-bond the concept of dou-... 

If, instead of dimer interactions, many-body effects are calculated, the Boys-Bemardi recipe is in a straightforward way extended to read each subsystem is to be calculated in the complete basis of the supersystem , a recipe that has been applied to trimer interactions and, albeit approximately, to cluster calculations . Wells and Wilson call this the site-site counterpoise function method and formulate it nicely for two-body, three-body, etc., interactions. Computing only a counterpoise correction for pairs of monomers and assuming additivity proved to overestimate the BSSE even for small systems . 

The best estimate obtained for the correlation contribution to the interaction energy with the many-body approach, the counterpoise-corrected result with the largest basis set (150 functions), is - 0.70 kcal/mol. This value required 9 hr of Cray X-MP time to compute even so, it recovers only some 70% of the total correlation effect. Smaller sets yield only half the true value. In summary, the authors were pessimistic about the ability of computing very accurate correlation contributions, especially for systems larger than the water dimer. 

For extensive basis sets, an optimal description of the subsystems X and Y and the supersystem X... Y will be obtained. The basis set superposition error will then be very small. In recent work. Wells and Wilson did not use the function counterpoise correction in the usual fashion described above. They pointed out not only that the Boys-Bemardi procedure overcorrects for basis set superposition effects but also that it cannot be uniquely generalized for the calculation of a many-body interaction. Wells and Wilson argue that the function counterpoise correction should be used as a test for basis set superposition errors. 

Function counterpoise correction for the ground state of the neon atom calculated using diagrammatic many-body perturbation theory and employing a systematic sequence of even-tempered basis sets of Gaussian-type functions. In this table G represents a set of ghost orbitals. The NeG internuclear separation is 5.0 bohr. ... 

In this approach it is assumed that the basis set superposition error in the many-body cluster can be approximated by the sum of the Boys-Bemardi function counterpoise corrections for pairs of bodies. Hence the total interactions for an N-body cluster using the pairwise additive function counterpoise correction is given by... 

P, Valiron and I. Mayer, Chem. Phys. Lett., 275, 46 (1997). Hierarchy of Counterpoise Corrections for N-Body Clusters Generalization of the Boys-Bernardi Scheme. 

Numbers in parenthesis correspond to counterpoise-corrected values These results have been estimated from the counterpoise-corrected 4+5+6-body interaction energies... 

In Fig. 6 the various contribution to the cohesive energy of magnesium are presented. For the embedded eluster the cohesive contribution of the one-body increment is defined as the difference between the correlation energy of the embedded atom (Aa ) and the free atom fre" As = ea The basis set superposition error (BSSE) was corrected applying the counterpoise (CP) method the free atom, described with cc-pVTZ was surrounded by two shells of ghost atoms. The one-body contribution is... 

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