A Bond-Equivalent Model for Inner-Shell Correlation

A Bond-Equivalent Model for Inner-Shell Correlation 

In a pilot Wlh calculation on benzene [1], it was found that 85 % of the CPU time was spent on the inner-shell correlation step. Given that this contribution is about 0.5 % of the TAE of benzene, the CPU time proportion appears to be lopsided to say the least. On the other hand, a contribution of 7 kcal/mol clearly cannot be neglected by any reasonable standard. However, inner-shell correlation is by its very nature a much more local phenomenon than valence correlation, and a relative error of a few percent in such a small contribution is more tolerable than a corresponding error in the major contributions, Martin, Sundermann, Fast and Truhlar (MSFT) [43] investigated the applicability of a bond equivalent model. 

We started by generating a data base of inner-shell correlation contributions for some 130 molecules that cover the first two rows of the periodic table. In order to reduce the number of parameters in the model to be fitted, we introduced a Mulliken-type approximation for the parameters Dab (Da+Db)/2. Furthermore we did retain different parameters for single and multiple bonds, but assumed Da=b (3/2)Da=b- 

The model (which requires essentially no CPU time) was found to work very satisfactorily its performance for the W2-1 set can be seen in Table 2.3. Somewhat to our surprise, we found that the same model performs reasonably well when applied to the scalar relativistic contributions, albeit with larger individual deviations. 

It was recently suggested by Nicklass and Peterson [60] that the use of core polarization potentials (CPPs) [61] could be an inexpensive and effective way to account, for the effects of inner shell correlation. The great potential advantage of this indeed rather inexpensive method over the MSFT bond-equivalent model is that it does not depend on 

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