[molpro-user] CBS extrapolations

Mikael Johansson mikael.johansson at helsinki.fi
Wed Sep 22 15:51:19 BST 2010

Hello John!

On Wed, 22 Sep 2010, John Keith wrote:

> Might someone be able to share expertise doing CBS extrapolations on 
> molecules?

A few comments, expertise not implied:

The convergence of the HF energy and the correlation energy is different. 
Therefore, for the most accurate results, it is a good idea to converge 
the two separately. You should also use different basis set series for HF 
and correlation. Jensen's polarisation consistent (pc-n) bases are good 
for HF (and DFT), and Dunning's for the correlation.

There's plenty of different extrapolation schemes available (I don't know 
what Molpro's default is). I like to keep it simple, and therefore use the 
two-point scheme by Halkier et al (CPL 286 (1998) 243) for the correlation 
energy. In the article they also show/conclude that using only the two 
largest basis sets in the extrapolation is to be preferred over including 
smaller basis sets and more points, the reason being that the inferiority 
of the smaller basis sets outweigh the added information of an additional 
data point.

For the HF extrapolation, Jensen has suggested a few schemes in connection 
with his pc-n sets, see TCA 113 (2005) 267.

In addition to CBS extrapolation, you could also extrapolate to the FCI 
limit, based on the HF -> CCSD -> CCSD(T) series, employing the continued 
fraction method of Goodson, JCP 116 (2002) 6948.

When extrapolating, getting a lower energy does not mean that it is closer 
to the FCI/CBS limit, so you cannot directly use that criterion for 
evaluating the quality of a given scheme (re the different formulas you 

I've used the above scheme and found it to be quite robust. For an 
application example, you can check out JCTC 4 (2008) 1460, 

Have a nice day,
     Mikael J.

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