From owner-chemistry ^%at%^ ccl.net Wed May 31 17:25:00 2006
From: "Serguei Patchkovskii ps.:.ned.sims.nrc.ca" <owner-chemistry . server.ccl.net>
To: CCL
Subject: CCL: negative bsse content
Message-Id: <-31876-060531172244-31239-H4GfxyatwKBbp35/necG+g . server.ccl.net>
X-Original-From: Serguei Patchkovskii <ps*_*ned.sims.nrc.ca>
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Date: Wed, 31 May 2006 16:41:53 -0400 (EDT)
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Sent to CCL by: Serguei Patchkovskii [ps,ned.sims.nrc.ca]
On Wed, 31 May 2006, Jozsef Csontos jozsefcsontos|a|creighton.edu wrote:

> BSSE = E_{A}^{AB}(AB) + E_{B}^{AB}(AB) - E_{A}^{A}(AB) - E_{B}^{B}(AB)

[...]

> So, apart from the signs, I should always get results on the same side
> of zero, but I didn't.

Given the above definition, you can expect BSSE to be non-positive as long 
as the method used to calculate the energies is variational. The argument
goes as follows: A bigger variational space (A in the combined A+B basis set) 
can only lead to lower energies compared a smaller variational space (A in
the A basis set alone). Therefore, the difference E_{A}^{AB}(AB)-E_{A}^{A}(AB)
must be negative (or zero). Same holds for the energy of B - so the sum of
the two quantities must be non-positive as well.

This argument breaks down if:

a) the method you are using is not variational

or

b) the basis set alone does not represent the entire variational space of
   the method

or

c) there is numerical noise in the calculations, which exceeds the magnitude
   of the BSSE

Because MP2 energy is not variational, there is no reason to expect a
definite sign of BSSE for MP2 (either canonical or localized).

In the case of DFT, there is both a "hidden" variational space (numerical
integration grid) and a possibility of having significant numerical noise.
Both effects should decrease with the use of better grids.

Serguei