Subject: combining different basis sets - an addition

From: "Moshe Olshansky" <[email-masked]>
Date: Tue, 28 Nov 95 16:36:37 IST

Dear netters!
After posting the summary of the responses I got an additional
note which may be of interest to some of you.  Here it is:

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Date: Mon, 27 Nov 1995 16:23:15 -0330 (NST)
From: Uli Salzner <[email-masked]>
Subject: basis set mixing

Dear Moshe,
I just read read the answers you received according basis set mixing and I think
one important point was not addressed. It is definetly important that a basis
set has to be balanced but that does not mean that you have to use the same
basis set for each atom. In fact, to use the "same" basis set for different
atoms may be the perfect way to get an unbalanced basis set.

For example:
consider the calculation of an ionic compound such as LiF. If you use 6-31G* on
both atoms, you have a very good basis set for Li. Since Li looses about 90% of
its 2s electron (maybe even more) when bound to F, it has almost no electrons in
the 2s and 2p. For such a cation a valence double zeta basis set is very good. On
the other hand fluorine is an anion with a diffuse charge distribution. For an
anion the 6-31G* basis set quite bad. What you get is spurious charge transfer
from  F to Li.

Thus, one uses different basis sets for different atoms all the time even if they
have the same name. What you have to figure out is how to combine different
basis sets in the right way. For the above example it would be a improvement to
use 6-31+G* on F. This gives a better balanced basis set than 6-31G* on both
atoms. Similar arguments hold for polarization functions. You have to decide
which atoms need them and which don't. For instance for third row systems you
definetely need d-functions. But there is no problem to combine a sulfer basis
set with d-functions with hydrogen basis set that contains only s-functions
because hydrogen d-orbitals are so high in energy that the effect would be
negligible.

Bets wishes,
Uli Salzner

[email-masked]

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P.S. and now I have an additional question:
     I am a mathematician,  not a chemist,  so let me look at the
     basis sets purely mathematically.  If one has a complete (and
     hence necessarily infinite) basis set,  he/she gets a limit
     of Hartree-Fock model.  Otherwise (with limited basis set) one
     gets some approximation to this limit and the more complete the
     basis set is the better is the approximation.  Now assume one
     uses a certain "standard" basis set and gets some result (from
     Hartree-Fock model).  And now we add ANY additional function to
     this basis set.  This does not make the basis set less complete
     and so it should lead to at least as good (or even better) an
     approximation as the original basis did (it is also possible
     to get the original solution by taking that additional function
     with zero coefficient for every electron).
     Is there anything wrong with this statement?

Moshe Olshansky
IBM Israel Science & Technology
<[email-masked]>