Subject: Re: CCL:combining different basis sets - an addition

From: [email-masked] (Steven Bachrach)
Date: Fri, 1 Dec 95 07:52:58 -0600

>        It of course depends on what you mean with "better".  The SCF will
>minimize the energy, adding any new function should give an energy closer
>to the HF limit.  However, most of the time this is not really interesting.
>When you want energies, you usually want relative energies, and then it's
>quite important that you make the same approximations, that is, calculate
>at a constant level of theory, so that systematic errors cancel.  Also, as
>you said in the part of the message I deleted, adding functions in an
>unbalanced way will definitely affect the charge distribution, probably not
>making it "better" :-)  Specific questions can sometimes be answered by
>including functions that are not atom-centered, but then you get the
>problem of findning a completely reproducable way of doing that for any
>system.

I hate to bring up this topic yet again on this list, but it strikes a nasty chord
in me. The whole problem rests on this idea of what's "better". How does one
decide what is a "better" charge distribution? There is no experimental test,
except to compare the full spatial distribution determined by calculations
with those determined experimentally (like an x-ray diffraction - but
resolution is a problem). Usually, the idea of "better" charge
distribution are numbers that make more intuitive sense according to
the researcher - hardly an non-empirical basis.

On the other hand, there is no question about the effects of added functions with
regards to energy - added functions WILL lower the energy every time,
sometimes not by much, but lower. And since the HF wavefunction is variational,
the lower the better!

Keep in mind, as Mulliken pointed out in the 50s, that one can construct
a perfectly good, HF-limit wavefunction for H2 by placing a huge set
of orbitals centered only on one of the hydrogens. A mulliken population
for this system would be meaningless in any intuitive sense (one hydrogen
has a charge of +1, the other a charge of -1), yet the energy and the 
(patial) density distribution are at the HF limit.

Steve

Steven Bachrach				
Department of Chemistry
Northern Illinois University
DeKalb, Il 60115			Phone: (815)753-6863
[email-masked]			Fax:   (815)753-4802