Subject: Re: CCL:basis set balance?

From: [email-masked] (Per-Ola Norrby)
Date: Mon, 27 Jan 1997 17:31:39 +0100

Douglas A. Smith asked:
>The question:  Can people please explain the concept of having a balanced
>basis set and the dangers inherent in an unbalanced set?  In particular, why
>can I not simply use a large basis, including extra split valance functions,
>polarization and diffuse functions, only on the atoms I need them on, and a
>smaller, more compact basis set on the "unimportant" atoms to my chemical
>question?  This would certainly save time and resources during the calculation.

        I'll give it a try, and hopefully I can do it in chemists language
without loosing too much accuracy.

        The basic problem is that all basis sets are incomplete.  There is
no way you can use a finite number of basis functions to describe the
electron density completely.  You can get fairly close, but at a high cost.
Now, what happens to an atom with an incomplete basis?  It has some
electron density that could be described better if it could use some
additional basis functions.  Now, if there are unused basis functions on a
neighboring atom, there is always SOME way that a linear combination of
those can be used to stabilize the electron density on the original atom
further.  Thus, the electron sharing between atoms is exaggerated and the
bonds look stronger than they actually are.

        Now, if all atoms have very few basis functions, there aren't too
many unused functions that can be used by the neighbors, so the errors
(basis set deficiency and superposition errors, BSDE and BSSE) partially
cancel.  However, if one atom has a very small basis set and the neighbor
many diffuse and polarization functions, you may get into a situation where
a very substantial part of the electron density of the first atom is
described by basis functions on the second.  If you try to do a Mulliken
analysis on such a system, you get weird results.  The electron density in
that region will also most probably be skewed, causing all kinds of
distortions.

        You CAN get away with things like this, if you are careful to do
only comparisons between very similar systems, where the effect stays
constant.  Naturally, you can get away with ANYTHING as long as you fulfill
that requirement :-)

        Per-Ola Norrby

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
 *  Per-Ola Norrby, Associate Professor
 *  The Royal Danish School of Pharmacy, Dept. of Med. Chem.
 *  Universitetsparken 2, DK 2100 Copenhagen, Denmark
 *  tel. +45-35376777-506, +45-35370850    fax +45-35372209
 *  Internet: [email-masked], http://compchem.dfh.dk/

---

From: Joerg Hill <[email-masked]>
Date: Mon, 27 Jan 1997 11:18:41 -0800 (PST)

> question?  This would certainly save time and resources during the
calculation.

One of the dangers of using an unbalanced basis set is that you might
get electron
density where it shouldn't be. If you put a good basis only where you
think important
things will happen and a poor basis everywhere else than the electrons
which are
at the atoms with the poor basis will (partially) move to the atoms with
the good basis
(since there is more flexibility in the basis and the total energy of
the system will be
lowered). So you might get the effect you were interested in, but only
because you
described the system the way you thought it would be.

The basis set is only an approximation used to describe the electron density
distribution (since there is currently no way to solve the Schroedinger
equation
for a larger system without this approximation). So you have to use the same
quality of approximation for the whole molecule if you want to get reasonable
results.

Joerg-R. Hill

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