Subject: Combining different basis sets - a summary

From: "Moshe Olshansky" <[email-masked]>
Date: Sun, 26 Nov 95 14:45:00 IST

Dear netters!
About 10 days ago I asked the following question:

> Dear CCL'ers!
> We are working on computational aspects of the Hartree-Fock procedure.
> For this purpose we would like to have some f-type basis functions
> but not too many of them,  while all the basis sets we have either
> do not have f functions at all or have too many of them (our trial
> molecule contains H C N and O atoms).
> Since we are not chemists I would like to ask the following
> (possibly very trivial) question:  does it make any sense to combine
> two different basis sets (for example,  take a smaller basis set for
> H and C and a larger one - containing d and f functions - for N and O)?

First of all,  I wish to thank all those who replied to this questions.
Basically I got two kinds of responses: some stress the dangers
of doing so (talking about Basis Set Superposition Error, etc.),
while others say it can (and is being) done,  though some caution
is needed.
Below are the responses I got.

Moshe Olshansky
IBM Israel Science and Technology
<[email-masked]>
=========================================================================
Date: Tue, 14 Nov 1995 17:46:52 +0100
From: [email-masked] (Ayaz Bakasov, Phys. Chem., ETH Zurich)
To: [email-masked]
Subject: Re: CCL:Combining different basis sets

Dear Mosche,

that naive idea of combining
(straightforwardly) arbitrary basis sets
is not so harmless as it could seem
at first glance.

The dangers have been recognized long ago,
and have been discussed, for instance,
in chapter 18 "Balancing basis sets"
(page 333) of the following review:

Sigeru HIZINAGA
"Basis sets for molecular evaluations"
Computer Physics Reports 2 (1985) 279-340.

The error caused by an unbalanced basis set
is normally called "basis set superposition error".

The best,
Ayaz Bakasov.
P.S.
Na pal'tsakh: slishkom bol'shoi basis
na kakom-libo atome "otsasyvaet"
neproportsional'no bol'shoi
ob'em volnovoi funktsii na etot atom.

=========================================================================
Date: Tue, 14 Nov 95 12:21:32 EST
From: "Janet Del Bene" <[email-masked]>
Subject: Your question -

Moshe,
     You did not state specifically the problem of interest, but I
am sure that you are aware that there is a basis-set dependence of
computed results.  To arbitrarily put a larger basis set on some atoms
and smaller sets on others would bias your results.
     Hope this helps.  Janet E. Del Bene
=========================================================================
Date: Tue, 14 Nov 1995 18:52:45 +0100
From: [email-masked] (Marek Sierka)
Message-Id: <[email-masked]>
Subject: Basis Set

Dear Moshe,

	Good basis set has to be properly balanced, otherwise it introduces
so called Basis Set Superposition Error. In case of the unbalanced basis set,
it leads to the artificial charge transfer, and also gives nonphysical,
stabilizing contributions to the enery of molecule. This stabilizing will
then occure irrespective of whether there is any genuine binding interaction
in the molecule or not. It will give a spurious increase in the binding
energy.The choice of proper basis set is kind of art, so you have to be
very careful about it. Try this:
http://www.emsl.pnl.gov:2080/forms/basisform.html
This www server contains several basis sets, so maybe you can find
something useful.

Marek Sierka
Max-Planck Society
Quantum Chemistry Group at the Humboldt Univ.
Joegerstrasse 10/11
D-10117 Berlin, Germany
e-mail: [email-masked]
=========================================================================
Date: Tue, 14 Nov 1995 13:23:54 -0500
From: "E. Lewars" <[email-masked]>
Subject: COMBINING BASIS SETS

Hello,   Yes, you can combine basis sets.  For example, the 3-21G* basis
has d orbotals on atoms beyond Ne, bot no d's on H--Ne.  Some people
would call it an "untempered" or uneven basis set, but it works well
(see *Practical Strategies for Electron Structure Calculations*, by
Warren Hehre, 1995).  Also, in papers in on oxirenes, I think Schaefer and coworkers
 used f and maybe g functions on some atoms but not other:
J Phys Chem 98 (1994) 8660
J Am Chem Soc  116 (19940 9311
j aM cHEM sOC 116 (1994) 10159
  oF COURSE, THE WIDELY-USED 6-31g* basis has d functions on He, Li, Be, etc,
   but not on H, and 6-31G** has p's on H but d's on He, Li, etc.
Errol Lewars
=========================================================================
From: David Heisterberg <[email-masked]>
Date: Tue, 14 Nov 1995 13:35:35 -0500
Subject: Re: CCL:Combining different basis sets

There is a school of thought that says that basis sets should be similar
for each atom, or at least similar for all important atoms, such as
those involved in bond breaking/making.  This is especially important
if you are interested in any basis-set dependent information, such as
partial charges.  But it might also be important for a purely
computational study -- during the SCF, an "unbalanced" basis-set might
exhibit changes in the density matrix that are really just artifacts,
and wouldn't appear as significant changes in the Fock matrix.

I would suggest looking at the basis sets available from PNL,
especially the so-called correlation consistent (cc) sets.
The cc-pVTZ set for C, N, and O are of the form (4S,3P,2D,1F).
They are web-accessible at

    http://www.emsl.pnl.gov:2080/forms/basisform.html

Dave Heisterberg
=========================================================================
From: Jiri Czernek <[email-masked]>
Subject: Re: CCL:Combining different basis sets
Date: Tue, 14 Nov 1995 20:30:42 +0100 (MET)

     Hi again ! :-)

I think you risc the basis set for your molecule will be ILL-BALANCED.
For explanation I'll cite from some book by Huzinaga: "If basis sets of
different quality are placed on atomic sites of a molecular system, the
calculated electron distribution may show artificial distortion. Improperly
balanced basis sets may yield results even worse than basis sets of
uniformly poorer quality."

Hope this helps :-)

                                                     Cordially ,
                                                           George

=========================================================================
From: [email-masked]
Date: Tue, 14 Nov 1995 17:28:00 EST
Subject: basis sets

 Hi Dr. Olshansky,

   You are apt to get two very different responses to this question.

From a purist's point of view differeent basis sets probably shouldn't be

combined but from a practical point of view its often necessary. I'm assuming

by d and f type functions you mean d and f type gaussians. These are frequently

treated as "polarization" functions and are often added to some atoms

in a molecule but not others. They are almost always necessary to accurately

model the behavior of nitrogen and oxygen atoms. Because we have such a small

computer here at URI we often have to combine basis sets. To toot my own horn:

A Comparitive Theoretical Study of Hydrazine", Brian K. Schmitz and William B.

Euler, Journal of Molecular Structure(Theochem), 257, 1992, 227. Here are some

other references I have to hand:

Binkley, J. S.; Pople, J.A.; Hehre, W.; Self-Consistent
Molecular Orbital Methods. XII. Further Extensions of Gaussian
Type Basis Sets for Use in Molecular Orbital Studies of
Organic Molecules, Journal of the American Chemical Society,
1980, 102, 939.

Boys, S. F.; Electronic-Wave Functions I. A General Method of
Calculation for the Stationary States of Any Molecular System,
Proceedings of the Royal Society (London), 1950, A200, 542.

Defrees, D. J.; Raghavachari,
K.; Schlegel, H. B.; Pople,    J.A.; Effect of Electron
Correlation on Theoretical Equilibrium Geometries. 2.
Comparison of Third-Order Perturbation and Configuration
Interaction Results with Experiment, Journal of the American
Chemical Society, 1982, 104, 5576.

Ditchfield, R.; Hehre,
W.J.; Pople, J.A.; Self-Consistent Molecular-Orbital
Method.IX. An Extended Gaussian-Type Basis for Molecular
Orbital Studies of Organic Molecules, Journal of Chemical
Physics, 1971, 54, 724.

Dunning, T. H.; Gaussian Basis Functions for Use In Molecular
Calculations. I. Contraction of Atomic Basis Sets for First
Row Atoms, Journal of Chemical Physics, 1970, 53,
2823.

Hariharan, P. C.; Pople, J. A.; The influence of polarization
Functions on Molecular Orbital hydrogenation Energies,
Theoretica Chimica Acta, 1973, 28, 213.

Hinchliffe, A.; Ab Initio Determination of Molecular
Properties, IOP Pub., ltd., England , 1987, 9.

Huzinaga, S.; Gaussian-Type Functions for Polyatomic
Systems.I., Journal of Chemical Physics, 1965, 2, 1293.

Jensen, J. H.; Gordon, M. S.; Splicing I. Using Mixed Basis
Sets in ab initio Calculations, Journal of Computational
Chemistry, 1991, 12, 421.

Klopper, W.; Kutzelnigg, W.; Gaussian Basis Sets and the
Nuclear Cusp Problem, Jorunal of Molecular
Structure(Theochem), 1986, 28, 339.

Krishnan, R.; Binkley, J.S.; Seeger, R.; Pople, J.A.;
Self-consistent Molecular Orbital Methods. XX. A Basis Set for
Correlated Functions, Journal of Chemical Physics, 1980, 72,
650.

Ohta, K.; Nahatsuji, H.; Hirao, K.; Yonezawa, T.; Ab initio
Calculation of Hyperfine Splitting Constants of Molecules,
Journal of Chemical Physics, 1980, 73, 1770.

Poirier, R.; Kari, R.; Csizmadia, I. G.; Handbook of
Gaussian Basis Sets, 1985, Elsevier, New York, Appendix F.

Pulay, P.; Fogarasi, G.; Pang, F.; Boggs, J. E.; Molecular
Geometries, Force Constants, and Dipole Moment Derivatives,
Journal of the American Chemical Society, 1979, 101, 2550.

Pulay, P.; Fogarsi, G.; Pongor, G.; Boggs, J.; Varga, A.;
Journal of the American Chemical Society, 1983, 105,
7037.

 Riggs, N. V.; Radom, L.;
The 3-21G(N*) Basis Set: An Economical Polarized Basis set for
ab initio Studies on Nitrogen Containing Molecules,
International Journal of Quantum Chemistry, 1987, 31, 93.

Riggs, N. V.; Radom, L.; An ab initio Investigation of the
Equilibrium Structures of Hydrazine and the Transition
Structures Connecting Them, Australian Journal of Chemistry,
1986, 39, 1917.

Shavitt, I.; Methods in Computational Physics, Vol. 2,
eds. Alder, B.; Fernbach, S.; Rothenburg, M; Academic Press,
New York, NY, 1963, 3.

                                         Yours truly,

                                         Brian Schmitz

                                e-mail: [email-masked]
=========================================================================
Date: Tue, 14 Nov 95 19:02:39 -0330
From: [email-masked] (Cory C. Pye)
Subject: Basis sets

For molecules containing only H, C, N, and O atoms, for a Hartree-Fock
calculation you probably don't need d or f-functions for C, since C is
(usually) in a fairly symmetric environment (especially sp3 carbons).
They might come in handy for an sp2 or sp carbon to help describe the
pi-bonds. Oxygen and Nitrogen should definitely have d-functions, and in
some of my work on BSSE (C. C. Pye, R. A. Poirier, D. Yu and P. R. Surjan,
{\em J. Mol. Struct. (Theochem)}, {\bf 307} (1994) 239 ), they were
somewhat important for Nitrogen (f-functions, that is). I think as long as
the occupied s & p functions are consistent for different atoms, you
probably won't have to worry about unbalanced basis sets too much. So from
best to worst: C df, N df, O df H p
               C d , N df, O df H p
               C d , N df, O d  H p
               C d , N d , O d  H p
               C d , N d , O d
                     N d , O d
                   <none>

(probably)

Hope this helps a bit.
-Cory
   *************
 *****************  !  Cory C. Pye
***   **    **  **  !  Graduate Student
**   *  ****        !  Unpaid Sys Admin
**      *  *        !  Theoretical and
**      *  *        !  Computational Chemistry
***     *  *    **  !
 *****************  !  Les Hartree-Focks
   *************    !  (Apologies to Montreal Canadien Fans)

=========================================================================
From: Christopher J Cramer <[email-masked]>
Subject: Re: CCL:Combining different basis sets
Date: Tue, 14 Nov 1995 17:06:51 -0600 (CST)

Moshe,
>
> We are working on computational aspects of the Hartree-Fock procedure.
> For this purpose we would like to have some f-type basis functions
> but not too many of them,  while all the basis sets we have either
> do not have f functions at all or have too many of them (our trial
> molecule contains H C N and O atoms).
> Since we are not chemists I would like to ask the following
> (possibly very trivial) question:  does it make any sense to combine
> two different basis sets (for example,  take a smaller basis set for
> H and C and a larger one - containing d and f functions - for N and O)?
>
   Particularly with respect to polarization functions, I believe that you
are correct in your assumption that they may be more important on some atoms
than on others. This is in fact widely accepted (if not necessarily
consciously) when one refers to atoms from different rows (e.g., 6-31G* puts
polarization functions on C but not H, 3-21G(*) puts polarization functions
on P but not C, etc.) It is much less common to discriminate between atoms
within the same row. However, we ourselves have recently optimized a
variation of the MIDI basis set (we call it MIDI! "midi-bang") with the goal
of developing a small basis set that gives high quality geometries and atomic
partial charges from HF calculations. In that process, we discovered that d
functions on C were unimportant even though they were critical for N and O
(this for a test set spanning a wide range of organic functionalities). Of
course, we are interested in properties other than the total energy, where
we have not tested the utility of the basis set (mind you, it will probably
perform no more poorly than any other small basis set). So, with some
judicious comparisons made first, I would say that you can legitimately
tailor your polarization space to suit your needs without fear of
catastrophic consequences.

Chris

--

Christopher J. Cramer
University of Minnesota
Department of Chemistry
207 Pleasant St. SE
Minneapolis, MN 55455-0431
--------------------------
Phone:  (612) 624-0859 || FAX:  (612) 626-7541
[email-masked]
http://dionysus.chem.umn.edu/

=========================================================================
From: Marcelo Giordan Santos <[email-masked]>
Subject: Combinning Different Basis Sets.
Date: Wed, 15 Nov 1995 12:34:21 -0200 (EDT)

	Dear Mosche,

	There are many examples in the literature, that combine different
kinds of basis sets, even among the same element. In my opinion there is no
problem in mixing different basis sets of different degree of quality for
the same molecule. But, you should examine your results in the light of this
apporach.

	I've an article about pyrrolizidine alkaloids in which i mix
different kinds of basis sets, utilizing pseudopotential and all-electrons
approach. It will appear in the fortcomming numbers of J. Comp. Chem.

	Best regards,
			Marcelo Giordan.
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