Subject: SUMMARY OF REPLIES TO 3-21G vs. 6-31G* QUESTION

From: "E. Lewars" <[email-masked]>
Date: Tue, 30 Jun 1998 13:03:03 -0400 (EDT)

1998 June 31

Here are the replies I got to my question about the 3-21G basis vs. the 6-31G*.
Thanks very much to [email-masked], Frank Jensen, Alan Shusterman, and
German Sastre Nava.

 Question:

> Mon, 1998 June 22
> 
> Hello,
> 
>  The 3-21G (strictly, 3-21G*) basis set gives geometries which are actually a
> bit better than those from the 6-31G* set (Hehre, "Practical Strategies for
> Electronic Structure Calculations", p 23; Hehre, Radom, Schleyer and Pople,
> "Ab Initio Molecular Orbital Theory", pp 175 and 185; this is for HF-level
> calculations; for correlated-level work one needs at least 6-31G*, of course).
> HF/3-21G* geometries are even used for Petersson's high-accuracy CBS-4 method.
> 
> So why (judging by the literature) is the 6-31G* basis usually preferred for
> HF-level geometries?  Is it because of an unexamined belief that bigger is
line 1 [h for help]> better?  Or is it because *relative energies* are better at the HF/6-31G* leve
l
> than at the HF/3-21G level?  If this is the reason, then in those cases where
>*both* HF and MP2 (or other correlated) calculations are reported, would it not
> be better to do the HF calculations using 3-21G optimizations (then use MP2/
> 6-31G* or bigger for the post-HF jobs)?
>     E. Lewars
=======================

REPLIES
#1  Cory

Date: Mon, 22 Jun 1998 18:43:30 -0600
To: [email-masked]
Subject: 3-21G* vs 6-31G*

One of the reasons that 6-31G* is preferred over 3-21G* is that, strictly speaki
ng, 3-21G* does not use polarization functions on 'first-row' atoms C,N,O,F.
This is a big problem for things like amines, where generally the amine is 
too flat (pyramidality is underestimated). We have noticed a similar thing
with R3O+ species (protonated benzene oxide, JPC A, 1997, 3371), but I'm sure
that this must have been noticed before. Another problem is that cationic-metal
to oxygen distances are a little too short (JPC, 1995, 3793 - 3-21G = 1.89,
6-31G* = 1.97, Expt = 1.96). This is a problem with the valence region, since
in other systems 6-21G ~ 3-21G, and not with the core, as we initially thought.

-Cory
=============

#2 Frank Jensen

 Jun 23 Frank Jensen       (66)   Re: CCL:3-21G vs. 6-31G(d) geom optCommand: Read MessageMessage 2/5 from Frank Jensen                            Jun 23 '98 at 7:51 am

Date: Tue, 23 Jun 1998 07:51:40 +0200 (METDST)
To: "E. Lewars" <[email-masked]>
Subject: Re: CCL:3-21G vs. 6-31G(d) geom opt
Message-ID: <[email-masked]>
MIME-Version: 1.0

        At the HF level, bigger basis means converging toward the
HF limit. This has some known deficiencies, like all (covalent) bonds
being too short. Using a smaller basis gives longer bond lengths,
and 3-21G(*) may be some sort of "Pauling" point, where some "magic"
cancellation of errors occurs. I would consider the 3-21G as being
too small in the core region, and results may in some case be
unpredictable, i.e. the average error may be better than 6-31G*,
but the maximum deviation may be larger. The 6-31G* should give more
uniform results, but they have a systematic error. Using the same basis
for HF and MP2 gives you a chance of evaluating the correlation effect,
independent of the basis set effect. One could probably come up with
an empirical scheme for adding corrections to the HF/6-31G* results
give give better answers than HF/3-21G(*), but then again DFT would
probably beat that any day...
        And yes, relative energies would certainly be better with
the 6-31G*, but again subject to systematic errors.

        Frank
=============
#3 Alan Shusterman
 Jun 22 Alan Shusterman    (42)   Re: CCL:3-21G vs. 6-31G(d) geom optCommand: Read MessageMessage 3/5 from Alan Shusterman                        Jun 22 '98 at 11:27 pm

Message-id: <[email-masked]>
Date: 22 Jun 98 23:27:10 PDT
Subject: Re: CCL:3-21G vs. 6-31G(d) geom opt
To: [email-masked]

--- You wrote:
The 3-21G (strictly, 3-21G*) basis set gives geometries which are actually a
bit better than those from the 6-31G* set (Hehre, "Practical Strategies for
Electronic Structure Calculations", p 23;
--- end of quote ---
I've read p 23, but I can't find a statement saying 3-21G* is "a bit better"
than 6-31G*. There certainly are examples in the tables where 3-21G(*) performs
better, but there are counter-examples too (and a statistical analysis,
assuming a fair one is possible, might show that 6-31G* errors are, on average,
smaller).

Another thing to keep in mind is that bond distances are only one aspect of
molecular geometry. The statement on p. 23 makes no mention of bond angles,
dihedral angles, and so on. 3-21G* is not very effective at certain problems,
such as amine bond angles.

These objections do not get at your real question, however, which is "why
should one do the extra work associated with a larger basis set?" (Larger, by
the way, only in regard to Gaussian primitives; the number of contracted
functions in 3-21G* and 6-31G* are the same.) 3-21G* geometries should be
satisfactory in most cases.

Alan

---------------
Alan Shusterman
Department of Chemistry
Reed College
Portland, OR
www.reed.edu/~alan
==========

#4  German Sastre Nava

 Jun 23 German Sastre Nava (48)   Re: CCL:3-21G vs. 6-31G(d) geom optCommand: Read MessageMessage 4/5 from German Sastre Navarro                   Jun 23 '98 at 4:18 am

Subject: Re: CCL:3-21G vs. 6-31G(d) geom opt
To: [email-masked] (E. Lewars)
Date: Tue, 23 Jun 1998 04:18:17 -0400 (EDT)

  Hi,

> So why (judging by the literature) is the 6-31G* basis usually preferred for
> HF-level geometries?  Is it because of an unexamined belief that bigger is
> better?  Or is it because *relative energies* are better at the HF/6-31G* leve
l
> than at the HF/3-21G level?  

  In the kind of reactions I'm used to work in (adsorption of organic mol.
  over alumino-silicates) this is indeed the case. 3-21g* tends to overestimate
  adsorption energies and also activation energies. Apart from that, another
  minor problem seems to be the relatively high atomic charge separation
  in 3-21g*.

>                              If this is the reason, then in those cases where
>*both* HF and MP2 (or other correlated) calculations are reported, would it not
t
> be better to do the HF calculations using 3-21G optimizations (then use MP2/
> 6-31G* or bigger for the post-HF jobs)?

  I very much agree. I hope the rest of the CCL can also give their view
  over this interesting question.

  Regards
  German
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