Sent to CCL by: Rene Fournier [renef(a)yorku.ca]
Hello,
I agree on
All commonly used basis
sets, even the Pople-style sets, are generated by optimizing
exponents and contraction coefficients to minimize (ab initio)
energies of atoms and sometimes molecules.
That's correct. But there are other problems with choices of basis
sets and that's where empiricism can creep in. How many contracted
functions is enough? What's the best contraction pattern?
(why 6-31G and not 6-21G? or 4-31G? or 9-61G? or 7-1111G?)
How many polarization functions? Why not throw in a few
bond-centered functions?
Many basis sets went into oblivion not because they gave higher energies
for atoms or molecules --- adding more functions and keeping them
uncontracted
always lowers energy. It's that they did not give good agreement
with experimental
bond lengths, bond energies etc. relative to other basis sets of comparable
computational cost. I'm not sure how to call methods where high-level theory
is used instead of experiment as the reference to assess goodness of
a lower level
of theory (maybe a smaller basis). I think it's still empirical
because there's
the assumption that if the low-level theory reproduces high-level theory to
within some accuracy for cases X, Y, Z, it will also reproduce high-level
level theory to that accuracy for other cases when we do applications.
( There's also the obvious point that if the high-level theory reference is
really, really good, then it IS the experimental result! )
It is possible to take empiricism out of basis set choice by doing
many calculations in a sequence with increasingly big basis sets defined
by only 1 and maybe 2 parameters, so that one can crank up accuracy smoothly,
and extrapolate results to "infinite basis set". Basis sets suitable
for
that are:
- even-tempered fully uncontracted basis sets (K Ruedenberg);
- plane-waves (increase energy cut-off and box size);
- all-numerical programs (mostly for diatomics, Becke's NUMOL for
polyatomics).
But I don't see that done very often, even with plane-waves where it would be
easy I suppose.
Regards,
Rene
Rene Fournier Office: 303 Petrie
Chemistry Dpt, York University Phone: (416) 736 2100 Ext. 30687
4700 Keele Street, Toronto FAX: (416)-736-5936
Ontario, CANADA M3J 1P3 e-mail: renef---yorku.ca
On Wed, 12 Dec 2007, Kirk Peterson kipeters-*-wsu.edu wrote:
Sent to CCL by: Kirk Peterson [kipeters-$-wsu.edu]
As a sidebar to this discussion, I have to strongly disagree that
basis set parameters, exponents or contraction coefficients,
use empirical data in their construction. All commonly used basis
sets, even the Pople-style sets, are generated by optimizing
exponents and contraction coefficients to minimize (ab initio)
energies of atoms and sometimes molecules. Some of the Pople-style
basis sets utilize scale factors to apply to atom-optimized exponents,
but these were based on (ab initio) molecular calculations
and not experimental data.
regards,
-Kirk
On Dec 12, 2007, at 8:21 AM, Rene Fournier renef+*+yorku.ca wrote:
>
> Sent to CCL by: Rene Fournier [renef\a/yorku.ca]
> David Craig and Robert Parr first used "ab initio" in quantum
> chemistry,
> see
> http://www.quantum-chemistry-history.com/Parr1.htm
> Near the middle of that page, Parr recounts:
>
> " Craig and I published this paper on "configuration interaction
in
> benzene", where we took the pi-system and did essentially a complete
> configuration interaction calculation on it.
>
> That has some trivial historical interest in that it was there that
> the
> word, the term ab initio was introduced. Craig and Ross had computed
> everything from the start in London and I had personally computed
> everything from start in Pittsburgh. Then we compared our answers
> when we
> were finished- This involved computing of all the integrals as best as
> they could be done and selecting the configurations to mix for the
> ground
> and exited states because there were electronic states that were of
> experimental interest and we checked our answers one against each
> other
> when we were finished. And what the paper says is, that these
> calculations
> were done ab initio by Craig and Ross and by me, independently. And
> Mulliken later said that this was the introduction of the term ab
> initio
> into quantum chemistry. In the short review that you have, I talk
> about
> this and reproduce a picture of a letter from Craig to me where he
> uses
> the term ab initio in a different context. So ab initio was
> introduced in
> the quantum chemistry by Craig in a letter to me and I put it into the
> manuscript. That's where ab initio came from. "
>
>
> Funny thing is Parr later became a champion of Density Functional
> Theory
> and for many years (70's, 80's) DFT practitioners were often
> criticized
> for doing calculations that were not "ab initio". I think views
have
> changed now; "first-principles" was introduced probably to say
> "mostly
> not empirical" but without the implications "ab initio" had
acquired
> over
> the years. The term "ab initio calculation", as it's commonly
used,
> very rarely refers to a calculation "devoid of empiricism", for
> example
> the choice of basis set parameters is almost always empirical,
> see discussion on
>
http://www.ccl.net/chemistry/resources/messages/2001/11/28.002-dir/index.html
>
> Rene Fournier Office: 303 Petrie
> Chemistry Dpt, York University Phone: (416) 736 2100 Ext. 30687
> 4700 Keele Street, Toronto FAX: (416)-736-5936
> Ontario, CANADA M3J 1P3 e-mail: renef*_*yorku.ca
>
>
> On Wed, 12 Dec 2007, Christoph Etzlstorfer christoph.etzlstorfer .
> jku.at wrote:
>
>> There is a story about that in Michael J.S. Dewars biography "A
>> semiempirical life", American Chemical Society, 1992, p. 129.
>>
>> Best regards
>>
>> Christoph
>>
>>
>> Am 11.12.2007 um 03:13 schrieb Tommy Ohyun Kwon ohyun.kwon _
>> chemistry.gatech.edu:
>>
>>>
>>> Sent to CCL by: Tommy Ohyun Kwon [ohyun.kwon .
chemistry.gatech.edu]
>>> Dear CCLers;
>>> I would appreciate it if anyone could tell me who used the term of
>>> "ab initio
>>> calculations" first.
>>> Thank you very much for your kind attention.
>>>
>>> Best wishes,
>>>
>>> Tommy
>>>
>>>
>>> --
>>> Tommy Ohyun Kwon, Ph.D
>>> School of Chemistry and Biochemistry
>>> Georgia Institute of Technology
>>> Atlanta Georgia, 30332
>>> Email: ohyun.kwon]*[chemistry.gatech.edu
>>>
>>>
>>>
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>>
>> ####################################################
>> www.etzlstorfer.com
>> ***********************************************************
>> Dr. Christoph Etzlstorfer Phone: *43-732-2468-8750
>> Universitaet Linz Fax: *43-732-2468-8747
>> A-4040 Linz E-mail: christoph.etzlstorfer,+,jku.at
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>>
>>
>>
>>
>
>
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