CCL: origin of ab initio/basis set empiricism



 Sent to CCL by: Marcel Swart [marcel.swart-*-icrea.es]
 About the basis sets extrapolation, it is done, see for instance:
 Bak, Jørgensen, Olsen, Helgaker, Klopper
 J. Chem. Phys. 2000, 112, 9229-9242
 On Dec 13, 2007, at 2:39 PM, Rene Fournier renef++yorku.ca wrote:
 
 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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 ===================================
 dr. Marcel Swart
 ICREA researcher at
 Institut de Química Computacional
 Universitat de Girona
 Parc Científic i Tecnològic
 Edifici Jaume Casademont (despatx A-27)
 Pic de Peguera 15
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 marcel.swart|-|udg.edu
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