Subject: Re: CCL:linearly dependent basis set or the mystery of the large alpha MO

From: uccatvm <[email-masked]>
Date: Wed, 23 Jan 2002 15:13:46 +0000 (GMT)

Dear Elena,
  
> I would like to learn more about the problem of nearly linearly
> dependent basis set and very large MO coefficients that arise thanks
> to this problem. I have read in the Gaussian manual that these large
> coefficients may lead to subtantial numerical errors and that in case
> any MO is larger than 1000, the calculation is aborted. Does any of
> you have an idea how big these numerical errors might be if my largest
> MO is of the order 100? When do I really need to start worry about
> numerical accuracy of the calculation, at which value of the largest
> MO coefficient? And finally, how does Gaussian program deal with the
> problem of very large coefficients, is it trying to correct the
> problem in any way (for example by excluding certain basis functions
> > from further calculation) or it just continues calculation
> irrespectively of what the error might be on the end?

Gaussian deletes eigenvectors of the overlap matrix belonging to small 
eigenvalues (threshold value 10E-5). You may want to read David Feller's
messages to CCL on this subject: see CCL archive of Jan 21, 2000. 

In my experience, you have to really careful if you compare energies
obtained with different programs, as these may have different threshold
values for deleting the eigenvectors. Feller reports an energy difference
of more than 4 millihartree for Ar computed with G98 and other programs
that do not delete almost linearly dependent functions.

> 
> I also tried to learn some more about this problem from the
> literature, but I was not very successful. The only paper touching
> this problem I found was 'A. Wallis, D.L.S. McElwain, H.O. Pritchard,
> "Variation method and the algebraic eigenvalue problem.",
> Int.J.Quantum Chem. 3(5), 711-722 (1969).' Does anybody know where can
> I find some more information about this?

I encountered problems with almost linearly dependent functions
with basis sets containing large sets of bondfunctions: see
T. van Mourik, R.J. Vos, J.H. van Lenthe and F.B. van Duijneveldt, 
Int. J. Quant. Chem. 63, 805 (1997). It is a bit of a special case,
but it may be of interest if you want to learn more about this subject.

Hope this of any use to you,

Tanja
-- 
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     Tanja van Mourik                                                
     Royal Society University Research Fellow
     Chemistry Department 
     University College London    phone:    +44 (0)20-7679-4663      
     20 Gordon Street             e-mail:   work: [email-masked] 
     London WC1H 0AJ, UK                    home: [email-masked]     

     http://www.chem.ucl.ac.uk/people/vanmourik/index.html
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