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

From: "Elena Jakubikova" <[email-masked]>
Date: Tue, 22 Jan 2002 20:22:35 -0700

Dear CClers,

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?

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?

Thank you very much for your help!

Elena

--------------------------
Elena Jakubikova
graduate student
Department of Chemistry
Colorado State University

_________________________________________________________________
Send and receive Hotmail on your mobile device: http://mobile.msn.com

---

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

Dear Elena,
  
> 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 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
-- 
  =====================================================================
     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
  =====================================================================