Subject: Problem with LCAO for solids

From: Andrew Horsfield <[email-masked]>
Date: Thu, 11 Nov 1999 14:47:57 +0000 (GMT)

Hi,

I have had a problem with applying an LCAO-DFT (using numerical orbitals)  
method to solids. When I expand the basis set from sdps*p* to sdps*p*d*
(i.e. I add an extra set of d orbitals), I suddenly get ghost states
(eigenvalues with very low energies - one or two orders of magnitude too
big). I originally thought this was due to the ill conditioning of the
overlap matrix. But on inspection I find that its smallest eigenvalues are
about 0.0005, which does not seem all that small. I have tried shifting
the small eigenvalues up in value, but this makes no difference at all.
Can anyone suggest another possible cause for this problem?

Cheers,

Andrew

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From: "Konstantin N. Kudin" <[email-masked]>
Date: Fri, 12 Nov 1999 13:59:28 -0600 (CST)

> Can anyone suggest another possible cause for this problem?

 What you have there is called linear dependencies (LD). The problem will
go away after you eliminate few smallest eigenvalues/eigenvectors from the
overlap matrix. The relation between the magnitude of smallest overlap
eigenvalue and LD is not very straightforward, and 0.0005 value can
certainly lead to LD in some occasions.

 You can also try to overcome the problem by increasing the accuracy of
the Kohn-Sham matrix evaluation or doubling the unit cell size.

 The following reference contains a discussion of LD for GTO basis sets,
however, the stuff is actually more general and can apply to your case as 
well:

 Choosing GTO basis sets for periodic HF calculations
A. Gruneich, B. A. Heb, Theor. Chem. Acc., 100, 253 (1998).

 Regards,
 Konstantin Kudin