Subject: Small eigenvalues of overlap matrix

From: Andrew Horsfield <[email-masked]>
Date: Thu, 4 Nov 1999 09:04:15 +0000 (GMT)

Hi,

I am writing an LCAO-DFT code using numerical orbitals. For some basis
sets the overlap matrix acquires very small eigenvalues, and this leads to
ghost states with very low energy.

I have heard of two ways to fix this:

1) Diagonalise the overlap matrix, shift the very small eigenvalues up,
   and then reconstruct the overlap matrix;

2) Diagonalise the overlap matrix, remove the eigenvectors with very small
   eigenvalues, and transform the overlap and Fock matrices accordingly.

Are there any recommendations as to which is better? (The first approach
would be a lot more convenient, but only if it works!)

Cheers,

Andrew

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---

From: [email-masked]
Date: Thu, 4 Nov 1999 10:31:05 -0800

On Nov 4,  9:04am, Andrew Horsfield wrote:
> Subject: CCL:Small eigenvalues of overlap matrix
> Hi,
>

Hi Andrew,

It might not be as good either way: both try to alter the overlap matrix (and
all the other things down the road).  I suggest you to precondition the basis
functions (only for atom-centered ones, of course) by schmidt orthogonalizing
those attached to the same nuclei.  This will eliminate much of the linear
dependencies that could be seen in methods utilizing analytical integration
with GTO basis functions, and can be done effortlessly on an atomic grid.

Good luck,
Liang