Subject: SCF Following SZABO AND OSTLUND.

From: Ahmed Bouferguene <[email-masked]>
Date: Thu, 13 Feb 1997 15:38:28 -0500 (EST)

Hi netters,

        Recently, I've sent an e-mail about the SCF procedure.  I am giving in the following a simple numerical example. 

I have the following overlap matrix : 

0.10000000000000D+01 0.99989484007995D+00 0.70348115348149D+00 0.69969766642474D+00 
0.99989484007995D+00 0.10000000000000D+01 0.69969766642474D+00 0.69602330987765D+00 
0.70348115348149D+00 0.69969766642474D+00 0.10000000000000D+01 0.99989484007995D+00 
0.69969766642474D+00 0.69602330987765D+00 0.99989484007995D+00 0.10000000000000D+01

Its eigenvalues are : 

0.274360D-04 0.155635D-03 0.600468D+00 0.339935D+01

and the eigenvectors are : 

-.503096D+00 -.499451D+00 -.496885D+00 0.500548D+00 
0.496885D+00 0.500548D+00 -.503096D+00 0.499451D+00 
0.503096D+00 -.499451D+00 0.496885D+00 0.500548D+00 
-.496885D+00 0.500548D+00 0.503096D+00 0.499451D+00

Following Szabo & Ostlund, the first column should not be used in the iterative process 
since it correponds to a small eigenvalue (Lower than 1.E-4). Thus when solving the 
equation H C = E S C where H is the matrix

-.11277523049429D+01 -.11280949486585D+01 -.97027798826701D+00 -.96980576230702D+00 
-.11280949486585D+01 -.11284603267647D+01 -.96980576230702D+00 -.96938059876316D+00 
-.97027798826701D+00 -.96980576230702D+00 -.11277523049429D+01 -.11280949486585D+01 
-.96980576230702D+00 -.96938059876316D+00 -.11280949486585D+01 -.11284603267647D+01

The results are as follows : 

Without dropping the vector correponding to the small eigenvalue I have the following energies :  
-.127209D+01 -.611606D+00 -.217560D+00 0.446120D+00

And by dropping that eigenvector I have :  
-.127209D+01 -.527195D+00 -.217560D+00 ----------

The first and the third are correct but the secon is not. That's my trouble. 

Do not hesitate to give me your point of view. Thanks in advance