Subject: Meaning of eigenvalues in density functional theory

From: Uli Salzner <[email-masked]>
Date: Tue, 19 Mar 1996 13:22:13 -0330 (NST)

Dear Netters,

Callaway and March (Sol. State Phys. 38, 135 (1984)) discuss the meaning 
or better "non-meaning" of eigenvalues in density functional methods. It 
seems that the band gap of a sufficiently large system can be calculated 
by taking the energy difference between the valence and the conduction 
band but that the difference between HOMO and LUMO in molecules can not 
be used in connection with Koopman's theorem. I am wondering whether this 
is the end of the story or whether it is possible for practical purposes 
to use HOMO and LUMO levels. Would that be a crude approximation or total 
garbage? 

I am especially interested in density functional methods as implemnented in 
GAUSSIAN 94, which lists the HOMO and LUMO levels in DFT just as for HF. It 
is quite tempting to use them and as far as I tried the results seem to be 
reasonable. What I would like to do is to compare solid state calculations 
(with Cerius2) and calculations for oligomers of increasing size and try to 
extrapolate towards the solid. I am only interested in systems at 0 
temperature where the occupation of the one-electron functions is either 
0 or 1.

I would be very thankful for any comments or related references. A 
summary of the answers will be posted.

Thanks in advance,
Uli

[email-masked]