Subject: summary: DFT MO energies

From: [email-masked] (Georg Schreckenbach)
Date: Wed, 15 Oct 1997 13:43:50 -0700

Dear CCL readers,

last week, I posted a question about DFT MO energies,
and how they are different in hybrid methods vs. GGA or LDA.
I got a few interesting replies -- thanx to those who took the
time to write! If anybody wants to comment further, please
do so, either to me, or to the CCL. I have posted this summary
also at my webpages, cf.
http://www.t12.lanl.gov/~schrecke/research.DIR/CCL_DFTMOEnergies.html

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Original question:

Date: Fri, 10 Oct 1997 10:59:01 -0700
Subject:DFT MO energies

Dear CCL readers,

is anybody aware of papers that study DFT orbital energies?
More precisely, I would like to learn how those orbital energies
(Kohn-Sham eigenvalues) are different in hybrid methods like
B3LYP as compared to GGAs like BP86 or PW91, or also as
compared to the LDA. If there are systematic differences (which
I am sure is the case) then I would like to know how they can
be understood.
    There was recently some discussion on the
list about the possible physical meaning of the Kohn-Sham
eigenvalues. While this is an interesting subject in itself,
it is, this time, *not* my question.

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Reply by Jon Rienstra <[email-masked]>

In general, the hybrid methods are to some degree sucessful in
incorporating some of the HF electron self-interaction cancellation, and
in many cases succeed in giving negative HOMO energies, even in anions.
GGA's on the other hand often give positive HOMO energies (esp in anions),
and much recent debate has focused on whether or not this is
problematic.
For more details see:
See Galbraith and Schaefer, J. Chem. Phys. 105, 1996 p. 862
and
Rosch and Trickey, J. Chem. Phys. 106, 1997 p. 8940

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Reply by P. A. Politzer <[email-masked]>

Dear Dr. Schreckenbach,
We have recently finished a comparison of Hartree-Fock and various DFT
Kohn-Sham orbital energies.  There are indeed some interesting patters.
The paper has been submitted to Theoretical Chemical Accounts.  I will
be glad to send you a preprint.     Best regards,   Peter Politzer

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Reply by Ulrike Salzner <[email-masked]>
(this one was also posted to the CCL)

Dear Georg,
I have testet DFT orbital energies for some small and medium sized
organic systems with pi-bonds (acetylene oligomers, thiophene monomer
through trimer, pyrrole and similar systems). There are significant
differences between LSDA and hybrid methods. The paper will soon appear
in the Journal of Computational Chemistry.

 To summarize: The IPs (negative HOMO energies) are closer to experiment
with hybrid functionals than at LSDA. The P86 correlation functional
seems to work better than the LYP correlation functional. All IPs with
DFT are smaller than experimental values (about 0.5 - 1 eV) and smaller than
at HF with the same basis set which are quite close to experiment. In my
limited data set it looks like there is little depenedence of the quality
of IP on the size of the system.

 The negative LUMO energies used as EAs are by far superior with all DFT
methods than with HF. LSDA works slightly better than hybrid
functionals. Again the P86 correlation functional works better than LYP.
I obtained the "experimental EAs" using experimental IPs and excitation
energies. So they have to be treated with some caution. It looks like the
agreement improves as the systems get larger. But the data are more than
insecure.

According to this, DFT corrects for the main deficiency of HF theory and
brings the LUMO down. I reasoned that this must have to do with the error
in the Coulomb terms in HF which seems to be absent in DFT. I was pleased
to see that Baerends et al. came to a similar conclusion in their feature
article in J. Phys. Chem.

 The main error in DFT seems to be due to the IP and not to the EA. Taking the
difference between the two, I got very nice excitation energies. These
improve as the systems get larger. The agreement is pretty poor for
monomers but with trimers of purrole and thiophene the excitation
energies become good.

I also tried what happens when the weight of the HF exchange is
increased. I got the best HOMO-LUMO gaps with 30% HF exchange instead of
20%. Geometries were not changed by this. For ethylene I increased the HF
exchange stepwise up to 100%. There is no convergence. With 100% HF
exchange the gap is as bad as with HF but the orbital levels are shifted
compared to those at HF. So all this fudging is empirical and can - at
least for now - not be put on solid theoretical ground.

As for my personel interest in the band gaps of conducting polymers this
is good enough. Needless to say that I had major problems to publish
this. It took 1 1/2 years and one reviewer said it was not interesting
enough for rapid publication.  But the first paper is in press now as
mentioned above. There will be two more papers extending these findings
to band gaps of polymers by extrapolation. These are submitted to J.
Phys. Chem. and Synth. Met. Maybe in two years you can read them.

By the way. You're right I am German. I keep writing in English so more
people can read it.

 Cheers,

Dr. Ulrike Salzner

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Reply by Heinz Schiffer <[email-masked]>

Hi George,
see table III in : Garnet K.-L. Chan, David J. Tozer, and
Nicholas C. Handy, Correlation potentials and functionals
in Hartree-Fock-Kohn-Sham theory, J. Chem. Phys. 107(5) (1997) 1536-1543
Ciao
Heinz
-----------------------------------------------
(End of summary)

Best regards, Georg

--
Dr. Georg Schreckenbach           Tel:     (USA)-505-667 7605
Theoretical Chemistry T-12        FAX:     (USA)-505-665 3909
M.S. B268, Los Alamos National      E-mail:  [email-masked]
Laboratory, Los Alamos, New Mexico, 87545, USA
Internet:    http://www.t12.lanl.gov/~schrecke/