Subject: SUMMARY: DFT AND SPIN STATES

From: Sergey Gorelsky <[email-masked]>
Date: Mon, 20 Mar 2000 12:38:29 -0500 (EST)

There was a clear interest of many people to see the results on the topic
"DFT and spin states". Here is a summary of what I got from my (I am sure,
not complete) library search and replies from

Dmitry Khoroshun ([email-masked])
Klaus Stark ([email-masked])
T. Daniel Crawford ([email-masked])

Definitely, the Hartree-Fock model with no account of correlation effects
will significantly overstabilize high-spin states. Since LSD and GGA
include correlation, their performance will be superior to HF. However, it
looks like they (and LSD, in particular) have "too much correlation and
too little exchange" and, thus, they overstabilize low-spin states. The
hybrid functionals in which a fraction (around 20%) of the Hartree-Fock
exchange energy is combined with the density functional exchange seems to
correct this "correlation-exchange" misbalance and, as a result, they give
quite accurate results for molecular energetics.  

For instance, for (C5H5)CrCl2(PH3)n the energy of the doublet state is
going up compared to the energy of the quartet state by 5-7 kcal/mol when
going from BLYP to B3LYP functionals. [Cacelli, I.; Keogh, D. W.; Poli,
R.; Rizzo, A. J. Phys. Chem. A 1997, 101, 9801]

So, all of this can be summarized in the following diagram:

                    "OVERSTABILIZATION"
low spin <----------------- 0 -------------------> high spin
 states                                             states

  LSD <-------- GGA <-------hydrid functionals -----> HF

There is a recent paper "Assessment of exchange correlation
functionals" by A. J. Cohen and N. C. Handy [Chem. Phys. Lett., 316
(2000), 160]. However, I did not find similar reviews on the performance
of DFT with respect to the energies of different spin states. 

It is also to be kept in mind that
"LSD and GGA accounts of correlation are expected to be more trustworthy
for antiparallel spins than for parallel spins, although the practical
consequences of this for open-shell systems are not yet clear" (see
K. Burke and J. P. Perdew, Intr. J. quant. Chem., 1995, v. 56, 199 and
recent review of J. Li, L. Noodleman and D. A. Case in "Inorganic
Electronic Structure and Spectroscopy, Volume I, p.661, John Wiley &
Sons: 1999)
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From: Dr. Klaus Stark <[email-masked]>

DFT has a problem with high-spin states. With most functionals the
low-spin state is preferred over the high-spin state even is the latter is
known to be the minimum energy state. However, the bond lengths and angles
are reproduced very nicely. In some cases BP86 is able to reproduce the
correct minimum spin state. I heard that B3LYP should work better,
however, I cannot give a reference. If your systems allows, you can check
the spin state energy order with less costly methods on the DFT geometry,
ZINDO works nicely, for instance. It gives the correct qualitative spin
state order. However, it is not clear if the quantitative energy
difference is reproduced very well.
__________________________________________________

From
T. Daniel Crawford, Ph.D.                Institute for Theoretical
Chemistry
[email-masked]            Departments of Chemistry and
Biochemistry
http://zopyros.ccqc.uga.edu/~crawdad/         The University of Texas

There have been numerous UDFT computations on transition-metal compounds,
including open-shell states. See the recent review article by Siegbahn,
for example:

P. E. M. Siegbahn, "Electronic Structure Calculations for Molecules
Containing Transition Metals", Adv. Chem. Phys., 1996, 93, 333

Many of the more recent computations for metals have included "broken
symmetry" calculations for antiferromagnetically coupled singlets. These
are simply the DFT analogs of the well-known UHF approach where and
RHF->UHF orbital instability has been followed to obtain different alpha
and beta densities.  You may want to look at a reference by Noodleman for
a reasonable review of this issue:

L. Noodleman and D. A. Case, "Density-Functional Theory of Spin
Polarization and
 Spin Coupling in Iron-Slufur Clusters", Adv. Inorg. Chem., 1992, 38, 423

Please feel free to send your additional comments to me.

Sergey Gorelsky

________________________________________________________________  

  Sergey Gorelsky, M. Sc.                   
         Department of Chemistry, York University                        
         4700 Keele St., Toronto, Ontario M3J 1P3, Canada            
         tel.(416) 736-2100 ext#77720 and ext#70131
         fax:(416) 736-5936   
  http://www.chem.yorku.ca/grad/SG/                                   
________________________________________________________________