>Date: Fri, 26 Apr 91 17:08:05 CDT
>From: jwa@hidalgo.cray.com (Jan Andzelm)
>To: jkl%ccl.net@timbuk.cray.com

TO: John E. Bloor (bloor@utkvx1.bitnet)
FROM: Jan W. Andzelm (jwa@cray.com)


Hi John,

Thanks for interest in DGauss. The another program, you are interested in
is Dmol from Biosym.
Here is some information as to the method and applications of DGauss.
DGauss was developed in Cray and it is distributed within a Unichem
system. Since you have asked about the references and the accuracy 
of the method I will skip issue of performance. I only mention 
that the DFT method can be design as a N**3 algorithm, so it can be
much faster than the Hartree-Fock and the wave-function based  
correlated methods. The method used in DGauss has been developed and
applied for the last ten years by several research groups, to mention 
only some names:  B.I. Dunlap, D.R. Salahub, J.W. Mintmire, N. Rosch,
F.W. Averill, J.W. Andzelm, N. Russo, E. Wimmer.

DGauss is a density functional (DFT) program utilizing 
Gaussian orbitals.  It solves Kohn-Sham equations
--P.Hohenberg, W.Kohn, Phys. Rev. B 136 (1964) 864;
--W. Kohn and L.J. Sham, Phys. Rev. A 140 (1965) 1133;
using Local Spin Density Hamiltonian (VWN) of Vosko et al.
--S.H. Vosko, L. Wilk and M. Nusair, Can. J. Phys. 58 (1980) 1200.

A few words about the technique, LCGTO-LSD, used in DGauss follows.
The idea of using gaussians in DFT goes back to 1975
--H. Sambe and R.H. Felton, J.Chem.Phys. 62 (1975) 1122; 
it was refined substantially by Dunlap et al. 
--B.I. Dunlap, J.W.D. Connolly and J.R. Sabin, J.Chem.Phys. 71(1979)3396;
the development of the method and applications up to 1987 are in
--D.R. Salahub, in "Ab initio Methods in Quantum Chemistry-II",
Ed. K.P. Lawley, J.Wiley & Sons, New York, (1987) p447;
the present status and many references to the method you can get
from the work of Dunlap, Salahub, Andzelm, Mintmire, Wimmer et al., in
--"Density Functional Methods in Chemistry", Springer-Verlag, 
Eds. J.K. Labanowski and J.W. Andzelm, Springer-Verlag, 1991.  (**)

In short, the LCGTO-LSD method relies on the variational,
analytical approximation to the density ( Dunlap et al.,
J.Chem. Phys. 71 (1979) 3396). This requires, that the three
center Coulomb-type integrals are calculated exactly. That can be
accomplished, very efficiently if Gaussians are used. 
Very recently, the method gained a variational approximation to the
exchange-correlation potential (Phys. Rev. A42 (1990) 6354) but this
is not yet programmed in DGauss. Instead, a fitting of the exchange-
correlation potential involving numerical integration is done.

LCGTO-LSD technique can utilize popular Pople's Gaussian
basis sets and this is ok for geometry, but for energetics the
LSD optimized basis sets or LSD pseudopotentials should be used.
Some literature on the LSD basis sets and their performance follows:
--N. Godbout, J.W. Andzelm, E. Wimmer and D.R. Salahub, Can. J. Chem.
to be submitted.
--J.W. Andzelm, E. Radzio and D.R. Salahub, J. Comput. Chem. 6(1985) 520;
J. Chem. Phys. 83 (1985) 4573.
--Salahub, Andzelm, Dixon, Redington, Caldwell, Hill et al. in
"Density Functional Methods in Chemistry", Springer-Verlag, 1991. 

LCGTO-LSD method has now analytic gradients. 
The theory of gradients and some applications to geometry optimization,
of relevance to DGauss are in the following papers:
--J.W. Andzelm, in "Density Functional Methods in Chemistry",
Eds. J.K. Labanowski and J.W. Andzelm, Springer-Verlag, 1991 p155; 
--D.R. Salahub, R. Fournier, P. Mlynarski, I. Papai, A. St-Amant and 
J. Ushio, ibid. p77;
--D.A. Dixon, J. Andzelm, G. Fitzgerald, E. Wimmer and P. Jasien,
ibid. p33
--R.A. Hill, J.K. Labanowski, D.J. Heisterberg and D.D. Miller,
ibid. p357.
--P.K. Redington and J.W. Andzelm, ibid. p411.
--J.W. Andzelm, E. Wimmer and D.R. Salahub, in 
"The Challenge of d and f electrons", Eds. D.R. Salahub and 
M.C. Zerner, ACS No.394, 1989 p228;
--R. Fournier, J.W. Andzelm  and D.R. Salahub, J.Chem.Phys. 90(1989)6371;
--A. St-Amant and D.R. Salahub, Chem. Phys. Lett. 169 (1990) 387.
--B.I. Dunlap, J. Andzelm and J.W. Mintmire, Phys. Rev. A 42 (1990) 6354;
--B.I. Dunlap and N. Rosch, J. Chim. Phys-chim. Biol., 86 (1989) 671;
The above work profits from the earlier work of
--L. Versluis and T. Ziegler, J. Chem. Phys. 88 (1988) 322.
--F.W. Averill and G.S. Painter, Phys. Rev. B 32 (1985) 2141.
--P. Bendt and A. Zunger, Phys. Rev. Lett. 50 (1983) 1684;
--C. Satoko, Chem. Phys. Lett. 83 (1981) 111; Phys. Rev. B30 (1984) 1754;
and, of course, entire Hartree-Fock-Gaussian methodology.

The finding, so far, is that the LSD method is accurate enough
to reproduce bond distances within ~0.01-0.05A and angles within ~1-5deg
for various organic and organometallic molecules. 
We are writing at present a major paper with applications of LSD
to many (~100) molecules; I will send you a preprint when it is done.
In some cases LSD geometries are bad.
Those are weak interactions like hydrogen bonded systems and 
certain organometallics like carbonyls. The reason is the LSD
hamiltonian; one should use a Nonlocal Spin Density (NLSD) approach
instead.

Dgauss can calculate Nonlocal Gradient Corrections (NLSD)
to LSD energy using Becke and Perdew (so called BP)
--A.D. Becke, J.Chem.Phys. 88 (1988) 2547;
--J.P. Perdew, Phys.Rev.B 33 (1986) 8822;
or Becke  and Stoll et al. (so called BSPP)
--A.D. Becke, J.Chem.Phys. 84 (1986) 4524;
--H. Stoll, C.M.E. Pavlidou and H. Preuss, Theor.Chim.Acta 49(1978)143 
exchange and correlation gradient corrections.
Those nonlocal corrections are necessary to obtain
good dissociation energies and energetics of reactions.
Yes, NLSD can dissociate the bonds in molecules, in many cases the
accuracy obtained is comparable or better to that from ab initio methods.

We did many reactions (see e.g. in 
--"Density Functional Methods in Chemistry", Springer-Verlag, (1991)
p33, p155; and to be published;
including A-B bond dissociation reactions, hydrogenation,
reactions relating multiple and single bonds, isodesmic reactions,
acidities and proton affinities. I compare the results with those
reported by Hehre et al., in "Ab initio Molecular Orbital Theory",
W.J. Hehre, L. Radom, P.vR. Schleyer and J.A. Pople, J.Wiley&Sons, 1986.
In most cases NLSD is better than LSD, in some the difference is dramatic.
Both energetics and zero-point vibrations compare very well (typically within 
a few kcal/mol or better) with the experiment and the MP2-MP4 results.

By the way, there is an error in Table 3 of my paper in
"Density Functional Methods in Chemistry", p155.
Experimental dissociation energy of ethylene is reported as 164 kcal/mol
Obviously, the value of 177 kcal/mol obtained using NLSD method of 
Becke-Perdew, reported in Table 3, is not good. But recently, I have 
found experimental value for dissociation of ethylene of 
179.0 +/- 2.5 kcal/mol (see E.A. Carter and W.A. Goddard III,
J. Chem. Phys. 88 (1988) 3132). Now, the NLSD energy is in a very
good agreement with experimental data. The value for LSD dissociation
energy is 205 kcal/mol and, as always, it overestimates binding energy.

Good luck in using DFT method; keep us informed about your experience.

Jan W. Andzelm
(jwa@cray.com)

(**) I do not get any royalties from the sales of this book.