Subject: CCL: Density Functional Theory

From: [email-masked] (George Fitzgerald)
Date: Fri, 25 Feb 94 15:40:41 CST

Dear Netters,

In response to Bob Williams' questions on DFT, I would like to make
the following observations:

> What is the relative speed of DFT optimization
> and frequency calculations on a large molecule
> at modest levels of theory
> (compared to a similar RHF/4-31G job)

The question of relative speed can not be answered without further 
discussion of different "flavors" of DFT.  In the codes such as DGauss
(from Cray) or deMon (from Montreal) the Coulomb term is replaced by 
a three-center integral based on Dunlap's charge fitting scheme.  This 
gives a significant speedup relative to doing the exact 4-center Coulomb
integration.  However, not all DFT codes do this.  I understand that 
both Gaussian's and CADPAC's DFT routines use 4-center Coulomb integrals.

Since I do only 3-center Coulomb integrals in my work, I can only make the
comparison between 3-center DFT and 4-center Hartree-Fock.  In my 
experience, such DFT codes are at least one order of magnitude (10x) 
faster for SCF, gradient, & hessian calculations.

> Also, we would like to know something about
> the quality of the force matrix and frequencies
> produced by modest level DFT calculations,
> and about the transferability of scale factors.
> That is: how does the "cancelation of errors" produced by
> DFT compare to that from the 4-31G level.

Less work exists comparing DFT force constants to experiment than
Hartree-Fock vs. experiment.  In my experience, the average error 
of DFT frequency (not force constant) is about 5% vs expt.  The 
value typically quoted for Hartree-Fock 6-31G* is about 10%.  However,
the Hartree-Fock seem to be more consistent than the DFT.  That is,
Hartree-Fock scaled by .9 (or what ever your favorite scale factor is)
are quite reliable.  In my experience, there is no comparable,
reliable scale factor for DFT computations, but given the relative speed
of DFT, many users still find it extraordinarily useful.

Be aware that at this point in time, the number of DFT results in the 
literature is tiny compared with the Hartree-Fock.  With the recent 
advancements in analytic DFT 2nd derivative methods we can expect the 
DFTers to begin to catch up.  

It is also important to keep in mind that the 4-31G basis may not be 
suitable for DFT computations.  This is certainly the case if one does
charge fitting.  We generally use basis sets which are comparable in 
size to 6-31G*, although we have re-optimized them for the DFT potential.

George Fitzgerald
Cray Research, Inc.
655E Lone Oak Dr.
Eagan, MN 55121
[email-masked]