Subject: DFT cancellation of errors

From: [email-masked] (Dave Young)
Date: Fri, 25 Feb 94 08:19:40 -0500

In response to the previous allusion to a cancellation of errors
in DFT (Density Functional Theory).

	When the current generation of ab initio programs reports
frequencies, they are reporting frequencies as predicted by the 
harmonic oscillator approximation.  Since the real internuclear potential
actually looks more like a Morse potential than a harmonic potential,
these calculations tend to report frequencies that are too high by
about 10%.

	In the DFT calculations, we have been seeing frequencies
which are closer to the experimental frequencies than predicted by 
Hartree Fock, MPn or nCI.  If the calculation were really getting the 
shape of the internuclear potential correct, we would be getting 
results approaching the Harmonic frequencies not the observed frequencies.

	Thus the cancellation of errors is that the error due to the
harmonic oscillator approximation is cancelled by the error due to the 
wrong shape of the internuclear potential.  

	Note that this cancellation is not perfectly consistent, but it 
does result in DFT frequencies being closer to observed than the 
other ab initio methods.

	A good reference, where frequencies are compared to both the 
observed and the harmonic frequencies is the paper by B. G. Johnson,
P. M. W. Gill & J. A. Pople, J. Chem. Phys.  98 (7), page 5612, 1 Apr 93.

				Dave Young
				[email-masked]
				youngdc@msucem