Subject: DFT: NO ORBITALS, NO WAVEFUNTION

From: elewars <[email-masked]>
Date: Sat, 19 Aug 2000 16:48:07 -0400

Sat, 2000 Aug 19

Hello,

We know that in pure DFT (in contrast to wavefunction theory) there are
are no orbitals and there is no wavefunction; the Kohn-Sham orbitals of
current practical DFT methods were introduced to make the calculation of
the electron density tractable.

QUESTIONS
(1) An important feature of ab initio (and semiempirical) calculations
is that one can visualize the orbitals, particularly the HOMO and LUMO
(frontier orbitals) and make chemical deductions. In a _pure_ DFT
calculation a question about the shape and energy of these orbitals
would be meaningless, right?

(2) The Fukui function (R. G. Parr and W. Yang, J Am Chem Soc, 1984,
106, 4049) seems to be always discussed in the context of DFT; yet this
function is "a chemical reactivity index in the sense of the
frontier-electron theory of reactivity..." (R. G. Parr and W. Yang,
"Density-Functional Theory of Atoms and Molecules", Oxford, New York,
1989, p. 101). But in pure DFT theory there are no frontier orbitals.
Isn't this strange?

(3)
If, as has been suggested (Parr and Yang, "Density-Funtional Theory...",
p. 53) wave mechanics can be reformulated without the wavefunction
concept, what are we to make of the 80-year-old debate in physics and
philosophy about the meaning of the wavefunction (wavefunction collapse,
Schroedinger's cat, the many-worlds theory of QM, etc, etc, etc; see
e.g. "Einstein, Bohr and the Quantum Dilemma", A. Whitaker, Cambridge
University Press, Cambridge, 1996, and _many_ other books and
papers...). Was this debate a meaningless exercise that would never have
occurred if QM had been originally formulated in terms of electron (or
more generally, particle) density rather than the wavefunction?

Thanks,

E. Lewars
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