Subject: CCL:phase/orbitals

From: "N. Sukumar" <[email-masked]>
Date: Wed, 13 Jun 2001 21:26:05 -0400

The approximate nature of orbitals in many-electron systems is indeed a very
different issue from the question of "observability" or "physical reality".

LCAO orbitals do not "exist" in many-electron atoms and pi-electron density
is an approximation in polyatomic molecules, but natural orbitals are
well-defined as functions that diagonalize the many-electron density matrix.
Does this mean that natural orbitals are observable?

Electronic phase is certainly not an "observable" in the sense of being an
expectation value of a Hermitian operator, but experimental manifestations of
phase differences can be observed as e.g. the interference of electrons in
the molecular Aharonov-Bohm effect and the Berry phase (Mead and Truhlar, JCP
70, 2284, 1979, exptl.cofirmation by Delacretaz et al. PRL 56, 2598, 1986)

It has been argued likewise that bond lengths and bond angles in polyatomic
molecules are equally "unobservable", being defined only within the
Born-Oppenheimer approximation and ignoring indistinguishability of protons
(extensive discussion by many authors in Israel J. Chem, vol.19, 1980). The
fact that bond distances obtained from quantum calculations performed within
the nonrelativistic B.O. approximation in a finite basis correspond
approximately to distances obtained from an X-ray structure is analogous to
the approximate correspondence between Hartree-Fock orbital energies and
experimental ionization potentials.

For a one-electron system the gradient of the electronic phase has a direct
interpretation as the velocity field, which when multiplied by the electron
density, gives the current density. Madelung (Z. Phys. 40, 332) in 1926
established the fluid dynamical analogy of quantum mechanics by transforming
the Shroedinger equation into a pair of fluid dynamical equations (one of
which is the familiar continuity equation: d/dt(rho) + del.j = 0

So are natural orbitals observable? Well, the total one-electron density is
observable; experimental manifestations of electronic phase differences are
observable. The total current density can now be constructed from the natural
orbital densities and gradients of the orbital phases (orbital velocity
fields). More discussion can be found in my paper "Phase associated with the
single-particle density of many-electron systems", Int. J. Quantum. Chem. 40,
501-510 (1991). If a mathematical construct is suitably defined to correspond
to an experimental situation, it is to me a physical concept.

Dr. N. Sukumar
Rennselaer Department of Chemistry

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/  Dr. N. SUKUMAR		     /
/  Department of Chemistry           /
/  Rensselaer Polytechnic Institute  /
/  Troy, NY 12180-3590               /
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