*From*: Rene Fournier - 1999-07-07 <renef.-at-.yorku.ca>*Subject*: orbitals*Date*: Wed, 28 May 2003 16:51:44 -0400 (EDT)

Leif Laaksonen makes an important point: only observables are "real" in QM. So the question arises: is it possible to define orbitals as QM observables. It entirely depends on how you define the word "orbital". If one says orbitals are one-electron functions and nothing more, then of course orbitals can be made to be QM observables. For example, just integrate an exact squared wavefunction over all electron coordinates but one to get the electron density, then take the square root, multiply by a phase factor and you get "density orbitals". [G Hunter, Int J Quantum Chem 9 (1975) 237]. They may not be very useful as orbitals, but they are "real" in the sense of QM observables. Orbitals are always defined as one-electron functions, but THAT does not make them "unreal". The electron density is a one electron function and very real for any N-electron system, not only for the H atom. One "ab initio" way to define orbitals is to start from exact wavefunctions and calculate the overlap of a N-electron wavefunction (neutral) and the ground and various excited states a (N-1)-electron wavefunction (ion) (Dyson orbitals are defined in such a way I think). I'm sure there are definitions that will make such orbitals unique, but does that make them QM observables? I don't think so, but I'd like to hear from the CCL community on that. There are other ways to define orbitals > from exact wavefunctions, I'm sure: are any of them QM observables? As for Kohn-Sham orbitals, they may not be real individually but the N lowest energy ones squared and summed give the true electron density (an observable) and the negative of the KS HOMO energy is exactly equal to the first IP (another observable) so there are at least some bits of reality built in KS orbitals! Here's some relevant articles: 1) Kohn, Becke, Parr, J Phys Chem 100 (1996) 12974 2) "Kohn-Sham Orbitals and Orbital Energies: Fictitious Constructs but Good Approximations All the Same" by S. Hamel, P. Duffy, M.E. Casida, and D.R. Salahub Journal of Electron Spectroscopy and Related Phenomena (2002?) 3) Chong, Gritsenko, Baerends, J Chem Phys 116 (2002) 1760 -------------------------------------------------------------------- | Rene Fournier | Office: 303 Petrie | | Chemistry Dpt, York University| Phone: (416) 736 2100 Ext. 30687 | | 4700 Keele Street, Toronto | FAX: (416)-736-5936 | | Ontario, CANADA M3J 1P3 | e-mail: renef.-at-.yorku.ca | -------------------------------------------------------------------- | http://www.chem.yorku.ca/profs/renef/ | --------------------------------------------------------------------