NFCR, Senior Investigator; Professor Emeritus at Uppsala University, Uppsala, Sweden.
Some properties of the bivariational Hartree–Fock scheme for complex symmetric many-particle operators†
Article first published online: 19 OCT 2004
Copyright © 1989 John Wiley & Sons, Inc.
International Journal of Quantum Chemistry
Volume 36, Issue 2, pages 93–103, August 1989
How to Cite
Löwdin, P.-O., Froelich, P. and Mishra, M. (1989), Some properties of the bivariational Hartree–Fock scheme for complex symmetric many-particle operators. Int. J. Quantum Chem., 36: 93–103. doi: 10.1002/qua.560360202
Some of the results of this paper were first presented as a poster contribution at the 1987 Sanibel Symposium on Atomic, Molecular, and Solid-State Theory, March 1987.
- Issue published online: 19 OCT 2004
- Article first published online: 19 OCT 2004
- Manuscript Accepted: 13 OCT 1988
- Manuscript Received: 6 JUL 1987
The bivariational Hartree–Fock scheme for a general many-body operator T is discussed with particular reference to the complex symmetric case: T† = T*. It shown that, even in the case when the complex symmetric operator T is real and hence also self-adjoint, the complex symmetric Hartree–Fock scheme does not reduce to the conventional real form, unless one introduces the constraint that the N-dimensional space spanned by the Hartree–Fock functions ϕ should be stable under complex conjugation, so that ϕ* = ϕα. If one omits this constraint, one gets a complex symmetric formulation of the Hartree–Fock scheme for a real N-electron Hamiltonian having the properties H = H* = H†, in which the effective Hamiltonian Heff (1) may have complex eigenvalues εk. By using the method of complex scaling, it is indicated that these complex eigenvalues—at least for certain systems—may be related to the existence of so-called physical resonance states, and a simple example is given. Full details will be given elsewhere.