CONCERNING THE SYMMETRY PROPERTIES OF THE REDUCED DENSITY MATRIX AND THE NATURAL SPIN ORBITALS AND SPIN GEMINALS (THE NATURAL ONE- AND TWO-ELECTRON FUNCTIONS)

Journal Article · Tue Oct 01 04:00:00 EDT 1963 · Zeitschrift fuer Naturforschung (West Germany) Divided into Z. Nautrforsch., A, and Z. Naturforsch., B: Anorg. Chem., Org. Chem., Biochem., Biophys.,

OSTI ID:4125831

Kutzelnigg, W

The density operator (density matrix) of a quantum mechenical system can be decomposed into operators which transform as irreducible representations of the symmetry group in coordinate and spin space. Each of these components has a physical meaning connected with the expectation values of certain operators. The reduced density matrices can be decomposed in a completely analogous way. The symmetry properties of the total wave function give rise to degeneracies of the eigenvalues of the reduced density matrices. These degeneracies can be removed by requiring that the natural spin orbitals (NSO, defined as the eigenfunctions of the first-order density matrix), as well as the natural spin geminals (NSG, the eigenfunctions of the second-order density matrix) and their spinless counterparts transform as irreducible representations of the symmetry group and are eigenfunctions of S/sup 2/ and S/sub z/. In many cases this requirement is compatible with the original definition of the NSO, the NSG, etc., e.g., when there is no spatial degeneracy of the total wave function and when the Z- component of the total spin vanishes. When these conditions are not fulfilled an alternative definition of the NSO and the NSG is proposed. (auth)

• Research Organization: Universite, Paris
• NSA Number: NSA-18-006072
• OSTI ID: 4125831
• Journal Information: Zeitschrift fuer Naturforschung (West Germany) Divided into Z. Nautrforsch., A, and Z. Naturforsch., B: Anorg. Chem., Org. Chem., Biochem., Biophys.,, Journal Name: Zeitschrift fuer Naturforschung (West Germany) Divided into Z. Nautrforsch., A, and Z. Naturforsch., B: Anorg. Chem., Org. Chem., Biochem., Biophys., Vol. Vol: 18a; ISSN ZNTFA
• Country of Publication: Country unknown/Code not available
• Language: German

Related Subjects

ATOMIC MODELS
CONFIGURATION
EIGENVALUES
ELECTRONS
EXPECTATION VALUE
GROUP THEORY
MATHEMATICS
MATRICES
ORBITS
PHYSICS
QUANTUM MECHANICS
SPIN
SYMMETRY