THE DENSITY MATRIX IN MANY-ELECTRON QUANTUM MECHANICS. I. GENERALIZED PRODUCT FUNCTIONS. FACTORIZATION AND PHYSICAL INTERPRETATION OF THE DENSITY MATRICES

Journal Article · Tue Nov 24 04:00:00 EST 1959 · Proc. Roy. Soc. (London)

DOI:https://doi.org/10.1098/rspa.1959.0191· OSTI ID:4201067

McWeeny, R

Many-electron wave functions are usually constructed from antisymmetrized products of one-electron orbitals (determinants) and energy calculations are based on the matrix element expressions due to Slater (1931). The orbitals in such a product are replaced by "group functions," each describing any number of electrons, and the necessary generalization of Slater's results is carried out. It is first necessary to develop the density matrix theory of N- particle systems and to show that for systems described by "generalized product functions" the density matrices of the whole system may be expressed in terms of those of the component electron groups. The matrix elements of the Hamiltonian between generalized product functions are then given by expressions which resemble those of Slater, the "coulomb" and "exchange" integrals being replaced by integrals containing the one-electron density matrices of the various groups. By setting up an "effective" Hamiltonian for each electron group in the presence of the others, the discussion of a many-particle system in which groups or "shells" can be distinguished (e.g. atomic K, L, M,..., shells) can rigorously be reduced to a discussion of smaller subsystems. A single generalized product (cf. the single determinant of Hartree-Fock theory) provides a conconvenient first approximation; and the effect of admitting "excited" products (cf. conflguration interaction) can be estimated by a perturbatlon method The energy expression may then be discussed In terms of the electron density and "pair" functions. The energy is a sum of group energies supplemented by interaction terms which represent (i) electrostatic repulsions between change clouds, (ii) the polarization of each group in the field of the others, and (iii) "dlspersion" effects of the type defined by London. All these terms can be calculated, for group functions of any kind, in terms of the density matrices of the separate groups. Applications to the theory of intermolecular forces and to pi -electron systems are discussed. (auth)

• Research Organization: University Coll. of North Staffordshire, Eng.
• Sponsoring Organization: USDOE
• NSA Number: NSA-14-006804
• OSTI ID: 4201067
• Journal Information: Proc. Roy. Soc. (London), Journal Name: Proc. Roy. Soc. (London) Vol. Vol: A253
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

ATOMS
CONFIGURATION
DENSITY
DIFFERENTIAL EQUATIONS
DISPERSIONS
ELECTRIC CHARGES
ELECTRONS
ELECTROSTATICS
ENERGY
ENERGY LEVELS
EXCITATION
GROUP THEORY
HAMILTONIAN
HARTREE-FOCK METHOD
INTEGRALS
INTERACTIONS
MATRICES
MOLECULES
NUMERICALS
ORBITS
PARTICLES
PERTURBATION THEORY
PHYSICS
PIONS
POLARIZATION
PRODUCTION
QUANTUM MECHANICS