Momentum eigenfunctions in the complex momentum plane. III. Hartree--Fock functions

Journal Article · Fri Feb 15 04:00:00 EST 1980 · J. Chem. Phys.; (United States)

DOI:https://doi.org/10.1063/1.439485· OSTI ID:5484566

Huo, W M; Lassettre, E N

The singular points of a Hartree--Fock wave function in the complex momentum (P) plane have been located using a method developed by Lassettre (J. Chem. Phys. 64, 4375 (1976); 70, 3468 (1979)). In the case of a closed shell Hartree--Fock function these positions are determined by the orbital energies (diagonal Lagrangian multipliers) and for an open shell restricted Hartree--Fock function they are determined by both the diagonal and off-diagonal Lagrangian multipliers. For bound state functions these singlular points all lie on the imaginary P axis and they form an infinite but discrete set, with the singular point closest to the real P axis determined by the Lagrangian multipliers associated with the most diffuse orbital. By means of conformal mappings based on the location of these singular points, a power series representation of the Hartree--Fock function in momentum space is obtained which converges not only on the real P axis but also on portions of the complex P plane. An inverse Fourier transform gives a Hartree--Fock function in coordinate space expressed in terms of a Slater basis set. The exponents appearing in this basis set are determined by the positions of singularities in the P plane. Numerical calculations on Ne and Ar using the theoretically derived exponents are presented.

• Research Organization: Radiation Laboratory, University of Notre Dame, Notre Dame, Indiana 46556
• OSTI ID: 5484566
• Journal Information: J. Chem. Phys.; (United States), Journal Name: J. Chem. Phys.; (United States) Vol. 72:4; ISSN JCPSA
• Country of Publication: United States
• Language: English

Related Subjects

640305* -- Atomic
Molecular & Chemical Physics-- Atomic & Molecular Theory-- (-1987)
74 ATOMIC AND MOLECULAR PHYSICS
ARGON
ATOMIC MODELS
BOUND STATE
ELECTRONIC STRUCTURE
ELEMENTS
FUNCTIONS
HARTREE-FOCK METHOD
LAGRANGIAN FUNCTION
MATHEMATICAL MODELS
NEON
NONMETALS
RARE GASES
WAVE FUNCTIONS