Asymptotic regularity of solutions to hartree-fock equations with coulomb potential

Mathematical Methods in the Applied Sciences

Volumn 31, Issue 18, 2008, Pages 2172-2201

  Flad, Heinz Jürgen ^a,c   Schneider, Reinhold ^a   Schulze, Bert Wolfgang ^b  

^a UNIVERSITY OF KIEL   (Germany)

^b UNIVERSITY OF POTSDAM   (Germany)

^c TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

Author keywords

Asymptotics of eigenfunctions; Conical singularities; Hartree Fock equation

Indexed keywords

CABLE STAYED BRIDGES; COULOMB BLOCKADE; DIFFERENTIAL EQUATIONS; DIFFERENTIATION (CALCULUS); ELECTRIC FIELDS; EQUATIONS OF MOTION; MATHEMATICAL OPERATORS; MOLECULAR PHYSICS; PROBABILITY DENSITY FUNCTION; SURFACE STRUCTURE;

ASYMPTOTICS OF EIGENFUNCTIONS; CONICAL SINGULARITIES; COULOMB POTENTIALS; COULOMB SYSTEMS; DIFFERENTIAL OPERATORS; FIELD SOLUTIONS; FOCK OPERATORS; HARTREE-FOCK EQUATION; HF EQUATIONS; LOCAL PARTS; NONLINEAR TERMS; POINT APPROACHES; REGULARITY CONDITIONS; REGULARITY OF SOLUTIONS;

ASYMPTOTIC ANALYSIS;

EID: 56749170131     PISSN: 01704214     EISSN: 10991476     Source Type: Journal    
DOI: 10.1002/mma.1021     Document Type: Article

References (16)

1. Lieb EH, Simon B. The Hartree-Fock theory for Coulomb systems. Communications in Mathematical Physics 1977; 53: 185-194.
2. Lions PL. Solutions of Hartree-Fock equations for Coulomb systems. Communications in Mathematical Physics 1987; 109: 33-97.
3. Helgaker T, Jørgenscn P, Olsen J. Molecular Electronic-structure Theory. Wiley: New York, 1999.
4. Flad H-J, Hackbusch W, Schneider R. Best N-term approximation in electronic structure calculations. I. One-electron reduced density matrix. ESAIM: Mathematical Modelling and Numerical Analysis 2006; 40: 49-61.
5. Hoffmann-Ostenhof M, Hoffmann-Ostenhof T, østergaard Sørensen T, Electron wavcfuncdons and densities for atoms. Annales Henri Poincaré 2001; 2: 77-100.
6. Fournais S, Hoffmann-Ostenhof M, Hoffmann-Ostenhof T, østcrgaard Sørensen T. The electron density is smooth away from the nuclei. Communications in Mathematical Physics 2002; 228: 401-415.
7. Fournais S, Hoffmann-Ostenhof M, Hoffmann-Ostenhof T, østergaard Sørensen T. Analyticity of the density of electronic wavefunctions. Arkiv för Matematik 2004; 42: 87-106.
8. Fournais S, Hoffmann-Ostenhof M, Hoffmann-østenhof T, østcrgaard Sørensen T. Non-isotropic cusp conditions and regularity of the electron density of molecules at the nuclei. Annales Henri Poincaré 2007; 8: 731-748.
9. Egorov YV, Schulze B-W. Pseudo-differential Operators, Singularities, Applications. Birkhäuser: Basel, 1997.
10. Schulze B-W. Boundary Value Problems and Singular Pseudo-differential Operators. Wiley: New York, 1998.
11. Gilbarg D, Trudinger NS. Elliptic Partial Differential Equations of Second Order. Springer: Berlin, 1998.
12. Cancès E. SCF algorithms for HF electronic calculations. In Mathematical Models and Methods for Ab Initio Quantum Chemistry, Defranceschi M, Le Bris C (eds). Lecture Notes in Chemistry, vol. 74. Springer: Berlin, 2000; 17-43.
13. Cancès E, Le Bris C. On the convergence of SCF algorithms for the Hartree-Fock equations. ESAIM: Mathematical Modelling and Numerical Analysis 2000; 34: 749-774.
14. Triebel H. Higher Analysis. Barth: Leipzig, 1992.
15. Hill RN. Rates of convergence and error estimation formulas for the Rayleigh-Ritz variational method. Journal of Chemical Physics 1985; 83: 1173-1196.
16. Stein EM. Harmonic Analysis: Real-variable Methods, Orthogonality, and Oscillatory Integrals. Princeton University Press: Princeton, NJ, 1993.