메뉴 건너뛰기




Volumn 30, Issue 4, 2007, Pages 429-447

Finite dimensional approximations for the electronic ground state solution of a molecular system

Author keywords

Convergence; Finite dimensional approximation; Ground state; Nonlinear eigenvalue; Thomas Fermi von Weizs cker equation

Indexed keywords

APPROXIMATION THEORY; EIGENVALUES AND EIGENFUNCTIONS; FERMI LEVEL; FINITE ELEMENT METHOD; GALERKIN METHODS; GROUND STATE; NONLINEAR EQUATIONS;

EID: 33847042208     PISSN: 01704214     EISSN: 10991476     Source Type: Journal    
DOI: 10.1002/mma.793     Document Type: Article
Times cited : (26)

References (49)
  • 3
    • 0042113153 scopus 로고
    • Self-consistent equations including exchange and correlation effects
    • Kohn W, Sham LJ. Self-consistent equations including exchange and correlation effects. Physical Review 1965; 140:A1133-A1138.
    • (1965) Physical Review , vol.140
    • Kohn, W.1    Sham, L.J.2
  • 4
    • 33847031493 scopus 로고    scopus 로고
    • Le Bris C (ed.). Handbook of Numerical Analysis. X. Special Issue: Computational Chemistry. North-Holland: Amsterdam, 2003.
    • Le Bris C (ed.). Handbook of Numerical Analysis. Vol. X. Special Issue: Computational Chemistry. North-Holland: Amsterdam, 2003.
  • 5
    • 19844366465 scopus 로고    scopus 로고
    • Computational chemistry from the perspective of numerical analysis
    • Le Bris C. Computational chemistry from the perspective of numerical analysis. Acta Numerica 2005; 14:363-444.
    • (2005) Acta Numerica , vol.14 , pp. 363-444
    • Le Bris, C.1
  • 10
    • 4043068419 scopus 로고    scopus 로고
    • Conjugate-gradient optimization method for orbital-free density functional calculations
    • Jiang H, Yang W. Conjugate-gradient optimization method for orbital-free density functional calculations. Journal of Chemical Physics 2004; 121:2030-2036.
    • (2004) Journal of Chemical Physics , vol.121 , pp. 2030-2036
    • Jiang, H.1    Yang, W.2
  • 11
    • 0344667553 scopus 로고    scopus 로고
    • Fisher information in density functional theory
    • Nagy A. Fisher information in density functional theory. Journal of Chemical Physics 2003; 119:9401-9405.
    • (2003) Journal of Chemical Physics , vol.119 , pp. 9401-9405
    • Nagy, A.1
  • 12
    • 0242636550 scopus 로고    scopus 로고
    • Fully local orbital-free calculation of electronic structure using pseudopotentials
    • Pino R, Markvoort AJ, van Santen RA, Hilbers PAJ. Fully local orbital-free calculation of electronic structure using pseudopotentials. Physica B 2003; 339:119-129.
    • (2003) Physica B , vol.339 , pp. 119-129
    • Pino, R.1    Markvoort, A.J.2    van Santen, R.A.3    Hilbers, P.A.J.4
  • 13
    • 0000658214 scopus 로고    scopus 로고
    • Orbital-free kinetic-energy functionals for the nearly free electron gas
    • Wang YA, Govind N, Carter EA. Orbital-free kinetic-energy functionals for the nearly free electron gas. Physical Review B 1998; 58:13465-13471.
    • (1998) Physical Review B , vol.58 , pp. 13465-13471
    • Wang, Y.A.1    Govind, N.2    Carter, E.A.3
  • 14
    • 0001549358 scopus 로고    scopus 로고
    • Orbital-free kinetic-energy functionals with a density-dependent kernel
    • Wang YA, Govind N, Carter EA. Orbital-free kinetic-energy functionals with a density-dependent kernel. Physical Review B 1999; 60:16350-16358.
    • (1999) Physical Review B , vol.60 , pp. 16350-16358
    • Wang, Y.A.1    Govind, N.2    Carter, E.A.3
  • 15
    • 0000377022 scopus 로고    scopus 로고
    • Orbital-free kinetic-energy density functional theory
    • Schwartz SD ed, Kluwer: Dordrecht
    • Wang YA, Carter EA. Orbital-free kinetic-energy density functional theory. In Theoretical Methods in Condensed Phase Chemistry, Schwartz SD (ed.). Kluwer: Dordrecht, 2000; 117-184.
    • (2000) Theoretical Methods in Condensed Phase Chemistry , pp. 117-184
    • Wang, Y.A.1    Carter, E.A.2
  • 17
    • 0001473913 scopus 로고
    • Un methodo statistico per la determinazione di alcune priorieta deH'atome
    • Fermi E. Un methodo statistico per la determinazione di alcune priorieta deH'atome. Rend. Accad. Naz. Lincei 1927; 6:602-607.
    • (1927) Rend. Accad. Naz. Lincei , vol.6 , pp. 602-607
    • Fermi, E.1
  • 19
    • 33847043281 scopus 로고
    • Thomas-Fermi and related theories of atoms and molecules
    • Lieb EH. Thomas-Fermi and related theories of atoms and molecules. Reviews of Modern Physics 1981; 53:603-641.
    • (1981) Reviews of Modern Physics , vol.53 , pp. 603-641
    • Lieb, E.H.1
  • 20
    • 33846040104 scopus 로고
    • The Thomas-Fermi theory of atoms, molecules and solids
    • Lieb EH, Simon B. The Thomas-Fermi theory of atoms, molecules and solids. Advances in Mathematics 1977; 23:22-116.
    • (1977) Advances in Mathematics , vol.23 , pp. 22-116
    • Lieb, E.H.1    Simon, B.2
  • 24
    • 0034676963 scopus 로고    scopus 로고
    • Numerical solution of the two-dimensional Gross-Pitaevskii equation for trapped interacting atoms
    • Adhikari SK. Numerical solution of the two-dimensional Gross-Pitaevskii equation for trapped interacting atoms. Physics Letters E 2000; 265:91-95.
    • (2000) Physics Letters E , vol.265 , pp. 91-95
    • Adhikari, S.K.1
  • 26
    • 0001642649 scopus 로고
    • Numerical solution of the nonlinear Schrödinger equation for small samples of trapped neutral atoms
    • Edwards M, Burnett K. Numerical solution of the nonlinear Schrödinger equation for small samples of trapped neutral atoms. Physical Review A 1995; 51:1382-1387.
    • (1995) Physical Review A , vol.51 , pp. 1382-1387
    • Edwards, M.1    Burnett, K.2
  • 27
    • 1642308839 scopus 로고    scopus 로고
    • An analysis of finite-dimensional approximations for the ground state solution of Bose-Einstein condensates
    • Zhou A. An analysis of finite-dimensional approximations for the ground state solution of Bose-Einstein condensates. Nonlinearity 2004; 17:541-550.
    • (2004) Nonlinearity , vol.17 , pp. 541-550
    • Zhou, A.1
  • 28
    • 0007416047 scopus 로고
    • General properties of the Hartree-Fock problem demonstrated on the frontier orbital model II: Analysis of the customary iterative procedure
    • Bonacic V, Koutecky J. General properties of the Hartree-Fock problem demonstrated on the frontier orbital model II: analysis of the customary iterative procedure. Theoretica Chimica Acta 1975; 36:163-180.
    • (1975) Theoretica Chimica Acta , vol.36 , pp. 163-180
    • Bonacic, V.1    Koutecky, J.2
  • 29
    • 0007417257 scopus 로고
    • On convergence difficulties in the iterative Hartree-Fock procedure
    • Koutecky J, Bonacic V. On convergence difficulties in the iterative Hartree-Fock procedure. Journal of Chemical Physics 1972; 55:2408-2413.
    • (1972) Journal of Chemical Physics , vol.55 , pp. 2408-2413
    • Koutecky, J.1    Bonacic, V.2
  • 30
    • 33847073926 scopus 로고    scopus 로고
    • Error bars and quadratically convergent methods for the numerical simulation of the Hartree-Fock equations
    • Maday Y, Turinici G. Error bars and quadratically convergent methods for the numerical simulation of the Hartree-Fock equations. Numerische Mathematik 1998; 94:121-147.
    • (1998) Numerische Mathematik , vol.94 , pp. 121-147
    • Maday, Y.1    Turinici, G.2
  • 31
    • 0003967609 scopus 로고    scopus 로고
    • Mathematical Theory of Thermodynamic Limits: Thomas-Fermi Type Models
    • Oxford University Press: Oxford
    • Catto I, Le Bris C, Lions P-L. Mathematical Theory of Thermodynamic Limits: Thomas-Fermi Type Models. Oxford Mathematical Monogrphs. Oxford University Press: Oxford, 1998.
    • (1998) Oxford Mathematical Monogrphs
    • Catto, I.1    Le Bris, C.2    Lions, P.-L.3
  • 33
    • 0031546440 scopus 로고    scopus 로고
    • Pair corrections and exchange phenomena in the free electron gas
    • Friesecke G. Pair corrections and exchange phenomena in the free electron gas. Communications in Mathematical Physics 1997; 184:143-171.
    • (1997) Communications in Mathematical Physics , vol.184 , pp. 143-171
    • Friesecke, G.1
  • 34
    • 0001929193 scopus 로고
    • Solutions of Hartree-Fock equations for Coulomb systems
    • Lions PL. Solutions of Hartree-Fock equations for Coulomb systems. Communications in Mathematical Physics 1987; 109:33-97.
    • (1987) Communications in Mathematical Physics , vol.109 , pp. 33-97
    • Lions, P.L.1
  • 37
    • 0006965592 scopus 로고
    • Accurate solution of the Thomas-Fermi-Dirac-Weizsacker variational equations for the case of neutral atoms and positive ions
    • Stich W, Gross EKU, Malzacher P, Dreizler RM. Accurate solution of the Thomas-Fermi-Dirac-Weizsacker variational equations for the case of neutral atoms and positive ions. Zeitschrift fur Physik A 1982; 309:5-11.
    • (1982) Zeitschrift fur Physik A , vol.309 , pp. 5-11
    • Stich, W.1    Gross, E.K.U.2    Malzacher, P.3    Dreizler, R.M.4
  • 38
    • 0038300876 scopus 로고
    • Solution of the Thomas-Fermi-Dirac equation with a modified Weizsacker correction
    • Tomishima Y, Yonei K. Solution of the Thomas-Fermi-Dirac equation with a modified Weizsacker correction. Journal of the Physical Society of Japan 1966; 21:142-153.
    • (1966) Journal of the Physical Society of Japan , vol.21 , pp. 142-153
    • Tomishima, Y.1    Yonei, K.2
  • 39
    • 84966243578 scopus 로고
    • Finite element-Galerkin approximation for the eigenvalues and eigenvectors of selfadjoint problems
    • Babuska I, Osborn JE. Finite element-Galerkin approximation for the eigenvalues and eigenvectors of selfadjoint problems. Mathematics of Computation 1989; 52:275-297.
    • (1989) Mathematics of Computation , vol.52 , pp. 275-297
    • Babuska, I.1    Osborn, J.E.2
  • 40
    • 54249116319 scopus 로고    scopus 로고
    • Babuska I, Osborn JE. Eigenvalue problems. In Handbook of Numerical Analysis, II, Finite Element Methods (Part I), Ciarlet Lions JL (eds). Elsevier: Amsterdam, 1991; 641-792.
    • Babuska I, Osborn JE. Eigenvalue problems. In Handbook of Numerical Analysis, Vol. II, Finite Element Methods (Part I), Ciarlet PG, Lions JL (eds). Elsevier: Amsterdam, 1991; 641-792.
  • 42
    • 6344289363 scopus 로고    scopus 로고
    • Computing the ground state solution of Bose-Einstein condensates by a normalized gradient flow
    • Bao W, Du Q. Computing the ground state solution of Bose-Einstein condensates by a normalized gradient flow. SIAM Journal on Scientific Computing 2004; 25:1674-1697.
    • (2004) SIAM Journal on Scientific Computing , vol.25 , pp. 1674-1697
    • Bao, W.1    Du, Q.2
  • 43
    • 0037406449 scopus 로고    scopus 로고
    • Ground state solution of trapped interacting Bose-Einstein condensate by directly minimizing the energy functional
    • Bao W, Tang W. Ground state solution of trapped interacting Bose-Einstein condensate by directly minimizing the energy functional. Journal of Computational Physics 2003; 187:230-254.
    • (2003) Journal of Computational Physics , vol.187 , pp. 230-254
    • Bao, W.1    Tang, W.2
  • 47
    • 0001439552 scopus 로고    scopus 로고
    • Towards grid-based O(N) density-functional theory methods: Optimized nonorthogonal Orbitals and multigrid acceleration
    • Fattebert J-L, Bernholc J. Towards grid-based O(N) density-functional theory methods: optimized nonorthogonal Orbitals and multigrid acceleration. Physical Review B 2000; 62:1713-1722.
    • (2000) Physical Review B , vol.62 , pp. 1713-1722
    • Fattebert, J.-L.1    Bernholc, J.2
  • 48
    • 0003308407 scopus 로고    scopus 로고
    • An Introduction to Banach Space Theory
    • Springer: Berlin
    • Megginson RE. An Introduction to Banach Space Theory. Graduate Texts in Mathematics, vol. 183. Springer: Berlin, 1998.
    • (1998) Graduate Texts in Mathematics , vol.183
    • Megginson, R.E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.