Free Access
Issue
ESAIM: M2AN
Volume 46, Number 5, September-October 2012
Page(s) 1055 - 1080
DOI https://doi.org/10.1051/m2an/2011077
Published online 13 February 2012
  1. D. Andrae, Numerical self-consistent field method for polyatomic molecules. Mol. Phys. 99 (2001) 327–334. [CrossRef] [Google Scholar]
  2. T.A. Arias, Multiresolution analysis of electronic structure : Semicardinal and wavelet bases. Rev. Mod. Phys. 71 (1999) 267–312. [CrossRef] [Google Scholar]
  3. O. Beck, D. Heinemann and D. Kolb, Fast and accurate molecular Hartree-Fock with a finite-element multigrid method. arXiv:physics/0307108 (2003). [Google Scholar]
  4. F.A. Bischoff and E.F. Valeev, Low-order tensor approximations for electronic wave functions : Hartree-Fock method with guaranteed precision. J. Chem. Phys. 134 (2011) 104104. [CrossRef] [PubMed] [Google Scholar]
  5. D. Braess, Asymptotics for the approximation of wave functions by exponential sums. J. Approx. Theory 83 (1995) 93–103. [CrossRef] [MathSciNet] [Google Scholar]
  6. S.C. Brenner and L. Ridgway Scott, The Mathematical Theory of Finite Element Methods. Springer, New York (2008). [Google Scholar]
  7. H.-J. Bungartz and M. Griebel, Sparse grids. Acta Numer. 13 (2004) 147–269. [CrossRef] [MathSciNet] [Google Scholar]
  8. E. Cancès, SCF algorithms for HF electronic calculations, in Mathematical Models and Methods for Ab Initio Quantum Chemistry, edited by M. Defranceschi and C. Le Bris, Springer, Berlin. Lect. Notes Chem. 74 (2000) 17–43. [Google Scholar]
  9. E. Cancès and C. Le Bris, On the convergence of SCF algorithms for the Hartree-Fock equations. ESAIM : M2AN 34 (2000) 749–774. [CrossRef] [EDP Sciences] [Google Scholar]
  10. A. Cohen, W. Dahmen and R.A. DeVore, Adaptive wavelet methods for elliptic operator equations, convergence rates. Math. Comp. 70 (2001) 27–75. [CrossRef] [MathSciNet] [Google Scholar]
  11. W. Dahmen, T. Rohwedder, R. Schneider and A. Zeiser, Adaptive eigenvalue computation : complexity estimates. Numer. Math. 110 (2008) 277–312. [CrossRef] [Google Scholar]
  12. R.A. DeVore, Nonlinear approximation. Acta Numer. 7 (1998) 51–150. [CrossRef] [Google Scholar]
  13. Y.V. Egorov and B.-W. Schulze, Pseudo-Differential Operators, Singularities, Applications. Birkhäuser, Basel (1997). [Google Scholar]
  14. T.D. Engeness and T.A. Arias, Multiresolution analysis for efficient, high precision all-electron density-functional calculations. Phys. Rev. B 65 (2002) 165106. [CrossRef] [Google Scholar]
  15. H.-J. Flad, W. Hackbusch and R. Schneider, Best N-term approximation in electronic structure calculation. I. One-electron reduced density matrix. ESAIM : M2AN 40 (2006) 49–61. [CrossRef] [EDP Sciences] [Google Scholar]
  16. H.-J. Flad, R. Schneider and B.-W. Schulze, Asymptotic regularity of solutions of Hartree-Fock equations with Coulomb potential. Math. Methods Appl. Sci. 31 (2008) 2172–2201. [CrossRef] [Google Scholar]
  17. H. Flanders, Differentiation under the integral sign. Amer. Math. Monthly 80 (1973) 615–627. [CrossRef] [Google Scholar]
  18. L. Genovese, T. Deutsch, A. Neelov, S. Goedecker and G. Beylkin, Efficient solution of Poisson’s equation with free boundary conditions. J. Chem. Phys. 125 (2006) 074105. [CrossRef] [PubMed] [Google Scholar]
  19. L. Genovese, A. Neelov, S. Goedecker, T. Deutsch, S.A. Ghasemi, A. Willand, D. Caliste, O. Zilberberg, M. Rayson, A. Bergman and R. Schneider, Daubechies wavelets as a basis set for density functional pseudopotential calculations. J. Chem. Phys. 129 (2008) 014109. [CrossRef] [PubMed] [Google Scholar]
  20. D. Gilbarg and N.S. Trudinger, Elliptic Partial Differential Equations of Second Order. Springer, Berlin (1998). [Google Scholar]
  21. M. Griebel and J. Hamaekers, Tensor product multiscale many-particle spaces with finite-order weights for the electronic Schrödinger equation. Z. Phys. Chem. 224 (2010) 527–543. [CrossRef] [Google Scholar]
  22. P. Hajłasz, P. Koskela and H. Tuominen, Sobolev embeddings, extensions and measure density condition. J. Funct. Anal. 254 (2008) 1217–1234. [CrossRef] [Google Scholar]
  23. R.J. Harrison, G.I. Fann, T. Yanai, Z. Gan and G. Beylkin, Multiresolution quantum chemistry : Basic theory and initial applications. J. Chem. Phys. 121 (2004) 11587–11598. [CrossRef] [PubMed] [Google Scholar]
  24. D. Heinemann, A. Rosén and B. Fricke, Solution of the Hartree-Fock equations for atoms and diatomic molecules with the finite element method. Phys. Scr. 42 (1990) 692–696. [CrossRef] [Google Scholar]
  25. T. Helgaker, P. Jørgensen and J. Olsen, Molecular Electronic-Structure Theory. Wiley, New York (1999). [Google Scholar]
  26. W. Klopper, F.R. Manby, S. Ten-No and E.F. Valeev, R12 methods in explicitly correlated molecular electronic structure theory. Int. Rev. Phys. Chem. 25 (2006) 427–468. [CrossRef] [Google Scholar]
  27. J. Kobus, L. Laaksonen and D. Sundholm, A numerical Hartree-Fock program for diatomic molecules. Comput. Phys. Commun. 98 (1996) 346–358. [CrossRef] [Google Scholar]
  28. W. Kutzelnigg, Theory of the expansion of wave functions in a Gaussian basis. Int. J. Quantum Chem. 51 (1994) 447–463. [CrossRef] [Google Scholar]
  29. E.H. Lieb and B. Simon, The Hartree-Fock theory for Coulomb systems. Commun. Math. Phys. 53 (1977) 185–194. [CrossRef] [MathSciNet] [Google Scholar]
  30. P.L. Lions, Solutions of Hartree-Fock equations for Coulomb systems. Commun. Math. Phys. 109 (1987) 33–97. [CrossRef] [MathSciNet] [Google Scholar]
  31. A.I. Neelov and S. Goedecker, An efficient numerical quadrature for the calculation of the potential energy of wavefunctions expressed in the Daubechies wavelet basis. J. Comp. Phys. 217 (2006) 312–339. [CrossRef] [MathSciNet] [Google Scholar]
  32. T. Rohwedder, R. Schneider and A. Zeiser, Perturbed preconditioned inverse iteration for operator eigenvalue problems with applications to adaptive wavelet discretization. Adv. Comput. Math. 34 (2011) 43–66. [CrossRef] [MathSciNet] [Google Scholar]
  33. R. Schneider, Multiskalen-und Wavelet-Matrixkompression. Teubner, Stuttgart (1998). [Google Scholar]
  34. C. Schwab and R. Stevenson, Adaptive wavelet algorithms for elliptic PDE’s on product domains. Math. Comp. 77 (2008) 71–92. [CrossRef] [MathSciNet] [Google Scholar]
  35. O. Sinanoğlu, Perturbation theory of many-electron atoms and molecules. Phys. Rev. 122 (1961) 493–499. [CrossRef] [MathSciNet] [Google Scholar]
  36. O. Sinanoğlu, Theory of electron correlation in atoms and molecules. Proc. R. Soc. Lond., Ser. A 260 (1961) 379–392. [CrossRef] [Google Scholar]
  37. R. Stevenson, On the compressibility of operators in wavelet coordinates. SIAM J. Math. Anal. 35 (2004) 1110–1132. [CrossRef] [MathSciNet] [Google Scholar]
  38. T. Yanai, G.I. Fann, Z. Gan, R.J. Harrison and G. Beylkin, Multiresolution quantum chemistry in multiwavelet basis : Hartree-Fock exchange. J. Chem. Phys. 121 (2004) 6680–6688. [CrossRef] [PubMed] [Google Scholar]
  39. H. Yserentant, On the regularity of the electronic Schrödinger equation in Hilbert spaces of mixed derivatives. Numer. Math. 98 (2004) 731–759. [CrossRef] [MathSciNet] [Google Scholar]

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