Free Access
Issue
ESAIM: M2AN
Volume 41, Number 2, March-April 2007
Special issue on Molecular Modelling
Page(s) 261 - 279
DOI https://doi.org/10.1051/m2an:2007016
Published online 16 June 2007
  1. S. Agmon, Lectures on exponential decay of solutions of second-order elliptic equations: Bounds on eigenfunctions of N-body Schrödinger operators, Mathematical Notes 29. Princeton University Press (1982). [Google Scholar]
  2. H.-J. Bungartz and M. Griebel, Sparse grids. Acta Numer. 13 (2004) 147–269. [CrossRef] [MathSciNet] [Google Scholar]
  3. C.E. Campbell, E. Krotscheck and T. Pang, Electron correlations in atomic systems. Phys. Rep. 223 (1992) 1–42. [CrossRef] [Google Scholar]
  4. D. Ceperley, Ground state of the fermion one-component plasma: A Monte Carlo study in two and three dimensions. Phys. Rev. B 18 (1978) 3126–3138. [Google Scholar]
  5. J.W. Clark, Variational theory of nuclear matter, in Progress in Nuclear and Particle Physics, Vol. 2, D.H. Wilkinson Ed., Pergamon, Oxford (1979) 89–199. [Google Scholar]
  6. E.T. Copson, Asymptotic Expansions. Cambridge University Press, Cambridge (1967). [Google Scholar]
  7. W. Dahmen, S. Prößdorf and R. Schneider, Wavelet approximation methods for pseudodifferential equations. II: Matrix compression and fast solution. Adv. Comp. Maths. 1 (1993) 259–335. [Google Scholar]
  8. W. Dahmen, S. Prößdorf and R. Schneider, Wavelet approximation methods for pseudodifferential equations. I: Stability and convergence. Math. Z. 215 (1994) 583–620. [CrossRef] [MathSciNet] [Google Scholar]
  9. R.A. DeVore, Nonlinear approximation. Acta Numer. 7 (1998) 51–150. [CrossRef] [Google Scholar]
  10. R.A. DeVore, B. Jawerth and V. Popov, Compression of wavelet decompositions. Amer. J. Math. 114 (1992) 737–785. [CrossRef] [MathSciNet] [Google Scholar]
  11. R.A. DeVore, S.V. Konyagin and V.N. Temlyakov, Hyperbolic wavelet approximation. Constr. Approx. 14 (1998) 1–26. [Google Scholar]
  12. N.D. Drummond, M.D. Towler and R.J. Needs, Jastrow correlation factor for atoms, molecules, and solids. Phys. Rev. B 70 (2004) 235119. [CrossRef] [Google Scholar]
  13. H.-J. Flad and A. Savin, Transfer of electron correlation from the electron gas to inhomogeneous systems via Jastrow factors. Phys. Rev. A. 50 (1994) 3742–3746. [CrossRef] [PubMed] [Google Scholar]
  14. H.-J. Flad and A. Savin, A new Jastrow factor for atoms and molecules, using two-electron systems as a guiding principle. J. Chem. Phys. 103 (1995) 691–697. [CrossRef] [Google Scholar]
  15. H.-J. Flad, W. Hackbusch, D. Kolb and R. Schneider, Wavelet approximation of correlated wavefunctions. I. Basics. J. Chem. Phys. 116 (2002) 9641–9657. [CrossRef] [Google Scholar]
  16. H.-J. Flad, W. Hackbusch, H. Luo and D. Kolb, Diagrammatic multiresolution analysis for electron correlations. Phys. Rev. B 71 (2005) 125115. [Google Scholar]
  17. H.-J. Flad, W. Hackbusch and R. Schneider, Best N-term approximation in electronic structure calculations. I. One-electron reduced density matrix. ESAIM: M2AN 40 (2006) 49–61. [Google Scholar]
  18. S. Fournais, M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof and T. Ostergaard S orensen, Sharp regularity results for Coulombic many-electron wave functions. Commun. Math. Phys. 255 (2005) 183–227. [CrossRef] [Google Scholar]
  19. D.E. Freund, B.D. Huxtable and J.D. Morgan III, Variational calculations on the helium isoelectronic sequence. Phys. Rev. A 29 (1984) 980–982. [CrossRef] [Google Scholar]
  20. P. Fulde, Electron Correlations in Molecules and Solids, 2nd edition. Springer, Berlin (1993). [Google Scholar]
  21. P. Fulde, Ground-state wave functions and energies of solids. Int. J. Quant. Chem. 76 (2000) 385–395. [CrossRef] [Google Scholar]
  22. J. Garcke and M. Griebel, On the computation of the eigenproblems of hydrogen and helium in strong magnetic and electric fields with the sparse grid combination technique. J. Comp. Phys. 165 (2000) 694–716. [Google Scholar]
  23. R. Gaudoin, M. Nekovee, W.M.C. Foulkes, R.J. Needs and G. Rajagopal, Inhomogeneous random-phase approximation and many-electron trial wave functions. Phys. Rev. B 63 (2001) 115115. [CrossRef] [Google Scholar]
  24. W. Hackbusch, B.N. Khoromskij and E. Tyrtyshnikov, Hierarchical Kronecker tensor-product approximation. J. Numer. Math. 13 (2005) 119–156. [CrossRef] [MathSciNet] [Google Scholar]
  25. A. Halkier, T. Helgaker, P. Jørgensen, W. Klopper, H. Koch, J. Olsen and A.K. Wilson, Basis-set convergence in correlated calculations on Ne, N2, and H2O. Chem. Phys. Lett. 286 (1998) 243–252. [CrossRef] [Google Scholar]
  26. T. Helgaker, W. Klopper, H. Koch and J. Noga, Basis-set convergence of correlated calculations on water. J. Chem. Phys. 106 (1997) 9639–9646. [NASA ADS] [CrossRef] [Google Scholar]
  27. T. Helgaker, P. Jørgensen and J. Olsen, Molecular Electronic-Structure Theory. Wiley, New York (1999). [Google Scholar]
  28. R.N. Hill, Rates of convergence and error estimation formulas for the Rayleigh-Ritz variational method. J. Chem. Phys. 83 (1985) 1173–1196. [CrossRef] [Google Scholar]
  29. M. Hoffmann-Ostenhof and R. Seiler, Cusp conditions for eigenfunctions of n-electron systems. Phys. Rev. A 23 (1981) 21–23. [CrossRef] [MathSciNet] [Google Scholar]
  30. M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof and H. Stremnitzer, Local properties of Coulombic wave functions. Commun. Math. Phys. 163 (1994) 185–215. [CrossRef] [Google Scholar]
  31. C.-J. Huang, C.J. Umrigar and M.P. Nightingale, Accuracy of electronic wave functions in quantum Monte Carlo: The effect of high-order correlations. J. Chem. Phys. 107 (1997) 3007–3013. [CrossRef] [Google Scholar]
  32. T. Kato, On the eigenfunctions of many-particle systems in quantum mechanics. Commun. Pure Appl. Math. 10 (1957) 151–177. [Google Scholar]
  33. E. Krotscheck, Variations on the electron gas. Ann. Phys. (N.Y.) 155 (1984) 1–55. [CrossRef] [Google Scholar]
  34. E. Krotscheck, Theory of inhomogeneous quantum systems. III. Variational wave functions for Fermi fluids. Phys. Rev. B 31 (1985) 4267–4278. [CrossRef] [Google Scholar]
  35. E. Krotscheck, W. Kohn and G.-X. Qian, Theory of inhomogeneous quantum systems. IV. Variational calculations of metal surfaces. Phys. Rev. B 32 (1985) 5693–5712. [CrossRef] [Google Scholar]
  36. W. Kutzelnigg, r12-Dependent terms in the wave function as closed sums of partial wave amplitudes for large l. Theoret. Chim. Acta 68 (1985) 445–469. [Google Scholar]
  37. W. Kutzelnigg and J.D. Morgan III, Rates of convergence of the partial-wave expansions of atomic correlation energies. J. Chem. Phys. 96 (1992) 4484–4508. [CrossRef] [Google Scholar]
  38. H. Luo, D. Kolb, H.-J. Flad, W. Hackbusch and T. Koprucki, Wavelet approximation of correlated wavefunctions. II. Hyperbolic wavelets and adaptive approximation schemes. J. Chem. Phys. 117 (2002) 3625–3638. [CrossRef] [Google Scholar]
  39. H. Luo, D. Kolb, H.-J. Flad and W. Hackbusch, Perturbative calculation of Jastrow factors. Phys. Rev. B. 75 (2007) 125111. [CrossRef] [Google Scholar]
  40. P.-A. Nitsche, Sparse approximation of singularity functions. Constr. Approx. 21 (2005) 63–81. [MathSciNet] [Google Scholar]
  41. P.-A. Nitsche, Best N-term approximation spaces for tensor product wavelet bases. Constr. Approx. 24 (2006) 49–70. [CrossRef] [MathSciNet] [Google Scholar]
  42. T. Pang, C.E. Campbell and E. Krotscheck, Local structure of electron correlations in atomic systems. Chem. Phys. Lett. 163 (1989) 537–541. [CrossRef] [Google Scholar]
  43. K.E. Schmidt and J.W. Moskowitz, Correlated Monte Carlo wave functions for the atoms He through Ne. J. Chem. Phys. 93 (1990) 4172–4178. [CrossRef] [Google Scholar]
  44. E.M. Stein, Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals. Princeton University Press (1993). [Google Scholar]
  45. G. Stollhoff, The local ansatz extended. J. Chem. Phys. 105 (1996) 227–234. [CrossRef] [Google Scholar]
  46. G. Stollhoff and P. Fulde, On the computation of electronic correlation energies within the local approach. J. Chem. Phys. 73 (1980) 4548–4561. [CrossRef] [Google Scholar]
  47. J.D. Talman, Linked-cluster expansion for Jastrow-type wave functions and its application to the electron-gas problem. Phys. Rev. A 10 (1974) 1333–1344. [CrossRef] [Google Scholar]
  48. J.D. Talman, Variational calculation for the electron gas at intermediate densities. Phys. Rev. A 13 (1976) 1200–1208. [CrossRef] [Google Scholar]
  49. C.J. Umrigar, K.G. Wilson and J.W. Wilkins, Optimized trial wave functions for quantum Monte Carlo calculations. Phys. Rev. Lett. 60 (1988) 1719–1722. [CrossRef] [PubMed] [Google Scholar]
  50. A.J. Williamson, S.D. Kenny, G. Rajagopal, A.J. James, R.J. Needs, L.M. Fraser, W.M.C. Foulkes and P. Maccallum, Optimized wavefunctions for quantum Monte Carlo studies of atoms and solids. Phys. Rev. B 53 (1996) 9640–9648. [CrossRef] [Google Scholar]
  51. 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]
  52. H. Yserentant, Sparse grid spaces for the numerical solution of the electronic Schrödinger equation. Numer. Math. 101 (2005) 381–389. [CrossRef] [MathSciNet] [Google Scholar]

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