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Volumn 312, Issue , 2016, Pages 19-30

Grid-based electronic structure calculations: The tensor decomposition approach

Author keywords

Cross approximation method; Hartree Fock equation; Integral iteration; Kohn Sham equation; Multidimensional convolution; Tensor decompositions

Indexed keywords

ATOMS; COMPUTATIONAL COMPLEXITY; CONVOLUTION; ELECTRONIC STRUCTURE; HARTREE APPROXIMATION; ITERATIVE METHODS; MOLECULAR PHYSICS;

EID: 84958259400     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2016.02.023     Document Type: Article
Times cited : (22)

References (44)
  • 2
    • 0042113153 scopus 로고
    • Self-consistent equations including exchange and correlation effects
    • Kohn W., Sham L.J. Self-consistent equations including exchange and correlation effects. Phys. Rev. 1965, 140(4A).
    • (1965) Phys. Rev. , vol.140 , Issue.4
    • Kohn, W.1    Sham, L.J.2
  • 3
    • 11044224123 scopus 로고    scopus 로고
    • Multiresolution quantum chemistry: basic theory and initial applications
    • Harrison R.J., Fann G.I., Yanai T., Gan Z., Beylkin G. Multiresolution quantum chemistry: basic theory and initial applications. J. Chem. Phys. 2004, 121(23):11587-11598.
    • (2004) J. Chem. Phys. , vol.121 , Issue.23 , pp. 11587-11598
    • Harrison, R.J.1    Fann, G.I.2    Yanai, T.3    Gan, Z.4    Beylkin, G.5
  • 4
    • 79952665459 scopus 로고    scopus 로고
    • Low-order tensor approximations for electronic wave functions: Hartree-Fock method with guaranteed precision
    • Bischoff F.A., Valeev E.F. Low-order tensor approximations for electronic wave functions: Hartree-Fock method with guaranteed precision. J. Chem. Phys. 2011, 134(10).
    • (2011) J. Chem. Phys. , vol.134 , Issue.10
    • Bischoff, F.A.1    Valeev, E.F.2
  • 5
    • 84882448172 scopus 로고    scopus 로고
    • Fully adaptive algorithms for multivariate integral equations using the non-standard form and multiwavelets with applications to the Poisson and bound-state Helmholtz kernels in three dimensions
    • Frediani L., Fossgaard E., Flå T., Ruud K. Fully adaptive algorithms for multivariate integral equations using the non-standard form and multiwavelets with applications to the Poisson and bound-state Helmholtz kernels in three dimensions. Mol. Phys. 2013, 111(9-11):1143-1160.
    • (2013) Mol. Phys. , vol.111 , Issue.9-11 , pp. 1143-1160
    • Frediani, L.1    Fossgaard, E.2    Flå, T.3    Ruud, K.4
  • 6
    • 84881506171 scopus 로고    scopus 로고
    • Higher-order adaptive finite-element methods for Kohn-Sham density functional theory
    • Motamarri P., Nowak M.R., Leiter K., Knap J., Gavini V. Higher-order adaptive finite-element methods for Kohn-Sham density functional theory. J. Comput. Phys. 2013, 253:308-343.
    • (2013) J. Comput. Phys. , vol.253 , pp. 308-343
    • Motamarri, P.1    Nowak, M.R.2    Leiter, K.3    Knap, J.4    Gavini, V.5
  • 7
    • 3843133047 scopus 로고
    • Finite-difference-pseudopotential method: electronic structure calculations without a basis
    • Chelikowsky J.R., Troullier N., Saad Y. Finite-difference-pseudopotential method: electronic structure calculations without a basis. Phys. Rev. Lett. 1994, 72(8):1240.
    • (1994) Phys. Rev. Lett. , vol.72 , Issue.8 , pp. 1240
    • Chelikowsky, J.R.1    Troullier, N.2    Saad, Y.3
  • 8
    • 15444377222 scopus 로고    scopus 로고
    • Real-space grid implementation of the projector augmented wave method
    • Mortensen J.J., Hansen L.B., Jacobsen K.W. Real-space grid implementation of the projector augmented wave method. Phys. Rev. B 2005, 71(3).
    • (2005) Phys. Rev. B , vol.71 , Issue.3
    • Mortensen, J.J.1    Hansen, L.B.2    Jacobsen, K.W.3
  • 9
    • 84880611682 scopus 로고    scopus 로고
    • Tensor-structured factorized calculation of two-electron integrals in a general basis
    • Khoromskaia V., Khoromskij B.N., Schneider R. Tensor-structured factorized calculation of two-electron integrals in a general basis. SIAM J. Sci. Comput. 2013, 35(2):A987-A1010. 10.1137/120884067.
    • (2013) SIAM J. Sci. Comput. , vol.35 , Issue.2 , pp. A987-A1010
    • Khoromskaia, V.1    Khoromskij, B.N.2    Schneider, R.3
  • 10
    • 84948466347 scopus 로고    scopus 로고
    • Computation of the Hartree-Fock exchange by tensor-structured methods
    • Khoromskaia V. Computation of the Hartree-Fock exchange by tensor-structured methods. Comput. Methods Appl. Math. 2010, 10(2).
    • (2010) Comput. Methods Appl. Math. , vol.10 , Issue.2
    • Khoromskaia, V.1
  • 11
    • 67649378419 scopus 로고    scopus 로고
    • Tensor decomposition in electronic structure calculations on 3D Cartesian grids
    • Khoromskij B.N., Khoromskaia V., Chinnamsetty S.R., Flad H.-J. Tensor decomposition in electronic structure calculations on 3D Cartesian grids. J. Comput. Phys. 2009, 228(16):5749-5762. 10.1016/j.jcp.2009.04.043.
    • (2009) J. Comput. Phys. , vol.228 , Issue.16 , pp. 5749-5762
    • Khoromskij, B.N.1    Khoromskaia, V.2    Chinnamsetty, S.R.3    Flad, H.-J.4
  • 13
    • 79952297523 scopus 로고    scopus 로고
    • Numerical solution of the Hartree-Fock equation in multilevel tensor-structured format
    • Khoromskij B.N., Khoromskaia V., Flad H.-J. Numerical solution of the Hartree-Fock equation in multilevel tensor-structured format. SIAM J. Sci. Comput. 2011, 33(1):45-65. 10.1137/090777372.
    • (2011) SIAM J. Sci. Comput. , vol.33 , Issue.1 , pp. 45-65
    • Khoromskij, B.N.1    Khoromskaia, V.2    Flad, H.-J.3
  • 14
    • 80053918083 scopus 로고    scopus 로고
    • QTT representation of the Hartree and exchange operators in electronic structure calculations
    • Khoromskaia V., Khoromskij B.N., Schneider R. QTT representation of the Hartree and exchange operators in electronic structure calculations. Comput. Methods Appl. Math. 2011, 11(3):327-341.
    • (2011) Comput. Methods Appl. Math. , vol.11 , Issue.3 , pp. 327-341
    • Khoromskaia, V.1    Khoromskij, B.N.2    Schneider, R.3
  • 15
    • 84898646167 scopus 로고    scopus 로고
    • Black-box Hartree-Fock solver by tensor numerical methods
    • Khoromskaia V. Black-box Hartree-Fock solver by tensor numerical methods. Comput. Methods Appl. Math. 2014, 14(1):89-111. 10.1515/cmam-2013-0023.
    • (2014) Comput. Methods Appl. Math. , vol.14 , Issue.1 , pp. 89-111
    • Khoromskaia, V.1
  • 16
    • 84897586218 scopus 로고    scopus 로고
    • Multigrid accelerated tensor approximation of function related multidimensional arrays
    • Khoromskij B.N., Khoromskaia V. Multigrid accelerated tensor approximation of function related multidimensional arrays. SIAM J. Sci. Comput. 2009, 31(4):3002-3026. 10.1137/080730408.
    • (2009) SIAM J. Sci. Comput. , vol.31 , Issue.4 , pp. 3002-3026
    • Khoromskij, B.N.1    Khoromskaia, V.2
  • 17
    • 84946806151 scopus 로고    scopus 로고
    • Tensor numerical methods in quantum chemistry: from Hartree-Fock to excitation energies
    • Khoromskaia V., Khoromskij B.N. Tensor numerical methods in quantum chemistry: from Hartree-Fock to excitation energies. Phys. Chem. Chem. Phys. 2015, 17(47).
    • (2015) Phys. Chem. Chem. Phys. , vol.17 , Issue.47
    • Khoromskaia, V.1    Khoromskij, B.N.2
  • 19
    • 26144450583 scopus 로고
    • Self-interaction correction to density-functional approximations for many-electron systems
    • Perdew J.P., Zunger A. Self-interaction correction to density-functional approximations for many-electron systems. Phys. Rev. B 1981, 23(10):5048.
    • (1981) Phys. Rev. B , vol.23 , Issue.10 , pp. 5048
    • Perdew, J.P.1    Zunger, A.2
  • 20
    • 0002200027 scopus 로고
    • Implications of factor analysis of three-way matrices for measurement of change
    • Tucker L. Implications of factor analysis of three-way matrices for measurement of change. Problems in Measuring Change 1963, 122-137.
    • (1963) Problems in Measuring Change , pp. 122-137
    • Tucker, L.1
  • 22
    • 34447513756 scopus 로고    scopus 로고
    • Low rank Tucker-type tensor approximation to classical potentials
    • Khoromskij B.N., Khoromskaia V. Low rank Tucker-type tensor approximation to classical potentials. Cent. Eur. J. Math. 2007, 5(3):523-550. 10.2478/s11533-007-0018-0.
    • (2007) Cent. Eur. J. Math. , vol.5 , Issue.3 , pp. 523-550
    • Khoromskij, B.N.1    Khoromskaia, V.2
  • 23
    • 36149019811 scopus 로고
    • Monte Carlo calculations of the ground state of three- and four-body nuclei
    • Kalos M. Monte Carlo calculations of the ground state of three- and four-body nuclei. Phys. Rev. 1962, 128(4):1791.
    • (1962) Phys. Rev. , vol.128 , Issue.4 , pp. 1791
    • Kalos, M.1
  • 24
    • 85189846738 scopus 로고    scopus 로고
    • Direct minimization for calculating invariant subspaces in density functional computations of the electronic structure
    • submitted for publication
    • R. Schneider, T. Rohwedder, A. Neelov, J. Blauert, Direct minimization for calculating invariant subspaces in density functional computations of the electronic structure, J. Comput. Math., submitted for publication, . arxiv:0805.1190v1.
    • J. Comput. Math
    • Schneider, R.1    Rohwedder, T.2    Neelov, A.3    Blauert, J.4
  • 25
    • 11944256577 scopus 로고
    • Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients
    • Payne M.C., Teter M.P., Allan D.C., Arias T., Joannopoulos J. Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients. Rev. Mod. Phys. 1992, 64(4):1045.
    • (1992) Rev. Mod. Phys. , vol.64 , Issue.4 , pp. 1045
    • Payne, M.C.1    Teter, M.P.2    Allan, D.C.3    Arias, T.4    Joannopoulos, J.5
  • 26
    • 0041058023 scopus 로고
    • On the asymptotic behavior of Hartree-Fock orbitals
    • Ishida T., Ohno K. On the asymptotic behavior of Hartree-Fock orbitals. Theor. Chim. Acta 1992, 81(6):355-364.
    • (1992) Theor. Chim. Acta , vol.81 , Issue.6 , pp. 355-364
    • Ishida, T.1    Ohno, K.2
  • 28
    • 0038805356 scopus 로고    scopus 로고
    • Incomplete cross approximation in the mosaic-skeleton method
    • Tyrtyshnikov E.E. Incomplete cross approximation in the mosaic-skeleton method. Computing 2000, 64(4):367-380. 10.1007/s006070070031.
    • (2000) Computing , vol.64 , Issue.4 , pp. 367-380
    • Tyrtyshnikov, E.E.1
  • 29
    • 5844381624 scopus 로고    scopus 로고
    • Approximation of boundary element matrices
    • Bebendorf M. Approximation of boundary element matrices. Numer. Math. 2000, 86(4):565-589. 10.1007/pl00005410.
    • (2000) Numer. Math. , vol.86 , Issue.4 , pp. 565-589
    • Bebendorf, M.1
  • 30
    • 51849118006 scopus 로고    scopus 로고
    • Tucker dimensionality reduction of three-dimensional arrays in linear time
    • Oseledets I.V., Savostianov D.V., Tyrtyshnikov E.E. Tucker dimensionality reduction of three-dimensional arrays in linear time. SIAM J. Matrix Anal. Appl. 2008, 30(3):939-956. 10.1137/060655894.
    • (2008) SIAM J. Matrix Anal. Appl. , vol.30 , Issue.3 , pp. 939-956
    • Oseledets, I.V.1    Savostianov, D.V.2    Tyrtyshnikov, E.E.3
  • 31
    • 84928966851 scopus 로고    scopus 로고
    • Fast multidimensional convolution in low-rank tensor formats via cross approximation
    • Rakhuba M.V., Oseledets I.V. Fast multidimensional convolution in low-rank tensor formats via cross approximation. SIAM J. Sci. Comput. 2015, 37(2):A565-A582. 10.1137/140958529.
    • (2015) SIAM J. Sci. Comput. , vol.37 , Issue.2 , pp. A565-A582
    • Rakhuba, M.V.1    Oseledets, I.V.2
  • 32
    • 84884918548 scopus 로고    scopus 로고
    • Multilevel Toeplitz matrices generated by tensor-structured vectors and convolution with logarithmic complexity
    • Kazeev V., Khoromskij B., Tyrtyshnikov E. Multilevel Toeplitz matrices generated by tensor-structured vectors and convolution with logarithmic complexity. SIAM J. Sci. Comput. 2013, 35(3):A1511-A1536. 10.1137/110844830.
    • (2013) SIAM J. Sci. Comput. , vol.35 , Issue.3 , pp. A1511-A1536
    • Kazeev, V.1    Khoromskij, B.2    Tyrtyshnikov, E.3
  • 33
    • 75949087785 scopus 로고    scopus 로고
    • Approximation by exponential sums revisited
    • Beylkin G., Monzón L. Approximation by exponential sums revisited. Appl. Comput. Harmon. Anal. 2010, 28(2):131-149.
    • (2010) Appl. Comput. Harmon. Anal. , vol.28 , Issue.2 , pp. 131-149
    • Beylkin, G.1    Monzón, L.2
  • 34
    • 72949093768 scopus 로고    scopus 로고
    • Fast orthogonalization to the kernel of discrete gradient operator with application to the Stokes problem
    • Oseledets I.V., Muravleva E.A. Fast orthogonalization to the kernel of discrete gradient operator with application to the Stokes problem. Linear Algebra Appl. 2010, 432(6):1492-1500. 10.1016/j.laa.2009.11.010.
    • (2010) Linear Algebra Appl. , vol.432 , Issue.6 , pp. 1492-1500
    • Oseledets, I.V.1    Muravleva, E.A.2
  • 36
    • 0015141223 scopus 로고
    • Survey of extrapolation processes in numerical analysis
    • Joyce D.C. Survey of extrapolation processes in numerical analysis. SIAM Rev. 1971, 13(4):435-490.
    • (1971) SIAM Rev. , vol.13 , Issue.4 , pp. 435-490
    • Joyce, D.C.1
  • 37
    • 36449000932 scopus 로고
    • Improved Roothaan-Hartree-Fock wave functions for atoms and ions with n≤54
    • Koga T., Watanabe S., Kanayama K., Yasuda R., Thakkar A.J. Improved Roothaan-Hartree-Fock wave functions for atoms and ions with n≤54. J. Chem. Phys. 1995, 103(8):3000-3005.
    • (1995) J. Chem. Phys. , vol.103 , Issue.8 , pp. 3000-3005
    • Koga, T.1    Watanabe, S.2    Kanayama, K.3    Yasuda, R.4    Thakkar, A.J.5
  • 39
    • 4344648428 scopus 로고    scopus 로고
    • Multiresolution quantum chemistry in multiwavelet bases: analytic derivatives for Hartree-Fock and density functional theory
    • Yanai T., Fann G.I., Gan Z., Harrison R.J., Beylkin G. Multiresolution quantum chemistry in multiwavelet bases: analytic derivatives for Hartree-Fock and density functional theory. J. Chem. Phys. 2004, 121(7):2866-2876.
    • (2004) J. Chem. Phys. , vol.121 , Issue.7 , pp. 2866-2876
    • Yanai, T.1    Fann, G.I.2    Gan, Z.3    Harrison, R.J.4    Beylkin, G.5
  • 42
    • 20344365516 scopus 로고
    • Integral approximations for LCAO-SCF calculations
    • Vahtras O., Almlöf J., Feyereisen M. Integral approximations for LCAO-SCF calculations. Chem. Phys. Lett. 1993, 213(5):514-518.
    • (1993) Chem. Phys. Lett. , vol.213 , Issue.5 , pp. 514-518
    • Vahtras, O.1    Almlöf, J.2    Feyereisen, M.3
  • 43
    • 34047253234 scopus 로고    scopus 로고
    • Quasi-continuum orbital-free density-functional theory: a route to multi-million atom non-periodic DFT calculation
    • Gavini V., Bhattacharya K., Ortiz M. Quasi-continuum orbital-free density-functional theory: a route to multi-million atom non-periodic DFT calculation. J. Mech. Phys. Solids 2007, 55(4):697-718.
    • (2007) J. Mech. Phys. Solids , vol.55 , Issue.4 , pp. 697-718
    • Gavini, V.1    Bhattacharya, K.2    Ortiz, M.3
  • 44
    • 84856233829 scopus 로고    scopus 로고
    • Approximation of the electron density of aluminium clusters in tensor-product format
    • Blesgen T., Gavini V., Khoromskaia V. Approximation of the electron density of aluminium clusters in tensor-product format. J. Comput. Phys. 2012, 231(6):2551-2564.
    • (2012) J. Comput. Phys. , vol.231 , Issue.6 , pp. 2551-2564
    • Blesgen, T.1    Gavini, V.2    Khoromskaia, V.3


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