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Volumn 11, Issue 3, 2011, Pages 327-341

QTT representation of the hartree and exchange operators in electronic structure calculations

Author keywords

Coloumb and exchange operators; Electronic structure calculations; Hartree Fock equation; QTT format; Tensor structured methods

Indexed keywords


EID: 80053918083     PISSN: 16094840     EISSN: 16099389     Source Type: Journal    
DOI: 10.2478/cmam-2011-0018     Document Type: Article
Times cited : (22)

References (46)
  • 1
    • 0001871197 scopus 로고
    • Direct methods in electronic structure theory
    • D. R. Yarkony, Ed. , World Scientific, Singapore
    • J. Almlöf, Direct methods in electronic structure theory, In D. R. Yarkony, Ed., Modern Electronic Structure Theory, World Scientific, Singapore, 2 (1995), pp. 110-151.
    • (1995) Modern Electronic Structure Theory , vol.2 , pp. 110-151
    • Almlöf, J.1
  • 2
    • 33846877429 scopus 로고    scopus 로고
    • Multilevel domain decomposition for electronic structure calculations
    • M. Barrault, E. Cancés, W. Hager, and Le Bris, Multilevel domain decomposition for electronic structure calculations, J. Comput. Phys. 222 (2007), pp. 86-109.
    • (2007) J. Comput. Phys. , vol.222 , pp. 86-109
    • Barrault, M.1    Cancés, E.2    Hager, W.3    Bris, L.4
  • 4
    • 79952665459 scopus 로고    scopus 로고
    • Low-order tensor approximations for electronic wave functions: HartreeFock method with guaranteed precision
    • F. A. Bischoff and E. F. Valeev, Low-order tensor approximations for electronic wave functions: HartreeFock method with guaranteed precision, J. of Chem. Phys., 134 (2011), pp. 104104-1-10.
    • (2011) J. of Chem. Phys. , vol.134 , pp. 1041041-10410410
    • Bischoff, F.A.1    Valeev, E.F.2
  • 5
    • 33746614482 scopus 로고
    • Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen
    • T.H. Dunning Jr, Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen, J. Chem. Phys., 90 (1989), pp. 1007-1023.
    • (1989) J. Chem. Phys. , vol.90 , pp. 1007-1023
    • Dunning Jr., T.H.1
  • 8
    • 84969641356 scopus 로고    scopus 로고
    • Concept of data-sparse tensor-product approximation in many-particle modeling
    • V. Olshevsky and E. Tyrtyshnikov, eds., World Scientific Publishers, Singapoure
    • H.-J. Flad, W. Hackbusch, B.N. Khoromskij, and R. Schneider. Concept of data-sparse tensor-product approximation in many-particle modeling, In: "Matrix Methods: Theory, Algorithms, Applications", V. Olshevsky and E. Tyrtyshnikov, eds., World Scientific Publishers, Singapoure, (2010), pp. 313-347.
    • (2010) Matrix Methods: Theory, Algorithms, Applications , pp. 313-347
    • Flad, H.-J.1    Hackbusch, W.2    Khoromskij, B.N.3    Schneider, R.4
  • 9
    • 17144410769 scopus 로고    scopus 로고
    • Hierarchical tensor-product approximation to the inverse and related operators for high-dimensional elliptic problems
    • DOI 10.1007/s00607-004-0086-y
    • I.P. Gavrilyuk, W. Hackbusch, and B.N. Khoromskij, Tensor-product approximation to elliptic and parabolic solution operators in higher dimensions, Computing 74 (2005), pp. 131-157. (Pubitemid 40512277)
    • (2005) Computing (Vienna/New York) , vol.74 , Issue.2 , pp. 131-157
    • Gavrilyuk, I.P.1    Hackbusch, W.2    Khoromskij, B.N.3
  • 12
    • 34547545863 scopus 로고    scopus 로고
    • Sparse grids for the Schrödinger equation
    • M. Griebel and J. Hamaekers, Sparse grids for the Schrödinger equation, M2AN, 41 (2007), pp. 215-247.
    • (2007) M2AN , vol.41 , pp. 215-247
    • Griebel, M.1    Hamaekers, J.2
  • 13
    • 29144513721 scopus 로고    scopus 로고
    • Low-rank Kronecker-product approximation to multi-dimensional nonlocal operators. Part I. Separable approximation of multi-variate functions
    • DOI 10.1007/s00607-005-0144-0
    • W. Hackbusch and B.N. Khoromskij, Low-rank Kronecker product approximation to multi-dimensional nonlocal operators. Part I. Separable approximation of multi-variate functions, Computing 76 (2006), pp. 177-202. (Pubitemid 41813085)
    • (2006) Computing (Vienna/New York) , vol.76 , Issue.3-4 , pp. 177-202
    • Hackbusch, W.1    Khoromskij, B.N.2
  • 16
    • 11044224123 scopus 로고    scopus 로고
    • Multiresolution quantum chemistry: Basic theory and initial applications
    • DOI 10.1063/1.1791051, 12
    • R.J. Harrison, G.I. Fann, T. Yanai, Z. Gan, and G. Beylkin, Multiresolution quantum chemistry: Basic theory and initial applications, J. of Chemical Physics, 121 (2004), no. 23, pp. 11587-11598. (Pubitemid 40044262)
    • (2004) Journal of Chemical Physics , vol.121 , Issue.23 , pp. 11587-11598
    • Harrison, R.J.1    Fann, G.I.2    Yanai, T.3    Gan, Z.4    Beylkin, G.5
  • 18
    • 85162707890 scopus 로고
    • The expression of a tensor or a polyadic as a sum of products
    • F.L. Hitchcock, The expression of a tensor or a polyadic as a sum of products, J. Math. Phys., 6 (1927), pp. 164-189.
    • (1927) J. Math. Phys. , vol.6 , pp. 164-189
    • Hitchcock, F.L.1
  • 19
    • 79960985026 scopus 로고    scopus 로고
    • On manifold of tensors of fixed TT-rank
    • TU Berlin
    • S. Holtz, Th. Rohwedder, and R. Schneider, On manifold of tensors of fixed TT-rank, Tehn. Rep. 61, TU Berlin, 2010.
    • (2010) Tehn. Rep. , vol.61
    • Holtz, S.1    Rohwedder, Th.2    Schneider, R.3
  • 23
    • 84948466347 scopus 로고    scopus 로고
    • Computation of the hartree-fock exchange in the tensor-structured format
    • V. Khoromskaia, Computation of the Hartree-Fock Exchange in the Tensor-structured Format, Computational Methods in Applied Mathematics, 10 (2010), no. 2, pp. 204-218.
    • (2010) Computational Methods in Applied Mathematics , vol.10 , Issue.2 , pp. 204-218
    • Khoromskaia, V.1
  • 25
    • 77955278344 scopus 로고    scopus 로고
    • Fast and Accurate Tensor Approximation of a Multivariate Convolution with Linear Scaling in Dimension
    • B.N. Khoromskij, Fast and Accurate Tensor Approximation of a Multivariate Convolution with Linear Scaling in Dimension, J. of Comp. Appl. Math., 234 (2010), pp. 3122-3139.
    • (2010) J. of Comp. Appl. Math. , vol.234 , pp. 3122-3139
    • Khoromskij, B.N.1
  • 26
    • 79960994573 scopus 로고    scopus 로고
    • O(d logN)-Quantics Approximation of N-d Tensors in High-Dimensional Numerical Modeling
    • DOI: 10.1007/s00365-011-9131-1. Preprint 55/2009 MPI MiS, Leipzig 2009
    • B.N. Khoromskij, O(d logN)-Quantics Approximation of N-d Tensors in High-Dimensional Numerical Modeling, J. Constr. Approx. 2011, DOI: 10.1007/s00365-011-9131-1. Preprint 55/2009 MPI MiS, Leipzig 2009.
    • (2011) J. Constr. Approx.
    • Khoromskij, B.N.1
  • 27
    • 80053910275 scopus 로고    scopus 로고
    • Lecture Notes, University/ETH Zuerich, Preprint 06-2011, Uni. Zuerich
    • B.N. Khoromskij, Introduction to Tensor Numerical Methods in Scientific Computing, Lecture Notes, University/ETH Zuerich, Preprint 06-2011, Uni. Zuerich 2011, pp. 1-238, URL http://www.math.uzh.ch/fileadmin/math/preprints/06 11.pdf.
    • (2011) Introduction to Tensor Numerical Methods in Scientific Computing , pp. 1-238
    • Khoromskij, B.N.1
  • 28
    • 84897586218 scopus 로고    scopus 로고
    • Multigrid tensor approximation of function related multidimensional arrays
    • B.N. Khoromskij and V. Khoromskaia, Multigrid tensor approximation of function related multidimensional arrays, SIAM J. on Sci. Comp., 31 (2009), no. 4, pp. 3002-3026.
    • (2009) SIAM J. on Sci. Comp. , vol.31 , Issue.4 , pp. 3002-3026
    • Khoromskij, B.N.1    Khoromskaia, V.2
  • 29
    • 67649378419 scopus 로고    scopus 로고
    • Tensor Decomposition in Electronic Structure Calculations on 3D Cartesian Grids
    • B.N. Khoromskij, V. Khoromskaia, S. R. Chinnamsetty, and H.-J. Flad, Tensor Decomposition in Electronic Structure Calculations on 3D Cartesian Grids, J. of Comput. Phys., 228 (2009), pp. 57495762.
    • (2009) J. of Comput. Phys. , vol.228 , pp. 57495762
    • Khoromskij, B.N.1    Khoromskaia, V.2    Chinnamsetty, S.R.3    Flad, H.-J.4
  • 30
    • 79952297523 scopus 로고    scopus 로고
    • Numerical solution of the hartree-fock equation in multilevel tensor-structured format
    • B.N. Khoromskij, V. Khoromskaia, and H.-J. Flad, Numerical Solution of the Hartree-Fock Equation in Multilevel Tensor-structured Format, SIAM J. on Sci. Comp., 33 (2011), no. 1, pp. 45-65.
    • (2011) SIAM J. on Sci. Comp. , vol.33 , Issue.1 , pp. 45-65
    • Khoromskij, B.N.1    Khoromskaia, V.2    Flad, H.-J.3
  • 31
    • 79960448781 scopus 로고    scopus 로고
    • Quantics-TT approximation of elliptic solution operators in higher dimensions
    • B.N. Khoromskij and I. Oseledets, Quantics-TT approximation of elliptic solution operators in higher dimensions, Russ. J. Numer. Anal. Math. Modelling, 26 (2011), no. 3, pp. 303-322.
    • (2011) Russ. J. Numer. Anal. Math. Modelling , vol.26 , Issue.3 , pp. 303-322
    • Khoromskij, B.N.1    Oseledets, I.2
  • 33
    • 68649096448 scopus 로고    scopus 로고
    • Tensor decompositions and applications
    • T. G. Kolda and B. W. Bader, Tensor Decompositions and Applications, SIAM Review, 51 (2009), no. 3, pp. 455-500.
    • (2009) SIAM Review , vol.51 , Issue.3 , pp. 455-500
    • Kolda, T.G.1    Bader, B.W.2
  • 34
    • 19844366465 scopus 로고    scopus 로고
    • Computational chemistry from the perspective of numerical analysis
    • DOI 10.1017/S096249290400025X
    • C. Le Bris, Computational chemistry from the perspective of numerical analysis, Acta Numerica, (2005), pp. 363-444. (Pubitemid 40763886)
    • (2005) Acta Numerica , vol.14 , pp. 363-444
    • Le Bris, C.1
  • 35
    • 77956042755 scopus 로고    scopus 로고
    • Approximation of 2d × 2d matrices using tensor decomposition
    • I.V. Oseledets, Approximation of 2d × 2d matrices using tensor decomposition, SIAM J. Matrix Anal. Appl., 31 (2010), no. 4, pp. 2130-2145.
    • (2010) SIAM J. Matrix Anal. Appl. , vol.31 , Issue.4 , pp. 2130-2145
    • Oseledets, I.V.1
  • 37
    • 51849118006 scopus 로고    scopus 로고
    • Tucker dimensionality reduction of threedimensional arrays in linear time
    • I.V. Oseledets, D.V. Savostyanov, and E.E. Tyrtyshnikov, Tucker dimensionality reduction of threedimensional arrays in linear time, SIMAX, 30 (2008), no. 3, pp. 939-956.
    • (2008) SIMAX , vol.30 , Issue.3 , pp. 939-956
    • Oseledets, I.V.1    Savostyanov, D.V.2    Tyrtyshnikov, E.E.3
  • 38
    • 70449528138 scopus 로고    scopus 로고
    • Breaking the curse of dimensionality or How to Use SVD in Many Dimensions
    • I.V. Oseledets and E.E. Tyrtyshnikov, Breaking the Curse of Dimensionality, or How to Use SVD in Many Dimensions, SIAM J. Sci. Comp., 31 (2009), pp. 3744-3759.
    • (2009) SIAM J. Sci. Comp. , vol.31 , pp. 3744-3759
    • Oseledets, I.V.1    Tyrtyshnikov, E.E.2
  • 39
    • 44349162071 scopus 로고
    • Improved SCF convergence acceleration
    • P. Pulay, Improved SCF convergence acceleration, J. Comput. Chem., 3 (1982), pp. 556-560.
    • (1982) J. Comput. Chem. , vol.3 , pp. 556-560
    • Pulay, P.1
  • 41
    • 65349138836 scopus 로고    scopus 로고
    • Direct minimization for calculating invariant subspaces in density functional computations of the electronic structure
    • R. Schneider, Th. Rohwedder, J. Blauert, and A. Neelov, Direct minimization for calculating invariant subspaces in density functional computations of the electronic structure, J. of Comp. Math., 27 (2009), no. 2-3, pp. 360-387.
    • (2009) J. of Comp. Math. , vol.27 , Issue.2-3 , pp. 360-387
    • Schneider, R.1    Rohwedder, Th.2    Blauert, J.3    Neelov, A.4
  • 42
    • 23844520141 scopus 로고    scopus 로고
    • The density-matrix renormalization group
    • DOI 10.1103/RevModPhys.77.259
    • U. Schollwöck, The Density-Matrix Renormalization Group, Rev. Mod. Phys. 77 (2005), pp. 259-315. (Pubitemid 41490660)
    • (2005) Reviews of Modern Physics , vol.77 , Issue.1 , pp. 259-315
    • Schollwock, U.1
  • 43
    • 0242425255 scopus 로고    scopus 로고
    • Efficient classical simulation of slightly entangled quantum computations
    • G. Vidal, Efficient classical simulation of slightly entangled quantum computations, Phys. Rev. Lett., 91 (2003), no. 14, 147902-1 147902-4.
    • (2003) Phys. Rev. Lett. , vol.91 , Issue.14 , pp. 1479021-1479024
    • Vidal, G.1
  • 44
    • 0042767657 scopus 로고    scopus 로고
    • Multilayer formulation of the multiconfiguration time-dependent Hartree theory
    • H. Wang and M. Thoss, Multilayer formulation of the multiconfiguration time-dependent Hartree theory, J. Chem. Phys. 119 (2003), pp. 1289-1299.
    • (2003) J. Chem. Phys. , vol.119 , pp. 1289-1299
    • Wang, H.1    Thoss, M.2
  • 46
    • 20044389808 scopus 로고
    • Density-matrix algorithms for quantum renormalization groups
    • S.R. White, Density-matrix algorithms for quantum renormalization groups, Phys. Rev. B, 48 (1993), no. 14, pp. 10345-10356.
    • (1993) Phys. Rev. B , vol.48 , Issue.14 , pp. 10345-10356
    • White, S.R.1


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