Computation of the Hartree-Fock Exchange by the Tensor-Structured Methods

Computational Methods in Applied Mathematics

Volumn 10, Issue 2, 2010, Pages 204-218

  Khoromskaia, V ^a  

^a MAX PLANCK INSTITUTE FOR MATHEMATICS IN THE SCIENCES   (Germany)

Author keywords

canonical model; discrete tensor convolution; exchange matrix; Hartree Fock operator; tensor product basis functions; tensor structured methods

Indexed keywords

EID: 84948466347     PISSN: 16094840     EISSN: 16099389     Source Type: Journal    
DOI: 10.2478/cmam-2010-0012     Document Type: Article

References (27)

1. E. Acar, T. G. Kolda, and D. M. Dunlavy, An Optimization Approach for Fitting Canonical Tensor Decompositions, Technical Report Number SAND2009-0857, Sandia National Laboratories, Albuquerque, NM and Livermore, CA, February 2009.
2. C. Bertoglio and B. N. Khoromskij, Low rank tensor-product approximation of projected Green kernels via sinc-quadratures, Preprint 79/2008, MPI MIS Leipzig, 2008 (submitted).
3. L. De Lathauwer, B. De Moor, and J. Vandewalle, On the best rank-1 and rank-(R\, RN) approximation of higher-order tensors, SIAM J. Matrix Anal. Appl, 21 (2000), pp. 1324-1342.
4. L. De Lathauwer, B. De Moor, J. Vandewalle, A multilinear singular value decomposition, SIAM J. Matrix Anal. Appl, 21 (2000), pp. 1253-1278.
5. I.P. Gavrilyuk, W. Hackbusch, and B.N. Khoromskij, Hierarchical Tensor-Product Approximation to the Inverse and Related Operators in High-Dimensional Elliptic Problems, Computing, 74 (2005), pp. 131-157.
6. I. P. Gavrilyuk, W. Hackbusch, and B. N. Khoromskij, Data-sparse approximation of a class of operator-valued functions, Math. Comp, 74 (2005), pp. 681-708.
7. H.-J. Flad, W. Hackbusch, B.N. Khoromskij, and R. Schneider, Concept of Data-Sparse Tensor-Product Approximation in Many-Particle Modeling, Matrix Methods: Theory, Algorithms, Applications, World Scientific publishing, Singapoure, (2010), pp. 313-347.
8. W. Hackbusch, B.N. Khoromskij, and E.E. Tyrtyshnikov, Hierarchical Kronecker tensor-product approximations, J. Numer. Math. 13 (2005), pp. 119-156.
9. V. Khoromskaia, Numerical Solution of the Hartree-Fock equation by the Tensor-Structured Methods, PhD Dissertation, (in preparation), MPI MiS, Leipzig, 2010.
10. B. N. Khoromskij, Structured Rank-(r\,., r¿) Decomposition of Function-related Tensors in Rd, Comp. Meth. in Applied Math., 6 (2006), no 2, pp. 194-220.
11. B. N. Khoromskij, On Tensor Approximation of Green Iterations for Kohn-Sham equations, Computing and Visualisation in Science, 11 (2008), pp. 259-271.
12. B. N. Khoromskij, Tensor-structured Preconditioners and Approximate Inverse of Elliptic Operators in Rd, J. Constructive Approximation, 30 (2009), pp. 599-620.
13. B. N. Khoromskij, Fast and Accurate Tensor Approximation of Multivariate Convolution with Linear Scaling in Dimension, Preprint MPI MIS, Leipzig 36 (2008); J. Comp. Appl. Math., to appear.
14. B. N. Khoromskij and V. Khoromskaia, Low Rank Tucker Tensor Approximation to the Classical Potentials, Central European J. of Math, 5 (2007), no. 3, pp. 1-28.
15. B.N. Khoromskij and V. Khoromskaia, Multigrid Tensor Approximation of Function Related Arrays, SIAM J. on Sci. Comp, 31 (2009), no. 4, pp. 3002-3026.
16. B.N. Khoromskij, V. Khoromskaia, and H.-J. Flad, Numerical solution of the Hartree-Fock equation in multilevel tensor-structured format, Preprint 44/2009 MPI MIS, Leipzig, 2009.
17. 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. 5749-5762.
18. T.G. Kolda and B. W. Bader, Tensor Decompositions and Applications, SIAM Rev, 51 (2009), no. 3, pp. 455-500.
19. C. Le Bris, ed., Handbook of Numerical Analysis, Vol. X, Computational Chemistry, North-Holland, 2003.
20. C. Le Bris. Computational chemistry from the perspective of numerical analysis, Acta Numerica, 14 (2005), pp. 363-444.
21. I. Oseledets, D. Savostyanov, and E. E. Tyrtyshnikov, Cross approximation in electron density computations, Num. Lin. Alg. Appl., submitted, 2009.
22. I. Oseledets, D. Savostyanov, and E. E. Tyrtyshnikov. Linear algebra for tensor problems, Computing, 85 (2009), pp. 169-188.
23. R. Polly, H.-J. Werner, F. R. Manby, and P. J. Knowles. Fast Hartree-Fock theory using density fitting approximations, Mol.Phys, 102 (2004), pp. 2311-2321.
24. J. Sielk, H. F. von Horsten, F. Krüger, R. Schneider, and B. Hartke, Quantum-mechanical wavepacket propagation in a sparse, adaptive basis of interpolating Gaussians with collocation, Physical Chemistry Chemical Physics, 11 (2009), pp. 463-475.
25. J. VandeVondele, M. Krack, F. Mohamed, M. Parinello, Th. Chassaing, and J. Hutter, QUICKSTEP: Fast and accurate density functional calculations using a mixed gaussian and plane waves approach, Comp. Phys. Comm, 167 (2005), pp. 103-128.
26. H.-J. Werner, P.J. Knowles et al, MOLPRO, version 2002.10, a package of ab initio programs for electronic structure calculations.
27. T. Yanai, G. Fann, Z. Gan, R. Harrison, and G. Beylkin, Multiresolution quantum chemistry: Hartree-Fock exchange, J. Chem. Phys, 121 (2004), no. 14, pp. 6680-6688.