×

zbMATH — the first resource for mathematics

Computing localized representations of the Kohn-Sham subspace via randomization and refinement. (English) Zbl 1382.82022

MSC:
82C10 Quantum dynamics and nonequilibrium statistical mechanics (general)
81V55 Molecular physics
65Z05 Applications to the sciences
65F30 Other matrix algorithms (MSC2010)
PDF BibTeX Cite
Full Text: DOI arXiv
References:
[1] E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen, LAPACK Users’ Guide, 3rd ed., SIAM, Philadelphia, 1999. · Zbl 0934.65030
[2] F. Aquilante, T. B. Pedersen, A. S. de Merás, and H. Koch, Fast noniterative orbital localization for large molecules, J. Chem. Phys., 125 (2006), 174101.
[3] A. D. Becke, Density functional thermochemistry. III. The role of exact exchange, J. Chem. Phys., 98 (1993), pp. 5648–5652.
[4] M. Benzi, P. Boito, and N. Razouk, Decay properties of spectral projectors with applications to electronic structure, SIAM Rev., 55 (2013), pp. 3–64. · Zbl 1377.65155
[5] L. S. Blackford, J. Choi, A. Cleary, E. D’Azevedo, J. Demmel, I. Dhillon, J. Dongarra, S. Hammarling, G. Henry, A. Petitet, K. Stanley, D. Walker, and R. C. Whaley, ScaLAPACK Users’ Guide, SIAM, Philadelphia, 1997.
[6] E. I. Blount, Formalisms of Band Theory, Solid State Phys. 13, Academic Press, New York, 1962, pp. 305–373.
[7] C. Brouder, G. Panati, M. Calandra, C. Mourougane, and N. Marzari, Exponential localization of Wannier functions in insulators, Phys. Rev. Lett., 98 (2007), 046402.
[8] J. Cloizeaux, Analytical properties of \(n\)-dimensional energy bands and Wannier functions, Phys. Rev., 135 (1964), pp. A698–A707.
[9] J. Cloizeaux, Energy bands and projection operators in a crystal: Analytic and asymptotic properties, Phys. Rev., 135 (1964), pp. A685–A697.
[10] A. Damle, L. Lin, and L. Ying, Compressed representation of Kohn–Sham orbitals via selected columns of the density matrix, J. Chem. Theory Comput., 11 (2015), pp. 1463–1469.
[11] A. Damle, L. Lin, and L. Ying, SCDM-K: Localized orbitals for solids via selected columns of the density matrix, J. Comput. Phys., 334 (2017), pp. 1–15. · Zbl 1375.81255
[12] J. Demmel, L. Grigori, M. Gu, and H. Xiang, Communication Avoiding Rank Revealing QR Factorization with Column Pivoting, Tech. Report UCB/EECS-2013-46, EECS Department, University of California, Berkeley, 2013. · Zbl 1327.65078
[13] J. A. Duersch and M. Gu, Randomized QR with column pivoting, SIAM J. Sci. Comput., 39 (2017), pp. C263–C291. · Zbl 1371.65026
[14] W. E, T. Li, and J. Lu, Localized bases of eigensubspaces and operator compression, Proc. Natl. Acad. Sci. USA, 107 (2010), pp. 1273–1278. · Zbl 1205.15017
[15] J. M. Foster and S. F. Boys, Canonical configurational interaction procedure, Rev. Modern Phys., 32 (1960), pp. 300–302.
[16] P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L Chiarotti, M. Cococcioni, I. Dabo, A. Dal Corso, S. de Gironcoli, S. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos, N. Marzari, F. Mauri, R. Mazzarello, S. Paolini, A. Pasquarello, L. Paulatto, C. Sbraccia, S. Scandolo, G. Sclauzero, A. P Seitsonen, A. Smogunov, P. Umari, and R. M Wentzcovitch, Quantum ESPRESSO: A modular and open-source software project for quantum simulations of materials, J. Phys. Condens. Matter, 21 (2009), 395502.
[17] G. H. Golub and C. F. Van Loan, Matrix Computations, 3rd ed., Johns Hopkins University Press, Baltimore, 1996. · Zbl 0865.65009
[18] F. Gygi, Compact representations of Kohn–Sham invariant subspaces, Phys. Rev. Lett., 102 (2009), 166406.
[19] F. Gygi and I. Duchemin, Efficient computation of Hartree–Fock exchange using recursive subspace bisection, J. Chem. Theory Comput., 9 (2012), pp. 582–587.
[20] M. Z. Hasan and C. L. Kane, Colloquium: Topological insulators, Rev. Modern Phys., 82 (2010), 3045.
[21] P. Hohenberg and W. Kohn, Inhomogeneous electron gas, Phys. Rev., 136 (1964), pp. B864–B871.
[22] W. Humphrey, A. Dalke, and K. Schulten, VMD—Visual molecular dynamics, J. Molecular Graphics, 14 (1996), pp. 33–38.
[23] W. Kohn, Density functional and density matrix method scaling linearly with the number of atoms, Phys. Rev. Lett., 76 (1996), pp. 3168–3171.
[24] W. Kohn and L. Sham, Self-consistent equations including exchange and correlation effects, Phys. Rev., 140 (1965), pp. A1133–A1138.
[25] L. Lin and J. Lu, Sharp Decay Estimates of Discretized Green’s Functions for Schrödinger Type Operators, , 2015.
[26] M. W. Mahoney and P. Drineas, Cur matrix decompositions for improved data analysis, Proc. Nat. Acad. Sci. USA, 106 (2009), pp. 697–702. · Zbl 1202.68480
[27] R. Martin, Electronic Structure: Basic Theory and Practical Methods, Cambridge University Press, New York, 2004. · Zbl 1152.74303
[28] P. G. Martinsson, G. Ortí, N. Heavner, and R. van de Geijn, Householder QR factorization with randomization for column pivoting (HQRRP), SIAM J. Sci. Comput., 39 (2017), pp. C96–C115. · Zbl 1365.65070
[29] N. Marzari, A. A. Mostofi, J. R. Yates, I. Souza, and D. Vanderbilt, Maximally localized Wannier functions: Theory and applications, Rev. Modern Phys., 84 (2012), pp. 1419–1475.
[30] N. Marzari and D. Vanderbilt, Maximally localized generalized Wannier functions for composite energy bands, Phys. Rev. B, 56 (1997), pp. 12847–12865.
[31] A. A. Mostofi, J. R. Yates, Y. Lee, I. Souza, D. Vanderbilt, and N. Marzari, Wannier\(90\): A tool for obtaining maximally-localised Wannier functions, Comput. Phys. Comm., 178 (2008), pp. 685–699. · Zbl 1196.81033
[32] J. I. Mustafa, S. Coh, M. L. Cohen, and S. G. Louie, Automated construction of maximally localized Wannier functions: Optimized projection functions method, Phys. Rev. B, 92 (2015), 165134.
[33] G. Nenciu, Existence of the exponentially localised Wannier functions, Comm. Math. Phys., 91 (1983), pp. 81–85. · Zbl 0545.47012
[34] V. Ozoliņš, R. Lai, R. Caflisch, and S. Osher, Compressed modes for variational problems in mathematics and physics, Proc. Natl. Acad. Sci. USA, 110 (2013), pp. 18368–18373. · Zbl 1292.81024
[35] J. P. Perdew, M. Ernzerhof, and K. Burke, Rationale for mixing exact exchange with density functional approximations, J. Chem. Phys., 105 (1996), pp. 9982–9985.
[36] E. Prodan and W. Kohn, Nearsightedness of electronic matter, Proc. Natl. Acad. Sci. USA, 102 (2005), pp. 11635–11638.
[37] X. Wu, A. Selloni, and R. Car, Order-N implementation of exact exchange in extended insulating systems, Phys. Rev. B, 79 (2009), 085102.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.