Coarse-graining kohn-sham density functional theory

Journal of the Mechanics and Physics of Solids

Volumn 61, Issue 1, 2013, Pages 38-60

  Suryanarayana, Phanish ^a   Bhattacharya, Kaushik ^b   Ortiz, Michael ^b  

^a Georgia Institute of Technology   (United States)

^b California Institute of Technology   (United States)

Author keywords

Coarse graining; Defects; Density Functional Theory; Gauss quadrature; Linear scaling

Indexed keywords

APPROXIMATION SCHEME; COARSE GRAINING; COARSE-GRAINED; COMPUTATIONAL COSTS; FINE RESOLUTION; GAUSS QUADRATURES; HAMILTONIAN OPERATORS; LINEAR SCALING METHOD; LINEAR-SCALING; LOSS OF ACCURACY; MATERIAL DEFECT; ORBITALS; REAL-SPACE; SELECTED EXAMPLES; SELF-CONSISTENT FIELD METHOD;

DEFECTS; HAMILTONIANS; ITERATIVE METHODS; MATHEMATICAL OPERATORS;

DENSITY FUNCTIONAL THEORY;

EID: 84867582892     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmps.2012.09.002     Document Type: Article

References (57)

1. G.B. Bachelet, D.R. Hamann, and M. Schlüter Pseudopotentials that work from H to Pu Phys. Rev. B 26 8 1982 4199 4228
2. M. Barrault, E. Cances, W. Hager, and C.L. Bris Multilevel domain decomposition for electronic structure calculations J. Comput. Phys. 222 1 2007 86 109
3. N. Bernstein, J.R. Kermode, and G. Csanyi Hybrid atomistic simulation methods for materials systems Rep. Prog. Phys. 72 2 2009 026501 (25pp)
4. D.R. Bowler, and T. Miyazaki O (N) methods in electronic structure calculations Rep. Prog. Phys. 75 3 2012 036503
5. E. Cances, C.L. Bris, and P.-L. Lions Molecular simulation and related topics some open mathematical problems Nonlinearity 21 9 2008 T165
6. A. Castro, H. Appel, M. Oliveira, C.A. Rozzi, X. Andrade, F. Lorenzen, M.A.L. Marques, E.K.U. Gross, and A. Rubio Octopus a tool for the application of time-dependent density functional theory Phys. Status Solidi B Basic Solid State Phys. 243 11 2006 2465 2488 (Pubitemid 44368981)
7. J.R. Chelikowsky, N. Troullier, and Y. Saad Finite-difference- pseudopotential method electronic structure calculations without a basis Phys. Rev. Lett. 72 8 1994 1240 1243 (Pubitemid 24975768)
8. Choly, N., Lu, G., Weinan, E., Kaxiras, E., March 2005. Multiscale simulations in simple metals: a density-functional-based methodology. Phys. Rev. B 71 (9), 094101.
9. A. Cuitino, L. Stainier, G. Wang, A. Strachan, T. Cagin, W. Goddard, and M. Ortiz A multiscale approach for modeling crystalline solids J. Comput. Aided Mater 8 January (2-3) 2002 127 149
10. H.-r. Fang, and Y. Saad Two classes of multisecant methods for nonlinear acceleration Numer. Linear Algebra Appl. 16 March (3) 2009 197 221
11. M. Finnis Interatomic Forces in Condensed Matter 2003 Oxford University Press
12. C. Fiolhais, J.P. Perdew, S.Q. Armster, J.M. MacLaren, and M. Brajczewska Dominant density parameters and local pseudopotentials for simple metals Phys. Rev. B 51 20 1995 14001 14011
13. G. Forsythe, M. Malcolm, and C. Moler Computer Methods for Mathematical Computations 1973 Prentice-Hall
14. G. Galli, and M. Parrinello Large scale electronic structure calculations Phys. Rev. Lett. 69 December (24) 1992 3547 3550
15. García-Cervera, C.J., Lu, J., Xuan, Y., Weinan, E., March 2009. Linear-scaling subspace-iteration algorithm with optimally localized nonorthogonal wave functions for Kohn-Sham density functional theory. Phys. Rev. B 79 (11), 115110.
16. V. Gavini, K. Bhattacharya, and M. Ortiz Quasi-continuum orbital-free density-functional theory a route to multi-million atom non-periodic dft calculation J. Mech. Phys. Solids 55 January (4) 2007 697 718 (Pubitemid 46551181)
17. M.J. Gillan Calculation of the vacancy formation energy in aluminium J. Phys. Condens. Matter 1 4 1989 689
18. S. Goedecker Linear scaling electronic structure methods Rev. Mod. Phys. 71 July (4) 1999 1085 1123 (Pubitemid 129336905)
19. G. Golub, and G. Meurant Matrices, Moments and Quadrature with Applications 2010 Princeton University Press
20. X. Gonze, J.M. Beuken, R. Caracas, F. Detraux, M. Fuchs, G.M. Rignanese, L. Sindic, M. Verstraete, G. Zerah, F. Jollet, M. Torrent, A. Roy, M. Mikami, P. Ghosez, J.Y. Raty, and D.C. Allan First-principles computation of material properties the abinit software project Comput. Mater. Sci. 25 2002 478 492 (15) (Pubitemid 35251749)
21. N. Govind, Y.A. Wang, and E.A. Carter Electronic-structure calculations by first-principles density-based embedding of explicitly correlated systems J. Chem. Phys. 110 16 1999 7677 7688
22. R. Haydock Solid State Physics vol. 35 1980 Academic Press
23. R. Haydock, V. Heine, and M. Kelly Electronic-structure based on local atomic environment for tight-binding bands J. Phys. C Solid State 5 January (20) 1972 pp. 2845-2858
24. R. Haydock, V. Heine, and M. Kelly Electronic-structure based on local atomic environment for tight-binding bands II J. Phys. C Solid State 8 January (16) 1975 2591 2605
25. P. Hohenberg, and W. Kohn Inhomogeneous electron gas Phys. Rev. 136 3B 1964 B864 B871
26. S. Ismail-Beigi, and T.A. Arias New algebraic formulation of density functional calculation Comput. Phys. Commun. 128 1-2 2000 1 45
27. L. Kleinman, and D.M. Bylander Efficacious form for model pseudopotentials Phys. Rev. Lett. 48 20 1982 1425 1428
28. J. Knap, and M. Ortiz An analysis of the quasicontinuum method J. Mech. Phys. Solids 49 September (9) 2001 1899 1923 (Pubitemid 32768095)
29. G.D. Knott Interpolating Cubic Splines 2000 Springer-Verlag
30. W. Kohn, and L.J. Sham Self-consistent equations including exchange and correlation effects Phys. Rev. 140 4A 1965 A1133 A1138
31. G. Kresse, and J. Furthmüller Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set Phys. Rev. B 54 16 1996 11169 11186
32. D.C. Langreth, and M.J. Mehl Beyond the local-density approximation in calculations of ground-state electronic properties Phys. Rev. B 28 4 1983 1809 1834
33. G. Lu, E.B. Tadmor, and E. Kaxiras From electrons to finite elements a concurrent multiscale approach for metals Phys. Rev. B Condens. Matter Mater. Phys. 73 2 2006 024108
34. R. Martin Electronic Structure Basic Theory and Practical Methods 2004 Cambridge University Press
35. F. Mauri, G. Galli, and R. Car Orbital formulation for electronic-structure calculations with linear system-size scaling Phys. Rev. B 47 April (15) 1993 9973 9976
36. R.E. Miller, and E.B. Tadmor A unified framework and performance benchmark of fourteen multiscale atomistic/continuum coupling methods Model. Simul. Mater. Sci. 17 January (5) 2009 053001
37. A. Moren, and A. Branquinho Coimbra Lecture Notes on Orthogonal Polynomials 2008 Nova Science Publishers
38. R. Parr, and W. Yang Density-Functional Theory of Atoms and Molecules 1989 Oxford University Press
39. J.E. Pask, B.M. Klein, C.Y. Fong, and P.A. Sterne Real-space local polynomial basis for solid-state electronic-structure calculations a finite-element approach Phys. Rev. B 59 19 1999 12352 12358
40. J.P. Perdew, J.A. Chevary, S.H. Vosko, K.A. Jackson, M.R. Pederson, D.J. Singh, and C. Fiolhais Atoms, molecules, solids, and surfaces applications of the generalized gradient approximation for exchange and correlation Phys. Rev. B 46 11 1992 6671 6687
41. R. Phillips Crystals, Defects and Microstructure Modeling Across Scales 2001 Cambridge University Press
42. A.M. Rappe, K.M. Rabe, E. Kaxiras, and J.D. Joannopoulos Optimized pseudopotentials Phys. Rev. B 41 2 1990 1227 1230
43. W. Rudin Functional Analysis 1991 Mc Graw Hill
44. Y. Saad, and M.H. Schultz GMRES a generalized minimal residual algorithm for solving nonsymmetric linear systems SIAM J. Sci. Stat. Comput. 7 3 1986 856 869
45. M.D. Segall, P.J.D. Lindan, M.J. Probert, C.J. Pickard, P.J. Hasnip, S.J. Clark, and M.C. Payne First-principles simulation ideas, illustrations and the CASTEP code J. Phys. Condens. Matter 14 11 2002 2717 2744 (Pubitemid 34288361)
46. C.-K. Skylaris, P.D. Haynes, A.A. Mostofi, and M.C. Payne Introducing ONETEP linear-scaling density functional simulations on parallel computers J. Chem. Phys. 122 8 2005 084119
47. S.P. Suetin Padé approximants and efficient analytic continuation of a power series Russ. Math. Surv. 57 1 2002 43
48. P. Suryanarayana, K. Bhattacharya, and M. Ortiz A mesh-free convex approximation scheme for Kohn-Sham density functional theory J. Comput. Phys. 230 13 2011 5226 5238
49. P. Suryanarayana, V. Gavini, T. Blesgen, K. Bhattacharya, and M. Ortiz Non-periodic finite-element formulation of Kohn-Sham density functional theory J. Mech. Phys. Solids 58 2 2010 256 280
50. E. Tadmor, M. Ortiz, and R. Phillips Quasicontinuum analysis of defects in solids Philos. Mag. A Phys. Condens. Matter Struct. Defects Mech. Prop. 73 June (6) 1996 1529 1563 (Pubitemid 126310376)
51. N. Troullier, and J.L. Martins Efficient pseudopotentials for plane-wave calculations Phys. Rev. B 43 3 1991 1993 2006
52. E. Tsuchida Ab initio molecular-dynamics study of liquid formamide J. Chem. Phys. 121 10 2004 4740 4746
53. W. Van Assche Padé and hermite-padé approximation and orthogonality Surv. Approx. Theory 2 2006 61 91
54. D. Vanderbilt Soft self-consistent pseudopotentials in a generalized eigenvalue formalism Phys. Rev. B 41 11 1990 7892 7895
55. L. Vitos, A. Ruban, H. Skriver, and J. Kollár The surface energy of metals Surf. Sci. 411 1-2 1998 186 202 (Pubitemid 128431152)
56. C.R. Vogel Computational Methods for Inverse Problems 2002 Society for Industrial and Applied Mathematics
57. M. Weinert, and J.W. Davenport Fractional occupations and density-functional energies and forces Phys. Rev. B 45 June (23) 1992 13709 13712