Journal of Chemical Physics
Feedback | Help | Exit
The Journal of Chemical Physics
   
 
 
 
Previous Article
Nonadiabatic electron wavepacket dynamics of molecules in an intense optical field: An ab initio electronic state study
A theory of quantum electron wavepacket dynamics that nonadiabatically couples with classical nuclear motions in intense optical fields is studied. The formalism is intended to track the laser-driven ...
Next Article
Quantum trajectories in complex space: One-dimensional stationary scattering problems
One-dimensional time-independent scattering problems are investigated in the framework of the quantum Hamilton–Jacobi formalism. The equation for the local approximate quantum trajectories near ...

Turbo charging time-dependent density-functional theory with Lanczos chains

J. Chem. Phys. 128, 154105 (2008); doi:10.1063/1.2899649

Published 16 April 2008

You are logged in to this journal.

Dario Rocca,1,2 Ralph Gebauer,3,2 Yousef Saad,4 and Stefano Baroni1,2
1Scuola Internazionale Superiore di Studi Avanzati (SISSA), Via Beirut 2-4, I-34014 Trieste, Italy
2CNR-INFM DEMOCRITOS Theory@Elettra Group, I-34014 Trieste, Italy
3The Abdus Salam International Centre for Theoretical Physics (ICTP), Strada Costiera 11, I-34014 Trieste, Italy
4Department of Computer Science and Engineering, University of Minnesota, and Minnesota Supercomputing Institute, Minneapolis, Minnesota 55455, USA
We introduce a new implementation of time-dependent density-functional theory which allows the entire spectrum of a molecule or extended system to be computed with a numerical effort comparable to that of a single standard ground-state calculation. This method is particularly well suited for large systems and/or large basis sets, such as plane waves or real-space grids. By using a superoperator formulation of linearized time-dependent density-functional theory, we first represent the dynamical polarizability of an interacting-electron system as an off-diagonal matrix element of the resolvent of the Liouvillian superoperator. One-electron operators and density matrices are treated using a representation borrowed from time-independent density-functional perturbation theory, which permits us to avoid the calculation of unoccupied Kohn–Sham orbitals. The resolvent of the Liouvillian is evaluated through a newly developed algorithm based on the nonsymmetric Lanczos method. Each step of the Lanczos recursion essentially requires twice as many operations as a single step of the iterative diagonalization of the unperturbed Kohn–Sham Hamiltonian. Suitable extrapolation of the Lanczos coefficients allows for a dramatic reduction of the number of Lanczos steps necessary to obtain well converged spectra, bringing such number down to hundreds (or a few thousands, at worst) in typical plane-wave pseudopotential applications. The resulting numerical workload is only a few times larger than that needed by a ground-state Kohn–Sham calculation for a same system. Our method is demonstrated with the calculation of the spectra of benzene, C60 fullerene, and of chlorophyll a. ©2008 American Institute of Physics
History: Received 9 January 2008; accepted 27 February 2008; published 16 April 2008
Permalink: http://link.aip.org/link/?JCPSA6/128/154105/1
FULL TEXT OPTIONS   (FREE)
Download HTML Download Sectioned HTML Download PDF (627 kB) Author Select

KEYWORDS and PACS

Keywords
PACS
  • 31.15.E-
    Density-functional theory (atoms and molecules)
  • 36.40.-c
    Atomic and molecular clusters
  • 31.15.xp
    Perturbation theory in atomic and molecular physics
  • YEAR: 2008

RELATED DATABASES

Web of Science

View this record in Web of Science

View Web of Science related articles

PUBLICATION DATA

ISSN:
0021-9606 (print)   1089-7690 (online)
Publisher:
AIP is a member of CrossRef AIP

REFERENCES (65)
View in Separate Window/Tab
  1. E. Runge and E. K. U. Gross, Phys. Rev. Lett. 52, 997 (1984).
  2. G. Onida, L. Reining, and A. Rubio, Rev. Mod. Phys. 74, 601 (2002).
  3. P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964).
  4. W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965).
  5. R. Bauernschmitt and R. Ahlrichs, Chem. Phys. Lett. 256, 454 (1996).
  6. M. E. Casida, in Recent Advances in Density Functional Methods, Part I, edited by D. P. Chong (World Scientific, Singapore, 1995), p. 155.
  7. D. J. Thouless, Nucl. Phys. 21, 225 (1960).
  8. A. D. McLachlan and M. A. Ball, Rev. Mod. Phys. 36, 844 (1964).
  9. J. Olsen, H. J. A. Jensen, and P. Jørgensen, J. Comput. Phys. 74, 265 (1988). [ISI] [ChemPort]
  10. R. E. Stratmann, G. E. Scuseria, and M. J. Frisch, J. Chem. Phys. 109, 8218 (1998).
  11. I. Tamm, J. Phys. (Moscow) 9, 449 (1945).
  12. S. M. Dancoff, Phys. Rev. 78, 382 (1950). [ISI]
  13. S. Hirata and M. Head-Gordon, Chem. Phys. Lett. 314, 291 (1999). [Inspec]
  14. S. Baroni, P. Giannozzi, and A. Testa, Phys. Rev. Lett. 58, 1861 (1987). [MEDLINE]
  15. X. Gonze, Phys. Rev. A 52, 1096 (1995). [MEDLINE]
  16. S. Baroni, S. de Gironcoli, A. Dal Corso, and P. Giannozzi, Rev. Mod. Phys. 73, 515 (2001).
  17. F. Furche, J. Chem. Phys. 114, 5982 (2001);
    18. F. Furche, personal communication (2007).
  18. J. Hutter, J. Chem. Phys. 118, 3928 (2003).
  19. J. R. Chelikowsky, Y. Saad, and I. Vasiliev, Time-Dependent Density Functional Theory, Lecture Notes in Physics Vol. 706 (Springer-Verlag, Berlin, Heidelberg, 2006), Chap. 17, pp. 259–269.
  20. F. Furche and D. Rappoport, in Computational Photochemistry, Theoretical and Computational Chemistry Vol. 16, edited by M. Olivucci (Elsevier Science, Amsterdam, 2005), Chap. III, pp. 93–128.
  21. M. Petersilka, U. J. Gossmann, and E. K. U. Gross, Phys. Rev. Lett. 76, 1212 (1996). [MEDLINE] [ChemPort]
  22. K. Yabana and G. F. Bertsch, Phys. Rev. B 54, 4484 (1996). [MEDLINE]
  23. M. A. L. Marques, A. Castro, G. F. Bertsch, and A. Rubio, Comput. Phys. Commun. 151, 60 (2003).
  24. X. Qian, J. Li, X. Lin, and S. Yip, Phys. Rev. B 73, 035408 (2006).
  25. B. Walker and R. Gebauer, J. Chem. Phys. 127, 164106 (2007). [MEDLINE]
  26. B. Walker, A. M. Saitta, R. Gebauer, and S. Baroni, Phys. Rev. Lett. 96, 113001 (2006). [MEDLINE]
  27. D. Vanderbilt, Phys. Rev. B 41, 7892 (1990). [MEDLINE]
  28. E. Tsiper, J. Phys. B 34, L401 (2001). [Inspec] [ISI] [ChemPort]
  29. C. Ochsenfeld and M. Head-Gordon, Chem. Phys. Lett. 270, 399 (1997). [Inspec] [ISI] [ChemPort]
  30. The batch representation of response functions has been rediscovered several times, and given several different names, in the quantum chemistry community, since it was introduced in the context of DFPT (Ref. 14). See, e.g., Refs. 17,29,18.
  31. Y. Saad, Iterative Methods for Sparse Linear Systems, 2nd ed. (SIAM, Philadelphia, 2003).
  32. R. Haydock, V. Heine, and M. J. Kelly, J. Phys. C 5, 2845 (1972).
  33. R. Haydock, V. Heine, and M. J. Kelly, J. Phys. C 8, 2591 (1975). [Inspec] [ISI]
  34. D. W. Bullet, R. Haydock, V. Heine, and M. Kelly, Solid State Physics (Academic, New York, 1980), Vol. 35.
  35. G. Grosso and G. P. Parravivicini, Adv. Chem. Phys. 62, 133 (1985). [ChemPort]
  36. G. H. Golub and C. F. V. Loan, Matrix Computations, 3rd ed. (Johns Hopkins University Press, Baltimore, MD, 1996).
  37. Y. Saad, Iterative Methods for Sparse Linear Systems, 2nd ed. (SIAM, Philadelphia, 2003), p. 185.
  38. Y. Saad, Proceedings of the International Symposium MTNS-89, edited by M. A. Kaashoek, J. H. van Schuppen, and A. C. Ran (Birkhauser, Boston, 1990), Vol. 3, pp. 401–410.
  39. P. Feldmann and R. W. Freund, EURO-DAC '94: Proceedings of the Conference on European Design Automation (IEEE Computer Society Press, Los Alamitos, 1994), pp. 170–175.
  40. E. J. Grimme, D. C. Sorensen, and P. Van Dooren, Numer. Algorithms 12, 1 (1996).
  41. K. Yabana and G. F. Bertsch, Int. J. Quantum Chem. 75, 55 (1999). [Inspec] [ISI] [ChemPort]
  42. QUANTUM ESPRESSO is a community project for high-quality quantum-simulation software, based on density-functional theory, coordinated by Paolo Giannozzi. See http://www.quantum-espresso.org and http://www.pwscf.org.
  43. J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996). [MEDLINE]
  44. Ultrasoft pseudopotentials are taken from the public QUANTUM ESPRESSO pseudopotential library. Pseudopotential files can be downloaded from URL http://www.pwscf.org/pseudo/1.3/UPF/xxx, where xxx = C.pbe-rrkjus.UPF, H.pbe-rrkjus.UPF, C.pw91-van_ak.UPF, H.pw91-van_ak.UPF, Mg.pw91-np-van.UPF.N.pw91-van_ak.UPF.o.pw91-van_ak.UPF.
  45. E. E. Koch and A. Otto, Chem. Phys. Lett. 12, 476 (1972).
  46. A. R. A. Castro and M. A. L. Marques, J. Chem. Phys. 121, 3425 (2004). [MEDLINE]
  47. B. N. Parlett, D. R. Taylor, and Z. S. Liu, Math. Comput. 44, 105 (1985). [Inspec]
  48. R. W. Freund, M. H. Gutknecht, and N. M. Nachtigal, SIAM J. Sci. Comput. (USA) 14, 470 (1993).
  49. J. Cullum, W. Kerner, and R. Willoughby, Comput. Phys. Commun. 53, 19 (1989). [Inspec] [ISI]
  50. P. Turchi, F. Ducastelle, and G. Treglia, J. Phys. C 15, 2891 (1982). [Inspec] [ISI] [ChemPort]
  51. R. Bauernschmit, R. Ahlrichs, F. H. Hennrich, and M. M. Kappes, J. Am. Chem. Soc. 120, 5052 (1998).
  52. S. Leach, R. Vervloet, A. Despres, E. Breheret, J. P. Hare, T. J. Dennis, R. Taylor, and D. R. M. Walton, Chem. Phys. 160, 451 (1992). [Inspec] [ISI] [ChemPort]
  53. T. A. Niehaus, S. Suhai, F. della Sala, P. Lugli, M. Elstner, G. Seifert, and T. Fraunheim, Phys. Rev. B 63, 085108 (2001).
  54. A. Tsolakidis, D. Sànchez-Portal, and R. M. Martin, Phys. Rev. B 66, 235416 (2002).
  55. X. Blase and P. Ordejón, Phys. Rev. B 69, 085111 (2004). [ISI]
  56. M. Gouterman, J. Mol. Spectrosc. 6, 138 (1961). [ISI] [ChemPort]
  57. D. Sundholm, Chem. Phys. Lett. 302, 480 (1999). [Inspec] [ISI] [ChemPort]
  58. D. Sundholm, Chem. Phys. Lett. 317, 545 (2000). [Inspec] [ISI] [ChemPort]
  59. J. Linnanto and J. Korppi-Tommola, Phys. Chem. Chem. Phys. 2, 4962 (2000).
  60. M. G. Dahlbom and J. R. Reimers, Mol. Phys. 103, 1057 (2005). [Inspec] [ChemPort]
  61. J. Linnanto and J. Korppi-Tommola, Phys. Chem. Chem. Phys. 8, 663 (2006). [MEDLINE]
  62. Z. L. Cai, M. J. Crossley, J. R. Reimers, R. Kobayashi, and R. D. Amos, J. Phys. Chem. B 110, 15624 (2006). [Inspec]
  63. J. P. Perdew and Y. Wang, Phys. Rev. B 45, 13244 (1992). [MEDLINE]
  64. H. Du, R. C. A. Fuh, J. Li, L. A. Corkan, and J. S. Lindsey, Photochem. Photobiol. 68, 141 (1998);
    65. http://omlc.ogi.edu/spectra/PhotochemCAD/html/index.html.
  65. S. Wang, Phys. Rev. A 60, 262 (1999). [ISI] [ChemPort]

Copyright © American Institute of Physics