No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
Turbo charging time-dependent density-functional theory with Lanczos chains
6.M. E. Casida, in Recent Advances in Density Functional Methods, Part I, edited by D. P. Chong (World Scientific, Singapore, 1995), p. 155.
11.I. Tamm, J. Phys. (Moscow) 9, 449 (1945).
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.
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, and 18.
31.Y. Saad, Iterative Methods for Sparse Linear Systems, 2nd ed. (SIAM, Philadelphia, 2003).
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).
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.
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.
49.J. Cullum, W. Kerner, and R. Willoughby, Comput. Phys. Commun. 53, 19 (1989).
60.M. G. Dahlbom and J. R. Reimers, Mol. Phys. 103, 1057 (2005).
Article metrics loading...
We introduce a new implementation of time-dependent density-functional theory which allows the entirespectrum 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, fullerene, and of chlorophyll a.
Full text loading...
Most read this month