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Time versus frequency space techniques

Authors: M.A.L. Marques, and Angel Rubio

Ref.: in Time-dependent density functional theory, ed. by M.A.L. Marques, C. Ullrich, F. Nogueira, A. Rubio, K. Burke, and E.K.U. Gross, Lecture Notes in Physics, Vol. 706, Springer, Berlin, 227-243 (2006)

Abstract: Let us imagine a young student (or a not so young professor who still has time to do research by him- or herself) who wants to do an ab-initio study of the excitation properties of one of those fashionable nanostructures that fill high-impact journals nowadays. The student has heard of TDDFT, and believes that it is just the right tool for the job. The first thing to do is to make sure that our fancy molecule is not part of the set of the difficult, "pathological" cases -- not a bulk semiconductor, check!; the system does not involve charge-transfer excitations, check!; not a "strongly-correlated" system, check! As everything looks fine, the student starts the quest to find an adequate computer program to use in his or her research.

After a couple of hours googling, the student comes up with 15 different programs that seem to be adequate for this problem. All the programs appear to be quite easy to compile/install, and they all have nice, simple interfaces that make working with them a pleasure and not a torture. Digging a bit further, the student finds that these programs use very different techniques to obtain the excitations of the system: some use Greens functions and linear response theory, some use linear response theory but without the Greens functions, others propagate in time the TDDFT equations. What to choose? Reading the documentation of the programs is not much of a help, as they all claim to be the fastest and least memory consuming. So, what is the most efficient method? The answer to this question is quite tricky, not only due to the "political" issues that any answer could provoke, but also because "efficiency" is a very ill-defined concept in the world of numerics. A more pragmatic measurement is computer time, but this, of course, depends on the method used, the implementation, the hardware, the size of the problem, and sometimes even on the phase of the moon!

In this article, we try to give a hand to our student by comparing different methods to calculate excitation energies within TDDFT. Our purpose is to show how these methods scale with the size (i.e. number of atoms) of the system, namely in what concerns CPU time and memory requirements. Clearly, our approach is not exhaustive, and is mostly determined by our own scientific background.

Citations: 17 (Google scholar)

DOI: 10.1007/3-540-35426-3_15



	doi = {10.1007/3-540-35426-3_15},
	url = {https://doi.org/10.1007%2F3-540-35426-3_15},
	year = 2006,
	publisher = {Springer Berlin Heidelberg},
	pages = {227--240},
	author = {M.A.L. Marques and A. Rubio},
	title = {Time Versus Frequency Space Techniques},
	booktitle = {Time-Dependent Density Functional Theory}