Real-space computational methods for linear and nonlinear polarizabilities

Issue title: Computational aspects of electric polarizability calculations: Atoms, Molecules and clusters, Part I

Article type: Research Article

Authors: Iwata, Jun-Ichi^{a; *} | Yabana, Kazuhiro^b | Bertsch, George F.^c

Affiliations: [a] Nanotechnology Research Institute, National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba 305-8568, Japan | [b] Institute of Physics, University of Tsukuba, Tsukuba 305-8571, Japan | [c] Department of Physics and National Institute for Nuclear Theory, University of Washington, Seattle, Washington 98195, USA

Correspondence: [*] Corresponding author. E-mail: [email protected].

Abstract: We present a real-space method for computing the linear and nonlinear polarizabilities in the time-dependent density-functional theory. In our method, the three-dimensional Cartesian coordinate is discretized on a uniform grid and the wave functions are represented on the grid points. The dynamic polarizabilities may be calculated perturbatively by expanding the dipole moment in a power series of the external field strength or directly by integrating the real-time equations of motion under the time-varying external field. We describe the equations and computational techniques for the both methods. Besides calculating second-order and third-order hyperpolarizabilities, the method can be applied to photon-absorption cross sections, and we show examples of this application as well. We also present here for the first time calculations of the nonlinear polarizabilities using the real-time method.

Keywords: time-dependent density-functional theory, real-space method, real-time method, polarizability, hyperpolarizability, response function method

DOI: 10.3233/JCM-2004-4321

Journal: Journal of Computational Methods in Sciences and Engineering, vol. 4, no. 3, pp. 461-479, 2004