Real-space, real-time calculation of dynamic hyperpolarizabilities

Abstract

The finite-difference method to calculate hyperpolarizabilities is generalized for dynamical case. The calculation of the dynamical hyperpolarizabilities from non-perturbative, explicitly time-dependent single particle states obtained in the framework of the time-dependent density functional theory, is implemented in real space and real time. The optical response functions up to the third order are extracted in frequency domain. The present approach is free of deficiencies associated with atom centered basis sets and allows treatment of large molecules. The calculated results are in good agreement with experiments and with other theoretical calculations for various test cases.

Accurate Evaluation of Real-Time Density Functional Theory Providing Access to Challenging Electron Dynamics

“…There are numerous ways that the propagator can be represented numerically. As the intention of our article is not a review or discussion of propagator approximations, we refer the reader to refs , , , , , − , , and − for different ways that efficient numerical propagation can be achieved. We stress that the method that our article describes (i.e., the efficient evaluation of spectral observables) can be combined with any propagator as it uses just the time-dependent density.…”

“…On the technical side, there have been two development strands. On the one hand, real-time TDDFT started with implementations that represent the orbitals on real-space grids. ,− ,,− In some cases, the decision for a grid has been related to the fact that grids represent orbitals without a particular focus on specific regions of space, contrary to atom-centered basis sets, and are therefore well suited to describing nonperturbative dynamics ,,− and long-range emission processes. − However, real-space grids have also remained popular because of the excellent further parallelization that they offer due to their underlying sparse matrix algebra, leading to efficient codes with many applications. ,− …”

“…In recent years, techniques have been developed which aim at extracting the electrical response from real-time simulations with increased accuracy and reduced computational cost. For example, by analogy to techniques used in static response calculations, , fitting procedures have been developed to extract response coefficients. , However, they require several propagation runs with perturbations of different frequencies and/or field strengths. Thus, they are still computationally demanding and better suited for obtaining nonlinear response coefficients of small molecules than for obtaining insight into the reponse of large systems.…”

Large Hyperpolarizabilities of the Second Harmonic Generation Induced by Nonuniform Optical Near Fields

“…The molecules were symmetric pDNB and asymmetric pNA. For the excitation of pNA, the hyperpolarizability β was estimated by using the finite field method. − In this section, we briefly explain the theoretical framework of TDDFT and the finite field method and describe the optical properties of pDNB and pNA.…”

“…The finite field method − extracts the optical response of a specific order by calculating the induced dipole moment P i ( t ) for several intensities of the incident light and adding or subtracting them. In particular, we adopted the finite field method by using continuous-wave incident fields to estimate the value of β ijj (2ω).…”