Couplings between electronic transitions in a subsystem formulation of time-dependent density functional theory

Abstract

A subsystem formulation of time-dependent density functional theory (TDDFT) within the frozen-density embedding (FDE) framework and its practical implementation are presented, based on the formal TDDFT generalization of the FDE approach by Casida and Wesolowski [Int. J. Quantum Chem. 96, 577 (2004)]. It is shown how couplings between electronic transitions on different subsystems can be seamlessly incorporated into the formalism to overcome some of the shortcomings of the approximate TDDFT-FDE approach in use so far, which was only applicable for local subsystem excitations. In contrast to that, the approach presented here allows to include couplings between excitations on different subsystems, which become very important in aggregates composed of several similar chromophores, e.g., in biological or biomimetic light-harvesting systems. A connection to Forster- and Dexter-type excitation energy coupling expressions is established. A hybrid approach is presented and tested, in which excitation energy couplings are selectively included between different chromophore fragments, but neglected for inactive parts of the environment. It is furthermore demonstrated that the coupled TDDFT-FDE approach can cure the inability of the uncoupled FDE approach to describe induced circular dichroism in dimeric chromophores, a feature known as a "couplet," which is also related to couplings between (nearly) degenerate electronic transitions.

A simplified approach for the coupling of excitation energy transfer

“…The electronic coupling between the initial and final state is a fundamental quantity that measures the speed of EET processes [1,16,17]. The literature on the calculation of the electronic coupling is voluminous [1][2][3][4][5][6][7][8][9][10][16][17][18][19][20][21][22][23][24][25][26].…”

Nonuniform Continuum Model for Solvatochromism Based on Frozen‐Density Embedding Theory

“…[46] The NDRE approximation is applicable in the case of local excitations and negligible absorption by the environment in the investigated spectral range, as shown comprehensively by Neugebauer. [46] In such a case, the functional derivative of the embedding potential with respect to 1 A ðrÞ contributes to the response kernel f ðr;r 0 Þ defined in LR-TDDFT with Equation (6): [45] …”

“…[44] If the dynamic response of the environment is neglected, [45] the approximations are known in the literature as neglect of dynamic response of the environment (NDRE) or uncoupled frozen density embedding [FDE(u)]. [46] The NDRE approximation is applicable in the case of local excitations and negligible absorption by the environment in the investigated spectral range, as shown comprehensively by Neugebauer. [46] In such a case, the functional derivative of the embedding potential with respect to 1 A ðrÞ contributes to the response kernel f ðr;r 0 Þ defined in LR-TDDFT with Equation (6): [45] …”

Computing the Optical Properties of Large Systems

“…The method of converging localised excitations in different regions A, B ... and then coupling them in a post-processing step by assuming that global transition density matrices can be written as linear combinations of transition density matrices of the individual subsystems is analogous to the coupled frozen-density-embedding TDDFT (FDEc-TDDFT) approach introduced by Neugebauer et al [148][149][150]. However, their approach shows a number of differences, mainly in how the ground state calculation is treated.…”