Exciton scattering approach for optical spectra calculations in branched conjugated macromolecules

Abstract

The exciton scattering (ES) technique is a multiscale approach based on the concept of a particle in a box and developed for efficient calculations of excited-state electronic structure and optical spectra in low-dimensional conjugated macromolecules. Within the ES method, electronic excitations in molecular structure are attributed to standing waves representing quantum quasi-particles (excitons), which reside on the graph whose edges and nodes stand for the molecular linear segments and vertices, respectively. Exciton propagation on the linear segments is characterized by the exciton dispersion, whereas exciton scattering at the branching centers is determined by the energy-dependent scattering matrices. Using these ES energetic parameters, the excitation energies are then found by solving a set of generalized "particle in a box" problems on the graph that represents the molecule. Similarly, unique energy-dependent ES dipolar parameters permit calculations of the corresponding oscillator strengths, thus, completing optical spectra modeling. Both the energetic and dipolar parameters can be extracted from quantum-chemical computations in small molecular fragments and tabulated in the ES library for further applications. Subsequently, spectroscopic modeling for any macrostructure within a considered molecular family could be performed with negligible numerical effort. We demonstrate the ES method application to molecular families of branched conjugated phenylacetylenes and ladder poly-para-phenylenes, as well as structures with electron donor and acceptor chemical substituents. Time-dependent density functional theory (TD-DFT) is used as a reference model for electronic structure. The ES calculations accurately reproduce the optical spectra compared to the reference quantum chemistry results, and make possible to predict spectra of complex macromolecules, where conventional electronic structure calculations are unfeasible.

How Geometric Distortions Scatter Electronic Excitations in Conjugated Macromolecules

“…Consequently, finding the excitation energies, ω, and the exciton wave functions is equivalent to solving a generalized "particle in a box" problem, which contains a set of ω-dependent linear wave equations (the so-called ES equations). Given the exciton dispersion, ω(k), and scattering matrices, Γ(ω), which can be extracted from commonly used quantum chemical computations in molecular fragments of moderate size, 20,25,26 the ES approach substantially reduces the numerical expense of the excited-state computations to the cubic order in the number of the linear segments, which otherwise scales as O(N 2 )−O(N 5 ) (where N is the number of electron orbitals) in modern quantum chemical methodologies. 27 Founded on the concept of plane waves and building blocks, the ES approach works amazingly well for static and ideal molecular structures with certain tolerance to slight geometric deformations.…”

“…We have recently developed the exciton scattering (ES) approach − that efficiently characterizes the electronic excited states in branched conjugated macromolecules using a quasiparticle representation. Within the ES approach, a quasi-1-D molecular structure is considered as a graph that consists of edges and nodes denoting molecular linear segments and vertices, respectively.…”