Counting the number of excited states in organic semiconductor systems using topology

Catanzaro, Michael J.; Shi, Tian; Tretiak, Sergei; Chernyak, Vladimir

doi:10.1063/1.4908560

Cited by 3 publications

(2 citation statements)

References 19 publications

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“…The tight-binding models can be build in an efficient way by studying the the topological properties of the scattering matrices, namely the integer-valued topological charge, or equivalently winding number associated with the corresponding scattering matrix [48]. The topological charge provides useful information on how many cites in the related tight-binding model are needed to adequately describe a scattering center.…”

Section: Discussionmentioning

confidence: 99%

Exciton scattering approach for optical spectra calculations in branched conjugated macromolecules

Malinin

et al. 2016

Chemical Physics

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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.

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Section: Discussionmentioning

confidence: 99%

Exciton scattering approach for optical spectra calculations in branched conjugated macromolecules

Malinin

et al. 2016

Chemical Physics

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“…Previously we have characterized how a molecular vertex affects the number of excitonic states in a molecule in terms of the analytical and topological properties of the ES matrix. 28,29,36 In the case of PA bond-length alternation, the topological charge Q T = (w(Γ) − 1)/2 = 0 has been found due to w(ϕ 0 ) = w(ϕ 1 ) = 1, where the winding number w describes how many times the scattering amplitude e iϕ(k) winds over the unit circle it resides on, while the quasimomentum k goes once over the Brillouin zone. In addition, a bound state localized in the vicinity of the stretched CC has been observed in the structures with triple-bond length change >3% or has been expected in sufficiently long molecules with moderately stretched (≤3%) triple bond.…”

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How Geometric Distortions Scatter Electronic Excitations in Conjugated Macromolecules

Shi

Tretiak

et al. 2014

J. Phys. Chem. Lett.

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Effects of disorder and exciton-phonon interactions are the major factors controlling photoinduced dynamics and energy-transfer processes in conjugated organic semiconductors, thus defining their electronic functionality. All-atom quantum-chemical simulations are potentially capable of describing such phenomena in complex "soft" organic structures, yet they are frequently computationally restrictive. Here we efficiently characterize how electronic excitations in branched conjugated molecules interact with molecular distortions using the exciton scattering (ES) approach as a fundamental principle combined with effective tight-binding models. Molecule geometry deformations are incorporated to the ES view of electronic excitations by identifying the dependence of the Frenkel-type exciton Hamiltonian parameters on the characteristic geometry parameters. We illustrate our methodology using two examples of intermolecular distortions, bond length alternation and single bond rotation, which constitute vibrational degrees of freedom strongly coupled to the electronic system in a variety of conjugated systems. The effect on excited-state electronic structures has been attributed to localized variation of exciton on-site energies and couplings. As a result, modifications of the entire electronic spectra due to geometric distortions can be efficiently and accurately accounted for with negligible numerical cost. The presented approach can be potentially extended to model electronic structures and photoinduced processes in bulk amorphous polymer materials.

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Exciton scattering via algebraic topology

2019

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This paper introduces an intersection theory problem for maps into a smooth manifold equipped with a stratification. We investigate the problem in the special case when the target is the unitary group U (n) and the domain is a circle. The first main result is an index theorem that equates a global intersection index with a finite sum of locally defined intersection indices. The local indices are integers arising from the geometry of the stratification.The result is used to study a well-known problem in chemical physics, namely, the problem of enumerating the electronic excitations (excitons) of a molecule equipped with scattering data.

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Counting the number of excited states in organic semiconductor systems using topology

Cited by 3 publications

References 19 publications

Exciton scattering approach for optical spectra calculations in branched conjugated macromolecules

Exciton scattering approach for optical spectra calculations in branched conjugated macromolecules

How Geometric Distortions Scatter Electronic Excitations in Conjugated Macromolecules

Exciton scattering via algebraic topology

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