Excited-State Structure Modifications Due to Molecular Substituents and Exciton Scattering in Conjugated Molecules

Abstract

Attachment of chemical substituents (such as polar moieties) constitutes an efficient and convenient way to modify physical and chemical properties of conjugated polymers and oligomers.Associated modifications in the molecular electronic states can be comprehensively described by examining scattering of excitons in the polymer's backbone at the scattering center representing the chemical substituent. Here, we implement effective tight-binding models as a tool to examine the analytical properties of the exciton scattering matrices in semi-infinite polymer chains with substitutions. We demonstrate that chemical interactions between the substitution and attached polymer is adequately described by the analytical properties of the scattering matrices. In particular, resonant and bound electronic excitations are expressed via the positions of zeros and poles of the scattering amplitude, analytically continued to complex values of exciton quasimomenta.We exemplify the formulated concepts by analyzing excited states in conjugated phenylacetylenes substituted by perylene.

Exciton scattering approach for optical spectra calculations in branched conjugated macromolecules

“…The topological charge provides useful information on how many cites in the related tight-binding model are needed to adequately describe a scattering center. Studying analytical (geometrical) properties of the scattering matrices, namely the analytical continuations of Γ(k) with k being the quasimomentum, from the Brillouin zone, represented by a unit circle in the complex plane (or its compactified version, known as the projective space CP 1 ) provide useful microscopic insights into the chemical properties of molecular substituents [49], connected to polymer backbones. The positions of poles (or zeros) of Γ(k) in CP 1 describe the energies and spectral widths of the bound and resonant states that occur in a conjugated molecule due to the presence of the substituent, with the above energies sometimes being very different form the energetics of an uncoupled fragment.…”

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

“…Chemical coupling between the linear segments and scattering centers modifies the excitations in the latter, resulting in bound and resonant states 8 . The resonant states that fall inside the exciton band show up as resonances in the density of states, or equivalently in sharp 2π-rotations of the det Γ a (k) in the narrow regions of k around the resonance of ω(k) with a state at the scattering center, referred to as kinks 8,10 are much harder to analyze, compared to bound states. Our counting result allows for a following interpretation: the number N res of resonant states in a finite structure is given by just the sum N res = a Q a of the topological charges, associated with the scattering centers.…”

“…The presented theory provides an explicit link between the graph topology (connectivity) of the branched system the interlining molecular electronic and optical properties defined by the spectrum of electronic excitations: The excitedstate electronic structure in a finite molecule is a result of complex interplay between excitations in linear segments, determined by the exciton band structure in infinite polymers and electronic excitations in scattering centers. Chemical coupling between the linear segments and scattering centers modifies the excitations in the latter, resulting in bound and resonant states 8 . The resonant states that fall inside the exciton band show up as resonances in the density of states, or equivalently in sharp 2π-rotations of the det Γ a (k) in the narrow regions of k around the resonance of ω(k) with a state at the scattering center, referred to as kinks 8,10 are much harder to analyze, compared to bound states.…”

“…Our previous studies have demonstrated accurate calculations of excited state transition energies 4,5 and optical spectra 6 in very large, low-dimensional molecular systems with negligible computational cost using this technique. Moreover, this framework enables an efficient characterization of excited-state electronic structure modifications due to different branching pattern and donor/acceptor substitutions 7,8 . We reiterate that all information on the system Hamiltonian and further approximations (e.g., the quantum chemistry method involved, basis sets, etc.)…”

Optical Signatures of the Coupling between Excitons and Charge Transfer States in Linear Molecular Aggregates

“…Already in the previous century the effects of close packing have been linked to the formation of charge transfer (CT) states. [1][2][3] With CT states being found recently in new materials [4][5][6][7][8] and their appearance in biological light-harvesting systems, [9][10][11][12] interest in modeling of CT systems persisted [13][14][15][16][17] which fuelled the need for a better understanding how the competition between various interactions leads to specific observable properties.…”