Exciton Scattering on Symmetric Branching Centers in Conjugated Molecules

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

Exciton scattering theory attributes excited electronic states to standing waves in quasi-one-dimensional molecular materials by assuming a quasi-particle picture of optical excitations. The quasi-particle properties at branching centers are described by the corresponding scattering matrices. Here, we identify the topological invariant of a scattering center, referred to as its winding number, and apply topological intersection theory to count the number of quantum states in a quasi-one-dimensional system.

How Geometric Distortions Scatter Electronic Excitations in Conjugated Macromolecules

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.

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

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 are 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 quasi-momenta. We exemplify the formulated concepts by analyzing excited states in conjugated phenylacetylenes substituted by perylene.

Natural Atomic Orbital Representation for Optical Spectra Calculations in the Exciton Scattering Approach

The exciton scattering (ES) method allows efficient calculations of spectroscopic observables in large low-dimensional conjugated molecular systems. To compute the transition dipoles between the ground and excited electronic states, we should extract the ES dipole parameters from quantum chemistry calculations in simple molecular fragments. In this manuscript, we show how to retrieve these parameters from any reference quantum chemistry model that uses an arbitrary nonorthogonal and possibly overcomplete atomic orbital basis set. Our approach relies on the natural atomic orbital (NAO) representation, in which the basis functions are orthonormal and the atom-like character is preserved. We apply the ES approach, combined with the NAO analysis to optical spectra of branched phenylacetylene oligomers. Absorption spectra predicted by the ES method demonstrate close agreement with the results of direct quantum chemistry calculations, when the Time-Dependent Density Functional Theory (TD-DFT) being used as a reference. This testifies applicability of a variety of quantum-chemical techniques, where the NAO population analysis can be conducted, for the ES framework.