Exciton scattering approach for branched conjugated molecules and complexes. I. Formalism

The Kuramoto–Lohe model and collective absorption of a photon

Light absorption by molecular exciton states in disordered networks is studied. The main purpose of this paper is to look at how phases of the intermediate ground–excited state superposition interfere during the absorption process. How does this phase average enable, or suppress, absorption to a delocalized state? To address this question, a theory for phase oscillators is used to predict the purity of the collective excited state of the network. The results of the study suggest that collective absorption by molecular exciton states requires a sufficiently large electronic coupling between molecules in the network compared to the random distribution of transition energies at the sites, even when the molecular network is completely isolated from the environment degrees of freedom. The ‘dividing line’ between absorption to a mixture of, essentially, localized excited states and coherent excitation of a pure delocalized exciton state is suggested to be predicted by the threshold of phase synchronization.

Excitons in poly(para phenylene vinylene): a quantum-chemical perspective based on high-level ab initio calculations

Exciton analyses of high-level quantum-chemical computations for poly(paraphenylene vinylene) reveal the nature of the excitonic bands in PPV oligomers.

New tools for the systematic analysis and visualization of electronic excitations. I. Formalism

A variety of density matrix based methods for the analysis and visualization of electronic excitations are discussed and their implementation within the framework of the algebraic diagrammatic construction of the polarization propagator is reported. Their mathematical expressions are given and an extensive phenomenological discussion is provided to aid the interpretation of the results. Starting from several standard procedures, e.g., population analysis, natural orbital decomposition, and density plotting, we proceed to more advanced concepts of natural transition orbitals and attachment/detachment densities. In addition, special focus is laid on information coded in the transition density matrix and its phenomenological analysis in terms of an electron-hole picture. Taking advantage of both the orbital and real space representations of the density matrices, the physical information in these analysis methods is outlined, and similarities and differences between the approaches are highlighted. Moreover, new analysis tools for excited states are introduced including state averaged natural transition orbitals, which give a compact description of a number of states simultaneously, and natural difference orbitals (defined as the eigenvectors of the difference density matrix), which reveal details about orbital relaxation effects.

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.

Exciton scattering approach for branched conjugated molecules and complexes. IV. Transition dipoles and optical spectra

The electronic excitation energies and transition dipole moments are the essential ingredients to compute an optical spectrum of any molecular system. Here we extend the exciton scattering (ES) approach, originally developed for computing excitation energies in branched conjugated molecules, to the calculation of the transition dipole moments. The ES parameters that characterize contributions of molecular building blocks to the total transition dipole can be extracted from the quantum-chemical calculations of the excited states in simple molecular fragments. Using these extracted parameters, one can then effortlessly calculate the oscillator strengths and optical spectra of various large molecular structures. We illustrate application of this extended ES approach using an example of phenylacetylene-based molecules. Absorption spectra predicted by the ES approach show close agreement with the results of the reference quantum-chemical calculations.

Exciton scattering approach for branched conjugated molecules and complexes. III. Applications

The exciton scattering (ES) approach is an efficient tool to calculate the excited states electronic structure in large branched polymeric molecules. Using the previously extracted parameters, we apply the ES approach to a number of phenylacetylene-based test molecules. Comparison of ES predictions with direct quantum chemistry results for the excitation energies shows an agreement within several meV. The ES framework provides powerful insights into photophysics of macromolecules by revealing the connections between the molecular structure and the properties of the collective electronic states, including spatial localization of excitations controlled by the energy.