The exciton scattering (ES) approach attributes excited electronic states in quasi-1D branched polymer molecules to standing waves of quantum quasiparticles (excitons) scattered at the molecular vertices. We extract their dispersion and frequency-dependent scattering matrices at termini, ortho, and meta joints for pi-conjugated phenylacetylene-based molecules from atomistic time-dependent density-functional theory (TD DFT) calculations. This allows electronic spectra for any structure of arbitrary size within the considered molecular family to be obtained with negligible numerical effort. The agreement is within 10-20 meV for all test cases, when comparing the ES results with the reference TD DFT calculations.
In many experimental situations, a physical system undergoes stochastic evolution which may be described via random maps between two compact spaces. In the current work, we study the applicability of large deviations theory to time-averaged quantities which describe such stochastic maps, in particular time-averaged currents and density functionals. We derive the large deviations principle for these quantities, as well as for global topological currents, and formulate variational, thermodynamic relations to establish large deviation properties of the topological currents. We illustrate the theory with a nontrivial example of a Heisenberg spin-chain with a topological driving of the Wess-Zumino type. The Cramér functional of the topological current is found explicitly in the instanton gas regime for the spin-chain model in the weak-noise limit. In the context of the Morse theory, we discuss a general reduction of continuous stochastic models with weak noise to effective Markov chains describing transitions between stable fixed points.
We obtain the parameters of the exciton scattering (ES) model from the quantum-chemical calculations of the electronic excitations in simple phenylacetylene-based molecules. We determine the exciton dispersion and the frequency-dependent scattering matrices which describe scattering properties of the molecular ends as well as of meta- and orthoconjugated links. The extracted functions are smooth, which confirms the validity of the ES picture. We find a good agreement between the ES and quantum-chemical results for the excitation energies in simple test molecules.
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