Open Access Dissertation
Date of Award
Vladimir Y. Chernyak
The exciton scattering (ES) approach has been developed to study electronic excitations in large branched conjugated molecules. It attributes excited states to standing waves in the quasi-one-dimensional system by assuming a quasi-particle picture of optical excitations. Tight binding models extend capability of the ES approach to investigate the exciton-phonon coupling.
The topological counting method plays a substantial role in constructing tight binding models. It depicts the ES equations as a topological intersection problem. Then, by applying the index theorem, we can get the total number of excited states, which is equal to the number of repeat units plus topological charges for all scattering centers. Ultimately, the number of lattice sites associated with repeat units and scattering centers are obtained systematically.
The exciton-phonon coupling, i.e. dependence of electronic excitations on geometric distortions, is characterized by the dependence of Frenkel-type exciton Hamiltonian parameters on geometry parameters, such as bond length. The effect on excited-state electronic structures is attributed to variation of exciton on-site energies and coupling constants in tight binding models. 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 is potentially used to model photoinduced relaxation and energy transfer processes in bulk amorphous polymer materials.
Tight binding models can be used to describe exciton band structures of conjugated molecules with complicate molecular structures, like polyfluorenes. Compared with poly(p-phenylene), linear molecules with phenyl rings connected by single bonds, the polyfluorenes are constructed alternately by two different building blocks, which result in intra- and inter-band interactions. They can be efficiently characterized by on-site energies and inter-band coupling constants in tight binding models.
A software GPView has been developed to explore electronic excitations in conjugated molecules. It can extract transition density matrices (TDMs) from quantum chemistry software Gaussian 09 and calculate contracted TDMs, whose contour plots are fingerprints of excited states. As to the wave function based analysis, GPView can calculate and generate molecular orbitals, natural orbitals, natural transition orbitals and natural difference orbitals by density matrices and parameters from Gaussian 09.
Shi, Tian, "How Geometric Distortions Scatter Electronic Excitations In Conjugated Macromolecules: Towards Photoinduced Relaxation And Energy Transfer" (2016). Wayne State University Dissertations. 1590.