Exciton Scattering on Symmetric Branching Centers in Conjugated Molecules

Abstract

The capability of the exciton scattering approach, an efficient methodology for excited states in branched conjugated molecules, is extended to include symmetric triple and quadruple joints that connect linear segments on the basis of the phenylacetylene backbone. The obtained scattering matrices that characterize these vertices are used in application of our approach to several test structures, where we find excellent agreement with the transition energies computed by the reference quantum chemistry. We introduce topological charges, associated with the scattering matrices, which help to formulate useful relations between the number of excitations in the exciton band and the number of repeat units. The obtained features of the scattering phases are analyzed in terms of the observed excited state electronic structure.

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

“…Note that Eq. (9) reflects one of the statements of the index theorem for the case of linear molecules presented in our earlier work [32], and…”

“…It is worth mentioning that shifting the reference point of reflection by ∆j results in a factor of z 2∆j in r(z) [32], and changes of both n A and n T by 2∆j, which followed by the change of Q A and Q T by ∆j; the latter is compensated in Eqs. (8) and (9) In summary, within a nearest-neighbor hopping lattice model a molecular terminus is described by the reflection coefficient r(z), characterized by its topological charge Q T and analytical charge Q A ≥ Q T , and represented by a meromorphic function on CP 1 in a form given by Eq.…”

Exciton scattering approach for optical spectra calculations in branched conjugated macromolecules

“…All ES parameters described above can be obtained using traditional "reference" quantum-chemical excited states calculations in relatively simple molecular fragments associated with the building blocks of the original superstructure [25,[30][31][32][33]. Previously, applications of the ES approach has been made to a variety of molecular systems.…”

“…For example, the exciton spectra k(ω) have been extracted for phenylacetylene (PA) oligomers and donor-acceptor molecules [25,31,32,34]. Furthermore, the scattering matrices of symmetric double, triple, and quadruple joints have been retrieved by utilizing their geometrical symmetries [33]. To model molecular optical spectra, a technique for the transition dipole calculations within the ES framework has been developed [34][35][36].…”

“…As reference quantum-chemical methodologies, we have been using both semiempirical and ab initio techniques. The former applications [32][33][34][35] were based on the Collective Electronic Oscillator (CEO) method, which uses the Time-Dependent Hartree-Fock (TDHF) approach combined with the semiempirical Hamiltonians [17,27]. The latter applications [25,36] relied on TD-DFT electronic structure approach [21,37].…”