Unified Hamiltonian for conducting polymers

Abstract

Two transferable physical parameters are incorporated into the Su-Schrieffer-Heeger Hamiltonian to model conducting polymers beyond polyacetylene: the parameter γ scales the electron-phonon coupling strength in aromatic rings and the other parameter ε specifies the heterogeneous core charges. This generic Hamiltonian predicts the fundamental band gaps of polythiophene, polypyrrole, polyfuran, poly-(p-phenylene), poly-(p-phenylene vinylene), and polyacenes, and their oligomers of all lengths, with an accuracy exceeding time-dependent density functional theory. Its computational costs for moderate-length polymer chains are more than eight orders of magnitude lower than first-principles approaches.

Structure and Optical Bandgap Relationship of π-Conjugated Systems

“…The heterojunctions require additional - stacking Hamiltonians as discussed separately by Shin and Lin. [25] The determination of the parameters for , , and benzene bonds is discussed in our previous works [23], [24], while the values for Ö we now re-determine using the widely overlooked lowest energy UV-vis absorption peak from polyfuran (PFu). [36] Newly determined for this work are the parameters for using pyridine, [37] using thieno[3,4-c]pyrrole-4,6-dione polymer, [38] and the bridge for perpendicular fused rings using poly-isothianaphthene.…”

“…C-C bonds in six-membered aromatic rings and the bridge bonds between perpendicular fused rings require .aReference: [24].bOriginal parameters from [19].…”

“…In our previous works [23], [24], we developed the adapted Su-Schrieffer-Heeger (aSSH) Hamiltonian and demonstrated its accuracy to be better than that of TDDFT, while still correctly describing polarons and their effects, as well as photoinduced charge transfer when - stacking inter-chain terms are added. [25] We have chosen to neglect explicit correlations, which may be needed to describe a few phenomena such as negative spin-density waves [26], multiple gap states [27], and 3D conformation couplings [28], in favor of a simpler model that can be solved quickly through a single diagonalization of the Hamiltonian.…”

Self-localized domain walls at π-conjugated branching junctions

“…(1) clearly stands out among all quantitative and efficient electronic structure methods because it provides the necessary subtle balance between localization and delocalization of electrons through the explicit electron-phonon couplings. 6,18,20 …”

“…As a side note, the band gaps of conducting polymers computed by HF are significantly larger than the experimental values, while the aSSH band gaps are more accurate than the time-dependent DFT values. 6,20 Second, two new localized states are formed, one lying below the bottom of the valence band and the other above the top of the conduction band, marked with arrows in Fig. 2(a) and 2(a ).…”