Energetics, structure, and charge distribution of reduced and oxidized n-pyrrole oligomers: a density functional approach.

Polypyrrole is a conjugated polymer prototype of conducting polymers. The energetically preferred spatial conformation of n-pyrrole oligomers (n=1-24) in both the reduced and oxidized phases is obtained and analyzed in this paper within the hybrid density functional theory. Binding energies, gap energies, radius of gyration, end-to-end distance, and vibrational frequencies are reported as functions of oligomer length. Reduced n-pyrrole are bent chains for all sizes showing a dramatic departure from planarity. Vibrational spectra of n-pyrrole oligomers indicate the presence of two fairly size-insensitive frequency regions, which increase in intensity with increasing oligomer size. Several oxidation levels were analyzed for n-pyrrole through the distribution of the carbon-carbon bond orders and single/double bond lengths. It is shown that the oxidation level is directly related to the way positive charge localizes along the n-pyrrole oligomer chain. If charge/n<13, the oligomers are bent and charge is delocalized; if charge/n>/=13, the oligomers are planar and charge notoriously localizes in n/charge regions along the backbone. Calculations with electronegative dopants show that charge localizes in the neighborhood of the dopant. It is demonstrated that one localized state in the gap between the highest occupied and lowest-unoccupied states appears for every +2e in the oxidation level. The band structure of infinite reduced polypyrrole gives a band gap energy in excellent agreement with experiment. The evolution of the band gap and the charge-localized band as a function of polypyrrole oxidation level is reported.