Electronic decoherence induced by intramolecular vibrational motions in a betaine dye molecule

Electronic decoherence induced only by intramolecular vibrational motions is investigated in a betaine molecule, pyridinium N-phenoxide betaine [4-(1-pyridinio)phenolate], having 60 vibrational modes. The analysis is based on the nuclear overlap/phase function (NOPF) that appears in the electronic reduced density matrix. To do so, geometry optimizations and vibrational normal-mode analysis in the ground state and the first excited state are performed. Coherence dissipation times according to alternative approximations are obtained, including analysis of the role of frequency shifts and Duschinsky rotation. Geometry optimization reveals a large difference between the central torsional angles of the ground and the first excited state, with a tilted geometry of the pyridinium ring also observed in the first excited state. Nevertheless, the Duschinsky rotation matrix appears nearly diagonal with only a few considerable off-diagonal elements. We find that the low frequency torsional motion does not make any significant contribution to the decay of the NOPF. Frequency shifts have more effect on the decay of the NOPF than the Duschinsky rotation does, but the simplest spin-boson model alone describes coherence decay quite well. At times long compared to the main Gaussian decay, we also observe an exponential decay modulated by phase recurrence, but the exponential decay is dominant only for the last 10-20% of the relaxation. The calculated coherence dissipation time arising from intramolecular vibrational motions of 3.7 A is much shorter than an estimate of the contribution to the decoherence time due to typical solvent molecules, indicating that nuclear motions in a solute molecule can have more influence on the total electronic decoherence than do solvent molecules even for a charge-transfer system such as the present case.