Ab Initio Time-Domain Study of the Triplet State in a Semiconducting Carbon Nanotube: Intersystem Crossing, Phosphorescence Time, and Line Width

Motivated by recent experiments (J. Am. Chem. Soc. 2011, 133, 17156), we used nonadiabatic (NA) molecular dynamics implemented within ab initio time-domain density functional theory to investigate the evolution of the excited electronic singlet and triplet states in the (6,4) carbon nanotube (CNT). The simulation simultaneously included the NA electron-phonon interaction and the spin-orbit (SO) interaction and focused on the intersystem crossing (ISC) from the first excited singlet state (S-1) to the triplet state (T-1) and subsequent relaxation to the ground electronic state (S-0). For the first time, the state-of-the-art methodology (Phys. Rev. Lett. 2005, 95, 163001; Phys. Rev. Lett. 2008, 100, 197402) has been advanced to include triplet states. The S-1-T-1 ISC was calculated to occur within tens of picoseconds, in agreement with the experimental data. This time scale is on the same order as the S-1-S-0 nonradiative decay time obtained previously for the (6,4) CNT. The homogeneous phosphorescence line width, which can be measured in single-molecule experiments, was predicted to be on the order of 10 meV at room temperature. This value is similar to the fluorescence line widths of CNTs suspended in air. The NA electron-phonon and SO couplings were found to be on the order of 1 meV; however, the former fluctuates much more than the latter, causing the ISC rate to be limited by the SO interaction rather than NA interaction. The electronic energy lost nonradiatively during ISC is deposited into high-frequency optical phonons of the CNT arising from C-C stretching motions. The calculations indicate that ISC can contribute to the nonradiative energy losses and low photoluminescence quantum yields observed in semiconducting CNTs.