The vibrational energy relaxation rates of excited C-H,D,T stretching modes on hydrogen, deuterium, and tritium-terminated H,D,T/C(111)1×1 diamond surfaces, respectively, are calculated using the Bloch-Redfield theory combined with classical molecular dynamics simulation. A valence force field is used to model the interactions between carbon atoms in the bulk. The calculated lifetimes of 30 and 0.2 ps for the first excited states of the C-H and C-D stretching modes agree well with the experimental results of 19 and 0.2 ps, respectively. The lifetime of the first excited state for the C-T stretching mode on the tritium-terminated T/C(111)1×1 diamond surface is predicted to be 0.3 ps. Analysis of the power spectra of the fluctuating force along the C-H,D,T bonds suggests that the vibrational energy relaxation of 1:3 resonance for the first excited state of the C-H stretching mode and 1:2 resonance for C-D and C-T stretching modes results in a difference of lifetimes by an order of 2 between the C-H stretching mode and C-D and C-T stretching modes on the hydrogen, deuterium, and tritium-terminated H,D,T/C(111)1×1 diamond surfaces. Calculations of the relaxation rates for the v=2 states of C-H, C-D, and C-T stretches give lifetimes of 0.1, 0.2, and 0.4 ps, respectively, all on the time scale of tenths of a picosecond.
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