A unified model for simulating liquid and gas phase, intermolecular energy transfer: N2 + C6F6 collisions

Abstract

Molecular dynamics simulations were used to study relaxation of a vibrationally excited C6F6* molecule in a N2 bath. Ab initio calculations were performed to develop N2-N2 and N2-C6F6 intermolecular potentials for the simulations. Energy transfer from "hot" C6F6 is studied versus the bath density (pressure) and number of bath molecules. For the large bath limit, there is no heating of the bath. As C6F6* is relaxed, the average energy of C6F6* is determined versus time, i.e., ⟨E(t)⟩, and for each bath density ⟨E(t)⟩ is energy dependent and cannot be fit by a single exponential. In the long-time limit C6F6 is fully equilibrated with the bath. For a large bath and low pressures, the simulations are in the fixed temperature, independent collision regime and the simulation results may be compared with gas phase experiments of collisional energy transfer. The derivative d[⟨E(t)⟩]/dt divided by the collision frequency ω of the N2 bath gives the average energy transferred from C6F6* per collision ⟨ΔE(c)⟩, which is in excellent agreement with experiment. For the ~100-300 ps simulations reported here, energy transfer from C6F6* is to N2 rotation and translation in accord with the equipartition model, with no energy transfer to N2 vibration. The energy transfer dynamics from C6F6* is not statistically sensitive to fine details of the N2-C6F6 intermolecular potential. Tests, with simulation ensembles of different sizes, show that a relatively modest ensemble of only 24 trajectories gives statistically meaningful results.

Bath Model for N2 + C6F6 Gas-Phase Collisions. Details of the Intermolecular Energy Transfer Dynamics

“…33 In the inset of Figure 8 the results of the simulations described above for classical microcanonical, classical microcanonical + ZPE, and quantum microcanonical sampling are presented. The classical microcanonical sampling result was presented previously, 26 and its initial ⟨E⟩ is smaller since it does (2) a The vibrational frequencies are in cm −1 . For "model C 6 H 6 " the masses of the F-atoms are changed to that for the H-atom without changing any of the other potential parameters.…”

“…In the low-pressure, single collision limit for C 6 F 6 + N 2 energy transfer, the proportionality constants C 1 and C 2 for k 1 and k 2 , i.e.. k = C × ρ, become independent of density ρ. The previous study 26 indicated that a 40 kg/m 3 N 2 bath density well approximates the single collision limit for the C 6 F 6 −N 2 system since the C 1 and C 2 parameters were very similar for the 40 and 80 kg/m 3 N 2 bath densities. For the work reported here, an additional simulation was performed for a lower N 2 bath density of 20 kg/m 3 to ensure the single collision convergence of the previous 40 kg/m 3 simulation.…”

“…In our previous study, 26 we found that a 40 kg/m 3 N 2 bath density represents the low-pressure, single collision limit for the C 6 F 6 −N 2 system. 26 To further test this finding, an additional simulation was performed for a lower N 2 bath density of 20 kg/ m 3 .…”

“…This analysis indicates that the 40 kg/m 3 simulation is in the single collision limit as suggested previously. 26 It is also of interest that the fitted E(∞) for the 20 kg/m 3 bath density is 20.0 kcal/mol, which is very close to the total average energy of 20.6 kcal/mol for fully equilibrated C 6 F 6 at 315 K. For 40 kg/m 3 , E(∞) = 22.2 kcal/mol.…”

“…As discussed in our earlier paper, 26 the final average energy of C 6 F 6 at the end of the 312 ps trajectories for a N 2 bath density of 40 kg/m 3 is 28.0 kcal/mol and does not reach the fully equilibrated thermal energy of 20.6 kcal/mol for the T = 315 K bath temperature. It is also of interest to compare the value of ⟨ΔE 2 ⟩ 1/2 at the end of the simulation with the value for the C 6 F 6 Boltzmann distribution at 315 K. To check this, only the C 6 F 6 vibrational energy was considered since its average value is an order of magnitude larger than the translation/rotation average energy of 1.9 kcal/mol.…”