We compare algorithms to sample initial positions and momenta of a molecular system for classical trajectory simulations. We aim at reproducing the phase space quantum distribution for a vibrational eigenstate, as in Wigner theory. Moreover, we address the issue of controlling the total energy and the energy partition among the vibrational modes. In fact, Wigner's energy distributions are very broad, quite at variance with quantum eigenenergies. Many molecular processes depend sharply on the available energy, so a better energy definition is important. Two approaches are introduced and tested: the first consists in constraining the total energy of each trajectory to equal the quantum eigenenergy. The second approach modifies the phase space distribution so as to reduce the deviation of the single mode energies from the correct quantum values. A combination of the two approaches is also presented.

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The 3CH2 + 3O2 reaction has a quite complex ground state singlet potential energy surface (PES). There are multiple minima and transition states before forming the 10 possible reaction products. A previous direct chemical dynamics simulation at the UM06/6-311++G­(d,p) level of theory (J. Phys. Chem. A201912343604369) found that reaction on this PES is predominantly direct without trapping in the potential minima. The first minima 3CH2 + 3O2 encounters is that for the 1CH2O2 Criegee intermediate and statistical theory assumes the reactive system is trapped in this intermediate with a lifetime given by Rice–Ramsperger–Kassel–Marcus (RRKM) theory. In the work presented here, a direct dynamics simulation is performed with the above UM06 theory, with the trajectories initialized in the 1CH2O2 intermediate with a random distribution of vibrational energy as assumed by RRKM theory. There are substantial differences between the dynamics for 1CH2O2 dissociation and 3CH2 + 3O2 reaction. For the former there are four product channels, while for the latter there are seven in agreement with experiment. Product energy partitioning for the two simulations are in overall good agreement for the CO2 + H2 and CO + H2O product channels, but in significant disagreement for the HCO + OH product channel. Though 1CH2O2 is excited randomly in accord with RRKM theory, its dissociation probability is biexponential and not exponential as assumed by RRKM. In addition, the 1CH2O2 dissociation dynamics follow non-intrinsic reaction coordinate (non-IRC) pathways. An important finding is that the nonstatistical dynamics for the 3CH2 + 3O2 reaction give results in agreement with experiment.

Quasi-classical direct dynamics simulations, performed with the B3LYP-D3/cc-pVDZ electronic structure theory, are reported for vibrational relaxation of the three NH stretches of the −NH 3 + group of protonated tryptophan (TrpH + ), excited to the n = 1 local mode states. The intramolecular vibrational energy relaxation (IVR) rates determined for these states, from the simulations, are in good agreement with the experiment. In accordance with the experiment, IVR for the free NH stretch is slowest, with faster IVR for the remaining two NH stretches which have intermolecular couplings with an O atom and a benzenoid ring. For the free NH and the NH coupled to the benzenoid ring, there are beats (i.e., recurrences) in their relaxations versus time. For the free NH stretch, 50% of the population remained in n = 1 when the trajectories were terminated at 0.4 ps. IVR for the free NH stretch is substantially slower than for the CH stretch in benzene. The agreement found in this study between quasi-classical direct dynamics simulations and experiments indicates the possible applicability of this simulation method to larger biological molecules. Because IVR can drive or inhibit reactions, calculations of IVR time scales are of interest, for example, in unimolecular reactions, mode-specific chemistry, and many photochemical processes.