On Modeling the Pressure-dependent Photoisomerization of trans-Stilbene by Including Slow Intramolecular Vibrational Energy Redistribution

Potential Nonstatistical Effects on the Unimolecular Decomposition of H2O2

An attempt is made to evaluate the nonstatistical effects in the thermal decomposition of hydrogen peroxide (H₂O₂). Previous experimental studies on this reaction reported an unusual pressure dependence of the rate constant indicating broader falloff behavior than expected from conventional theory. In this work, the possibility that the rate constant is affected by nonstatistical effects is investigated based on classical trajectory calculations on the global potential energy surfaces of H₂O₂ and H₂O₂ + Ar. The emphasis is on the intramolecular energy redistribution from the K-rotor, that is, the external rotor for rotation around the principal axis of least moment of inertia. The calculations for the H₂O₂ molecules excited above the dissociation threshold suggest that the energy redistribution from the torsion and K-rotor to vibrations can be competitive with dissociation. In particular, the slow redistribution of the energy associated with the K-rotor significantly affects the dissociation rate. The successive trajectory calculations for collisions of H₂O₂ with Ar show that the energy associated with the K-rotor can be collisionally transferred more efficiently than the vibrational energy. On the basis of these results and several assumptions, a simple model is proposed to account for the nonstatistical effects on the pressure-dependent thermal rate constants. The model predicts significant broadening of the falloff curve of the rate constants but still cannot fully explain the experimental data.

Molecules and the Eigenstate Thermalization Hypothesis

We review a theory that predicts the onset of thermalization in a quantum mechanical coupled non-linear oscillator system, which models the vibrational degrees of freedom of a molecule. A system of N non-linear oscillators perturbed by cubic anharmonic interactions exhibits a many-body localization (MBL) transition in the vibrational state space (VSS) of the molecule. This transition can occur at rather high energy in a sizable molecule because the density of states coupled by cubic anharmonic terms scales as N³, in marked contrast to the total density of states, which scales as exp(aN), where a is a constant. The emergence of a MBL transition in the VSS is seen by analysis of a random matrix ensemble that captures the locality of coupling in the VSS, referred to as local random matrix theory (LRMT). Upon introducing higher order anharmonicity, the location of the MBL transition of even a sizable molecule, such as an organic molecule with tens of atoms, still lies at an energy that may exceed the energy to surmount a barrier to reaction, such as a barrier to conformational change. Illustrative calculations are provided, and some recent work on the influence of thermalization on thermal conduction in molecular junctions is also discussed.

Photoisomerization of Stilbene: The Detailed XMCQDPT2 Treatment

We report the detailed XMCQDPT2/cc-pVTZ study of trans-cis photoisomerization in one of the core systems of both experimental and computational photochemistry-the stilbene molecule. For the first time, the potential energy surface (PES) of the S1 state has been directly optimized and scanned using a multistate multiconfiguration second-order perturbation theory. We characterize the trans-stilbene, pyramidalized (phantom), and DHP-cis-stilbene geometric domains of the S1 state and describe their stationary points including the transition states between them, as well as S1/S0 intersections. Also reported are the minima and the activation barriers in the ground state. Our calculations correctly predict the kinetic isotope effect due to H/D exchange at ethylenic hydrogens, the dynamic behavior of excited cis-stilbene, and trans-cis branching ratio after relaxation to S0 through a rather unsymmetric conical intersection. In general, the XMCQDPT2 results confirm the qualitative adequacy of the TDDFT (especially SF-TDDFT) picture of the excited stilbene but also reveal quantitative discrepancies that deserve further exploration.

Master equation simulations of competing unimolecular and bimolecular reactions: application to OH production in the reaction of acetyl radical with O2

Master equation calculations were carried out to simulate the production of hydroxyl free radicals initiated by the reaction of acetyl free radicals (CH3(C=O).) with molecular oxygen. In particular, the competition between the unimolecular reactions and bimolecular reactions of vibrationally excited intermediates was modeled by using a single master equation. The vibrationally excited intermediates (isomers of acetylperoxyl radicals) result from the initial reaction of acetyl free radical with O2. The bimolecular reactions were modeled using a novel pseudo-first-order microcanonical rate constant approach. Stationary points on the multi-well, multi-channel potential energy surface (PES) were calculated at the DFT(B3LYP)/6-311G(2df,p) level of theory. Some additional calculations were carried out at the CASPT2(7,5)/6-31G(d) level of theory to investigate barrierless reactions and other features of the PES. The master equation simulations are in excellent agreement with the experimental OH yields measured in N2 or He buffer gas near 300 K, but they do not explain a recent report that the OH yields are independent of pressure in nearly pure O2 buffer gas.

Master equation methods for multiple well systems: application to the 1-,2-pentyl system

The master equation (ME) provides a powerful technique for modeling reactions that involve at least one potential energy well. It can be widely applied to reactions with several connected energy wells and multiple product channels. The application of the technique is reviewed by reference to the H + SO(2) reaction, where phenomenological rate constants for use, for example, in a combustion model can be extracted through an analysis of the eigenvalues and eigenvectors of the collision matrix, M, that describes formation of the adducts HSO(2) and HOSO from the source H + SO(2), collisional energy transfer in the adduct wells and reaction via the product channel (sink) OH + SO. The approach is extended to systems with more than one sink and it is demonstrated that macroscopic (phenomenological) rate coefficients derived from a ME obey detailed balance if the original ME is appropriately constructed. The method has been applied to the 1-, 2-pentyl radical system, that includes isomerisation and dissociation via two channels to form C(3)H(6) + C(2)H(5) and C(2)H(4) + C(3)H(7). The calculations clearly demonstrate the importance of indirect dissociation channels, in which an isomer can dissociate to form the product set to which it is not directly connected, e.g. formation of C(3)H(6) + C(2)H(5) from 1-pentyl, via the energized states of 2-pentyl. As in previous studies of pentyl dissociation, there is a convergence of the chemically significant eigenvalues and the internal energy relaxation eigenvalues above approximately 1000 K; the consequences of this convergence are discussed.