Eigenstates of Thiophosgene Near the Dissociation Threshold: Deviations From Ergodicity

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.

Thermalization and Thermal Transport in Molecules

The nature and rate of thermal transport through molecular junctions depend on the length over which thermalization occurs. For junctions formed by alkane chains, in which thermalization occurs only slowly, measurements reveal that thermal resistance is controlled by bonding with the substrates, whereas fluorination can introduce thermal resistance within the molecules themselves, although the mechanism remains unclear. Here we present results of quantum-mechanical calculations of elastic and inelastic scattering rates, the length over which thermalization occurs, and thermal conductance in alkane and perfluoroalkane junctions. The contribution to thermalization of quantum effects that give rise to many-body localization (MBL) in isolated molecules is examined. While MBL does not occur due to dephasing, thermalization is typically too slow to establish local temperature if the same molecule in isolation exhibits MBL. The results indicate limitations on the applicability of classical molecular simulations in modeling thermal transport in molecular junctions.

Quantum Statistical Ensemble Resilient to Thermalization

The sampling of the wave function within a suitable ensemble is an important tool in the statistical analysis of a molecule interacting with its environment. The uniform statistical distribution of quantum pure states in an active space is often the privileged choice. However, such a distribution with constant average populations of eigenstates is not preserved upon the interaction between quantum systems. This appears as a severe methodological shortcoming, as long as a quantum system can be always considered as the result of interactions among previously isolated subsystems. In the present work we formulate an alternative statistical ensemble of pure states that is robust with respect to interaction, and it is thus preserved when subsystems are merged. It is derived from the condition of invariance of the average populations upon interaction between quantum systems in the same thermal state. These average populations allow a simple identification of the thermodynamic properties of the system. We find that such a statistical distribution is robust with respect to interaction of systems at different temperatures reproducing the thermalization of macroscopic bodies, and for this reason we identify it as the Thermalization Resilient Ensemble.

Large scale vibrational calculations on IVR in S0 thiophosgene

In this work, using a recently derived refined potential energy surface for [Formula: see text] thiophosgene, we perform large scale vibrational calculations to explore the IVR characteristics and vibrational mixing at very high vibrational excitation energies, ranging up to the dissociation limit (at [Formula: see text]20,000[Formula: see text]cm[Formula: see text]). The results from our calculations have been compared to the conclusions based on the available experimentally measured dataset (obtained from SEP and LIF spectra) as well as to the conclusions from the analyses by other authors using local coupling models.