REACTION RATE CONSTANTS IN CONDENSED PHASE. A NUMERICALLY EXACT QUANTUM STUDY

The long term aim of this project was the interaction between Hydrogen atoms and graphene-like surfaces, typical condensed-phase processes. In particular we were interested in the InterStellar Medium (ISM) environment, where the extremely low temperature, combined with the relevant wave-like behavior of a light atom such as H, makes quantum effects not negligible. The main theoretical challenge lies in the huge computational cost required by an exact quantum calculation. Indeed, in order to model a surface, we need to consider a high number of degrees of freedom, which leads to an exponential increase of the computational time. However, since the substrate importance essentially resides in its capability to activate the process and its role in reaching an equilibrium, we can approximate the environment as an ensemble of independent Harmonic Oscillators (HOs), called bath, coupled with the main system (H atom). With this strategy we can simulate the reaction dynamics taking into account the quantum coherence, the thermal fluctuations and the dissipation of energy excess generated during the reaction, and strongly reduce the computational cost. In order to perform the dynamics of the entire setup (system+bath) we exploited a high-dimensional wave-packet technique, the MultiConfiguration Time-Dependent Hartree (MCTDH) approach, computationally cheaper than standard quantum dynamics methods, operating with the Multi Layer (ML) extension of the Heidelberg package. Combining a Monte Carlo sampling of the initial bath state (described with both normal and effective mode representation) with the means of MCTDH dynamics, we obtained thermal rate constants for several temperatures and system-bath friction values. In order to model the condensed-phase processes we were interested in, we considered at first a simple problem described by a symmetric monodimensional potential, useful as diffusion model. We tested the methodology comparing our results with the ones obtained with other techniques, investigating a wide range of reaction regimes and focusing on the quantum-classical crossover. Our results obtained at very low temperatures have been used as benchmarks for the Ring Polymer Instanton (RPI) technique, employed in the Theoretical Molecular Quantum Dynamics research group of Professor Jeremy Richardson, at the Swiss Federal Institute of Technology in Zurich (ETH). Once a full study of the symmetric problem was conducted, we switched to an asymmetrical potential (again monodimensional) that can be a first approximation of a phenomenon involved in the hydrogen formation in interstellar clouds: the transition from the physisorption well to the chemisorption one of H atoms on interstellar dust grains.