On the Role of Nuclear Quantum Effects in Reactive Dynamics Simulations

This thesis mainly focuses on the study of reactive systems, exploring how Nuclear Quantum Effects (NQEs), in particular tunneling and Zero Point Energy (ZPE), can affect the dynamical and thermodynamical properties of a chemical reaction. In principle, in order to include NQEs, one should solve the time-dependent Schrödinger equation for the atomic nuclei, but this is possible only for systems with few degrees of freedom. For this reason, different approximate methods were developed in the past in order to take into account those effects without excessive computational effort. In this thesis, we will discuss in detail two approaches: Ring Polymer Molecular Dynamics (RPMD), and the Quantum Thermal Bath (QTB). The first one is based on the Path Integral formalism outlined by Feynman, while the second one uses a generalized Langevin equation in order to introduce Zero Point Energy (ZPE) in an otherwise classical simulation. First, we investigate how the ZPE of the system affects an unimolecular fragmentation, comparing rate constants and activation energies for both classical and quantum results obtained with RPMD and QTB methods. The system is described by an analytical potential, and in order to explore a different ranges of temperature, the potential was modified, changing the barrier of the reaction. Furthermore, a benchmark with the exact result is obtained for a 1D model system (a simple Morse potential). Results show that RPMD is able to capture correctly the NQEs on rate constants (and therefore activation energy). Instead, QTB largely overestimates the rate constants in all the systems. The reason of this wrong behaviour, is to search in the distance distribution, where the QTB describes poorly the tail of the probability distribution which is fundamental to describe the fragmentation correctly. Then, we study the double proton transfer in Guanine-Cytosine DNA base pairs. In particular we focus on how NQEs and environment can affect this reaction, thus the thermodynamics and dynamical properties. In order to study the mechanism, the free energy landscape was obtained using Umbrella Sampling for both classical and Path Integral based simulations. Furthermore, an ensemble of trajectories was performed starting from the tautomeric form and was let free to go back to the more stable form (the canonical one). The results show that for the dimer in gas phase the mechanism is concerted, and the effect of NQEs is to speed up the reaction up to a factor of 30 in comparison with classical results. When the environment is included the mechanism becomes step-wise, the NQEs still speed up the reaction, but what is more affected is the free energy landscape, for which the intermediate ceases to be a local minimum, making the proton transfer almost barrierless. The last part concerns the study of heavy atoms tunneling for a prototypical reaction, the Cope Rearrangement of Semibullvalene. We focus on the reaction within transition state theory (TST) approximation, by computing the free energy barrier with Umbrella Sampling technique for both classical and RPMD methods. We also correct the TST by the recrossing factor, in order to estimate the accuracy of this approximation. We found that in the case of RPMD when the temperature is lower than the cross over temperature, the free energy profile in the transition state region is completely flat, showing a typical marker for tunneling. The inclusion of tunneling speeds up the reaction up to 60 order of magnitude at 25 K, and this difference disappears in the classical limit, as we expected. The computation of the recrossing factor, shows that it is significant only at the lowest temperature (25 K), where this value is about 0.6. It should be noted that even if the rate constant is lowered by the inclusion of the recrossing factor in this low temperature regime, it is not comparable with the impact of tunneling which, as we said before, speeds up the reaction up to 60 order of magnitude.