Extension of the ring polymer molecular dynamics approach to state-selective molecular reactive scattering simulations

Abstract

The state-resolved knowledge of molecular scattering dynamics is paramount to the understanding and control of chemical reactions. The ideal approach to rigorously simulate such systems is a full-dimensional treatment with quantum mechanical calculations. Current generation of computers allows such calculations to be carried out up to six atoms for zero total angular momentum. It is not likely that the computational power will allow significant progress in the near future, as the computational time grows exponentially with the number of degrees of freedom. Thus, there is a demand for alternative methods that would allow the inclusion of quantum effects while remaining computationally efficient. This thesis consists of the development of such an approach. Inspired by the success of the efficient ring polymer molecular dynamics (RPMD) approach applied to quantum systems at thermal equilibrium, I extend the scope of RPMD to stateselective chemistry. I start by presenting the method development groundwork toward microcanonical simulations of triatomic reactions using RPMD. I expose the steps to prepare a specific initial vibrational state for a diatomic molecule. The assessment of the method revolves around the computation of integral cross sections (ICS) in the ring polymer phase space. I report an ansatz for the reciprocal temperature depending on the characteristics of the reactions. The benchmark reactions Mu/H/D +H2 with H2 either in its ground (v = 0) or first excited vibrational state (v = 1) are chosen to test the method. Good agreement for the Mu/H/D + H2(v = 0, 1) reactions with exact quantum scattering calculations is found. It is shown that RPMD can describe to a good approximation zero-point energy (ZPE) effects and tunneling effects for these reactions while remaining computationally efficient. Following these encouraging preliminary results, the robustness and applicability of the method is further tested. I present a detailed review of the approach. The reactions Mu/H/D/Cl/F+H2(v = 0, 1) are considered over a wide range of collision energies. The accuracy and stability of the vibrational excitation scheme are tested. It is found that the ICS results are strongly sensitive to the spring constant of the ring polymers. A refined ansatz for the reciprocal temperature is suggested. I observe a convergence of the ICS above a number of beads that depends on the characteristics of the diatomic reactant. I show that the tunneling contributions to the reactivity stem from the spatial extension of both ring polymer reactants. However, it is found that RPMD is unable to describe dynamical resonance effects. Shortcomings in the vibrational excitation scheme at low collision energies are reported. Finally, I further test the approach with larger and more intricate systems. In particular, the reactions F,H+CH4 and its isotopic variants for the case of the ground state CH4 and CHD3 and, in the presence of the C-H excited stretch in CHD3. Accurate RPMD ICS results for most of the aforementioned reactions are reported. It is found that the ZPE leakage problem usually present in classical dynamics is prevented. It is found that the vibrational excitation scheme is accurate for most purposes except for reactions involving a very low energy barrier.