79 research outputs found
An alternative derivation of ring-polymer molecular dynamics transition-state theory.
No full textIn a previous article [T. J. H. Hele and S. C. Althorpe, J. Chem. Phys. 138, 084108 (2013)], we showed that the t → 0+ limit of ring-polymer molecular dynamics (RPMD) rate-theory is also the t → 0+ limit of a new type of quantum flux-side time-correlation function, in which the dividing surfaces are invariant to imaginary-time translation; in other words, that RPMD transition-state theory (RMPD-TST) is a t → 0+ quantum transition-state theory (QTST). Recently, Jang and Voth [J. Chem. Phys. 144, 084110 (2016)] rederived this quantum t → 0+ limit and claimed that it gives instead the centroid-density approximation. Here we show that the t → 0+ limit derived by Jang and Voth is in fact RPMD-TST
Instanton calculations of tunneling splittings for water dimer and trimer
No full textWe investigate the ability of the recently developed ring-polymer instanton (RPI) method [J. O. Richardson and S. C. Althorpe, J. Chem. Phys. 134, 054109 (2011)] to treat tunneling in water clusters. We show that the RPI method is easy to extend to treat tunneling between more than two minima, using elementary graph theory. Tests of the method on water dimer and trimer yield a set of instanton periodic orbits which correspond to all known tunneling pathways in these systems. Splitting patterns obtained from the orbits are in good overall agreement with experiment. The agreement is closer for the deuterated than for the protonated clusters, almost certainly because the main approximation in the calculations is neglect of anharmonicity perpendicular to the tunneling path. All the calculations were performed on a desktop computer, which suggests that similar calculations will be possible on much larger clusters
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Ring-polymer approaches to instanton theory
No full textInspired by the success of the ring-polymer molecular dynamics (RPMD) method,
we derive a transition-state-theory version (RPTST) with a dividing surface which is, in general, conical in ring-polymer space. It is explained why this conical form is a good approximation to the optimal dividing surface and therefore why centroid-based quantum transition-state theories are inaccurate for asymmetric barriers at low temperatures.
The geometry of the ring-polymer transition state is found to describe a finite-difference approximation to the semi-classical instanton trajectory (a classical periodic orbit of length βħ on the inverted potential). Based on this, a new practical method for locating multidimensional instantons is proposed, by computing saddle points on the ring-polymer surface, and a derivation for the reaction rate constant based on the "ImF" premise using the ring-polymer formalism is shown to be far simpler than in previous instanton approaches based on functional determinants. The resulting expression is based only on the ring-polymer potential at the transition-state and its Hessian, and is applied to evaluate the rate in a number of polyatomic systems. We show that a free-energy version of the ImF instanton theory is related to RPTST and thereby provide an explanation for why RPMD produces accurate results for thermal reaction rates in the deep-tunnelling regime and demonstrate how it can be made more efficient and systematically improved. From this, we also explain why RPMD is seen to underestimate the rates of symmetric reactions and overestimate the rates of asymmetric reactions.
We also present a ring-polymer instanton derivation of a theory for calculating tunnelling splittings leading to another new practical method, which owing to its simple form, is easily extended to determine the entire tunnelling-splitting pattern of molecular clusters with two or more degenerate wells. This method is applied to the water dimer, trimer, and octamer, and shown to be in good overall agreement with experiment and to provide a deeper understanding of the tunnelling pathways
Conical intersections and photochemical mechanisms: Characterising the conical intersection hyperline using gradients, second-derivatives, and dynamics
No full textConical intersections and photochemical mechanisms: Characterising the conical intersection hyperline using gradients, second-derivatives, and dynamics
No full textQuantum rates in dissipative systems with spatially varying friction
No full textWe investigate whether making the friction spatially dependent on the reaction coordinate introduces quantum effects into the thermal reaction rates for dissipative reactions. Quantum rates are calculated using the numerically exact multi-configuration time-dependent Hartree (MCTDH) method, as well as the approximate ring-polymer molecular dynamics (RPMD), ring-polymer instanton (RPI) methods, and classical mechanics. By conducting simulations across a wide range of temperatures and friction strengths, we can identify the various regimes that govern the reactive dynamics. At high temperatures, in addition to the spatial-diffusion and energy-diffusion regimes predicted by Kramer\u27s rate theory, a (coherent) tunnelling-dominated regime is identified at low friction. At low temperatures, incoherent tunnelling dominates most of Kramer\u27s curve, except at very low friction when coherent tunnelling becomes dominant. Unlike in classical mechanics, the bath\u27s influence changes the equilibrium time-independent properties of the system, leading to a complex interplay between spatially dependent friction and nuclear quantum effects even at high temperatures. More specifically, a realistic friction profile can lead to an increase (decrease) of the quantum (classical) rates with friction within the spatial-diffusion regime, showing that classical and quantum rates display qualitatively different behaviours. Except at very low frictions, we find that RPMD captures most of the quantum effects in the thermal reaction rates
Time-dependent plane wave packet formulation of quantum scattering with application to H+D2→HD+D
No full textGeneral explanation of geometric phase effects in reactive systems: Unwinding the nuclear wave function using simple topology
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