Related papers: Divide-and-Conquer Method for Instanton Rate Theor…
Instanton theory has arisen as a practical tool for calculating tunneling splittings in molecular systems. Unfortunately, the original formulation of instanton theory fundamentally breaks down when trying to calculate the level splitting in…
Canonical instanton theory is a widespread approach to describe the dynamics of chemical reactions in low temperature environments when tunneling effects become dominant. It is a semiclassical theory which requires locating classical…
Instanton rate theory is used to study tunneling events in a wide range of systems including low-temperature chemical reactions. Despite many successful applications, the method has never been obtained from first principles, relying instead…
Instanton theory is an established method to calculate rate constants of chemical reactions including atom tunneling. Technical and methodological improvements increased its applicability. Still, a large number of energy and gradient…
Instanton theory relates the rate constant for tunneling through a barrier to the periodic classical trajectory on the upturned potential energy surface whose period is $\tau=\hbar/(k_{\rm B}T)$. Unfortunately, the standard theory is only…
Microcanonical instanton theory offers the promise of providing rate constants for chemical reactions including quantum tunneling of atoms over the whole temperature range. We discuss different rate expressions, which require the…
Constructing an accurate approximation to nonadiabatic rate theory which is valid for arbitrary values of the electronic coupling has been a long-standing challenge in theoretical chemistry. Ring-polymer instanton theories offer a very…
Semiclassical instanton theory is a form of quantum transition-state theory which can be applied to computing thermal reaction rates for complex molecular systems including quantum tunneling effects. There have been a number of attempts to…
Reactions involving adsorbates on metallic surfaces and impurities in bulk metals are ubiquitous in a wide range of technological applications. The theoretical modelling of such reactions presents a formidable challenge for theory because…
We take the golden-rule instanton method derived in the previous paper [arXiv:1509.04919] and reformulate it using a ring-polymer approach. This gives equations which can be used to compute the rates of electron-transfer reactions in the…
In this paper, we derive a perturbatively-corrected instanton rate theory in the ring-polymer framework (RPI+PC), which significantly enhances the accuracy of instanton theory by using third and fourth derivatives of the potential to…
The quantum instanton approximation is a type of quantum transition state theory that calculates the chemical reaction rate using the reactive flux correlation function and its low order derivatives at time zero. Here we present several…
We consider quantum tunnelling in asymmetric double-well systems for which the local minima in the two wells have the same energy, but the frequencies differ slightly. We derive a generalization of instanton theory for these asymmetric…
A general method for the direct evaluation of the temperature dependence of the quantum-mechanical reaction rate constant in many-dimensional systems is described. The method is based on the quantum instanton approximation for the rate…
We explore the relation between the quantum and semiclassical instanton approximations for the reaction rate constant. From the quantum instanton expression, we analyze the contributions to the rate constant in terms of minimum-action paths…
We apply Thermostatted Ring Polymer Molecular Dynamics (TRPMD), a recently-proposed approximate quantum dynamics method, to the computation of thermal reaction rates. Its short-time Transition-State Theory (TST) limit is identical to…
This Feature Article presents an overview of the current status of Ring Polymer Molecular Dynamics (RPMD) rate theory. We first analyze the RPMD approach and its connection to quantum transition-state theory. We then focus on its practical…
Canonical instanton theory is known to overestimate the rate constant close to a system-dependent crossover temperature and is inapplicable above that temperature. We compare the accuracy of the reaction rate constants calculated using…
Extreme events play a crucial role in fluid turbulence. Inspired by methods from field theory, these extreme events, their evolution and probability can be computed with help of the instanton formalism as minimizers of a suitable action…
It is shown that periodic instanton solutions may have bifurcations which qualitatively change the behaviour of the finite temperature transition rate. These bifurcations are studied numerically in a quantum mechanical model and in the…