Publication

Accelerating path integral evaluation of equilibrium and kinetic isotope effects

Konstantin Karandashev
2018
Thèse EPFL
Résumé

Investigating the effect of isotope substitution on equilibrium and kinetic properties of molecules has become an important tool for estimating the importance of nuclear quantum effects. In this work, we discuss calculating both equilibrium and kinetic isotope effects, i.e., the isotope effects on a system's partition function and a reaction's rate constant. With the help of Feynman's path integral formalism, both quantities can be estimated using standard Monte Carlo methods that scale favorably with system's dimensionality; improving efficiency of such approaches is the main focus of this work.

First of all, we developed a novel procedure for changing mass stochastically during an equilibrium isotope effect calculation, and evaluated the numerical benefits of combining it with two popular approaches for calculating isotope effects, using either direct estimators or thermodynamic integration. We demonstrate that the modification improves statistical convergence of both methods, and that it additionally allows to eliminate integration error of thermodynamic integration. The improved methods are tested on equilibrium isotope effects in a model harmonic system and in methane.

Then we turn our attention to kinetic isotope effect calculations with the quantum instanton approximation, a method whose path integral implementation belongs among the most accurate approaches for evaluating reaction rate constants in polyatomic systems. To accelerate quantum instanton calculations of kinetic isotope effects, we combine higher-order Boltzmann operator factorization with virial estimators, allowing us to speed up both the convergence to the quantum limit and statistical convergence of the calculation. We estimate the overall resulting acceleration using H+H2/D+D2 as a benchmark system, and then apply the accelerated method to several kinetic isotope effects associated with the H+CH4=H2+CH3 exchange.

Last but not least, we explored ways to improve on the quantum instanton approximation for reaction rate constants. To that end, we review quantum instanton and Hansen-Andersen approximations, and propose a combined method, which, as the Hansen-Andersen approximation, has the correct high-temperature behavior, and at the same time, as the quantum instanton approximation, has more flexibility by allowing the dividing surface for the reaction to split into two surfaces at low temperatures. The properties of the combined method are tested on symmetric and asymmetric Eckart barrier.

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Concepts associés (35)
Effet isotopique cinétique
L'effet isotopique cinétique (en anglais, kinetic isotope effect ou KIE) est la variation de la vitesse d'une réaction chimique lorsqu'un atome d'un des réactifs est remplacé par l'un de ses isotopes. Par exemple, le remplacement d'un atome C par un atome C conduit à un effet isotopique cinétique défini par le rapport des constantes de vitesse (on met en général au numérateur la constante qui concerne l'isotope le plus léger). Dans la substitution nucléophile du bromure de méthyle par l'ion cyanure, le rapport mesuré est de .
Reaction rate
The reaction rate or rate of reaction is the speed at which a chemical reaction takes place, defined as proportional to the increase in the concentration of a product per unit time and to the decrease in the concentration of a reactant per unit time. Reaction rates can vary dramatically. For example, the oxidative rusting of iron under Earth's atmosphere is a slow reaction that can take many years, but the combustion of cellulose in a fire is a reaction that takes place in fractions of a second.
Rate equation
In chemistry, the rate law or rate equation for a chemical reaction is a mathematical equation that links the rate of forward reaction with the concentrations or pressures of the reactants and constant parameters (normally rate coefficients and partial reaction orders). For many reactions, the initial rate is given by a power law such as where [\mathrm{A}] and [\mathrm{B}] express the concentration of the species \mathrm{A} and \mathrm{B}, usually in moles per liter (molarity, M).
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