Accelerating equilibrium isotope effect calculations: I. Stochastic thermodynamic integration with respect to mass

Accurate path integral Monte Carlo or molecular dynamics calculations of isotope effects have until recently been expensive because of the necessity to reduce three types of errors present in such calculations: statistical errors due to sampling, path integral discretization errors, and thermodynamic integration errors. While the statistical errors can be reduced with virial estimators and path integral discretization errors with high-order factorization of the Boltzmann operator, here we propose a method for accelerating isotope effect calculations by eliminating the integration error. We show that the integration error can be removed entirely by changing particle masses stochastically during the calculation and by using a piecewise linear umbrella biasing potential. Moreover, we demonstrate numerically that this approach does not increase the statistical error. The resulting acceleration of isotope effect calculations is demonstrated on a model harmonic system and on deuterated species of methane

A Cultural Perspective on Romantic Love

The article presents a conceptual, historical, anthropological, psychological, and sociological review of cultural perspectives on love: how culture affects our experience and expression of love. The evidence suggests that love is a universal emotion experienced by a majority of people, in various historical eras, and in all the world’s cultures, but manifests itself in different ways because culture has an impact on people’s conceptions of love and the way they feel, think, and behave in romantic relationships

Accelerating path integral evaluation of equilibrium and kinetic isotope effects

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

Understanding Representations by Exploring Galaxies in Chemical Space

We present a Monte Carlo approach for studying chemical feature distributions of molecules without training a machine learning model or performing exhaustive enumeration. The algorithm generates molecules with predefined similarity to a given one for any representation. It serves as a diagnostic tool to understand which molecules are grouped in feature space and to identify shortcomings of representations and embeddings from unsupervised learning. In this work, we first study clusters surrounding chosen molecules and demonstrate that common representations do not yield a constant density of molecules in feature space, with possible implications for learning behavior. Next, we observe a connection between representations and properties: a linear correlation between the property value of a central molecule and the average radial slope of that property in chemical space. Molecules with extremal property values have the largest property derivative values in chemical space, which provides a route to improve the data efficiency of a representation by tailoring it towards a given property. Finally, we demonstrate applications for sampling molecules with specified metric-dependent distributions to generate molecules biased toward graph spaces of interest