Extrapolation and interpolation strategies for efficiently estimating structural observables as a function of temperature and density

A structure-dynamics relationship enables prediction of the water hydrogen bond exchange activation energy from experimental data

It has long been understood that the structural features of water are determined by hydrogen bonding (H-bonding) and that the exchange of, or "jumps" between, H-bond partners underlies many of the dynamical processes in water. Despite the importance of H-bond exchanges there is, as yet, no direct method for experimentally measuring the timescale of the process or its associated activation energy. Here, we identify and exploit relationships between water's structural and dynamical properties that provide an indirect route for determining the H-bond exchange activation energy from experimental data. Specifically, we show that the enthalpy and entropy determining the radial distribution function in liquid water are linearly correlated with the activation energies for H-bond jumps, OH reorientation, and diffusion. Using temperature-dependent measurements of the radial distribution function from the literature, we demonstrate how these correlations allow us to infer the value of the jump activation energy, Ea,0, from experimental results. This analysis gives Ea,0 = 3.43 kcal mol-1, which is in good agreement with that predicted by the TIP4P/2005 water model. We also illustrate other approaches for estimating this activation energy consistent with these estimates.

Departures from perfect isomorph behavior in Lennard-Jones fluids and solids

Isomorphs are lines on a fluid or solid phase diagram along which the microstructure is invariant on affine density scaling of the molecular coordinates. Only inverse power (IP) and hard sphere potential systems are perfectly isomorphic. This work provides new theoretical tools and criteria to determine the extent of deviation from perfect isomorphicity for other pair potentials using the Lennard-Jones (LJ) system as a test case. A simple prescription for predicting isomorphs in the fluid range using the freezing line as a reference is shown to be quite accurate for the LJ system. The shear viscosity and self-diffusion coefficient scale well are calculated using this method, which enables comments on the physical significance of the correlations found previously in the literature to be made. The virial–potential energy fluctuation and the concept of an effective IPL system and exponent, n′, are investigated, particularly with reference to the LJ freezing and melting lines. It is shown that the exponent, n′, converges to the value 12 at a high temperature as ∼ T−1/2, where T is the temperature. Analytic expressions are derived for the density, temperature, and radius derivatives of the radial distribution function along an isomorph that can be used in molecular simulation. The variance of the radial distribution function and radial fluctuation function are shown to be isomorph invariant.

Temperature Extrapolation of Henry's Law Constants and the Isosteric Heat of Adsorption

Computational screening of adsorbent materials often uses the Henry's law constant (K_H) (at a particular temperature) as a first discriminator metric due to its relative ease of calculation. The isosteric heat of adsorption in the limit of zero pressure (q_st^∞) is often calculated along with the Henry's law constant, and both properties are informative metrics of adsorbent material performance at low-pressure conditions. In this article, we introduce a method for extrapolating K_H as a function of temperature, using series-expansion coefficients that are easily computed at the same time as K_H itself; the extrapolation function also yields q_st^∞. The extrapolation is highly accurate over a wide range of temperatures when the basis temperature is sufficiently high, for a wide range of adsorbent materials and adsorbate gases. Various results suggest that the extrapolation is accurate when the extrapolation range in inverse-temperature space is limited to |β - β₀ | < 0.5 mol/kJ. Application of the extrapolation to a large set of materials is shown to be successful provided that K_H is not extremely large and/or the extrapolation coefficients converge satisfactorily. The extrapolation is also able to predict q_st^∞ for a system that shows an unusually large temperature dependence. The work provides a robust method for predicting K_H and q_st^∞ over a wide range of industrially relevant temperatures with minimal effort beyond that necessary to compute those properties at a single temperature, which facilitates the addition of practical operating (or processing) conditions to computational screening exercises.

Bottom-up Coarse-Graining: Principles and Perspectives

Large-scale computational molecular models provide scientists a means to investigate the effect of microscopic details on emergent mesoscopic behavior. Elucidating the relationship between variations on the molecular scale and macroscopic observable properties facilitates an understanding of the molecular interactions driving the properties of real world materials and complex systems (e.g., those found in biology, chemistry, and materials science). As a result, discovering an explicit, systematic connection between microscopic nature and emergent mesoscopic behavior is a fundamental goal for this type of investigation. The molecular forces critical to driving the behavior of complex heterogeneous systems are often unclear. More problematically, simulations of representative model systems are often prohibitively expensive from both spatial and temporal perspectives, impeding straightforward investigations over possible hypotheses characterizing molecular behavior. While the reduction in resolution of a study, such as moving from an atomistic simulation to that of the resolution of large coarse-grained (CG) groups of atoms, can partially ameliorate the cost of individual simulations, the relationship between the proposed microscopic details and this intermediate resolution is nontrivial and presents new obstacles to study. Small portions of these complex systems can be realistically simulated. Alone, these smaller simulations likely do not provide insight into collectively emergent behavior. However, by proposing that the driving forces in both smaller and larger systems (containing many related copies of the smaller system) have an explicit connection, systematic bottom-up CG techniques can be used to transfer CG hypotheses discovered using a smaller scale system to a larger system of primary interest. The proposed connection between different CG systems is prescribed by (i) the CG representation (mapping) and (ii) the functional form and parameters used to represent the CG energetics, which approximate potentials of mean force (PMFs). As a result, the design of CG methods that facilitate a variety of physically relevant representations, approximations, and force fields is critical to moving the frontier of systematic CG forward. Crucially, the proposed connection between the system used for parametrization and the system of interest is orthogonal to the optimization used to approximate the potential of mean force present in all systematic CG methods. The empirical efficacy of machine learning techniques on a variety of tasks provides strong motivation to consider these approaches for approximating the PMF and analyzing these approximations.

Learning Efficient, Collective Monte Carlo Moves with Variational Autoencoders

Discovering meaningful collective variables for enhancing sampling, via applied biasing potentials or tailored MC move sets, remains a major challenge within molecular simulation. While recent studies identifying collective variables with variational autoencoders (VAEs) have focused on the encoding and latent space discovered by a VAE, the impact of the decoding and its ability to act as a generative model remains unexplored. We demonstrate how VAEs may be used to learn (on-the-fly and with minimal human intervention) highly efficient, collective Monte Carlo moves that accelerate sampling along the learned collective variable. In contrast to many machine learning-based efforts to bias sampling and generate novel configurations, our methods result in exact sampling in the ensemble of interest and do not require reweighting. In fact, we show that the acceptance rates of our moves approach unity for a perfect VAE model. While this is never observed in practice, VAE-based Monte Carlo moves still enhance sampling of new configurations. We demonstrate, however, that the form of the encoding and decoding distributions, in particular the extent to which the decoder reflects the underlying physics, greatly impacts the performance of the trained VAE.

Some aspects of extrapolation based on interpolation polynomials

The problem of extrapolation on the basis of interpolation polynomials is considered in the paper. A simple computational procedure is proposed to find the predicted value for a polynomial of any degree under conditions of a uniform grid. An algorithm for determining the best polynomial for extrapolation is proposed. To construction of integral transformation for operator of equation of convective diffusion under mixed boundary conditions.

A microcanonical approach to temperature-transferable coarse-grained models using the relative entropy

Bottom-up coarse-graining methods provide systematic tools for creating simplified models of molecular systems. However, coarse-grained (CG) models produced with such methods frequently fail to accurately reproduce all thermodynamic properties of the reference atomistic systems they seek to model and, moreover, can fail in even more significant ways when used at thermodynamic state points different from the reference conditions. These related problems of representability and transferability limit the usefulness of CG models, especially those of strongly state-dependent systems. In this work, we present a new strategy for creating temperature-transferable CG models using a single reference system and temperature. The approach is based on two complementary concepts. First, we switch to a microcanonical basis for formulating CG models, focusing on effective entropy functions rather than energy functions. This allows CG models to naturally represent information about underlying atomistic energy fluctuations, which would otherwise be lost. Such information not only reproduces energy distributions of the reference model but also successfully predicts the correct temperature dependence of the CG interactions, enabling temperature transferability. Second, we show that relative entropy minimization provides a direct and systematic approach to parameterize such classes of temperature-transferable CG models. We calibrate the approach initially using idealized model systems and then demonstrate its ability to create temperature-transferable CG models for several complex molecular liquids.

The kernel-weighted local polynomial regression (KwLPR) approach: an efficient, novel tool for development of QSAR/QSAAR toxicity extrapolation models

The ability of accurate predictions of biological response (biological activity/property/toxicity) of a given chemical makes the quantitative structure‐activity/property/toxicity relationship (QSAR/QSPR/QSTR) models unique among the in silico tools. In addition, experimental data of selected species can also be used as an independent variable along with other structural as well as physicochemical variables to predict the response for different species formulating quantitative activity–activity relationship (QAAR)/quantitative structure–activity–activity relationship (QSAAR) approach. Irrespective of the models' type, the developed model's quality, and reliability need to be checked through multiple classical stringent validation metrics. Among the validation metrics, error-based metrics are more significant as the basic idea of a good predictive model is to improve the predictions' quality by lowering the predicted residuals for new query compounds. Following the concept, we have checked the predictive quality of the QSAR and QSAAR models employing kernel-weighted local polynomial regression (KwLPR) approach over the traditional linear and non-linear regression-based approaches tools such as multiple linear regression (MLR) and k nearest neighbors (kNN). Five datasets which were previously modeled using linear and non-linear regression method were considered to implement the KwPLR approach, followed by comparison of their validation metrics outcomes. For all five cases, the KwLPR based models reported better results over the traditional approaches. The present study's focus is not to develop a better or improved QSAR/QSAAR model over the previous ones, but to demonstrate the advantage, prediction power, and reliability of the KwLPR algorithm and establishing it as a novel, powerful cheminformatic tool. To facilitate the use of the KwLPR algorithm for QSAR/QSPR/QSTR/QSAAR modeling, the authors provide an in-house developed KwLPR.RMD script under the open-source R programming language.