First-principles energetics of water clusters and ice: A many-body analysis

Standard forms of density-functional theory (DFT) have good predictive power for many materials, but are not yet fully satisfactory for cluster, solid, and liquid forms of water. Recent work has stressed the importance of DFT errors in describing dispersion, but we note that errors in other parts of the energy may also contribute. We obtain information about the nature of DFT errors by using a many-body separation of the total energy into its 1-body, 2-body, and beyond-2-body components to analyze the deficiencies of the popular PBE and BLYP approximations for the energetics of water clusters and ice structures. The errors of these approximations are computed by using accurate benchmark energies from the coupled-cluster technique of molecular quantum chemistry and from quantum Monte Carlo calculations. The systems studied are isomers of the water hexamer cluster, the crystal structures Ih, II, XV, and VIII of ice, and two clusters extracted from ice VIII. For the binding energies of these systems, we use the machine-learning technique of Gaussian Approximation Potentials to correct successively for 1-body and 2-body errors of the DFT approximations. We find that even after correction for these errors, substantial beyond-2-body errors remain. The characteristics of the 2-body and beyond-2-body errors of PBE are completely different from those of BLYP, but the errors of both approximations disfavor the close approach of non-hydrogen-bonded monomers. We note the possible relevance of our findings to the understanding of liquid water

Building nonparametric nn-body force fields using Gaussian process regression

Constructing a classical potential suited to simulate a given atomic system is a remarkably difficult task. This chapter presents a framework under which this problem can be tackled, based on the Bayesian construction of nonparametric force fields of a given order using Gaussian process (GP) priors. The formalism of GP regression is first reviewed, particularly in relation to its application in learning local atomic energies and forces. For accurate regression it is fundamental to incorporate prior knowledge into the GP kernel function. To this end, this chapter details how properties of smoothness, invariance and interaction order of a force field can be encoded into corresponding kernel properties. A range of kernels is then proposed, possessing all the required properties and an adjustable parameter $n$ governing the interaction order modelled. The order $n$ best suited to describe a given system can be found automatically within the Bayesian framework by maximisation of the marginal likelihood. The procedure is first tested on a toy model of known interaction and later applied to two real materials described at the DFT level of accuracy. The models automatically selected for the two materials were found to be in agreement with physical intuition. More in general, it was found that lower order (simpler) models should be chosen when the data are not sufficient to resolve more complex interactions. Low $n$ GPs can be further sped up by orders of magnitude by constructing the corresponding tabulated force field, here named "MFF".Comment: 31 pages, 11 figures, book chapte

Machine-learning of atomic-scale properties based on physical principles

We briefly summarize the kernel regression approach, as used recently in materials modelling, to fitting functions, particularly potential energy surfaces, and highlight how the linear algebra framework can be used to both predict and train from linear functionals of the potential energy, such as the total energy and atomic forces. We then give a detailed account of the Smooth Overlap of Atomic Positions (SOAP) representation and kernel, showing how it arises from an abstract representation of smooth atomic densities, and how it is related to several popular density-based representations of atomic structure. We also discuss recent generalisations that allow fine control of correlations between different atomic species, prediction and fitting of tensorial properties, and also how to construct structural kernels---applicable to comparing entire molecules or periodic systems---that go beyond an additive combination of local environments

Gaussian Process Regression for Materials and Molecules.

We provide an introduction to Gaussian process regression (GPR) machine-learning methods in computational materials science and chemistry. The focus of the present review is on the regression of atomistic properties: in particular, on the construction of interatomic potentials, or force fields, in the Gaussian Approximation Potential (GAP) framework; beyond this, we also discuss the fitting of arbitrary scalar, vectorial, and tensorial quantities. Methodological aspects of reference data generation, representation, and regression, as well as the question of how a data-driven model may be validated, are reviewed and critically discussed. A survey of applications to a variety of research questions in chemistry and materials science illustrates the rapid growth in the field. A vision is outlined for the development of the methodology in the years to come

Structural Simplicity as a Restraint on the Structure of Amorphous Silicon

Understanding the structural origins of the properties of amorphous materials remains one of the most important challenges in structural science. In this study we demonstrate that local ‘structural simplicity’, embodied by the degree to which atomic environments within a material are similar to each other, is powerful concept for rationalising the structure of canonical amorphous material amorphous silicon (a-Si). We show, by restraining a reverse Monte Carlo refinement against pair distribution function (PDF) data to be simpler, that the simplest model consistent with the PDF is a continuous random network (CRN). A further effect of producing a simple model of a-Si is the generation of a (pseudo)gap in the electronic density of states, suggesting that structural ho- mogeneity drives electronic homogeneity. That this method produces models of a-Si that approach the state-of-the-art without the need for chemically specific restraints (beyond the assumption of homogeneity) suggests that simplicity-based refinement approaches may allow experiment-driven structural modelling techniques to be developed for the wide variety of amorphous semiconductors with strong local order.Sidney Sussex College, Cambridge to M.J.C.; EPSRC to C.P.G. and R.P.K. under Grant No. EP/K030132/1 EPSRC (EP/G004528/2) and ERC (Grant Ref: 279705) to M.J.C and A.L.G.. A.P.B. was supported by a Leverhulme Early Career Fellowship with joint funding from the Isaac Newton Trust. Via our membership of the UK’s HEC Materials Chemistry Consortium, which is funded by the EPSRC (EP/L000202), this work used the ARCHER UK National Supercomputing Service (http://archer.ac.uk)

Big-Data-Driven Materials Science and its FAIR Data Infrastructure

This chapter addresses the forth paradigm of materials research -- big-data driven materials science. Its concepts and state-of-the-art are described, and its challenges and chances are discussed. For furthering the field, Open Data and an all-embracing sharing, an efficient data infrastructure, and the rich ecosystem of computer codes used in the community are of critical importance. For shaping this forth paradigm and contributing to the development or discovery of improved and novel materials, data must be what is now called FAIR -- Findable, Accessible, Interoperable and Re-purposable/Re-usable. This sets the stage for advances of methods from artificial intelligence that operate on large data sets to find trends and patterns that cannot be obtained from individual calculations and not even directly from high-throughput studies. Recent progress is reviewed and demonstrated, and the chapter is concluded by a forward-looking perspective, addressing important not yet solved challenges.Comment: submitted to the Handbook of Materials Modeling (eds. S. Yip and W. Andreoni), Springer 2018/201

Understanding high pressure hydrogen with a hierarchical machine-learned potential

The hydrogen phase diagram has a number of unusual features which are generally well reproduced by density functional calculations. Unfortunately, these calculations fail to provide good physical insights into why those features occur. In this paper, we parameterize a model potential for molecular hydrogen which permits long and large simulations. The model shows excellent reproduction of the phase diagram, including the broken-symmetry Phase II, an efficiently-packed phase III and the maximum in the melt curve. It also gives an excellent reproduction of the vibrational frequencies, including the maximum in the vibrational frequency $\nu(P)$ and negative thermal expansion. By detailed study of lengthy molecular dynamics, we give intuitive explanations for observed and calculated properties. All solid structures approximate to hexagonal close packed, with symmetry broken by molecular orientation. At high pressure, Phase I shows significant short-ranged correlations between molecular orientations. The turnover in Raman frequency is due to increased coupling between neighboring molecules, rather than weakening of the bond. The liquid is denser than the close-packed solid because, at molecular separations below 2.3\AA, the favoured relative orientation switches from quadrupole-energy-minimising to steric-repulsion-minimising. The latter allows molecules to get closer together, without atoms getting closer but this cannot be achieved within the constraints of a close-packed layer

Search for dark matter produced in association with a Higgs boson decaying to a pair of bottom quarks in proton-proton collisions at root s=13TeV

A search for dark matter produced in association with a Higgs boson decaying to a pair of bottom quarks is performed in proton-proton collisions at a center-of-mass energy of 13 TeV collected with the CMS detector at the LHC. The analyzed data sample corresponds to an integrated luminosity of 35.9 fb(-1). The signal is characterized by a large missing transverse momentum recoiling against a bottom quark-antiquark system that has a large Lorentz boost. The number of events observed in the data is consistent with the standard model background prediction. Results are interpreted in terms of limits both on parameters of the type-2 two-Higgs doublet model extended by an additional light pseudoscalar boson a (2HDM+a) and on parameters of a baryonic Z simplified model. The 2HDM+a model is tested experimentally for the first time. For the baryonic Z model, the presented results constitute the most stringent constraints to date.Peer reviewe

A Deep Neural Network for Simultaneous Estimation of b Jet Energy and Resolution

We describe a method to obtain point and dispersion estimates for the energies of jets arising from b quarks produced in proton-proton collisions at an energy of s = 13 TeV at the CERN LHC. The algorithm is trained on a large sample of simulated b jets and validated on data recorded by the CMS detector in 2017 corresponding to an integrated luminosity of 41 fb - 1 . A multivariate regression algorithm based on a deep feed-forward neural network employs jet composition and shape information, and the properties of reconstructed secondary vertices associated with the jet. The results of the algorithm are used to improve the sensitivity of analyses that make use of b jets in the final state, such as the observation of Higgs boson decay to b b ¯