arXiv subjects

Albert P. Bartók

Publications and source records attributed to Albert P. Bartók.

36 records · Page 2Linked to original sources

arXiv2020

On the Completeness of Atomic Structure Representations

Many-body descriptors are widely used to represent atomic environments in the construction of machine learned interatomic potentials and more broadly for fitting, classification and embedding tasks on atomic structures. It was generally believed that 3-body descriptors uniquely specify the environment of an atom, up to a rotation and permutation of like atoms. We produce several counterexamples to this belief, with the consequence that any classifier, regression or embedding model for atom-centred properties that uses 3 (or 4)-body features will incorrectly give identical results for different configurations. Writing global properties (such as total energies) as a sum of many atom-centred contributions mitigates, but does not eliminate, the impact of this fundamental deficiency -- explaining the success of current "machine-learning" force fields. We anticipate the issues that will arise as the desired accuracy increases, and suggest potential solutions.

physics.chem-ph↗

arXiv2020

Combining phonon accuracy with high transferability in Gaussian approximation potential models

Machine learning driven interatomic potentials, including Gaussian approximation potential (GAP) models, are emerging tools for atomistic simulations. Here, we address the methodological question of how one can fit GAP models that accurately predict vibrational properties in specific regions of configuration space, whilst retaining flexibility and transferability to others. We use an adaptive regularization of the GAP fit that scales with the absolute force magnitude on any given atom, thereby exploring the Bayesian interpretation of GAP regularization as an "expected error", and its impact on the prediction of physical properties for a material of interest. The approach enables excellent predictions of phonon modes (to within 0.1-0.2 THz) for structurally diverse silicon allotropes, and it can be coupled with existing fitting databases for high transferability. These findings and workflows are expected to be useful for GAP-driven materials modeling more generally.

cond-mat.mtrl-sci↗

arXiv2020

Gaussian Approximation Potentials: a brief tutorial introduction

We present a swift walk-through of our recent work that uses machine learning to fit interatomic potentials based on quantum mechanical data. We describe our Gaussian Approximation Potentials (GAP) framework, discussing a variety of descriptors, how to train the model on total energies and derivatives and the simultaneous use of multiple models. We also show a small example using QUIP, the software sandbox implementation of GAP that is available for non-commercial use.

cond-mat.mtrl-sci↗

arXiv2020

Comparing molecules and solids across structural and alchemical space

Evaluating the (dis)similarity of crystalline, disordered and molecular compounds is a critical step in the development of algorithms to navigate automatically the configuration space of complex materials. For instance, a structural similarity metric is crucial for classifying structures, searching chemical space for better compounds and materials, and driving the next generation of machine-learning techniques for predicting the stability and properties of molecules and materials. In the last few years several strategies have been designed to compare atomic coordination environments. In particular, the Smooth Overlap of Atomic Positions (SOAP) has emerged as an elegant framework to obtain translation, rotation and permutation-invariant descriptors of groups of atoms, driven by the design of various classes of machine-learned inter-atomic potentials. Here we discuss how one can combine such local descriptors using a Regularized Entropy Match (REMatch) approach to describe the similarity of both whole molecular and bulk periodic structures, introducing powerful metrics that enable the navigation of alchemical and structural complexity within a unified framework. Furthermore, using this kernel and a ridge regression method we can predict atomization energies for a database of small organic molecules with a mean absolute error below 1kcal/mol, reaching an important milestone in the application of machine-learning techniques to the evaluation of molecular properties.

cond-mat.mtrl-sci↗

arXiv2020

Ultrasoft pseudopotentials with kinetic energy density support: implementing the modified Becke-Johnson potential

We extend the Vanderbilt ultrasoft pseudopotential scheme by adding kinetic energy density terms, in order to use meta-GGA exchange potentials, such as the Becke-Johnson or Tran-Blaha potentials, in the planewave-pseudopotential implementation of Density Functional Theory. Having implemented kinetic energy augmentation and non-linear core correction terms in the CASTEP density functional package, we evaluate the validity of our approach by comparing the calculated electronic structure of isolated atoms and semiconductor crystals to all-electron benchmark calculations. Based on our results, we provide recommendations for the practical use of the Tran-Blaha exchange in planewave-pseudopotential codes.

cond-mat.mtrl-sci↗

arXiv2020

Efficient prediction of Nucleus Independent Chemical Shifts for polycyclic aromatic hydrocarbons

Nuclear Magnetic Resonance (NMR) is one of the most powerful experimental techniques to characterize the structure of molecules and confined liquids. Nevertheless, the complexity of the systems under investigation usually requires complementary computational studies to interpret the NMR results. In this work we focus on polycyclic aromatic hydrocarbons (PAHs), an important class of organic molecules which have been commonly used as simple analogues for the spectroscopic properties of more complex systems, such as porous disordered carbons. We use Density Functional Theory (DFT) to calculate 13C chemical shifts and Nucleus Independent Chemical Shifts (NICS) for 34 PAHs. The results show a clear molecular size dependence of the two quantities, as well as the convergence of the 13C NMR shifts towards the values observed for graphene. We then present two computationally cheap models for the prediction of NICS in simple PAHs. We show that while a simple dipolar model fails to produce accurate values, a perturbative tight-binding approach can be successfully applied for the prediction of NICS in this series of molecules, including some non-planar ones containing 5- and 7-membered rings. This model, one to two orders of magnitudes faster than DFT calculations, is very promising and can be further refined in order to study more complex systems.

physics.chem-ph↗

arXiv2019

On the calculation of the bandgap of periodic solids with MGGA functionals using the total energy

During the last few years, it has become more and more clear that functionals of the meta generalized gradient approximation (MGGA) are more accurate than GGA functionals for the geometry and energetics of electronic systems. However, MGGA functionals are also potentially more interesting for the electronic structure, in particular when the potential is non-multiplicative (i.e., when MGGAs are implemented in the generalized Kohn-Sham framework), which may help to get more accurate bandgaps. Here, we show that the calculation of bandgap of solids with MGGA functionals can be done very accurately also in a non-self-consistent manner. This scheme uses only the total energy and can, therefore, be very useful when the self-consistent implementation of a particular MGGA functional is not available. Since self-consistent MGGA calculations may be difficult to converge, the non-self-consistent scheme may also help to speed-up the calculations. Furthermore, it can be applied to any other types of functionals, for which the implementation of the corresponding potential is not trivial.

cond-mat.mtrl-sci↗

arXiv2019

Regularized SCAN functional

We propose modifications to the functional form of the SCAN density functional to eliminate numerical instabilities. This is necessary to allow reliable, automatic generation of pseudopotentials (including PAW potentials). The regularized SCAN is designed to match the original form very closely, and we show that its performance remains comparable.

cond-mat.mtrl-sci↗

arXiv2018

Realistic atomistic structure of amorphous silicon from machine-learning-driven molecular dynamics

Amorphous silicon (a-Si) is a widely studied non-crystalline material, and yet the subtle details of its atomistic structure are still unclear. Here, we show that accurate structural models of a-Si can be obtained by harnessing the power of machine-learning algorithms to create interatomic potentials. Our best a-Si network is obtained by cooling from the melt in molecular-dynamics simulations, at a rate of 10$^{11}$ K/s (that is, on the 10 ns timescale). This structure shows a defect concentration of below 2% and agrees with experiments regarding excess energies, diffraction data, as well as $^{29}$Si solid-state NMR chemical shifts. We show that this level of quality is impossible to achieve with faster quench simulations. We then generate a 4,096-atom system which correctly reproduces the magnitude of the first sharp diffraction peak (FSDP) in the structure factor, achieving the closest agreement with experiments to date. Our study demonstrates the broader impact of machine-learning interatomic potentials for elucidating accurate structures and properties of amorphous functional materials.

cond-mat.mtrl-sci↗

arXiv2017

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 homogeneity 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.

cond-mat.mtrl-sci↗

arXiv2017

Polytypism in the ground state structure of the Lennard-Jonesium

We present a systematic study of the stability of nineteen different periodic structures using the finite range Lennard-Jones potential model discussing the effects of pressure, potential truncation, cutoff distance and Lennard-Jones exponents. The structures considered are the hexagonal close packed (hcp), face centred cubic (fcc) and seventeen other polytype stacking sequences, such as dhcp and $9R$. We found that at certain pressure and cutoff distance values, neither fcc nor hcp is the ground state structure as previously documented, but different polytypic sequences. This behaviour shows a strong dependence on the way the tail of the potential is truncated.

cond-mat.mtrl-sci↗

arXiv2016

Determining pressure-temperature phase diagrams of materials

We extend the nested sampling algorithm to simulate materials under periodic boundary and constant pressure conditions, and show how it can be used to determine the complete equilibrium phase diagram, for a given potential energy function, efficiently and in a highly automated fashion. The only inputs required are the composition and the desired pressure and temperature ranges, in particular, solid-solid phase transitions are recovered without any a priori knowledge about the structure of solid phases. We benchmark and showcase the algorithm on the periodic Lennard-Jones system, aluminium and NiTi.

cond-mat.mtrl-sci↗

arXiv2014

Accuracy and transferability of GAP models for tungsten

We introduce interatomic potentials for tungsten in the bcc crystal phase and its defects within the Gaussian Approximation Potential (GAP) framework, fitted to a database of first principles density functional theory (DFT) calculations. We investigate the performance of a sequence of models based on databases of increasing coverage in configuration space and showcase our strategy of choosing representative small unit cells to train models that predict properties only observable using thousands of atoms. The most comprehensive model is then used to calculate properties of the screw dislocation, including its structure, the Peierls barrier and the energetics of the vacancy-dislocation interaction. All software and raw data are available at www.libatoms.org.

cond-mat.mtrl-sci↗

arXiv2014

Nested sampling for materials: the case of hard spheres

The recently introduced nested sampling algorithm allows the direct and efficient calculation of the partition function of atomistic systems. We demonstrate its applicability to condensed phase systems with periodic boundary conditions by studying the three dimensional hard sphere model. Having obtained the partition function, we show how easy it is to calculate the compressibility and the free energy as functions of the packing fraction and local order, verifying that the transition to crystallinity has a very small barrier, and that the entropic contribution of jammed states to the free energy is negligible for packing fractions above the phase transition. We quantify the previously proposed schematic phase diagram and estimate the extent of the region of jammed states. We find that within our samples, the maximally random jammed configuration is surprisingly disordered.

cond-mat.stat-mech↗

arXiv2013

On representing chemical environments

We review some recently published methods to represent atomic neighbourhood environments, and analyse their relative merits in terms of their faithfulness and suitability for fitting potential energy surfaces. The crucial properties that such representations (sometimes called descriptors) must have are differentiability with respect to moving the atoms, and invariance to the basic symmetries of physics: rotation, reflection, translation, and permutation of atoms of the same species. We demonstrate that certain widely used descriptors that initially look quite different are specific cases of a general approach, in which a finite set of basis functions with increasing angular wave numbers are used to expand the atomic neighbourhood density function. Using the example system of small clusters, we quantitatively show that this expansion needs to be carried to higher and higher wave numbers as the number of neighbours increases in order to obtain a faithful representation, and that variants of the descriptors converge at very different rates. We also propose an altogether new approach, called Smooth Overlap of Atomic Positions (SOAP), that sidesteps these difficulties by directly defining the similarity between any two neighbourhood environments, and show that it is still closely connected to the invariant descriptors. We test the performance of the various representations by fitting models to the potential energy surface of small silicon clusters and the bulk crystal.

physics.comp-ph↗

arXiv2010

Efficient sampling of atomic configurational spaces

We describe a method to explore the configurational phase space of chemical systems. It is based on the nested sampling algorithm recently proposed by Skilling [Skilling J. (2004) In AIP Conference Proceedings, vol. 735, p. 395.; Skilling J. (2006) J of Bayesian Analysis 1:833-860.] and allows us to explore the entire potential energy surface (PES) efficiently in an unbiased way. The algorithm has two parameters which directly control the trade-off between the resolution with which the space is explored and the computational cost. We demonstrate the use of nested sampling on Lennard-Jones (LJ) clusters. Nested sampling provides a straightforward approximation for the partition function, thus evaluating expectation values of arbitrary smooth operators at arbitrary temperatures becomes a simple post-processing step. Access to absolute free energies allows us to determine the temperature-density phase diagram for LJ cluster stability. Even for relatively small clusters, the efficiency gain over parallel tempering in calculating the heat capacity is more than an order of magnitude. Furthermore, by analysing the topology of the resulting samples we are able to visualise the PES in a new and illuminating way. We identify a discretely valued order parameter with basins and supra-basins of the PES allowing a straightforward and unambiguous definition of macroscopic states of an atomistic system and the evaluation of the associated free energies.

cond-mat.stat-mech↗

arXiv2010

Gaussian Approximation Potential: an interatomic potential derived from first principles Quantum Mechanics

Simulation of materials at the atomistic level is an important tool in studying microscopic structure and processes. The atomic interactions necessary for the simulation are correctly described by Quantum Mechanics. However, the computational resources required to solve the quantum mechanical equations limits the use of Quantum Mechanics at most to a few hundreds of atoms and only to a small fraction of the available configurational space. This thesis presents the results of my research on the development of a new interatomic potential generation scheme, which we refer to as Gaussian Approximation Potentials. In our framework, the quantum mechanical potential energy surface is interpolated between a set of predetermined values at different points in atomic configurational space by a non-linear, non-parametric regression method, the Gaussian Process. To perform the fitting, we represent the atomic environments by the bispectrum, which is invariant to permutations of the atoms in the neighbourhood and to global rotations. The result is a general scheme, that allows one to generate interatomic potentials based on arbitrary quantum mechanical data. We built a series of Gaussian Approximation Potentials using data obtained from Density Functional Theory and tested the capabilities of the method. We showed that our models reproduce the quantum mechanical potential energy surface remarkably well for the group IV semiconductors, iron and gallium nitride. Our potentials, while maintaining quantum mechanical accuracy, are several orders of magnitude faster than Quantum Mechanical methods.

cond-mat.mtrl-sci↗

arXiv2009

Gaussian Approximation Potentials: the accuracy of quantum mechanics, without the electrons

We introduce a class of interatomic potential models that can be automatically generated from data consisting of the energies and forces experienced by atoms, derived from quantum mechanical calculations. The resulting model does not have a fixed functional form and hence is capable of modeling complex potential energy landscapes. It is systematically improvable with more data. We apply the method to bulk carbon, silicon and germanium and test it by calculating properties of the crystals at high temperatures. Using the interatomic potential to generate the long molecular dynamics trajectories required for such calculations saves orders of magnitude in computational cost.

physics.comp-ph↗