Machine learning for predictive condensed-phase simulation

We show how machine learning techniques based on Bayesian inference can be used to reach new levels of realism in the computer simulation of molecular materials, focusing here on water. We train our machine-learning algorithm using accurate, correlated quantum chemistry, and predict energies and forces in molecular aggregates ranging from clusters to solid and liquid phases. The widely used electronic-structure methods based on density-functional theory (DFT) give poor accuracy for molecular materials like water, and we show how our techniques can be used to generate systematically improvable corrections to DFT. The resulting corrected DFT scheme gives remarkably accurate predictions for the relative energies of small water clusters and of different ice structures, and greatly improves the description of the structure and dynamics of liquid water.

Communication: energy benchmarking with quantum Monte Carlo for water nano-droplets and bulk liquid water.

We show the feasibility of using quantum Monte Carlo (QMC) to compute benchmark energies for configuration samples of thermal-equilibrium water clusters and the bulk liquid containing up to 64 molecules. Evidence that the accuracy of these benchmarks approaches that of basis-set converged coupled-cluster calculations is noted. We illustrate the usefulness of the benchmarks by using them to analyze the errors of the popular BLYP approximation of density functional theory (DFT). The results indicate the possibility of using QMC as a routine tool for analyzing DFT errors for non-covalent bonding in many types of condensed-phase molecular system.

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.

Stabilization of a complex perovskite superstructure under ambient conditions: Influence of cation composition and ordering, and evaluation as an SOFC cathode

Ba1.6Ca2.3Y1.1Fe5O13 is an Fe3+ oxide adopting a complex perovskite superstructure, which is an ordered intergrowth between the Ca2Fe2O5 and YBa2Fe3O8 structures featuring octahedral, square pyramidal, and tetrahedral B sites and three distinct A site environments. The distribution of A site cations was evaluated by combined neutron and X-ray powder diffraction. Consistent with the Fe3+ charge state, the material is an antiferromagnetic insulator with a Néel temperature of 480-485 °C and has a relatively low d.c. conductivity of 2.06 S cm-1 at 700 °C. The observed area specific resistance in symmetrical cell cathodes with the samarium-doped ceria electrolyte is 0.87 Ω cm2 at 700 °C, consistent with the square pyramidal Fe3+ layer favoring oxide ion formation and mobility in the oxygen reduction reaction. Density functional theory calculations reveal factors favoring the observed cation ordering and its influence on the electronic structure, in particular the frontier occupied and unoccupied electronic states. © 2010 American Chemical Society.

First principles interatomic potential for tungsten based on Gaussian process regression

An accurate description of atomic interactions, such as that provided by first principles quantum mechanics, is fundamental to realistic prediction of the properties that govern plasticity, fracture or crack propagation in metals. However, the computational complexity associated with modern schemes explicitly based on quantum mechanics limits their applications to systems of a few hundreds of atoms at most. This thesis investigates the application of the Gaussian Approximation Potential (GAP) scheme to atomistic modelling of tungsten - a bcc transition metal which exhibits a brittle-to-ductile transition and whose plasticity behaviour is controlled by the properties of $\frac{1}{2} \langle 111 \rangle$ screw dislocations. We apply Gaussian process regression to interpolate the quantum-mechanical (QM) potential energy surface from a set of points in atomic configuration space. Our training data is based on QM information that is computed directly using density functional theory (DFT). To perform the fitting, we represent atomic environments using a set of rotationally, permutationally and reflection invariant parameters which act as the independent variables in our equations of non-parametric, non-linear regression. We develop a protocol for generating GAP models capable of describing lattice defects in metals by building a series of interatomic potentials for tungsten. We then demonstrate that a GAP potential based on a Smooth Overlap of Atomic Positions (SOAP) covariance function provides a description of the $\frac{1}{2} \langle 111 \rangle$ screw dislocation that is in agreement with the DFT model. We use this potential to simulate the mobility of $\frac{1}{2} \langle 111 \rangle$ screw dislocations by computing the Peierls barrier and model dislocation-vacancy interactions to QM accuracy in a system containing more than 100,000 atoms.

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.