Discovering charge density functionals and structure-property relationships with PROPhet: A general framework for coupling machine learning and first-principles methods.

Modern ab initio methods have rapidly increased our understanding of solid state materials properties, chemical reactions, and the quantum interactions between atoms. However, poor scaling often renders direct ab initio calculations intractable for large or complex systems. There are two obvious avenues through which to remedy this problem: (i) develop new, less expensive methods to calculate system properties, or (ii) make existing methods faster. This paper describes an open source framework designed to pursue both of these avenues. PROPhet (short for PROPerty Prophet) utilizes machine learning techniques to find complex, non-linear mappings between sets of material or system properties. The result is a single code capable of learning analytical potentials, non-linear density functionals, and other structure-property or property-property relationships. These capabilities enable highly accurate mesoscopic simulations, facilitate computation of expensive properties, and enable the development of predictive models for systematic materials design and optimization. This work explores the coupling of machine learning to ab initio methods through means both familiar (e.g., the creation of various potentials and energy functionals) and less familiar (e.g., the creation of density functionals for arbitrary properties), serving both to demonstrate PROPhet's ability to create exciting post-processing analysis tools and to open the door to improving ab initio methods themselves with these powerful machine learning techniques.

Representing Global Reactive Potential Energy Surfaces Using Gaussian Processes.

Representation of multidimensional global potential energy surfaces suitable for spectral and dynamical calculations from high-level ab initio calculations remains a challenge. Here, we present a detailed study on constructing potential energy surfaces using a machine learning method, namely, Gaussian process regression. Tests for the 3A″ state of SH2, which facilitates the SH + H ↔ S(3P) + H2 abstraction reaction and the SH + H' ↔ SH' + H exchange reaction, suggest that the Gaussian process is capable of providing a reasonable potential energy surface with a small number (∼1 × 102) of ab initio points, but it needs substantially more points (∼1 × 103) to converge reaction probabilities. The implications of these observations for construction of potential energy surfaces are discussed.

High-Dimensional Atomistic Neural Network Potentials for Molecule-Surface Interactions: HCl Scattering from Au(111).

Ab initio molecular dynamics (AIMD) simulations of molecule-surface scattering allow first-principles characterization of the dynamics. However, the large number of density functional theory calculations along the trajectories is very costly, limiting simulations of long-time events and giving rise to poor statistics. To avoid this computational bottleneck, we report here the development of a high-dimensional molecule-surface interaction potential energy surface (PES) with movable surface atoms, using a machine learning approach. With 60 degrees of freedom, this PES allows energy transfer between the energetic impinging molecule and thermal surface atoms. Classical trajectory calculations for the scattering of DCl from Au(111) on this PES are found to agree well with AIMD simulations, with ∼105-fold acceleration. Scattering of HCl from Au(111) is further investigated and compared with available experimental results.

Communication: Energy transfer and reaction dynamics for DCl scattering on Au(111): An ab initio molecular dynamics study.

Scattering and dissociative chemisorption of DCl on Au(111) are investigated using ab initio molecular dynamics with a slab model, in which the top two layers of Au are mobile. Substantial kinetic energy loss in the scattered DCl is found, but the amount of energy transfer is notably smaller than that observed in the experiment. On the other hand, the dissociative chemisorption probability reproduces the experimental trend with respect to the initial kinetic energy, but is about one order of magnitude larger than the reported initial sticking probability. While the theory-experiment agreement is significantly improved from the previous rigid surface model, the remaining discrepancies are still substantial, calling for further scrutiny in both theory and experiment.

Permutation invariant potential energy surfaces for polyatomic reactions using atomistic neural networks.

The applicability and accuracy of the Behler-Parrinello atomistic neural network method for fitting reactive potential energy surfaces is critically examined in three systems, H + H2 → H2 + H, H + H2O → H2 + OH, and H + CH4 → H2 + CH3. A pragmatic Monte Carlo method is proposed to make efficient choice of the atom-centered mapping functions. The accuracy of the potential energy surfaces is not only tested by fitting errors but also validated by direct comparison in dynamically important regions and by quantum scattering calculations. Our results suggest this method is both accurate and efficient in representing multidimensional potential energy surfaces even when dissociation continua are involved.

Control of valence and conduction band energies in layered transition metal phosphates via surface functionalization.

Layered transition metal phosphates and phosphites (TMPs) are a class of materials composed of layers of 2D sheets bound together via van der Waals interactions and/or hydrogen bonds. Explored primarily for use in proton transfer, their unique chemical tunability also makes TMPs of interest for forming large-scale hybrid materials. Further, unlike many layered materials, TMPs can readily be solution exfoliated to form single 2D sheets or bilayers, making them exciting candidates for a variety of applications. However, the electronic properties of TMPs have largely been unstudied to date. In this work, we use first-principles computations to investigate the atomic and electronic structure of TMPs with a variety of stoichiometries. We demonstrate that there exists a strong linear relationship between the band gap and the ionic radius of the transition metal cation in these materials, and show that this relationship, which opens opportunities for engineering new compositions with a wide range of band gaps, arises from constraints imposed by the phosphorus-oxygen bond geometry. In addition, we find that the energies of the valence and conduction band edges can be systematically tuned over a range of ∼3 eV via modification of the functional group extending from the phosphorus. Based on the Hammett constant of this functional group, we identify a simple, predictive relationship for the ionization potential and electron affinity of layered TMPs. Our results thus provide guidelines for systematic design of TMP-derived functional materials, which may enable new approaches for optimizing charge transfer in electronics, photovoltaics, electrocatalysts, and other applications.

Binding interactions in dimers of phenalenyl and closed-shell analogues.

Phenalenyl, an open-shell neutral radical that can form both π-stacked dimers and conducting molecular crystals, has gained attention for its interesting and potentially useful electrical and magnetic properties. The properties of this complex physical system are fairly well understood, making it an ideal testing ground for the newly developed van der Waals density functional (vdW-DF). We invoke a simple approximation, allowing the vdW-DF to be used within spin-polarized density functional theory and test this approximation on the π-stacked phenalenyl dimer. The results indicate that the vdW-DF is capable of qualitatively describing the interaction between two neutral radicals in the π-stacked configuration, producing, in line with experiment, binding distances that are significantly below the sum of the van der Waals radii. This is a nontypical distance range where most other theories fail. We then investigate two hypothetical closed-shell analogues of this dimer, one formed by replacing the central carbon of phenalenyl with a nitrogen atom and the other formed by replacing the central carbon with a boron atom. In these cases, relatively strong interaction energies are obtained at more typical equilibrium distances for van der Waals dimers. The nitrogen-substituted dimer shows an unexpected rotational barrier that is dictated by the electronic kinetic energy within the system. The torsional curve of the boron-substituted dimer also exhibits a rotational barrier, but this is found to disappear when exact exchange is used in place of a local or semilocal exchange functional.

Structural evolution of amino acid crystals under stress from a non-empirical density functional.

Use of the non-local correlation functional vdW-DF (from 'van der Waals density functional'; Dion M et al 2004 Phys. Rev. Lett. 92 246401) has become a popular approach for including van der Waals interactions within density functional theory. In this work, we extend the vdW-DF theory and derive the corresponding stress tensor in a fashion similar to the LDA and GGA approach, which allows for a straightforward implementation in any electronic structure code. We then apply our methodology to investigate the structural evolution of amino acid crystals of glycine and l-alanine under pressure up to 10 GPa-with and without van der Waals interactions-and find that for an accurate description of intermolecular interactions and phase transitions in these systems, the inclusion of van der Waals interactions is crucial. For glycine, calculations including the vdW-DF (vdW-DF-c09x) functional are found to systematically overestimate (underestimate) the crystal lattice parameters, yet the stability ordering of the different polymorphs is determined accurately, at variance with the GGA case. In the case of l-alanine, our vdW-DF results agree with recent experiments that question the phase transition reported for this crystal at 2.3 GPa, as the a and c cell parameters happen to become equal but no phase transition is observed.