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We introduce a novel class of localized atomic environment representations, based upon the Coulomb matrix. By combining these functions with the Gaussian approximation potential approach, we present LC-GAP, a new system for generating…
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…
A simple yet general method for constructing basis sets for molecular electronic structure calculations is presented. These basis sets consist of atomic natural orbitals from a multi-configurational self-consistent field calculation…
The need for accurate calculations on atoms and diatomic molecules is motivated by the opportunities and challenges of such studies. The most commonly-used approach for all-electron electronic structure calculations in general - the linear…
By using Poisson's summation formula, we calculate periodic integrals over Gaussian basis functions by partitioning the lattice summations between the real and reciprocal space, where both sums converge exponentially fast with a large…
Non-Gaussian bosonic states are ubiquitous in interacting light--matter systems, many-body platforms, and relativistic quantum field settings, but their quantitative characterization is hindered by the infinite-dimensional Hilbert space and…
We consider the problem of efficiently simulating stochastic models of chemical kinetics. The Gillespie Stochastic Simulation algorithm (SSA) is often used to simulate these models, however, in many scenarios of interest, the computational…
We introduce nested gausslet (NG) bases, an improvement on previous gausslet bases which can treat systems containing atoms with much larger atomic number. We also introduce pure Gaussian distorted gausslet bases, which allow the…
Perhaps the simplest first-principles approach to electronic structure is to fit the charge distribution of each orbital pair and use those fits wherever they appear in the entire electron-electron (EE) interaction energy. The charge…
We present a new hybrid method to solve the relativistic Hartree-Fock-Roothan equations where the one- and two-electron radial integrals are evaluated numerically by defining the basis functions on a grid. This procedure reduces the…
Hydrogenation of amorphous silicon (a-Si:H) is critical for reducing defect densities, passivating mid-gap states and surfaces, and improving photoconductivity in silicon-based electro-optical devices. Modelling the atomic scale structure…
The Spectral Neighbor Analysis Potential (SNAP) is a classical interatomic potential that expresses the energy of each atom as a linear function of selected bispectrum components of the neighbor atoms. An extension of the SNAP form is…
We have derived a new method which allows to compute the full and the Pauli reference kinetic potentials for atoms and molecules in a real space representation. This is done by applying the optimized effective potential (OEP) method to…
The accuracy of a single s-orbital representation of Cu towards enabling multi-thousand atom ab initio calculations of electronic structure is evaluated in this work. If an electrostatic compensation charge of approximately 0.3 electrons…
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,…
Recently, we introduced a class of molecular representations for kernel-based regression methods -- the spectrum of approximated Hamiltonian matrices (SPA$^\mathrm{H}$M) -- that takes advantage of lightweight one-electron Hamiltonians…
We introduce a Gaussian approximation potential (GAP) for atomistic simulations of liquid and amorphous elemental carbon. Based on a machine-learning representation of the density-functional theory (DFT) potential-energy surface, such…
Machine learning (ML) has become widely used in the development of interatomic potentials for molecular dynamics simulations. However, most ML potentials are still much slower than classical interatomic potentials and are usually trained…
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…
This chapter discusses the importance of incorporating three-dimensional symmetries in the context of statistical learning models geared towards the interpolation of the tensorial properties of atomic-scale structures. We focus on Gaussian…