Density Functionals with Quantum Chemical Accuracy: From Machine Learning to Molecular Dynamics

Abstract

<div> <div> <div> <p>Kohn-Sham density functional theory (DFT) is a standard tool in most branches of chemistry, but accuracies for many molecules are limited to 2-3 kcal/mol with presently-available functionals. <i>Ab initio </i>methods, such as coupled-cluster, routinely produce much higher accuracy, but computational costs limit their application to small molecules. We create density functionals from coupled-cluster energies, based only on DFT densities, via machine learning. These functionals attain quantum chemical accuracy (errors below 1 kcal/mol). Moreover, density-based ∆-learning (learning only the correction to a standard DFT calculation, ∆-DFT) significantly reduces the amount of training data required. We demonstrate these concepts for a single water molecule, and then illustrate how to include molecular symmetries with ethanol. Finally, we highlight the robustness of ∆-DFT by correcting DFT simulations of resorcinol on the fly to obtain molecular dynamics (MD) trajectories with coupled-cluster accuracy. Thus ∆-DFT opens the door to running gas-phase MD simulations with quantum chemical accuracy, even for strained geometries and conformer changes where standard DFT is quantitatively incorrect. </p> </div> </div> </div>

Electron density learning of non-covalent systems

“…The rst machine-learning model of r(r) was developed on the basis of the Hohenberg-Kohn mapping between the nuclear potential and the electron density. 55,56 Although successful, the choice of the nuclear potential as a representation of the different molecular conformations and the expansion of the electron density in an orthogonal plane-wave basis effectively constrained this landmark model to relatively small and rigid molecules with limited transferability to larger systems. Recently, we proposed an atom-centered, symmetry-adapted Gaussian process regression 57 (SA-GPR) framework explicitly targeting the learning of the electron density.…”

Machine learning for the solution of the Schrödinger equation

“…Dick and Fernandez-Serra [135,136] and Bogojeski et al [122] used NNs to learn corrections to energies (of gas phase and liquid water) obtained with a lower-level method, based on DFT densities. Rather than using directly the density as input, they developed atom-centered density-based descriptors and used Behler-type NNs (i.e.…”

“…They were able to machine-learn density-potential and density-energy mapping which was accurate enough to model several small molecules and to perform molecular dynamics simulations on malonaldehyde capturing the intramolecular proton transfer process. This approach was recently used to machine-learn density functionals from coupled-cluster energies based only on DFT densities to chemical accuracy, for water and ethanol [122]. The authors showed that one can reduce the computational effort by learning only the correction to a standard DFT calculation.…”

Machine Learning Accurate Exchange and Correlation Functionals of the Electronic Density

“…Bogojeski et al [22] construct a density functional on top of a reasonably cheap baseline DFT calculation (GGA) that can achieve accuracies close to coupledcluster results. The main difference between our approaches lies in the choice of basis functions, and the way symmetries are encoded.…”

“…Molecular dynamics. Using our ML model as a potential instead of merely adding an energy correction as proposed in earlier work by the authors [21] and in related work [22], has the advantage that electron densities are self-consistent with respect to the underlying functional. Self-consistency makes the Hellmann-Feynman theorem [23] applicable, allowing us to obtain accurate, energypreserving forces that can be used to study dynamical and statistical properties of a system.…”