No Arabic abstract
Quantum-chemical processes in liquid environments impact broad areas of science, from molecular biology to geology to electrochemistry. While density-functional theory (DFT) has enabled efficient quantum-mechanical calculations which profoundly impact understanding of atomic-scale phenomena, realistic description of the liquid remains a challenge. Here, we present an approach based on joint density-functional theory (JDFT) which addresses this challenge by leveraging the DFT approach not only for the quantum mechanics of the electrons in a solute, but also simultaneously for the statistical mechanics of the molecules in a surrounding equilibrium liquid solvent. Specifically, we develop a new universal description for the interaction of electrons with an arbitrary liquid, providing the missing link to finally transform JDFT into a practical tool for the realistic description of chemical processes in solution. This approach predicts accurate solvation free energies and surrounding atomic-scale liquid structure for molecules and surfaces in multiple solvents without refitting, all at a fraction of the computational cost of methods of comparable detail and accuracy. To demonstrate the potential impact of this method, we determine the structure of the solid/liquid interface, offering compelling agreement with more accurate (but much more computationally intensive) theories and with X-ray reflectivity measurements.
Reliable first-principles calculations of electrochemical processes require accurate prediction of the interfacial capacitance, a challenge for current computationally-efficient continuum solvation methodologies. We develop a model for the double layer of a metallic electrode that reproduces the features of the experimental capacitance of Ag(100) in a non-adsorbing, aqueous electrolyte, including a broad hump in the capacitance near the Potential of Zero Charge (PZC), and a dip in the capacitance under conditions of low ionic strength. Using this model, we identify the necessary characteristics of a solvation model suitable for first-principles electrochemistry of metal surfaces in non-adsorbing, aqueous electrolytes: dielectric and ionic nonlinearity, and a dielectric-only region at the interface. The dielectric nonlinearity, caused by the saturation of dipole rotational response in water, creates the capacitance hump, while ionic nonlinearity, caused by the compactness of the diffuse layer, generates the capacitance dip seen at low ionic strength. We show that none of the previously developed solvation models simultaneously meet all these criteria. We design the Nonlinear Electrochemical Soft-Sphere solvation model (NESS) which both captures the capacitance features observed experimentally, and serves as a general-purpose continuum solvation model.
Continuum solvation models enable electronic structure calculations of systems in liquid environments, but because of the large number of empirical parameters, they are limited to the class of systems in their fit set (typically organic molecules). Here, we derive a solvation model with no empirical parameters for the dielectric response by taking the linear response limit of a classical density functional for molecular liquids. This model directly incorporates the nonlocal dielectric response of the liquid using an angular momentum expansion, and with a single fit parameter for dispersion contributions it predicts solvation energies of neutral molecules with an RMS error of 1.3 kcal/mol in water and 0.8 kcal/mol in chloroform and carbon tetrachloride. We show that this model is more accurate for strongly polar and charged systems than previous solvation models because of the parameter-free electric response, and demonstrate its suitability for ab initio solvation, including self-consistent solvation in quantum Monte Carlo calculations.
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.
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 process regression, and in particular on the construction of structural representations, and the associated kernel functions, that are endowed with the geometric covariance properties compatible with those of the learning targets. We summarize the general formulation of such a symmetry-adapted Gaussian process regression model, and how it can be implemented based on a scheme that generalizes the popular smooth overlap of atomic positions representation. We give examples of the performance of this framework when learning the polarizability and the ground-state electron density of a molecule.
To explore the electronic structure of the first aromatic superconductor, potassium-doped solid picene which has been recently discovered by Mitsuhashi et al with the transition temperatures $T_c=7 - 20$ K, we have obtained a first-principles electronic structure of solid picene as a first step toward the elucidation of the mechanism of the superconductivity. The undoped crystal is found to have four conduction bands, which are characterized in terms of the maximally localized Wannier orbitals. We have revealed how the band structure reflects the stacked arrangement of molecular orbitals for both undoped and doped (K$_3$picene) cases, where the bands are not rigid. The Fermi surface for K$_3$picene is a curious composite of a warped two-dimensional surface and a three-dimensional one.