Practical Approach to Large-Scale Electronic Structure Calculations in Electrolyte Solutions via Continuum-Embedded Linear-Scaling Density Functional Theory

Abstract

We present the implementation of a hybrid continuum-atomistic model for including the effects of surrounding electrolyte in large-scale density functional theory (DFT) calculations within the onetep linear-scaling DFT code, which allows the simulation of large complex systems such as electrochemical interfaces. The model represents the electrolyte ions as a scalar field and the solvent as a polarisable dielectric continuum, both surrounding the quantum solute. The overall energy expression is a grand canonical functional incorporating the electron kinetic and exchange correlation energies, the total electrostatic energy, entropy and chemical potentials of surrounding electrolyte, osmotic pressure, and the effects of cavitation, dispersion and repulsion. The DFT calculation is performed fully self-consistently in the electrolyte model, allowing the quantum mechanical system and the surrounding continuum environment to interact and mutually polarize. A bespoke parallel Poisson-Boltzmann solver library, dl mg, deals with the electrostatic problem, solving a generalized Poisson-Boltzmann equation. Our model supports open boundary conditions, which allows the treatment of molecules, entire biomolecules or larger nanoparticle assemblies in electrolyte. We have also implemented the model for periodic boundary conditions, allowing the treatment of extended systems such as electrode surfaces in contact with electrolyte. A key feature of the model is the use of solute-size and solvation-shell-aware accessibility functions that prevent the unphysical accumulation of electrolyte charge near the quantum solute boundary. The model has a small number of parameters-here we demonstrate their calibration against experimental mean activity coefficients. We also present an exemplar simulation of a 1634-atom model of the interface between a graphite anode and LiPF 6 electrolyte in ethylene carbonate solvent. We compare the cases where Li atoms are intercalated at opposite edges of the graphite slab and in solution, demonstrating a potential application of the model in simulations of fundamental processes in Li-ion batteries.

Charge transport modelling of Lithium-ion batteries

“…However, they are fast to compute with and so are often used on larger-scale systems, such as pouch cells which are fabricated by stacking many single cells on top of each other, where the primary goal may be to investigate the thermal behaviour of the system, see for example [75,97], or to develop a battery management system. At the opposite end of the scale, density functional theory is applied to study battery physics on the atomistic scale, but the computational costs are so high that the simulation of even a single battery cell is out of reach of the most powerful modern computers, see [28]. The charge transport models discussed here provide a useful compromise between capturing meaningful physics, but nevertheless being cheap enough to use on problems of engineering relevance.…”

Dielectric continuum methods for quantum chemistry

“…Inserting this ansatz into Poisson's equation [Equation ()] affords a model in which the dielectric interface is smooth, rather than sharp as it is in PCMs, yet one where the definition of the interface is updated self‐consistently as the density ρ ( r ) is iterated to convergence. The dependence of ε ( r ) on the density does mean that the Fock operator acquires an extra term relative to what was discussed in Section 2.1, namely 262 The SCCS model is increasingly being used in ab initio simulations of materials, for example, to model the aqueous electrolyte/solid‐state interfaces relevant in electrochemistry 28,82,264,268–274 . Some of that work points to limitations of the linear dielectric model itself (i.e., a breakdown of the assumption that P ∝ E ), which can result either from high field strength (“dielectric saturation”), 275,276 or else because the rotational response of the water molecules saturates at the electrode interface and consequently the susceptibility is smaller than it is in bulk water 271,272 .…”

“…These arise due to statistical correlations between ion positions that are neglected by the model in Equation (). It is therefore worth noting that for the small solutes that characterize most quantum chemistry applications, the effect of the mobile ions on is quite modest, 73,79 although there are effects on activity coefficients 73,82 . These effects are presumably magnified for a solute the size of a protein, but the intermediate size regime has hardly been explored.…”

“…The SCCS model is increasingly being used in ab initio simulations of materials, for example, to model the aqueous electrolyte/solid-state interfaces relevant in electrochemistry. 28,82,264,[268][269][270][271][272][273][274] Some of that work points to limitations of the linear dielectric model itself (i.e., a breakdown of the assumption that P / E), which can result either from high field strength ("dielectric saturation"), 275,276 or else because the rotational response of the water molecules saturates at the electrode interface and consequently the susceptibility is smaller than it is in bulk water. 271,272 Limitations in the linearized Poisson-Boltzmann description of electrolyte effects have also been demonstrated.…”

“…675,677,686,687 Fundamentally, however, the interfacial solvation problem seems to cry out for a permittivity function ε(r) that assumes different values in different regions of space, that is, a method that solves the generalized Poisson equation with an anisotropic permittivity function, ε(r). Such a strategy has been pursued to describe the interface between a solid-state electrode and an aqueous electrolyte, 28,82,264,[268][269][270][271][272][273][274] as well as host/guest systems where the guest experiences a low-dielectric environment despite the fact that the host is dissolved in water. 688 Finally, anisotropic models have been used to compute VIEs of solutes at the air/water interface, 44,588 in order to connect with liquid microjet photoelectron spectroscopy.…”