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We present the implementation of a hybrid continuum-atomistic model for including the effects of a surrounding electrolyte in large-scale density functional theory (DFT) calculations within the Order-NElectronic Total Energy Package (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 polarizable 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 the 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 highly parallel multigrid 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 the electrolyte. We have also implemented the model for periodic boundary conditions, allowing the treatment of extended systems such as electrode surfaces in contact with the 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 an 1634-atom model of the interface between a graphite anode and LiPF6electrolyte in an 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.

The solution of the Poisson equation is a crucial step in electronic structure calculations, yielding the electrostatic potential—a key component of the quantum mechanical Hamiltonian. In recent decades, theoretical advances and increases in computer performance have made it possible to simulate the electronic structure of extended systems in complex environments. This requires the solution of more complicated variants of the Poisson equation, featuring nonhomogeneous dielectric permittivities, ionic concentrations with nonlinear dependencies, and diverse boundary conditions. The analytic solutions generally used to solve the Poisson equation in vacuum (or with homogeneous permittivity) are not applicable in these circumstances, and numerical methods must be used. In this work, we present DL_MG, a flexible, scalable, and accurate solver library, developed specifically to tackle the challenges of solving the Poisson equation in modern large-scale electronic structure calculations on parallel computers. Our solver is based on the multigrid approach and uses an iterative high-order defect correction method to improve the accuracy of solutions. Using two chemically relevant model systems, we tested the accuracy and computational performance of DL_MG when solving the generalized Poisson and Poisson–Boltzmann equations, demonstrating excellent agreement with analytic solutions and efficient scaling to ∼109unknowns and 100s of CPU cores. We also applied DL_MG in actual large-scale electronic structure calculations, using the ONETEP linear-scaling electronic structure package to study a 2615 atom protein–ligand complex with routinely available computational resources. In these calculations, the overall execution time with DL_MG was not significantly greater than the time required for calculations using a conventional FFT-based solver.

We present a method for computing excitation energies for molecules in solvent, based on the combination of a minimal parameter implicit solvent model and the equation-of-motion coupled-cluster singles and doubles method (EOM-CCSD). In this method, the solvent medium is represented by a smoothly varying dielectric function, constructed directly from the quantum mechanical electronic density using only two tunable parameters. The solvent–solute electrostatic interactions are computed by numerical solution of the nonhomogeneous Poisson equation and incorporated at the Hartree–Fock stage of the EOM-CCSD calculation by modification of the electrostatic potential. We demonstrate the method by computing excited state transition energies and solvent shifts for several small molecules in water. Results are presented for solvated H2O, formaldehyde, acetone, and trans-acrolein, which have low-lying n→ π* transitions and associated blue shifts in aqueous solution. Comparisons are made with experimental data and other theoretical approaches, including popular implicit solvation models and QM/MM methods. We find that our approach provides surprisingly good agreement with both experiment and the other models, despite its comparative simplicity. This approach only requires modification of the Fock operator and total energy expressions at the Hartree–Fock levelsolvation effects enter into the EOM-CCSD calculation only through the Hartree–Fock orbitals. Our model provides a theoretically and computationally simple route for accurate simulations of excited state spectra of molecules in solution, paving the way for studies of larger and more complex molecules.