Finite field methods for the supercell modeling of charged insulator/electrolyte interfaces

Surfaces of ionic solids interacting with an ionic solution can build up charge by exchange of ions. The surface charge is compensated by a strip of excess charge at the border of the electrolyte forming an electric double layer. These electric double layers are very hard to model using the supercell's methods of computational condensed phase science. The problem arises when the solid is an electric insulator (as most ionic solids are) permitting a finite interior electric field over the width of the slab representing the solid in the supercell. The slab acts as a capacitor. The stored charge is a deficit in the solution failing to compensate fully for the solid surface charge. Here, we show how these problems can be overcome using the finite field methods developed by Stengel, Spaldin, and Vanderbilt [Nat. Phys. 5, 304 (2009)]. We also show how the capacitance of the double layer can be computed once overall electric neutrality of the double layer is restored by application of a finite macroscopic field $\textbf{E}$ or alternatively by zero electric displacement $\textbf{D}$. The method is validated for a classical model of a solid-electrolyte interface using the finite-temperature molecular dynamics adaptation of the constant field method presented previously [C. Zhang and M. Sprik, Phys. Rev. B 93, 144201 (2016)]. Because ions in electrolytes can diffuse across supercell boundaries, this application turns out to be a critical illustration of the multivaluedness of polarization in periodic systems.Research fellowship (No. ZH 477/1-1) provided by German Research Foundation (DFG) for CZ is gratefully acknowledged

Computing the dielectric constant of liquid water at constant dielectric displacement

This is the author accepted manuscript. The final version is available from the American Physical Society via http://dx.doi.org/10.1103/PhysRevB.93.144201The static dielectric constant of liquid water is computed using classical force field based molecular dynamics simulation at fixed electric displacement D. The method to constrain the electric displacement is the finite temperature classical variant of the constant-D method developed by Stengel, Spaldin and Vanderbilt (Nat. Phys. 2009, 5: 304). There is also a modification of this scheme imposing fixed values of the macroscopic field E. The method is applied to the popular SPC/E model of liquid water. We compare four different estimates of the dielectric constant, two obtained from fluctuations of the polarization at D = 0 and E = 0 and two from the variation of polarization with finite D and E. It is found that all four estimates agree when properly converged. The computational effort to achieve convergence varies however, with constant D calculations being substantially more efficient. We attribute this difference to the much shorter relaxation time of longitudinal polarization compared to transverse polarization accelerating constant D calculations.Research fellowship (Grant No. ZH 477/1-1) provided by Deutsche Forschungsgemeinschaft (DFG) for C.Z. is gratefully acknowledged

Finite field formalism for bulk electrolyte solutions

The manner in which electrolyte solutions respond to electric fields is crucial to understanding the behavior of these systems both at, and away from, equilibrium. The present formulation of linear response theory for such systems is inconsistent with common molecular dynamics (MD) implementations. Using the finite field formalism, suitably adapted for finite temperature MD, we investigate the response of bulk aqueous NaCl solutions to both finite Maxwell ($\mathbf{E}$) and electric displacement ($\mathbf{D}$) fields. The constant $\mathbf{E}$ Hamiltonian allows us to derive the linear response relation for the ionic conductivity in a simple manner that is consistent with the forces used in conventional MD simulations. Simulations of a simple point charge model of an electrolyte solution at constant $\mathbf{E}$ yield conductivities at infinite dilution within 15% of experimental values. The finite field approach also allows us to measure the solvent's dielectric constant from its polarization response, which is seen to decrease with increasing ionic strength. Comparison of the dielectric constant measured from polarization response versus polarization fluctuations enables direct evaluation of the dynamic contribution to this dielectric decrement, which we find to be small but not insignificant. Using the constant $\mathbf{D}$ formulation, we also rederive the Stillinger-Lovett conditions, which place strict constraints on the coupling between solvent and ionic polarization fluctuations.We are grateful for computational support from the UK Materials and Molecular Modelling Hub, which is partially funded by EPSRC (Grant No. EP/P020194), for which access was obtained via the UKCP consortium and funded by EPSRC Grant Ref. No. EP/P022561/1. S.J.C. is supported by a Royal Commission for the Exhibition of 1851 Research Fellowship

Tunneling and delocalization in hydrogen bonded systems: a study in position and momentum space

Novel experimental and computational studies have uncovered the proton momentum distribution in hydrogen bonded systems. In this work, we utilize recently developed open path integral Car-Parrinello molecular dynamics methodology in order to study the momentum distribution in phases of high pressure ice. Some of these phases exhibit symmetric hydrogen bonds and quantum tunneling. We find that the symmetric hydrogen bonded phase possesses a narrowed momentum distribution as compared with a covalently bonded phase, in agreement with recent experimental findings. The signatures of tunneling that we observe are a narrowed distribution in the low-to-intermediate momentum region, with a tail that extends to match the result of the covalently bonded state. The transition to tunneling behavior shows similarity to features observed in recent experiments performed on confined water. We corroborate our ice simulations with a study of a particle in a model one-dimensional double well potential that mimics some of the effects observed in bulk simulations. The temperature dependence of the momentum distribution in the one-dimensional model allows for the differentiation between ground state and mixed state tunneling effects.Comment: 14 pages, 13 figure

Finite Maxwell field and electric displacement Hamiltonians derived from a current dependent Lagrangian

In the common Ewald summation technique for the evaluation of electrostatic forces, the average electric field E is strictly zero. Finite uniform E can be accounted for by adding it as a new degree of freedom in an extended Lagrangian. Representing the uniform polarization P as the time integral of the internal current and E as the time derivative of a uniform vector field A, we define such an extended Lagrangian coupling A to the total current j_t(internal plus external) and hence derive a Hamiltonian resembling the minimal coupling Hamiltonian of electrodynamics. Next, applying a procedure borrowed from nonrelativistic molecular electrodynamics the j_t · A coupling is transformed to P · D form where D is the electric displacement acting as an electrostatic boundary condition. The resulting Hamiltonian is identical to the constant-D Hamiltonian obtained by Stengel, Spaldin and Vanderbilt (SSV) using thermodynamic arguments. The corresponding SSV constant E Hamiltonian is derived from an alternative extended Lagrangian

Viscoelastic response of sonic band-gap materials

A brief report is presented on the effect of viscoelastic losses in a high density contrast sonic band-gap material of close-packed rubber spheres in air. The scattering properties of such a material are computed with an on-shell multiple scattering method, properties which are compared with the lossless case. The existence of an appreciable omnidirectional gap in the transmission spectrum, when losses are present, is also reported.Comment: 5 pages, 4 figures, submitted to PR

Water adsorption on the P-rich GaP(100) surface: Optical spectroscopy from first principles

The contact of water with semiconductors typically changes its surface electronic structure by oxidation or corrosion processes. A detailed knowledge - or even control of - the surface structure is highly desirable, as it impacts the performance of opto-electronic devices from gas-sensing to energy conversion applications. It is also a prerequisite for density functional theory-based modelling of the electronic structure in contact with an electrolyte. The P-rich GaP(100) surface is extraordinary with respect to its contact with gas-phase water, as it undergoes a surface reordering, but does not oxidise. We investigate the underlying changes of the surface in contact with water by means of theoretically derived reflection anisotropy spectroscopy (RAS). A comparison of our results with experiment reveals that a water-induced hydrogen-rich phase on the surface is compatible with the boundary conditions from experiment, reproducing the optical spectra. We discuss potential reaction paths that comprise a water-enhanced hydrogen mobility on the surface. Our results also show that computational RAS - required for the interpretation of experimental signatures - is feasible for GaP in contact with water double layers. Here, RAS is sensitive to surface electric fields, which are an important ingredient of the Helmholtz-layer. This paves the way for future investigations of RAS at the semiconductor-electrolyte interface

Wetting to Non-wetting Transition in Sodium-Coated C_60

Based on ab initi and density-functional theory calculations, an empirical potential is proposed to model the interaction between a fullerene molecule and many sodium atoms. This model predicts homogeneous coverage of C_60 below 8 Na atoms, and a progressive droplet formation above this size. The effects of ionization, temperature, and external electric field indicate that the various, and apparently contradictory, experimental results can indeed be put into agreement.Comment: 4 pages, 4 postscript figure