  Continuum solvent models have become a standard technique in the context of
electronic structure calculations, yet, no implementations have been reported
capable to perform molecular dynamics at solid-liquid interfaces. We propose
here such a continuum approach in a DFT framework, using plane-waves basis sets
and periodic boundary conditions. Our work stems from a recent model designed
for Car-Parrinello simulations of quantum solutes in a dielectric medium [J.
Chem. Phys. 124, 74103 (2006)], for which the permittivity of the solvent is
defined as a function of the electronic density of the solute. This strategy
turns out to be inadequate for systems extended in two dimensions, by
introducing new term in the Kohn-Sham potential which becomes unphysically
large at the interfacial region, seriously affecting the convergence. If the
dielectric medium is properly redefined as a function of the atomic
coordinates, a good convergence is obtained and the constant of motion is
conserved during the molecular dynamics simulations. Moreover, a significant
gain in efficiency can be achieved if the simulation box is partitioned in two,
solving the Poisson problem separately for the "dry" region using fast Fourier
transforms, and for the solvated or "wet" region using a multigrid method.
Eventually both solutions are combined in a self-consistent procedure, and in
this way Car-Parrinello molecular dynamics simulations of solid-liquid
interfaces can be performed at a very moderate computational cost. This scheme
is employed to investigate the acid-base equilibrium at the TiO2-water
interface.
