Joint Density-Functional Methods For First-Principles Chemistry In Solution

Abstract

Solvents play an important role in many technologically relevant chemical processes and most biological systems, but thermodynamic phase-space sampling complicates their description in ab initio calculations. Joint density-functional theory (JDFT), which combines an electronic-density functional description of the solute with a classical density-functional description of the solvent, avoids phase-space sampling and enables an in-principle exact, intuitive description of solvated systems. In this dissertation, we develop the key ingredients for accurate joint density-functional calculations, derive simplified solvation models from JDFT and test these methods on model electrochemical systems. First, for the solute subsystem requiring a detailed electronic-structure description, hybrid density-functionals, which mix in a fraction of the exact exchange energy, provide greater accuracy than standard semi-local approximations to electronic density-functional theory. However, for periodic systems, these functionals require denser Brillouin-zone sampling to resolve the zero wave-vector singularity in the exchange energy. We show that truncating the exchange kernel on the Wigner-Seitz cell of the k-point sampled superlattice converges the energy of hybrid functionals exponentially with k-points, on par with that of semi-local and screened-exchange functionals. Next, practical JDFT calculations require computationally-efficient and accurate free energy functional approximations for real liquids. We develop the framework for treating molecular fluids starting with the exact free energy of an ideal gas of rigid molecules. Within this framework, we construct a free energy functional for liquid water based on a microscopic picture of hydrogen bonding, present a general recipe to construct functionals for liquids of small molecules constrained to the bulk equation of state, and demonstrate that these functionals adequately capture the cavity formation energies and non-linear dielectric response of the solvent that are critical to a successful theory of ab initio solvation. Simplified solvation models could further reduce the computational cost and enable a more intuitive description. However, standard polarizable continuum models (PCM's) that replace the solvent by a dielectric cavity along with empirical corrections, require a plethora of adjustable parameters. We derive a hierarchy of PCM's as limits of JDFT and demonstrate chemical accuracy for solvation energies of molecules with at most two adjustable parameters. Finally, we study the underpotential deposition of Cu on Pt(111) as a model electrochemical system for testing theories of ab initio solvation, and demonstrate that an accurate solvation model is critical for a qualitatively correct description of the various adsorbate configurations on the surface, as well as for a quantitative prediction of the electrochemical potentials for the transitions between these configurations.