Quantum chemistry in arbitrary dielectric environments: Theory and implementation of nonequilibrium Poisson boundary conditions and application to compute vertical ionization energies at the air/water interface

Abstract

Widely used continuum solvation models for electronic structure calculations, including popular polarizable continuum models (PCMs), usually assume that the continuum environment is isotropic and characterized by a scalar dielectric constant, ε. This assumption is invalid at a liquid/vapor interface or any other anisotropic solvation environment. To address such scenarios, we introduce a more general formalism based on solution of Poisson's equation for a spatially varying dielectric function, ε(r). Inspired by nonequilibrium versions of PCMs, we develop a similar formalism within the context of Poisson's equation that includes the out-of-equilibrium dielectric response that accompanies a sudden change in the electron density of the solute, such as that which occurs in a vertical ionization process. A multigrid solver for Poisson's equation is developed to accommodate the large spatial grids necessary to discretize the three-dimensional electron density. We apply this methodology to compute vertical ionization energies (VIEs) of various solutes at the air/water interface and compare them to VIEs computed in bulk water, finding only very small differences between the two environments. VIEs computed using approximately two solvation shells of explicit water molecules are in excellent agreement with experiment for F(aq), Cl(aq), neat liquid water, and the hydrated electron, although errors for Li(aq) and Na(aq) are somewhat larger. Nonequilibrium corrections modify VIEs by up to 1.2 eV, relative to models based only on the static dielectric constant, and are therefore essential to obtain agreement with experiment. Given that the experiments (liquid microjet photoelectron spectroscopy) may be more sensitive to solutes situated at the air/water interface as compared to those in bulk water, our calculations provide some confidence that these experiments can indeed be interpreted as measurements of VIEs in bulk water.

Probing Interfacial Effects on Ionization Energies: The Surprising Banality of Anion-Water Hydrogen Bonding at the Air/Water Interface

“…The VIE for the ion-water cluster is then computed using electronic structure theory with dielectric continuum boundary conditions, 95 based on a Poisson equation solver (PEqS). 80,81,105 As described in detail elsewhere, 81 this approach uses a three-dimensional permittivity function ε(r) to interpolate between the values ε = 1 within the atomistic region (described using quantum chemistry), and ε = 78 in the continuum region, representing bulk water. A solvent-accessible surface 95,106 is used to define the boundary across which this interpolation occurs.…”

“…A solvent-accessible surface 95,106 is used to define the boundary across which this interpolation occurs. A permittivity function for the air/water interface can be constructed in similar fashion, 80,81,95 using the Gibbs dividing surface (GDS) to define the boundary between ε = 1 (air) and ε = 78 (water). A schematic of this setup is shown in Fig.…”

“…73 Whereas interfacial effects on the photochemistry 74 and ultraviolet spectroscopy 75,76 of small aqueous solutes have been demonstrated, there has been no systematic investigation of whether VIEs themselves are sensitive to the presence of the air/water interface; the only detailed studies concern the rather unique case of the hydrated electron. 66,[77][78][79][80][81][82][83] It is known that the VIE of liquid water is largely unaffected by dissolved ions, 84 shifting by < 0.2 eV over an 8 M concentration range, 84 and the VIE of I − (aq) is similarly unaffected by concentration. 85 It is not yet known whether VIEs of aqueous ions are sensitive to the air/water interface or not.…”

The Poisson–Boltzmann model for implicit solvation of electrolyte solutions: Quantum chemical implementation and assessment via Sechenov coefficients

“…where (r) is the spatially dependent dielectric permittivity, ρ sol (r) is the charge distribution of the solute, and the explicit expressions for f (φ tot (r), r) define the different approximations we will discuss in the following. Following the implementation of the Poisson equation solver in the Q-Chem program package by one of us, 33 we define the spatially dependent dielectric constant as a product of error functions for each atom…”

“…Our implementation builds up on a previous multigrid solver for the Poisson equation. 33,38 Unlike the Poisson solver that is reported in Ref. 33, we do not apply Gaussian blurring to the nuclear contribution to the electrostatic potential.…”