The hydrated electronthe species that results from the addition of a single excess electron to liquid waterhas been the focus of much interest both because of its role in radiation chemistry and other chemical reactions, and because it provides for a deceptively simple system that can serve as a means to confront the predictions of quantum molecular dynamics simulations with experiment. Despite all this interest, there is still considerable debate over the molecular structure of the hydrated electron: does it occupy a cavity, have a significant number of interior water molecules, or have a structure somewhere in between? The reason for all this debate is that different computer simulations have produced each of these different structures, yet the predicted properties for these different structures are still in reasonable agreement with experiment. In this Feature Article, we explore the reasons underlying why different structures are produced when different pseudopotentials are used in quantum simulations of the hydrated electron. We also show that essentially all the different models for the hydrated electron, including those from fully ab initio calculations, have relatively little direct overlap of the electron’s wave function with the nearby water molecules. Thus, a non-cavity hydrated electron is better thought of as an “inverse plum pudding” model, with interior waters that locally expel the surrounding electron’s charge density. Finally, we also explore the agreement between different hydrated electron models and certain key experiments, such as resonance Raman spectroscopy and the temperature dependence and degree of homogeneous broadening of the optical absorption spectrum, in order to distinguish between the different simulated structures. Taken together, we conclude that the hydrated electron likely has a significant number of interior water molecules.

No abstract

Mixed quantum/classical (MQC) simulations treat the majority of a system classically and reserve quantum mechanics only for a few degrees of freedom that actively participate in the chemical process(es) of interest. In MQC calculations, the quantum and classical degrees of freedom are coupled together using pseudopotentials. Although most pseudopotentials are developed empirically, there are methods for deriving pseudopotentials using the results of quantum chemistry calculations, which guarantee that the explicitly-treated valence electron wave functions remain orthogonal to the implicitly-treated core electron orbitals. Whether empirical or analytically derived in nature, to date all such pseudopotentials have been subject to the frozen core approximation (FCA) that ignores how changes in the nuclear coordinates alter the core orbitals, which in turn affects the wave function of the valence electrons. In this paper, we present a way to go beyond the FCA by developing pseudopotentials that respond to these changes. In other words, we show how to derive an analytic expression for a pseudopotential that is an explicit function of nuclear coordinates, thus accounting for the polarization effects experienced by atomic cores in different chemical environments. We then use this formalism to develop a coordinate-dependent pseudopotential for the bonding electron of the sodium dimer cation molecule and we show how the analytic representation of this potential can be used in one-electron MQC simulations that provide the accuracy of a fully quantum mechanical Hartree-Fock (HF) calculation at all internuclear separations. We also show that one-electron MQC simulations of Na(2)(+) using our coordinate-dependent pseudopotential provide a significant advantage in accuracy compared to frozen core potentials with no additional computational expense. This is because use of a frozen core potential produces a charge density for the bonding electron of Na(2)(+) that is too localized on the molecule, leading to significant overbinding of the valence electron. This means that FCA calculations are subject to inaccuracies of order ~10% in the calculated bond length and vibrational frequency of the molecule relative to a full HF calculation; these errors are fully corrected by using our coordinate-dependent pseudopotential. Overall, our findings indicate that even for molecules like Na(2)(+), which have a simple electronic structure that might be expected to be well-treated within the FCA, the importance of including the effects of the changing core molecular orbitals on the bonding electrons cannot be overlooked.

In our original paper, 1 we presented a method for the development of coordinate-dependent pseudopotentials that was designed to reproduce all-electron quantum chemistry calculations of Hartree-Fock (HF) quality from bonding to complete dissociation. Our method is based on the Phillips-Kleinman formalism (PK), 2 and as such, can be straightfor

Stoll, Fuentealba, and Szentpály (SFS) argue that the coordinate-dependent pseudopotential we developed for the sodium dimer cation molecule is inferior to other potentials that have been presented in the literature for this molecule. The goal of our work, however, was to present a novel method for the development of rigorous coordinate-dependent pseudopotentials. Our method is designed to reproduce all-electron Hartree-Fock calculations without the inclusion of adjustable parameters. Moreover, our method starts from the superposition of unoptimized, non-norm-conserved atomic potentials, so that when complete, the resulting norm-conserving potential can reproduce an all-electron Hartree-Fock calculation without the inclusion of adjustable parameters. We chose the sodium dimer cation system as a proof of principle for our method, and showed that our method does indeed allow a one-electron calculation to correctly reproduce the all-electron Hartree-Fock calculation from bonding to the dissociation limit. Our purpose in developing this method is to use such potentials in condensed-phase mixed quantum/classical molecular dynamics simulations, where inclusion of valence polarization effects is unimportant or can be added on after the fact. Thus we do not claim that our method provides a potential that is superior to potentials that have been specifically constructed to go beyond the static exchange approximation and/or include valence polarization effects—such potentials are beyond the scope of our work. We also note that although we made a numerical error in the application of our method to \documentclass[12pt]{minimal}\begin{document}${\rm Na}_2^+$\end{document} Na 2+ in our original work [A. Kahros and B. J. Schwartz, J. Chem. Phys. 138, 054110 (2013)] that led to an overestimation of the magnitude of core polarization effects for this particular molecule, out method does work as derived for this molecule and the error does not affect the significance of our method or its general applicability.