Empirically Optimized One-Electron Pseudopotential for the Hydrated Electron: A Proof-of-Concept Study

Abstract

Mixed quantum-classical molecular dynamics simulations have been important tools for studying the hydrated electron. They generally use a oneelectron pseudopotential to describe the interactions of an electron with the water molecules. This approximation shows both the strength and weakness of the approach. On the one hand, it enables extensive statistical sampling and large system sizes that are not possible with more accurate ab initio molecular dynamics methods. On the other hand, there has (justifiably) been much debate about the ability of pseudopotentials to accurately and quantitatively describe the hydrated electron properties. These pseudopotentials have largely been derived by fitting them to ab initio calculations of an electron interacting with a single water molecule. In this paper, we present a proof-of-concept demonstration of an alternative approach in which the pseudopotential parameters are determined by optimizing them to reproduce key experimental properties. Specifically, we develop a new pseudopotential, using the existing TBOpt model as a starting point, which correctly describes the hydrated electron vertical detachment energy and radius of gyration. In addition to these properties, this empirically optimized model displays a significantly modified solvation structure, which improves, for example, the prediction of the partial molar volume.

Partial Molar Solvation Volume of the Hydrated Electron Simulated Via DFT

“…At this stage, we cannot state with certainty whether the mismatch between the 128-water simulations and the experimental value is due to the finite system size, the use of DFT, or some combination of both, but the fact that no DFT-based simulations at any tractable system size can predict V M correctly to within a factor of 2 of experiment indicates that there are aspects of the DFT-predicted RDFs that disagree with experiment. The MQC TB model and a recent “soft-cavity” MQC model optimized to reproduce the electron’s experimental radius of gyration and eigenvalue both produce a qualitatively different structure than DFT with V M ’s that are closer to experiment . It remains to be seen whether larger simulation sizes or the use of different exchange–correlation functionals with DFT can predict a solvation structure with the correct V M .…”

“…The quantum mechanical treatment of the single excess electron allows for efficient solution of the one-electron Schrödinger equation, while classical treatment of the solvent permits simulations with many hundreds of solvent molecules for times up to nanoseconds. For MQC simulations, the interaction between the excess electron and solvent is accounted for using a pseudopotential, and for hydrated electrons in particular, several different pseudopotentials have been presented. − There is an extensive literature investigating the performance of different MQC-based e hyd – models, each of which produces a unique hydration structure; ,,, to date, no single MQC model has been able to reproduce all of the various experimental observables listed above. We note that our group has previously advocated for a noncavity model of the hydrated electron, but a recent work has suggested that a cavity model is closer to the correct structure.…”

2-in-1 Phase Space Sampling for Calculating the Absorption Spectrum of the Hydrated Electron

“…In particular, the one-electron Schrödinger equation for the excess electron is solved in the field of classical water molecules modeled by a flexible simple point-charge model (SPC + flex) . The interaction of the excess electron and the water molecules is represented by a pseudopotential; in the present case, we apply the Turi–Borgis (TB) pseudopotential. , The TB potential, despite its simple analytical form, has proved to provide semiquantitative agreement on many characteristic properties of the bulk hydrated electron and water cluster anions. ,,,,, Most recently, two modifications have been proposed to the original form, , but for the sake of consistency with our previous studies, we remain to use the original TB potential. The wave function of the excess electron is represented by its wave function on a finite grid evenly distributed in a cubic box.…”

“…The most recent theoretical attempts aim at at least three more-or-less distinct directions: (a) to improve the one-electron pseudopotential in the mixed quantum-classical molecular dynamics (QCMD) approach to achieve more accurate predictions of the experimental observations, namely, the resonant Raman spectrum or the temperature dependence of the absorption spectrum; , (b) to introduce more precise hydrated electron potential energy surfaces in the simulations using ab initio MD (AIMD) techniques or, slightly more approximately, machine learning (ML)-based methods; , and (c) to treat the nuclei quantum-mechanically, which opens the possibility of examining nuclear quantum effects (NQEs) in hydrated electron systems. , …”

“…Most notably, it was found that three s–p type transitions dominate the spectrum and that solvent fluctuations also significantly contribute to the spectrum’s shape and breadth . Subsequent improvements of the pseudopotential resulted in a more satisfactory agreement of the position of the spectral maximum with experiment ,, the latest reoptimized pseudopotential was even able to capture the temperature dependence of the maximum of the absorption spectrumbut the long tail has still eluded the theoretical efforts. The first real success came with the time-dependent density functional theory (TD-DFT) calculations by Herbert and his co-workers.…”