A Machine Learning Model for the Chemistry of a Solvated Electron

TL;DR

This work develops an electron-aware machine-learning force field, in which an excess electron of interest is modeled quantum mechanically, while the remaining short-range interactions and long-range Coulombic forces are machine-learned to reproduce a density functional theory calculation.

Abstract

In molecular simulations, machine-learning force fields can achieve ab initio accuracy at a lower cost but remain limited in the explicit modeling of electrons. In this work, we develop an electron-aware machine-learning force field, in which an excess electron of interest is modeled quantum mechanically, while the remaining short-range interactions and long-range Coulombic forces are machine-learned to reproduce a density functional theory calculation. We demonstrate the method on the solvated electron in bulk water and its reaction with a hydronium ion. We identify a proton transfer mechanism by which the excess proton recombines with the electron. We determine the forward reaction rates between 350 K and 450 K from first-passage survival functions, which yield an Arrhenius relationship with an activation energy of 3.2 kcal$\cdot$mol$^{-1}$, in good agreement with experiment. From an enhanced sampling simulation, we determine the equilibrium constant, and thus the reaction free energy, which is also consistent with experimental measurements.

Figures (7)

• Figure 1: (a) Sketch of the neighborhood of e$^-_{\mathrm{(aq)}}$. (b) MLWF centers (small purple dots) and the WC (large purple dot) for one water molecule. (c) The potential $V_{\mathrm{emb}}$ generated by $\rho_{\mathrm{emb}}$; brighter color means higher energy. (d) Electron density $n_{\mathrm{e}^-}$ obtained from Eq. (\ref{['se']}). The heatmaps (c) and (d) display the $xy$-plane values centered at the MLWF center of e$^-$.
• Figure 2: (a) The proton hops and forms an Eigen-like H$_3$O$^+$ beside the excess electron. Three outcomes follow: (1) reaction, (2) back-hop, and (3) forward relay. The excess electron (blue) is shown schematically; its spatial extent may exceed the rendering and can be non-isotropic during the reaction marsalek2010hydrogen.
• Figure 3: (a) Arrhenius plot for the predicted $\log_{10} k_2$ versus inverse temperature, compared with experimental data from Shiraishi et al. shiraishi1994temperature and Elliot elliot1994rate. (b) van 't Hoff plot of the log of the equilibrium constant $K_1$ versus inverse temperature, compared with the experimental data of Shiraishi et al. shiraishi1994temperature.
• Figure 4: Parity plots of the total energy and force from DFT vs the trained DPLR-q model for both training and validation data. The energy is shifted to be positive.
• Figure 5: Modeled electron's energy and spatial spread compared to the Kohn-Sham energy and MLWF spread from DFT. These plots are based on the initial DFT trajectories in our training data. The distance $r$ between H$^+$ and e$^-$ is indicated by color.