^{1}, Ross E. Larsen

^{1}and Benjamin J. Schwartz

^{1,a)}

### Abstract

In polar fluids such as water and methanol, the peak of the solvated electron’s absorptionspectrum in the red has been assigned as a sum of transitions between an -like ground state and three nearly degenerate -like excited states bound in a quasispherical cavity. In contrast, in weakly polar solvents such as tetrahydrofuran (THF), the solvated electron has an absorptionspectrum that peaks in the mid-infrared, but no definitive assignment has been offered about the origins of the spectrum or the underlying structure. In this paper, we present the results of adiabatic mixed quantum/classical molecular dynamic simulations of the solvated electron in THF, and provide a detailed explanation of the THF-solvated electron’s absorptionspectrum and electronic structure. Using a classical solvent model and a fully quantum mechanical excess electron, our simulations show that although the ground and first excited states are bound in a quasispherical cavity, a multitude of other, nearby solventcavities support numerous, nearly degenerate, bound excited states that have little Franck–Condon overlap with the ground state. We show that these solventcavities, which are partially polarized so that they act as electron trapping sites, are an inherent property of the way THF molecules pack in the liquid. The absorptionspectrum is thus assigned to a sum of bound-to-bound transitions between a localized ground state and multiple disjoint excited states scattered throughout the fluid. Furthermore, we find that the usual spherical harmonic labels (e.g., -like, -like) are not good descriptors of the excited-statewave functions of the solvated electron in THF. Our observation of multiple disjoint excited states is consistent with femtosecond pump-probe experiments in the literature that suggest that photoexcitation of solvated electrons in THF causes them to relocalize into solventcavities far from where they originated.

This work was supported by a grant from the National Science Foundation (CHE-0240776). The authors would like to thank C. Jay Smallwood for helping to modify the electron-THF pseudopotential. The images in Fig. 4 were created using the UCSF Chimera package from the Computer Graphics Laboratory, University of California, San Francisco (supported by Grant No. NIH P41 RR-01081).^{62}

I. INTRODUCTION

II. COMPUTATIONAL METHODS

III. RESULTS

IV. DISCUSSION

### Key Topics

- Excited states
- 78.0
- Absorption spectra
- 72.0
- Solvents
- 67.0
- Solvated electrons
- 65.0
- Ground states
- 44.0

## Figures

Gaussian–Lorentzian fits to the experimental absorption spectra of the solvated electron in THF (solid curve), HMPA (dashed curve), water (dash-dot curve), and methanol (dotted curve). The fitting parameters were taken from Ref. 12.

Gaussian–Lorentzian fits to the experimental absorption spectra of the solvated electron in THF (solid curve), HMPA (dashed curve), water (dash-dot curve), and methanol (dotted curve). The fitting parameters were taken from Ref. 12.

Time dependence of (a) the eigenvalues, (b) the transition dipole moments, and (c) the spherical harmonic projections of the lowest six eigenstates of the THF-solvated electron shown over a small window in the middle of our equilibrium trajectory. The key for panel (b) should be read as the transition from the ground state (labeled as 0) to the excited state; is the energy of state and is the energy gap between the ground state and the state. The projection (see the Appendix and Ref. 58) of each excited eigenfunction onto the (-like) spherical harmonic is shown, as is the projection of the ground state onto the (-like) spherical harmonic. The spherical harmonic projection of the sixth excited state is not shown in panel (c) because this state has no significant spherical symmetry. The arrows indicate the specific configuration examined in Fig. 4.

Time dependence of (a) the eigenvalues, (b) the transition dipole moments, and (c) the spherical harmonic projections of the lowest six eigenstates of the THF-solvated electron shown over a small window in the middle of our equilibrium trajectory. The key for panel (b) should be read as the transition from the ground state (labeled as 0) to the excited state; is the energy of state and is the energy gap between the ground state and the state. The projection (see the Appendix and Ref. 58) of each excited eigenfunction onto the (-like) spherical harmonic is shown, as is the projection of the ground state onto the (-like) spherical harmonic. The spherical harmonic projection of the sixth excited state is not shown in panel (c) because this state has no significant spherical symmetry. The arrows indicate the specific configuration examined in Fig. 4.

(a) Calculated absorption spectrum for an excess electron in THF using Eq. (3). Underlying the total spectrum (thick black curve) are the individual transitions from the ground to each of the excited states (thin gray and black curves). (b) The scaled density of energy gaps of the THF-solvated electron between the ground and each of the six lowest excited states, defined as the distribution of instantaneous energy gaps between the ground and each of the excited states.

(a) Calculated absorption spectrum for an excess electron in THF using Eq. (3). Underlying the total spectrum (thick black curve) are the individual transitions from the ground to each of the excited states (thin gray and black curves). (b) The scaled density of energy gaps of the THF-solvated electron between the ground and each of the six lowest excited states, defined as the distribution of instantaneous energy gaps between the ground and each of the excited states.

(Color) Attractive cavities (orange surface) and charge densities (wire meshes) for the solvated electron in THF, calculated as described in the text. The wire meshes shown are contours drawn at 10% of the maximum charge density. Panel (a) shows the ground state, (b) the first excited state, (c) the second excited state (d) the third (red) and fifth (blue) excited states, (e) the fourth excited state, and (f) the sixth excited state. The drop shadows are placed under each state’s center of mass to aid in perspective and are not meant to convey size information. Note that for clarity, the cavity surface contours are drawn away from the nearest solvent molecule, and thus do represent the entire volume available to trap the electron (see text). The cubes shown represent the entire volume of the simulation cell with side .

(Color) Attractive cavities (orange surface) and charge densities (wire meshes) for the solvated electron in THF, calculated as described in the text. The wire meshes shown are contours drawn at 10% of the maximum charge density. Panel (a) shows the ground state, (b) the first excited state, (c) the second excited state (d) the third (red) and fifth (blue) excited states, (e) the fourth excited state, and (f) the sixth excited state. The drop shadows are placed under each state’s center of mass to aid in perspective and are not meant to convey size information. Note that for clarity, the cavity surface contours are drawn away from the nearest solvent molecule, and thus do represent the entire volume available to trap the electron (see text). The cubes shown represent the entire volume of the simulation cell with side .

Comparison between the normalized distributions of energy for the equilibrated THF-solvated electron eigenstates (solid curves) and for the eigenstates of an excess electron injected into neat THF (dashed curves). The energy probability distributions in the neat liquid were calculated from an trajectory, whereas the distributions for the solvated electron were calculated from the full equilibrium trajectory.

Comparison between the normalized distributions of energy for the equilibrated THF-solvated electron eigenstates (solid curves) and for the eigenstates of an excess electron injected into neat THF (dashed curves). The energy probability distributions in the neat liquid were calculated from an trajectory, whereas the distributions for the solvated electron were calculated from the full equilibrium trajectory.

## Tables

Parameters for the classical THF-solvent potential (Lennard-Jones plus Coulomb), taken from Ref. 32, and the quantum THF-electron pseudopotential [Eq. (1)], which was modified from the hydrocarbon-electron pseudopotential presented in Ref. 27. Interactions between different sites were calculated using these parameters and the standard Lorentz–Berthelot combining rules.

Parameters for the classical THF-solvent potential (Lennard-Jones plus Coulomb), taken from Ref. 32, and the quantum THF-electron pseudopotential [Eq. (1)], which was modified from the hydrocarbon-electron pseudopotential presented in Ref. 27. Interactions between different sites were calculated using these parameters and the standard Lorentz–Berthelot combining rules.

Results for the projections of the wave functions of solvated electrons in THF and water onto the spherical harmonics [Eq. (A1)], the projections of the THF-solvated electron were calculated from configurations spanning of the total equilibrium trajectory, and the projections for the hydrated electron were calculated from configurations spanning a run (Ref. 59). In all cases except the time average, the two standard deviation error bars are less than 1%. The time average is the percentage of time each state is projected more than onto its maximally projected spherical harmonic (the maximally projected spherical harmonics are shown in bold face.). That is, the second excited state of the solvated electron in THF has a projection onto the spherical harmonics only 17% of the time, meaning that it meets our criterion for -like only 17% of the time. The one standard deviation error bars for the time averages are given in parentheses.

Results for the projections of the wave functions of solvated electrons in THF and water onto the spherical harmonics [Eq. (A1)], the projections of the THF-solvated electron were calculated from configurations spanning of the total equilibrium trajectory, and the projections for the hydrated electron were calculated from configurations spanning a run (Ref. 59). In all cases except the time average, the two standard deviation error bars are less than 1%. The time average is the percentage of time each state is projected more than onto its maximally projected spherical harmonic (the maximally projected spherical harmonics are shown in bold face.). That is, the second excited state of the solvated electron in THF has a projection onto the spherical harmonics only 17% of the time, meaning that it meets our criterion for -like only 17% of the time. The one standard deviation error bars for the time averages are given in parentheses.

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