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Cite this: Chem. Sci., 2022, 13, 3837
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Shallow and deep trap states of solvated electrons
in methanol and their formation, electronic
excitation, and relaxation dynamics†
Jinggang Lan,‡*a Yo-ichi Yamamoto,b Toshinori Suzuki
and Vladimir V. Rybkin §*a*b

We present condensed-phase ﬁrst-principles molecular dynamics simulations to elucidate the presence of
diﬀerent electron trapping sites in liquid methanol and their roles in the formation, electronic transitions,and relaxation of solvated electrons (emet) in methanol. Excess electrons injected into liquid methanol
are most likely trapped by methyl groups, but rapidly diﬀuse to more stable trapping sites with dangling
OH bonds. After localization at the sites with one free OH bond (1OH trapping sites), reorientation ofother methanol molecules increases the OH coordination number and the trap depth, and ultimately
four OH bonds become coordinated with the excess electrons under thermal conditions. The simulation
identiﬁed four distinct trapping states with diﬀerent OH coordination numbers. The simulation results
Received 29th November 2021
Accepted 24th February 2022
DOI: 10.1039/d1sc06666h
rsc.li/chemical-science1also revealed that electronic transitions of emet are primarily due to charge transfer between electron
trapping sites (cavities) formed by OH and methyl groups, and that these transitions diﬀer fromhydrogenic electronic transitions involving aqueous solvated electrons (eaq). Such charge transfer also
explains the alkyl-chain-length dependence of the photoabsorption peak wavelength and the excitedstate lifetime of solvated electrons in primary alcohols.

Introduction

Since solvated electrons (esol) were spectroscopically identiedin the 1960s, they have attracted much attention as prototypicalfree radicals and the most fundamental reducing reagents insolutions.1,2 They play crucial roles in ionization, charge transfer, and redox processes in solutions, and also potentially causeradiation damage of biological systems.3 However, owing totheir short lifetimes and low concentrations, experimental
determination of their geometrical structures using electron/Xray diﬀraction or nuclear magnetic resonance has been diﬃcult.
Consequently, structural information has been obtained indirectly using electronic, vibrational, and electron paramagnetic
resonance spectroscopy. In view of these experimental limitations, theoretical studies are expected to be of assistance inelucidating the structure and dynamics of esol, even though
theoretical studies are as challenging as experimental ones.4–7
aDepartment of Chemistry, University of Zurich, Winterthurerstrasse 190, Zurich 8057,
Switzerland. E-mail: jinggang.lan@ep.ch; vladimir.rybkin@quantumsimulations.deb

Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 6068502, Japan. E-mail: suzuki@kuchem.kyoto-u.ac.jp† Electronic supplementary
10.1039/d1sc06666h

information(ESI)

available.

See

DOI:

‡ Present address: Chaire de Simulation à l'Echelle Atomique (CSEA), Ecole
Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland.
§ Present address: HQS Quantum Simulations GmbH, Haid-und-Neu-Straße 7,
D-76131 Karlsruhe, Germany.

© 2022 The Author(s). Published by the Royal Society of Chemistry

So far, most attention has been devoted to aqueous solvatedelectrons, eaq; however, their analogues in other solvents arealso highly interesting and valuable for practical applications.
esol in ammonia have been utilized for organic synthesis
processes such as Birch reduction.8 However, since Birch
reduction requires low temperatures and the use of liquidammonia, eﬀorts have been made to develop alternative reactions using other solvents such as alcohols and ethers.9,10 The
Bouveault–Blanc reaction employs esol in alcohols for reducing
esters to primary alcohols.11 Thus, a detailed study on the
structure and dynamics of esol in alcohols may contribute todeveloping highly eﬃcient and environmentally benign reduction reactions.9–11
Despite apparent similarities, solvated electrons in methanol, emet, exhibit some notable diﬀerences from eaq. Most
importantly, two trap states – shallow and deep – have been
experimentally identied for emet in the ground electronic
state.12 The shallow trap state with a near-infrared absorption
band was identied in low-temperature (4–77 K) glass, and its
transformation to a deep trap state was observed at temperatures above 77 K, based on the emergence of a visible absorption band.13,14 The deep trap state has been observed for a liquidmethanol microjet using photoemission spectroscopy.15–17 A
recent femtosecond pump–probe photoemission spectroscopy
study of emet (ref. 12) found that the vertical electron binding
energy (VBE) for these two trap states is 2.1 eV (shallow) and
3.4 eV (deep), and that the transformation among these trap

Chem. Sci., 2022, 13, 3837–3844 | 3837

Chemical Sciencestates takes place within tens of picoseconds under ambientconditions. Such multiple trap states have not been identied
for esol in water or ammonia. It has been suggested that electrons trapped on the water surface and in the bulk havediﬀerent VBEs of 1.6 and 3.3 eV,18,19 respectively, but this claim
has not been supported by clear evidence.20
Another noteworthy diﬀerence between eaq and emet is in
their UV-visible absorption spectrum.21–23 Although both spectra
exhibit a broad peak with a maximum at similar photon energies (1.7 eV for water and 2.0 eV for methanol), emet exhibits
a much higher spectral intensity beyond 3.0 eV. Previous theoretical studies indicated that the main absorption band for eaqis due to overlapping electronic transitions from s-like groundstate orbitals to three p-like orbitals and ascribed a long “bluetail” to transitions to higher bound/continuum states.24 A
similar assignment has been proposed for emet.25,26 However,while the spectra computed so far for emet reproduced themain absorption band, they did not reproduce the intense
absorption feature observed beyond 3.0 eV. It should also be
noted that the experimental results indicate that the lifetimes ofthe electronically excited states for esol in primary alcohols
depend on the carbon chain length, hinting at a qualitatively
diﬀerent character for these states from those for eaq.23,27,28
These intriguing experimental observations deserve detailed
theoretical and computational analyses. Some important theoretical studies have already been published for emet. For
example, Walker and Bartels29 performed calculations on
negatively charged methanol clusters in a dielectric medium
and suggested that the structure of emet in a bulk solution isa cavity state that is tetrahedrally coordinated with four hydroxygroups, similar to eaq. This species with a binding energy of
3.5 eV likely corresponds to the deep trap state. Similar structures have been obtained using condensed-phase molecular
dynamics (MD) simulations with empirical force elds
augmented by a one-electron Hamiltonian for the excess electron.25,30–32 These cluster and bulk simulations suggested thatthe methyl groups of methanol contribute to trapping of excess
electrons with a coordination number of 5–7;25,30,33,34 however, it
has not been claried how such trapping contributes to theformation, electronic excitation, and relaxation dynamics ofemet.
Theoretical study of electron dynamics in methanol isa challenging task, requiring reliable and accurate computational methods. The aforementioned force-eld one-electron
Hamiltonian models provided important insights into excess
electrons; however, these computations were critically dependent on multiple parameters, various choices of which led toqualitatively diﬀerent results. For example, in the case of eaq,diﬀerent parametrizations predicted completely diﬀerent
structures for the cavity and non-cavity states.35–38 Similarly, two
diﬀerent model parameters for emet led to diﬀerent structureswith solvation by either methyl or hydroxy groups.39 An alternative less unambiguous approach taken in the present study is
to use modern many-electron quantum-chemical methods ofdispersion-corrected hybrid density functional theory (DFT) andsecond-order Møller–Plesset perturbation theory (MP2), whichhave recently become available for large-scale condensed-phase3838 | Chem. Sci., 2022, 13, 3837–3844

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MD. They involve only a few (dispersion-corrected hybrid DFT)
or no (MP2) tunable parameters and provide a reliable
description of esol while keeping the pernicious selfinteraction error under control.40 The accuracy of thesecomputational methods has been demonstrated for electrons41–43 and dielectrons in liquid water44 and ammonia,45 andfor the reaction of eaq with carbon dioxide.46
In the present study, we attempt to elucidate the nature ofelectron trap states in liquid methanol. This is achieved bycondensed-phase MD simulations driven by dispersioncorrected hybrid DFT and MP2. Aer injection of an excess
electron into neat liquid methanol, we trace its localization inreal time from the “birth” of a shallow trap state to its conversion into the deep trap state in several picoseconds. Although
this timescale is insuﬃcient to achieve thermalization of emet,
we can capture and characterize the time-evolution of the trap
state. The results illustrate essential diﬀerences in the electronic structure and relaxation dynamics between emet andeel.

2 Computational methods
2.1

Molecular dynamics

We performed MD simulations under periodic boundary
conditions for two diﬀerent system sizes of 39 and 55 methanol
molecules with a single excess electron. We calculated thetemporal evolution of the system (in the microcanonicalensemble) aer injection of an electron into neat liquid methanol under ambient conditions. The initial solvent structures
were obtained by equilibration in the NVT ensemble at 300 K ata density corresponding to the experimental value.
Relaxation of the excess electron was traced up to 5 ps with 5
trajectories for each system size using dispersion-correctedhybrid DFT. For the smaller system with 39 molecules, twotrajectories were computed up to ca. 1 ps with MP2 to conrm
the validity of the DFT calculations. MP2 calculations for thelarger system are unfeasible at the current state of hardware andsoware. Thus, most of the analysis was performed on the DFT
trajectories, unless otherwise specied. Although the experimentally measured relaxation times are much longer than thetime scale of our simulations, the latter are still suﬃcient for
capturing the formation of both shallow and deep trap states.
More details on the MD simulations are given in the ESI(Section C).†
2.2

Electronic structure theory

As described earlier, ab initio MD simulations were performed
using hybrid DFT and MP2,47,48 which previously provided
highly accurate computational results for eaq.41,47,49,50 The
functional of choice is PBE(a) with 50% exact exchange witha non-local van der Waals correction, rVV10,51 using a triple-zeta
quality basis set,52 which is proven to provide spin densities anddynamics accurately, similar to those for MP2. A correlationconsistent triple-zeta quality basis set was employed forMP2.53 We computed the photoabsorption spectra for theframes along the trajectories using time-dependent DFT© 2022 The Author(s). Published by the Royal Society of Chemistry

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Chemical Science(TDDFT) calculations with the same functional and basis set.
We also performed a calculation based on the density functional embedding theory54 for a selected representative structure of emet. All periodic calculations were performed using theCP2K program55 in the spin-unrestricted formalism for theexcess electron using a uniform positive background charge tocompensate for the excess electron's negative charge. The
calculations of the cluster model were performed using the
ORCA program.56 More details of the electronic structure
calculations are given in the ESI (Sections A (DFT), B (MP2) andD (TDDFT)).†
2.3

Binding energy

We estimated the VBE for emet from the (negative) energy ofa singly occupied molecular orbital (SOMO) containing theexcess electron. However, the diﬃculty with this approach using
MD simulations with periodic boundary conditions is that thecalculated SOMO energy, E(SOMO), is dened with respect to anarbitrary zero of energy, so that its absolute energy shisrandomly for each snapshot.49,57 In order to eliminate thisrandom shi, we calculated the energy of the semi-core oxygen
2s-orbital, E(O2s), which is expected to be unaﬀected by the
nuclear conguration or the presence of the excess electron,and subtracted E(O2s) from E(SOMO). For calculations of theVBE, the vacuum energy level is a necessary parameter. In our
calculations, we simply assumed that the initial electronicenergy upon excess electron injection to liquid methanol isequal to the vacuum level; therefore, the VBE calculated for thei-th frame of the MD simulation is approximated as the energy
diﬀerence between the i-th frame and the zeroth frame of thesnapshot:
VBEi ¼ E(SOMO)i  E(O2s)i  (E(SOMO)0  E(O2s)0),(1)

where i is the index of the snapshot. As described later, VBEs
thus computed were found to be systematically smaller than theexperimental values by 0.4 eV; therefore, the calculated VBE
values were shied by +0.4 eV for comparison with the experimental values.

3 Results and discussion
3.1

Structure and dynamics

The geometrical structure of emet is more complex than that ofesol in water41,42 or ammonia45 due to the bipolar nature of thesolvent with a non-polar methyl- and polar hydroxy-group.
Thus, we categorized the cavities into the following ve types(see Fig. 1 for the cavities and Fig. 2(a–c) for the radial distribution functions):(1) CH3-cavity: formed by 4–6 methyl groups.
(2) 1OH-cavity: formed by one hydroxyl- and several methylgroups.
(3) 2OH-cavity: formed by two hydroxyl- and two methylgroups.
(4) 3OH-cavity: formed by three hydroxyl- and one methylgroup.
(5) 4OH-cavity: formed by four hydroxyl-groups.

© 2022 The Author(s). Published by the Royal Society of ChemistryCH3-cavities occur naturally in liquid methanol because thehydrogen bonding network is one-dimensional. Our simulations indicate that the excess electron is initially localized ina CH3-cavity with a compact and relatively isotropic spin-density
distribution, in addition to a small VBE, small gyration radius,
and weak anisotropy, as shown in Fig. 2(e) (see ESI, Section F†).
As soon as one of the hydrogen bonds between solvent molecules breaks to form a dangling OH bond in the vicinity of theCH3-cavity, the electron swily moves to this polar trap (1OHcavity). This process is similar in nature to transient diﬀusionof eaq (see Fig. 1(a–c)).42 If a polar trap already exists at the timeof electron injection, the electron is most likely trapped
immediately in the 1OH-cavity. Thus, at the early stages, theexcess electron “looks for” and moves to the most energeticallyfavorable localization site, which may be either a CH3- or a 1OHcavity. This is consistent with the previously discussed conceptof the excess electron as “a trap-seeker and not a trap
digger”.12–14
The dynamics dramatically changes aer 2OH-, 3OH- and4OH-cavities are formed: the solvated electron now behaves asa “trap-digger”. While the electron resides in the same cavity,
the methanol molecules initially coordinating their CH3-groupto the excess electron gradually reorient themselves to coordinate their OH-group. This can occur with one or two molecules
at a time (as shown in Fig. 1). For reorientation of a methanol
molecule in the rst solvation shell, the hydrogen bond between
the methanol molecules in the rst and second solvation shells
must be disrupted. Therefore, the second solvation shell also
plays an important role in the solvation dynamics of emet,
which is reminiscent of the reaction of eaq with CO2.46 The
entire localization process generally follows the following
scheme:CH3-cavity / 1OH-cavity / 2OH-cavity / 3OH-cavity /4OH-cavity

However, some of these stages may be completely bypassedor rapidly passed through.
In simulations of the smaller system, three trajectories
reached the 4OH-cavity, one 3OH-cavity, and one 2OH-cavity in
5 ps. In the two trajectory calculations at the MP2 level for thesmaller system, one trajectory evolved from the CH3-cavity to
the 2OH-cavity via the 1OH-intermediate, and the other transformed from a 3OH-cavity to a 4OH-cavity by reorientation ofa methanol molecule: the trajectories at the MP2 level are
qualitatively consistent with the results of hybrid DFT calculations. On the other hand, DFT calculations of the larger system
indicated that three trajectories reached the 3OH-cavity and two
trajectories reached the 2OH-cavity within 5 ps, but no trajectory reached the most stable 4OH-cavity. This is qualitatively
consistent with the experimentally measured formation time(tens of picoseconds) for the deep trap state.12 However, due torestricted statistics any quantitative theoretical estimates of thetransformation time from the shallow are beyond the scope of
the present study. We computed the properties of the 4OHcavity in the larger system by creating its geometrical

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Fig. 1 (a–c) Transient diﬀusion from the CH3-cavity to the 1OH-cavity; (d–f) transition from the 2OH-cavity to the 4OH-cavity. Color code:
carbon (grey), oxygen (red), hydrogen (white) and positive spin density (blue), negative density (yellow) where the isovalue is 0.001 a.u.

structure as the initial conguration and thermally relaxing it
using MD simulations.
The geometrical structure of emet can be examined in moredetail using the radial distribution function (RDF: g(e–X) with X¼ C, H or O) for C, H, and O atoms with respect to the center ofthe spin density distribution as shown in Fig. 2(a–c). We
generally observe that the structure becomes more ordered withincreasing OH coordination number even in the case of g(e–C),
for which the rst peak gradually shis to a larger distance andbecomes sharper. For g(e–H), the CH3- and 1OH-cavities havevery similar distributions. The lower-coordinated cavities tend
to have shorter distances between the center of the spin-density
distribution and the dangling OH-bond, as seen for the g(e–O)
and g(e–H) distributions.
3.2

Binding energy

Binding energies calculated for diﬀerent cavity types are shownin Fig. 2(d): the VBE values obtained for diﬀerent trajectories
generally agree within the error margins. Since the VBE values
obtained using eqn (1) were systematically lower than theexperimental values by 0.4 eV, the calculated values are shiedby +0.4 eV in Fig. 2(d) for close comparison with the experimental values. This also implies that the initial state (seeSection 2.3 and eqn (1)) in our simulation was actually weakly
bound (ca. 0.4 eV), possibly with an excess electron in the
conduction band of liquid methanol, with respect to thevacuum level. This interpretation is qualitatively supported by
calculations of an electron binding energy for a methanol
cluster (see ESI, Section G†). We note that our simulations
identify four rather than two (shallow and deep) trap states with

3840 | Chem. Sci., 2022, 13, 3837–3844

distinct VBE values that are strongly dependent on the OH
coordination number. The results indicate that the VBE gradually increases with increasing OH coordination number.
These computational results encouraged us to reinterpretthe experimental results reported by Hara et al.,12 who analyzed
the results assuming only two trap states. They performed
ultrafast photoemission spectroscopy of liquid methanol with
9.3 eV vacuum UV pulses and examined the subsequent
formation of solvated electrons on a picosecond timescale.
Based on the VBE values, they classied the observed spectrumof emet to be associated with shallow or deep trap states. These
two trap states, however, also exhibited a VBE that increased
with time due to solvation (time constants of 15 and 50 ps,
respectively). Therefore, neither of these trap states was
stationary. The time-evolution of the observed VBE distribution
was also analyzed by global tting, in which the time-dependent
photoemission spectra were t using linear combinations oftime-independent spectra of several transient species with
diﬀerent lifetimes (these spectra are called decay associatedspectra: DAS). In this analysis scheme, sequential formation offour diﬀerent species was necessary in order to explain theexperimental data. The decay times for these four species were
determined to be 5.1 ps, 14 ps, 24 ps, and >5 ns. The VBE
distributions for these four states, not presented in the original
paper by Hara et al.,12 are shown in Fig. 2(d). The four states
have average VBE values of 1.7, 2.2, 2.8, and 3.3 eV, which arealmost equally spaced. Close examination of Fig. 2(d) reveals
that the rst species has a rather wide VBE distribution and its
high-energy tail exceeds 3.0 eV. This implies that some of theelectrons are directly trapped in the region where multiple© 2022 The Author(s). Published by the Royal Society of Chemistry

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Chemical Science(a–c) Radial distribution functions for main structures (55 molecules): electron distribution center to carbon (a), hydrogen (b), oxygen (c).
(d) Vertical electron binding energies (shifted by 0.4 eV to compare with experimental results) of diﬀerent cavity types as obtained from 39
molecule-system using hybrid functional (red), 39 molecules using MP2 frames (blue), and 55 molecules using hybrid functional frames (green).
Decay associated spectra (DAS) calculated by global ﬁtting of photoemission spectra with four-step sequential kinetics model. The spectra aremeasured by liquid methanol excited by 9.3 eV vacuum UV pulses and probed by 4.3 eV UV pulses (e) vertical binding energies vs. spin density
gyration radius (55 molecules). The color map corresponds to spin density distribution anisotropy.

Fig. 2

dangling OH-bonds stabilize the electrons, which agrees with
our simulation results.
3.3

Electronic spectraPreviously, the one-electron model for emet assigned the photoabsorption maximum at 2.0 eV to three overlapping transitions from s- to p-type orbitals, similar to the case of eaq, but
the model did not reproduce the strong absorption by emet
beyond 3.0 eV.25 On the other hand, our results suggest that themain absorption peak associated with emet in OH-cavities
arises from electronic transitions to charge transfer statesrather than the hydrogenic electronic transitions discussed sofar; in fact, our calculations identied no hydrogenic transitionsin the studied energy range. Our calculations predicted theabsorption maximum to be ca. 2.2 eV for 3OH- and 4OH-cavities
and ca. 1.7 eV for 2OH-cavities (see Fig. 3(c)). With a moderate
blue shi of 0.2 eV, these values agree reasonably well with the© 2022 The Author(s). Published by the Royal Society of Chemistry

experimentally observed absorption maxima for the shallow(1.5 eV) and the deep trap (2.0 eV) states.12 We ensured that the
charge-transfer excited states are not spurious by performing
the Mulliken averaged conguration diagnostic58–60 as
described in the ESI, (Section D).†
Photoabsorption by emet in 1OH-cavities is weak andexhibits an absorption maximum below 1 eV. Nevertheless, itsband closely resembles the photoabsorption spectrum (broken
line in Fig. 3(c)) of an intermediate species reported by Thaller
et al.61 The relatively strong photoabsorption extending beyond
3.0 eV is also ascribed to charge-transfer transitions, which
explains why the spectral features in this energy region are
diﬀerent from those for eaq.
What causes this diﬀerence in the nature of the excited states
for emet between the previous and current computations? Webelieve that the one-electron model calculations conned theexcess electron to a single cavity too strongly and prevented

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SOMO (blue – positive values, yellow – negative values) and the dominant virtual spin–orbital in the ﬁrst excited state (light blue – positive
values, green – negative values) for a typical (a) 2OH-cavity structure and (b) 4OH-cavity structure (shallow-trap ground state). Isovalue – 0.02
a.u. (c) Simulated and experimental electronic spectra of the solvated electron in methanol, including 20 excited states. The black solid line is anabsorption spectrum of emet at thermal equilibrium,21 and the black broken line is of an early transient species observed in photoionization ofliquid methanol.61
Fig. 3charge transfer to nearby cavities. To examine this problem, we
performed embedded TDDFT calculations for one of the four
OH-cavity structures, in which the methanol molecules forming
the 4OH-cavity were embedded in the eﬀective potential
conning the electron in the cavity. As anticipated, the calculation provided only transitions from s- to p-type orbitals (aerremoval of spurious delocalized states), as described in moredetail in the ESI (Section E).†
Charge transfer to spatial voids has previously been foundfor photoabsorption by esol in tetrahydrofuran (THF),62
although the rst three excited states are still localized in thecentral cavity with a diminished hydrogenic character. In thissense, esol in THF exhibits an intermediate character between
emet and eaq. This correlates well with the densities (water:
998, THF: 890, methanol: 793 kg m3 at 293 K) and the occurrence of voids in these liquids.

Since the excited states of emet have a charge-transfer
character, the internal conversion of emet can be viewed asreverse non-radiative charge transfer. If this picture also holds
for other primary alcohols, the rate of internal conversion
possibly varies with the carbon chain length, since this changes
the distance between the two cavities: the longer the alkyl
group, the larger the lifetime of the excited state. Even though
the two cavities may not be located at opposite ends of thealcohol molecule, the distance between the two cavities iscorrelated with the chain length. This agrees with the measured
lifetime for the excited states of esol in simple alcohols, whichtends to increase with increasing carbon chain length.23,27,28,63
To illustrate charge-transfer excitation of emet, a simple
one-dimensional double square-well model is considered. Here
we assume the well depth to be equal to that for the nOH(ground) and CH3- (excited) cavities, its width to be the electron
gyration radius, and the distance between the two wells to be(a) Double square well model: potential; energies and probability density distributions of the ground and ﬁrst excited states. WOH and WCH3
are width of the two wells; d is the distance between the wells; DOH; DCH3 are the well depths and DE is the excitation energy between the groundand the ﬁrst excited states. (b) Excitation energies (eV) obtained from the double square well model with diﬀerent inter-cavity distances d andwell depths DOH. The other parameters are: DCH3 eV, WOH ¼ 2.2 
A and WCH3 ¼ 2.5 
A. The experimental values indicated in the ﬁgure are takenfrom ref. 21 and 63 and the references therein.
Fig. 43842 | Chem. Sci., 2022, 13, 3837–3844© 2022 The Author(s). Published by the Royal Society of Chemistry

Edge Article
the alkyl chain length (see Fig. 4(a)). Using appropriate values
for these parameters, this simple model produces reasonably
good agreement between the calculated excitation energies tothe rst excited states and the experimental spectra (seeFig. 4(b) and ESI, Section H†). The wave functions are mostly
localized in the corresponding wells (see Fig. 4(a)). Increasing
the distance between the wells, we obtain a red-shiedabsorption peak maximum as experimentally observed foresol in ethanol and propanol. A more precise model can beconstructed by assuming three-dimensional multiple shallow
wells around the central deep well; however, here we restricted
ourselves to the simplest double square-well model to illustrate
the essence of the physics involved.

4 Conclusions
By performing the rst condensed-phase MD simulation withhigh-level electronic structure theory for excess electrons inmethanol, we identied the bound states of the solvated electronsand classied them according to the number of OH- (and CH3-)
groups contributing to the cavity. Upon electron injection, theexcess electrons occupy naturally preexisting trapping sites
formed by CH3-groups and then ow to more energetically stable
OH-sites. Dangling OH-bonds are stochastically formed byhydrogen-bonding dynamics in solution. This trap-seeking
behavior of the excess electrons changes to a trap-digging one
once the excess electrons are trapped in the OH-sites, and the four
methanol molecules in the rst solvation shell reorient themselves one by one to coordinate the OH-groups to the electron.
Thus, there are four trap states classied by the number ofcoordinated hydroxy groups rather than the two (shallow anddeep) that are suggested by the experiments. The computed VBEs
for these four trap states agree with the range of VBE values
experimentally measured. Another important conclusion of thepresent study is a diﬀerence in the nature of the excited electronic
states for emet from those for eaq: the former are charge-transfer
states, and the latter are hydrogenic ones. The charge-transfer
nature explains the intense photoabsorption prole for emet
beyond 3.0 eV, which is not present in the spectrum of eaq, andthe internal conversion time for esol that varies with the alkyl
chain length. Electronic transitions of emet are rationalized witha simple asymmetric double square-well potential; the model
provides qualitative insights into the spectroscopy of esol inother primary alcohols, explaining the alkyl-chain-length dependence of the maximum absorption peak and the internalconversion time. These ndings may be exploited for the rational
design of new reduction reagents in alcohol solutions.

Data availability
Experimental and computational data are available from theauthors upon a reasonable request.

Author contributions
TS and VR conceived the project. JL and VR performed theoretical simulations, and YY and TS analyzed experimental© 2022 The Author(s). Published by the Royal Society of Chemistry

Chemical Science
results. All authors have contributed to the discussion andwriting of the paper.

Conﬂicts of interest
There are no conicts to declare.

Acknowledgements
This work is funded by the Swiss National Science Foundation(SNSF) Sinergia grant and the University Research Priority
Program (URPP) for solar light to chemical energy conversion(LightChEC) of the University of Zurich. Computing resourceswere provided by the grant from Partnership for Advanced
Computing in Europe under project ID pr92 and a grant fromthe Swiss National Supercomputing Centre (CSCS) under
project ID uzh1. VVR has been supported by the SNSF in theform of Ambizione grant no. PZ00P2_174227. T. S. acknowledges support from the JSPS KAKENHI grants no. JP15H05753
and JP21H04970 and the Mitsubishi Foundation. We thankProfessor Jürg Hutter and Dr Anna Hehn (University of Zurich)for the support and discussions.

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