Electron Solvation in Liquid Ammonia: Lithium, Sodium, Magnesium,and Calcium as Electron SourcesVitaly V. Chaban*,† and Oleg V. Prezhdo*,‡

†Instituto de Ciencia e Tecnologia, Universidade Federal de Sao Paulo, 12231-280 Sao Jose dos Campos, SP Brazil‡Department of Chemistry, University of Southern California, Los Angeles, California 90089, United States

ABSTRACT: A free electron in solution, known as a solvatedelectron, is the smallest possible anion. Alkali and alkaline earthatoms serve as electron donors in solvents that mediate outer-sphere electron transfer. We report herein ab initio moleculardynamics simulations of lithium, sodium, magnesium, andcalcium in liquid ammonia at 250 K. By analyzing the electronicproperties and the ionic and solvation structures and dynamics,we systematically characterize these metals as electron donorsand ammonia molecules as electron acceptors. We show thatthe solvated metal strongly modifies the properties of itssolvation shells and that the observed effect is metal-specific. Specifically, the radius and charge exhibit major impacts. The singlesolvated electron present in the alkali metal systems is distributed more uniformly among the solvent molecules of each metal’stwo solvation shells. In contrast, alkaline earth metals favor a less uniform distribution of the electron density. Alkali and alkalineearth atoms are coordinated by four and six NH3 molecules, respectively. The smaller atoms, Li and Mg, are stronger electrondonors than Na and Ca. This result is surprising, as smaller atoms in a column of the periodic table have higher ionizationpotentials. However, it can be explained by stronger electron donor−acceptor interactions between the smaller atoms and thesolvent molecules. The structure of the first solvation shell is sharpest for Mg, which has a large charge and a small radius.Solvation is weakest for Na, which has a small charge and a large radius. Weak solvation leads to rapid dynamics, as reflected inthe diffusion coefficients of NH3 molecules of the first two solvation shells and the Na atom. The properties of the solvatedelectrons established in the present study are important for radiation chemistry, synthetic chemistry, condensed-matter chargetransfer, and energy sources.

■ INTRODUCTION

The solvated electron constitutes an intriguing phenomenonthat has continued to draw attention since its discovery.1−17

Understanding the trends and peculiarities of electron solvationin different solvents is helpful to a variety of fields, includingradiation chemistry, energy storage, and organic synthesis.Solvated electrons are particularly interesting in the context ofelectron-transfer phenomena. Solvated electrons occupy spacesbetween solvent molecules and solute particles. Although thesolvated electron does not covalently bind to any of theseentities, it interacts with them electrostatically. It can be saidthat both the solute and the solvent exhibit comparableaffinities to the electron. The valence electron, therefore,obtains enough potential energy to exceed the first ionizationpotential of a metal. It is agreed in the research community thatlithium and sodium, in combination with a few types of polarsolvents, can act as donors of solvated electrons. These solventsinclude ammonia, water, tetrahydrofuran containing organicradicals, and polyaromatic hydrocarbons.18−21

Lithium in liquid ammonia gives rise to the most well-knownexample of the solvated electron. Humphry Davy was the firstto describe blue-colored solutions of alkali metals in liquidammonia two centuries ago. A theoretical identification of thephenomenon of the solvated electron arrived much later. The

properties of solvated electrons are still being activelyinvestigated. Modern studies address fingerprints of solvatedelectrons in water, ammonia, acetonitrile, biphenyl intetrahydrofuran, and other systems.11,13,22,23 The existence ofthe solvated electron can be hypothesized theoretically in somepolar solvents, but plausible experimental evidence has not yetbeen obtained.Schiller and Horvath24 considered a model consisting of a

Rydberg atom interacting with thermodynamic fluctuations ofthe medium. Applied to supercritical water and ammonia, themodel provided good agreement with the experimental data.Yazami and co-workers20 reported conductivity measurementsand Fourier-transform infrared (FTIR) studies on solvated-electron solutions obtained in solutions of lithium intetrahydrofuran with biphenyl as an electron acceptor. Theyachieved significant conductivity, 12.0 mS cm−1, using thespecies ratio n(Li)/n(biphenyl)/n(solvent) = 1:1:8.2. Thesolutions exhibited metallic behavior. Fingerprint peaks werefound in the FTIR spectra.

Received: January 13, 2016Revised: February 16, 2016Published: February 17, 2016

Article

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An interesting series of studies concerning excess electrons inliquid acetonitrile were reported by Doan and Schwartz.11,22

The excess electron exists in two forms in liquid acetonitrile:the traditional solvated electron absorbing in the near-IR regionand a solvated molecular dimer anion. The latter absorbsweakly in the visible spectral region. The solvated electron islocalized right after being produced, but it tends to form adimer anion later. Yoshida and co-workers25 used pulseradiolysis to study the solvated electron in alkylammoniumionic liquids. A number of different cations and anions werecombined to reveal the effects of the ions. The absorption peakat 1100 nm in all studied ionic liquids was ascribed to thesolvated electron. The reaction rate constant of the identifiedelectron with pyrene was found to exceed viscosity-baseddiffusion-controlled limits by 1 order of magnitude. Theauthors made an interesting conclusion that the macroscaleviscosity of the alkylammonium ionic liquids appearedsystematically higher than the effective viscosity on themolecular scale. Vertical electron binding energies were directlymeasured by Suzuki and co-workers for the solvated electron inmethanol and ethanol.23 Time-resolved photoelectron spec-troscopy at ultralow kinetic energy was applied to liquid beamsof sodium iodide solutions. The solvated electron was formedfrom the iodide anions by reactions involving charge transfer tothe solvent. The authors concluded that the cavity radii in waterand low alcohols were very similar.Rossky and collaborators12,26−28 pioneered time-domain

modeling of solvated electrons, motivated by ultrafast pump−probe experiments.29−32 They showed that the shape of thecavity created by the solvated electron depends strongly on thequantum state of the electron. The cavity is spherical in theground state, whereas it is elongated in the excited state. Theirsimulations demonstrated and characterized a complex inter-play between electronic and nuclear degrees of freedom,involving solvation dynamics, charge transfer, and nonradiativeelectronic transitions.Having studied solvated electrons in water clusters, Turi,

Sheu, and Rossky12 identified distinct spectral signatures of theelectron’s surface and interior states and concluded, based onan analysis of experimental data, that the electron in small waterclusters is stabilized by surface-bound states. Jacobson andHerbert33 investigated the temperature dependence of solvatedelectrons in water clusters. Having characterized four types ofstates, namely, dipole-bound, surface-bound, partially embed-ded, and cavity states, they showed by extrapolation to largecluster sizes that electrons in very cold clusters prefer the cavitystate whereas warm clusters create surface-bound electronstates. As the cluster size decreases, the surface-bound statetransforms into the partially embedded state.In addition to previously known surface and cavity states,

Sommerfeld and Jordan identified a new binding motif in whichan excess electron permeates the hydrogen-bonding network.34

Electrostatic binding of an excess electron dominates only inthe isomers with large dipole moments, whereas polarizationand correlation effects prevail in all other water cluster isomers.Clusters from (H2O)12

− to (H2O)24− were considered.34

Shkrob used density functional theory (DFT) calculations onsingly negatively charged water clusters (comprising 2, 8, 20,and 24 molecules) to interpret solution-phase electronparamagnetic resonance (EPR)/electron spin−echo envelopemodulation (ESEEM) experiments on an aqueous electron.35

The majority of solvated-electron studies have beenexperimental. The current state of the ab initio methods allows

one to conduct relevant simulations and to characterize theexperimental results. Most ab initio simulations to date havebeen performed using relatively small and typically finitesystems,1,9,36−41 and more systematic investigations aredesirable. In the present article, we report a study of thesolvated electron in liquid ammonia, where the source of theelectron is an atom of lithium, sodium, magnesium, or calcium(Figure 1). The calculations were implemented using ab initio

molecular dynamics (MD) simulations of the neutral periodicsystems powered by plane-wave DFT. We investigate theeffects of the solvated electron on the structures and dynamicsof these solutions.

■ METHODOLOGYElectronic structure calculations and adiabatic moleculardynamics simulations were computed by means of the Viennaab Initio Simulation Package (VASP).42 VASP uses pure DFTwith a converged plane-wave basis set, which allows for theefficient simulation of periodic (infinite) systems. A metal atom(Li, Na, Mg, or Ca) was surrounded by 32 ammonia moleculesmaintaining the experimental density (ca. 730 kg m−3). Thefour resulting systems were placed into periodic cubic cells;additionally, a larger system, comprising one lithium atom and72 ammonia molecules, was simulated (Table 1). Metals wereadded to the simulated systems as atoms, rather than ions, sothat the neutrality of the periodic cells was preserved.The generalized gradient approximation for the exchange-

correlation functional proposed by Perdew, Burke, andErnzerhof was employed,43 as was also done in prior studieson similar systems.40,44 The projector-augmented wave methodto substitute ultrasoft pseudopotentials was used for all atoms.45

Figure 1. Electron density distribution in the equilibrated systemcontaining a metal atom (Li, Na, Mg, Ca) and 32 NH3 molecules. Thelocation of the electron donor atom is highlighted in red. Note that allsimulated systems were neutral, because the metals were supplied asatoms, rather than as cations.

Table 1. Simulated Systems and Their Parameters

systemno. metala

no. of NH3molecules

no. ofelectrons

no. ofexplicitelectrons

boxvolume(Å3)

sidelength(Å)

1 Li 32 323 257 1253 10.782 Na 32 331 257 1289 10.883 Mg 32 332 258 1292 10.894 Ca 32 340 264 1328 10.995 Li 72 723 577 2803 14.10

aIn each case, there was one metal atom.

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The plane-wave energy cutoff was set to 400 eV for chargecomputation and to 250 eV for MD simulations. The systemswere gradually heated from 0 to 250 K by the conventionalvelocity rescaling procedure. The production MD runs wereperformed with an integration time step of 0.5 fs. Every systemwas simulated for 10.0 ps after equilibration to recordmolecular trajectories for further processing.Partial electronic charges were computed following the Bader

partitioning scheme46,47 that is part of the quantum theory ofatoms in molecules. The definition of an atom is drawn purelyfrom the charge density distribution. In typical molecularsystems, charge density reaches a minimum between atoms.This minimum is considered to be a natural place to separateatoms from each other. The radial distribution function (RDF)shows the extent to which the local density at a giveninteratomic distance exceeds the average density with respect toa certain atom type. The cumulative coordination number(CCN) indicates how many solvent molecules are locatedwithin a certain radius of the solute particle. The CCN isproportional to the integral of the RDF taken from zero to thegiven distance. The mean-squared displacement (MSD)characterizes the mobility of particles in the infinite system.The slope of the MSD with respect to the time axis providesthe diffusion coefficient, D, numerically. The Visual MolecularDynamics (VMD) package48 was used for the preparation ofmolecular images.

■ RESULTS AND DISCUSSIONFigure 2 shows partial electron charges (deficient electrons) oneach metal atom. Because of their smaller sizes and, hence,

higher electron densities, smaller atoms (Li, Mg) are strongerelectron donors. Larger atoms (Na, Ca) are somewhat weakerelectron donors, although the difference is not dramatic. Thealkaline earth elements tend to form doubly charged cations.Therefore, they donate two electrons (1.58−1.65e), and thesolvated-electron concentration is higher in the cases of Mg andCa. The electron deficiencies per equivalent of donatedelectron, defined to be 1 for Li and Na, and 2 for Mg andCa, are very similar. Interestingly, the observed trend inelectron deficiency down a column of the periodic table doesnot follow the corresponding trend in the ionization potential,as one might expect. Na and Ca are less electron deficient thanLi and Mg, respectively, even though they should ionize moreeasily. This effect arises because smaller ions are capable ofinteracting with solvent molecules more strongly. A strongerdonor−acceptor interaction facilitates greater electron transfer.The solvated electron has to be shared between the solute

and the solvent to exist in equilibrium. The ammonia molecule

is a pyramid, with the nitrogen atom constituting one of thevertices. Because nitrogen is more electronegative thanhydrogen, ammonia coordinates the cations through thenitrogen atom. Figures 3 and 4 report the average numbersof valence electrons on the individual ammonia molecules.

The single solvated electron present in the alkali metalsystems is distributed relatively uniformly among thesurrounding NH3 molecules (two solvation shells). This resultis rather surprising, as the ammonia molecules of the firstsolvation shell (FSS) could be expected to obtain systematicallymore electron density. However, Figure 3 demonstrates thatthe numbers of electrons localized on all ammonia moleculesare quite similar, irrespective of the solvation shell. Thesituation is different in the case of the alkaline earth metals(Mg, Ca; see Figure 4). Some solvent molecules accommodatemore electron density than others. Detailed analysis of thelocations of these atoms revealed that many of them belong tothe FSS of the metal atoms. Therefore, larger numbers ofelectrons favor less uniform distributions. One can expect thatthe same impact would be achieved with a high concentrationof alkali atoms in the simulations, because more electronswould be solvated, leading to higher concentrations of excesselectrons.Table 2 presents the standard deviations of the electron

charges on the solvent molecules surrounding the four metalatoms. The standard deviations characterize how evenly thecharge is spread within the solvent. The data support ourconclusion that the solvated electron is spread more uniformlyin the alkali metal systems than in the alkaline earth systems.For instance, the data in Table 2 show that the charge is

Figure 2. Deficient electrons on the metal atoms in the equilibratedsystems. The analysis was performed following the Bader algorithm.

Figure 3. Excess negative charge localized on each ammonia moleculein the alkali metal systems: Li, red solid line; Na, green dashed line.Some strongly charged NH3 molecules belonging to the first solvationshell (FSS) of the metal atom are denoted by FSS. The results aregiven in electron charges, qe = −1.602 × 10−19 C.

Figure 4. Excess negative charge localized on each ammonia moleculein the alkaline earth metal systems: Mg, red solid line; Ca, greendashed line. Some strongly charged NH3 molecules belonging to thefirst solvation shell of the metal atom are denoted by FSS. The resultsare given in electron charges, qe = −1.602 × 10−19 C.

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delocalized most evenly in the case of Na and least evenly in thecase of Ca, the difference being a factor of 2.The behaviors of the solvated electrons in the studied

systems can be rationalized further in terms of structuralproperties, such as RDFs (Figures 5 and 6). The metal atoms

are strongly coordinated in the NH3 solutions, which is inagreement with their ionization upon the liberation of thesolvated electrons. When the solvated electron is cleaved, theinteraction between the metal and NH3 becomes predom-inantly electrostatic, especially in the case of the alkaline earthmetals. The position of the first peak in the metal−nitrogenRDFs is in line with the ion charge and the empirical atomiccovalent radii, as published by Slater:49 r(Li) < r(Mg) < r(Na)= r(Ca). In turn, the height of the first peak is largely influencedby the charge acquired by the metal (Figure 2). The highestpeak is that of Mg, at 16 units, whereas Li and Ca exhibit similarheights of 11−12 units. Despite having equal atomic radii, theRDF peak for Mg−NH3 appears at somewhat smaller distancesthan that for Ca−NH3. This should be understood as a result of

stronger Mg−NH3 binding, as suggested by the larger height ofthis peak. Solvation of Na in NH3 is weakest, 7 units, accordingto the MD simulations, although the solvated electron isclassically known to exist in this system. It is easy to see that thedeficient electrons (Figure 2) do not directly correlate with theRDFs. The second peaks are located within 0.4−0.5 nm, but arenevertheless quite modest, ca. 2 units. We suppose that thesepeaks are properly pronounced at somewhat lower temper-atures, such as 200−230 K. Our simulations were performed at250 K, which is slightly above the normal boiling point of pureammonia. Note that metals decrease this boiling point, so thesimulations were likely done for pressures of metal−ammoniasystems below 1 bar. The simulations at relatively hightemperature were carried out to accelerate the dynamics inthe investigated systems.The effect of the metal atom on the structure of NH3 in its

first and second solvation shells (Figure 6) is insignificant. Thefirst peaks located between 0.32 and 0.35 nm (in perfectagreement with the van der Waals diameter of nitrogen) arebroadened. The second peaks are absent. This sort of RDFconfirms that the MD simulations were performed with goodaccuracy, because the results are well expected bothqualitatively and quantitatively.As is known classically, cations exhibit coordination numbers

of either four or six depending on their size, charge, and solventnature. Figure 7 shows that both ionized alkali atoms are

coordinated by four NH3 molecules. In turn, Mg and Ca arecoordinated by six NH3 molecules. Therefore, charge plays amajor role in this case. This observation is also important toshow that the behaviors of the chosen metal atoms in theammonia solution are similar to the behaviors of thecorresponding cations. Note that the FSS is better defined inthe case of Li and Mg, because cumulative coordinationnumbers do not grow until the first minimum in the RDF(Figure 5).The dynamics of the ions and molecules (Figure 8) in

solution constitutes a fine tool that characterizes the structureand solvation in general very well. Stronger solvation impliesslow dynamics of the solvation shells. In addition, the shape andmass of the cation are important. The least mobile NH3molecules are observed in the lithium solution. The fastestNH3 molecules are in the sodium and magnesium solutions.Ionized magnesium and its solvation shell are unexpectedlymobile, likely because of the low atomic mass of Mg. It isnoteworthy that Mg is more mobile than Ca, with diffusioncoefficients of 3.2 × 10−9 versus 1.4 × 10−9 m2 s−1, respectively.Although Mg is lighter than Ca, 24 versus 40 amu, Mg bindsNH3 more strongly. Because the solvent molecules in the Mgshells are somewhat less mobile than those in the Ca shells, we

Table 2. Standard Deviations in the Charges Localized onAmmonia Molecules in the Four Metal Systemsa,b

metal atom σ (×10−2e)

Li 0.13Na 0.10Mg 0.17Ca 0.20

aResults are given in electron charges, qe = −1.602 × 10−19 C. bThethreshold for a molecule to be considered charged was set to 0.03e inthe systems with Li and Na, which donate one electron, and to 0.06ein the systems with Mg and Ca, which donate two electrons. Thesevalues were chosen to be commensurate with thermal fluctuations ofthis property.

Figure 5. Metal−nitrogen radial distribution functions depending onthe electron donor, as indicated in the legend.

Figure 6. Nitrogen−nitrogen radial distribution functions in differentsystems, as indicated in the legend.

Figure 7. Cumulative coordination numbers of the electron donorswith respect to NH3 molecules.

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assume that NH3 becomes slower as a result of strong bindingto the cation.It should be noted that pure density functionals of the type

used in the present work tend to delocalize electrons.Compared with an extra electron in a pure solvent, forinstance, the problem is not particularly strong in the presentsystems, because the solvated electrons are localized byinteraction with the metal cation. To test this known pitfallof pure DFT, we computed the electron distribution within theNH3 molecules (Figure 9) using Møller−Plesset perturbation

theory of the second order and the 6-311++G** split-valencetriple-ζ basis set. Figure 9 demonstrates that the solvatedelectron is shared by six NH3 molecules. The partial charges inthe case of the positively charged magnesium cation arecompletely uniform. This result agrees with the correspondingdata from Figure 4. Figure 4 shows that the ammonia moleculesin the first solvation shell are more electron-rich than otherammonia molecules. It also shows that the NH3 molecules inthe FSS have comparable charges (see points denoted FSS inthe plot). The central panel of Figure 9 shows a similardistribution of charges. The left panel of Figure 9 demonstratesthat NH3 molecules are much more electron-rich in the absenceof the metal cation and that the variation in the charges on theindividual NH3 molecules is greater.Because the excess electron contributed by the metal atoms

is significantly delocalized, especially for the alkali metals, it isappropriate to investigate the dependence of the results on the

size of the simulation box. By increasing the box size, one bothcreates an opportunity for electron localization due to thepresence of a larger number of solvation shells and increasedsolvent fluctuations and heterogeneity and decreases theconcentration of solvated species. Because the simulation cellis periodically replicated in plane-wave DFT, the systems underinvestigation represent rather concentrated solutions of metalatoms. We repeated the calculation for the Li system byincreasing the amount of solvent by more than a factor of 2.Figure 10 depicts charges on solvent molecules for the

simulation comprising 72 ammonia molecules. Dilution fostersfurther electron delocalization and, therefore, increases theelectron volume. Note that the charges on the ammoniamolecules are generally smaller in the larger system (cf. Figure10 and Figure 3). The electron remains delocalized among thesolvent molecules, supporting our original conclusion.

■ CONCLUSIONSIn this article, we have reported ab initio MD simulations of Li,Na, Mg, and Ca in NH3 solutions. To our knowledge, this is thefirst systematic plane-wave DFT investigation comparing thealkali and alkaline earth metals in liquid ammonia. The metalatoms act as an electron donor, sharing electrons with thesolvent, giving rise to the so-called solvated electron. Eventhough solvated electrons were first observed in ammonia,electrons solvated by bulk water and water clusters havereceived much greater attention, as discussed in theIntroduction. Studies of the hydrated electron have revealed abroad spectrum of solvation structures, showing dependenceson temperature, cluster size, and interaction potential model,suggesting that further investigations into ammoniatedelectrons are needed. Whereas the cases of alkali atoms aselectron donors were considered before, information regardingMg and Ca is scarce, irrespective of the solvent. Having studiedthe electronic properties, we correlated them with the structureand dynamics of the solution. This work provides new insightsregarding the structure and dynamics of the solvated electrondonated by alkali and alkaline earth elements in periodicsystems.The single solvated electron present in the alkali metal

systems is distributed more or less uniformly among thesurrounding solvent molecules. Quite unexpectedly, addition ofthe second electron in the case of alkaline earth metals favors aless uniform distribution of the electron density. Lighter atoms,namely, Li versus Na and Mg versus Ca, are somewhat strongerelectron donors, which is also rather surprising, because heavieratoms in the same column of the periodic table have smallerionization potentials. The explanation for this finding resides in

Figure 8. Dynamics of NH3 and metal atoms: (left) mean-squareddisplacements (MSDs) of nitrogen atoms constituting the first twosolvation shells of the respective metal atom; (right) diffusioncoefficients, D, of the metal atoms (red solid line) and ammoniamolecules constituting the first two solvation shells of the respectivemetal atom (green dashed line). The simulations were performed at250 K.

Figure 9. Excessive/deficient electrons localized on the NH3molecules in the doubly negatively charged complex of six NH3molecules (left), in the neutral Mg(NH3)6 complex (center), and inthe Mg2+ solvation shell (right).

Figure 10. Excess negative charge localized on ammonia molecules inthe Li + 72NH3 system. The results are given in electron charges, qe =−1.602 × 10−19 C.

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the ability of the smaller atoms to interact more strongly withthe solvent molecules, creating more opportunities for donor−acceptor interactions and charge transfer.Both alkali atoms are coordinated by four NH3 molecules. In

turn, Mg and Ca are coordinated by six NH3 molecules. Chargeplays a major role in this case. The structure of the firstsolvation shell is sharpest for Mg, which has a large charge anda small radius. Li and Ca show similar solvation-shell features,whereas solvation of Na in NH3 is weakest among theconsidered metal atoms. Ionized Na exhibits a larger radiusthan Li but a smaller charge than Ca. Lighter atoms have a largeadmixture of covalence in the ionic bonds that they form withthe solvent molecules, because of wave-function overlapping.Weak solvation generally implies rapid solvation-shell dynam-ics. Indeed, the NH3 molecules of the first two solvation shellsand the metal atom itself exhibit fastest dynamics in the Nasolution. The reported results advance the understanding of thebehavior of the solvated electron in different systems, asrequired in a variety of fields, including energy storage,radiation chemistry, and organic synthesis.

■ AUTHOR INFORMATION

Corresponding Authors*E-mail: vvchaban@gmail.com (V.V.C.).*E-mail: prezhdo@usc.edu (O.V.P.).

NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTS

V.V.C. was funded through CAPES. O.V.P. acknowledgessupport from the U.S. Department of Energy (Grant DE-SC0014429).

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