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Electron Solvation in Liquid Ammonia: Lithium, Sodium, Magnesium, and Calcium as Electron Sources Vitaly V. Chaban, and Oleg V. Prezhdo J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.6b00412 • Publication Date (Web): 17 Feb 2016 Downloaded from http://pubs.acs.org on February 20, 2016

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The Journal of Physical Chemistry

Electron Solvation in Liquid Ammonia: Lithium, Sodium, Magnesium, and Calcium as Electron Sources Vitaly V. Chaban1,* and Oleg V. Prezhdo2,* 1

Instituto de Ciência e Tecnologia, Universidade Federal de São Paulo, 12231-280, São José dos

Campos, SP, Brazil 2

Department of Chemistry, University of Southern California, Los Angeles, CA 90089, USA

Abstract. A free electron in solution, known as the solvated electron, is the smallest possible anion. Alkali and alkali earth atoms serve as electron donors in solvents that mediate outersphere electron transfer. We report ab initio molecular dynamics simulations of lithium, sodium, magnesium and calcium in liquid ammonia at 250 K. By analyzing electronic properties, ionic and solvation structure and dynamics, we systematically characterize the above metals as electron donors and ammonia molecules as electron acceptors. We show that the solvated metal strongly modifies the properties of its solvation shells, and that the observed effect is metal specific. Herewith, the radius and charge exhibit a major impact. The single solvated electron present in the alkali metal systems is distributed more uniformly among the solvent molecules of the metals’ two solvation shells. In contrast, alkali earth metals favor less uniform distribution of the electron density. Alkali and alkali earth atoms are coordinated by four and six NH3 molecules, respectively. Smaller atoms, Li and Mg, are stronger electron donors relative to Na and Ca. This result is surprising, since smaller atoms in a periodic table column have higher ionization potentials. It can be explained by stronger electron donor-acceptor interactions between the smaller atoms and solvent 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 in the diffusion coefficients of NH3 molecules of the first two solvation shells and the Na atom. The properties of the solvated electrons established in the present study are important for radiation chemistry, synthetic chemistry, condensed matter charge transfer and energy sources.

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Introduction The solvated electron constitutes an intriguing phenomenon that continues to draw attention since its discovery.1-17 Understanding trends and peculiarities of electron solvation in different solvents is helpful to a variety of fields, including radiation chemistry, energy storage and organic synthesis. Solvated electrons are particularly interesting in the context of electron transfer phenomena. Solvated electrons occupy spaces between solvent molecules and solute particle. While the solvated electron does not covalently bind to any of these entities, it interacts with them electrostatically. It can be said that both the solute and the solvent exhibit comparable affinities to the electron. The valence electron, therefore, obtains enough potential energy to exceed the first ionization potential of a metal. It is agreed in the community that lithium and sodium, in combination with a few types of polar solvents, can act as donors of solvated electrons. The solvents include ammonia, water, tetrahydrofuran containing organic radicals, and polyaromatic hydrocarbons.18-21 Lithium in liquid ammonia gives rise to the most known example of the solvated electron. Humphry Davy was the first to describe blue-colored solutions of alkali metals in liquid ammonia two centuries ago. A theoretical identification of the solvated electron phenomenon arrived much later. The properties of solvated electrons are still actively investigated. Modern studies address fingerprints of solvated electrons in water, ammonia, acetonitrile, biphenyl in tetrahydrofuran, and other systems.11,

13, 22-23

Existence of the solvated electron can be

hypothesized theoretically in some polar solvents, but plausible experimental evidence was not yet obtained. Schiller and Horvath24 considered a model, which consists of a Rydberg atom interacting with thermodynamic fluctuations of the medium. Applied to supercritical water and ammonia, the model provided good agreement with the experimental data. Yazami and coworkers20 reported conductivity measurements and Fourier-transform infrared (FTIR) studies on solvated


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electron solutions obtained in solutions of lithium in tetrahydrofuran with biphenyl as an electron acceptor. These authors achieved significant conductivity, 12.0 mS cm-1, using the following species ratio, n(Li) : n(biphenyl) : n(solvent)=1 : 1 : 8.2. The solutions exhibited metallic behavior. Fingerprint peaks were found in the FTIR spectra. An interesting series of studies concerning excess electrons in liquid 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 near-IR and a solvated molecular dimer anion. The latter absorbs weakly in the visible spectral region. The solvated electron is localized right after being produced, but tends to form a dimer anion later. Yoshida and coworkers25 used pulse radiolysis to study the solvated electron in alkylammonium ionic liquids. A number of cations and anions were combined to reveal effects of the ions. The absorption peak at 1100 nm in all studied ionic liquids was ascribed to the solvated electron. The reaction rate constant of the identified electron with pyrene was found to exceed viscosity-based diffusioncontrolled limits by one order to magnitude. The authors made an interesting conclusion that a macroscale viscosity of the alkylammonium ionic liquids appeared systematically higher than an effective viscosity on the molecular scale. Vertical electron binding energies were directly measured by Suzuki and coworkers for the solvated electron in methanol and ethanol.23 Timeresolved photoelectron spectroscopy at ultralow kinetic energy was applied to liquid beams of sodium iodide solutions. The solvated electron was formed from the iodide anions by charge transfer to solvent reactions. The authors concluded that the cavity radii in water and 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 the cavity created by the solvated electron depends strongly on the quantum state of the electron. The cavity is spherical in the ground state, while it is elongated in the excited state. The simulation



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showed and characterized a complex interplay between electronic and nuclear degrees of freedom, involving solvation dynamics, charge transfer, and non-radiative electronic transitions. Having studied solvated electrons in water clusters, Turi and Rossky12 identified distinct spectral signatures of electron’s surface and interior states, and concluded based on analysis of experimental data, that the electron in small water clusters is stabilized by surface-bound states. Jacobson and Herbert33 investigated temperature dependence of solvated electrons in water clusters. Having characterized four types of states, namely, dipole-bound, surface-bound, partially embedded and cavity states, they showed by extrapolation to large cluster size that electrons in very cold clusters prefer the cavity state, while warm clusters create surface-bound electron states. As the cluster size decreases, the surface bound state transforms into the partially embedded state. In addition to previously known surface and cavity states, Sommerfeld and Jordan identified a new binding motif, in which an excess electron permeates the hydrogen-bonding network. Electrostatic binding of an excess electron dominates only in the isomers with large dipole moments, whereas polarization and correlation effects prevail in all other water cluster isomers. (H2O)–12 to (H2O)–24 clusters were considered.34 Shkrob used density functional theory (DFT) calculations on the singly negatively charged water clusters (comprising 2, 8, 20, 24 molecules) to interpret solution-phase EPR/ESEEM experiments on aqueous electron.35 The majority of solvated electron studies are experimental. The current state of the ab initio methods allows one to conduct relevant simulations and to characterize the experimental results. Most ab initio simulations to-date have been performed using relatively small and typically finite systems,1, 9, 36-41 and more systematic investigations are desirable. In the present paper, we report the solvated electron in liquid ammonia, whereas its source is lithium, sodium, magnesium, and calcium (Figure 1). The calculations were implemented using ab initio molecular dynamics (MD) simulations of the neutral periodic systems powered by the plane-


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wave DFT. We investigate an effect of the solvated electron on structure and dynamics of these solutions.

Figure 1. An electronic density distribution in the equilibrated system containing a metal atom (Li, Na, Mg, Ca) and 32 NH3 molecules. Location of the electron donor atom is highlighted in red. Note that all simulated systems are neutral, because the metals were supplied as atoms, rather than as cations.

Methodology The electronic structure calculations and adiabatic molecular dynamics simulations were computed by means of the Vienna Ab initio Simulation Package (VASP).42 VASP uses pure DFT with a converged plane-wave basis set, which allows for efficient simulation of periodic (infinite) systems. A metal atom (Li, Na, Mg, Ca) was surrounded by 32 ammonia molecules maintaining the experimental density (ca. 730 kg m-3). These four systems were placed into periodic cubic cells; additionally, a larger system, comprising one lithium atom and 72 ammonia molecules, was simulated (Table 1). Metals rather than ions were added to the simulated systems as atoms, therefore neutrality of the periodic cells was preserved. Table 1. Simulated systems and their parameters # 1 2 3 4 5

Metal 1 Li 1 Na 1 Mg 1 Ca 1 Li

# NH3 32 32 32 32 72

# electrons 323 331 332 340 723

# explicit electrons 257 257 258 264 577


Box volume, Å3 1253 1289 1292 1328 2803

Side length, Å 10.78 10.88 10.89 10.99 14.10


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The generalized gradient approximation for the exchange-correlation functional proposed by Perdew, Burke, and Ernzerhof was employed,43 used in prior studies on similar systems.40, 44 The projector-augmented wave method to substitute ultrasoft pseudopotentials was used for all atoms.45 The plane-wave energy cut-off was set to 400 eV for charge computation and to 250 eV for MD. The systems were gradually heated from 0 to 250 K by the conventional velocity rescaling procedure. The production MD runs were performed with an integration time-step of 0.5 fs. Every system was simulated for 10.0 ps after equilibration to record molecular trajectories for further processing. Partial electronic charges were computed following the Bader partitioning scheme,46-47 which is a part of the quantum theory of atoms in molecules. The definition of an atom is drawn purely from the charge density distribution. In typical molecular systems, charge density reaches a minimum between atoms. The minimum is considered a natural place to separate atoms from each other. The radial distribution function (RDF) shows by how many times a local density at a given inter-atomic distance exceeds the average density, with respect to a certain atom type. The cumulative coordination number (CCN) shows how many solvent molecules are located within a certain radius from the solute particle. CCN is proportional to the integral of RDF taken from zero to the given distance. The mean-squared displacement (MSD) characterizes the mobility of particles in the infinite system. The slope of MSD to the time axis provides the diffusion coefficient, D, numerically. The Visual Molecular Dynamics (VMD) package48 was used for preparation of molecular images.

Results and Discussion Figure 2 shows partial electron charges (deficient electrons) on each metal atom. Due to their smaller size, and hence, higher electron density, smaller atoms (Li, Mg) are stronger electron donors. Larger atoms (Na, Ca) are somewhat weaker electron donors, although the


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difference is not drastic. The alkaline earth elements tend to form doubly charged cations. Therefore, they give out two electrons (1.58-1.65e), and the solvated electron concentration is higher in the case of Mg and Ca. The electron deficiencies per equivalent of donated electron, define to be 1 for Li and Na, and 2 for Mg and Ca, are very similar. Interestingly, the observed trend in the electron deficiency down a column of the periodic table does not follow the corresponding trend in the ionization potential, as one might expect. Na and Ca are less electron deficient than Li and Mg, respectively, even though they should ionize more easily. The effect arises because smaller ions are capable of interacting with the solvent molecules more strongly. A stronger donor-acceptor interaction facilitates larger electron transfer.

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

The solvated electron has to be shared between the solute and the solvent to exist in equilibrium. The ammonia molecule is a pyramid, whereby the nitrogen atom constitutes one of the vertices. Since nitrogen is more electronegative than hydrogen, ammonia coordinates the cations by the nitrogen atom. Figures 3-4 demonstrate an average number of valence electrons on the individual ammonia molecules.



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Figure 3. Excess negative charge localized on each ammonia molecule in the alkali metal systems: Li – red solid line, and Na – green dashed line. Some strongly charged NH3 molecules belonging to the first solvation shell of the metal atom are designated by FSS. The results are given in electron charges, qe = -1.602×10−19 C.

The single solvated electron present in the alkali metal systems is distributed relatively uniformly among the surrounding NH3 molecules (two solvation shells). This result is rather surprising, as the ammonia molecules of the first solvation shell (FSS) could be expected to obtain systematically more electron density. However, Figure 3 demonstrates that the numbers of electrons localized on all ammonia molecules are quite similar, irrespectively of the solvation shell. The situation is different in the case of the alkaline earth metals (Mg, Ca), Figure 4. Some solvent molecules accommodate more electron density than others. Detailed analysis of the location of these atoms revealed that many of them belong to the FSS of the metal atoms. Therefore, larger numbers of electrons favor less uniform distribution. One can expect that the same impact will be achieved with a high concentrations of alkali atoms in the simulations, because more electrons will be solvated leading to higher excess electron concentrations.


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Figure 4. Excess negative charge localized on each ammonia molecule in the alkaline earth metal systems: Mg – red solid line, Ca – green dashed line. Some strongly charged NH3 molecules belonging to the first solvation shell of the metal atom are designated by FSS. The results are given in electron charges, qe = -1.602×10−19 C.

Table 2 presents standard deviations of the electron charge on solvent molecules surrounding the four metal atoms. The standard deviations characterize how evenly the charge is spread within the solvent. The data support our conclusion that the solvated electron is spread more uniformly in the alkali metal systems than in the alkali earth systems. For instance, the data of Table 2 show that the charge is delocalized most evenly in the case of Na and least evenly in the case of Ca, the difference being a factor of two. Table 2. Standard deviations in the charges localized on ammonia molecules in the four metal systems. The threshold for a molecule to be considered charged was set to 0.03e in Li and Na systems, which donate one electron, and to 0.06e in Mg and Ca systems, which donate two electrons. These values are chosen to be commensurate with thermal fluctuations of this property. The results are given in electron charges, qe = -1.602×10−19 C. metal atom σ, 10-2 e

Li 0.13

Na 0.10

Mg 0.17

Ca 0.20

The behavior of the solvated electrons can be rationalized further in terms of structural properties, such as RDFs (Figures 5-6). The metal atoms are strongly coordinated in the NH3 solutions, which is in concordance with their ionization due to liberation of the solvated electrons. When the solvated electron is cleaved, an interaction between metals and NH3 becomes predominantly electrostatic, especially in the case of the alkaline earth metals. The ACS Paragon Plus Environment


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position of the first peak in the metal-nitrogen RDFs is in line with the ion charge and the empirical atomic covalent radii, as published by Slater:49 r (Li) < r (Mg) < r (Na) = r (Ca). In turn, the height of the first peak is largely influenced by the metal acquired charge (Figure 2). The highest peak is that of Mg, 16 units, whereas Li and Ca exhibit similar height, 11-12 units. Despite having equal atomic radii, the RDF peak for Mg-NH3 appears at somewhat smaller distances than that for Ca-NH3. This should be understood as a result of stronger Mg-NH3 binding, as suggested by a larger height of this peak. Solvation of Na in NH3 is weakest, 7 units, according to the MD simulations, although the solvated electron is classically known to exist in this system. It is easy to see that the deficient electrons (Figure 2) do not directly correlate to the RDFs. The second peaks are located within 0.4-0.5 nm, being nevertheless quite modest, ca. 2 units. We suppose that these peaks are properly pronounced at somewhat lower temperatures, e.g. 200-230 K. Our simulation was performed at 250 K, which is slightly above the pure ammonia normal boiling point. Note that metals decrease this boiling point, thus the simulations were likely done for pressures of metal-ammonia systems below 1 bar. The simulations at relatively high temperature were carried out to accelerate dynamics in the investigated systems.

Figure 5. Metal-nitrogen radial distribution functions depending on the electron donor, according to the legend.

An effect of the metal atom on the structure of NH3 in its first and second solvation shells (Figure 6) is insignificant. The first peaks located between 0.32 and 0.35 nm (in perfect ACS Paragon Plus Environment

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agreement with the van der Waals diameter of nitrogen) are broadened. The second peaks are absent. This sort of RDF confirms that the MD simulations were performed with good accuracy, since the results are well expected both qualitatively and quantitatively.

Figure 6. Nitrogen-nitrogen radial distribution functions in different systems, according to the legend.

As known classically, cations exhibit coordination numbers of either four or six depending on their size, charge and solvent nature. Figure 7 shows that both ionized alkali atoms are coordinated by four NH3 molecules. In turn, Mg and Ca are coordinated by six NH3 molecules. Therefore, charge plays a major role in this case. This observation is also important to show that the behavior of the chosen metal atoms in the ammonia solution are similar to the behaviors of the corresponding cations. Note that FSS is better defined in the case of Li and Mg, since cumulative coordination numbers do not grow until the first minima in RDF (Figure 5).



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Figure 7. Cumulative coordination number of the electron donor with respect to NH3 molecules.

Dynamics of the ions and molecules (Figure 8) in solution constitutes a fine tool that characterizes very well structure and solvation in general. Stronger solvation implies slow dynamics of the solvation shells. On top of that, the shape and mass of the cation are important. The least mobile NH3 molecules are observed in the lithium solution. The fastest NH3 molecules are in the sodium and magnesium solutions. Ionized magnesium and its solvation shell are unexpectedly mobile, likely due to a small atomic mass of Mg. It is noteworthy that Mg is more mobile than Ca, 3.2×10-9 vs. 1.4×10-9 m2 s-1. Although Mg is lighter than Ca, 24 vs. 40 a.m.u., Mg binds NH3 more strongly. Since the solvent molecules in the Mg shells are somewhat less mobile than those in the Ca shells, we assume that NH3 becomes slower due to a strong binding to the cation.


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Figure 8. Dynamics of NH3 and metal atoms: (left) mean-squared displacements (MSD) of nitrogen atoms constituting the first two solvation shells of the respective metal atom; (right) diffusion coefficients, D, of the metal atoms (red solid line) and ammonia molecules constituting the first two solvation shells of the respective metal atom (green dashed line). The simulations were performed at 250 K.

It should be noted that pure density functionals of the type used in the present work tend to delocalize electrons. Compared for instance with an extra electron in a pure solvent, the problem is not particularly strong in the present systems, because the solvated electrons are localized by interaction with the metal cation. To test this known pitfall of pure DFT, we computed electron distribution within the NH3 molecules (Figure 9) using the Møller-Plesset perturbation theory of the second order and the 6-311++G** split-valence triple-zeta basis set. Figure 9 demonstrates that the solvated electron is shared by 6 NH3 molecules. The partial charges in the case of the positively charged magnesium cation are totally uniform. This result agrees with the corresponding data from Figure 4. Figure 4 shows that the 1st solvation shell is more electron rich than other ammonia molecules. It also shows that NH3 molecules in FSS have comparable charges (see marks 'FSS' in the plot). The central panel of Figure 9 shows a similar distribution of charges. The left panel of Figure 9 demonstrates that NH3 molecules are much more electron



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rich in the absence of the metal cation, and the variation in the charges on individual NH3 molecules is greater.

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

Since the excess electron contributed by the metal atoms is significantly delocalized, especially for the alkali metals, it is appropriate to investigate the dependence of the results on the size of the simulation box. By increasing the box size, one both creates an opportunity for electron localization due to presence of a larger number of solvation shells and increased solvent fluctuations and heterogeneity, and lowers the concentration of solvated species. Since the simulation cell is periodically replicated in plane-wave DFT, the systems under investigation represent rather concentrated solutions of metal atoms. We repeated the calculation for the Li system by increasing 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 fosters further electron delocalization and, therefore, increases the electron volume. Note that the charges on the ammonia molecules are generally smaller in the larger system, cf. Fig. 10 and Fig. 3. The electron remains delocalized among the solvent molecules, supporting our original conclusion.


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.

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

Conclusions We reported ab initio MD simulations of Li, Na, Mg, Ca in NH3 solutions. To our knowledge, this is the first systematic plane-wave DFT investigation comparing the alkali and alkali earth metals in liquid ammonia. The metal atoms act as electron donors, sharing electrons with the solvent, giving rise to the name of the solvated electron. Even though solvated electrons were first observed in ammonia, electrons solvated by bulk water and water clusters received much greater attention, as discussed in the introduction. The hydrated electron studies reveal a broad spectrum of solvation structures, showing dependence on temperature, cluster size and interaction potential model, suggesting that further investigations into ammoniated electrons are needed. While the cases of alkali atoms as electron donors were considered before, information regarding Mg and Ca is scarce, irrespective of the solvent. Having studied the electronic properties, we correlate them with structure and dynamics of the solution. The work provides new insights regarding structure and dynamics of the solvated electron donated for the alkali and alkali earth elements in the periodic system. The single solvated electron present in the alkali metal systems is distributed more or less uniformly among the surrounding solvent molecules. Quite unexpectedly, addition of the second ACS Paragon Plus Environment


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electron in the case of alkali earth metals favors a less uniform distribution of the electron density. Lighter atoms, Li vs. Na and Mg vs. Ca, are somewhat stronger electron donors, which is also rather surprising, since heavier atoms down the same column of the periodic table have smaller ionization potentials. The explanation resides in the ability of the smaller atoms to interact more strongly with the solvent molecules, creating more opportunities for donoracceptor interactions and charge transfer. Both alkali atoms are coordinated by four NH3 molecules. In turn, Mg and Ca are coordinated by six NH3 molecules. Charge plays a major role in this case. The structure of the first solvation shell is sharpest for Mg, which has a large charge and a small radius. Li and Ca show similar solvation shell features, while solvation of Na in NH3 is weakest among the considered metal atoms. Ionized Na exhibits a larger radius than Li, but a smaller charge than Ca. Lighter atoms have a large admixture of covalence in the ionic bonds they form with the solvent molecules, due to wave function overlapping. Weak solvation generally implies rapid solvation shell dynamics. Indeed, NH3 molecules of the first two solvation shells and the metal atom itself exhibit fastest dynamics in the Na solution. The reported results advance understanding of the behavior of the solvated electron in different systems, as required in a variety of fields, including energy storage, radiation chemistry and organic synthesis.

Acknowledgments V.V.C. in funded through CAPES. O.V.P. acknowledges support from the US Department of Energy (Grant No. DE-SC0014429). Author Information E-mail addresses for correspondence: [email protected] (V.V.C.); [email protected] (O.V.P.)


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Electron Solvation in Liquid Ammonia - American Chemical Society

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