Magnesium(I) - American Chemical Society

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Reductions of Oxygen, Carbon Dioxide, and Acetonitrile by the Magnesium(II)/Magnesium(I) Couple in Aqueous Media: Theoretical Insights from a Nano-Sized Water Droplet Tim-Wai Lam, Han Zhang, and Chi-Kit Siu* Department of Biology and Chemistry, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon Tong, Hong Kong SAR, P. R. China W Web-Enhanced Feature * S Supporting Information *

ABSTRACT: Reductions of O2, CO2, and CH3CN by the halfreaction of the Mg(II)/Mg(I) couple (Mg2+ + e− → Mg+•) confined in a nanosized water droplet ([Mg(H2O)16]•+) have been examined theoretically by means of density functional theory based molecular dynamics methods. The present works have revealed many intriguing aspects of the reaction dynamics of the water clusters within several picoseconds or even in subpicoseconds. The reduction of O2 requires an overall doublet spin state of the system. The reductions of CO2 and CH3CN are facilitated by their bending vibrations and the electron-transfer processes complete within 0.5 ps. For all reactions studied, the radical anions, i.e., O2•−, CO2•−, and CH3CN•−, are initially formed on the cluster surface. O2•− and CO2•− can integrate into the clusters due to their high hydrophilicity. They are either solvated in the second solvation shell of Mg2+ as a solvent-separated ion pair (ssip) or directly coordinated to Mg2+ as a contact-ion pair (cip) having the 1η-[MgO2]•+ and 1η-[MgOCO]•+ coordination modes. The 1η[MgO2]•+ core is more crowded than the 1η-[MgOCO]•+ core. The reaction enthalpies of the formation of ssip and cip of [Mg(CO2)(H2O)16]•+ are −36 ± 4 kJ mol−1 and −30 ± 9 kJ mol−1, respectively, which were estimated based on the average temperature changes during the ion−molecule reaction between CO2 and [Mg(H2O)16]•+. The values for the formation of ssip and cip of [Mg(O2)(H2O)16]•+ are estimated to be −112 ± 18 kJ mol−1 and −128 ± 28 kJ mol−1, respectively. CH3CN•− undergoes protonation spontaneously to form the hydrophobic [CH3CN, H]•. Both CH3CN and [CH3CN, H]• cannot efficiently penetrate into the clusters with activation barriers of 22 kJ mol−1 and ∼40 kJ mol−1, respectively. These results provide fundamental insights into the solvation dynamics of the Mg2+/Mg•+ couple on the molecular level. as well.22−30 Therefore, understanding the redox properties of subvalent metal ions is of fundamental importance. The actual roles of Mg(I) in chemical reactions are largely unexplored probably because detail experimental investigation of its chemical properties is challenging because of its metastable characters in condensed phases. Isolation of ions in the gas phase inside a mass spectrometer provides a great opportunity to examine the reactivity of transient intermediates on the molecular level.31−46 Although the subvalent Mg•+ is unstable in the condensed phases, gas-phase [Mg(H2O)n]•+ clusters are isolable and exhibit rich redox chemistry that has attracted much experimental47−69 and theoretical70−85 interests in the past two decades. The solvation structure of [Mg(H2O)n]•+ has been well-characterized; each cluster consists of a Mg2+ and a hydrated electron solvated out from the 3s orbital of the original Mg•+ center (reaction 1).53,77−79 The solvated electron can reduce a water molecule to liberate a hydrogen atom, leaving the hydroxide ion solvated in the cluster (reaction 2). This reduction reaction is most efficient in medium-sized

1. INTRODUCTION Magnesium (Mg), an alkaline earth metal, is one of the most abundant elements on the Earth.1,2 It is an essential element for life3−5 and plays many important structural and physiological roles in biological systems.6−8 With its lightweight and nontoxic properties, alloys and compounds of Mg can be used as biomaterials.9,10 One of the greatest applications of metallic Mg is the preparation of the Grignard reagents for organic syntheses.11 The reaction mechanism involves the ratedetermining one-electron transfer from the Mg metal to an organic halide, forming an organic radical and a magnesium(I) halide as intermediates.12−15 Mg commonly exists in the ionic form, Mg2+, at its most stable +2 oxidation state.16,17 The subvalent Mg(I) species are in general unstable and involved in reaction mechanisms as a transient intermediate. The syntheses of isolable Mg(I) compounds are challenging.18 They are usually stabilized as organometallic complexes.19,20 Chlorophylls are important natural Mg-containing organometallic complexes for CO2 fixation by plants.21 Learning from nature, complexes of many other metals are being exploited for catalytic activation of CO2 or other substrates, and their reaction mechanisms often involve the subvalent metal centers © 2015 American Chemical Society

Received: November 17, 2014 Revised: February 5, 2015 Published: March 4, 2015 2780

DOI: 10.1021/jp511490n J. Phys. Chem. A 2015, 119, 2780−2792

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The Journal of Physical Chemistry A clusters with 6 ≤ n ≤ 14.53 In this size regime, on one hand, there are a sufficient number of water molecules in the clusters to stabilize the hydrated electron, on the other hand, there are not yet too many water molecules so that the hydrated electron is still in the vicinity of Mg2+. The Lewis acidity of Mg2+ can induce the autoionization of H2O86−95 and promote the halfequation of the hydrogen atom formation (reaction 3).79 [Mg(H 2O)n ]•+ → [Mg 2 +, (H 2O)n , {e•−}]

(1)

→[Mg 2 +, OH−, (H 2O)n − w ] + H• + w H 2O

(2)

H 2O + {e•−} ⇌ OH− + H+ + {e•} → OH− + H•

(3)

were described by pseudopotentials generated using the projector augmented wave (PAW) method112,113 with the 1s, 2s2p, and 2p3s electrons treated as the valence states for H, for C, N, and O, and for Mg, respectively. A planewave basis set with a cutoff energy of 283 eV (the default value for the hardest element (i.e., oxygen) in our system) was used. In the simulations, the ionic cluster was placed at the center of a cubic supercell with a size of 20 × 20 × 20 Å3, which is around twice the size of the cluster. Monopole, dipole, and quadrupole corrections to the energy of the charged clusters were also applied for all calculations. The dynamics of the atomic nuclei were treated by the classical Newtonian mechanics and the equations of motion were integrated with a time step of 0.5 fs. The MD trajectories were simulated under either the microcanonical ensemble condition at a constant energy (NVE) or the canonical ensemble condition at a constant temperature (NVT). The temperature of the latter was controlled by a Nosé thermostat.114 Interatomic distance constraint dynamics simulations were performed using the RATTLE method.115 The spin density distribution of some geometries selected from the trajectories were calculated at the M06/6-31++G(d,p) level using the Gaussian 09 quantum chemical package.116 Some binding energies of [Mg(H2O)16]•+ toward O2, CO2, or CH3CN obtained using the geometries optimized at the M06/6-31++G(d,p) level in previous studies97,98 and the present VASP/PBE level are listed in Table S1 in the Supporting Information. The values (ΔE without zero-point corrections) obtained from these levels are in reasonable agreement. [Mg(H2O)n]+• with n = 16 was employed. This size was chosen because it is sufficiently large that the 3s electron of Mg•+ is solvated out to the outer shells of the clusters77,79 and the intracluster H2O reduction (reaction 2) is no longer efficient.53 The solvation structure of [Mg(H2O)16]+• had been well-equilibrated at the constant temperature of 300 K.79,97 In the present works, reaction dynamics of the reagent molecules, including O2, CO2, and CH3CN toward [Mg(H2O)16]+• were examined. Three to four solvation configurations together with their atomic velocities were randomly chosen from the previously equilibrated trajectories. In each of these configurations, an electron was solvated on the cluster surface with its spin density widely distributed over the second and third solvation shells of the Mg center.79 For each chosen solvation configuration, a reagent molecule was first placed at a corner of the supercell with a position of around 12 Å remote from the Mg center of the cluster. It was repeated for all eight corners of the supercell. These 24−32 initial geometries were further equilibrated at 300 K for 500 fs with the distance between the reagent molecule and Mg being fixed. Then, the distance constraint was released and an arbitrary additional translational velocity of around 9 × 10−3 Å fs−1 was applied to the reagent molecule (i.e., a kinetic energy of about 12−17 kJ mol−1) with a direction pointing toward the center of mass of the cluster. All of these MD simulations were then run for 5−10 ps under the NVE condition. With this applied “collision energy”, the reagent molecule was arriving on the cluster surface after ∼0.6 ps. The actual arrival time varied for different solvation configurations and relative orientations of the reagent molecule. Nonetheless, there was a minimum of 0.5 ps available to obtain the average properties of the systems before the actual collision. In addition, this low collision energy also had minimal effects on the solvation structures of the clusters, unless reactions

With the quite negative reduction potential of the Mg2+/ Mg•+ couple in aqueous solution (estimated to be −4.87 V),96 it is not too surprising that the gas-phase [Mg(H2O)n]•+ can reduce O2, CO2, and CH3CN to presumably form O2•−, CO2•−, and CH3CN•−, respectively.97,98 Direct integrations of the reduced products were observed for O2 (reaction 4) and CO2 (reaction 5). For CH3CN, evaporation of [CH3CN, H]• from the cluster occurred (reaction 6). O2 + [Mg(H 2O)n ]•+ → [Mg, O2 , (H 2O)n − x ]•+ + x H 2O (4)

CO2 + [Mg(H 2O)n ]•+ → [Mg, CO2 , (H 2O)n − y ]•+ + y H 2O

(5)

CH3CN + [Mg(H 2O)n ]•+ → [Mg, OH, (H 2O)n − z ]+ + [CH3CN, H]• + z H 2O

(6)

All these reactions resulted in rapid water evaporation caused by the exothermicity of the reactions.97,98 Similar reactions of these reagent molecules with the hydrated electron clusters (H2O)n•− were also observed.99−106 Fascinating redox properties of the gas-phase [Mg(H2O)n]•+ have been revealed from extensive mass spectrometric experiments. However, further investigation of the dynamics for ion−molecule reactions of the gas-phase ions is challenging. It is because they probably involve many chemical processes, such as electron and proton transfers as well as the internal energy redistribution associated with these processes, which usually proceed in subpicosecond time scale.107 They are too fast that cannot be easily resolved by mass spectrometry. Molecular modeling can provide complementary information and theoretical insights into these processes in ion−molecule reactions in the gas phase.108,109 In this work, many intriguing ultrafast redox dynamics in a model consisting of the Mg2+/Mg•+ couple and the reagent molecules (O2, CO2, CH3CN), confined in a nanosized environment in [Mg(H2O)n]•+ of size n = 16 (a size that is slightly beyond the most efficient regime for the reduction of H2O (reaction 2)), have been demonstrated by means of DFTbased molecular dynamics (MD) methods. Their reaction thermodynamics have also been revealed theoretically.

2. COMPUTATIONAL DETAILS DFT-MD simulations were performed using the Vienna ab initio molecular simulation package (VASP, version 4.6).110 The Perdew−Burke−Ernzerhof (PBE)111 generalized gradient approximation was employed for the electronic energy calculations. The nucleus-electron interactions of all atoms 2781


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solid curve shows the RDF for [Mg(H2O)16]•+ collided with the triplet O2. These RDFs were the average of all trajectories. The two distributions are almost identical, indicating that the solvation structure of the Mg center was not altered by these nonreactive collisions. In our models, the Mg center was coordinated with 5, ∼6, and ∼5 water molecules, respectively, in the first, second, and third solvation shells, which were estimated from the area integrals of the corresponding RDF peaks. The five-coordinated structure, rather than the sixcoordinated structure that is preferred for Mg2+, was obtained, suggesting that the 3s electron is partially located on the Mg center for n = 16.97 It was suggested that the reaction of O2 with gas-phase hydrated electron (H2O)n•− probably involved an intersystem crossing from the overall quartet state of the reactant (3O2 + 2 (H2O)n•−) to the overall doublet state of the product (2[O2(H2O)n]•−).100 Similar change of spin was expected for the reaction between O2 and [Mg(H2O)n]•+. In order to examine the dynamical structure of the [Mg(O2)(H2O)n]•+ product, the overall quartet state of the system of each trajectory depicted in Figure 1a was manually switched to doublet state at around 0.5−1 ps when O2 was approaching close to the cluster surface. As expected, all doublet-state systems resulted in [Mg2+(H2O)nO2•−] with the spin localized at the dioxygen forming a superoxide anion. The O−O distance was increased from its average value of 1.3 Å in the system with overall quartet state to 1.4 Å for the doublet-state system. For most of these doublet-state trajectories (Figure 2a), the resultant O2•− was rapidly integrated into the hydrogen bonding network within the beginning 1−2 ps. They formed either a solvent-separated ion pair (ssip) (blue curves) or a contact-ion pair (cip) (green curves). For ssip (Figure 2b), the RDF peaks of the Mg−O1 pair (red curve) and Mg−O2 pair (blue curve) of O2•− (O1 and O2 denoted the two oxygen atoms of O2) were centered at around 3.8 Å, which were mainly located in the second solvation shell of Mg2+ (4.1 Å, gray curve). This ssip O2•− was well-solvated at this second-shell position with a narrow distribution between 3.5 and 4.1 Å. It was obvious that cip was formed via the formation of ssip. For

occurred (vide infra). Some representative trajectories are available as Web Enhanced Objects.

3. RESULTS AND DISCUSSION 3.1. O2 + [Mg(H2O)16]•+. A total of 24 MD simulations were performed for the reaction of the low-lying triplet O2 toward [Mg(H2O)16]•+ (with the overall quartet spin state). Figure 1a depicts the time evolution of the distance between

Figure 1. (a) Time evolution of the distance between Mg and the midpoint of the two oxygen atoms of O2 for the reaction of O2 toward [Mg(H2O)16]•+ (with overall quartet spin state). All trajectories are nonreactive with O2 being rebound by the cluster surface upon collision. (b) Radial distribution function (RDFs) of the Mg−Ow pair (Ow = oxygen atoms of water molecules) for [Mg(H2O)16]•+ collided (black solid curve) or not collided (red solid curve) with O2. The area integrals for the RDFs were shown to indicate the number water molecules in each solvation shell (dashed curves). An animation of a representative trajectory is available as a Web Enhanced Object (WEOs).

Mg and the midpoint of the O−O bond of O2 for all trajectories. All of them were nonreactive; i.e., O2 was immediately reflected by the cluster surface after the ion− molecule collision. Figure 1b shows the radial distribution functions (RDFs) of the Mg−Ow pair (where Ow denoted the oxygen atom of the water molecules). The red solid curve shows the RDF for the equilibrated [Mg(H2O)16]•+. The black

Figure 2. (a) Time evolution of the distance between Mg and the midpoint of the two oxygen atoms of O2 for the reaction of O2 toward [Mg(H2O)16]•+ (with overall doublet spin state). Solvent-separated ion pair (ssip) (blue), contact-ion pair (cip) (green), or evaporation of neutral HO2• (red) were observed. (b and c) RDFs of the Mg−O pair for the oxygen atoms of O2 (O1, red; O2 blue) and the oxygen atoms of water (Ow, gray) were obtained using the geometries from the last 4 ps of the trajectories corresponding to ssip and cip. The area integrals of the RDF of the Mg−Ow pair (gray dashed curves) are shown to indicate the number of water molecules in each solvation shell. Snapshots for both ssip and cip of Mg2+(O2)•−(H2O)16 are shown. The spin density distributions are shown with an isovalue of 0.015. An animation of the representative trajectory each for the formation of ssip and cip is available as WEOs. 2782


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Figure 3. RDFs (solid curves) and their area integrals (dashed curves) for the distance between the two oxygen atoms of O2•− (O1, blue; O2, red) and all hydrogen atoms in the doublet MD trajectories. The RDFs were obtained using geometries in five different time intervals, each with 1 ps duration.

Figure 4. (a) Time evolution of the Mg−C distance for the reaction of CO2 toward [Mg(H2O)16]•+. Effective collisions resulted in either solventseparated ion pair (ssip) (blue) or contact-ion pair (cip) (green). Ineffective collisions included CO2 being weakly solvated on the cluster surface (red) or directly reflected from the cluster (magenta) within the 5 ps simulation time. (b) and (c) RDFs for the Mg−CO2 (black, solid), Mg−OCO (O1, red solid; O2, blue solid), and Mg−Ow (gray) pairs obtained from the last 4 ps of the trajectories corresponding to ssip and cip. The area integrals of the RDF of the Mg−Ow pair (gray dashed curves) are shown to indicate the number of water molecules in each solvation shell. Snapshots for the ssip and the cip of Mg2+(CO2)•−(H2O)16 are shown. The spin density distributions are shown with an isovalue of 0.015.

cip (Figure 2c), one oxygen atom of O2•− was directly coordinated to Mg2+ (RDF peaks at ∼2.1 Å) and another oxygen atom of O2•− was located between the first and second solvation shells (RDF peaks at ∼3.0 Å), forming a 1η-[MgO2]+• coordination mode. Snapshots of the ssip and the cip of Mg2+(O2)•−(H2O)16 are shown in Figure 2. The exothermicity of the reaction warmed up the clusters significantly and could evaporate 0−3 water molecules during the present 5 ps simulation time. (Note: the atomic positions and velocities were preserved during the present manual switched of spin when O2 was approaching close to the cluster surface. However, at these times, the original quartet states were already higherlying than the doublet states. These energy differences of ca. 42 ± 17 kJ mol−1 (38 ± 19 kJ mol−1, evaluated by single-point calculations at the M06/6-31++G(d,p) level) were not deposited back to the clusters and they would be sufficient to evaporate one more water molecule.) The reaction also significantly changed the solvation structures, especially the third solvation shell (gray curves in Figure 2, parts b and c). For ssip, the third solvation shell was shifted from around 5 (Figure 1b) to 5.7 Å (Figure 2b). More pronounced effect was observed for cip (Figure 2c) in which the third solvation shell, approximately at 6.3 Å, was diffuse and not well-defined. On average, there were lesser water molecules in the first solvation shell of the Mg center for cip as compared with the case of ssip. It is probably because the first solvation shell in cip was crowded by O2•−. Similar inner-shell crowding effects were also

observed for Mg2+ hydrates.117 Photodissociation experiments and ab initio calculations suggested that the bare [MgO2]•+ ion has a Mg2+O2•− character having a 2η-[MgO2]+• coordination mode with the C2v symmetry.118,119 However, an initial geometry having the [2η-[MgO2]+•(H2O)16] structure converted back to the [1η-[MgO2]+•(H2O)16] structure in a MD simulation at 300 K, suggesting that O2•− was preferentially solvated by the water molecules rather than being coordinated to the Mg2+. Some doublet-state geometries of both ssip and cip with their spin manually switched to the quartet state resulted in much higher energies by 4.2 ± 0.3 and 4.0 ± 0.3 eV, respectively (or 4.8 ± 0.4 and 4.6 ± 0.2 eV, evaluated at the M06/6-31++G(d,p) level). MD simulations for the quartet state of these selected geometries underwent spontaneous cleavages of the O−O bond. These results further confirmed that the doublet state of [Mg(O2)(H2O)16]•+ is predominant under thermal conditions. The solvation dynamics of O2•− was further analyzed by monitoring the distance between its two oxygen atoms and their surrounding hydrogen atoms in five successive time intervals (Figure 3). In the time interval of 0−1 ps, O2•− was initially generated on the cluster surface and stabilized by protonation to form HO2•, indicated by the RDF peaks centered at around 1.1 Å. Summing the area integrals of the RDF peaks from 0.9 to 1.3 Å for both O2•− oxygen atoms yielded a value of around 0.5. This means that approximately 50% of O2•− were in the form of HO2• within the beginning 1 2783


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Figure 5. Time evolution of the temperature of the systems (red) and the OCO angle of CO2 (black) for the typical trajectories corresponding to (a) the nonreactive collision, (b) the formation of ssip, and (c) the formation of cip. The first vertical dashed line marked the approximate time at which CO2 had approached the cluster surface. The second vertical dashed line marked the approximate time at which CO2 had begun to leave the cluster for the nonreactive trajectory or at which ssip or cip were well established and remained intact throughout the remaining time of the trajectories. An animation each for these three trajectories (for parts a, b, and c) is available. Spin-density distributions of the snapshots are shown with an isovalue of 0.005.

ps after the electron transfer. A HO2• loss was observed in 3 out of the 24 trajectories (the red curves in Figure 2a). This result suggests that, in addition to the major H• loss of [MgOH(H2O)n]•+ (reaction 2),97 HO2• loss may also be a minor reaction channel contributing to the formation of [MgOH(H2O)n]+. The total area integral of the RDF peaks centered at 1.1 Å in Figure 3 dropped gradually with time to the value of less than 0.2 at the end of the simulation (i.e., 4−5 ps). By contrast, the areas of the RDF peaks centered at around 1.6 Å were growing with time, indicating that the hydrogen bonds around O2•− were established. The present MD simulations for the reaction between O2 and [Mg(H2O)16]•+ demonstrated that the overall doublet spin state of the system is required. Under such condition, O2 captures the hydrated electron spontaneously and initially forms O2•−. Then, it is stabilized by protonation to form the neutral HO2•, which can either evaporate from the cluster or integrate into the hydrogen bonding network. Majority of HO2• is being solvated into the cluster. The subsequent deprotonation of HO2• regenerates O2•− that is stabilized by hydrogen bonds to form ssip or to further coordinate to the Mg2+ center yielding cip having the 1η-[MgO2]+• coordination mode. 3.2. CO2 + [Mg(H2O)16]•+. Similar NVE collisional MD simulations for the reaction of CO2 toward [Mg(H2O)16]•+

were also performed. The time evolutions of the distance between Mg and the carbon atom of CO2 during the time interval of 0−7 ps for all 32 trajectories are shown in Figure 4a (some of them were run up to 10 ps). These trajectories can be categorized into four main types: (i) formation of ssip, (ii) formation of cip, (iii) surface solvated, and (iv) nonreactive. ssip and cip Formation Trajectories. In Figure 4a, the blue and green curves show the trajectories of the formation of ssip and cip, respectively. Both Mg···CO2 and Mg···OCO distances in the ssip of [Mg(CO2)(H2O)16]•+ were widely distributed between 3.5 and 5.5 Å, which were in the second or even third solvation shells of the Mg2+ center (Figure 4b). The third solvation shell of Mg2+ was also shifted to longer Mg−Ow distance with its RDF peak centered at 5.5 Å (Figure 4b), however, this shift was less pronounced than that in the case of [Mg(O2)(H2O)16]•+. The formation of cip by coordinating one oxygen atom of the solvated CO2•− to the first solvation shell of Mg2+ was observed in three trajectories, indicated by the RDF of the Mg−O pair peaked at 2.1 Å (Figure 4c). Another oxygen atom of CO2•− was approximately located at the second solvation shell with the Mg···OCO distance distributed between 3 and 4.5 Å, forming a 1η-[MgOCO]•+ coordination mode. Similar to [Mg(O2)(H2O)16]•+, a geometry of [Mg(CO2)(H2O)16]•+ having the possible 2η-[MgOCO]•+ coordi2784


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The Journal of Physical Chemistry A nation mode, as suggested for [Mg(CO2)n]•+,33,35 converted back to [1η-[MgOCO](H2O)16]•+ in a MD simulation at 300 K. The 1η-[MgOCO] is also a common coordination mode of Mg2+ with carboxylates in condensed phases and protein structures120,121 probably due to the presence of hydrates around the Mg2+ ion.39 From the RDF of the Mg−Ow pair, the solvation shell of Mg2+ in cip of [Mg(CO2)(H2O)16]•+ was less structured indicated by its more diffuse third solvation shell. Snapshots for the ssip and cip of Mg2+(CO2)•−(H2O)16 are shown in Figure 4. The spin is mainly localized on the carbon atom of CO2•−. The OCO angles averaged from the last 4 ps of the trajectories were 132° (standard deviation =4°) and 133° (standard deviation =3°) for ssip and cip, respectively, indicating that the structures of CO2•− formed in both solvation modes were very similar. The H2O evaporation was only occurred in one of these trajectories, indicating that the reaction with CO2 is milder than that with O2. Careful visual inspection for each of the trajectories found that CO2H• could be formed but with much lower statistical significance as compared with the case of the formation of HO2• as shown in Figure 3. Surface-Solvated and Nonreactive Trajectories. The surface-solvated trajectories are shown as the red curves in Figure 4a. In these trajectories, CO2 was mainly interacting weakly on the cluster surface during the first 7 ps. All (but two) of these surface-solvated structures eventually converted into ssip within the 10 ps simulation time. There were total 15 nonreactive trajectories (magenta curves in Figure 4a) in which CO2 was reflected by the clusters upon collisions, similar to the nonreactive triplet O2 collisions as shown in Figure 1a. In the surface-solvated and nonreactive trajectories, CO2 was remaining in its linear neutral structure with its average bond angles of 174 and 175°, respectively (both with a standard deviation of 3°). They were only slightly smaller than 180° caused by its bending vibrational mode.122,123 Although there were only 32 trajectories simulated and these MD simulations only reflected a narrow range of collision conditions (i.e., CO2 was colliding to the single-sized [Mg(H2O)16]•+ with a very soft translational kinetic energy of ∼15 kJ mol−1), they clearly demonstrated that the reactions are very efficient. The reduction of CO2 was observed in 16 trajectories (i.e., 50%) and they produced CO2•− that was coordinated to Mg2+ either as ssip (13 trajectories) or cip (3 trajectories) at the end of the simulations (7−10 ps). The branching ratios were qualitatively reasonable, albeit probably not quantitatively reliable. Direct occurrence of these reaction channels in our MD trajectories under the adiabatic conditions allows us to further analyze their electron transfer processes and thermodynamics. Electron-Transfer Reaction and Its Thermodynamics. Figure 5 shows the evolution of the temperature of the systems and the OCO angle of CO2 of the representative trajectory for (a) the nonreactive collision, (b) the formation of ssip, and (c) the formation of cip. The first vertical dashed line on each panel marked the approximate time at which CO2 had just arrived on the cluster surface. For the nonreactive trajectory (Figure 5a), CO2 was staying on the cluster surface for a short period of time before it began to leave the cluster at the time marked with the second vertical dashed line. A similar behavior, but at different times, was also observed for all other nonreactive trajectories as shown in Figure 4a. The OCO angle was oscillating about its average value of 175° and there was no apparent change in temperature during the entire simulation.

For the formation of ssip (Figure 5b) and cip (Figure 5c), when CO2 had just arrived on the cluster surface (also marked with the first vertical dashed line), during the subsequent ∼0.5 ps its OCO bending motion was apparently excited and the temperature of the system was initially decreasing. This cooling effect may be a sign of an activation energy needed for the OCO bending excitation. After this excitation period, a noticeable rise in temperature was observed when CO2 was further bent and vibrating approximately between 120° and 140°, signifying the reduction of CO2 to CO2•−. The second vertical dashed line in Figure 5, parts b and c, marked the times at which ssip and cip were well established and remained intact throughout the remaining time of the trajectories. These results were consistent with similar MD studies for the reaction between (H2O)n•− and CO2.122,124 Figure 5 also displays the spin-density distribution for the snapshots taken approximately at the time when CO2 had just arrived the cluster surface. For the snapshot of the nonreactive trajectory, CO2 was distant from the water molecules solvating the excess electron. For those snapshots for the formation of ssip and cip, CO2 was apparently closer to that electron. A detail analysis for the electron-transfer processes averaged from all trajectories is shown in Figure 6. The position of the

Figure 6. Time evolution of the Mg−C distance and the distances between the center of mass of the spin density and Mg (Mg-e) or C (C-e) for the trajectories corresponding to the formation of ssip and cip for the reaction of [Mg(H2O)16]•+ toward CO2. The horizontaldotted lines indicate the distances of Mg−C (black), Mg-e (red), and C-e (blue) for the nonreactive trajectories within ±0.1 ps of the time at which CO2 was closest to the cluster surface.

electron was first located that was defined by the center of mass of the spin density.79 Then the distances from this electron position to Mg (Mg-e) and C (C-e) as well as the Mg−C distance were determined and represented in Figure 6 by red, blue, and black colors, respectively. For each nonreactive trajectory, the distances of Mg-e, C-e, and Mg−C in 9 snapshots (each with 0.025 ps apart) within 0.2 ps time interval about the time at which CO2 was closest to the cluster surface were first determined. These distances for all nonreactive trajectories were then averaged and illustrated as the horizontal-dotted lines in Figure 6. The average Mg-e distance is 3.5 Å (standard error = 0.1 Å). The average Mg−C distance (5.8 Å, standard error = 0.3 Å) is shorter than the average C-e distance (6.2 Å, standard error = 0.4 Å), indicating that CO2 was not directly heading to the hydrated electron 2785


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The Journal of Physical Chemistry A when they came close to each other; it is natural that the electron transfer was not efficient in these trajectories. Figure 6 also shows the evolution of the Mg-e, C-e, and Mg− C distances for the reactive trajectories in the period from 1.0 ps before to 0.4 ps after CO2•− had completely formed. To obtain these plots, these distances in 10 snapshots (each with 0.01 ps apart) within a time interval of 0.1 ps along each trajectory were determined and averaged. Then, at a particular time interval, the values from all trajectories corresponding to the formation of ssip (solid curves) and cip (dashed curves) were further averaged. The standard error of each average distance is shown as its error bar in Figure 6. It is obvious that the C-e distances were decreasing when CO2 was approaching to the Mg center. In the period from −1.0 to −0.4 ps, the electron transfer had not begun. It can be indicated by the quite constant Mg-e distance within 3.3−3.7 Å, which is about the average Mg-e distance in the nonreactive trajectories. The Mg-e distances started to increase during the time interval between −0.4 and −0.2 ps and the C-e distances were continuously decreasing until 0 ps, signifying the electron transfer process to form CO2•−. During this process, the Mg−C distances were always longer than the C-e distances for both ssip and cip formation, suggesting that the electron-transfer reaction was effective only when the hydrated electron and CO2 were both on the same side of the Mg center. During the electron-transfer process, the Mg−C distances in the trajectories corresponding to the formation of ssip or cip were both longer than 6 Å and converged to the similar distances of ∼5 Å shortly after the electron transfer completed. These results also suggest that CO2 was reduced to CO2•− at distances remote from the Mg center and ssip was initially formed. There was no clear correlation between the electron-transfer process and the subsequent formation of ssip or cip, although the latter apparently proceeded slightly earlier in the present simulations. Comparing the average temperature difference (ΔT in K) between the beginning section (before the first vertical dashed line) and the end section (beyond the vertical dashed line) of a given trajectory of these NVE MD simulations as shown in Figure 5, the enthalpy change (ΔH in kJ mol−1) of the reaction at finite temperature could be estimated based on the equation,

Table 1. Changes in Average Temperatures (in K) and Enthalpies (in kJ mol−1) of the Reaction between CO2 and [Mg(H2O)16]•+ temperature change, ΔT/K

nonreactive formation of ssip formation of cip

enthalpy change, ΔH/ kJ mol−1

number of averages, p

mean of the averages, ΔT

standard error, sΔT/√p

mean of the averages, ΔT

standard error, sΔT/√p

15 8

−25 57

5 7

15 −36

3 4

3

48

14

−30

9

of CO2. For the formation of ssip (Figure 5b) and cip (Figure 5c), the means of the average temperature were increased by 57 ± 7 and 48 ± 14 K, respectively, which were equivalent to ΔH of −36 ± 4 and −30 ± 9 kJ mol−1. These values were comparable with the exothermic enthalpy for the reaction between CO2 and (H2O)n•− determined by nanocalorimetric experiments.102 The formation of cip was slightly less exothermic than the formation of ssip probably because the former required a larger change of solvation structure. It is consistent with the crowding effects on the inner solvation shell of Mg2+ hydrates.117 For comparison, the thermodynamics analyses for the reaction between O2 and [Mg(H2O)16]•+ were also performed. The nonreactive trajectories also resulted in the system cooling by 12 ± 4 K (or 8 ± 2 kJ mol−1). For the formation of ssip and cip of [Mg(O2)(H2O)16]•+, the enthalpy changes were estimated from the average temperature difference between the nonreactive trajectories (used as the beginning section) and the reactive trajectories (used as the end section). They were calculated to be −115 ± 8 K (or −70 ± 5 kJ mol−1) for ssip and −134 ± 36 K (or −86 ± 22 kJ mol−1) for cip. These estimated values were only qualitative because the energy differences between the quartet and doublet spin states of these systems were missing during the artificial switch of spin in the present MD studies. The reactions were expected to be more exothermic by approximately 42 ± 17 kJ mol−1, which was estimated from the energy differences between the quartet- and doublet-states at the time when the spin was manually switched. Therefore, the reaction enthalpies for the formation of ssip and cip are estimated to be −112 ± 18 and −128 ± 28 kJ mol−1, respectively. The formation of cip is slightly more exothermic than the formation of ssip, suggesting that O2•− is preferentially bound to Mg2+ in the cluster of size n = 16, consistent with the previous results obtained based on geometry optimizations at the UM06/6-31++G(d,p) level (also shown in Table S1 in the Supporting Information).97 The reaction of [Mg(H2O)16]•+ with O2 is more exothermic than that with CO2. This is also consistent with the experimental observations that the reaction rate of the former is faster.97 3.3. CH3CN + [Mg(H2O)16]•+. For the reaction between CH3CN and [Mg(H2O)16]•+, attachment of CH3CN onto the cluster by hydrogen bonds was exclusively observed for all 24 MD simulations (Figure 7a). It can be attributed to the highly polar character of CH3CN. The hydrogen-bonded CH3CN was mainly located at the second solvation shell of the Mg center or beyond with the RDF of the Mg−N pair peaked at around 4.3, 6.3, and 8.4 Å (Figure 7b). Snapshots for these structures are shown in Figure 7. No reduction of CH3CN was observed for

1 ΔH = − (DoF)R ΔT 2

where DoF is the total vibrational degrees of freedom of the system (3N − 6) and R is the gas constant (in kJ mol−1 K−1). For the nonreactive trajectories, the beginning section was the first 0.5 ps in which CO2 had not yet reached the cluster and the end section was 1 ps right after CO2 began to leave the cluster. For the formation of ssip and cip, the beginning and end sections were the first 0.5 fs and the last 4 ps of the trajectories, respectively. Only those trajectories, in which ssip or cip had been well established during the entire last 4 ps, were selected for this thermodynamics analysis. Table 1 summarizes the means of the average temperature differences (ΔT ) and their standard errors (sΔT /√p, where sΔT is the standard deviation of ΔT obtained from p numbers of trajectory) of the reaction channels. Interestingly, the nonreactive collisions resulted in a cooling of the systems by an average of 25 ± 5 K, which was equivalent to an enthalpy increase by 15 ± 3 kJ mol−1 (the standard errors were shown as the error bars). This cooling could be attributed to the energy absorbed by CO2. In other words, an enthalpy of 15 ± 3 kJ mol−1 did not provide sufficient energy to initiate the reduction 2786


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Figure 7. (a) Time evolution of the Mg−N distance for the reaction of CH3CN toward [Mg(H2O)16]•+. CH3CN could be solvated at the second (green), third (red), or higher (magenta) solvation shells. E-CH3CNH• was observed in one trajectory (blue). (b) RDFs of the Mg−N (black) and Mg−Ow (gray) pairs obtained from the last 4 ps of all trajectories. Snapshots for CH3CN being solvated in the second, third, and higher solvation shells of [Mg(CH3CN)(H2O)16]•+ are shown. The spin density distributions are shown with an isovalue of 0.005.

Figure 8. Time evolution of the NH distance (red) and the CCN angle of CH3CN (black) in the trajectory for the formation of E-CH3CNH• as shown in Figure 6a. Only the 0−2 ps of the total 5 ps were displayed. The spin density distributions of the snapshots are shown with an isovalue of 0.015. An animation for this trajectory is available as a WEO.

by the water molecules (0.5 ps) was transferred into the π* orbital of CH3CN to form CH3CN•− (1.0 ps). Subsequent proton transfer to CH3CN•− formed a vibrationally excited ECH3CNH•, which was rapidly thermalized with the water cluster within the next 0.5 ps. This E-CH3CNH• was solvated at the second solvation shell of Mg with an average Mg···N distance of 4.3 Å in the remaining simulation time (total 5 ps). This reaction was accompanied by an evaporation of one water molecule. Figure 9a shows the evolution of the electron location in this reactive trajectory during 1 ps time interval before and after the reduction of CH3CN. The electron transfer began at around 0.5 ps before it completed at 0 ps (i.e., ∼0.5 and ∼1.0 ps, respectively, in Figure 8). Similar to the reduction of CO2,

all trajectories, except one that was labeled in blue as shown in Figure 7a. In this particular trajectory, a hydrogen atom was transferred to CH3CN yielding E-CH3CNH• with an average CCN angle of 132°, which was significantly smaller than the value of 171° averaged from the other trajectories. The time evolutions of the N−H distance and CCN angle as well as some snapshots of this trajectory are shown as Figure 8. Similar to the reduction of CO2, the amplitude of the CCN bending motion of CH3CN was started to increase right after it formed a hydrogen bond with the cluster at around 0.5 ps. Reduction of CH3CN was revealed by the sharp geometrical change from its linear structure to the bent structure of CH3CN•− starting at around 1 ps. The snapshots as shown in Figure 8 also illustrated this reduction process; the electron that was originally solvated 2787


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Figure 9. Time evolution of the Mg−C distance and the distances between the center of mass of the spin density and Mg (Mg-e) or C (C-e) for the reaction of [Mg(H2O)16]•+ toward CH3CN: (a) the reactive trajectory forming E-CH3CNH•; (b, c) the nonreactive trajectories in which CH3CN formed hydrogen bonds with the water molecules in the 2nd, 3rd, or higher solvation shell of the Mg center.

products were usually formed when the Mg···N distance was just slightly shortened to 4−5 Å in the constraint MD simulations. The means of average interatomic forces between Mg and N atoms at different Mg···N distances and their standard errors are summarized in Figure 10a (the numerical values are tabulated in Table S2 in Supporting Information). Rough integrations for the interatomic forces with respect to the Mg···N distance resulted in the free energy surfaces (FESs) as shown in Figure 10b. The FES of the nonreduced CH3CN obtained from the NVT constraint MD simulations showed a local minimum at ∼4.3 Å (black curve in Figure 10b), which was consistent with the RDF of the Mg−N pair obtained from the NVE MD simulations (Figure 7b). The FES predicted that the CH3CN could directly coordinate to the Mg center with the Mg···N distance of ∼2.2 Å. This first-shell coordination mode was thermodynamically more favorable than the second-shell coordination mode by ∼5 kJ mol−1. In fact, direct binding of CH3CN to Mg2+ was experimentally observed in aqueous solution.125 However, no CH3CN was able to penetrate into the first-solvation shell of the Mg center in the NVE MD simulations (Figure 7a) probably because there was a barrier of about 22 kJ mol−1 from the local minimum at ∼4.3 Å to the local maximum at ∼3 Å. [Mg(H 2 O) 1 6 (CH 3 CN)] • + could actually exist as Mg2+(H2O)16−y(CH3CN)(H2O)y•−, illustrated by the snapshots as shown in Figure 7. Reduction of CH3CN by the hydrated electron resulted in CH3CN•−, which was followed by the rapid protonation to yield E-CH3CNH•, Z-CH3CNH•, or CH3CHN•. Penetrating these reduced products into the firstsolvation shell of the Mg center of the resulting MgOH+(H2O)15 would form the thermodynamically unfavorable first-shell coordination modes with Mg−N distance of ∼2.3 Å. These processes also required to overcome the transition states at Mg−N distance of ∼2.8−3.0 Å with barriers of ∼40 kJ mol−1, illustrated by their FESs as shown in Figure 10b. The FESs could explain why the clusters with stoichiometry of [Mg(H2O)n(CH3CN)]•+ were not observed experimentally;98 it is because CH3CN or its reduced products

CH3CN was remote from the Mg center with the Mg−C distance being ∼5.5 Å during the electron transfer process. Parts b−d of Figure 9 display the 1 ps time interval before and after CH3CN had arrived at the cluster surface and was solvated at the second, third, or higher solvation shells of the Mg center. In Figure 9b, the C-e distance was increasing once CH3CN had reached the cluster and stayed at the second solvation shell. And the hydrated electron was slightly moved closer to the Mg center. This result suggested that the hydrated electron was pushed away from CH3CN. Similar effect was also observed for CH3CN that was solvated at the third and higher solvation shells (Figure 9, parts c and d). For all trajectories as shown in Figure 7a, CH3CN was located in the outer solvation shells of the Mg center and could suppress its reduction reaction, supported by the results as shown in Figure 9. It could be attributed to the hydrophobic character of the methyl group which could presumably induce a significant change of the solvation structure if CH3CN would penetrate into the inner solvation shells. This assumption was further examined with a series of constraint MD simulations. Then 12 different solvation configurations of [Mg(H2O)16(CH3CN)]•+ with the Mg···N distance of 5 Å were selected. This distance represented the least probable solvation configuration of CH3CN which was located between the first and second solvation shells of the Mg center (Figure 7b). For each of these 12 initial geometries, a 5 ps MD simulation at 300 K (NVT) was performed with the Mg···N distance being fixed at 5.0 Å. Then, more MD simulations were run with the Mg···N distance fixed at other values, including 4.5, 4.0, 3.5, 3.0, 2.5, 2.3, and 2.2 Å. Before the actual 5 ps MD run for each of these constraint distances, a short (1 ps) MD simulation annealed from a higher temperature back to the target 300 K was first performed, in order to minimize the hysteresis effect arising from the simulation of the previous Mg···N distance. Among all these 96 constraint MD simulations (12 selected geometries each with 8 different Mg−N distances), the nonreduced CH3CN and the three isomers of the reduced E-CH3CNH•, ZCH3CNH•, and CH3CHN• were all observed. The reduced 2788


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hydrogen bonding network. They can be coordinated to Mg2+ in its first solvation shell as the contact-ion pair (cip), forming the 1η-[MgO2]•+ and 1η-[MgOCO]•+ coordination modes, or solvated in the second solvation shell as the solvent-separated ion pair (ssip) with the third solvation shell being significantly shifted to the longer Mg−Ow distances. The reaction enthalpies of the formation of ssip and cip of [Mg(CO2)(H2O)16]•+ are −36 ± 4 kJ mol−1 and −30 ± 9 kJ mol−1, respectively. The values for the formation of ssip and cip of [Mg(O2)(H2O)16]•+ are also estimated to be −112 ± 18 kJ mol−1 and −128 ± 28 kJ mol−1, respectively. The efficient integration of O2•− and CO2•− into the cluster is probably attributed to their high hydrophilicity. The nonreduced CH3CN and the reduced [CH 3 CN, H]• products, such as E/Z-CH 3 CNH • and CH3CHN•, are hydrophobic that cannot efficiently penetrate into the clusters with barriers of 22 kJ mol−1 (for CH3CN) and ∼40 kJ mol−1 (for [CH3CN, H]•). These results might suggest that the reduction of O2, CO2, and CH3CN by the Mg2+/Mg•+ couple in aqueous media interfacing with hydrophobic solvents would initially generate HO2•, CO2H• (with lesser extent) and E/Z-CH3CNH• or CH3CHN•, which would be dissolved in the hydrophobic layers (i.e., the vacuum in the present studies). In more hydrophilic environments, O2•− and CO2•− will be formed in the vicinity of the Mg2+ hydrates.

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Figure 10. (a) Interatomic forces between Mg and N. The data were obtained from a series of constrained MD simulations at 300 K under the NVT conditions with the Mg−N distance being fixed at various values. The data points were the mean of average forces obtained from several trajectories with the standard errors being shown as the error bars (Note: some of the standard errors were not clearly seen because their values were too small that the error bars were masked by the labels of the data point). The detail numbers were summarized in Table S1 in the Supporting Information. (b) Free energy surfaces were obtained from the rough integrations of the forces with respect to the Mg−N distance (Note: the FESs obtained in the present integration do not represent the relative energy among different isomers. The FES of each isomer is independently relative to its energy at the Mg···N distance of around 5 Å.).

ASSOCIATED CONTENT

S Supporting Information *

Some binding energies of [Mg(H2O)16]•+ toward O2, CO2, or CH3CN (Table S1) and the numerical data for Figure 10 (Table S2). This material is available free of charge via the Internet at http://pubs.acs.org. W Web-Enhanced Feature *

Animations of some representative trajectories as shown in Figures 1, 2, 5, and 8 are available in the HTML version of the paper.

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AUTHOR INFORMATION

Corresponding Author

would preferentially stay on the cluster surface and easily evaporate from the cluster. Similar mechanisms could also be expected for the reaction of CH3CN toward (H2O)n•−.104

*(C.-K.S.) Fax: (+) 852-3442-0522. E-mail: [email protected]. hk. Notes

4. CONCLUSIONS Reductions of O2, CO2, and CH3CN by the half-reaction of the Mg2+/Mg•+ couple confined in a nanosized water droplet, [Mg(H2O)16]•+, had been examined by DFT-MD methods. Many intriguing aspects of the reaction dynamics within several picoseconds or even in subpicoseconds have been revealed. For the reduction of O2, an overall quartet spin state of the system is nonreactive, and the high reactivity of the overall doublet spin state has been demonstrated, as also suggested in earlier experimental studies.100,101 For the reduction of CO2 and CH3CN, the electron transfer processes are facilitated by the bending vibrations with respect to the OCO and CCN angles, respectively, and complete within 0.5 ps. The reduced O2•− and CH3CN•− are spontaneously stabilized by protonations, forming HO2• and [CH3CN, H]•. Similar protonation of the initially formed CO2•−, yielding CO2H•, was also observed but with much lower statistical significance. The present MD studies illustrated that these protonation processes are preferentially occurred on the cluster surface. Unlike the nonreactive collisions that do not alter the solvation structures of the Mg center, O2•− and CO2•− can be integrated into the

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial supports from Research Grants Council, Hong Kong Special Administrative Region (the General Research Fund, Grant Number: CityU 102911) and City University of Hong Kong (Grant Number: 7004211) are gratefully acknowledged. We sincerely thank Prof. Dr. Martin K. Beyer for many inspiring discussions.

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REFERENCES

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