Competitive Interactions Within Cm (III) Solvation in Binary Water

Aug 1, 2018 - This work considers the competitive forces of ion−solvent versus solvent−solvent interactions and demonstrates that the solution str...
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Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX

Competitive Interactions Within Cm(III) Solvation in Binary Water/Methanol Solutions Morgan P. Kelley,*,†,§ Ping Yang,*,§ Sue B. Clark,†,∥ and Aurora E. Clark*,†,‡ Department of Chemistry and ‡Materials Science and Engineering Program, Washington State University, Pullman, Washington, United States § Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico, United States ∥ Pacific Northwest National Laboratory, Richland, Washington, United States Downloaded via UNIV AT BUFFALO STATE UNIV NEW YORK on August 5, 2018 at 02:04:59 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

†

S Supporting Information *

ABSTRACT: Competitive forces exist in multicomponent solutions, and within electrolytes they consist of both ion−solvent and solvent− solvent interactions. These can influence a myriad of processes, including ligand complexation. In the case of water/alcohol solutions, recent work revealed an interesting dilemma regarding the overall solution dynamics and organization as compared to solute−solvent interactions. This is particularly true for highly charged ions in solution, whose ion−solvent interactions were demonstrated to be highly sensitive to the composition of the immediate solvation environment. Faster solvent exchange should be observed about the ion, considering that second-order Møller−Plesset perturbation theory predicts an average decrease in ion-solvent dissociation energy when methanol enters the first solvation shell of Cm3+(aq). Yet the addition of methanol to water causes the dynamic features of the hydrogen-bond network of the entire solution to slow. The apparent competition between these contrary forces was examined using a combination of electronic structure calculations with both ab initio and classical molecular dynamics simulations, using binary water/methanol solutions and Cm3+ as a representative solute. This combination of theoretical methods predicts that, among the competitive effects of the solvent−solvent and ion−solvent interactions, the solution-phase dynamics imparted by the addition of methanol to water kinetically restricts the solvation exchange rates about Cm3+ in these binary solutions.

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INTRODUCTION The structural and dynamic features of ion solvation are directly related to a broad range of chemical reactions and can be singularly influenced by solution composition. This is particularly true of the highly charged ions found at the bottom of the periodic table, which cause extensive reorganization in polar solvents.1 As desolvation is often the initial step in metal complexation, even small changes in solvation structure can potentially perturb the mechanism, thermodynamics, and kinetics of complexation.2−8 Swain and co-workers have observed changes in the free energy of complexation reactions across a wide range of solvents, including that of transition metals by polyatomic anions.9 Additionally, the coordination environment of an ion clearly plays a role in ion−solvent interactions: water molecules that directly coordinate lanthanide ligand complexes have been observed to have exchange kinetics up to 2 orders of magnitude slower than in the aqua ion.10 Presumably, many of these perturbations derive from changes to the ion−solvent interaction energy as a result of the changing composition within the first coordination shell. However, cosolvents and solutes can also alter the structure and dynamics of the solution as a whole, for example, by interrupting hydrogen bonding in solutions with protic solvents.11−15 This in turn may © XXXX American Chemical Society

influence the solution-phase dynamics and presumably the solvation dynamics about the ion. As an example, methanol in water decreases the average number of hydrogen bonds per H2O by nearly 50% (1:3 CH3OH/H2O) and the average hydrogen-bond lifetime has been shown to increase.16−27 Molecular dynamics simulations have predicted that methanol as a cosolvent to water creates a more static hydrogen-bond network compared to either pure liquid. In these conditions, simulations of Na+ have exhibited significantly lengthened Na+water and Na+-methanol lifetimes (increasing by up to 200%) as the concentration of methanol is increased.14 The changes in ion−solvent lifetime were correlated to an increase in the stability of the solvent−solvent hydrogen bonds caused by the inclusion of methanol. Interestingly, this observation appears to be solely due to the solution dynamics, as the presence of methanol in the first solvation shell does not significantly alter the solvent binding energy with Na+, as evaluated via density functional theory (DFT) calculations. Yet for trivalent ions, like Cm3+, second-order Møller−Plesset perturbation theory (MP2) predicts large decreases to the ion−solvent interaction Received: May 3, 2018

A

DOI: 10.1021/acs.inorgchem.8b01214 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry energy as more methanol is included in the first solvation shell− by ∼6 kcal/mol between the Cm(H2O)8(CH3OH)3+ and Cm(H2O)(CH3OH)83+ structures.28 Given these observations, it appears that, for highly charged ions, two competing forces may alter their solvation dynamics in water/methanol solutions: one based upon changes in the ion−solvent binding energy (and presumably the exchange barrier) and the second based upon the perturbation of the solvent dynamics imparted by the methanol cosolvent. Though these competitive forces are relevant to a wide variety of industrial and analytical applications, including separations,29,30 methanol-based fuel cells,11,31 and electrospray mass spectrometry,32−35 they have not been explicitly examined in the literature. Consider that simple alcohols are cosolvents in wastes at Department of Energy sites,36 and cosolvation is known to significantly alter the behavior of environmental contaminant metals.37 Yet the extensive literature on ions in water/methanol solutions11,13,15,20−23,26,38 is largely limited to the study of singly charged ions,12,14,39−46 and significant work remains to understand the effect of water/methanol solvation about highly charged ions that may amplify the effects of cosolvation (as evidenced by the changes in ion−solvent binding energy). Herein, we focus upon Cm3+ due to the potential impact of cosolvation in nuclear wastes and reprocessing schemes. We specifically focus upon which of the competitive interactions (ion−solvent vs solvent−solvent) ends up influencing the dynamic features of the first solvation shell. It is demonstrated that in fact the solution dynamics prevail and that the ion−solvent dynamic features are retarded as the overall solution hydrogen bond dynamics slow.

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distribution of coordination numbers, the simulations used herein are instead initiated at the appropriate coordination number (CN) of 9 and have only tens of picoseconds of simulation time. This time scale is too short to have enough solvent exchange events to alter the average CN, and instead these data are used as a benchmark for the average geometry adopted by CN of 9 and the ion−solvent distances therein. These are then compared to static DFT and MP2 optimized calculations. The potential energy surface (PES) for the PBE Cm3+− OH2 interaction is shown relative to the MP2 PES, which is used to fit potentials used in the classical simulations, in Figure S7. While PBE does underestimate the interaction energy relative to MP2, the minima positions (Cm−O distances) are consistent between the two methods. The Cm3+ ion was simulated using a Troullier−Martins pseudopotential.56 An energy cutoff of 1.632 68 keV and a fake mass of 650 au with a time step of 0.157 fs were used, and trajectories were dumped every 16 timesteps. Simulation cells were equilibrated at 360 K for 2 ps, followed by 2 ps at 298.15 K. Trajectories were collected at 298.15 K in the NVT ensemble using the Nosé−Hoover thermostat.57,58 Because of the limited simulation time scales accessible to AIMD, complementary CMD simulations were performed using the DL_POLY_4 software package.59 The rigid TIP3P model for water60 and the TraPPE-UA61 methanol modelwhich models the CH3 group as a single unitwere used. Previous work has shown that TIP3P and TraPPE-UA models reproduce experimentally determined radial distribution functions for water/methanol solutions.14,62 The interatomic potentials for Cm3+ with water and methanol solvents were fit to MP2 data as described below. Cubic periodic simulation cells contained a single ion, water, and methanol, with the total number of solvent molecules fixed at 512, where the methanol content varied by mole fraction and included χCH3OH = 0, 0.25, 0.3047 (corresponding to 50% methanol by volume), 0.5, 0.75, 0.9, and 1. System details can be found in the Supporting Information, Table S1. Simulation boxes were constructed using the Packmol program54 and allowed to evolve in the NVT ensemble using the Nosé−Hoover thermostat57,58 at 360 K for 5 ns. The temperature of the thermostat was then reduced over several 1 ns simulations in increments of 10 K until 298 K was reached, at which point systems were equilibrated for a further 5 ns. Systems were then allowed to transition into the NPT ensemble and evolve for a further 10 ns, using a coupled Nosé−Hoover thermostat and barostat.63,64 The NPT and NVT ensembles were then employed in several successive 1 ns simulations to ensure they were at thermomechanical equilibrium. Production trajectories were acquired every 25 fs from separate 1 ns runs in the NVE ensemble. All simulations were run with a time step of 1 fs, an 8 Å cutoff for long-range interactions, and an Ewald summation precision of 1 × 10−10. The final equilibrium properties are reported in Table S1. Statistical errors were determined by comparison of three sets of 10 ns simulations and propagated across all 30 ns. Potential Fitting. Interatomic potentials for Cm3+ with the oxygen atoms of water and methanol were developed using force matching to the two-body dissociative PES of the solvated ion cluster and a single solvent molecule. Starting with the DFT-optimized structures of the pure water and pure methanol solvation shells [Cm(H2O)93+ and Cm(CH3OH)93+], a single solvent molecule was removed from the solvated ion in 0.1 Å increments to create the PES using MP2 with the aforementioned basis sets. At each point, the gradient and the energy were determined. A Lennard-Jones intermolecular potential between the metal ion and solvent of the form ÉÑ ÅÄÅ ÅÅij yz12 ij yz6ÑÑÑ qiqj ÅÅjj σ zz Ñ σ j z U (rij) = 4εÅÅÅjj zz − jjj zzz ÑÑÑÑ + j rij z ÑÑ 4πε0rij ÅÅj rij z ÅÅÇk { k { ÑÑÖ (1)

METHODS

Gas-Phase Electronic Structure Calculations. Solvated ion clusters of the form Cm(H2O)9−0(CH3OH)0−93+ were optimized via DFT using the hybrid B3LYP functional47,48 with an integral internal screening threshold of 1 × 10−16 and a numeric integration grid of 1 × 10−8. The Stuttgart relativistic small core pseudopotential (RSC) and its associated basis set was employed for Cm,49 while the aug-ccpVDZ basis sets were used for the water and methanol atoms. Singlepoint MP2 calculations,50 which have been shown to give more accurate hydration numbers than DFT when predicting the solvation of the Cm3+ ion,51 were used to determine the solvent dissociation energy (ΔE) of water and methanol molecules from the first solvation shell of Cm3+ using the same basis sets. All calculations were performed using NWChem.52 In cases where molecular geometries were taken from molecular dynamics simulation frames, hydrogen atoms were added to methanol (which was simulated using a united atom potential, as described below) assuming a tetrahedral geometry. These H atoms were then allowed to relax in a constrained MP2 optimization. Molecular Dynamics Simulations: ab Initio and Classical. Both ab initio Car−Parrinello dynamics (AIMD) and classical molecular dynamics (CMD) were performed to develop a robust understanding of multiple length and time scale features of the water/ methanol solution and the role of changing solution composition upon the structure and dynamics of ion solvation. Car−Parrinello dynamics53 as implemented in NWChem52 were performed using periodic simulation boxes that contained the Cm3+ ion with various compositions of water and methanol in its first solvation shell (Cm(H2O)n(CH3OH)9−n3+ with n = 0−9); solution-phase simulation cells using periodic boundary conditions were created by placing 75 water molecules around the DFT-optimized first solvation shell of Cm3+ using the packmol54 program. All AIMD simulations were performed using pseudopotential plane-wave basis sets with the PBE55 GGA exchange-correlation functional. Though GGA functionals may underestimate ion coordination, and thus lead to a poor equilibrium

was then fit to the gradients along the MP2 PES using the forcematching algorithm employed by the ForceFit software.65 In Equation 1, U(rij) is the potential energy between molecules i and j at distance r, σ and ε are the minimum distance and well depth, respectively, and q is the charge on each molecule. The ion charge was fixed at +3, while the B

DOI: 10.1021/acs.inorgchem.8b01214 Inorg. Chem. XXXX, XXX, XXX−XXX

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depths of the best fit for both Cm3+−OH2 and Cm3+−OHCH3 are overestimated by 16 and 17%, respectively, relative to the MP2calculated values. Although this overestimation of well depth will likely increase the lifetimes of the Cm3+ interactions, they will do so in the same way for both Cm3+−OH2 and Cm3+−OHCH3. In the absence of polarizable force fields, the trends in dynamic behavior will be qualitatively correct for the series under study. The focus of subsequent analyses of the CMD data is upon the trends within the structural organization and overall dynamic properties at long time scales,69 which is supported to the extent possible by the MP2 and AIMD data. Analysis of Solution and Solvation Structure and Dynamics. Portions of the AIMD and CMD trajectories were analyzed via intermolecular network theory (INT)70 using the ChemNetworks software package.71 Star graphs describing ion-solvent interactions (Figure 1) were used to identify specific coordination numbers within the first solvation shell; in these star graphs, all molecules (including the ion) were transformed into vertices of the graph. Water−water, water−methanol, and methanol−methanol hydrogen bonds were used to define edges between solvent molecules and employed a 2.5 Å O−H distance cutoff and a 150° O−H−O angle criterion, which has been previously used for water, methanol, and water/methanol mixtures.14 Ion−solvent interactions were defined by a distance between the Cm3+ and the solvent less than 3.2 Å for the first shell and 6.0 Å for the second shell. These cutoff distances were chosen at intermediate points between successive solvation shells, as judged by the radial distribution functions for Cm3+ with both water and methanol (see Supporting Information). Because of these strict geometric cutoffs, transient artifactsthat is, transient bonds or breaksare inevitably included in the networks when molecules temporarily move across the cutoff boundaries. To remove these artifacts, the strategy of Ozkanlar et al.72 is employed. Transient breaks and bonds are identified using the dynamic history of each interaction within the network over the course of the entire simulation; bonds are considered to be transient if they are intact for less than 50% of the persistence value P (the average uncorrected lifetime), while a break is considered transient if duration is shorter than the tolerance value T, which was set to 0.125 ps. This correction scheme has previously been employed for water−water, water− methanol, and methanol−methanol interactions, 13,14 and it has been shown to cause the structural and dynamic properties of the network to exhibit significantly less dependence on the specific geometric criterion applied.72 With the corrected networks, the average number of solvent− solvent hydrogen bonds, ion−solvent interactions, geometries within the first solvation shell of Cm3+, and the interaction lifetimes were determined. To first examine the solvent organization about Cm3+ a star graph describing all ion−solvent interactions was constructed for each frame of the simulation, with the number of edges to the ion being the coordination number. The network of interactions that accounts for the Cm3+−solvent and solvent−solvent interactions within the first shell were then analyzed to determine the polyhedral geometry of the first solvation shell in each snapshot using the PageRank algorithm73 in the same manner as that of Mooney et al.74 PageRank is sensitive to the unique connectivity patterns associated with the different polyhedral environments and gives a mathematically unique PageRank (PR) value for different geometries75,76 (0.148 144 for the tricapped trigonal prism, the experimentally determined geometry of trivalent actinide and lanthanide ions). The lifetimes τ of specific intermolecular interactions are calculated as the average time ti an interaction lasts for over all observations Pi:

Table 1. Lennard-Jones Parameters and Resulting Minima Position and Well Depth Both in the Fit and the MP2 Data, Using the Cm(H2O)93+ and Cm(CH3OH)93+ Clusters with 160 Data Points Eacha Cm3+−OH2

Cm3+−OHCH3

parameter

fit

ε σ rmin well depth RMSD ε σ rmin well depth RMSD ΔECH3OH‑H2O

1.00 2.70 2.47 28.1 5.8 1.55 2.64 2.40 35.0 4.4 6.9

MP2

2.48 24.3

2.40 29.9 5.6

a

The well depth is given as the energy difference between the M(H2O)n−1 cluster and the scanned solvent molecule. ΔECH3OH‑H2O is the well depth of methanol minus the well depth of water. The well depth and ε are given in kilocalories per mole, while rmin and σ are in angstroms. TIP3P water60 and TraPPE-UA charges were employed for CH3OH. The Lennard-Jones parameters fitted for the Cm3+-H2O(TIP3P) and Cm3+-CH3OH(TraPPE‑UA) interactions are given in Table 1. The quality of the fits is measured by several metrics, including the ability of the fitted curve to reproduce computed and available experimental data including dissociation energy (well-depth) and the minimum distance (rmin), presented in Table 1 and the Supporting Information (Figures S1−S5). Note that the metal−solvent potentials are nonpolarizable, a choice made largely because nonpolarizable force fields of the same type exist for both water, methanol, and the Cm3+ ion under study. A priori, it is first important to assess whether the nonpolarizable potentials adequately reproduce the experimentally known geometries and previous studies using both non- or polarizable potentials. It is well-established that polarizable potentials are generally necessary to reproduce experimental thermodynamic properties of solvated ions (i.e., the free energy of solvation) and for the highest level of fidelity with experimental geometric values within the first (and sometimes second) solvation shell. As demonstrated in Table S2, of all the previously developed potentials for the Cm3+-H2O interactions and those of some trivalent lanthanides, 10 are polarizable, and these generally yield slightly better bond distances (0.01−0.05 Å) and solvation coordination numbers than their nonpolarizable counterparts when compared to experimental extended X-ray absorption fine structure (EXAFS) data. By the time the second shell is reached, there is almost no difference between the polarizable and nonpolarizable simulations with respect to the geometry. Comparison to literature data is solely available for water, as no polarizable potentials have been developed for these ions with methanol, and to our knowledge no EXAFS data exist for these ions with methanol. However, EXAFS experiments on various divalent transition metals in pure methanol solutions show coordination numbers and M−O distances similar to those in aqueous solution.66−68 Within the nonpolarizable fits presented in this work, the goal is to obtain the best fits possible while at the same time maintaining the same relative amounts of error in the potentials for the Cm3+−H2O and Cm3+−OHCH3 interactions. The latter is particularly important, as the extent of polarizability of water and methanol is quite different. In this manner, a self-consistent set of potentials was developed for the solution-phase compositions under study, which reproduce the geometric features of the AIMD and static MP2 calculations but enable a qualitative study of the long-time scale behavior of the solvent exchange in relation to changes in the solution dynamic properties (which are well-reproduced using a nonpolarizable model). As presented in Table 1, the Cm3+−solvent distances at the minima of the PES are reproduced within 2% of the MP2 minima. The well

τ=

∑ tiP(ti) i

(2)

In other words, the reported lifetimes of ion−solvent and solvent− solvent interactions were determined as the average number of contiguous frames a given interaction remained intact. Similarly, the persistence of specific coordination states (defined by the coordination number and the composition within the solvation shell) were determinedin this case exchange events were ignored, unless they affected the composition or coordination number of the first solvation shell. C

DOI: 10.1021/acs.inorgchem.8b01214 Inorg. Chem. XXXX, XXX, XXX−XXX

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Figure 1. (a) A representative first solvation shell of Cm3+; (b) the complementary star graph of the first solvation shell; (c) the polyhedral organization of the first solvation shell identified by PageRank (tricapped trigonal prism).

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DISCUSSION Ab Initio Structure. As reported in our previous work,28 the optimized gas-phase structures of Cm3+ with its first solvation shell all maintain the tricapped trigonal prismatic geometry regardless of water/methanol composition (Figure 1). This does not change upon the inclusion of the ion and its first solvation shell into solution; in 10 ps of AIMD simulations of Cm(H2O)n(CH3OH)9−n3+ (n = 0−9) surrounded by 75 water molecules with periodic boundary conditions, only the tricapped trigonal prismatic geometry was observed. Though molecules within the first solvation shell are dynamically shifting, the polyhedral structure of the first solvation shell is remarkably consistent. Both the optimized gas-phase geometries and the AIMD geometries show that, on average, the solvent molecules are pushed further away from the ion when more methanol is included in the first solvation shell. Average Cm−solvent distances are given in Table 2. This effect is more pronounced in

this effect may be attributed to hydrogen bonding between solvation shells that is present in solution and is less pronounced in methanol solvation relative to water solvation because of the lower number of hydrogen bonds formed by methanol. Though the AIMD simulations reported here extend our understanding of the structure of the solvated Cm3+ ion, AIMD unfortunately cannot approach the time scales necessary to observe solvent exchange events or to collect information about ion−solvent dynamics. For these purposes, we turned to classical MD approaches. Classical Molecular Dynamics−Ion Solvation. Structurally, the first solvation shell of Cm3+ in the CMD simulations matches well with the AIMD simulations described above, as well as with published polarizable CMD simulations, AIMD simulations, and measured EXAFS data (see Supporting Information, Table S2).77−79 Also matching the AIMD simulations, Cm3+ maintains the tricapped trigonal prism geometry when the coordination number is 9. Unlike the AIMD simulations, the CMD simulations enable exploration of different coordination numbers in the first solvation shell that are less frequently observed but reveal themselves at longer time scales. In all classical simulations of the water/methanol solutions, Cm3+ has an average CN of nine, with preferential solvation by water over methanol. Table 3 presents the populated coordination states (CS) defined by the number of either water or methanol in the first solvation shell of the ion. Cm3+ has a significant occurrence of nonfully aqueous CS, with populations of both the Cm(H2O)8(CH3OH)3+ and Cm(H2O)7(CH3OH)23+ observed up to 50% of the time at higher methanol concentrations. This is consistent with experimental luminescence experiments on Eu3+ and Cm3+, where the first solvation shell of the ions had between zero and two methanol molecules even in solutions with χCH3OH = 0.9 (20.6 M methanol).80,81 In considering the second solvation shell properties, it is interesting to note that preferential solvation by water is maintained, though to a lesser extent than in the first shell. On average, there is a 0.11 ± 0.04 decrease in χCH3OH between the bulk solution and the second solvation shell. This preferential solvation by water is much stronger than that observed for similar simulations of singly charged ions in water/methanol solutions.14 Ion Solvation−Dynamic Behavior. Figure 2 shows that the average Cm3+-water lifetime in the first solvation shell is 1.29 ns in pure water. While the mean residence time of water within the first solvation shell of Cm3+ has not been studied experimentally, this nanosecond τ is of the same magnitude as previous aqueous Cm3+ simulations78 and as several experimental

Table 2. Average Cm3+−Solvent Distances for Optimized Gas-Phase Geometries28 and AIMD Simulations at Each First Solvation Shell Compositiona DFT first solvation shell

Cm − OH2

Cm(CH3OH)93+ Cm(H2O)(CH3OH)83+ Cm(H2O)2(CH3OH)73+ Cm(H2O)3(CH3OH)63+ Cm(H2O)4(CH3OH)53+ Cm(H2O)5(CH3OH)43+ Cm(H2O)6(CH3OH)33+ Cm(H2O)7(CH3OH)23+ Cm(H2O)8(CH3OH)3+ Cm(H2O)93+

2.7(1) 2.59(4) 2.60(6) 2.59(4) 2.59(5) 2.58(3) 2.57(3) 2.56(2) 2.55(1)

3+

AIMD

Cm − OHCH3 3+

2.57(7) 2.56(7) 2.55(3) 2.54(4) 2.53(4) 2.52(2) 2.52(2) 2.51(2) 2.50(2)

Cm − OH2 3+

2.5(1) 2.5(1) 2.4(1) 2.48(5) 2.47(4) 2.47(3) 2.47(4) 2.46(4) 2.43(4)

Cm3+− OHCH3 2.49(5) 2.5(1) 2.5(1) 2.5(1) 2.49(5) 2.50(4) 2.49(4) 2.47(2) 2.54(3)

a

Distances in angstroms; reported error is the standard deviation among all possible molecular geometries (DFT) or among all simulation frames (AIMD).

the gas-phase structures but is present in the solution simulations as well. For example, when the first solvation shell of the Cm3+ ion is pure water, the average Cm3+−OH2 distance is 2.43(4) Å, while in first shell compositions with the largest methanol content the average Cm3+−OH2 distance has increased to 2.5(1) Å. Interestingly, water ison averageslightly closer to the ion than methanol in the AIMD simulations, though the reverse is true in the optimized gas-phase geometries;28 D

DOI: 10.1021/acs.inorgchem.8b01214 Inorg. Chem. XXXX, XXX, XXX−XXX

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χCH3OH = 0.25 but is 224 ps in χCH3OH = 0.75. Additionally, the persistence values of CS with greater methanol content are also increased. Thus, both the specific Cm-solvent interactions as well as the overall intact coordination environments about Cm3+ are increased with increasing methanol content in the binary solutions. Note that both sets of persistence values decrease when the pure methanol solution is examined. These trends are consistent with well-known trends in hydrogenbond lifetimes of water/methanol solutions moving from pure water to the mixed system to pure methanol.17−23,38,39,85,86 Ion Solvation−Solvent Exchange. The mechanism and dynamics of solvent exchange are incredibly important when considering ion-complexant reactions that proceed by displacing solvent molecules from the first solvation shell. In their classical nonpolarizable MD simulations of aqueous Cm3+, Atta-Fynn et al.78 observed three different exchange mechanisms for water molecules from the first solvation shell of the ion: associative, dissociative, and intermediate exchanges. In associative exchange reactions, a short-lived CN = 10 intermediate (increased from the predominant CN = 9) was observed, while dissociative events went through a CN = 8 intermediate, each existing for 3−7 ps. Intermediate exchange reactions dispense with the short-lived coordination state, having an H2O entering the first solvation shell simultaneous to another leaving it. All three exchange mechanisms are observed in the aqueous simulations reported here, with persistence of the intermediate coordination states falling within a similar 3−15 ps range despite the differences in potential fitting between the two studies (AttaFynn et al. constructed their Cm-water potentials from DFT calculations on Cm3+−OH2 and H2O−Cm3+−OH2, while we considered the entire first solvation shell of the Cm3+ ion). In this work, intermediate exchange events are the most common for water with both associative and dissociative mechanisms occurring in less than 12% of observed exchange events. However, in the aqueous simulations of Atta-Fynn et al., the associative and dissociative mechanisms occurred with roughly equal frequency, though they collected data from only 4 ns of simulation compared to the 30 ns reported here.78 Interestingly, the observed mechanism changes dramatically in methanol solventwhere methanol is nearly always added to the first solvation shell of Cm3+ via an associative mechanism (Figure 3); the 10-coordinate intermediate structure predominantly maintains a bicapped square antiprismatic geometry. This is followed by another solvent molecule leaving the first solvation shell, returning the CN to 9 and the tricapped trigonal prismatic geometry. This type of transition is examined in Figure 4 and was further studied via MP2 calculations of the Cm ion and its 10 closest solvent molecules. Geometries were taken from CMD frames before, during, and after exchange events; H atoms were added to the methyl groups (modeled as a united atom potential in the CMD simulations), and all atoms aside from the Cm3+ and oxygens in the first solvation shell were geometry-optimized along the reaction pathway. This analysis shows that, as the 10th solvent molecule (water) enters the first solvation shell of Cm(H2O)8(CH3OH)3+, there is an increase of between 5 and 10 kcal/mol in the calculated MP2 energy of Cm(H2O)9(CH3OH)3+. This increased energy is maintained for ∼10 ps, the time in which both water molecules are closely associated with the ion. As the displaced water molecule leaves the first solvation shell and enters the second, the calculated MP2 energy returns to its initial value, closely tracking the movement of the solvent molecule away

Table 3. Occurrence and Persistence of Different Water/ Methanol First Solvation Shell Coordination States (CS) Obtained from CMD Simulationsa χCH3OH

No. H2O

No. CH3OH

occurrence

persistence (ps)

0 0.25

9 9 8 9 8 9 8 9 8 7 9 8 7 0 0

0 0 1 0 1 0 1 0 1 2 0 1 2 9 8

99.9 84.3 15.6 27.8 72.2 64.4 35.5 27.7 21.7 50.6 19.3 55.4 25.3 97.5 2.5

161 162 234 160 169 173 304 224 224 843 413 462 543 184 159

0.30 0.50 0.75

0.90

1 a

Occurrences are given for each ion in percentage. Only CS with percentage occurrence greater than 1% are shown.

Figure 2. Average Cm3+-water (dark gray) and Cm3+-methanol (light gray) lifetimes within the first solvation shell, calculated using eq 1. Uncertainty is the standard deviation of lifetimes across multiple simulations.

investigations of Ln3+ ions.82−84 Once again, we stress that the nonpolarizable potentials used here are unlikely to give quantitatively accurate results for solution dynamics with heavy atoms; further analyses are therefore based on trends across solution composition. The Cm3+-water lifetime increases as methanol is added to the simulation, lengthening to more than 4.5 ns in the χCH3OH = 0.9 simulation. The same trend is observed for the Cm3+-methanol interaction. The longest Cm3+-methanol lifetime is 1.94 ns, occurring in the χCH3OH = 0.75 system, which decreases to 0.66 ns at χCH3OH = 1. The persistence values of the specific CS for Cm3+ are given in Table 3. A CS is defined by the coordination number and the composition within the solvation shell, and the persistence value ignores exchange events, unless the composition or coordination number of the first solvation shell is altered. In general, the persistence of a specific CS increases as χCH3OH increases for example, the persistence of Cm(H2O)93+ is 162 ps in E

DOI: 10.1021/acs.inorgchem.8b01214 Inorg. Chem. XXXX, XXX, XXX−XXX

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Figure 3. Solvent addition to Cm3+. (a) A united atom methanol molecule approaches the ion, moving between the first and second solvation shells. (b) The solvent molecule substitutes into the first solvation shell of the ion, resulting in a CN of 10. (c) Another molecule leaves the first solvation shell, restoring the dominant CN of 9. Images taken from the χCH3OH = 0.75 classical simulation of Cm3+, 3.375 ps apart.

methanol-induced change that affects the ion−solvent dynamics for the highly charged ion studied here, as the Cm3+-solvent binding energy has been shown to change based on the water/ methanol composition of the first solvation shell of the Cm3+ ion.28 The effects of these two phenomena on the ion−solvent dynamics are explored below. MP2 solvent dissociation energy calculations reported previously for water and methanol with the Cm3+ ion and its first solvation shell predict that methanol has a consistently higher dissociation energy than water irrespective of first shell water/methanol composition.28 Furthermore, the dissociation energy of both solvents decreased as more methanol molecules were added to the first solvation shell. The computed energies according to Reactions r1 and r2 show the solvent dissociation energy of both solvents decreasing by ∼6 kcal/mol, as the amount of methanol in the first solvation shell increases, and methanol requiring ∼7 kcal/mol more energy to be removed from the ion than water within the same first shell composition.28 Cm(H 2O)x (CH3OH)y 3 +

Figure 4. Solvent exchange via an associative mechanism: Cm(H2O)8(CH3OH)3+ + H2O → Cm(H2O)9(CH3OH)3+ → Cm(H2O)8(CH3OH)3+ + H2O. (upper) Cm3+−OH2 distances of solvent molecules entering (blue) and leaving (red) the first solvation shell. (lower) Relative MP2 energy of Cm3+ and the 10 solvent molecules with geometries taken from the MD simulations. Methyl hydrogen atoms were added assuming a tetrahedral geometry; all H atoms were allowed to relax in a constrained MP2 optimization. Fifty frames before, during, or after the exchange event are depicted.

→ Cm(H 2O)x − 1(CH3OH)y 3 + + H 2O

(r1)

Cm(H 2O)x (CH3OH)y 3 + → Cm(H 2O)x (CH3OH)y − 13 + + CH3OH

(r2)

Unlike calculations on singly charged ions,14 as methanol is added to the first solvation shell less energy is required to remove solvent molecules of both types from the ion. This suggests that, for the trivalent Cm ion studied here, the ion− solvent dynamics should be faster as the methanol concentration in solution increases, and mixed water/methanol coordination states with greater numbers of methanol molecules should have shorter durations than coordination states with fewer methanol. However, the observed ion−solvent lifetimes in the CMD simulations do not follow this prediction; CS with greater methanol content generally have longer lifetimes (Table 3), and as methanol is added to the bulk solution both the ion−water and ion−methanol lifetimes increase (Figure 2). This increase in ion−water and ion−methanol lifetimes as the concentration of methanol in solution increases has been observed previously in singly charged ions14 (Na+ and Cl−). In that case, there was no significant trend in the solvent dissociation energy, and the ion−solvent dynamics were coupled with the solvent−solvent hydrogen-bond dynamics, which lengthen considerably as methanol is added to the mixed solution.13,14 Likewise, the increase in Cm3+-solvent lifetimes appears to correlate with the increase in the lifetimes of the hydrogen bonds despite the opposing effect from the solvent dissociation energy. Figure 5 shows the correlation between the Cm3+water lifetime and the hydrogen-bond lifetime.

from the ion. Figure 4 presents the fluctuation in the energy as the departing solvent molecule moves toward or away from the ion while in the intermediate region (between the first and second solvation shells); the MP2 energy can be seen increasing as the water molecule briefly moves closer to the ion at 36 ps. AIMD simulations were used to verify the classically simulated results described above. While the time scales needed to observe the ion−solvent dynamics are inaccessible by AIMD, simulations starting with a single solvent molecule intermediate in distance between the first and second solvation shells of the ion sometimes resulted in the associative, dissociative, or intermediate exchange events described above and observed over the full time period in the classical simulations; however, the number of these events observed was too small to provide statistically significant information about which exchange events are more probable. Comparison of Competitive Ion−Solvent and Solvent− Solvent Interactions. These data align with our prior studies of monovalent ions in water/methanol solutions, where the changes to the ion solvation dynamics were correlated solely with perturbations to the hydrogen-bond dynamics of the solution imparted by the methanol cosolvent.14 However, changes in the solvent−solvent interaction may not be the only F

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Inorganic Chemistry Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank D. Perez for valuable assistance with potential fitting. M.K. acknowledges support from the Los Alamos National Laboratory G.T. Seaborg Institute and the Dept. of Energy (DOE) Office of Science Graduate Student Research Fellowship. P.Y. was supported by the U.S. DOE, Office of Science, Basic Energy Sciences, Chemical Sciences, Biosciences, and Geosciences Division, Heavy Element Chemistry Program at Los Alamos National Laboratory under Contract No. DE-AC52-06NA25396 (operated by Los Alamos National Security, LLC, for the National Nuclear Security Administration of the U.S. DOE). S.C. acknowledges support from the U.S. DOE, Office of Science, Heavy Elements program, DE-SC-000-4102. A.C. acknowledges support from the U.S. DOE, Office of Science, Separations program, DE-SC000-1815. Calculations were performed using the Molecular Science Computing Facilities at William R. Wiley Environmental Molecular Sciences Laboratory, a national scientific user facility sponsored by the U.S. DOE BER and located at Pacific Northwest National Laboratory. This research also used resources of the Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory, which is supported by the Office of Science of the U.S. DOE under Contract No. DE-AC05-00OR22725.

Figure 5. Average solvent-Cm3+ lifetime (ns) in each methanol composition vs the average hydrogen-bond lifetime between all solvents within that system (ps). The linear fit has an R2 correlation of 0.83 (dotted line).

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CONCLUSIONS The solvation of trivalent Cm in binary water/methanol solutions has been thoroughly investigated, with an emphasis upon understanding the structure, dynamics, and mechanisms of solvent exchange as a function of solution composition. Unlike previously studied monovalent ions, Cm3+ has two competing effects on the ion−solvent dynamics. Electronic structure calculations of the solvent dissociation energy from the first solvation shell of the Cm3+ demonstrate that, as more methanol is introduced into the first shell, solvent molecules become easier to remove. This suggests that coordination states with greater methanol content should have more fluxional dynamics, which is the opposite of what is observed in the simulations. The effect of the solvent dissociation energy appears to be overridden by changes in the hydrogen-bond network of the solution as the amount of methanol in bulk solution increases, causing the network to become more static. Dynamic effects from the bulk solution dominate the ion− solvent interaction, significantly lengthening ion−solvent dynamics as the concentration of methanol in the solution increases.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.8b01214. Listings of simulation details, nonpolarizable and polarizable MD potential comparisons, MP2 data versus Lennard-Jones fits, radial distribution functions, PES dependence on basis sets and method (PDF)

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REFERENCES

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. (M.P.K.) *E-mail: [email protected]. (P.Y.) *E-mail: [email protected]. (A.E.C.) ORCID

Morgan P. Kelley: 0000-0001-5196-9821 Ping Yang: 0000-0003-4726-2860 Aurora E. Clark: 0000-0001-9381-721X G

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