Structure and Dynamics of the Uranyl Tricarbonate Complex in

Article pubs.acs.org/JPCB

Structure and Dynamics of the Uranyl Tricarbonate Complex in Aqueous Solution: Insights from Quantum Mechanical Charge Field Molecular Dynamics Andreas O. Tirler and Thomas S. Hofer* Theoretical Chemistry Division, Institute of General, Inorganic and Theoretical Chemistry, University of Innsbruck, Innrain 80-82, A-6020 Innsbruck, Austria ABSTRACT: This investigation presents the characterization of structural and dynamical properties of uranyl tricarbonate in aqueous solution employing an extended hybrid quantum mechanical/molecular mechanical (QM/MM) approach. It is shown that the inclusion of explicit solvent molecules in the quantum chemical treatment is essential to mimic the complex interaction occurring in an aqueous environment. Thus, in contrast to gas phase cluster calculations on a quantum chemical level proposing a 6-fold coordination of the three carbonates, the QMCF MD simulation proposes a 5-fold coordination. An extensive comparison of the simulation results to structural and dynamical data available in the literature was found to be in excellent agreement. Furthermore, this work is the first theoretical study on a quantum chemical level of theory able to observe the conversion of − carbonate (CO2− 3 ) to bicarbonate (HCO3 ) in the equatorial coordination sphere of the uranyl ion. From a comparison of the free energy ΔG values for the unprotonated educt [UO2(CO3)3]4− and the protonated [UO2(CO3)2(HCO3)]3−, it could be concluded that the reaction equilibrium is strongly shifted toward the product state confirming the benignity for the observed protonation reaction. Structural properties and the three-dimensional arrangement of carbonate ligands were analyzed via pair-, three-body, and angular distributions, the dynamical properties were evaluated by hydrogen-bond correlation functions and vibrational power spectra.

1. INTRODUCTION The past decades’ uranium mining for the production of nuclear weapons as well as for nuclear power plants has led to widespread contamination of the respective areas by uranium and its daughter products all over the world, including the U.S., France, Britain, Russia, Australia, and China.1,2 For this reason, special interest has grown in the determination of different released uranium species and their influence on ecological systems. Previous investigations have concentrated on uranium exploration, whereas the main interest has meanwhile shifted to the investigation of transport and migration mechanisms of uranium from contaminated sites.3 In aqueous solution, uranium exists mostly in the stable oxidation state of +VI in the form of the oxocation uranyl, UO+2 2 . A number of investigations report a strong complexation of uranyl ions by carbonate, due to its considerable concentration in natural water bodies, showing high stability constants.4−7 Therefore, carbonate-complexed uranium is probably the most relevant uranium species in aqueous bodies. A result of this complex formation is the increase in solubility due to the negative charge provided by carbonate.3 This also leads to a higher mobility of uranium in liquid systems, and hence diffusion processes become of environmental concern.8,9 Fortunately, there is evidence that uranyl carbonates adsorb onto several different kinds of minerals, thus representing a possibility to remove uranium from a contaminated liquid phase10−13 and knowledge of the fundamental mechanism of © 2014 American Chemical Society

adsorption of uranium on solid phases is of great interest for the remediation of contaminated environmental systems. A number of experimental as well as theoretical investigations were recently reported in literature contributing to a better understanding of these adsorption processes and structural motifs of uranyl carbonates on different surfaces.1,3,10−17 However, an accurate determination of the structure and dynamics of uranyl carbonate species in the liquid is an essential prerequisite to enable the experimental interpretation or theoretical modeling of uranyl carbonates onto minerals. This is of particular relevance when considering adsorption/ desorption processes and resulting distribution coefficients for uranyl carbonates at liquid/solid interfaces. There exist a number of different uranyl carbonates in aqueous solution which have been reported in the literature so far. Among them, besides the mononuclear UO2(CO3),18−27 [UO 2 (CO 3 ) 2 ] 2 − 1 9 , 2 1 , 2 4 , 2 7 − 3 0 and t he po ly nuclear [(UO2)3(CO3)6]6−,19,23,31,32 the tricarbonate [UO2(CO3)3]4−19,21,23,24,28,29,31−43 is the most extensively studied because of its prevailing existence at environmental conditions in aqueous solution.44 Thus, uranyl tricarbonate is probably the dominant species in liquid bodies and therefore may be the key structure concerning uranium remediation from Received: March 31, 2014 Revised: August 26, 2014 Published: August 26, 2014 12938

dx.doi.org/10.1021/jp503171g | J. Phys. Chem. B 2014, 118, 12938−12951

The Journal of Physical Chemistry B

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contaminated areas.45−47 There is still a lot of experimental and theoretical work focused to further characterize the uranyl tricarbonate system in aqueous solution. From the experimental point of view, several aspects have to be considered while interpreting collected data. On one hand, it is necessary to prepare a single species solution exceeding a concentration of 10−4 M,23 which is nearly impossible to realize because of the coexistence of various different U(VI) species under most of the reported experimental conditions,48 thus making investigations on selected uranium species in a diluted liquid system a challenging task. On the other hand, the time scale of experiments is often too large to observe rapidly occurring processes taking place in the nano- and picosecond regime. Theoretical investigations offer a complementary route for investigating chemical systems. By using theoretical frameworks, single species solutions can be modeled at nearly any concentration and on a time scale in the sub-picosecond range, providing valuable information for the interpretation of experimental data. Considering the theoretical modeling of uranyl carbonates in aqueous solution, a number of studies are available in the literature.19,24−26,28−30,32,37−39 However, to the best of our knowledge, no molecular dynamics (MD) simulation on a quantum chemical level of theory has been carried out as of yet. The available literature consists of a number of cluster calculations performing energy minimizations in vacuo and in the presence of implicit solvent as well as clusters with few explicitly treated solvent molecules at different levels of theory. A main disadvantage of such cluster calculations is the neglect of a proper embedding of the cluster by solvent molecules mimicking the presence of solvent. In addition, the result is often a single structure representing a (local) minimum on the potential hypersurface. Doing so, other important configurations, which are representative for the system, are in general not taken into account. MD simulations are versatile tools to overcome these limitations, covering the most important structural motifs and their time-dependence in configurational space. A number of MD simulations at a molecular mechanical (MM) level of theory based on empirically derived potentials are available in the literature, however.24,29 While the use of MM potentials enables the execution of rather long simulations addressing phenomena occurring on the nano- and even microsecond range, the construction of a set of reliable potential functions for all interactions in the system may be difficult and complicated, especially when treating highly charged species such as [UO2(CO3)3]4−. These potentials are highly dependent on the data used in the fitting procedure, and the achievable accuracy is in many cases limited due to the neglect or approximate description of polarization, chargetransfer, and/or many-body contributions. A further shortcoming of MM techniques is the incapability to model bond cleavage or formation. Because of the above-mentioned aspects, quantum chemical simulations including explicit solvent effects have shown to yield a more accurate description of charged solvated systems, since these approaches account for chargetransfer, polarization, and many-body effects in addition to the capability to describe the formation and cleavage of chemical bonds. A limitation when combining quantum chemistry and simulation techniques is the increased computational demand and the associated short sampling time being in the range of several picoseconds. Nevertheless, the achievable sampling time is often sufficient for the observation of important structural and dynamical properties. In the present study we report

structural and dynamical results obtained from a Quantum Mechanical Charge Field Molecular Dynamics (QMCF-MD) simulation 49−52 of the uranyl tricarbonate complex [UO2(CO3)3]4−. The obtained structural and dynamical data is compared to experimental as well as to theoretical data with regard to complementarity, accuracy, and reliability of results.

2. COMPUTATIONAL METHODS The reported MD simulation of uranyl tricarbonate [UO2(CO3)3]4− is based on a hybrid QM/MM approach,53−55 the Quantum Mechanical Charge Field (QMCF) methodology.49−52 The main advantage of this technique is the possibility to describe the solute, i.e., the uranyl ion on a quantum chemical level without the requirement of any empirical solute−solvent potential functions for the nonCoulombic interaction, typically required for the coupling between the QM and MM zone in conventional QM/MM schemes. The method has been successfully applied for the investigations of ions,56 organic molecules,57 and complex systems58 in solution and has furthermore proven to be advantageous when treating highly charged systems such as lanthanoid and actinoid ions,59−62 where reliable empirical potential functions are very difficult to obtain. To achieve this, the QMCF methodology further divides the QM region into a QM core and a QM layer subregion. The QM core usually contains the solute, while the QM layer consists of solvent molecules and, if need be, coordinating ligands and/or counterions for which adequate potential functions are available in the literature. Thus, the QM layer, which is treated like the QM core by quantum chemical methods, serves as a separation zone between the QM core and the MM zone if this separation zone is chosen sufficiently large63,64 because then the nonCoulombic solute−solvent contributions become negligibly small.51 The QMCF method has been already used for studying uranyl mono- and dicarbonate in aqueous solution and has proven to give results in good agreement with data reported in the literature.27 For more detailed information on the QMCF methodology and its implementation, the reader is referred to previous works.49−52 The required basis sets were chosen according to a previous investigation on similar uranyl carbonate systems in aqueous solution,27 which are the Stuttgart RSC (Relativistic Small Core) ECP basis set65 for uranium and 6-31g(d,p) basis sets66 for oxygen, carbon, and hydrogen, respectively. Also, other groups used these basis sets for uranium,19,28,29,38,67,68 oxygen, carbon, and hydrogen.28−30,39,69 In a previous work27 the application of different quantum chemical methods for the evaluation of QM energies and forces in the QM region has been discussed. Based on those conclusions and because of the above-mentioned difficulties arizing from the use of force field methods for the modeling of charged complexes, the Hartree− Fock (HF) approach was considered to represent a valid compromise between accuracy of results and computation time. Extensive gas phase cluster optimizations with Gaussian0970 at different levels of theory including implicit solvation effects were performed to evaluate the possible error made by neglecting electron correlation using HF. Qualitatively, it can be concluded that the use of appropriate basis sets results only in minor errors and were considered not to derogate the quality of results. However, an estimation of the influence of correlational effects was given elsewhere.68 Furthermore, recent QMCF-MD simulations on other uranyl carbonate systems 12939



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Figure 1. (a) Schematic representation of the used abbreviations for the different atomic species in the QMCF-MD simulation of [UO2(CO3)2(HCO3)]3−. (b) The starting configuration of the QMCF-MD simulation with a 6-fold coordination pattern (left) and its evolution toward a 5-fold coordination scheme during the re-equilibration of the QMCF-MD simulation of 10 ps (right).

Figure 2. Schematic representation of different relevant configurations of the coordinating bicarbonate ion observed during the QMCF-MD simulation of [UO2(CO3)2(HCO3)]3−: (a) H-bonded to upper Ou; (b) H-bonded to Oc; (c) bulk-oriented Hc parallel to uranyl axis; (d) bulkoriented Hc perpendicular to uranyl axis; (e) H-bonded to lower Ou; (f) H-bonded to Oc.

Coulombic contributions. The starting configuration for the pre-equilibration of the complex by a classical MD simulation for 200 ps was taken from an energy optimized geometry showing a 6-fold coordination of the three carbonates in the equatorial plane of the uranyl ion. For the subsequent QMCF MD simulation a QM core zone of 2.0 Å containing the uranyl cation was applied. All carbonate ligands together with more than 30 water molecules were located in the QM layer zone with a radius of 5.0 Å. Thus, a total radius of 7.0 Å for the QM region was obtained. After invoking the QMCF framework, the simulation box was re-equilibrated for 10 ps and subsequently a trajectory of 25 ps (i.e., 125000 MD steps) was generated,

showed that structural and dynamical properties obtained using HF do not deviate significantly from the literature.27 The MD simulation settings have been chosen in analogy to a preceding investigation.27 A cubic water box containing 1000 explicitly treated water molecules was used, enabling periodic boundary conditions. The MD configurations were collected in the NVT ensemble applying the Berendsen algorithm,71 obtaining a density of pure water of 0.997 g/m3 at 298.15 K. For the time propagation, the Velocity-Verlet algorithm72 with a time step of 0.2 fs was employed. Coulombic interactions were evaluated within a radius of 12.0 Å, and the reaction field method73,74 was used to account for the long-range nature of 12940



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Figure 3. Distance plot of Oc−Hw (red), Ow−Hw (blue), and Oc−Ow (black) within the third and the sixth picosecond of the QMCF MD simulation. Representations a−d emphasize four relevant configurations during the proton transfer.

collecting data every fifth step. This trajectory was used for the analysis of the structural and dynamical properties of the uranyl tricarbonate in aqueous solution. For the graphical depiction of molecular moieties, the visualization software VMD was used.75

classical MD simulation of the system, which was initially carried out to pre-equilibrate the simulation box before invoking the quantum chemical level of theory. However, if the QMCF methodology is applied as outlined above, the uranyl carbonate complex relaxes within the equilibration period toward a 5-fold coordination pattern as shown in Figure 1b. This 5-fold coordination of carbonates to uranium has already been reported in a previous classical MD simulation study as an intermediate and metastable state leading to ligand dissociation.29 A 6-fold coordination is not restored along the QM/MM simulation. Instead the protonation of the monodentately coordinating carbonate is observed after approximately 5 ps of

3. RESULTS AND DISCUSSION 3.1. Protonation of [UO2(CO3)3]4−. In order to facilitate the nomenclature of the several different atomic species present in the simulated system, abbreviations are used in the following, which are depicted in Figure 1a. According to the literature, the uranyl tricarbonate shows a 6-fold coordination in the equatorial plane perpendicular to the uranyl axis.19,23,28,31−33,37−39,41−43,76 This is also reflected by our 12941



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Figure 4. A thermodynamic cycle for the dissociation reaction of [UO2(CO3)2(HCO3)]3− into [UO2(CO3)3]4− and H+.

(298.15 K). Δn accounts for the change in the number of reactants being one in this case. ΔGR,vac on the other hand is defined as

simulation time. While this seems to be in contrast to other above-mentioned theoretical studies, it should be stressed that classical force fields are not capable of describing the formation and cleavage of chemical bonds effectively preventing the occurrence of such an event. The newly formed bicarbonate is showing, in contrast to the other two bidentately coordinating carbonates, high flexibility adapting several different configurations within the short simulation time of a few picoseconds. Figure 2 depicts some important conformations of the complex where the interaction of the bicarbonate with Ou and Oc oxygens via H-bonds can be seen, as well as intermediate configurations. The formation of bicarbonate in the coordination sphere of uranyl has not been reported in the literature so far, but Strom et al.77 reported the presence of coordinating bicarbonate to the uranyl ion based on C13 NMR measurements. The bicarbonate formation reaction is shown in Figure 3. It can be seen that various attempts are occurring until the proton is successfully transferred from a water molecule to the carbonate ion. In Figure 3a for instance, the first approach of water to carbonate is observed, whereas in Figure 3b the proton is already transferred temporarily to the carbonate prior dissociating again. Figure 3c shows an intermediate state of the proton transfer where the proton is shared between the water molecule and the carbonate. Finally, Figure 3d shows the successful proton transfer from the water to the carbonate and the subsequent diffusion of the newly formed hydroxide ion into the solution. To confirm that the proton transfer reaction is not an artifact of the HF treatment, the simulation was restarted from the same starting configuration using a DFT description (B3LYP functional).78 The observed proton transfer occurred after approximately 1 ps, i.e., even faster than in the HF case (data not shown). In order to obtain further information on this proton transfer reaction, an estimation of the corresponding reaction associated free energy ΔG was carried out. According to da Silva et al.79 the equilibrium of an investigated reaction may be obtained using well-established thermodynamical cycles as depicted in Figure 4. In our case, HA denotes the protonated complex [UO2(CO3)2(HCO3)]3− and A− the respective deprotonated species [UO2(CO3)3]4−. Since ΔGR,solv is a state function, its value only depends on the start and end state of the system, regardless of the path connecting them. Thus, ΔGR,solv can be obtained according to

ΔG R,vac = ΔG(H +) + E(A−) + GCorr(A−) − (E(HA) + GCorr(HA))

The value for ΔG(H ) results from the ideal gas partition functions at the respective temperature as −26.3 kJ/mol, which has been taken from the literature.80,82 (E (A−) + GCorr(A−)) and (E(HA) + GCorr(HA)) are obtained via frequency calculations and a subsequent thermochemical analysis of optimized gas phase structures of the respective species using Gaussian09.70 ΔGSolv(HA) and ΔGSolv(A−) are the respective energy differences between the optimized structures of the respective species using the improved implicit solvation model developed by Truhlar et al.,83 and the optimized structure in vacuum. The value for ΔGSolv(H+) of −1087 kJ/mol has also been taken from the literature.84 The thermodynamic cycle was calculated at three different levels of theory, namely, using HF, MP2, and B3LYP. The results are shown in Table 1. Table 1. Estimation of Free Energy ΔG Values for the Protonation Reaction of Uranyl Tricarbonate Using HF, MP2, and B3LYPa

a

method

ΔGSolv(HA)

ΔGSolv(A−)

ΔGR,vac

ΔGR,solv

HF MP2 B3LYP

−1668.98 −1616.76 −1622.04

−2803.68 −2774.71 −2768.83

2365.59 2376.47 2379.73

151.81 139.74 153.86

The reported energies are given in kJ/mol.

It can be seen that, irrespective of the applied level of theory, a dissociation of the protonated complex is not favorable since the obtained ΔG values evidence that a considerable amount of energy (at least 139.74 kJ/mol according to MP2 estimation) is required to abstract the proton, which is significantly higher than 1/2 RT being 1.24 kJ/mol. Therefore, the equilibrium of the reaction is strongly shifted toward the protonated state, confirming that the proton transfer reaction is neither an artifact of the HF treatment nor can be regarded as a metastable state of the system. However, after the proton transfer occurred, the MD simulation had to be interrupted and an additional proton was added to the newly formed hydroxide in order to restore the respective water molecule. After re-equilibration for another 20 000 MD steps (4 ps) to enable a proper relaxation of the perturbed system, the resulting [UO 2 (CO 3 ) 2 (HCO 3 )]3− remained stable for another 25 ps. Therefore, the first 10 ps of simulation were considered to be a re-equilibration of the simulation and were not considered for the following structural and dynamical analysis of the aqueous uranyl carbonate

ΔG R,solv = ΔG R,vac + ΔGSolv (A−) + ΔGSolv (H +) ̃ ) − ΔGSolv (HA) + ΔnRT ln(RT

(2)

+

(1)

The last term accounts for the different standard states being 1 mol/L for solutions and 1 atm in the case of gases.80,81 R and R̃ correspond to the ideal gas constants in different units being 8.314 J/(mol·K) and 0.0821 (L·atm)/(K·mol). The temperature T was set to the same value as in the MD simulation 12942



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Figure 5. Radial distribution functions within 10 Å of (a) all U−O species, (b) U−Ou, (c) U−Oc of the coordinating oxygens, (d) U−Oc of the noncoordinating oxygens and overlaying water, (e) all U−C species, (f) U−C of the bidentate coordinating carbonates, and (g) U−C of the monodentate coordinating bicarbonate.

solution may differ from that in the solid, especially in the absence of counterions. 3.2. Structure of [UO2(CO3)2(HCO3)]3−. Figure 5 shows pairwise radial distribution functions (RDF’s) of selected atomic species in the range of 10 Å, which are relevant for characterizing structural aspects of the investigated complex. The RDF is depicted as a continuous line, whereas the corresponding integration is shown as dashed line. Figure 5a depicts an overall RDF for all U−O species present in the system, i.e., Ou, Oc, and Ow, respectively. In order to distinguish the contributions of the different oxygen species to the overall RDF in Figure 5a, further RDF’s (Figure 5b−d) are shown. Figure 5b denotes the U−Ou RDF, showing covalently bound uranium oxygens, the corresponding integration of the peak yielding two. From the RDF in Figure 5b, a U−Ou distance of 1.76 Å can be deduced. The U−Oc RDF in Figure 5c shows the five carbonate oxygens that are coordinatively bound to uranium. It can clearly be seen that there is no evidence for a 6-fold coordination scheme. The integration of the peak yields exactly five, stressing the proposed 5-fold coordination. The average distance for the coordinating carbonate oxygens is 2.42 Å. Figure 5d shows a closeup of the small shoulder at about 4 Å. The integration of the RDF yields four (orange dashed line), indicating the four noncoordinating carbonate oxygens. Furthermore, it can be seen that the orange U−Oc RDF shows three peaks denoting three different carbonate oxygen distances. Thereby the highest peak reflects the carbonate oxygens of the bidentately coordinating carbonates with a maximum at 4.13 Å, while the remaining two peaks located at 3.85 and 4.58 Å result from the two oxygens of the monodentately coordinating carbonates. Because of the monodentate coordination of the third carbonate, the oxygens pointing into the bulk are more flexible, adapting several different configurations resulting in various distances to uranium. The blue U−Ow RDF in Figure 5d evidence the

complex. The reported data demonstrates the importance of a quantum mechanical description of energies and forces in MD simulations for the investigation of coordination complexes in an aqueous environment. The vast majority of classical MD simulation approaches24,29 are not capable to describe the formation of a bicarbonate species due to their inherent formalism and maintain instead the initial chemical topology throughout the simulation and eliminate the possibility of a chemical reaction to occur, which might be an important step leading to an energetically more favorable state. The use of reactive force fields85,86 might be an alternative to improve the description of such systems and to overcome this deficiency. Gas phase cluster calculations19,28,32,37,38 on the other hand employ quantum chemistry, but are limited to single configurations without a proper embedding by explicit solvent molecules formally corresponding to the structure at 0 K in vacuo. Also, in this case, the formation of bicarbonate cannot be observed due to the absence of explicit water molecules. From the experimental point of view, evidence exists that EXAFS studies are not able to distinguish between a monodentate and a bidentate coordination of carbonate in solution.17 A 6-fold coordination may be observed if counterions such as calcium(II) are present in the solution stabilizing the rather high 4-fold negative charge.14,34,40 This could be the reason why experimental data proposes a 6-fold coordination, which is probably not dilute enough to eliminate stabilizing effects arizing from the presence of counterions. Works by Wipff et al.87 and de Jong et al.88 give further evidence that counterions have a significant influence on the structure and stability of uranyl(VI) species and of actinoids in aqueous solution. In our simulation on the other hand, the overall charge of the complex was reduced via protonation. This agrees with conclusions made by de Jong et al.,19 noting that the 4-fold negative charge might destabilize the complex. An important conclusion of these findings is that the structure of a complex in aqueous 12943



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Table 2. Average Bond Distances of Uranyl Carbonates in Åa system

method

UO

U−Oc

U−C

reference

[UO2(CO3)2(HCO3)]3− [UO2(CO3)3]4−

QMCF-MD EXAFSb EXAFSb,e EXAFSb EXAFSc X-rayc DFT(B3LYP)d DFT(B3LYP)d DFT(B3LYP)d DFT(PW91)d DFT(SVWN/PBE96)d MBPT2d DFT(B3LYP/BP86)d MM-MD MBPT2d DFT(VWN/BP86)d X-rayc EXAFSc X-rayc X-rayc EXAFSb MM-MDb,e· X-rayc X-rayc X-rayc X-rayc X-rayc X-rayc X-rayc EXAFSb X-rayc EXAFSc XRDc

1.76 1.80 1.80−1.82 1.80 1.80−1.81 1.80 1.82 1.81 1.85 1.85 1.81−1.83 1.89 1.80−1.86 − 1.88 1.81−1.85 1.80 1.79 1.77−1.78 − 1.81 1.83 1.80 1.81 1.81 1.79 1.78−1.81 1.79 1.80 1.81 1.74 1.77 1.67

2.42 2.43 2.31−2.48 2.43 2.42−2.44 2.43 2.52 2.46 2.57 2.56 2.43−2.52 2.42 2.50−2.60 2.38−2.42 2.41 2.39−2.56 2.43 2.42 2.43 2.43 ± 0.03 2.44 2.39 2.43 2.43 2.44 2.43 2.41−2.46 2.44 2.45 2.44 2.44−2.52 2.46 2.46

2.88 2.88 2.88−2.95 2.89 2.89−2.90 2.88 2.97 2.93 − 3.01 2.91−2.99 2.89 − − 2.84 2.85−3.01 2.87−2.88 2.89 − − 2.90 2.79 2.88 2.90 2.89 2.88 − 2.90 2.90 2.92 2.94 2.94 2.86

this work 16 16 33 17 31 28 36 69 37 19 19 89 29 38 32 90 31 43 23 40 14 34 34 34 34 42 34 34 36 20 18 18

K4UO2(CO3)3

Ca2UO2(CO3)3

Sr2UO2(CO3)3 Ba2UO2(CO3)3 CaNa2UO2(CO3)3 CaMgUO2(CO3)3 Mg2UO2(CO3)3 Na4UO2(CO3)3 UO2CO3

a UO, U−Oc, and U−C denote bond distances of uranium to the axially bound uranyl oxygens, equatorial coordinating carbonate oxygens, and carbon atoms. bLiquid phase. cSolid state. dGas phase calculation. eAdsorbed.

presence of water overlaying with the carbonate oxygen RDF at this distance, leading to the overall RDF depicted in red. Figure 5e−g shows RDFs of U−C. Figure 5e depicts the overall U−C RDF, while Figure 5f,g separates the two peaks. In Figure 5f, the RDF shows the U−C RDF of the bidentately coordinated carbonates yielding an integration of two. The distance for these carbon atoms to uranium is 2.88 Å. Figure 5g indicates the third carbon atom, which is bound coordinatively with just one oxygen to uranium. This is why the coordination distance is enlarged to 3.48 Å indicating a weaker coordination of the third carbonate. The obtained bond distances from the QMCFMD simulation are collected in Table 2 and are compared extensively to the literature. From Table 2 it can be seen that the results are in excellent agreement with several different experimental results as well as with other theoretical investigations carried out at numerous levels of theory. The U−Oc and U−C bond distances match that of experimental results, and also the UO bond distance deviates only marginally from the experiment but is still within the range of the experimental uncertainty. Comparing our results obtained by a MD simulation on a quantum chemical level of theory to those obtained by cluster calculations in vacuo and with implicit solvent, it can be concluded that the explicit inclusion of solvation effects is essential for obtaining

accurate results for the description of the structure of coordinating carbonate ligands. Although the bond distances show only minor deviation from the experiment in the case of cluster calculations, the explicit solvation results in a considerable improvement in the description of coordinating ligands. Furthermore, Table 2 shows that the neglect of correlation effects by using Hartree−Fock does not effect the capability of predicting structural properties. It is also interesting to note that the presence of counterions does not influence the bond distances of the uranyl carbonate in a considerable way, neither does the nature of the counterion. Nevertheless, a change of the equatorial coordination number to six in the presence of counterions appears highly probable. Besides the radial distribution function, the volume slice projection analysis57 is helpful for obtaining useful information on the three-dimensional arrangement of the system. Thereby, the three-dimensional particle density is intersected by a number of planes parallel to a predefined reference plane. The reference plane may be defined via a three-dimensional orthogonal least-square fit to favorable atoms forming a plane. In our case, the uranium atom and the carbons of the bidentately coordinating carbonates were chosen for this purpose. The results of such a volume slice projection of the oxygen density distribution are shown in Figure 6. The left 12944



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Figure 6. Volume slice projections of the solvent oxygen spatial density with respect to the uranyl carbonate species (colormap scale) and of the uranyl carbonate species (grayscaling).

Figure 7. (a) Angular distribution functions for angles in the equatorial coordination sphere of the uranyl ion. The full-width-at-half-maximum (fwhm) is denoted in parentheses. (b) Three-body correlation functions of three hydration shells of the uranyl carbonate complex (solid line) and their comparison to the bulk (dashed line).

Figure 7a shows a schematic representation of the results of calculated angular distribution functions (ADF’s). The values in parentheses denote the full-width-at-half-maximum (fwhm) of the distribution of the respective angle which is useful for the interpretation. Figure 7a evidence a bite angle of 53° for the bidentately coordinating carbonates. The angle between these two carbonates is 85°. The remaining two angles between the third monodentately coordinating bicarbonate and the other two carbonates are between 80 and 83°, respectively. The shown arrangement of ligands in Figure 7a excludes on one hand the possibility of other ligands from entering the equatorial coordination sphere since the resulting repulsion may not lead to a stable configuration. On the other hand, the capability of H-bonding of the bicarbonate with its coligands and the uranyl oxygens prevents the bicarbonate from coordinating to the uranium in a bidentate way (see also Figure 2). Thus, according to the data resulting from an MD simulation on a quantum chemical level, a 6-fold equatorial coordination sphere cannot be supported for uranyl tricarbonate in aqueous solution to be a dominant configuration in the absence of counterions.

representation schematically shows the oxygen density distribution of the solvent and the different intersecting planes. The numbers (±1, ± 2, ± 3, ± 4) denote the position of the various planes with respect to the reference plane (0) and correspond to the numbers in the right graph in Figure 6. The spacing between the invidual planes is 1.7 Å, thus, covering with nine slices a region of ±6.8 Å, i.e., the quantum chemically treated region. In the right representation in Figure 6 the threedimensional particle density for the nine slices can be seen. The solute’s particle density of oxygens is depicted in gray, whereas that of the solvent is color-scaled, with reddish regions denoting high oxygen density. The volume slice projection evidence the flexibility of the monodentately coordinating bicarbonate ion, which apparently requires more volume for switching between different configurations. Furthermore, it can be seen that rather large regions of low, i.e., blueish regions, are observed at the solvent exposed oxygens of the bicarbonate, where the hydrogen is situated. The bidentately coordinating carbonate ions on the other hand keep their position in the equatorial coordiantion sphere of uranium and exhibit regions of high oxygen density at the solvent oriented carbonate oxygens indicating positions for H-bonding. 12945



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Figure 8. Intermittent hydrogen bond correlation C(t) (top, left) and the continuous hydrogen bond correlation S(t) (top,right) for Ou, Oc,coordinating, Oc,non‑coordinating, and Hc and the number of H-bonds (bottom, left) for the mentioned species with water molecules. A schematic representation of the uranyl carbonate complex is given, which is coded by colors according to the graphs.

lifetime of hydrogen bonds formed between carbonate ligands and water molecules, time correlation functions C(t) and S(t) of the following form may be used:

For the analysis of reorganizational patterns regarding hydration shells of hydrated species, so-called three-body correlation functions can be applied.57,91 The application of such a function (eq 3) enables the detection of an ordering or breakdown of the solvent surrounding the solute. A three-body correlation function f 3O1w−X−O2w(s,r,s) may be defined in the following form: fO31 − X − O2 (s , w w

⟨n(s , r , s)⟩ r , s) = 2 2 8π NXρshell rs 2Δs 2Δr

(3)

Nshell(Nshell − 1) 2 Vshell

h(0)h(t ) h

(5)

S(t ) =

h(0)H(t ) h

(6)

with h(t) and H(t) being defined hydrogen bond variables.92 The intermittent hydrogen bond correlation function C(t) and the continuous hydrogen bond correlation function S(t) have typically a double-exponential form and can therefore be fitted according eq 7. From the fitted time correlation functions (Figure 8), the long and the short contribution τl and τs of the respective correlation function can be extracted, where the respective τl is a measurement of the structural relaxation time of hydrogen bonds. In Figure 8 a schematic representation of the structure of the uranyl carbonate complex is given. The different atomic species are color-coded according to the depicted graphs in order to facilitate its interpretation. The long and short contributions τl and τs for C(t) and S(t) are shown in Table 3.

with ρshell =

C(t ) =

(4)

The three-body correlation functions for the first, second, and third hydration shell of the uranyl carbonate complex are shown in Figure 7b. The dashed line denotes the structural organization of bulk water, whereas the continuous line represents the three-body correlation function of the respective hydration shell. For the first hydration shell, a high degree of structural reorganization can be observed, which can be attributed to the negatively charged carbonate ions considerably altering the solvent’s structure. This effect is also present in the second hydration shell, which deviates significantly from the pattern of bulk water. A hypothetic third hydration shell cannot be observed, as can be deduced from Figure 7b. This shell shows almost bulk structural behavior, implying that the effect of uranyl carbonate on the structure of water does not exceed 7 Å, where the solvent is unaffected by the presence of the complex. 3.3. Dynamics of [UO2(CO3)2(HCO3)]3−. For the analysis of dynamical properties regarding the structural relaxation and

y = a ·e−t / τl + (1 − a) ·e−t / τs

(7)

From the graphs in Figure 8 in combination with Table 3, several conclusions can be drawn. It is shown that uranyl oxygens (Ou) form basically one hydrogen bond, which is consistently present but is frequently broken and reformed. Carbonate oxygens Oc,coord,distal of the bidentately coordinating carbonates, which are distal to the bicarbonate show a similar trend, but last even longer when formed. It is shown that also 12946



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Table 3. Long-Range and Short-Range Contribution τl and τs in fs for the Intermittent and Continuous Hydrogen Bond Correlation Functions C(t) and S(t) C(t) Ou Oc,coord,distal Oc,coord,proximal Oc,coord,monodent Oc,bident,bulk Oc,monodent,bulk Oc,monodent,proton Hc

to their excess of electron density, which also promotes the observed bicarbonate formation. Velocity autocorrelation functions (VACF’s) may be used for the calculation of vibrational power spectra.93,94 This approach does not consider any collective modes, however. Nevertheless, it proved to be particularly useful when force constants are calculated using this approach.95−97 The force constant may be calculated using the following expression:

S(t)

τl

τs

τl

τs

1050 1318 983 1827 1847 1191 417 443

107 102 75 71 132 148 44 64

116 227 294 225 65 106 49 27

29 29 80 66 490 483 195 141

k = 4·(π ·c·ν)̃ 2 ·μ

(8)

where c corresponds to the speed of light, ν̃ is the wavenumber, and μ is the reduced mass of the uranium−oxygen pairs. The vibrational power spectra are depicted in Figure 9. Figure 9a shows an overall spectrum of U−O pairs of the complex [UO2(CO3)2(HCO3)]3− and the different underlying contributions. In order to facilitate the interpretation, Figure 9b shows the UOu frequencies, while Figure 9c shows the vibrational power spectra of the carbonate and bicarbonate ligands. Again the overall spectrum of the carbonates is depicted as well as its respective contributions. Since it is wellknown that Hartree−Fock theory typically overestimates vibrational frequencies by approximately 10%, they may be scaled according to the literature.98−100 The obtained scaled vibrational frequencies are shown in Table 4 and are found to be in good agreement with experimental as well as theoretical data. It can be seen that the reliability of results using DFT is strongly dependent on the used functional. Apparently B3LYP calculations by Ikeda et al.36 fit experimental data best. The symmetric stretching frequency for the uranyl ion is 815 cm−1, which results in a force constant k = 587 N/m (5.9 mdyne/Å). This is in perfect agreement with Allen et. al,31 who reported a force constant k = 6.0 mdyne/Å. The small discrepancy can also be explained by the slightly different nature of the investigated systems. From Figure 9c several facts can be extracted. It is shown that the frequencies of the monodentately coordinating bicarbonate are red-shifted, which results from a

up to two H-bonds are formed at these positions. Regarding the carbonate oxygens Oc,coord,proximal of the bidentately coordinating carbonates that are proximal to the bicarbonate, the structural relaxation of H-bonds proceeds faster but when once formed is longer intact. Regarding the monodentately coordinating bicarbonate oxygen Oc,coord,monodent and those of the bidentate carbonate oxygen pointing toward bulk Oc,bident,bulk, it is interesting to note that H-bond relaxation occurs in nearly the same time. Nevertheless, in the latter case, formed H-bonds are much weaker, thus, they are much more frequently formed and reformed. Furthermore, up to four hydrogen bonds can be observed. The protonated bicarbonate oxygen Oc,monodent,proton and the other noncoordinating carbonate oxygens pointing toward bulk Oc,monodent,bulk show noticeable differences because of the presence of the proton. While Oc,monodent,proton shows a short relaxation and lifetime of basically one H-bond, Oc,monodent,bulk evidence two H-bonds with a slower relaxation and longer time of existence. Summarizing these findings, it can be said that uranyl oxygens are poor hydrogen bond acceptors due to the pronounced charge transfer to the uranium atom. However, those carbonate oxygens that do not coordinate toward the uranyl ion are good hydrogen bond acceptors due

Figure 9. Scaled vibrational power spectra of uranyl tricarbonate: (a) entire complex (black), uranyl ion (red), and carbonates coordinating bidentately (blue) and monodentately (orange); (b) uranyl ion; (c) coordinating carbonates (black) distinguishing between two carbonate coordinating bidentately (red), the carbonate residue of the monodentately coordinating bicarbonate (blue), and the proton of the bicarbonate (orange). 12947



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Table 4. A Comparison of Vibrational Frequencies of Uranyl Carbonate Species in Wavenumbers (cm−1): The Asymmetric ν3 and Symmetric ν1 Uranyl Stretching Frequencies (UO) and the Applied Method UO

UO

system

method

ν3 (asym.)

ν1 (sym.)

reference

[UO2(CO3)2(HCO3]3− [UO2(CO3)3]4−

QMCF-MD IR/RAMAN DFT(LDA) DFT(GGA) DFT(B3LYP) DFT(B3LYP) DFT(GGA) DFT(B3LYP/GGA) Raman Raman Raman Raman TRLFS TRLFS IR Raman Raman FTIR

864 889 827−872 862 854 − − 881 − − − 840−926 − − 882 843 859−873 902

815 813 760−783 778 811 871 737−777 775 812 ± 3 812 815 − 859 ± 6 777−805 806 808 805−810 −

this work Allen et al.31 de Jong et al.19 de Jong et al.19 Ikeda et al.36 Kubicki et al.28 Schlosser et al.32 Austin et al.89 Nguyen-Trung et al.101 Madic et al.102 Basile et al.103 Cejka et al.104 Amayri et al.34 Amayri et al.34 Anderson et al.90 Koglin et al.105 Frost et al.35 Amayri et al.76

Ma[UO2(CO3)3] K4[UO2(CO3)3] Na4[UO2(CO3)3] Na2Ca[UO2(CO3)3] a

M = Mg, Ca, Sr, Ba, NaCa, CaMg.

bidentate coordination of all three carbonates might lead to an unstable configuration in the coordination plane perpendicular to the uranyl axis. However, it appears probable that a 6-fold coordination can be achieved upon further cocomplexation with positive charged counterions such as calcium(II), which will be the focus of future simulation work. Another evidence for a 5-fold coordination in aqueous solution is the ability of the bicarbonate hydrogen atom to form H-bonds with the coordinating carbonate and uranyl oxygens, stabilizing the coordination sphere. Since it can be expected that the inclusion of counterions will stabilize a 6-fold coordination, we plan to conduct corresponding studies to confirm this hypothesis.

weaker coordination strength to the uranium. The average frequency for a U−Oc coordinative bond is 204 cm−1 (k = 37 N/m), while the frequency for the monodentate coordinative bond of U−Oc is 183 cm−1 (k = 30 N/m). Thus, the difference between a bidentate and monodentate coordination bond to the uranyl ion can be estimated to be 7 N/m.

4. CONCLUSIONS The presented MD simulation using an extended hybrid QM/ MM approach is capable to give extensive insight into structural and dynamical data of coordinative complexes in liquid environments. It enables detailed examination of ultrafast phenomena, which is valuable for the support of experimental findings. All presented data are found to be in excellent agreement with the reported literature. To our best knowledge, this is the first theoretical work that reports the formation of bicarbonate in the equatorial coordination sphere of the uranyl ion. The estimation of associated free energy ΔG values via a thermodynamic cycle performed at different levels of theory confirmed that, in the absence of counterions, the protonated species is thermodynamically favorable. Since classical MD simulations are in general not capable of describing the formation and cleavage of chemical bonds, instead of a proton transfer reaction, ligand dissociation was observed to reduce the overall charge density of the complex. This further highlights the capability of QM/ MM simulation techniques. However, the presented QMCFMD simulation covered a sampling time of 25 ps, which may be too short to observe a ligand exchange reaction occurring on a slower time scale, and thus the occurrence of such an exchange cannot be excluded based on the presented simulation data. The equatorial coordination number of five is in contrast with other theoretical investigations on a quantum level of theory. A possible explanation for this discrepancy is the absence of explicit solvent molecules of the investigated cluster and the consideration of a single configuration at 0 K in vacuo or implicit solvent, which underlines the capabilities of MD simulations at a quantum chemical level. Furthermore, a

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +43-512-507-57102. Fax: +43-512-507-57199. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS Financial support for this work by a Ph.D. scholarship of the Leopold-Franzens-University of Innsbruck (Rector Prof. Dr.Dr.hc.mult. Tilmann Märk) for A.O.T. is gratefully acknowledged. This work was supported by the Austrian Ministry of Science BMWF UniInfrastrukturprogramm as part of the Research Focal Point Scientific Computing at the University of Innsbruck.

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Structure and Dynamics of the Uranyl Tricarbonate Complex in

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