A Comparative Quantum Mechanical Charge Field Study of Uranyl

Article pubs.acs.org/JPCB

A Comparative Quantum Mechanical Charge Field Study of Uranyl Mono- and Dicarbonate Species in Aqueous Solution Andreas O. Tirler, Alexander K. H. Weiss, 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: A theoretical study of the structure and dynamics of the uranyl mono- and dicarbonate species in aqueous solution employing the quantum mechanical charge field-molecular dynamics (QMCF-MD) method is presented. The obtained structural and dynamical data were found to be in good agreement with several experimental data and theoretical investigations available in the literature. The fivefold coordination pattern observed for the equatorially bounded ligands of the uranyl ion was found to deviate from the results of a number of previous studies based on quantum chemical cluster calculations and classical molecular dynamics studies, however. The reason for the different description of the system can be seen on the one hand in the capability of QM/MM-type simulations to take charge transfer, polarization, and many-body effects into account, while the presence of a large number of MM solvent molecules ensures that the simulation system mimics the environment in the bulk of a liquid. In addition to pair, three-body and angular distributions, the use of spatial density data enabled a detailed characterization of the threedimensional arrangement of ligands in the vicinity of the complex. Further analysis of dynamical data such as hydrogen-bond correlation functions and mean lifetime analysis enabled a detailed characterization of the properties of the complexes in aqueous solution. It could be shown that the bulk-oriented oxygen atoms of the carbonate ions form strong hydrogen bonds with bulk molecules, while the tendency of the oxygen atoms of the uranyl(VI) show decreasing tendency to form hydrogen bonds upon complexation.

1. INTRODUCTION Uranium is among the heaviest naturally occurring elements on Earth. It is enclosed in several minerals such as uraninite, autunite, brannerite, and carnotite,1 leading to a natural mass concentration of uranium of approximately 3 mg/kg in Earth’s crust.2 Uranium can exist in a variety of stable oxidation states and possesses a rich coordination chemistry. Especially the high oxidation states of uranium, U(V) and U(VI), are of great importance for environmental and safety assessment.3 These species form linear, triatomic oxocations, the so-called “uranyl” ions (UO+2 and UO2+ 2 ), which are often strongly complexed by hard inorganic oxoligands such as nitrate, acetate, oxalate, phosphate, sulfate, and carbonate.4 Uranium is a strong αemitter with an energy of decay of 4.196 MeV and a half-life of 4.47 billion years.5 Diffusion and migration of such species from contaminated sites has been recognized as a serious environmental concern.6,7 Uranyl cations, especially the dominant UO2+ 2 species, are of special interest because they may form whenever uranium is released into the environment,3 be it from natural or anthropogenic processes. Uranyl ions are strongly complexed by carbonate in aqueous solutions, exhibiting high stability constants.8−10 Due to this strong complexation, the redox disproportionation reaction of the U(V)/U(VI) couple becomes irreversible,11 and the solubility of uranium is greatly © 2013 American Chemical Society

improved due to the negative charge of carbonates. Because of the high occurrence of strong complexation agents such as carbonate and bicarbonate in environmental systems,12−15 uranyl carbonates are highly relevant uranium complexes in aqueous solution and by far the most extensively studied actinoid complexes.4,6,7,12−53 Naturally occurring minerals, for example, rutherfordine, liebigite, and andersonite, additionally reflect the stability of uranyl carbonates.40,54,55 Three relevant uranyl carbonate species have been reported in aqueous solution, [UO2(CO3)n]2(1−n) (n = 1, 2, 3), the monocarbonate, the dicarbonate, and the tricarbonate, respectively. These uranyl carbonate species have also the tendency to oligomerization if the concentration is large enough,4,11 and studies of these systems aimed at managing and remediating uranium contaminated sites36−38 have gained increased interest in recent years. Unfortunately, the handling of uranium-containing substances in terms of sample preparation and the toxicity of uranium and its daughter products is not unproblematic, which makes theoretical investigations even more appreciated. Additionally, theoretical research is suitable to investigate the manifold oxidation states and transient species, which are not Received: July 19, 2013 Revised: November 7, 2013 Published: November 20, 2013 16174

dx.doi.org/10.1021/jp407179s | J. Phys. Chem. B 2013, 117, 16174−16187

The Journal of Physical Chemistry B

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yet accessible via experiment.11 As different uranyl carbonates are of great environmental relevance,34,35 a number of theoretical investigations regarding the structure and dynamics of uranyl carbonates have been carried out recently.4,43−51 These studies range from cluster calculations at different levels of theory, including density functional theory (DFT) and correlated methods to molecular mechanical simulation studies with empirically derived potentials. To the best of knowledge, no MD simulations at a quantum chemical level were conducted for any of the mentioned uranyl carbonate systems as of yet. In addition, most investigations concentrate on the uranyl tricarbonate species dominating in aqueous solution, leaving out the other important uranyl mono- and dicarbonate species, which have been shown to be of high relevance at environmental pH as well.35,56 From an experimental point of view, this is quite understandable because it is necessary to prepare an almost single species solution with a concentration above 10−4 M,52 which is hardly achievable due to the coexistence of several different aqueous U(VI) species under most experimental conditions.57 Theoretical investigations of uranyl mono- and dicarbonate on the other hand offer a complementary route for dealing with these highly dynamical systems as their time scale of observance lies in the subpicosecond range. Comparing uranyl tricarbonate to the respective dicarbonate, de Jong et al. showed that the latter is even more stable than the tricarbonate due to its lower charge.4 The benefit of theoretical studies at the molecular level for the understanding of fundamental microscopic mechanisms such as complexation and adsorption on different surfaces, enabling the prediction of possible migration processes of uranium,4 was also pointed out. Doudou et al.,44 on the other hand, discussed the problem arising from the use of empirically derived potentials in MD simulations and pointed out that quantum chemically derived potentials would give more reliable results, though such an approach appears difficult to achieve. Kubicki et al.43 performed gas-phase cluster calculations of various uranyl carbonate complexes and suggest that MD simulations in the framework of explicit solvent treatment should be carried out in order to compass the error made by treating such systems with implicit solvation techniques. This work presents a hybrid ab initio quantum chemical/ molecular mechanical MD simulations of the mono- and dicarbonate complexes of UO2+ 2 in aqueous solution. The microscopic structure of the systems is compared with spectroscopic data available in the literature, in particular, for mean values of bond distances and coordination numbers (CNs) in solution provided by X-ray diffraction58 and extended X-ray absorption fine structure (EXAFS).59 Furthermore, calculated vibrational frequencies are compared to various experimental data60 as well as to previous theoretical works.4,48

case three-body potentials) quite inevitable for a proper molecular mechanical description of the underlying interaction. However, a number of comparative simulation studies of simple ionic solutes (e.g., aqueous Mg(II),68 Al(III),69,70 as well as hydrated transition-metal ions71−73) have clearly indicated that the achievable accuracy of classical potentials is limited even if up to four exponential/polynomial terms are employed to formulate the respective interaction function. Furthermore, the ab initio quantum chemical calculations of points on the potential surface are typically performed for gas-phase systems, which may promote the occurrence of artificial charge transfer effects, especially in the case of systems with high oxidation states such as UO22+, and consequently, the constructed potential functions are parametrized to an unsuitable potential energy surface. The QMCF-MD approach was explicitly developed to avoid the need of any analytical non-Coulombic solute−solvent potential functions, enabling ab initio quantum chemical simulations of every kind of system in aqueous solution. Similar to QM/MM approaches, also in the QMCF method, the simulation box is divided into regions, where different levels of theory are applied. The main difference between a conventional QM/MM and the QMCF approach lies in the greater size of the QM region, which is enlarged in order to include more solvent molecules surrounding the solute. This expansion enables a partitioning of the QM region into two further subregions, referred to as the core zone and the layer zone, respectively. Previous works have shown that QMCF-MD simulations of ions in aqueous solution employing double-ζ + polarization basis sets at the Hartree−Fock level give satisfactory results in terms of accuracy and computational effort.73−75 Probably, the most challenging part in any QM/MM scheme is the description of interactions of QM particles with MM atoms. In our case, these interactions are partly introduced into the Hamiltonian ĥcHF via a perturbation term V̂ ′ ̂c ̂ c + V̂ ′ hQMCF = hHF M

V̂ ′ =

∑

(1)

qJ

r J = 1 IJ

(2)

A QM particle J in the QM core zone interacts with all other particles in the QM region via the quantum mechanical treatment, whereas the interactions with particles of the MM region are incorporated through an electrostatic embedding (FQM J ). Non-Coulombic interactions between particles in the core zone and the MM region can be neglected because the increased QM region enables a layer zone of at least 3 Å thickness, insulating the QM core zone from the short-ranged non-Coulombic interactions.76,77 A particle J in the QM layer zone is also treated quantum mechanically like particles in the QM core zone. Additionally, non-Coulombic contributions arising from interactions of the layer zone with the MM region are taken into account (FMM IJ ). For complexes, like in our case, this implies that solvent−ligand potentials have to be considered if the ligands (in this case the carbonate ions) are not included into the QM core zone. A particle J in the MM region is treated molecular mechanically, interacting with all other MM particles via a classical potential FMM IJ . Coulombic interactions with the QM region (N1 + N2) are evaluated dynamically by means of a Mulliken population analysis for all QM atoms,78 which is performed in every step of the MD

2. THEORETICAL METHODS The used QMCF-MD methodology (quantum mechanical charge field-molecular dynamics)61−64 is an enhanced QM/ MM approach,65−67 which does not require potential functions for all species present in the investigated system other than the solvent. Because the construction of such interaction potentials is especially challenging for charged solute species, with several thousand single-point energies to be computed using ab initio quantum chemical techniques, this methodical enhancement is of great benefit. Especially for charged species that are not spherically symmetric like the uranyl ion, the procedure is even more difficult, making many-body potentials (in the simplest 16175



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correlation was observed using MP2 and B3LYP in comparison to more accurate CCSD calculations. Furthermore, recent simulation studies have demonstrated that the commonly used DFT functionals BLYP (Becke−Lee−Young−Parr)80,81 and PBE (Perdew−Burke−Enzerhofer)82 lead to an inaccurate description of liquid water,83,84 resulting from a too strong hyrogen bonding, which was found to lead to melting temperatures of approximately 410−415 K.84 Although the application of dispersion-corrected DFT methods such as DFT +D85,86 improves the description of liquid water,87 it is not yet clear whether this is also the case when investigating hydrated solutes. For these reasons and considering the manageable computational effort, Hartree−Fock was chosen as the best compromise between the accuracy of the results and computational effort for the MD simulations of the uranyl carbonate species. From a theoretical point of view, some specific aspects have to be considered while treating actinoids. These elements are typically of high nuclear charge and possess a large number of electrons. On the one hand, this requires a considerable computational effort, and on the other hand, effects resulting from special relativity become significant. Further effects resulting from the presence of many low-lying 5fn electronic configurations may become relevant. After a comparison of data resulting from energy minimizations performed with Gaussian0988 using a number of basis sets available in the literature89,90 with previous works,4,43−45,48−51,79,91 the Stuttgart RSC (relativistic small core) ECP92 was considered the most appropriate basis set for uranium. This RSC ECP covers 60 electrons and accounts for correlation and relativistic effects of these core electrons. Former works using the QMCF approach61−64 have pointed out that at least double-ζ + polarization basis sets are necessary and sufficient to obtain an appropriate description of the respective species in solution. This is why other entities present in the system, that is, water, carbonate, and uranyl oxygens, were treated with Pople’s 6-31G(d,p) basis sets.93 This choice can also be argued by the results of previous works on highly charged ions in aqueous solution using QMCF.74 For the MD simulations, the uranyl cation UO+2 2 was placed in the center of the QM core zone having a radius of 2.0 Å. The coordinating carbonates were situated in the QM layer zone, which had a radius of 7.0 Å. Doing so, the inclusion of explicit carbonate− water non-Coulombic potentials was necessary, as discussed above. From the large number of potentials available in the literature,44,46,94−98 the recently reported potentials from Zeebe et al.97 were chosen because they were explicitly generated for the carbonate applied in connection with a SPC-type water model. The smoothing zone was set to 0.2 Å, that is, from 6.8 to 7.0 Å. The simulation of the uranyl carbonates [UO2(CO3)n]2(1−n) (n = 1, 2) was conducted in a simulation box containing 1000 explicitly treated water molecules, leading to a cubic box dimension of approximately 31 Å with the density of pure water of 0.997 g/cm3 at 298.15 K. The simulations were carried out in the canonical NVT ensemble employing the Berendsen algorithm99 to keep the system at 298.15 K. The equations of motion were solved by applying the velocity-Verlet algorithm100 with a time step of 0.2 fs to properly sample fast hydrogen movements. The Coulombic cutoff was set to 12.0 Å, and the reaction field method101,102 was employed to include longe-range Coulombic interactions. The water−water interactions were described by the flexible water model SPC-mTR of Liew et al.103 The size of the QM

simulation. The obtained partial charges are then included into the Coulombic term. Non-Coulombic contributions with particles of the layer zone are obtained via the evaluation of solvent−solvent potential functions, and if necessary, also of solvent−ligand potential functions M

F Jcore = F JQM +

∑ I=1

qJQM ·qIMM ⎡ ⎛ r ⎞3 ⎤ r ⎢1 + 2 ε + 1 ·⎜ IJ ⎟ ⎥ IJ ⎢⎣ 2ε − 1 ⎝ rc ⎠ ⎥⎦ || rIJ || rIJ2 (3)

QM MM ⎡ ⎧ ·qI ⎛ r ⎞3 ⎤ r ⎪ qJ ⎢1 + 2 ε + 1 ·⎜ IJ ⎟ ⎥ IJ · ⎢⎣ 2ε − 1 ⎝ rc ⎠ ⎥⎦ || rIJ || rIJ2 I=1 ⎩ M

F Jlayer = F JQM +

∑ ⎨⎪

⎫ ⎪ + FIJMM ⎬ ⎪ ⎭ M

FJMM =

(4) N1+ N2

∑ FIJMM + ∑ I=1 I≠J

I=1

qIQM ·qJMM rIJ2

·

⎡ ⎛ r ⎞3 ⎤ r ⎢1 + 2 ε + 1 ·⎜ IJ ⎟ ⎥ IJ + ⎢⎣ 2ε − 1 ⎝ rc ⎠ ⎥⎦ || rIJ ||

N2

∑ FIJMM I=1

(5)

To avoid discontinuities at the QM/MM interface, a smoothing function S(r) with a certain cutoff (rc − Δr to rc) is applied because at this interface, potentials Vs(r) and their respective derivatives Fs(r) are not continuous. This function continuously changes from values of 0 to 1, with the functions’ first and second derivatives being zero at the boundaries. It has been shown in numerous previous studies that a value Δr of 0.2 Å is convenient.61−64 F Jsmooth = S(r ) ·(F Jlayer − FJMM) + FJMM

(6)

⎧1 if r ≤ rc ⎪ 2 2 2 2 2 2 ⎪ (r − r ) (rc + 2r − 3(rc + Δr ) S(r ) = ⎨ c if rc ≤ r ≤ rc + Δr (rc2 − (rc + Δr )2 )3 ⎪ ⎪ if r ≥ rc + Δr ⎩0

(7)

For more detailed information about the QMCF method and its implementation, the reader is referred to the literature.61−64

3. SIMULATION DETAILS Previous works on rather small ions concerning their structure and dynamics in aqueous solution using the QMCF approach were found to be in good agreement with experimental literature.73−75 This work should serve to demonstrate the applicability of the QMCF approach to complex systems, namely, to uranyl mono- and dicarbonates. For this purpose, a proper choice of basis sets and a sufficiently high level of theory are of particular importance to achieve a satisfactory compromise between accuracy of results and computational effort. At present, the most advanced levels of theory for treating such systems in the context of QMCF-MD simulations are ab initio Hartree−Fock and hybrid density functional theory, whereas a correlated ab initio treatment of the quantum chemical region is still too expensive in terms of computational time. Nevertheless, Frick et al. gave an estimation of the influence of electron correlation for the UO+2 2 ion in aqueous solution.79 Qualitatively, an overestimation of electron 16176



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Figure 1. (a) Abbreviations for the different atomic species represented schematically for uranyl dicarbonate. Screenshot of representative configurations of (b) uranyl monocarbonate and (c) uranyl dicarbonate observed in the QMCF simulation.

Figure 2. Spherical radial pair distribution functions for uranyl monocarbonate (left) and for uranyl dicarbonate (right).

4. RESULTS AND DISCUSSION 4.1. Structure. In Figure 1a, abbreviations for the different atomic species of the uranyl carbonate systems are schematically depicted, which are used in all further discussions. Both uranyl carbonate complexes remained stable during the whole simulation, and no dissociation of ligands bound to the uranium atom was observed. Besides marginal deviations of a few degrees, the uranyl ion remained linear. The coordinating carbonate(s) and the respective water molecule(s) were situated in a plane perpendicular to the system’s main axis (Figure 1c and d). Radial distribution functions (RDFs) were calculated in order to characterize the coordination scheme highlighted in Figure 1b and c and to obtain different bond and coordination distances relevant for the systems. The spherical radial pair distribution functions are shown in Figure 2. Figure 2a and b shows the overall RDFs for uranium−oxygen distances for the uranyl monocarbonate and dicarbonate, respectively. As these RDFs correspond to an overlay of all oxygen species present in a range up to 10 Å, further RDFs were generated in order to distinguish the constituents, which resulted in Figure 2c−h. Figure 2c and d shows the RDFs of U−Ou, Figure 2e and f the respective U−Oc, and Figure 2g and h oxygen atoms of surrounding water molecules. The mean distance between U and Ou is found as 1.72 and 1.74 Å in case of the monocarbonate and dicarbonate, respectively. The integration of the peak yields a value of 2, corresponding to the two uranyl

region of 7.0 Å allowed an explicit treatment of the complex and, on average, 35 additional water molecules by quantum mechanics, embedding the uranyl carbonate complex in a proper aqueous environment. Energy and gradient calculations within the QMCF framework were calculated using the software package TURBOMOLE 6.3.104 The explicit treatment of overall up to 40 molecules on a quantum mechanical level resulted in computation times of approximately 13 months on an Intel Xeon 12-core system. An extensive classical equilibration of more than 200 ps ensured that that the observed five-fold coordination pattern provides a well-equilibrated configuration for the QMCF MD simulation. Furthermore, gas-phase cluster calculations with a different number of coordinating ligands were carried out, confirming a five-fold coordination to be the most suitable starting structure for the subsequent QMCF MD simulation. After invoking the QMCF treatment, a re-equilibration of 10 ps was performed prior to sampling. The observed structural relaxation did not lead to any change in the coordination number, which further confirms that the starting configuration was adequately prepared. Next, 125000 MD steps were generated for data sampling, leading to trajectories of 25 ps for each system, which were subsequently analyzed in terms of structure and dynamics. Graphical representations of molecules were created using the visualization software VMD.105 16177



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oxygens bound covalently to uranium. Figure 2e and f shows the coordinating carbonate oxygens of both systems. From the RDFs and the corresponding integration, it can be concluded that the carbonates coordinate via two oxygens in a bidentate arrangement to the uranium atom. The respective mean distance of those coordinated carbonate oxygens is 2.36 Å for the monocarbonate and 2.39 Å in the case of the dicarbonate species. The second, smaller peaks reflect the remaining carbonate oxygens pointing toward bulk with an average distance from uranium of 4.05 Å in the case of the monocarbonate and 4.10 Å in the case of uranyl dicarbonate. The integration yields values of 3 and 6, as expected. Figure 2g represents the water distribution around uranyl monocarbonate. It can be seen that two well-defined coordination shells are formed. The first hydration shell reflects three water molecules directly coordinated to uranium, as also visible in Figure 1b and from the integration of the peak in Figure 2g, yielding a value of 3. In the case of uranyl dicarbonate in Figure 2h, the integration equals 1, resulting from the single water molecule binding to uranium in this complex (Figure 1c). The distance of the coordinating water molecules is larger than that of the corresponding carbonate ligands, namely, 2.48 and 2.50 Å for mono- and dicarbonate, respectively. The increase of the U−O distance results from a more pronounced charge transfer from the carbonate ligand to the uranium atom in the case of the dicarbonate. This finding is also reflected by the time average Mulliken population of the uranium atom, amounting to 2.67 and 2.61 in the case of the mono- and dicarbonate species, respectively (see Figure 3).

To further investigate the change of the atomic populations, the partial charges obtained from a number of different gasphase clusters treated at the same level of theory as that in the MD simulation were compared (Table 1). The calculation of the Mulliken partial charges of each of those clusters was not just conducted for gas-phase clusters (vac.) but also using a Polarizable Continuum Model (PCM).106 In the case of the uranyl ion, it can be seen that the inclusion of explicit water molecules considerably improves the description of the system due to the explicit consideration of charge transfer effects. Further, increasing charge transfer can be observed by substituting water molecules with carbonate ions. Both substitutions lead to a further decrease of the uranium charge, which is in line with the data obtained from the simulation. However, as can be seen in Figure 3, the charges fluctuate around their mean value, which cannot be taken into account by considering one minimum geometry in the case of cluster computations. Nevertheless, the latter provide further evidence for the bond elongation in the case of the uranyl dicarbonate compared to the monocarbonate. For both uranyl complexes, a coordination number of five in the equatorial plane is observed, be it two carbonates coordinating bidentately and an additional water molecule for uranyl dicarbonate or a single carbonate and three water molecules in the case of uranyl monocarbonate. The observed charge transfer from the negatively charged carbonate ions to the uranyl observed in the QMCF-MD simulation makes an increase of the CN beyond five highly improbable. Classical MD simulations, which do not explicitly take this essential phenomenon into account, are unlikely to provide an adequate description of these systems, as has previously been implied by the authors of classical simulation studies.44 All observed uranium−oxygen distances are slightly increased in the dicarbonate system in comparison to the monocarbonate. The presence of two carbonate ions in uranyl dicarbonate provides additional electron density to the uranium, which leads to a weakening of the uranium−oxygen distances along with a decrease of the overall charge. As mentioned earlier, no ligand dissociation was observed during the simulation time of 25 ps, which agrees well with the experimental values for the water exchange at the uranyl ion reported as 1.3 × 106 s−1, that is, on average one exchange per microsecond.107 Although such exchange events may take place in a QMCF-MD simulation, the time scale is far beyond the sampling limit of MD simulations at the quantum chemical level, and the possibility to observe such an event is very small. The second coordination shell is, by nature, a little broader and has its maximum at 4.65 Å for the monocarbonate and at 4.83 Å in the case of uranyl dicarbonate. In order to obtain a more detailed understanding of the hydration of the investigated systems, hemispherical RDFs75 of Ou and Oc oxygens pointing toward bulk were calculated.

Figure 3. Time series of the Mulliken net charge of the uranium atom (black lines) in atomic units for uranyl monocarbonate (top) and uranyl dicarbonate (bottom) and the respective time average (red lines).

Table 1. Partial Charges for Uranium (qU), the Uranyl Oxygens (qOu), and the Uranyl Ion (qUO2+2 ) from a Mulliken Population Analysis in a Gas-Phase Calculation (vac.) and Using the Implicit Solvent Model PCM [UO2(H2O)5]2+

UO2+ 2

[UO2(CO3)(H2O)3]

[UO2(CO3)2(H2O)]2−

vac.

PCM

vac.

PCM

vac.

PCM

vac.

PCM

qU qOu

+2.86 −0.43

+3.34 −0.67

+2.69 −0.61

+2.83 −0.67

+2.51 −0.72

+2.70 −0.74

+2.46 −0.80

+2.56 −0.80

qUO2+2

+2.00

+2.00

+1.47

+1.49

+1.07

+1.22

+0.86

+0.96

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Figure 4. Hemispherical radial pair distribution functions for uranyl monocarbonate (a) Oc−Ow (red), Oc-Hw (black) and (c) Ou−Ow (red), Oc−Hw (black) and for uranyl dicarbonate (b) Oc−Ow (red), Oc−Hw (black) and (d) Ou−Ow (red), Oc−Hw (black).

Figure 4a and b shows the Oc−Ow and Oc−Hw pair distribution function, taking into account just the hemisphere pointing toward the bulk. It can be seen that in both systems, a distinct first hydration shell consisting of two or three water molecules is formed. These water molecules are weakly bound through hydrogen bonds characterized by fast dynamics because the integration of the RDFs yields noninteger values. Also, a second weaker hydration shell can be observed for both systems at a distance of approximately 3 Å. The first shell peak of the Hw− Oc distribution is located at 1.92 and 1.90 Å in case of the mono- and dicarbonates, respectively, that is, the characteristic distance for hydrogen bonding. The sharp peaks indicate the formation of strong hydrogen bonds with two to three water molecules. In Figure 4c and d, the hemispherical RDFs of Ou− Ow and Ou−Hw are depicted, also showing only the hemisphere oriented toward the bulk. Shoulders at the typical H-bonding distance of 2.0 Å are visible; however, the low intensity implies that these hydrogen bonds are much weaker, and it can be concluded that the respective lifetime is much lower compared to those formed by the solvent-exposed oxygen atoms of the carbonate ions discussed above. Therefore, a detailed analysis of the H-bond lifetimes has been performed, which is discussed in the Dynamics subsection below. In order to obtain more detailed information on the threedimensional arrangement of the system, a volume slice projection analysis75 was carried out. The basic idea is to intersect the three-dimensional particle density with a number of planes parallel to a predefined reference plane. In our case, the latter was defined via a three-dimensional orthogonal leastsquares fit to the position of the uranium atom and the coordinating oxygen atoms of the carbonate anions. For detailed information, the reader is referred to Weiss et al.75 In Figure 5, the volume slice projection of the oxygen density distribution is shown for uranyl monocarbonate (top) and uranyl dicarbonate (bottom). The numbers (±1, ± 2, ± 3, ± 4) in the graph depict the position of the various planes relative to the reference plane (0). The spacing between the individual layers was chosen to be 1.6 Å, leading to nine slices covering a region of ±6.4 Å. For a better understanding, the nine slices are

Figure 5. Volume slice projections of the solvent oxygen spatial density with respect to the uranyl carbonate species (color map scale) and the uranyl carbonate species (gray scaling), in the case of uranyl monocarbonate (top) and uranyl dicarbonate (bottom), respectively.

shown in a schematic representation of the simulation system in the left part of Figure 5. The density resulting from uranyl mono- and dicarbonates and the coordinating water molecules is depicted in a gray color scale located mainly in layers 0 and ±1. The oxygen density of the solvent water molecules is depicted via a color scale with red and yellow corresponding to high densities, whereas blue and white regions denote regions with low to zero density. A high oxygen density can be seen around the uranyl oxygens (slices −1, +2) and the coordinating carbonate (slices 0, +1), which leads to the conclusion that at those positions, hydrogen bonds are formed. Similar conclusions can also be made for the uranyl dicarbonate system. The volume slice projections in the lower part of Figure 5 clearly show the bidentate coordination 16179



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Table 2. Average Bond Distances of Uranyl Mono- and Dicarbonate in Åa system UO2CO3

[UO2(CO3)2]2−

method QMCF-MD LDAb MM-MD MM-MD B3LYPb MP2b CCDb CASMCSFb XRAYc QMCF-MD LDAb B3LYPb MM-MD B3LYPb MM-MD B3LYPb MP2b CCDb EXAFS

UO

U−Oc

1.72 1.776 1.83

U−Ow

2.36 2.136 2.36 2.34 2.18−2.33 2.14−2.26 2.17−2.18 2.16 2.44−2.48 2.39 2.295 2.47 2.38−2.40 2.36 2.35 2.36 2.33 2.34 2.31−2.47

1.75−1.77 1.78−1.81 1.74 1.69 1.74 1.74 1.814 1.80

1.79 1.82 1.76 1.80−1.82

2.48 2.51 2.49 2.61−2.80 2.56−2.77 2.56−2.77

2.50 2.63 2.48−2.51 2.50 2.49

ref this work de Jong et al.4 Kerisit et al.47 Kerisit et al.46 Majumdar et al.48−50 Majumdar et al.48−50 Majumdar et al.48,50 Majumdar et al.48 Finch et al.58 this work de Jong et al.4 Kubicki et al.43 Doudou et al.44 Doudou et al.44 Kerisit et al.46 Majumdar et al.50 Majumdar et al.50 Majumdar et al.50 Bargar et al.59

a

UO, U−Oc, and U−Ow denote bond distances of uranium to the axially bound uranyl oxygens, equatorial coordinating carbonate, and water oxygens. bGas-phase calculation. cSolid state.

of the carbonates and also the coordinating water molecule (greyish regions, slice 0, +1) around the uranyl species. Again, red moieties denote regions of high oxygen density. This is especially the case near the uranyl oxygens (slice −3, +2) and also at the carbonate oxygens that point toward the bulk (slice −1, +1). These regions indicate high probability for H-bonding. Other regions of high oxygen density can be observed also at the coordinating carbonate oxygens that are in proximity to the coordinating water molecule (slice 0). It can be assumed that this water molecule coordinating to uranium is further stabilized by the hydrogen-bond network. Table 2 summarizes the bond distances obtained from the QMCF-MD simulations in comparison to data available in the literature. As mentioned earlier, only few experimental data are available for uranyl mono- and dicarbonates in aqueous solution. Overall, good agreement with different data is observed. The obtained UO bond distances of 1.72 and 1.74 Å for uranyl mono- and dicarbonates reported earlier are in excellent agreement with experimental (1.74,58 1.80− 1.82 Å)59 as well as with other theoretical investigations for uranyl monocarbonate (1.69−1.77 Å)48,50 and -dicarbonate (1.76−1.82 Å),4,43,50 respectively. This is also the case for the coordinating U−Oc and U−Ow bond distances in uranyl monoand dicarbonates, which were reported earlier. Comparing our MD simulation results to a high-level calculation from Majumdar et al.,50 for instance, the obtained distances of U−Ou are consistent. The equatorial bond distances of carbonate and water are slightly higher in our case. Nevertheless, it should be noted that the calculations of Majumdar et al. were performed without taking explicit solvent molecules into account. From the comparison in Table 2, it can be concluded that electron correlation as well as relativistic effects beyond the ECP treatment might not influence the obtained results in a significant way. The angles corresponding to the peak maxima as well as the respective full width at half-maximum (fwhm) values observed in the angular distribution functions (ADFs) of atoms coordinating the uranium atom are depicted in Figure 6. It

Figure 6. Average angles (fwhm are given in parentheses) of first shell ligands located in the equatorial plane of uranyl monocarbonate (left) and uranyl dicarbonate (right) obtained from the QMCF MD simulation.

can be seen that the bite angle of the carbonate is almost unaffected by the nature of its co-ligands. The left picture provides evidence that the coordinating carbonate oxygens occupy a larger volume leading to a wider angle of the adjacent water molecules. The data in Figure 6 also demonstrate that the two vicinal carbonates repel each other, resulting in an angle slightly above 90°, while the angle between carbonate and water is close to 75°. Due to this finding, a six-fold coordination including one more water ligand, as proposed in previous works,43,44 cannot be supported by the MD simulation at the ab initio quantum chemical level of theory. For analyzing reorganizational patterns of hydration shells, so-called three-body correlation functions can be applied.108 The aim is to detect an ordering or breakdown of the surrounding solvent’s structure, employing a three-body particle correlation f 3O1w−X−O2w(s,r,s) of the following form fO31 −X−O2 (s , r , s) = w

w

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

(8)

with 16180



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Figure 7. A three-body particle correlation for the respective hydration shells of uranyl monocarbonate (left) and uranyl dicarbonate (right).

ρshell =

Table 3. Average CNs and MRT Values for Water at Uranium, the Uranyl Oxygens, and Pure Water in Uranyl Monocarbonate and Dicarbonate

Nshell(Nshell − 1) 2 Vshell

(9)

For further information, the reader is referred to Weiss and Hofer.75 The resulting three-body particle correlation of the different hydration shells of uranyl mono- and dicarbonate are shown in Figure 7. The left graphs of Figure 7 depict the threebody particle correlation for the solvation pattern of uranyl monocarbonate. The first hydration shell refers to the coordinating water molecules directly to uranium. As expected, the strong structure-forming properties within this shell can be clearly identified. The first hydration shell in the uranyl dicarbonate case (right graphs in Figure 7) cannot be analyzed via three-body correlations because only one water molecule is coordinating to uranium. The correlation functions for the other regions are very similar for both systems. The second hydration shell differs slightly as the additional carbonate in the dicarbonate case leads to a higher degree of solvent reorganization than that observed for the monocarbonate. The three-body correlations beyond the second shell are almost identical for both species, showing near-bulk-like features in the third shell and the presence of a bulk structure in a proposed fourth shell. This implies that no fourth hydration shell is formed in these systems and that the solvent beyond the third hydration shell has to be considered as bulk. 4.2. Dynamics. For investigations of dynamical properties of aqueous systems, the mean residence time (MRT) has proven to be an especially useful tool, following the motion of each ligand in a defined coordination shell. Whenever a ligand enters or leaves the shell for a defined time interval t*, it is considered as an exchange event. The MRT is obtained as the product of the average coordination number and the simulation time, divided by the number of registered exchanges. A t* value of 0.5 ps was reported to be a suitable choice,109 but also values for t* = 0.0 ps have been used in the past. In Table 3, MRT values for the water exchange of U, Ou, and Oc pointing toward bulk are listed. For both systems, no displacement of uraniumcoordinated water molecules was observed during the simulation. From Table 3, it can be seen that the values for

average CN t* = 0.5 ps U−Ow 1st shell U−Ow 2nd shell Ou−Hw 1st shell Oc−Hw 1st shell

3.0 15.8 0.7 2.9

U−Ow 1st shell U−Ow 2nd shell Ou−Hw 1st shell Oc−Hw 1st shell

1.0 12.6 0.7 3.0

Ou−Hw 1st shell Ou−Hw 2nd shell pure water110,111

exchanges t* = 0.5 ps

t* = 0.0 ps

Uranyl Monocarbonate 0 220 882 4 677 62 993 Uranyl Dicarbonate 0 206 814 7 774 56 1341 Uranyl Ion79 2 182 20 255 24

269

MRT in ps t* = 0.5 ps

t* = 0.0 ps

1.83 5.86 1.20

0.46 0.03 0.07

1.58 2.97 1.38

0.40 0.02 0.06

5.55 2.50

0.02 0.44

1.70

0.20

the number of exchanges and MRTs at Ou obtained for uranyl monocarbonate differ only slightly from values obtained for the uranyl ion in aqueous solution.79 However, when a second carbonate coordinates to uranium, the number of exchanges increases while the MRT value decreases significantly. The reason is the additional electron density provided by the second carbonate ion. The resulting charge transfer to uranium weakens the UOu bond, which in turn weakens the binding strength of H-bonds of Ou to water molecules, and the exchange of solvent molecules occurs faster and more frequently. Oc oxygens show considerably higher exchange rates than the respective Ou oxygens, which leads to the conclusion that the carbonate oxygens are highly dynamical positions in terms of H-bonding. The low MRT value provides evidence that several weak H-bonds with a very short lifetime are formed at these carbonate oxygens pointing toward the bulk. Comparing the MRT values and the numbers of 16181



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Figure 8. Intermittent H-bond time correlation C(t) for the uranyl oxygens (average), the uranium coordinating carbonate oxygens (average), and the carbonate oxygen toward bulk for uranyl monocarbonate (top) and uranyl dicarbonate (bottom).

Table 4. Long-Range and Short-Range Contribution τl and τs in fs of H-Bonds in the Case of Uranyl Monocarbonate and Uranyl Dicarbonate

successful exchanges of uranyl mono- and dicarbonate, it can be seen that exchange events at Oc oxygens are more frequent in the case of uranyl dicarbonate, whereas the MRT is longer compared to that of uranyl monocarbonate. This is rather surprising because more exchange events should lead to a decreased MRT value as the water molecules bind via H-bonds for a shorter time. A possible explanation could be that not all three water molecules coordinated to Oc exchange identically. This means that two water molecules exchange less frequently than the third one, which leads to an increased average for the MRT value. In order to analyze the structural relaxation of hydrogen bonds, a time correlation function C(t) of the following form may be used

C(t ) =

⟨h(0)h(t )⟩ ⟨h⟩

τl Uranyl Monocarbonate 1016 1423 1625 Uranyl Dicarbonate Ou−water 784 Oc,coord,distal−water 1544 Oc,coord,proximal−water 1193 Oc,bulk−water 1510 Ou−water Oc,coord−water Oc,bulk−water

72 106 76 77 77 88 73

uranyl oxgens are weak H-bond acceptors, resulting from the positive net charge of the uranyl ion, which can be assumed to increase the ligand mobility of water molecules near these atoms. The finding of high exchange rates associated with a low number of H-bonds ranging from 0 to 1 is in good agreement with previous studies on similar systems.113−117 In the case of the dicarbonate, this is even more recognizable compared to the monocarbonate. Apparently, the additional carbonate delivers extra electron density to the system, weakening the interaction of the uranyl oxygens with the solvent. This trend of lower H-bond lifetimes for the dicarbonate with respect to the monocarbonate can also be seen for the carbonate oxygens. Nevertheless, the carbonate oxygens may form quite strong H-bonds, especially those pointing toward the bulk. The coordinating carbonate oxygens

(10)

where h(t) is a defined hydrogen-bond population variable.112 The time correlation function can then be fitted with a doubleexponential expression (eq 11) in order to obtain the long and short contribution τl and τs of the respective correlation function. y = a ·e−t / τl + (1 − a) ·e−t / τs

τs

(11)

Figure 8 shows the time correlation function for different oxygen species of uranyl monocarbonate and dicarbonate, which are highlighted by colors in the snapshot to the right of the respective plot. The resulting long and short contributions are listed in Table 4. From these data, it can be concluded that 16182



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Figure 9. The vibrational power spectra of uranyl mono- (left) and dicarbonate (right): (a,b) entire complex, (c,d) complex without coordinating water, (e,f) uranyl ion, (g,h) carbonate ion(s), and (i,j) coordinating water molecule(s).

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 for uranyl monocarbonate (left column, that is, a−i) and uranyl dicarbonate (right column, that is, b−j). Thereby, each row denotes the spectrum of a different component present in the system. In the first row, an overall spectrum of the whole complex (the respective uranyl carbonate entity including coordinating water molecules) is shown. The second row depicts the uranyl carbonate components without coordinating water in order to obtain a deeper understanding of the vibrational properties of the uranyl carbonate complex. Figure 9e and f depicts the uranyl cation. In Figure 9g and h, the vibrational spectrum of the carbonate(s) can be seen. Finally, Figure 9i and j represents the coordinating water molecule(s). Compared to bulk water, a slight blue shift of the vibrational frequency for the coordinating water molecules can be seen. This shift to higher frequencies is stronger for the monocarbonate than that for the dicarbonate. In order to further investigate this phenomenon depicted in Figure 9i and j, force constants according to eq 12 were computed. For this purpose, the stretching frequency of uranium with the

might partly interact with the water molecules coordinating to uranium, which weakens the capability of hydrogen-bond formation with the surrounding bulk. This can be nicely seen in case of uranyl dicarbonate; while the carbonate oxygens proximal to the coordinating water molecule (blue-colored oxygens in Figure 8) show τl values of approximately 1.2 ps, the respective distal carbonate oxygens (orange-colored oxygens in Figure 8) show intermittent H-bond lifetimes similar to those of carbonate oxygens pointing toward the bulk, that is, ∼1.5 ps. Vibrational power spectra of different relevant components present in the system were calculated via Fourier transformation of the respective velocity autocorrelation functions (VACFs). Thereby, a pairwise analysis of the ion−O stretching component via the projected ion−O velocities are considered to compute the VACF.118,119 Although this approach does not consider any collective modes, it proved particularly useful 120−122 when examining the binding strength of a coordinating moiety in terms of the resulting force constant k, which can be deduced from the vibrational frequency k = 4·(π ·c·ν)̃ 2 ·μ

(12) 16183



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frequency of 1096 cm−1 results in a force constant of 1061 N/m, whereas the uranyl dicarbonate with a vibrational frequency of 995 cm−1 results in a force constant of 876 N/m. This considerable difference of 185 N/m results in a bond elongation of 0.2 Å for the UOu bond length (see Table 2).

coordinating water molecules was considered. Additionally, the frequencies were scaled according to Radom et al.123 to consider the overestimation of the frequencies by Hartree− Fock using the 6-31G(d,p) basis set. For the uranyl monocarbonate, having an average vibrational frequency of 314 cm−1 for the three coordinating water molecules, a force constant of 87 N/m is obtained, while in the case of the dicarbonate, the force constant is 66 N/m for an average vibrational frequency of 273 cm−1. The difference of 21 N/m clearly demonstrates that the coordination of the water molecules in the case of uranyl monocarbonate is stronger than that in the case of uranyl dicarbonate. These data provide an explanation for the stronger blue shift of the vibrational frequency for the coordinated solvent molecules in uranyl monocarbonate compared to that for the respective dicarbonate. This phenomenon is also reflected in a greater bond distance of the coordinating water molecule of 0.2 Å in the case of the uranyl dicarbonate in respect to the monocarbonate (see Table 2). Table 5 lists a comparison of the vibrational

5. CONCLUSIONS The presented work demonstrates that the QMCF ansatz proves to be a valuable method for the investigation of inorganic complexes in aqueous solution. All presented data are in good agreement with experimental and some theoretical data in the literature, where available. One of the most interesting conclusion of the MD simulations of the two uranyl complexes is that quantum chemical MD simulations provide a five-fold coordination in the equatorial plane, which deviates from the conclusions obtained from a number of previous reports, based either on classical molecular dynamics studies or quantum chemical calculations of simplified clusters in the gas phase and implict solvent. Kubicki et al. suggested that in addition to cluster calculations, molecular dynamics simulations at a quantum chemical level should be carried out43 to obtain a more reliable description of the interactions between the complex and its environment. Due to the charge transfer from the negatively charged carbonate anions to the uranium atom, an increase of the coordination number beyond 5 is less probable than that observed when employing classical, pairwise potentials, which explains the tendency to observe higher coordination numbers in classical simulation studies because these approaches do not take charge transfer into account. This comparative QMCF-MD simulation study enabled an extensive characterization of various structural and dynamical properties of [UO2(CO3)n]2(1−n) in aqueous solution. A pronounced red shift of 21 N/m corresponding to a shift of 41 cm−1 wavenumbers of the binding strength of water was observed upon complexation of UO2+ 2 by carbonate. It is expected that the application of the QMCF-MD approach to the last species of the uranyl carbonates in aqueous solution [UO2(CO3)3]4− planned for future studies will provide data of similar quality and, thus, extensive insight into the properties of this system.

Table 5. Comparison of Vibrational Frequencies of Uranyl Carbonate Species in Wavenumbers (cm−1) along with the Asymmetric and Symmetric Uranyl Stretching Frequencies (UO) for the Uranyl Cation, Uranyl Monocarbonate, and Uranyl Dicarbonate system UO2+ 2

UO2CO3

[UO2(CO3)2]2−

UO

UO

method

(asym.)

(sym.)

ref

B3LYP MP2 CCD IR (exptl.) QMCF-MD LDA B3LYP MP2 QMCF-MD LDA B3LYP MP2

1126 1024 1179 1140 1096 951 947 916 995 883 893 877

1027 923 1100 1041 1031 880 862 835 948 805 804 793

Majumdar et al.48 Majumdar et al.48 Majumdar et al.48 Hunt et al.60 this work de Jong et al.4 Majumdar et al.48 Majumdar et al.48 this work de Jong et al.4 Majumdar et al.48 Majumdar et al.48

frequencies obtained by the QMCF simulations to data available in literature. To the best of our knowledge, no experimental data have been reported, however. Comparing our frequencies to those obtained from gas-phase cluster calculations at DFT4,48 and MP2 levels,48 a deviation to higher wavenumbers is observed, but because the published data result from investigations of a single configuration without explicit consideration of solvent effects, deviations such as charge transfer and polarization were to be expected. On the other hand, the frequencies were deduced from approximately 125000 configurations of the respective complex in an explicit aqueous environment that also included anharmonic contributions. This is why a comparison in a quantitative way appears difficult, but a qualitative interpretation is possible. The collected data agree on the fact that the addition of carbonate(s) to the uranyl species results in a red shift, that is, a decrease of the wavenumbers for dicarbonate compared to the monocarbonate. The probable reason is the electron transfer from the carbonate(s) to the uranium, thereby weakening the UOu bond. This causes a bond elongation, which results in a weaker force constant and a higher wavenumber. For the uranyl monocarbonate, the vibrational

■

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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REFERENCES

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A Comparative Quantum Mechanical Charge Field Study of Uranyl

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