Erbium(III) in Aqueous Solution: An Ab Initio Molecular Dynamics

Article pubs.acs.org/JPCB

Erbium(III) in Aqueous Solution: An Ab Initio Molecular Dynamics Study Lorenz R. Canaval, Theerathad Sakwarathorn, and Bernd M. Rode* Theoretical Chemistry Division Institute of General, Inorganic and Theoretical Chemistry, University of Innsbruck, Innrain 80-82, A-6020 Innsbruck, Austria

Christoph B. Messner, Oliver M. D. Lutz, and Günther K. Bonn Institute for Analytical Chemistry and Radiochemistry, University of Innsbruck, Innrain 80-82, A-6020 Innsbruck, Austria ABSTRACT: Structural and dynamical properties of the erbium(III) ion in water have been obtained by means of ab initio quantum mechanical charge field molecular dynamics (QMCF-MD) simulations for the ground state and an excited state. The quality of the simulations has been monitored by recording UV/vis and Raman spectra of dilute solutions of ErCl3 and Er(NO3)3 in water and by comparison with EXAFS data from literature. Slight deviations between these data can be mainly attributed to relativistic effects, which are not sufficiently considered by the methodological framework. In both simulations, a mixture of coordination numbers eight and nine and a ligand exchange on the picosecond range are observed. The strength of the Er−ligand bond is considerably lower than that of trivalent transition metal ions but higher than that for La(III) and Ce(III) in aqueous solution. The main difference between ground state and excited state is the ligand exchange rate of the first shell. The second hydration shell is stable in both cases but with significantly different properties.

1. INTRODUCTION The increasing importance of the so-called rare earth elements, as lanthanoids are commonly termed, can be easily recognized from the economic problems caused by the present demand in industrialized countries and the restrictive export policy of the main producers. In the last few decades, many specific and highly appreciated properties of these elements have been discovered, and a contemporary list of technological use of lanthanoids covers many essential fields of industry. Erbium is one of the prominent members of the lanthanoid group and is used for a variety of applications, inter alia for lasers applied in medicine1−3 and optical spectroscopy,4 fiber amplifiers for optical communication,5 nuclear technology6 and dosimetry,7 spacecraft engineering,8 and luminescent materials.9−12 The Er(III) ion has recently been proven as agent for the separation of proteins superior to La(III).13−15 This wide range of use of erbium explains the strong interest in the properties of its ion, that is, the form in which it is present in aqueous solution including wastewater of some industrial processes. The structure of hydrated Er(III) has been investigated by various experimental methods, in particular, by extended X-ray absorption fine structure (EXAFS),16 but these investigations do not supply data for the dynamics of the aquo-complex. These dynamics are hardly accessible experimentally because measurements by NMR17 have indicated a very high ligand exchange rate, probably beyond the NMR time scale. Raman spectra of a series of lanthanoid ions have been reported,18 but erbium(III) was not included in this investigation. © 2013 American Chemical Society

Molecular dynamics studies of other lanthanoid ions, for example, La(III)19 and Ce(III),20 have also shown that ligand exchange around such ions mostly occurs in the picosecond range and that such theoretical studies are presently the most suitable tool to obtain insight into the dynamics of these ions in water. The example of La(III) has provided evidence, however, that a quantum mechanical (QM) evaluation of forces including two hydration shells is mandatory to achieve the necessary accuracy for the evaluation of ligand mean residence times and ion−water force constants.19,21

2. METHODICAL FRAMEWORK 2.1. Computational Details. The recently developed ab initio quantum mechanical charge-field molecular dynamics (QMCF-MD) methodology22,23 ensures the required accuracy, relying on a QM description of all solute−solvent interactions without the need for empirical potentials, a continuous adaptation of Coulombic interactions on the basis of quantum mechanically evaluated atomic charges and an electrostatic embedding of the QM region into a large molecular mechanical (MM) region, whose point charges form the basis for a perturbation term of the Hamiltonian. A smoothing procedure ensures continuous transitions of molecules between QM and MM region. The inclusion of two hydration shells in the QM Received: October 17, 2013 Revised: November 19, 2013 Published: November 19, 2013 15151

dx.doi.org/10.1021/jp410284z | J. Phys. Chem. B 2013, 117, 15151−15156

The Journal of Physical Chemistry B

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both MP2 approaches (24 and 27%). The energy difference between the ground and the excited states for the bare metal ion in the gas phase at the HF level of theory was calculated to be 57 kcal/mol. B3LYP does not lead to a stable 1:1 complex, and the data for the 1:2 complex deliver the worst ion−water distance and an equally too high binding energy. On the basis of these results, it was evident that MP2 level would not improve the results, B3LYP seems unsuitable, and as CCSD would lead to an unrealistic computational demand, HF is still the most satisfactory approach for the simulations of the systems under investigation. Two different simulations were carried out, one for the high spin configuration of the ion with multiplicity 4 (M = 4, ground state) and one for the energetically higher state with multiplicity 2 (M = 2). The joint evaluation of these two simulations enables a computation of the UV/vis spectrum of the ion in aqueous solution including the rovibrational influence and hence the bandwidth of the spectrum, as has been shown in the case of Li(I) ion.37 Structural and dynamical data extracted from the simulation trajectories comprised radial distribution functions (RDFs), angular distribution functions (ADFs), local density corrected three-body distribution functions38 (3BDFs), coordination number distributions (CNDs), mean ligand residence times (MRTs), and vibrational spectra including ion−O (ligand) force constants obtained by Fourier transformation (FT) of velocity autocorrelation functions (VACF). 2.2. Experimental Details. Erbium(III)chloride hexahydrate (99.9%), erbium(III)nitrate pentahydrate (99.9%), and water (LC−MS grade) were purchased from Sigma Aldrich Chemical, Vienna, Austria, and have not been further purified prior to the measurements. The UV spectroscopy measurements were carried out with a Genova Plus Spectrophotometer (Jenway, United Kingdom). A freshly prepared 0.1 M solution of erbium(III)chloride hexahydrate was utilized for the absorbance measurement. For the Raman measurements, 0.05 M concentrated solutions of erbium(III)chloride hexahydrate and erbium(III)nitrate pentahydrate in water were prepared. The spectra have been obtained with a Jobin-Yvon Labram-HR800 spectrometer (HORIBA Instruments, USA), utilizing a frequency-doubled Nd:YAG laser (100 mW, 532 nm). Because the lanthanoid− oxygen stretching motion has previously been reported as a very feeble band in the Raman spectrum, multiscan averaging has been employed (five replicates with 120 s measurement time each), improving the signal-to-noise ratio significantly and thus allowing an accurate prediction of the peak maxima.

region provides a sufficiently accurate description of hydrogen bonding between first and second hydration shell, which is known to be strongly influenced by highly charged ions.24 Details of the QMCF-MD simulation method have been published elsewhere.22 The ab initio QMCF molecular dynamics simulations have been set up with the following characteristic data: simulation box containing the erbium(III) ion and 1000 water molecules with the density of pure water, thermostatized at 298.15 K by the Berendsen algorithm,25 employing a time step of 0.2 fs. The diameter of the QM core zone, containing the ion and the first hydration shell, was set to 3.3 Å, and that of the QM layer zone containing only water molecules and the full second hydration shell was set to 5.7 Å, including a smoothing zone for the QM/ MM transition of solvent molecules of 0.2 Å. Long-range Coulombic interactions were considered by the reaction field method26 with an ε value of 78.35. The solvent in the MM region was described by the flexible BJH-CF2 water model,27,28 and the fluctuating atomic charges in the QM regions were evaluated by Mulliken population analysis29,30 which has proven to be the most compatible one in connection with the charges of the BJH-CF2 model.27,28 For the QM calculations done by the Turbomole 6.3 program,31−33 Dunning’s DZP basis sets34 were employed for H and O, and for Er, the Stuttgart RSC 1997 ECP basis set,35 with 28 electrons included in the relativistic effective core potential. As the computational effort enforces restrictions in the accuracy of the ab initio framework, a number of test calculations were carried out with these basis sets using the Gaussian09 programm,36 optimizing the geometry of small Er(III)−water complexes with one and two ligands. The results of these test calculations at Hartree−Fock (HF), MP2 (frozen core and full), and CCSD level are summarized in Table 1 and also compared with corresponding data of B3LYP DFT calculations. The comparison shows that HF delivers results closest to the most sophisticated correlated method CCSD, in particular, for the ion−water distance, which is most crucial for the correct coordination numbers in solution. The gas-phase binding energies are almost equally overrated by HF (28%) and Table 1. Ion−Water Distances (r), Total Energies (E), and Energies of Stabilization Per Water Ligand (Estab) Obtained from Quantum Mechanical Calculations of Erbium−Water Complexes at Different Levels of Theory method

r in Å

E in h

Estab in kcal/mol

2.2153 2.2552

−1087.2318100 −1163.4066201

−143.8 −112.1

2.2034 2.2410

−1087.5751261 −1163.9564080

−142.6 −115.3

2.1565 2.2070

−1088.3843069 −1164.7773071

−139.4 −113.0

2.2142 2.2515

−1087.5866345 −1163.9750973

−112.6 −99.7

HF 1 water 2 water MP2 (frozen core) 1 water 2 water MP2 (full) 1 water 2 water CCSD 1 water 2 water B3LYP 1 water 2 water a

3. RESULTS AND DISCUSSION 3.1. Electronic Excitation and Structural Features. To evaluate the spectral transition from the ground state (M = 4) to the excited state (M = 2), the energy differences between all points of both simulations have been evaluated, and the results are plotted in Figure 1. A broad peak with a maximum at ∼230 nm resulted. The experimental spectra of ErCl3 recorded for this work (see the Experimental Details) show this peak at 255 nm, as illustrated in Figure 1 as well. This is in very good agreement, probably the optimum achievable at the Hartree− Fock level with relativistic correction only via the ECP in the simulations. From the comparison of the two simulations, one can also extract the structural changes associated with the electronic excitation. Figure 2 demonstrates that the Er−O RDFs are very

a

2.2771

−1167.0976455

−115.6

Does not form a stable complex. 15152



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A comparison of the ADFs of both data sets (Figure 3) shows virtually no differences, and a comparison of the ADF with the structure-characteristic lines of ideal geometries suggests that the lower coordination number is associated with a square antiprism, the higher one with either a monocapped square antiprism or a tricapped trigonal prism. The CND analysis shows that in both simulations only coordination number 8 and 9 are populated, with 59.1% (M = 4) and 56.3% (M = 2) for the eight-fold arrangement in the first hydration shell. In the second shell, the distribution ranges from 14 to 24, with 19 being the most likely (25.2%) for the ground state (M = 4) and from 15 to 26 with a maximum probability at 21 (21.8%) for the excited state (M = 2). The local density-corrected three-body distribution functions38 prove that there is no significant difference between a hypothetical third solvation layer and the bulk. While the structural features are not much influenced by the electronic excitation, differences become more pronounced in the dynamical processes, as illustrated in the subsequent chapter. 3.2. Dynamics of Er(III) Aquo-Complexes in Ground State and Excited State. As could be expected from the broad O−Er−O ADF, the aquo-complexes show a high flexibility of their geometrical arrangement, and the composition of eight- and nine-fold coordinated species indicates ligand exchange processes during the simulation time. Such rapid exchanges in the first hydration shell on the picosecond scale are unusual for trivalent ions except for lanthanoid ions. For the latter, the mean ligand residence times (MRTs) can be quite different, however. Table 3 displays the characteristics of the exchange processes of the first and the second hydration shells. The MRT value for the first shell is unusually high and strongly differs for ground and excited states. In the second shell, the value of the system with M = 4 is still slightly higher than that for the complex with M = 2. A striking difference to other lanthanoid ions is the success rate for exchange processes between first and second shells, being close to 1, which means that almost every attempt of a ligand to migrate leads to a successful ligand exchange, while this is the case only for every 4th to 5th attempt between second shell and bulk. In the solvent itself,41 this value is still considerably higher (7.85), and the MRT with 1.6 ps is significantly lower than the values for the second shell in either simulation. Figure 4 illustrates exchange processes observed during the simulations by means of Er−O distance plots and hence also demonstrates the changes between coordination numbers eight and nine and the relative stability of both species in both the ground and the excited states. Associative (A) and dissociative (D) mechanisms of ligand exchange dominate, but in the excited state also a typical example of an associative interchange mechanism Ia is found. Finally, the strength of binding between Er(III) and water ligands was investigated by evaluating the vibrational frequencies and associated force constants for the Er−O bond from the Fourier-transformed velocity autocorrelation functions of the simulations. In addition, the Raman spectrum of ErCl 3 and Er(NO 3 ) 3 solutions was recorded (see Experimental Details) to compare computed and measured frequencies for the Er−O symmetric stretch vibration. Figure 5 shows the peak corresponding to the ion−ligand interaction resulting in a broad and asymmetric shape near 400 cm−1 and displaying some splittings and shoulders in both experiment and simulation. In the latter case, a separate evaluation of the eight- and nine-coordinated hydrate was possible, and Figure

Figure 1. (a) Theoretically derived spectral transition from ground state to excited state and (b) experimental spectrum of 0.5 M ErCl3.

Figure 2. Er−O radial distribution functions (solid) and the corresponding integration (dashed) for the erbium ion in aqueous solution for ground state (black) and first excited state (red).

similar, only a small contraction of ∼0.02 Å of the first shell becomes visible after zooming into the first peak. Such a contraction of the first hydration shell upon electronic excitation − although to a larger extent − has already been observed in the case of Li(I) in water.37 The second shell’s distance is not changed, but it contains two more ligands in the excited state. The characteristic data for the RDFs and the coordination numbers are collected in Tables 2 and 3. In both simulations, Table 2. Characteristic Values of the Radial Distribution Functions for Ground State and Excited State Simulations rmax1,O rmin1,O rmax2,O rmin1,O a

M=4

M=2

EXAFS16

X-ray diffraction39

2.464 3.5 4.75 5.75

2.445 3.5 4.74 5.95

2.399/2.409a

2.38 4.77

Mean distances for nine-fold coordination using different anions.

the average first-shell coordination number of Er(III) is 8.4 and hence comprises two main species, an eight-fold and a nine-fold coordinated one. The coordination number resulting from experiments vary from 7.840 to 8.9616, and the ion−oxygen distances from the most recent EXAFS measurements are in very good agreement with those resulting from the simulation. (See Table 2.) 15153



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Table 3. Dynamics of the First and Second Hydration Shell for the Er(III) Aquo-Ion for the Ground State and Excited State 1st shell average CN mean residence time in picoseconds sustainability coefficient 1/sustainability coefficient

2nd shell

M=4

M=2

M=4

M=2

solvent41 exp.

8.4 40.5 0.67 1.5

8.4 27.0 1.0 1.0

18.8 3.0 0.23 4.3

20.6 2.5 0.22 4.5

0.5 0.13 7.85

Figure 3. O−Er−O angular distribution functions for the erbium ion in aqueous solution for ground state (black) and first excited state (red), overlaid by peaks for ideal coordination polyhedra: (a) 8 ligands in a square antiprism and 9 ligands in (b) a monocapped square antiprism and (c) a tricapped trigonal prism.

Figure 4. Evolution of selected Er−O distances for (a−d) the ground state (M = 4) and (e−g) the excited state (M = 2), indicating numerous exchange attempts (tAn), a number of successful exchange events (tSn), and evolution of the coordination number.

5b displays the separate spectra of them, together with the overlay of both. Calculating the Er−O vibration frequencies for an Er(H2O)3+ complex in the gas phase, both HF and CCSD deliver very similar values (423 and 425 cm−1), which are too high compared with the experimental value in solution (400 cm−1). The deviation of the simulation value from the experimental one therefore appears to be rather a deficiency in the relativistic correction of the ECP used for erbium and not a problem of the neglect of electron correlation. Additionally it is known that too small QM zones (e.g., the ion plus one hydration shell) deliver rather poor results, which is especially true for power spectra. (See comparison of QM/MM-MD and QMCF-MD of La(III) in Table 4.) For for this reason, a larger QM zone including two hydration shells treated by HF was preferred to a correlated treatment of a smaller QM region. Table 4 lists the force constants for the Er−O vibration in comparison with those of other trivalent ions. In general, the values of lanthanoids are only about half of the bond strength of transition metal hydrates but apparently show characteristic differences among themselves. These differences probably result − besides the specific electron configuration − also from the distribution of coordination numbers, as indicated by the force constant difference between eight- and ninecoordinated Er(H2O)n. The simulation of the erbium(III) ion in the excited state does not produce significant differences in the Er−O force constant.

Figure 5. (a) Experimentally found Raman spectra for ErCl3 (black) and Er(NO3)3 (red) solutions and (b) data obtained from the groundstate simulation via VACF and subsequent FT (dashed-dotted red: eight-fold coordinated species, dashed-dotted black: nine-fold coordinated species, and solid black: sum of them).

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Table 4. Peak Maxima of Selected Ion−O Stretching Frequencies (Qion−O) and Corresponding Force Constants (kion−O) ion

Qion−O in cm−1

kion−O in N m−1

Al(III)QMCF−MD V(III)QMCF−MD Fe(III)QMCF−MD Ir(III)QMCF−MD La(III)QM/MM−MD La(III)QMCF−MD Ce(III)QMCF−MD Lu(III)QMCF−MD Er(III)QMCF−MD(CN=8) Er(III)QMCF−MD(CN=9) Er(III)QMCF−MD Er(III)experimental

560

185 203 193 260 54 110 106 112 118 95 110 138

513 253 360 354 360 371 333 360 400

work work work work

4. CONCLUSIONS The simulations of Er(III) ion in aqueous medium in the ground and excited states have produced sufficiently accurate data for hydrate structure and dynamics of the ion, and the experimental UV/vis and Raman spectra recorded are in good agreement with the data calculated from the simulations. Some deviations of the theoretical from the experimental values are attributed to an insufficient inclusion of relativistic effects in the QM part, which have to be accepted at present, as a full relativistic treatment of the QM region is beyond available computational resources and a reasonable time frame. Because of the very rapid ligand exchange rates of the lanthanoid ions, the ab initio QMCF-MD simulations have become a highly useful and sufficiently accurate tool to elucidate these exchange processes concerning mean ligand residence times and exchange mechanisms for ground and excited states. While dynamical properties such as ligand exchanges are found to be easily influenced by electronic excitation, the structural characteristics for both states are very similar, indicating that these changes require higher energies. The specific properties of the Er(III) ion in water obtained in this work should be helpful, also in comparison with other lanthanoid ions, to explain the chemistry of such ions, which have gained an ever increasing relevance in the past decades.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: +43-512-507-57160. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Ralf Tappert (Institute of Mineralogy and Petrography, University of Innsbruck) for conducting the Raman measurements. T.S. thanks the Thailand Research Fund for the Royal Golden Jubilee Ph.D. Programs (TRF.RGJ; Grant No. PHD/0233/2551) financial support and the Institute of General, Inorganic and Theoretical Chemistry, LeopoldFranzens-University of Innsbruck for the computational facilities. Financial support from a Ph.D. grant of the Leopold-Franzens-University of Innsbruck (Rector Univ.Prof. Dr. Dr.hc.mult. Tilmann D. Märk) for Lorenz R. Canaval is gratefully acknowledged. 15155



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