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J. Phys. Chem. B 2006, 110, 616-621
Temperature Effects on the Structural and Dynamical Properties of the Zn(II)-Water Complex in Aqueous Solution: A QM/MM Molecular Dynamics Study M. Qaiser Fatmi, Thomas S. Hofer, Bernhard R. Randolf, and Bernd M. Rode* Theoretical Chemistry DiVision, Institute of General, Inorganic, and Theoretical Chemistry, UniVersity of Innsbruck, Innrain 52a, A-6020 Innsbruck, Austria ReceiVed: August 18, 2005; In Final Form: October 28, 2005
An ab initio quantum mechanical/molecular mechanical (QM/MM) molecular dynamics (MD) simulation at double-ζ restricted Hartree-Fock (RHF) level was performed at an elevated temperature of 363 K (90 °C) to study the temperature effects on the structural and dynamical properties of a Zn(II)-water complex in aqueous solution. The first hydration shell, consisting of 6 water molecules at a mean Zn-O distance of 2.16 Å, was found to remain stable also at 90 °C with respect to exchange processes. The flexible second shell contains, in average, ∼27 water ligands. To fully characterize the hydration structure, several other parameters such as radial and angular distribution functions (RDF and ADF) and tilt- and θ-angle distributions were evaluated and compared to data obtained at 298 K (25 °C). Temperature effects on the dynamics of the Zn(II)-water complex were studied in terms of water reorientations, mean ligand residence times (MRTs), and number of ligand exchange processes. To get further insight into the solute dynamics, additional data, in particular, librational and vibrational motions of water ligands and Zn-O stretching frequencies, were calculated. The second shell is considerably influenced by the elevated temperature, as the ligands’ mean residence time is shortened to 4 ps from the value of 10.5 observed at room temperature. The values of the QM/MM MD simulation were also compared to the results of a classical molecular dynamics (CMD) simulation with two- plus three-body potential performed at 90 °C, revealing that an accurate description of the second shell and the dynamics of the Zn(II) hydrate needs the inclusion of quantum mechanics in the description.
1. Introduction publications,1,2
In recent structural and dynamical properties of the zinc-water complex have been extensively investigated at 298 K (25 °C) by using a combined quantum mechanical/ molecular mechanical (QM/MM) molecular dynamic (MD) simulation, which revealed [Zn(H2O)6]2+ to be a very stable complex. Being fourth among all metals in world production and an essential element in industrial and biological as well as geochemical processes, it was, therefore, interesting to investigate temperature effects on the structure and, in particular, the dynamics of hydrated zinc ion. In general, the first shell hydration numbers of small ions are relatively insensitive to temperature variations due to strong coordination of the ligands to the metal ion. However, ligands’ mean residence times (MRTs) are lower at high temperatures.3,4 Recent variabletemperature 17O and 19F NMR studies on the rates of water exchange of Th(H2O)104+, Th(H2O)94+, U(H2O)104+, UF(H2O)93+, UO22+, and UO2(oxalate)F(H2O)- confirmed that water exchange rates increase as the solution temperature increases.5-7 In general, the major modifications in the structure (e.g., radial and angular distribution functions, coordination number distributions, etc.) and the dynamics (e.g., ligands’ mean residence times, ion-ligand stretching frequency, librational and vibrational frequencies, and reorientational times of water molecules) at higher temperatures are accompanied by a decrease in density and weakening of hydrogen bonding, with an associated fall in the dielectric constant and viscosity.8 The positive increase of entropy and enthalpy values due to higher * Corresponding author. E-mail:
[email protected]. Telephone: +43-512-507-5160. Fax: +43-512-507-2714.
kinetic energy at higher temperatures affect the Gibbs free energy in opposite ways.9-11 In continuation of our study on the zinc ion,1 the present work discusses results of a CMD simulation with two- plus threebody potential and a Hartree-Fock-based QM/MM MD simulation of 499 water molecules and one Zn2+ ion confined in a cubic box of 24.71 Å side length at an elevated temperature of 363.16 K. The results obtained from both the CMD and the QM/MM MD simulation are compared with previous simulations performed at room temperature (25 °C)1,2 for otherwise identical conditions. To our knowledge, no experimental/theoretical data for Zn(II) at elevated temperatures (i.e., T > 298 K) in aqueous solution are available except those of Lee et al.12 and Rudolph et al.,13 who have reported the thermodynamical and spectral properties of the zinc-water complex at different temperatures. However, there exists some literature for Li+, Na+, Rb+, Cs+, and Th4+ at higher temperatures, discussing structure and dynamics.3,4,7 2. Computational Details Details of the choice of basis sets and level of theory applied in the QM region have already been reported in our previous publication.1 It has been found that correlation effects are minor in the case of hydrated Zn(II) and that the B3-LYP DFT formalism and the ab initio HF method produce results in good agreement with correlated methods.1 Because of the higher basis set superposition error (BSSE) and other known deficiencies of DFT methods in the description of hydrated ions,14-16 the HF method was preferred as it also has yielded results in good
10.1021/jp0546655 CCC: $33.50 © 2006 American Chemical Society Published on Web 12/10/2005
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TABLE 1: Optimized Parameters for the Zn-O and Zn-H Two-Body and the O-Zn-O Three-Body Interactions two-body parameters in kcal/mol Zn-O Zn-H
A
B
C
D
-9519.05 -1156.34
19094.37 6116.94
-34732.56 -50493.35
32684.47 50951.42
three-body parameters in kcal/mol O-Zn-O
A
B
C
0.6467210
0.2366643
0.4879461
agreement with experimental data.1 The details of the construction of the pair and three-body potentials have been previously published,1 a short description of these functions is given in eqs 1 and 2, respectively, and the optimized parameters are summarized in Table 1.
E2bd Fit )
qZn2+qO r
+
AO
+
r5 2
∑ i)1
BO
+
CO
+
DO
+ r6 r10 r12 qZn2+qH AH BH CH DH + + + + (1) ri ri5 ri7 ri11 ri12
(
)
A, B, C, and D are the fitting parameters (Table 1), qZn2+, qO, and qH are the charges of zinc, oxygen, and hydrogen, respectively, and r and ri are the distances Zn-O and Zn-H, respectively. -B(r1+r2) exp-Cr3(CL - r1)2(CL - r2)2 (2) E3bd Fit ) A exp
A, B, and C are the fitting parameters (Table 1) and r1 and r2 are the distances Zn-O1 and Zn-O2, respectively, r3 is the distance between O1 and O2. CL is a cutoff limit set to 6.0 Å, where three-body terms become negligible. For the classical molecular dynamics (CMD) simulation, a cubic box with a side length of 24.71 Å containing one Zn(II) and 499 water molecules was used, corresponding to a density of the system as that of the pure solvent at 363 K (0.965 g/cm3). A canonical NVT ensemble was used by employing periodic boundary conditions, and the temperature was kept constant at 363.16 K by using the Berendsen algorithm17,18 with a relaxation time of 0.1 ps. The cutoff distances were set to 5.0 Å for O-H and 3.0 Å for H-H non-Coulombic interactions. For all other pair interactions, the cutoff was set to 12.35 Å. To account for the long-range electrostatic interactions, the reaction field method was employed.19 The flexible BJH-CF2 water model20,21 was used, which includes an intramolecular potential enabling explicit hydrogen movements. Therefore, the time step for the simulation was set to 0.2 fs. The CMD simulation was performed for 100 ps (after 10 ps of equilibration, starting from the configuration at 25 °C) by using the previously reported two- plus three-body potentials.1 The QM/MM MD simulation was started by a further 3 ps reequilibration of the classical three-body-corrected simulation performed for 363 K, followed by 25 ps of sampling. The radius of the QM region was set to 3.4 Å, in accordance with the Zn-O RDF obtained from the CMD simulation, to include the full first hydration shell plus some part of the intershell region. The total force acting on a particle is calculated according to eq 3. QM MM Ftot ) Fsys MM + S(r)*(FQM - FQM )
(3)
sys Ftot is the total force acting on a particle, FMM is the MM QM MM force of the whole system, and FQM and FQM are QM and MM
Figure 1. RDFs and their running integration numbers obtained from the QM/MM simulations at 90 °C (solid line) and 25 °C (dashed line) (a) Zn-O RDFs and (b) Zn-H RDFs.
TABLE 2: Characteristic Values of Radial Distribution Functions gZn-O(r) and gZn-H(r) for Zn2+ in Aqueous Solution Obtained from the CMD and QM/MM MD Simulation at 25 and 90 °Ca rM1 (Å)
rM2 rm1 (Å) CNav,1 (Å)
rm2 (Å) CNav,2
4.74 4.73 4.62 4.50
6.06 5.60 5.47 5.06
26.7 21.0 19.3 14.7
this work 1 this work 1
5.25 5.22 5.04 5.10
6.44 6.35 6.23 5.96
60.8 60.2 55.0 50.6
this work 1 this work 1
classical (90 °C) classical (25 °C) QM/MM (90 °C) QM/MM (25 °C)
2.26 2.24 2.16 2.18
Zn-O 3.39 5.8 3.33 5.8 2.79 6.0 2.70 6.0
classical (90 °C) classical (25 °C) QM/MM (90 °C) QM/MM (25 °C)
2.98 2.99/3.01 2.83 2.82
Zn-H 3.80 11.9 3.76 11.5 3.56 12.0 3.52 12.0
a
ref
rM Denotes Maxima and rm Minima in Å Observed in the RDFs.
forces calculated for the QM region separately. A smoothing function S(r) is applied in a region of 0.2 Å to ensure a smooth transition of water molecules22 between QM and MM region.
S(r) ) 1, S(r) )
for r e r1
(r02 - r2)2(r02 + 2r2 - 3r12) , (r02 - r12)3
S(r) ) 0,
for r1 < r e r0
(4)
for r > r0
The QM/MM MD simulation was performed for 25 ps after a reequilibration period of 3 ps. 3. Results and Discussion 3.1. Structural Properties. The Zn-O and Zn-H radial distribution functions (RDFs) together with their running integration numbers, obtained from the QM/MM MD simulation at both temperatures (25 and 90 °C), are displayed in Figure 1, the main structural parameters obtained from the CMD and QM/ MM MD simulations at both temperatures are given in Table 2. Two well-defined peaks in both Zn-O and Zn-H RDFs indicate structured first and second hydration shells. The peak maxima (rM1) of the first and second hydration shell obtained
618 J. Phys. Chem. B, Vol. 110, No. 1, 2006
Figure 2. Coordination number distributions of first and second hydration shell of hydrated Zn(II) obtained from the QM/MM MD simulations at (a) 90 °C and (b) 25 °C.
from the QM/MM MD simulation at 90 °C appeared at closer distances compared to the CMD, namely 2.16 and 4.62 Å for the Zn-O and 2.83 and 5.04 Å for the Zn-H, respectively. The intensity of the first shell peak obtained from the QM/MM MD simulation is 30-35% higher than the corresponding CMD peak, suggesting a comparatively rigid structure description by the QM/MM MD simulation. A slight decrease in the first shell coordination number in the case of the CMD simulation is also observed in both Zn-O and Zn-H RDFs in comparison to the QM/MM MD simulation, indicating the occurrence of dissociative ligand exchange reactions within the simulation time. Both Zn-O and Zn-H RDFs obtained from the QM/MM simulation at higher temperature are very similar to those obtained from the QM/MM simulation at room temperature,1 Figure 1a and b, except for the slightly shifted and broader second shell peaks. The coordination number distributions (CND) depicted in Figure 2, however, reveal clear differences between 25 and 90 °C. While no significant temperature effect is observed for the first shell coordination number, as already reported for other ions,3,4 the average second shell coordination number increases from 14 to 19 at 90 °C showing a broader distribution ranging from 15 to 25. At 25 °C, the coordination number distribution (CND) varies between 11 and 19 only.1 On the other hand, the CMD simulation showed both 5- and 6-fold coordination for the first shell, with probabilities of ∼20 and ∼80%, respectively, clearly indicating a dominant dissociative mode of water exchange reaction between the first and second shell which is typical for d,8 d9, and d10 systems such as Ni(II), Cu(II), and Zn(II).23-26 The CMD simulation significantly overestimates the second shell coordination number, showing a maximum probability of 27. Figure 3 shows the O-Zn2+-O angle distribution functions (ADF) within the first shell obtained from the QM/MM MD simulations at 25 and 90 °C. At 90 °C, the slightly broader and less intense peaks are located at ∼89° and ∼171°, which are approximately the same values as obtained for 25 °C, indicating a negligible effect of temperature on the structure of the first shell. The CMD simulation at 90 °C gives peak locations similar to those of the QM/MM MD simulation at 90 °C. Two more angles were defined to describe the orientation of water ligands relative to the ion (Figure 4): “θ” as the angle between the Zn-O vector and the dipole vector, and “tilt” as the angle between Zn-O connection vector and the plane formed by the O-H vector. A slightly broader distribution for both angles is observed at 90 °C, pointing at a small temperature effect on the structure of the first shell with regard to ligand flexibility.
Fatmi et al.
Figure 3. Angular distributions of the O-Zn(II)-O angle in deg obtained from the QM/MM simulations at 90 °C (solid line) and 25 °C (dashed line).
Figure 4. Tilt (a) and θ (b) angle distributions of the Zn(II)-water geometry obtained from the QM/MM simulations at 90 °C (solid line) and 25 °C (dashed line).
Figure 5. Power spectra of the Zn-O stretching frequency in cm-1 obtained from the QM/MM simulations at 90 °C (solid line) and 25 °C (dashed line).
3.2. Dynamical Properties. Figure 5 displays the power spectra of the Zn-O stretching frequency obtained from the QM/MM simulation at both temperatures, scaled by the standard factor of 0.89.27,28 The peak at 90 °C is clearly red-shifted to 271 cm-1 (force constant 56 N/m), compared to the value at 25
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Figure 6. Power spectra of librational and vibrational modes for water in cm-1 obtained from the QM/MM simulation at 90 °C for the first (solid line) and the second hydration shell (dashed line) and the bulk (dotted line).
TABLE 3: Librational and Vibrational Frequencies in cm-1 of Water Molecules in the First and Second Hydration Shell and the Bulk of the Zn(II) Ion in Aqueous Solution Obtained from the QM/MM MD Simulation at 25 and 90 °C QM/MM (90 °C) QM/MM (25 °C)b liquidc gasd gase
1st shella 2nd shell bulk 1st shella 2nd shell bulk
Rx
Ry
Rz
Q1
Q2
Q3
625 430 420 630 440 420
560 530 530 575 530 540
380 400 400 410 430 410
3565 3460 3475 3550 3450 3450 3345 3657 3641
1630 1700 1700 1630 1700 1700 1645 1595 1601
3620 3575 3600 3620 3535 3560 3445 3756 3756
a Values scaled by a factor of 0.89.27,28 b Values obtained from the QM/MM MD simulation at 25 °C.1 c Experimental values in liquid water.29 d Experimental values in gas phase.30 e Scaled gas-phase vibrational frequencies using the DZP basis set for water.31
°C1 (282 cm-1, force constant 60 N/m), reflecting a temperatureinduced weakening of the Zn-O binding, in good agreement with data reported by Rudolph et al.13 for [Zn(H2O)6]2+ in 3.54 mol l-1 Zn(ClO4)2. The small shoulder, observed at 25 °C, disappears at 90 °C in favor of a broader and less intense peak with a noticeable tailing toward lower frequencies. The power spectra of librational and vibrational modes for water molecules obtained from the QM/MM MD simulation by using velocity autocorrelation functions (VACFs) are shown in Figure 6, and their characteristic values are listed in Table 3. The frequencies of the water molecules located in the QM region were scaled by a standard factor of 0.89.27,28 The orders of librational motions of water molecules in the first and second hydration shell of the QM/MM MD simulation are Rx > Ry > Rz and Ry > Rx > Rz, respectively, as previously reported for Zn(II) in aqueous solution at 25 °C.1,2 In the first shell of Zn(II), the rotational frequencies around x and y axes and the symmetric (Q1) and asymmetric (Q3) stretching frequencies are blue-
TABLE 4: Reorientational Times τ in ps of First and Second Order of Water Molecules in the First and Second Shell and the Bulk of Zn(II) Obtained from the QM/MM MD Simulation of the Zn(II) in Aqueous Solution at 25 and 90 °C. reorientational time in ps phase
τ1x
τ1y
τ1z
τ2x
τ2y
τ2z
QM/MM (90 °C)
1st shell 7.4 29.3 6.8 3.8 9.7 3.1 2nd shell 3.1 3.4 2.3 1.4 1.3 0.9 bulk 2.7 2.6 1.7 1.2 1.0 0.8 QM/MM (25 °C) 1st shell 54.8 100.2 47.0 19.1 33.3 16.0 2nd shell 10.6 10.8 8.0 4.3 4.0 3.0 bulk 6.6 6.8 4.4 3.0 2.6 2.0 H2O (exptl)a (25 °C) 7.5 2.5 a
Experimental reorientational correlation time of water.32
shifted, while the rotational frequency around the z axis and the bending frequency (Q2) are red-shifted with respect to the bulk as already reported previously,1,2 reflecting only minor temperature effects in the first shell. Small shifts in the second shell values are observed for Rx, Rz, Q1, and Q3 when the temperature rises from 25 to 90 °C, most of them making the ligands very similar to bulk molecules. Table 4 lists the first- and second-order reorientational times for water molecules around x, y, and z axes in the first and second shell and in the bulk, obtained from the QM/MM MD simulations at 25 and 90 °C. In both QM/MM MD simulations, the first shell shows the highest relaxation time for rotations around the y axis, and consequently, this is the most hindered rotation. As to be expected, the relaxation times obtained from the QM/MM MD simulation at 90 °C, particularly in the first hydration shell, are much lower than the corresponding values obtained at 25 °C, reflecting the higher mobility at elevated temperature. The characteristic values of ligand exchange reactions obtained from both the CMD and the QM/MM MD simulations
620 J. Phys. Chem. B, Vol. 110, No. 1, 2006
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TABLE 5: Mean Ligand Residence Time τd0.5 in ps Evaluated with the Direct Method for t* Value of 0.5 ps, Number of Accounted Ligand Exchange Events NEx0.0 and NEx0.5 for t* ) 0.0 and 0.5 ps, Respectively, Sustainability of Migration Processes to/from the First and Second Hydration Shell SEx Obtained from the QM/MM MD and the CMD Simulations method
Nex0.0/ Nex0.5/ 10 ps 10 ps
τd0.5
1st Shell H2O 2-shell QM/MM 129 28 1.5 Zn-water classical (90 °C) 5.0 1.9 30.5 classical (25 °C) 1.92 0.4 146.3 Zn-water classical (90 °C) classical (25 °C) QM/MM (90 °C) QM/MM (25 °C)
2nd Shell 530 79.8 453 35.4 419 47.6 306 14.0
3.35 5.93 4.04 10.5
Sex 1/Sex 0.21 0.38 0.2
4.6 2.6 4.8
0.15 6.64 0.07 12.8 0.11 8.80 0.04 21.8
ref 33 this work 1 this work 1 this work 1
at 90 and 25 °C are summarized in Table 5. The ligands’ mean residence time (MRT) for the second shell in the QM/MM MD simulation at 90 °C has decreased considerably from 10.5 (obtained for 25 °C) to 4.0 ps, reflecting the higher kinetic energy of water ligands at the higher temperature. The MRT values for the second shell obtained by the CMD simulation are considerably shorter than those of the QM/MM simulation. No first shell exchange was observed in the QM/MM MD simulation at 90 °C within the simulation time of 25 ps. However, in comparison to the classical simulation at 25 °C, a prominent temperature effect is observed in the CMD simulation at 90 °C, illustrated in Figure 7. As the first shell MRT decreased from 146 to 30 ps due to the higher temperature, several first shell exchange processes could be seen during the simulation time. Classical MD simulations of other ions such as Li+, Na+, Rb+, Cs+ and Th4+ have also shown a reduction of water ligand MRTs with increasing temperature.3,4,7 Table 5 also lists the sustainability of migration processes between second shell and bulk, Sex, and the number of attempts needed for one successful exchange process, 1/Sex. It is clear that the number of attempts made for a real exchange process to/from the second shell in the QM/MM MD simulation at 90 °C has significantly decreased from ∼22 (obtained for 25 °C) to ∼9. Similarly, the number of attempts needed for a successful exchange event in the first shell has reduced nearly to its half (from ∼4.8 to ∼2.6) at 90 °C in the CMD simulation.
Figure 7. Ligand exchange processes obtained from the CMD simulation at 90 °C.
4. Conclusion The comparison of structural and dynamical properties of Zn(II) in aqueous solution obtained from the CMD and the QM/ MM MD simulation at 25 and 90 °C revealed that the dynamics of the zinc-water system are more sensitive to the temperature variation than the structure of the hydrate. Within the simulation time, no first shell exchange was observed in the QM/MM simulation even at 90 °C. However, the second shell MRT value for 90 °C has decreased from 10.5 at room temperature, to 4.0 ps. The first shell coordination number remained 6, reflecting the stability of the [Zn(H2O)6]2+ complex at 90 °C. The second shell is much more influenced by the higher temperature, which increases its average coordination number to 19. In general, CMD simulations appear less suitable to evaluate the detailed structure and the dynamics of hydrated ions, but they seem suitable to obtain starting structures for more accurate simulations, hoping thus to reduce the equilibration time needed. As the second shell MRT values obtained by the CMD simulation are considerably shorter than those of the QM/MM simulation, the first shell MRT value at 90 °C obtained by the CMD simulation can also be assumed to be too short by at least 20%. To confirm this, a much more prolonged QM/MM simulation would be necessary, whose associated computational effort of several more months is not feasible, however, at present. Acknowledgment. Financial support for this work by the Austrian Science Foundation (FWF) (project P16221-N08) and an Austrian technology grant (BMBWK/RFTE) for M.Q.F. are gratefully acknowledged. References and Notes (1) Fatmi, M. Q.; Hofer, T. S.; Randolf, B. R.; Rode, B. M. J. Chem. Phys. 2005, 123, 4514. (2) Mohammed, A. M.; Loeffler, H. H.; Inada, Y.; Tanada, K.; Funahashi, S. J. Mol. Liq. 2005, 119, 55. (3) Noworyta, J. P.; Koneshan, S.; Rasaiah, J. C. J. Am. Chem. Soc. 2000, 122, 11194. (4) Egorov, A. V.; Komolkin, A. V.; Chizhik, V. I.; Yashmanov, P. V.; Lyubartsev, A. P.; Laaksonen, A. J. Phys. Chem. B 2003, 107, 3243. (5) Farkas, I.; Banyai, I.; Szabo, Z.; Wahlgren, U.; Grenthe, I. Inorg. Chem. 2000, 39, 799. (6) Farkas, I.; Grenthe, I.; Banyai. J. Phys. Chem. A 2000, 104, 1201. (7) Yang, T.; Tsushima, S.; Suzuki, A. Chem. Phys. Lett. 2002, 360, 534. (8) Seward, T. M. Metal Complex Formation in Aqueous Solution at EleVated Temperature and Pressure; Pergamon: Oxford, 1981. (9) Rao, L.; Garnov, A. Y.; Jiang, J.; Bernardo, P. D.; Zanonato, P.; Bismondo, A. Inorg. Chem. 2003, 42, 3685. (10) Seward, T. M. Geochim. Cosmochim. Acta 1984, 48, 121. (11) Ruaya, J. R.; Seward, T. M. Geochim. Cosmochim. Acta 1986, 50, 651. (12) Lee, S.; Kim, J.; Park, J. K.; Kim, K. S. J. Phys. Chem. 1996, 100, 14329. (13) Rudolph, W. W.; Pye, C. C. Phys. Chem. Chem. Phys. 1999, 1, 4583. (14) Schwenk, C. F.; Loeffler, H. H.; Rode, B. M. J. Chem. Phys. 2001, 115, 10808. (15) Schwenk, C. F.; Rode, B. M. J. Chem. Phys. 2003, 119, 9523. (16) Schwenk, C. F.; Hofer, T. S.; Rode, B. M. J. Phys. Chem. A 2004, 108, 1509. (17) Berendsen, H. J.; Grigera, J. R.; Straatsma, T. P. J. Phys. Chem. 1987, 91, 6269. (18) Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids; Oxford Science Publications: Oxford, 2003. (19) Adams, D. J.; Adams, E. M.; Hills, G. J. Mol. Phys. 1979, 38, 387. (20) Stillinger, F. H.; Rahman, A. J. Chem. Phys. 1978, 68, 666. (21) Bopp, P.; Jansco, G.; Heinzinger, K. Chem. Phys. Lett. 1983, 98, 129. (22) Yagu¨e, J. I.; Mohammed, A. M.; Loeffler, H. H.; Rode, B. M. J. Phys. Chem. A 2001, 105, 7646.
Zn(II)-Water Complex in Aqueous Solution (23) Hartmann, M.; Clark, T.; van Eldik, R. J. Am. Chem. Soc. 1997, 119, 7843. (24) Rotzinger, F. P. J. Am. Chem. Soc. 1997, 119, 5230. (25) Rotzinger, F. P. J. Am. Chem. Soc. 1996, 118, 6760. (26) Helm, L.; Merbach, A. E. Coord. Chem. ReV. 1999, 187, 151. (27) Scott, A. P.; Radom, L. J. Phys. Chem. 1996, 100, 16502. (28) DeFrees, D. J.; McLean, A. D. J. Chem. Phys. 1985, 82, 333. (29) Murphy, W. F.; Bernstein, H. J. J. Phys. Chem. 1972, 76, 1147.
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