First Principles Simulation of the Bonding, Vibrational, and Electronic

Jan 15, 2010 - H-bond decomposition shows significant bulk-like structure within the second .... Emilie Cauët , Stuart Bogatko , John H. Weare , John...
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J. Phys. Chem. A 2010, 114, 2189–2200

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First Principles Simulation of the Bonding, Vibrational, and Electronic Properties of the Hydration Shells of the High-Spin Fe3+ Ion in Aqueous Solutions Stuart A. Bogatko, Eric J. Bylaska, and John H. Weare* Chemistry and Biochemistry Department, UniVersity of California San Diego, San Diego, CA, Pacific Northwest Laboratories, Richland, WA ReceiVed: May 27, 2009; ReVised Manuscript ReceiVed: October 15, 2009

Results of parameter-free first principles simulations of a spin up 3d5 Fe3+ ion hydrated in an aqueous solution (64 waters, 30 ps, 300 K) are reported. The first hydration shell associated with the first maximum of the radial distribution function, gFeO(r), at d(Fe-OI) ) 2.11-2.15 Å, contains 6 waters with average d(OH) ) 0.99 Å, in good agreement with observations. A second shell with average coordination number 13.3 can be identified with average shell radius of d(Fe-OII) ) 4.21-4.32 Å. The waters in this hydration shell are coordinated to the first shell via a trigonal H-bond network with d(OI-OII) ) 2.7-2.9 Å, also in agreement with experimental measurements. The first shell tilt angle average is 33.4° as compared to the reported value of 41°. Wannier-Boys orbitals (WBO) show an interaction between the unoccupied 3d orbitals of the Fe3+ valence (spin up, 3d5) and the occupied spin down lone pair orbitals of first shell waters. The effect of the spin ordering of the Fe3+ ion on the WBO is not observed beyond the first shell. From this local bond analysis and consistent with other observations, the electronic structure of waters in the second shell is similar to that of a bulk water even in this strongly interacting system. H-bond decomposition shows significant bulk-like structure within the second shell for Fe3+. The vibrational density of states shows a first shell red shift of 230 cm-1 for the V1,2V2,V3 overtone, in reasonable agreement with experimental estimates for trivalent cations (300 cm-1). No exchanges between first and second shell were observed. Waters in the second shell exchanged with bulk waters via dissociative and associative mechanisms. Results are compared with an AIMD study of Al3+ and 64 waters. For Fe3+ the average first shell tilt angle is larger and the tilt angle distribution wider. H-bond decomposition shows that second shell to second shell H-bonding is enhanced in Fe3+ suggesting an earlier onset of bulk-like water structure. 1. Introduction 1

Hydrated highly charged (charge g2+) metal ions are frequently encountered as important constituents in chemical processes. They play critical roles in, for example, mineral formation and extraction,2,3 the stability of surfaces and nanoparticles,4,5 as partially solvated ions (cofactors) activating biochemical reactions,6–8 and in the transport of toxic materials.9 The mechanisms of these processes are dependent on the interaction of the solvated metal ion with surrounding ligands, such as: the polarization of the hydrating waters; disturbance of the bulk hydrogen bond structure in the hydration region; the formation of ion pair species; and activation of neighboring bonds. Therefore, a fundamental understanding of the structure and dynamics of the hydration shells surrounding an ion is critical to the interpretation of aqueous chemistry. The detailed structure of the hydration region surrounding an ion is difficult to observe. Experimental methods such as X-ray absorption and X-ray and Neutron scattering resolve important space- and time-averaged structural features.10–31 Dynamical properties such as ligand exchange rates in the first and second hydration shell may be indirectly observed by NMR and infrared spectroscopy.32–35 Recently, new XAS measurements have been reported that are sensitive to the electronic interactions of ligand molecules with the hydrated ions.36,37 * To whom correspondence should be addressed. E-mail: jweare@ ucsd.edu.

Singly charged ions are known to have a fairly well ordered first hydration shell with water structure returning to bulk structure beyond this region.1,32 The properties of regions beyond the first shell are less well determined.18–24,29 A second hydration shell in which the structure is significantly different from bulk water is expected for highly charged ions. The largely Coulombic nature of the ion-water interactions lead to an increased stability of the hydration shell with increasing ionic charge and decreasing ionic radius. Support for this concept is found in cation hydration enthalpies which correlate well with Z2/reff, where Z is the cation charge and reff is the effective ionic radius.1 However, even for ions of the same charge there may be substantial differences in chemical properties. For example the Al3+ ion is similar to the Fe3+ ion in charge and size (54 and 65 pm for Al3+ and high-spin Fe3+, respectively),1 both exhibit an octahedral first hydration shell1,32 and the existence of a second hydration shell has been determined experimentally.13,19,23–26,28,29 Because of the smaller reff the hydration energy of Al3+ is expected to be larger than Fe3+ resulting in a more strongly bound hydration shell. However, the hydrolysis constant, 2.16 and 4.97, and exchange rate constants, 1.6 × 102 and 1.29 s-1, for Fe3+ and Al3+ are orders of magnitude different.1,32 These dramatic differences in properties may be related to the valence electronic structure of the transition metal Fe3+ ion. Recent XAS experiments demonstrate “orbital mixing” between first shell waters and the transition metal ions Fe3+ and Cr3+ whereas no interaction is observed for Al3+.36 To understand these behaviors a more detailed theory, that takes

10.1021/jp904967n  2010 American Chemical Society Published on Web 01/15/2010

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into account the differences in valence electronic structure of the ions, is required. Direct simulation methods (e.g., molecular dynamics (MD) and Monte Carlo methods) provide the most reliable finite temperature interpretation of condensed fluid systems. Conventional molecular dynamics (CMD), in which the interaction potential is represented by two-body interactions, has been very successful32,38 in treating relatively weakly interacting systems (e.g., hydration of singly charged ions). However, a major limitation to the broader application of CMD is that it is difficult to account for many-body effects (e.g., density and distance dependent strong polarization, possible solute-solvent electronic interactions, proton exchange, etc.) which are important in more strongly interacting systems.39–44 Quantum interference effects such as bond saturation and Jahn-Teller distortions also are difficult to capture with a phenomenological potential as in CMD. Here we report first principle MD simulations of the Fe3+-H2O system. In this method the interaction potential is calculated directly from the electronic Schro¨dinger equation using density functional theory45–47 and containing all manybody interactions. A previous ab initio molecular dynamics (AIMD) study of this system39 produced good first shell structure. However, the small simulation cell (L ) 10 Å, 32 waters) and short sampling time (7 ps) used in this calculation limited their interpretation of second shell properties. The present study addresses both these problems by including 64 waters in the simulation and collecting data for 30 ps. We also perform a detailed comparison of the results obtained with the results of the similar Al3+-64 water AIMD simulation by Bylaska et al.48 and discuss differences in structure, dynamics, and valence electronic structure. 2. Details of the Simulation The high-spin (3d5) Fe3+-64 water system was simulated using the PSPW option of NWchem.49 The system contained one Fe3+ ion and 64 water molecules for a total of 517 electrons. To simulate the open shell valence of Fe3+, a 5v spin ordered ion, separate orbitals were assigned to the spin up (R) and spin down (β) electrons. The PBE96 exchange correlation functional50–52 was used in a 12.414 Å cubic simulation cell (density near 1 g/cm3) with periodic boundary conditions. The Fe3+ charge centers were neutralized by including a homogeneous negative background. Following the prescription laid out by Kleinman and Bylander,53 Hamann pseudopotentials54 were made fully nonlocal and used to describe the O and H cores of solvent waters. A nonlocal Troullier-Martins pseudopotential55 was used for the Fe3+ core, and a nonlinear core correction56 for the Fe3+ pseudopotential was included in order to address the nonlinearity of the exchange-correlation energy. Plane wave energy cutoffs of 40 hartree for the wave function and 80 hartree for the density were used. The system was propagated in time using a Car-Parrinello molecular dynamics (CPMD) scheme57 with a time step of 0.169 fs and a fictitious orbital mass of 750 au. In order to slow the OH bond dynamics the hydrogen atoms were replaced with deuterium. We note here that the effects of neglecting the quantization of nuclear motion are not discussed in this work and have been investigated by, for example, Schwegler et al.58 Calculation of the initial ground state orbitals was performed using the conjugate-gradient on Grassman manifolds method.59 The temperature was controlled by coupling the electronic and ionic degrees of freedom to separate Nose´-Hoover thermostats,60 resulting in an ion temperature of 300 K and a fictitious

Bogatko et al. electron kinetic energy on the order of 10-4 hartrees per electron. In several previous AIMD simulations61–63 the use of thermostats has been limited or avoided altogether in favor of collecting data in the microcanonical ensemble and controlling temperature by rescaling the ionic velocities. The canonical ensemble was chosen here because the length of the simulation (30 ps) is so great that a significant amount velocity rescaling and quenching of the electronic degrees of freedom would be required to ensure a constant temperature and that the electrons remain in the ground state. The system was allowed 2 ps of equilibration time before the 30 ps of simulation data was collected. The aqueous Fe3+ is known to readily hydrolyze the first hydration shell with the dominant species being heavily dependent on solution pH. In neutral (pH ) 7) solutions the dominant species are expected to be [Fe(OH)2(H2O)4]+ and [Fe(OH)3(H2O)4].64 However, in the total 32 ps of simulation time there were no transfers of hydrogens from the first shell to the bulk. A 12 ps AIMD simulation of 64 waters (no ions) was performed using the same parameters as in the Fe3+ simulation as a baseline for our discussion. Double occupation of the electronic orbitals was used in this simulation. Gas phase geometry optimization calculations of [Fe(H2O)6]3+, [Al(H2O)6]3+, and H2O were performed to help analyze effects due to metal coordination and hydration. These gas phase calculations were also performed with the same level of theory as the Fe3+-64 water and 64 water simulations. To further analyze the behavior of the Fe3+ system we compared results with prior Al3+ calculations at the same level of theory. The details of the 17 ps AIMD simulation of the Al3+-64 water system can be found in ref 48. Occupation of the hydration shells were estimated using the running integration number, nMO(r), computed by integrating gMO(r′) from r′ ) 0 to r′ ) r. The first shell coordination number (CN) is given by nMO(r) in the region between the first and second shells (CNI ) nMO(rI); rI ) 3.0 Å). To assign a value for the second shell we evaluated nMO(r) at the first minimum of gMO(r) beyond the second shell peak and subtract the first shell value (CNII ) nMO(rII) - CNI; rII ) 4.95 Å). The Fe3+ first and second shell properties were estimated by computing averages and standard deviations (σ) in the ranges 0.0-3.0 Å and 3.0-4.95 Å, respectively. For data plotted against Fe-O distance, averages and standard deviations were computed for a bin size of 0.08 Å. 3. Results and Discussion The Fe-O and Al-O radial distribution functions are plotted in Figure 1. Tables 1 and 2 contain the structural parameters from the first and second hydration shells of Fe3+ and Al3+, results from a 64 water AIMD simulation, and experimental observations. For comparison the computed gas phase structure parameters for the [Fe(H2O)6]3+ species are dFeO ) 2.11 Å, dOH ) 0.96 Å, θHOH ) 107.6°; for the [Al(H2O)6]3+ species dAlO ) 1.94 Å, dOH ) 0.96 Å, θHOH ) 107.4°; and for a vacuum water molecule dOH ) 0.95 Å, θHOH ) 105.5°. We have also computed the gas phase optimized geometries of the [Fe(H2O)6]3+ and [Al(H2O)6]3+ species using the same exchange correlation functional (PBE96) and the local basis set Ahlrichs-pVDZ.65 The M-O bond lengths of the [Al(H2O)6]3+ complex are identical to those obtained under the PSPW level of theory used here while those of the [Fe(H2O)6]3+ species are slightly shorter by 0.04 Å (i.e., 2.07 Å). 3.1. First Shell Structure. The first shell peak position of 2.10 Å and the average Fe-OI distance of 2.12 Å (σ ) 0.088 Å) are consistent with our DFT gas phase calculations. The gas

Hydration Shells of the High-Spin Fe3+ Ion

Figure 1. Radial distribution functions gMO(r) and running integration number nMO(r) for the Fe3+ (red) and Al3+ (blue) simulations, T ) 300K, F ) 1 g/cm3.

phase Al3+-O distance of the Al(H2O)63+ species is identical to that determined by the AIMD study of Bylaska et al.48 However, the first shell Fe-OI distance of this AIMD study and the Al-OI distance from Bylaska et al. are slightly larger than the experimentally determined values (Table 1). The first shell OH distance and HOH angle agree well with the only available first shell data from a triply charged ion neutron diffraction experiment of the Cr3+-H2O system11 (dOH ) 0.99 Å and θHOH ) 108-114°). Relative to gas phase H2O the first shell water OH bonds are elongated by 0.04 Å and HOH angle is increased by ∼2°. Relative to the gas phase [Fe(H2O)6]3+ and [Al(H2O)6]3+ water ligands additional hydration shells leads to a lengthening of the OH bond in the hydrating water by about 0.03 Å. No significant effect from additional hydration is observed in the first shell M-O distance (M ) Fe3+ or Al3+) and HOH angle (Table 1) for first shell waters. The average tilt of a first shell water, the angle formed between the H-O-H plane and the vector connecting the O atom and central ion, can be deduced from neutron scattering. For the triply charged ions Cr3+ and Fe3+ this angle has been estimated to be 34 and 41°, respectively.11,13 In the analysis of experimental data the average ion-oxygen and ion-hydrogen distances extracted from the scattering intensities are used with a reasonable estimate of the HOH angle and OH distance to obtain the tilt angle. Using the same method and values from Table 1 with dFeH ) 2.75 Å our data yields an average first shell water tilt angle of 33.4° (vs the observed angle of 41°). This is slightly larger, 4.4°, than value computed for the Al3+ first shell of 27.8° (Table 1). These values suggest that the first shell waters of Fe3+ and Al3+ experience differing ion-water interactions and H-bonding interactions with other hydrating waters. We note that the tilt angle of the gas phase hexaqua species is 0.0°. Instead of using the method employed in diffraction experiments to calculate tilt angles, which relies on the MO and MH radial distribution functions and an estimate of the water geometry, the dipole tilt angle may be used. In this estimate the angle between the M-O vector and the dipole direction of the water molecule is used to provide a value which can be evaluated at every time step. Using this method the average “dipole tilt” angles for Fe3+ and Al3+ first shell waters are θ ) 30°, σ ) 15 and θ ) 24°, σ ) 13° respectively. The distribution

J. Phys. Chem. A, Vol. 114, No. 5, 2010 2191 of first shell water dipole tilt angles, Figure 2, is broad and flat with a slow decay to zero at ∼80° for Fe3+ (red data points). This may be compared to the first shell dipole tilt distribution for Al3+ (blue data points in Figure 2) which is narrower and biased toward smaller values of tilt relative to the Fe3+ data. This suggests that the first shell waters of Fe3+ are less restricted than the first shell waters of Al3+ and is consistent with the smaller radius of Al3+. To further interpret the interactions leading to the structure in the hydration shell, in Figure 3 the tilt angle (Figure 3A), OH distance (Figure 3B), density of donor (Figure 3C), and acceptor (Figure 3D) hydrogen bonds from second shell waters are plotted for the first shells of Fe3+ and Al3+ versus normalized distance of separation of the hydrating water from the ion center (rM-O / < rM-O >). (The criterion d(O1-O2) e 3.2 Å and ∠(O1H1 · · · O2) g 140° was used to define a hydrogen bond. A donor H-bond is formed when a water molecule (the donor) makes an H-bond to a neighboring water (the acceptor) by coordinating its OH bond to the neighboring water’s lone pair. In a standard strength H-bond the proton is associated with the donor. An acceptor bond is formed by a water molecule sharing a lone pair with a neighboring molecule.) At short M-OI bond distances (strong water-ion interaction) the first shell tilt angle is small (Figure 3A), the OH bonds are slightly lengthened (Figure 3B), the second shell coordination is predominantly donor bonds from first shell waters to second shell waters (Figure 3C), and there are very few acceptor bonds from the second shell to the first shell (Figure 3D). As the M-O distance increases the first shell tilt increases for both Al3+ and Fe3+ and OH bond length decreases. There is also a decrease in donor bonding from the first to the second shell and an increase in acceptor bonding to the first shell waters as M-O increases for both species. The increase in acceptor bonding is very small in the Al3+ data and much larger in the Fe3+ data, where there is a significant increase in acceptor bonding to the second shell as access to the water lone pairs increases with tilt. The behavior of first shell tilt, OH distance and hydrogen bond coordination all support the idea of a strong metal-water interaction inducing a trigonal or dipole orientation (in which each first shell water coordinates 2 s shell waters via donor H-bonds) when the water is as close as possible to the metal ion. For larger M-O distances higher tilt angles lead to near tetrahedral coordination (in which each first shell water coordinates 3 s shell waters via 1 acceptor and 2 donor H-bonds). This behavior is more common in Fe3+ than in Al3+ suggesting a more structured second shell for the Al3+ system. 3.2. Second Shell Structure. For triply charged metal ions the presence of a well ordered second shell trigonally bonded to the six first shell waters is consistent with X-ray and neutron data11,13,14,17,19–22,24,29,66 and supported by prior calculations.39,48,67 In a perfect trigonal structure the second shell would contain exactly 12 hydrating waters interacting with the first shell via acceptor bonds and the bulk waters (e.g., waters beyond the second shell) via donor bonds resulting in 3 H-bonds per water. The second shell in the Fe3+ system is associated with the peak at ≈4.2 Å in Figure 1. The average Fe-OII distance (4.30 Å, σ ) 0.30 Å) and OI-OII distance (2.70 Å, σ ) 0.15) are consistent with experimental values in the second shell (Fe-OII ≈ 4.09-4.8 Å, OI-OII ≈ 2.62-2.84 Å) while the number of waters (CNII ) 13.3, σ ) 1.3) is larger than the ideal value for a trigonal structure (CNII ) 12).13,24–26,29 Compared with the second shell of Fe3+ the Al3+ second shell has a smaller average Al-OII distance, a similar OI-OII distance, and contains fewer waters (CNII ) 12).

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TABLE 1: Fe3+ and Al3+ First Shell Properties and Bulk Water Values

e

average parameters

Fe3+-64H2Oa

Al3+-64H2Ob

temperature (K) collection time (ps) d(M-O) (Å) σ(M-O) (Å) d(O-H) (Å) σ(O-H) (Å) θ(H-O-H) (°) σ(H-O-H) (°) tilt ∠ (°)

300 30 2.12 0.088 0.99 0.04 107.21 5.47 33.4

327 17.34 1.94 0.074 0.99 0.038 107.35 5.44 27.8

Fe3+(aq.) exp.c

Al3+(aq.) exp.d

64H2Oe 300 12

1.94 - 2.08 0.077-0.09 0.99f

1.88-1.902 0.04 - 0.1 0.99f

108-114f

108-114

41

34f

f

0.97 0.03 105.45 5.19

a This work. b Reference 48. c References 13, 24–26, 28, 29, 95 and private communication with Dr. Robert Mayanovic. d References 19, 23. Unpublished AIMD of 64 H2O at 300 K. f Values taken from Cr3+ ref 11, which performs a detailed analysis of first shell water geometry.

TABLE 2: Fe3+ and Al3+ Second Shell Properties and Bulk Water Values average parameters d(OI-OII) (Å) σ(OI-OII) (Å) d(M-OII) (Å) σ(M-OII) (Å) ∠OI-HI-OII (°) σ∠OI-HI-OII (°) H2O second shell

Fe3+-64 H2Oa f

2.70 f 0.15 4.30 0.30 f 163.37 f 8.66 13.3

Al3+-64 H2Ob 2.68 0.14 4.09 0.23 163.8 8.19 12

Fe3+ (aq.) expc

Al3+ (aq.) exp.d

2.62-2.84 0.038-0.058 4.09-4.8 0.01-0.02 180g

2.683-2.73 0.02-0.09 4.01-4.15 0.22-0.33 180g

12g

12g

64H2Oe 2.83 0.16 160.58 9.42

a This work. b Reference 48. c References 13, 24–26, 28, 29, 95 and private communication with Dr. Robert Mayanovic. d References 19, 23. Unpublished AIMD of 64 H2O at 300 K. f For trigonal first - second shell coordination (for Fe system). g A 12 coordinate trigonally coordinated second hydration shell was invoked to fit their data.

e

Figure 2. The broad and flat distribution of first shell tilt angles for Fe3+ (red) compared with the narrow distribution for the first shell of Al3+ (blue). (normalized counts per degree, bin size 4.5°).

An example of the structure of the second shell of the Fe3+ system is given in Figure 4, where the first shell is partially obscured by a transparent surface. The light blue water of Figure 4 identifies a 13th water interacting via a donor bond to the first shell. The remaining orange waters show some tendency to coordinate to neighboring second shell waters in addition to the expected trigonal structure. In the Al3+ simulations there were no donor bonds to waters in the first hydration shell. Although our results fall within the range of second shell coordination numbers predicted by conventional molecular dynamics (e.g., 12-15 waters)40,41,68–71 we note that these values show dependence on the particular potential that is implemented. 3.3. Electronic Structure of Solvating Waters. The electronic structure information generated by AIMD provides a basis for interpretation of the interactions in terms of molecular bonding and possibly connection with spectroscopic measurements. However, the Kohn-Sham DFT implemented in AIMD is based on delocalized molecular orbitals. For systems of this size (517 orbitals) these are difficult to interpret. Boys and others have shown that it is possible to obtain a localized representation of the density by performing a unitary transformation on the

occupied molecular orbitals to form the maximally localized Wannier-Boys Orbitals (WBO).72–75 The WBO provide a representation of the electronic structure which can be interpreted in terms of local bond formation. In Figures 5 A and B the spin up and spin down WBO are calculated for a single frame roughly 7 ps into the Fe3+-64 water AIMD simulation. It has been proposed that the near trigonal configurations of solvating waters should result in a rehybridization of the first shell water oxygens toward sp2.22 The HOH angle for sp2 hybridized water would be greatly increased to 120° and should be easily detectable in our data. The maximum HOH angle detected in our first shell data is 108°, which is not consistent with sp2 hybridization. The spin up and spin down WBO illustrated in Figure 5, panels A and B, support sp3 hybridization for first shell, second shell and bulk waters. A WBO representation also allows for an accurate estimation of the dipole moment of water molecules.76,77 The average dipole moment for our bulk water simulation is found to be 3.1 ( 0.1 D, in agreement with published results.78,79 The dipole moments of first shell water are 3.6 ( 0.2 and 4.1 ( 0.2 D for the Fe3+and Al3+-64 water simulations, respectively. The waters in the second hydration shell of Fe3+ and Al3+ show average dipole moments of 2.9 ( 0.2 and 3.0 ( 0.2 D, respectively; and beyond the second hydration shell they are 2.8 ( 0.1 D for both systems. These results show that the first shells of these 3+ metals are significantly polarized relative to bulk water. Furthermore, waters in the second shell and beyond exhibit dipole moments consistent with a bulk water environment showing that the strong polarizing characters of the Fe3+ and Al3+ centers do not extend beyond the first hydration shell. There is a small but significant contribution to the spin down electronic structure on the Fe3+ metal center (circled in Figure 5B). To study this further we performed a detailed analysis of the ion water interactions in terms of the positions of the centers of the WBO relative to the oxygen center of the water molecule (Wannier-Boys function center, WFC). This representation has been shown by Lightstone et al.80 to provide a revealing representation of metal ion-water interactions. If there is a

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Figure 4. H-bond interaction between second shell waters and the first shell. The orange waters are trigonally H-bonded to the first shell (which is partially obscured to show the interactions more clearly). The light blue water is coordinated by a first shell acceptor bond.

Figure 3. (A) Distribution of Fe3+ (red) and Al3+ (blue) first shell average tilt angle, (B) OH distance, (C) donor, and (D) acceptor hydrogen bond density per water (to the second shell) as a function of M-O distance divided by average M-O distance plotted over the normalized distribution of M-O distances (M ) Fe3+, Al3+; bin size 0.02).

significant impact of the presence of the ions on the electronic structure of a water molecule, the distance from the O center to the WFC, dO-WFC, and the angle formed by the WFCs and the O center, θWFC-O-WFC, in the molecule should be altered relative to those found in bulk water. The results of this analysis are shown in Table 3. For comparison the WBO for the Al3+-64 water and the 64 water simulations are also analyzed. The inset in Table 3 defines the angles and distances for the lone pair orbitals (LPO) and bonding orbitals (BO). For the electronic structure of the waters in the first hydration shell, the spin up (R) and down (β) dO-WFC of the Fe3+ and the restricted dO-WFC of the Al3+ BO are all shortened by ∼0.02 Å relative to the bulk water values (Table 3). The dO-WFC for the first shell water spin up Fe3+ and the restricted Al3+ LPO are close to bulk water values. The dO-WFC for the first shell spin down LPO of Fe3+ (0.38 Å) is lengthened by 0.05 Å relative to bulk water. The θWFC-O-WFC angles for the first shell spin up BO of Fe3+ and restricted BO of Al3+ are close to the bulk values. An increase of 4° is observed for the θWFC-O-WFC of

Figure 5. Spin up (A) and spin down (B) bonding and lonepair WBO for the six first shell waters (yellow and light green), one second shell water (purple and light blue), and one bulk water (dark green and dark blue) showing sp3 configuration. Surfaces are generated from a contour of constant |φ| ) 0.3 for each orbital. Occupation of spin down 3d valence of the Fe3+ ion is indicated by circles in (B).

the spin down BO of Fe3+. The θWFC-O-WFC of the spin up Fe3+ and the restricted Al3+ LPO are smaller than the bulk values. The θWFC-O-WFC of the spin down Fe3+ LPO is decreased by ∼23°. These results demonstrate that down spin lone pair WBO show considerably more interaction with the Fe3+ ion core. These changes are in the direction of sp2 hybridization. Beyond the first shell no difference between the spin up and spin down positions of the WFCs is observed. The waters in this region have dO-WFC distances for BO and LPO WFCs that are very close to those of the 64 water simulation. There are

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TABLE 3: Electronic Structure for the Solvation Shells Represented by Spin up (r), Spin down (β) or Restricted (r) WFC

first hydration shell dO-WFC a

LPO

0.48 0.48 0.48

0.32 0.38 0.34

BO Fe3+-64 H2O Fe3+-64 H2O Al3+-64 H2O 64 H2O a

R β rc r

second hydration shell dO-WFC

θWFC-O-WFC b

Bulk

θWFC-O-WFC

dO-WFC

θWFC-O-WFC

BO

LPO

BO

LPO

BO

LPO

BO

LPO

BO

LPO

106 110 106

112 92 110

0.50 0.50 0.50

0.33 0.33 0.33

104 104 103

118 118 117

0.50 0.50 0.50 0.50

0.33 0.33 0.32 0.33

103 103 103 106

119 119 119 115

Bonding orbital. b Lone pair orbital. c Doubly occupied (restricted) orbital.

Figure 6. Cross-section of lone pair Wannier-Boys orbitals (LPO): (A) spin down LPO of a first shell water of Fe3+ (B), spin up LPO of a first shell water of Fe3+, (C) restricted LPO of a first shell water of Al3+, (D and E) spin down and spin up LPO for a second shell water of Fe3+, and (F) the restricted LPO for a second shell water of Al3+. Color scale ranges from blue ) -0.1 to red ) 0.1 with step ) 0.02.

small differences in the θWFC-O-WFC angle for the BO and LPO for the second hydration shells and bulk regions of Fe3+ and Al3+ when these are compared to the θWFC-O-WFC of the 64 water simulation. This suggests that the electronic structure of the waters in the second shell and beyond have returned to bulklike electronic structure and hybridization and is consistent with recent measurement and theoretical results performed on weakly interacting charged ions in electrolyte solutions.37,80 The electron density for the WBO, of the same configuration as above, for a selection of bonds is illustrated in Figure 6. These orbitals are plotted based on a scale of -0.1 (blue) to 0.1 (red) on a plane containing the oxygen atoms involved and/or the

central ion (all WBO are filled). The first shell spin down LPO that showed the most distortion in Table 3 is illustrated in Figure 6A. This figure clearly shows the interaction of the lone pair with the empty virtual d electron valence orbital. This character is not displayed by the spin up lone pair (Figure 6B) or the Al3+ restricted lone pair (Figure 6C). This is consistent with the dO-WFC distances in Table 3. The LPO from the second shell are illustrated in Figure 6, panels D-F. The similarity of LPO illustrated in panels D and E suggests that the effect of the localized spin on the Fe3+ ion is confined to the first shell. Recently Na¨slund et al.36 reported X-ray absorption spectra that they assigned to transitions from the oxygen 1s core orbital of a hydrating water to the oxygen p component of the unoccupied spin down molecular orbitals of the hydrated Fe3+ ion. The WBO description provides a local view of the bonding but cannot be used to interpret spectral properties because the unoccupied orbitals are not included in the WBO description. To provide information about these interactions we use the Kohn-Sham molecular orbitals calculated for the gas phase [Fe(H2O)6]3+ in a perfect octahedral structure (the same cut off parameters as in the AIMD calculations are used). In the octahedral solvation shell the Fe3+ valence atomic orbitals interact with the orbitals of the hydrating waters to form spin up and spin down t2g and eg extended orbitals. In Figure 7 we illustrate several of the lowest down spin virtual orbitals (Figure 7A and 7B) and the down spin filled molecular orbital with the largest d contribution (Figure 7C). In Table 4 the corresponding eigenvalues, orbital symmetry (eg or t2g) and mulliken populations (indicating the s, p, or d contributions to the MO) are given. Naslund et al.36 assign their observed X-ray absorption spectrum to transitions from the oxygen 1s core orbital of a hydrating water to virtual down spin antibonding MO created by the interaction between the waters in the hydration shell and the Fe3+ open d shell. Supporting this conjecture our calculations show the lowest unoccupied molecular orbital (LUMO) and the next lowest unoccupied MO (LUMO+1) are the antibonding eg and t2g symmetry orbitals with large d character. The filled down spin orbital with the largest d contribution, Figure 7C, shows considerable interaction with the spin down Fe3+ d(x2-y2) and dz2 atomic orbitals. This is consistent with the long dWFC-O length observed in the WBO representation (0.38 vs 0.33 for bulk water) and the transfer of charge as illustrated

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Figure 7. Selected orbitals of the [Fe(H2O)6]3+ cluster. (A) The LUMO+1, (B) the LUMO, and (A) the HOMO-4 orbitals.

in Figure 5B. Because of the absence of a 3d valence shell in Al3+ these interactions do not occur. 3.4. Hydrogen Bonding. A charged ion in an aqueous solution forms strong, primarily ionic bonds with neighboring waters forming structure in the first hydration shell that breaks the tetrahedral H-bonding structure of the solution. The metal ion-water bond is stronger than the H-bonds in solution and the motion of the first shell hydrating waters is hindered. Through this mechanism a strong enough interaction (2+ and higher ions) inhibits the waters in the first shell from forming acceptor bonds to other waters in the second hydration shell, leading to trigonal structure as illustrated in Figure 4 (orange waters) and the further breakup of the bulk H-bonding structure. There is an ongoing discussion as to the performance of the various exchange correlation functionals when applied to hydrogen bonded systems such as solvated metals. The applicability of the PBE96 functional has been demonstrated in refs 63, 78, and 81. For more information the interested reader is referred to refs 62 and 82. The bond length of the donor bonds between the first shell and second shell waters are consistent with observed values (2.62-2.84 Å, Table 2). These bonds show a significant shortening and an increased hydrogen bond angle relative to bulk water (2.83 Å, 160.58°) suggesting stronger H-bond formation in this region.83 There is also a small contribution to the Fe3+ first-second shell interaction from acceptor bonds (dOI-OII ) 2.94 Å, σd ) 0.17 Å; θ ) 157.41°, σθ ) 9.92°). These interactions have a smaller average hydrogen bond angle and a larger average H-bond distance than the donor type of coordination and are correlated with the large tilt angle at large

Figure 8. The distribution of acceptor bonds per water originating from donor waters in the first shell (red circles), second shell (blue triangles) and the bulk (green diamonds) for the Fe3+ (Figure 8A) and the Al3+ (Figure 8B) 64 water simulations.

M-O distances of first shell waters shown in Figure 3A and 3D. The trigonal type H-bonding between first and second shell waters of Fe3+ is similar to the Al3+ system. However, the acceptor type coordination, which is responsible for ∼2% of the first-second shell H-bond coordination for Fe3+, is not present in the Al3+ simulation (i.e., less than 0.01% of the total first-second shell H-bonding). By decomposing the radial distribution of H-bonds in terms of acceptor bonds originating from a water in the first shell, second shell or the bulk to a water at an M-O distance, x, it is possible to characterize the shell-by-shell contribution to the H-bond structure. This can be used to identify differences between ion hydration shell structures and to quantify the transition from the first shell trigonal structure to the tetrahedral structure of bulk water.48 This decomposition is illustrated in Figure 8 for the Fe3+ (Figure 8A) and the Al3+ (Figure 8B) 64 water simulations. The metal-oxygen radial distribution func-

TABLE 4: Orbital Eigenvalues, Symmetry and Mulliken Populations of the LUMO+1, LUMO, and HOMO-4 of the [Fe(H2O)6]3+ Cluster Mulliken population orbital LUMO+1 LUMO HOMO-4

panel of Figure 7 A B C

eigenvalue (eV) -18.587 -19.736 -25.295

symmetry

s

p

d

eg t2g eg

0.0456 0.0026 0.0999

0.1132 0.1321 0.6795

0.8412 0.8654 0.2206

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tions gFeO(r) and gAlO(r) are also plotted on Figure 8A and 8B for reference. For Fe3+ and Al3+ the acceptor bonds from a first shell donor (red circles) begins with a water at about 3.2 Å near the beginning of the second shell. There is a maximum of ∼1.5 acceptor bonds near 3.2-3.5 Å in both simulations. In a perfect trigonal structure each second shell water molecule would coordinate only one first shell water via acceptor bonds. However, there are a few waters in the second shell (note that gAlO(r) and gFeO(r) are very small in this range), that have a bridged structure (two acceptor bonds) with two waters in the first shell leading to the maximum ∼1.5 value. Farther into the second shell the acceptor bond density from first shell donors is close to 1, consistent with a trigonal structure. A better indicator of the structure of the second shell and the difference between Fe3+ and Al3+ is the acceptor bond density from second shell waters (blue triangles). For the Fe3+ ion there is a slow increase in acceptor coordination starting within the first shell (Figure 8A, ≈ 2 Å). Near 2.6 Å there is a maximum of 0.4 acceptor bonds from donors in the second shell as x moves out of the first hydration shell. Note that there are no acceptor bonds from second shell waters observed in the Al3+ data (Figure 8B). A qualitative picture of the second shell coordination can be inferred by evaluating the acceptor distributions at the maximum of gMO(r), near ∼4.2 Å in Figure 8A and ∼4.0 Å in Figure 8B. From this we estimate 1.7 and 1.6 acceptor bonds per water in the second shell of Fe3+ and Al3+, respectively. These values decompose to 1 acceptor bond to donors in the first shell (red circles) for both Fe3+ and Al3+, 0.2 and 0.1 acceptor bonds to donors in the second shell, respectively, and 0.5 acceptor bonds to waters in the bulk region for both ions. The acceptor coordination to the first shell is consistent with a trigonal second shell structure for both systems whereas the presence of second shell acceptor bonds originating from donors in the second shell suggests a transition to bulk-like hydrogen bonding begins in the second shell. This behavior is more evident in the Fe3+ system than in the Al3+ system. Acceptor bonds to the first shell from the bulk (green diamonds) are rare. For waters beyond the second shell, acceptor bonding approaches a value consistent with the 64 water AIMD simulation (3.1 total H-bonds/water or ∼1.6 acceptor bonds) and suggests that the solvent structure has now returned to that of bulk water. 3.5. Analysis of the Solution Vibrational Structure. The vibrational density of states (DOS) reflecting potential interactions between species34,35,84,85 in the solution may be compared to the IR data and may be generated from simulation data by taking the temporal Fourier transform of the velocity autocorrelation function.86 The DOS for these simulations were computed using the velocity coordinates of the Fe3+-64 water (30 ps), Al3+-64 water (17 ps) and 64 water (12 ps) simulations. The data was smoothed by averaging 11 data points (a frequency range of about 10 cm-1) for the Fe3+, Al3+, and 64 water systems. Assignment of these bands to the motions of the water molecule is discussed in many IR studies.34,87 For D2O, the bending (V2, the fluctuation of the D-O-D angle) vibration occurs at 1209 cm-1, a combination of bending and libration (V2 + VL) occurs at 1555 cm-1, a large band (stretch band) at 2504 cm-1 contains three features at 2400 cm-1 (2V2), 2600 cm-1 (V3), and 2500 cm-1 (V1), and a V1 + V2 band occurs at 3840 cm-1. The very low wavenumber range (0-750 cm-1) is the domain of the librational (VL) or collective motion of many water molecules and is difficult to interpret. Band centers were estimated in a range determined by the width at Half Max for the libration (VL), bend (V2) and stretch (V1,2V2,V3) bands. The first shell vibrational DOS was also calculated using the velocity

Bogatko et al.

Figure 9. The vibrational density of states of the first shells of Fe3+ (red) and Al3+ (blue). Bending (v2) bands are centered at 1170 and 1196 cm-1, the stretch (V1,2V2,V3) bands at 2032 and 2057 cm-1 and librational (VL) bands at 520 and 573 cm-1 for Fe3+ and Al3+, respectively.

TABLE 5: Peak Positions Computed from the Vibrational DOS of First Shell Waters from the Fe3+ and Al3+ AIMD Simulations and from the 64 Water AIMD Simulationa Peak

Fe3+

Al3+

H2 O

V2 ∆V2 V1,2V2,V3 ∆V1,2V2,V3 VL ∆VL

1170 -19 2032 -230 520 139

1196 7 2057 -205 573 192

1189 2262 381

a ∆ denotes the shift relative to the computed bulk water values for the Fe3+ and Al3+ data.

coordinates of the 6 first shell waters of Fe3+ and Al3+ and is provided in Figure 9. To facilitate an easier comparison, both data sets have been normalized by a constant such that the area under the two curves is 1. In our spectra computed for the 64 water simulation we can identify the bending band (V2) and the stretch band (V1, 2V2, V3). The V2 + VL and V1 + V2 bands were unresolved in all simulations. There is a large red-shift of roughly 240 cm-1of the bulk water stretch band in our AIMD simulation relative to the experimental data. This has been discussed elsewhere and apparently results from the inclusion of gradient corrections to the exchange-correlation functional.39,62,67 We also see the libration domain (VL) (∼0-750 cm-1, centered at 381 cm-1) but do not observe any significant effects of ion solvation. Likewise, the bend and stretch bands from the vibrational DOS computed for the 64 water molecules solvating the Fe3+ ion and the 64 waters solvating the Al3+ ion show negligible shift relative to those computed for the 64 water simulation suggesting the presence of the ion has little effect on the bulk vibrational properties. The differences in vibrational properties are localized in the first solvation shell where the waters interact directly with the 3+ ion. The DOS for the first shell waters of Fe3+ and Al3+ is given in Figure 9. In Table 5 the VL, V2, and V1,2V2,V3 band centers are presented and compared with those obtained from our bulk water simulation. The libration bands for the Fe3+ and Al3+ first shell waters are centered at 520 and 573 cm-1, respectively, blue-shifted by 139 and 192 cm-1 relative to the librational band center of VL ) 381 cm-1 of bulk water. The first shell water bending band (V2) is centered at 1170 and 1196 cm-1 for Fe3+ and Al3+, respectively. The V1,2V2,V3 band is broad and centered at 2032 and 2057 cm-1 for Fe3+ and Al3+. As

Hydration Shells of the High-Spin Fe3+ Ion shown in Figure 9 and Table 5 the Fe3+ first shell V2 and V1,2V2,V3 bands are red-shifted by 19 and 230 cm-1, respectively, relative to that of the 64 water simulation (V2 ) 1189 cm-1, V1,2V2,V3 ) 2262 cm-1). The Al3+ first shell V2 band shows a negligible blue shift of 7 cm-1 but an appreciable red-shift of 205 cm-1 for the V1,2V2,V3 band. The DOS in Figure 9 also suggests that the stretch band is roughly similar for these systems. This is not surprising since it has been observed in various alkali-halide and alkaline-earth chloride salts that variation in IR spectra is related to the number of coordinating water molecules.85 Our results suggest that this is also true for the more highly charged 3+ ions. These results are also consistent with recent experimental and theoretical investigations. An IR study of first shell waters was carried out by Bergstrom et. al in which the first shell OD stretch of three trivalent cations (Al3+,Cr3+ and Rh3+) was estimated to have a frequency of 2200 cm-1, a redshift of ∼300 cm-1 relative to bulk D2O.34 The Fe3+-32 water, 7 ps Car-Parrinello MD study of Amira et al.39 predicts the frequency shift of Fe3+ first shell waters at 180 cm-1. They have also performed a Car-Parrinello MD study of Al3+ and 32 waters for 10 ps67 in which the first shell frequency shift was estimated to be in the range of 120-210 cm-1. 3.6. Intershell Exchange Dynamics. The waters in the first hydration shell are tightly bound to the ion center. Their observed first shell oxygen residence times (ie., 10-5 to 10-3s for Fe3+ and 0.78-6s for Al3+) and hydrogen residence times (10-7s for Fe3+ and 10-3s for Al3+) are well out of the range of these simulations32 and no water exchanges between the first and second hydration shells were observed. Furthermore, as mentioned earlier, no proton transfers to bulk waters were observed and the species remained in their hexahydrate forms. The binding time of a water molecule in the second shell of Fe3+ has not been directly measured. However, IQENS experiments have placed an upper limit of 5 ns from their second shell water-proton binding times measured for Fe3+ and other trivalent metals.17,88,89 NMR based estimates of second shell binding times of 128 ps33 for Cr3+ have been reported. The prior simulations for the Al3+ system predict transfers occurring on a picosecond time scale.48 It is reasonable to assume that the Fe3+ second shell waters would have a shorter lifetime than either Cr3+ or Al3+ systems, both of which have much longer first shell lifetimes (Fe3+ (10-3 sec), Al3+ (1 s) and Cr3+ (∼105 sec)).32 The reaction mechanism of a second shell-bulk water transfer is generally classified as proceeding via an associative exchange mechanism, which begins with a bulk water entering the second shell, a dissociative mechanism, which begins with a water leaving the second shell, or an intermediate mechanism in which there is no discernible intermediate structure.1,33 In the two studies mentioned above, Bleuzen et al. proposed an intermediate mechanism for Cr3+33 and Bylaska et al. identified a dissociative mechanism for Al3+.48 In our simulations these mechanisms are identified by analyzing the Fe3+-O distances of the waters involved along a particular trajectory. For an associative event the entering water approaches the average Fe3+-OII distance before the exiting water begins its escape. For dissociative exchange the Fe3+-OII distance of the exiting water will be greater than the second shell-bulk water boundary before the entering water begins its approach. In Figures 10 and 11 the trajectories of dissociative and associative second shell-bulk exchanges are shown. In both figures the initial, intermediate and final configurations are illustrated and the Fe-O distance is plotted against simulation time. In the

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Figure 10. Three snapshots of the initial, intermediate and final configuration of a dissociative second shell-bulk water transfer are illustrated in panels A.1, A.2, A.3 and the Fe-O distance is plotted against simulation time in panel B.

Figure 11. Three snapshots of the initial, intermediate and final configuration of an associative second shell-bulk water transfer are illustrated in panels A.1, A.2, A.3 and the Fe-O distance is plotted against simulation time in panel B.

dissociative transfer of Figure 10 the orange water is initially coordinating the first shell with a green water nearby in the bulk (Figure 10A.1 corresponding to 10B at 20-20.5 ps). Figures 10A.2, 10A.3 correspond to 20.65 ps and 20.8-21.4 ps of the trajectory in Figure 10B. The leaving water (colored orange) crosses the second shell-bulk water boundary (∼4.8 Å) before the incoming water (colored green). An associative exchange involving 3 waters is represented in Figure 11. Here a water (green) initially in the bulk (Figure 11A.1) moves into the second shell and displaces a second shell water (blue) (Figure 11B at 8.5-9.2 ps). The displaced water moves to coordinate a nearby first shell water in a donor orientation allowing it to remain in the second shell (Figure 11A.2 and Figure 11B at 9.5-11 ps). After a rotation (Figure 11B at 11-11.3 ps) the displaced water acceptor coordinates to the first shell, displacing

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a third water (orange) into the bulk (Figure 11A.3, Figure 11B at 11.3-12 ps). The Fe-O distances plotted in Figure 11B show that this all occurs within the second shell very close to the average Fe-OII distance. The associative mechanism identified here, Figure 11, could not occur in the Al3+ system due to the rigidity of the first shell and subsequent inability to form acceptor bonds to the second shell. 4. Conclusions Because of its large environmental2–5,9 and technological importance there have been a number of attempts to simulate the Fe3+-H2O system using a variety of methods, that is, effective two-body potentials,70 two- and three-body potentials with conventional molecular dynamics,69 hydrated ion models (HI)usingafixedfirstshellstructure,33,90–92 QM/MMapproaches,93,94 and first principles molecular dynamics39 as used here. All of these approaches have contributed to the understanding of this complex system. However, each method has significant limitations. For example the structure predicted by effective two-body/ three-body potential methods show a dependence on the particular potential implemented and HI models and QM/MM approaches treat sub regions of the hydration shells with different levels of theory and, therefore, cannot be reliably used to treat systems in which the boundaries are crossed (e.g., as in transfers between the hydration shells). In addition, most QM/ MM methods are based on local basis solutions to the electronic Schro¨dinger equations and the solution in the QM region is very slow,69,93,94 making sampling in this region inefficient. The AIMD method employed in this work is based on an “on the fly” solution to the electronic Schro¨dinger equation for the entire system, thus avoiding the problems of these other approaches, to provide parameter free and reliable predictions. Results of an AIMD simulation of the Fe3+ ion and 64 water molecules in a periodic simulation cell at a temperature of 300 K and density near 1 g/cm-1 are reported here. This simulation is for a considerably longer time and larger system size than has been previously reported.39 The results obtained are compared with a previous AIMD study of the Al3+ ion + 64 water48 system and new 64 water (pure water) AIMD simulation. Stable first and second hydration shells with occupation numbers and average distances consistent with experimental data were obtained in the metal ion simulations. The stable 6-coordinate first hydration shell of Fe3+ has a Fe-OI distance of 2.12 Å (σ ) 0.088 Å, experimental result Fe-OI ) 1.94-2.08 Å) and average tilt angle of 33.4°. The average coordination number of the second shell is 13.3 and is substantially larger than the 12 coordinate trigonally structured second hydration shell typically invoked when analyzing experimental results. The average Fe-OII distance is 4.30 Å (σ ) 0.30 Å, experimental result Fe3+-OII ) 4.09-4.80 Å) and average OI-OII distance is 2.70 Å (σ ) 0.15). The Al3+ first shell also contains 6 waters with a smaller average Al3+-OI distance of 1.94 Å (σ ) 0.074 Å, experimental result Al3+-OI ) 1.88-1.902 Å) and average tilt angle of 27.8°. The Al3+ second shell is smaller with an average of 12 waters at 4.09 Å (σ ) 0.23 Å, experimental result Al3+-OII ) 4.01-4.15 Å) and a similar OI-OII distance of 2.68 Å (σ ) 0.14 Å). The average first shell waters OH distance, 0.99 Å, and HOH angle, 107°, of Fe3+ and Al3+ are nearly identical. The range of motion of the water molecules in the first shell is related to the tilt angle distribution of the first shell waters. For Fe3+ these waters have a broad and flat distribution of tilt angles whereas the distribution for the first shell of Al3+ is narrow and biased toward smaller angles. This is consistent with

Bogatko et al. the simulation results that waters in the first shell of Fe3+ readily form acceptor bonds from second shell donor waters whereas the first shell of Al3+, whose first shell waters are restricted to smaller tilt angles, do not. This may also be interpreted as the first shell waters of Fe3+, which are less tightly bound relative to the first shell of Al3+, being stabilized by acceptor H-bonds from second shell and bulk waters. Analysis of the electronic structure via WBO72–75 demonstrates the spin down LPO of the Fe3+ first shell waters show significant differences compared to the spin up LPO and the Al3+ first shell water LPO. These appear as a result of the mixing of the 3d valence of Fe3+ and the first shell water molecular orbitals (MO) to form the t2g and eg orbitals. The spin up MO receive contributions from the Fe3+ spin up 3d and the first shell water LPO while the spin down MO receive only contributions from the spin down LPO. The occupation of the spin down MO results in a charge transfer to the Fe3+ center. This is not observed in the Al3+ system since it has no d-valence structure. Our results are consistent with a recent XAS study36 on Fe3+, Cr3+, and Al3+ aqueous solutions that observes that oxygen core 1s orbitals of first shell waters are excited into valence MO made up of d orbitals on the metal ion centers mixing with the orbitals of the hexaqua water for the Fe3+ and Cr3+ systems. No similar effect was observed in Al3+ aqueous systems. We also observe that there is no spin-dependent electronic interaction observed in the region beyond the first shell of Fe3+. Analysis of H-bond distributions shows significant acceptor coordination in the first shell of Fe3+ from donor waters in the second shell. The presence of these acceptor H-bonds are responsible for second shell occupation numbers larger than 12 for Fe3+ and are also observed to play a role in the second shell-bulk exchange mechanism. The Al3+ second shell contains 12 waters and is consistent with nearly pure trigonal planar H-bond geometry. There is also more intrasecond shell Hbonding occurring in the Fe3+ than in Al3+ second shells suggesting that there is an earlier onset of tetrahedral or bulklike H-bonding in this system. The Fe3+ and Al3+ first shell V2 bands (bending vibration) show small shifts relative to bulk water while the V1,2V2,V3 bands (stretch bands) are red-shifted by 230 and 205 cm-1, respectively, in reasonable agreement with the experimental estimate34 of 300 cm-1. The second shell and bulk waters are observed to exchange via dissociative and associative mechanisms on a time scale of 1-2 ps. The dissociative mechanism proceeds by breaking and forming H-bonds to donor waters in the first shell and is similar to the dissociative mechanism observed in the Al3+ simulation. In the associative mechanism there is an additional step in which an H-bond to an acceptor in the first shell is formed. The appearance of this mechanism in Fe3+ is a result of the availability of first shell waters to form acceptor bonds to the second shell and does not occur in the trigonally structured second shell of Al3+. We have demonstrated the great importance of a quantum representation of the metal-water interactions near the highly charged metal ions Fe3+ and Al3+. In particular, the electronic interactions of the first shell waters with the spin up 3d5 Fe3+ are observed to, relative to the first shell of Al3+, lead to a less strongly bound first hydration shell which, in turn, facilitates an earlier return to bulk-like H-bond structure, that is, in the second hydration shell. The appearance of an additional exchange mechanism, that is, associative, between the second shell and bulk is also observed. Acknowledgment. This research was supported by the BES Geosciences program of the U.S. Department of Energy, Office

Hydration Shells of the High-Spin Fe3+ Ion of Science ∼DE-AC06-76RLO 1830 and DE-FG02-06ER1 5767, and the NSF grant NSF-EAR-0545811. The Pacific Northwest National Laboratory is operated by Battelle Memorial Institute. Some of the calculations were performed on the MPP2 and Chinook computing systems at the Molecular Science Computing Facility in the William R. Wiley Environmental Molecular Sciences Laboratory (EMSL) at PNNL. EMSL operations are supported by the DOE’s Office of Biological and Environmental Research. We also wish to thank the Scientific Computing Staff, Office of Energy Research, and the U.S. Department of Energy for a grant of computer time at the National Energy Research Scientific Computing Center (Berkeley, CA). The authors thank Professor Robert Mayanovic of Missouri State University. Supporting Information Available: This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Richens, D. T. The Chemistry of Aqua Ions; John Wiley & Sons: 1997. (2) Weare, J. H. ReV. Mineral. 1987, 17, 143. (3) Hochella, M. F.; Lower, S. K.; Maurice, P. A.; Penn, R. L.; Sahai, N.; Sparks, D. L.; Twining, B. S. Science 2008, 319, 1631. (4) Kerisit, S.; Cooke, D. J.; Spagnoli, D.; Parker, S. C. J. Mater. Chem. 2005, 15, 1454. (5) Spagnoli, D.; Cooke, D. J.; Kerisit, S.; Parker, S. C. J. Mater. Chem. 2006, 16, 1997. (6) Lippard, S. J.; Berg, J. M. Principles of Bioinorganic Chemistry; University Science Books: Mill Valley, CA, 1994. (7) Valiev, M.; Kawai, R.; Adams, J. A.; Weare, J. H. J. Am. Chem. Soc. 2003, 125, 9926. (8) Valiev, M.; Yang, J.; Adams, J. A.; Taylor, S. S.; Weare, J. H. J. Phys. Chem. B 2007, 111, 13455. (9) Clark, D. L.; Hobart, D. E.; Neu, M. P. Chem. ReV. 1995, 95, 25. (10) Bacon, G. E.; Gardner, W. E. Proc. R. Soc. London Ser. A: Math. Phys. Sci. 1958, 246, 78. (11) Broadbent, R. D.; Neilson, G. W.; Sandstrom, M. J. Phys.: Condens. Matter 1992, 4, 639. (12) Enderby, J. E. Chem. Soc. ReV. 1995, 24, 159. (13) Herdman, G. J.; Neilson, G. W. J. Phys.: Condens. Matter 1992, 4, 627. (14) Hewish, N. A.; Enderby, J. E.; Howells, W. S. Phys. ReV. Lett. 1982, 48, 756. (15) Leberman, R.; Soper, A. K. Nature 1995, 378, 364. (16) Neilson, G. W.; Newsome, J. R.; Sandstrom, M. J. Chem. Soc., Faraday Trans. II 1981, 77, 1245. (17) Salmon, P. S.; Herdman, G. J.; Lindgren, J.; Read, M. C.; Sandstrom, M. J. Phys.: Condens. Matter 1989, 1, 3459. (18) Bol, W.; Gerrits, G. J. A. Panthale, C. J. Appl. Crystallogr. 1970, 3, 486. (19) Bol, W.; Welzen, T. Chem. Phys. Lett. 1977, 49, 189. (20) Caminiti, R.; Licheri, G.; Piccaluga, G.; Pinna, G. J. Chem. Phys. 1976, 65, 3134. (21) Caminiti, R.; Licheri, G.; Piccaluga, G.; Pinna, G. Chem. Phys. 1977, 19, 371. (22) Caminiti, R.; Licheri, G.; Piccaluga, G.; Pinna, G. J. Chem. Phys. 1978, 69, 1. (23) Caminiti, R.; Licheri, G.; Piccaluga, G.; Pinna, G.; Radnai, T. J. Chem. Phys. 1979, 71, 2473. (24) Caminiti, R.; Magini, M. Chem. Phys. Lett. 1979, 61, 40. (25) Magini, M. J. Inorg. Nuclear Chem. 1978, 40, 43. (26) Magini, M. J. Chem. Phys. 1979, 70, 317. (27) Magini, M. J. Chem. Phys. 1982, 76, 1111. (28) Magini, M.; Caminiti, R. J. Inorg. Nuclear Chem. 1977, 39, 91. (29) Magini, M.; Radnai, T. J. Chem. Phys. 1979, 71, 4255. (30) Mayanovic, R. A.; Anderson, A. J.; Bassett, W. A.; Chou, I. M. Chem. Geol. 2007, 239, 266. (31) Mayanovic, R. A.; Jayanetti, S.; Anderson, A. J.; Bassett, W. A.; Chou, I. M. J. Chem. Phys. 2003, 118, 719. (32) Ohtaki, H.; Radnai, T. Chem. ReV. 1993, 93, 1157. (33) Bleuzen, A.; Foglia, F.; Furet, E.; Helm, L.; Merbach, A. E.; Weber, J. J. Am. Chem. Soc. 1996, 118, 12777. (34) Bergstrom, P. A.; Lindgren, J.; Read, M.; Sandstrom, M. J. Phys. Chem. 1991, 95, 7650. (35) Kristiansson, O.; Lindgren, J.; Devillepin, J. J. Phys. Chem. 1988, 92, 2680.

J. Phys. Chem. A, Vol. 114, No. 5, 2010 2199 (36) Naslund, L. A.; Cavalleri, M.; Ogasawara, H.; Nilsson, A.; Pettersson, L. G. M.; Wernet, P.; Edwards, D. C.; Sandstrom, M.; Myneni, S. J. Phys. Chem. A 2003, 107, 6869. (37) Naslund, L. A.; Edwards, D. C.; Wernet, P.; Bergmann, U.; Ogasawara, H.; Pettersson, L. G. M.; Myneni, S.; Nilsson, A. J. Phys. Chem. A 2005, 109, 5995. (38) Hermansson, K.; Wojcik, M. J. Phys. Chem. B 1998, 102, 6089. (39) Amira, S.; Spangberg, D.; Zelin, V.; Probst, M.; Hermansson, K. J. Phys. Chem. B 2005, 109, 14235. (40) Curtiss, L. A.; Halley, J. W.; Hautman, J.; Rahman, A. J. Chem. Phys. 1987, 86, 2319. (41) Degreve, L.; Quintale, C. J. Electroanal. Chem. 1996, 409, 25. (42) Floris, F.; Persico, M.; Tani, A.; Tomasi, J. Chem. Phys. Lett. 1992, 199, 518. (43) Guardia, E.; Padro, J. A. Chem. Phys. 1990, 144, 353. (44) Kneifel, C. L.; Friedman, H. L.; Newton, M. D. J. Phys. Sci., A 1989, 44, 385. (45) Kohn, W.; Sham, L. J. Phys. ReV. 1965, 140, 1133. (46) Kohn, W.; Sham, L. J. Phys. ReV. 1965, 1, 1697. (47) Sham, L. J.; Kohn, W. Phys. ReV. 1966, 145, 561. (48) Bylaska, E. J.; Valiev, M.; Rustad, J. R.; Weare, J. H. J. Chem. Phys. 2007, 126, 104505. (49) Bylaska, E. J. Kowalski, W. A. d. J., K. Straatsma, T. P. Valiev, M. Wang, D. Apra`, E. Windus, T. L. Hirata, S. Hackler, M. T. Zhao, Y. Fan, P.-D. Harrison, R. J. Dupuis, M. Smith, D. M. A. Nieplocha, J. Tipparaju, V. Krishnan, M. Auer, A. A. Nooijen, M. Brown, E. Cisneros, G. Fann, G. I. Fru¨chtl, H. Garza, J. Hirao, K. Kendall, R. Nichols, J. A. Tsemekhman, K. Wolinski, K. Anchell, J. Bernholdt, D. Borowski, P. Clark, T. Clerc, D. Dachsel, H. Deegan, M. Dyall, K. Elwood, D. Glendening, E. Gutowski, M. Hess, A. Jaffe, J. Johnson, B. Ju, J. Kobayashi, R. Kutteh, R. Lin, Z. Littlefield, R. Long, X. Meng, B. Nakajima, T. Niu, S. Pollack, L. Rosing, M. Sandrone, G. Stave, M. Taylor, H. Thomas, G. van Lenthe, J. Wong, A. Zhang, Z. NWchem, A Computational Chemistry Package for Parallel Computers; 5.0 ed.; Pacific Northwest National Laboratory: Richland, WA 99352-0999, USA, 2006. (50) Becke, A. D. Phys. ReV. A 1988, 38, 3098. (51) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. ReV. Lett. 1996, 77, 3865. (52) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. ReV. Lett. 1997, 78, 1396. (53) Kleinman, L.; Bylander, D. M. Phys. ReV. Lett. 1982, 48, 1425. (54) Hamann, D. R. Phys. ReV. B 1989, 40, 2980. (55) Troullier, N.; Martins, J. L. Phys. ReV. B 1991, 43, 1993. (56) Louie, S. G.; Froyen, S.; Cohen, M. L. Phys. ReV. B 1982, 26, 1738. (57) Car, R.; Parrinello, M. Phys. ReV. Lett. 1985, 55, 2471. (58) Schwegler, E.; Grossman, J. C.; Gygi, F.; Galli, G. J. Chem. Phys. 2004, 121, 5400. (59) Edelman, A.; Arias, T. A.; Smith, S. T. Siam J. Matrix Anal. Appl. 1998, 20, 303. (60) Nose, S. J. Chem. Phys. 1984, 81, 511. (61) Lyubartsev, A. P.; Laasonen, K.; Laaksonen, A. J. Chem. Phys. 2001, 114, 3120. (62) Sprik, M.; Hutter, J.; Parrinello, M. J. Chem. Phys. 1996, 105, 1142. (63) White, J. A.; Schwegler, E.; Galli, G.; Gygi, F. J. Chem. Phys. 2000, 113, 4668. (64) Martin, R. B. J. Inorg. Biochem. 1991, 44, 141. (65) Schafer, A.; Horn, H.; Ahlrichs, R. J. Chem. Phys. 1992, 97, 2571. (66) Caminiti, R. L. G.; Piccaluga, G.; Pinna, G.; Magini, M. ReV. Inorg. Chem. 1979, 1, 333. (67) Amira, S.; Spangberg, D.; Hermansson, K. J. Chem. Phys. 2006, 124. (68) Mohammed, A. M. Bull. Chem. Soc. Ethiopia 2006, 20, 121. (69) Remsungnen, T.; Rode, B. M. Chem. Phys. Lett. 2004, 385, 491. (70) Amira, S.; Spangberg, D.; Probst, M.; Hermansson, K. J. Phys. Chem. B 2004, 108, 496. (71) Kritayakornupong, C.; Yague, J. I.; Rode, B. M. J. Phys. Chem. A 2002, 106, 10584. (72) Berghold, G.; Mundy, C. J.; Romero, A. H.; Hutter, J.; Parrinello, M. Phys. ReV. B 2000, 61, 10040. (73) Foster, J. M.; Boys, S. F. ReV. Mod. Phys. 1960, 32, 300. (74) Silvestrelli, P. L.; Marzari, N.; Vanderbilt, D.; Parrinello, M. Solid State Commun. 1998, 107, 7. (75) Wannier, G. H. Phys. ReV. 1937, 52, 0191. (76) Marzari, N.; Vanderbilt, D. Phys. ReV. B 1997, 56, 12847. (77) Vanderbilt, D.; Kingsmith, R. D. Phys. ReV. B 1993, 48, 4442. (78) Lightstone, F. C.; Schwegler, E.; Hood, R. Q.; Gygi, F.; Galli, G. Chem. Phys. Lett. 2001, 343, 549. (79) Silvestrelli, P. L.; Parrinello, M. Phys. ReV. Lett. 1999, 82, 3308. (80) Lightstone, F. C.; Schwegler, E.; Allesch, M.; Gygi, F.; Galli, G. Chemphyschem 2005, 6, 1745. (81) Schwegler, E.; Galli, G.; Gygi, F. Phys. ReV. Lett. 2000, 84, 2429.

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J. Phys. Chem. A, Vol. 114, No. 5, 2010

(82) Boese, A. D.; Martin, J. M. L.; Klopper, W. J. Phys. Chem. A 2007, 111, 11122. (83) Brown, I. D. Acta Crystallogr., Sect. A 1976, 32, 24. (84) Bakker, H. J.; Kropman, M. F.; Omta, A. W. J. Phys.: Condens. Matter 2005, 17, S3215. (85) Max, J. J.; Chapados, C. J. Chem. Phys. 2001, 115, 2664. (86) Allen, M. P.; Tildesley, D. J. Computer Simulations of Liquids; Oxford University Press: 1989. (87) Venyaminov, S. Y.; Prendergast, F. G. Anal. Biochem. 1997, 248, 234. (88) Herdman, G. J.; Salmon, P. S. J. Am. Chem. Soc. 1991, 113, 2930. (89) Salmon, P. S.; Lond, P. B. Physica B 1992, 182, 421.

Bogatko et al. (90) Martinez, J. M.; Pappalardo, R. R.; Marcos, E. S. J. Chem. Phys. 1998, 109, 1445. (91) Wasserman, E.; Rustad, J. R.; Xantheas, S. S. J. Chem. Phys. 1997, 106, 9769. (92) Martinez, J. M.; Pappalardo, R. R.; Marcos, E. S. J. Am. Chem. Soc. 1999, 121, 3175. (93) Remsungnen, T.; Rode, B. M. J. Phys. Chem. A 2003, 107, 2324. (94) Remsungnen, T.; Rode, B. M. Chem. Phys. Lett. 2003, 367, 586. (95) Sham, T. K.; Hastings, J. B.; Perlman, M. L. J. Am. Chem. Soc. 1980, 102, 5904.

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