Weakly bound water structure, bond valence saturation and water dynamics at the goethite (100) surface/aqueous interface: ab initio dynamical simulations
© The Author(s) 2017
Received: 28 December 2016
Accepted: 10 March 2017
Published: 31 March 2017
Many important geochemical and biogeochemical reactions occur in the mineral/formation water interface of the highly abundant mineral, goethite [α-Fe(OOH)]. Ab initio molecular dynamics (AIMD) simulations of the goethite α-FeOOH (100) surface and the structure, water bond formation and dynamics of water molecules in the mineral/aqueous interface are presented. Several exchange correlation functionals were employed (PBE96, PBE96 + Grimme, and PBE0) in the simulations of a (3 × 2) goethite surface with 65 absorbed water molecules in a 3D-periodic supercell (a = 30 Å, FeOOH slab ~12 Å thick, solvation layer ~18 Å thick).
The lowest energy goethite (100) surface termination model was determined to have an exposed surface Fe3+ that was loosely capped by a water molecule and a shared hydroxide with a neighboring surface Fe3+. The water molecules capping surface Fe3+ ions were found to be loosely bound at all DFT levels with and without Grimme corrections, indicative that each surface Fe3+ was coordinated with only five neighbors. These long bonds were supported by bond valence theory calculations, which showed that the bond valence of the surface Fe3+ was saturated and surface has a neutral charge. The polarization of the water layer adjacent to the surface was found to be small and affected only the nearest water. Analysis by density difference plots and localized Boys orbitals identified three types of water molecules: those loosely bound to the surface Fe3+, those hydrogen bonded to the surface hydroxyl, and bulk water with tetrahedral coordination. Boys orbital analysis showed that the spin down lone pair orbital of the weakly absorbed water interact more strongly with the spin up Fe3+ ion. These weakly bound surface water molecules were found to rapidly exchange with the second water layer (~0.025 exchanges/ps) using a dissociative mechanism.
KeywordsGoethite Goethite (100) surface Fe-oxyhydroxide Mineral water interface Dissociative exchange Ab initio molecular dynamics DFT Electronic structure Bond valence theory Water interaction with mineral surface Condensed matter Grimme corrections
As the thermodynamically most stable Fe-oxyhydroxide, goethite(α-FeOOH) occurs widely in natural environments [1–3] and is the dominant reactive mineral in lake and marine sediments . It is found in weathering products, primary hydrothermal minerals, acid mine drainage precipitates, bog and marine environments [3–5] and has been observed in abundance on Mars . The surface reactivity of the goethite-water interface has been extensively studied and is known to absorb a large number of reactive species including protons [7, 8], chromate , carboxylates , carbonate , arsenic [12, 13], and a host of soluble uranium [14, 15] and plutonium species . To support interpretation of these processes we report here results of electronic structure simulations of the structure, reactivity and dynamics in the surface/aqueous liquid interface of this mineral.
Several molecular modeling studies of goethite and the goethite-water interfaces have been reported in the literature [24–28]. Most of these studies have used classical molecular dynamics (MD) to predict the structure and hydration behavior of these interfaces [24–33]. Multisite complexion models (i.e. MUSIC model [34, 35]) have also been used to predict their proton affinity. In addition to molecular dynamics studies, electronic structure calculations, i.e. DFT calculations with no dynamics, have been used to determine the structure and energetics of the goethite surfaces [2, 12, 21, 36], including those with absorbed water [2, 37]. The most thorough of these have been reported by Kubicki et al. . They performed optimization studies for a single water absorbed on the goethite (100) surface termination at the DFT + U  level. In their calculations, the bond length between the first layer of water and the exposed surface Fe3+ atom were found to be very long (>2.3 Å); the adjacent water only weakly interacting with the surface Fe3+. This suggests that the exposed surface Fe3+ are fivefold coordinated rather than sixfold coordinated as in the bulk . This under-coordination disagrees with prior MD simulations that reported a surface Fe3+–OH2 distance of 2.13 Å for the isolated surface (2.21 Å microsolvated)  and is does not support the accepted approach for generating surface models for oxides in which the metal cations retain the coordination of the bulk. De Leeuw and Cooper in prior work suggested such an under-coordination was possible for this surface even though their MD results predicted Fe3+–OH2 distances that were only slightly longer than bulk Fe–OH distances .
The results of Kubicki et al. also disagree with recent Crystal Truncation Rod (CTR) studies of the solvated goethite (100) surface by Ghose et al.  who obtained a distance of 2.152 Å from the analysis of their CTR intensities. This distance is slightly longer than the Fe–OH distances (~2.09 Å experiment, ~2.13 Å DFT) seen for the bulk (see Fig. 1). However, there is some uncertainty in the interpretation of the CTR spectra, because it was fit to a distribution of hypothesized structural models. In their paper, Kubicki et al.  rationalized the discrepancies of DFT from prior molecular dynamics results and the CTR experiment by pointing out that the bond length was very sensitive the solvation and additional layers of water molecules were needed to properly model the bulk goethite (100) water interface. Because of the computational cost they were not able to carry out these larger DFT simulations.
For weakly bound systems it is difficult to identify structures in a fluid that reliably reflect the average structure of the fluctuating system for use in direct optimization methods. While dynamics are available from MD, it can be quite challenging to accurately capture the strong polarization and other chemical interactions of the surrounding water molecules near complex transition-metal oxide surfaces [27, 32] using parameterized force fields. Ab initio molecular dynamics methods (AIMD) implement the calculation of forces on the fly from an approximate solution to the electronic Schrödinger equation (Density Functional Theory, DFT [38, 40, 41]). Chemical changes such as polarization, bond breaking and formation, etc. are straightforwardly incorporated in this approach, but at the cost of a much more expensive time step than MD. In this article we report results using AIMD simulations to predict the structural, bonding and dynamical properties of the solvated (~6 water layers) goethite (100) surface.
All DFT  geometry optimizations and Car–Parrinello simulations [40, 41] in this study were performed with the plane-wave NWPW module  contained in the NWChem software package . The DFT PBE96  exchange correlation function was used for the majority of these calculations, however, the PBE96 + Grimme2 [44–46], and the hybrid  PBE0  exchange correlation potentials were also used in the analysis. A recent review has proposed that Grimme corrections may be important in describing bulk water systems . However, our careful comparisons of DFT results for Fe3+ and other first row transition metal aqua ions with experimental EXAFS data found that the effects of these additional corrections were quite small for solvated ions . The interactions between valence electrons and the atom centers were approximated using generalized norm-conserving Hamann pseudopotentials [49, 50] for O, and H and a norm-conserving Troullier–Martin pseudopotential , which contained 4s, 4p, and 3d projectors and a semi-core correction was used for Fe. The pseudopotentials were modified into a separable form as suggested by Kleinman and Bylander . For gradient corrected calculations, the NWPW module automatically generates pseudopotentials using the specified exchange correlation functional. The original pseudopotential parameterization suggested by Hamann were slightly softened by increasing the core raii: H: rcs = 0.8 a.u., rcp = 0.8 a.u.; O: rcs = 0.7 a.u., rcp = 0.7 a.u., and rcd = 0.7 a.u. The radial cutoffs for the Troullier–Martin pseudopotential for Fe were rcs = 1.24 a.u., rcp = 1.24 a.u., rcd = 1.23 a.u., and the s-channel pseudopotentials was chosen for the local potential in the Kleinman and Bylander expansion. Since this is a spin ordered system, unrestricted DFT calculations were performed. The electronic wavefunctions were expanded using a plane-wave basis with periodic boundary conditions at the Γ-point with a wavefunction cutoff energy of 100 Ry and a density cutoff energy of 200 Ry.
To establish the accuracy of the DFT PBE96 approach used in this manuscript, we evaluated its accuracy by calculating the bulk structural properties of the perfect goethite crystal. The orthorhombic unit cell contains 4 Fe atoms, 8 Oxygen atoms and 4 Hydrogen atoms (see Fig. 1). The lattice parameters were optimized using a 1 × 3 × 2 supercell Γ-point calculation. Relaxing the unit cell gave lattice parameters of 10.067, 9.155, and 9.204 Å (a = 10.067 Å, b = 3.0517 Å, c = 4.6020 Å), which are within 1.5% of experimental results [22, 53, 54]. These results are slightly better than found by Rosso and Rustad  in their DFT calculations, but not in as good agreement as those reported by Kubicki et al. , which were within 0.5% of experimental results  for lattice constants.
Goethite is antiferromagnetic at standard temperature (298.15 K) and pressure (1 atm). Three different spin orderings of the magnetic Fe atoms were calculated ([++−], [+−+], and [+−+−] along the a axis). A spin-penalty scheme was used to initialize the antiferromagnetic configurations . The [+−+−] spin configuration shown in Fig. 1 was found to have the lowest energy (see Ying et al. ), which is in agreement with the prior calculations of Kubicki et al. . These calculations predict a Fe site local spin S = 3.5/2 compared S = 3.8/2 seen in experiment .
To simulate the goethite (100) (or (010) Pbnm) surface a 30.0 Å × 9.155 Å × 9.204 Å periodic unit cell was used for all surface calculations in this study. This cell contains a 3 × 2 (100) surface slab with approximately 10 Å between slabs. The goethite surface slab contained 24 Fe, 48 O and 60 H atoms, and the thickness of the slab was 9.4 Å (distance in a direction between two oxygen atoms on surface). The slab has a relatively small number of 4 Fe layers, however, the expansion between the layers from the bulk values was observed to only be a couple of percent in these studies.
AIMD simulations were performed using open shell DFT. The system was propagated in time using Car–Parrinello Molecular dynamics (CPMD) scheme . A plane wave basis and Γ point sampling were used to expand DFT wavefunctions. Simulations were carried out using both the PBE96 exchange correlation potential and PBE96 plus the Grimme2 correction for dispersion to check the importance of dispersion corrections for the water–water interactions . The same pseudopotential and cutoff energies used in plane-wave optimization part were used in the dynamic AIMD simulations. Equation of motions in CPMD were integrated using position Verlet algorithm, with a time step 0.12 fs and fictitious orbital mass 600.0 au. All hydrogen atoms were replaced by deuterium to facilitate the integration. The simulation was carried out in a constant temperature canonical ensemble (300 K) using Nose–Hoover thermostats [57–59] to control the temperatures of the ions and the 1-electron orbitals.
The simulation of the solvated interface included 65 waters between the slabs (including 12 water molecules from the goethite surface). The water density in between the slabs was near 1.0 g/cm3. The relatively small thickness between the slabs results in a nano-confined water layer that will not formally capture several important properties of bulk water (e.g. diffusion, dielectric relaxation response), however the water layer is expected to be large enough to describe the structure of the water-surface interface. This large simulation contained 1024 valence electrons (512 spin up electrons and 512 spin down electrons). To initiate the simulation, the 53 water molecules in between the slabs were pointed away from hydrated goethite surfaces. An initial simulation time of at 1.5 ps was performed to equilibrate the system after which trajectory snapshots were collected.
Results and discussion
Termination of (100) surface without interface water layers
Total and relative energies from DFT PBE96 simulations for the vacuum surface models and solvated surfaces models of the (100) surface of goethite
Molecular formula of supercell
Average total energy (a.u.)
Relative energy (kJ/mol)
Vacuum surface models
3 × 2 surface I
3 × 2 surface II
3 × 2 surface ID
Solvated surface models
3 × 2 surface I + 53H2O
3 × 2 surface II + 53H2O
3 × 2 surface ID + 53H2O
For the lowest energy surface, surface I, it was found that the water molecules capping each surface Fe, were very weakly bonded. Optimization of surface I resulted in a large Fe–OH2 bond distance of 2.45 Å. This is considerably larger than 2.15 Å distance in the model fitted from CTR data . Kubicki et al. saw a similar result in their PBE96 + U calculations . Further support of the weak interaction between water and surface Fe3+ was obtained from AIMD simulations of the isolated surface I (Fig. 2). These simulations performed at 300 K showed that the capping waters readily leave the surface to form a thin water layer. The other higher energy surface structures, surface II and surface ID, which were instead capped by hydroxide, had distances of 1.94 and 1.95 Å respectively. These distances are significantly smaller than the 2.15 Å distance predicted from the CTR analysis  and 2.13 Å distance from prior MD calculations .
Even though the large Fe–OH2 distances for the lowest energy surface (surface I) found in DFT calculations do not agree with prior MD calculations [8, 27, 28, 33] or with the structural model fit from CTR experiments , the large distances make chemical sense because (in a ionic lattice model) the negative charge due to the neighboring ions near the surface Fe3+ is −3. This makes the region near the surface Fe3+ effectively neutral, which in turn makes the Coulomb attraction to the dipole in the water molecule very small. To quantify this one can sum up the effective charge of the neighboring groups and add it to the +3 charge of the surface Fe3+ to determine its effective charging. Each surface Fe3+, without counting the surface water, is neighbors with 3 O2− that are shared by 3 Fe3+ (shown as green spheres in Fig. 2c), and 2 OH− that are shared by 2 Fe3+ (shown as blue spheres in Fig. 2c). This analysis shows that each surface Fe3+ is surrounded by a valence charge of 3(−2)/3 + 2(−1)/2 = −3 with only 5 neighbors. On the other hand, the bulk Fe3+ atoms are neighbors with 3 OH− shared by 3 Fe3+ and 3 O2− shared by 3 Fe3+, resulting in a valence charge of 3(−1)/3 + 3(−2)/3 = −3. This simple analysis clearly shows that the long surface Fe–OH2 distance can be rationalized by the fact that the surface Fe3+ atoms are already fully charge balanced (i.e. valence saturated) with only 5 neighbors.
Fe–O bond distances for the surface I slab model of the (100) surface of goethite
Surface Fe–O distances
PBE96 + Grimme2
Exp. CTR model
Fe–O (Fe–Oi, Fe–Oii)
1st layer Fe–O distances
PBE96 + Grimme2
2.17, 2.17, 2.17
2.14, 2.14, 2.19
2.15, 2.15, 2.16
2.13, 2.13, 2.16
2.19, 2.19, 2.10
1.91, 1.91, 1.91
1.94, 2.01, 2.01
1.93, 2.00, 2.00
1.98, 2.00, 2.00
1.94, 1.93, 1.93
It is also possible that electronic structure effects missing from the PBE96 exchange correlation functional may be able to contract the large Fe–OH2 distances. It is well know that DFT has major problems predicting the electronic structure near the Fermi level (e.g. band gap)  for transition metal oxides and oxyhydroxides and other strongly correlated systems. These errors at the Fermi level can sometimes, but not always, produce anomalous structures, e.g. including exact exchange might effect the charge distribution between the metal and oxygen atoms and, therefore the bond formation of the water to the surface. To check for these possible effects, hybrid DFT PBE0 (presumed to be a better level of exchange correlation in DFT ) were carried out for the 3 × 2 Surface I model. In addition, DFT as mean field theory cannot correctly treat long-range dispersion forces and as a result dispersion forces can be underestimated. To estimate the effects of dispersion, PBE96 + Grimme2  calculations were also carried out for the 3 × 2 Surface I model. These calculations, results given in Table 2, also lead to large Fe–OH2 distances (2.45 Å PBE96, 2.39 Å PBE96 + Grimme2, and 2.41 Å PBE0). This suggests that the prediction of large distances is not overly sensitive to the level of theory used in the electronic structure calculations. These calculations clearly show that there is a strong disagreement in the results for the Fe–OH2 distances using different theories. Electronic structure calculations and bond valence theory calculations predict large distances, and prior classical molecular dynamics potentials and the model fitted to CTR experiments  predicts distances that are just slightly larger (~2.15A Å) than the bulk distances for Fe–OH in goethite (~2.09 Å).
AIMD simulations of goethite (100) water interface
To further check the relative energetics of the three terminations and resulting surfaces we added 53 H2O molecules between the slabs and ran AIMD simulations using the PBE96 exchange correlation functional for at least 10 ps. Each of three simulations was performed using a unit cell that contained a total of 24 Fe atoms, 113 O atoms and 154 H atoms (Fe24O60H48 + 53 H2O). The simulations were designed to have water densities in between the slabs near 1.0 g/cm3. The average potential energies, given in the lower part of Table 1, show that the solvated surfaces have nearly the same relative energetics as the vacuum terminated surfaces. Given that Surface I was found to have a significantly lower energy than the other two surface models in vacuo and with solvation, the rest of the manuscript only presents results for this surface.
The structure of the surface I + water interface
The first outside layer of oxygen atoms (OI) located at z ≈ −10.4 Å, 10.4 Å were the hydroxides bonded to the surface Fe atoms (see Fig. 4c for definition of oxygen labels). The integration of these peaks produced exactly 6 oxygen atoms for the PBE96 and PBE96 + Grimme2 simulations. The second outside layer of oxygen atoms (OII) located at z ≈ −9.0 Å, 9.0 Å were the water molecules attached to the surface Fe atoms. This layer of water molecules was loosely bound to the surface, and the bond between the water O and the surface Fe3+ were observed to frequently break and reform during the simulations. In some cases these water molecules exchange with the more bulk-like water molecules of the next layer. The integration of these peaks produced 4.63 and 5.98 oxygen atoms for the PBE96 and PBE96 + Grimme2 simulations respectively. The first inside layer of oxygen atoms (Oi) located at z ≈ −11.9 Å, 11.9 Å were ~180° away from the OI oxygen atoms, and the second inside layer of oxygen atoms (Oii) located at z ≈ −13.0 Å, 13.0 Å were nearly ~180° away from the OII oxygen atoms.
Comparison of surface structure parameters for the (100) surface goethite + water between PBE96 AIMD and PBE96 + Grimme2 AIMD simulations of Fe24O60H48 + 53 H2O and fitted structure from CTR experiments of Ghose et al. 
Surface structure parameters
PBE96 + Grimme2 AIMD
Exp. CTR model
Electronic structure of interfacial water
Electronic structure for the Solvation shells represented by spin up (α), Spin down (β) Wannier Function Centers (WFC)
Interface water α
Interface water β
First hydration shell
Second hydration shell
Fe3+-64 H2O α
Fe3+-64 H2O β
These results suggest that the electronic structure of the water molecules beyond the OII water molecules has returned to that of the bulk. Even the OII interfacial waters, which are often considered part of the surface, showed very little polarization presumably because the surface has a neutral charge.
Dynamic processes on the interface
DFT optimization (including PBE96, PBE96 + Grimme2, PBE0) and AIMD simulations (PBE96 and PBE96 + Grimme2) were carried out for the anhydrous goethite (100) surface and the goethite (100) + water interface. The simulations were performed for a (3 × 2) surface slab containing 65 water molecules between the slabs (near 1 g/cm3) at temperature of 300 K.
The surface energies calculated from DFT PBE96 optimization of three likely fully solvated neutral surface terminations in which the Fe3+ cations remain in an octahedral coordination, were compared. It was found that the lowest energy surface containing an exposed surface Fe3+ is capped by a (weakly bound) water molecule and shares a hydroxide with a neighboring Fe3+ (see surface I in Fig. 2). This surface termination agrees with the assumed largest fraction surface found in fitting CTR data by Ghose et al. . The other two surfaces examined, which were capped by two hydroxides, were found to be approximately 27 and 34 kJ/mol less stable per 1 × 1 surface slab (or 431 and 564 kJ/mol for the 3 × 2 surface slab). The solvation of the slabs with 53 H2O molecules had little effect on the relative surface energetics between the slabs. The solvated 3 × 2 slabs capped by two hydroxides (surface II and surface IID in Figs. 3 and 4) were found to have average energies that were 398 and 575 kJ/mol higher then the solvated Surface I slab (3 × 2 surface slab, Fig. 2).
For the most stable surface it was found that the water molecule formed by protonation of an unsaturated OH from the termination, and capping a surface Fe was very loosely bound (see Fig. 2). The resulting optimized or equilibrated long Fe3+–OH2 bond length does not agree with prior results obtained from fitting CTR data or from prior MD simulations [8, 27, 28, 33], which predicted Fe–OH2 distances only slightly longer than the bulk goethite Fe–OH distances. However, this result does agree with the prior DFT + U optimizations of Kubicki et al. . Furthermore, the DFT PBE96 results were checked using hybrid PBE0 and dispersion corrected PBE96 + Grimme2 exchange correlation functionals and the results were found to change very little (weak bonding prediction upheld). These results support a terminated surface model in which the Fe3+ ion in the surface is coordinated by only 5 neighbors versus 6 in the bulk. Nevertheless, the surface is neutral (and not very polar). This structure was supported by bond valence (BV) theory calculations. While BV theory is essentially an empirical methodology. It has been shown to produce remarkably accurate predictions for many materials applications .
Full AIMD simulations of 100 goethite + water interface (Surface I cleavage) were carried out. Solvating the slabs with 53 H2O molecules led to a slight contraction of the distance to the nearest water from the surface (OII in Fig. 2). The average Fe–OH2 bond distances in the AIMD simulations that were found to be 2.40 and 2.34 Å for the PBE96 and PBE96 + Grimme2 theories respectively were still considerably larger than 2.15 Å distance seen in the model fitted from CTR data  and the 2.13–2.21 Å distances from prior MD calculations . In summary all the DFT calculations support the long bond and weak interaction. The good agreement of the BV methodology with DFT predictions of bond length changes support the further investigation of this method for surface structures.
The polarization of the water layer due to the surface (and vice versa) is small and localized only to the immediate vicinity of the interface. Density difference plots and Wannier–Boys orbitals analysis support the classification into three types of water molecules observed in the simulations (see Fig. 7). The first is the capping water molecule (OII, Fig. 7) that is loosely bonded to the surface Fe3+. The second (OIII, Fig. 7) is hydrogen bonded to the surface hydroxyl, and the third type is similar to bulk water. The analysis shows that by the third layer the coordination and bonding are essentially that of bulk water. Even though the OII and OIII water molecules form ordered water layers on surface they do not bond to the surface strongly and as a result these water molecules readily exchanged with the bulk-like water molecules.
These results might suggest that other mineral surfaces may also have surface cations with only five neighbors. For instance, oxide surfaces where a surface cation is capped by a water molecule such as the (100) plane of diaspore, and the R-planes of sapphire and hematite.
ab initio molecular dynamics
crystal truncation rod
density functional theory
extended X-ray absorption fine structure
multi site complexation
NorthWest Plane-Wave module of NWChem
Perdew, Burke and Ernzerhof 1996 exchange correlation functional
hybrid extension of Perdew, Burke and Ernzerhof 1996 exchange correlation functional
lone pair orbital
Wannier–Boys Function Center
The manuscript was written and reviewed by all authors, YC and EB carried out the simulations and prepared all figures and tables. EB developed the AIMD simulation code and other analysis codes used in this work. All authors read and approved the final manuscript.
The authors declare that they have no competing interests.
Availability of data and materials
Simulation data and analysis programs used in this work can be obtained from the Open Science Framework (https://osf.io/) from the following link: https://osf.io/cz7d7/ . The AIMD simulation program used in this work can be obtained from the NWChem website (http://www.nwchem-sw.org/).
This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Chemical Sciences, Geosciences, and Biosciences Division~ DE-AC06-76RLO 1830. Additional support from EMSL operations. EMSL operations are supported by the DOE’s Office of Biological and Environmental Research. We 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). Some of the calculations were performed on the Cascade computing systems at the Molecular Science Computing Facility in the William R. Wiley Environmental Molecular Sciences Laboratory (EMSL) at PNNL.
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