Dispersion Effects on the Thermodynamics and Transition States of

Article pubs.acs.org/JPCA

Dispersion Effects on the Thermodynamics and Transition States of Dimethylarsinic Acid Adsorption on Hydrated Iron (Oxyhydr)oxide Clusters from Density Functional Theory Calculations Adrian Adamescu,† I. P. Hamilton,‡ and Hind A. Al-Abadleh*,‡ †

Chemistry Department, University of Waterloo Waterloo, Ontario N2L 3G1, Canada Department of Chemistry and Biochemistry, Wilfrid Laurier University Waterloo, Ontario N2L 3C5, Canada

‡

S Supporting Information *

ABSTRACT: Reaction pathway information and transition states are crucial for understanding adsorption mechanisms of pollutants, such as dimethylarsinic acid (DMA), at the liquid− solid interface. We report a detailed computational analysis of the complexes of DMA on iron (oxyhydr)oxides, including activation energies, transition states, Gibbs free energies of adsorption, Mulliken charges, charge redistribution upon adsorption, and stretching frequencies of As−O bonds for comparison with experimental spectroscopic data. Calculations were performed using density functional theory (DFT) at the B3LYP/6-311+G(d,p) level using both implicit and explicit hydration. For comparison, calculations were also performed for arsenate. Dispersion corrections were included since experimental data showed that DMA forms mostly outer-sphere complexes. Calculated electronic energies indicate that dispersion corrections are important when dealing with outer-sphere complexes, and that there is a high activation barrier of ca. 43 kJ mol−1 to transition from mono- to bidentate DMA complexes. Additionally, extending the modeled iron (oxyhydr)oxides surface to include four Fe centers and analyzing the charge distribution upon adsorption of DMA reveals that electrostatics play a role in the transition from outer-sphere to monodentate complexes. The significance of our results for the overall surface complexation mechanism of DMA and arsenate is discussed.

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INTRODUCTION Dimethylarsinic acid (DMA), (CH3)2AsO2H, is an important organoarsenical compound detected in arsenic speciation studies of environmental samples. It is formed as a byproduct in the pyrolysis of oil shale1 and, historically, has been used as a herbicide on large agricultural fields.2 Biological methylation through the Challenger mechanism by microbes and fungi can also transform inorganic forms of arsenic into DMA.3,4 This compound is more mobile in the environment because of its lower affinity to soil components, such as iron and aluminum oxides.5−10 This poses a risk since arsenic compounds in their various forms are known carcinogens and have been correlated to various diseases.11−13 In particular, DMA has been shown to promote multiorgan tumor activity in rodents, particularly in the rat bladder.13 The interaction of pollutants (such as DMA) with soil particles controls their transport and bioavailability, and hence overall environmental fate.14 These interactions occur at the water−solid interface, which have been the subject of extensive research by our group and others using surface-sensitive techniques. The goal is to quantify the thermodynamics and kinetics of binding, and also to obtain structural data on the adsorbed surface complexes. Examples of these techniques are © XXXX American Chemical Society

attenuated total internal reflectance Fourier transform infrared (ATR-FTIR)15 spectroscopy and extended X-ray absorption fine structure (EXAFS) spectroscopy,16 suitable for studying surface complexes under environmentally relevant conditions. At neutral pH, DMA is a negatively charged oxyanion (pKa ∼ 6.1) whose adsorption on the positively charged sites of iron (oxyhydr)oxides (point of zero charge >8)17 is largely driven by electrostatics with ligand exchange taking place at the interfacial region, releasing weaker ligands in the process.5,7−10,18−22 Molecular modeling studies using density functional theory (DFT) can aid in quantifying the adsorption energetics of DMA on iron (oxyhydr)oxides and are important for understanding binding mechanisms. Hybrid molecular orbital/density functional theory (MO/DFT) proved to be adequate for calculating electronic energies, optimized structural parameters, vibrational frequencies and binding thermodynamics of oxyanions and organic molecules with iron and aluminum (oxyhydr)oxides.23−28 In most of these calculations, the surface of the metal (oxyhydr)oxides was simulated with Received: August 18, 2016 Revised: October 27, 2016 Published: October 28, 2016 A

DOI: 10.1021/acs.jpca.6b08367 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A

the B3LYP functional and the 6-311+G(d,p) basis set. The calculations were performed on clusters with a net charge of −1, 0, or +1, at 298.15 K (25 °C) and 1 atm pressure. Solvation was simulated by explicitly adding 4−6 water molecules around each structure and also by using the integral equation formalism polarizable continuum model (IEFPCM).36 Frequencies were computed to correlate the theoretical stretching mode of As− O, v(As−O), to experimental values, as well as to confirm that transition state structures had one imaginary frequency which animated the movement from reactant to product. Intrinsic reaction coordinate (IRC) calculations37 were also performed to confirm that the transition state along the DMA reaction pathway does indeed connect reactant to product, as shown in Figure S1 and Table S1 of the Supporting Information. To study the effects that van der Waals forces have on adsorption reactions, all calculations were performed using Grimme’s D3 dispersion scheme with Becke-Johnson damping (GD3BJ).38 The revised D3(BJ) approach was shown to be an improvement over the D3 approach with zero-damping for thermochemical problems that are sensitive to medium-range correlation effects and for noncovalent interactions,26 which are most relevant when dealing with outer-sphere complexes. Clusters containing two and four Fe centers in the oxidation state of +3 were calculated at high spin with five unpaired electrons for each Fe atom. Hence, for the clusters with two Fe atoms, a multiplicity of 11 was used and for the clusters with four Fe atoms, a multiplicity of 21 was used.39 To minimize computational cost, calculations were initially performed with the smaller 6-31G(d) basis set and explicit water molecules were added sequentially. Once the fully hydrated complexes had been optimized at this level of theory, the calculations were run at the B3LYP/6-311+G(d,p) level of theory with the IEFPCM solvation model and GD3BJ dispersion. Activation Barriers and Transition State Calculations. To calculate activation barriers for DMA complexes transitioning from outer-sphere to monodentate to bidentate, several restricted distance optimizations were performed along this reaction pathway. This was done stepwise by reducing the distance between one of the oxygen atoms of the AsO moiety and a central Fe atom by 0.1 Å and optimizing the geometry of the complex at each step with the restricted AsO−Fe distance, while allowing the rest of the complex to relax. The geometry with the highest energy along these reaction pathways was then used as the starting point for the transition state calculations. We found two transition state structures for DMA: TS1 for the outer-sphere to monodentate reaction and TS2 for the monodentate to bidentate reaction. Both transition state structures exhibited one imaginary frequency and in both cases the corresponding vibrational modes showed movement going from reactant to product, namely outer-sphere to monodentate for TS1 and monodentate to bidentate for TS2. A similar procedure was performed for p-arsanilic acid complexes on iron oxide surfaces, but no dispersion was used for those calculations.40 The well-studied arsenate complex is also calculated herein to investigate dispersion effects on adsorption and effect of organic substituents relative to the DMA system. Sun and Chen41 reported benchmarks of various functionals for the activation energies of zirconium−organic reactions, and concluded that, although the B3LYP functional overestimates activation energies, the calculated energy barriers are reasonable. Hence, activation energies for the clusters containing two and four Fe centers calculated herein are

two metal centers coordinated to either hydroxyl or water groups to adjust the overall charge of the cluster. To account for solvent effects in these calculations, a solvation model was used for implicit hydration such as the integral equation formalism polarizable continuum model (IEFPCM). Addition of water molecules around the clusters accounted for explicit hydration.25 Correlating calculated vibrational frequencies and interatomic distances with experimental ones for different surface complexes allows for drawing conclusions that aid in interpreting experimental spectroscopic data. Previous theoretical studies on DMA and iron (oxyhydr)oxide clusters showed that the adsorption process is thermodynamically favorable with the formation of the bidentate binuclear complex being the most favorable and having the lowest Gibbs free energy of adsorption (ΔGads).19 However, experimental data from real time and in situ measurements of surface DMA on hematite and goethite particles strongly suggests the formation of mostly weakly bound outer-sphere and monodentate DMA complexes.29,30 This experimental observation and the discrepancy with previous theoretical results is the motivation for the present study, which also investigates the effect of dispersion on outersphere and monodentate complex formation. Calculations that study the adsorption of oxyanions on metal oxides rarely include the effects of dispersion and this partly motivated the dispersion corrected DFT calculations reported in this paper. However, a number of recent DFT calculations with dispersion corrections were reported, involving the adsorption of other molecules on model metal oxide surfaces.31−33 For example, inclusion of dispersion in the calculations of CO adsorption on the MgO(001) surface resulted in shortening the Mg−C bond distance to 2.59 Å. This value represents a significant 0.45 Å difference when compared to Hartree−Fock without dispersion. These calculations also yielded an adsorption energy that is in better agreement with experimental values.31 Also, dispersion corrected DFT calculations used to study the adsorption energies of CO2 on CuO surfaces concluded that the energetically most stable CuO(111) surface has comparatively weaker binding of CO2 relative to the CuO(011) surface.32 Moreover, dispersion corrected DFT calculations of the adsorption energies of noble gas atoms on the TiO2(110) surface found that lateral interactions between coadsorbed atoms play an important role, modifying adsorption energies by up to 20%. After including these lateral interactions, agreement within 6% of experimental measurements could be achieved.33 The DFT calculations reported herein also track the adsorption of DMA by small incremental steps to obtain more information on the adsorption mechanism and activation barriers for the outer-sphere to monodentate, and monodentate to bidentate surface reactions. Similar reaction pathway calculations were performed for arsenate surface complexes on iron (oxyhydr)oxides clusters, which forms predominantly bidentate binuclear complexes25,34 to gain further insight into the effect of organic substituents on surface complexation process. In addition, charge transfer to the iron (oxyhydr)oxide clusters upon complex formation was also examined for two and four Fe centers to highlight the importance of extending models used in surface reactions.

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COMPUTATIONAL METHODS Geometry Optimization. Calculations were performed using Gaussian 09.35 All structures were energy minimized, without any symmetry or geometry constraints using DFT with B


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complexes will be referred to as OS(2Fe), MD(2Fe), and BD(2Fe) to distinguish them from those shown later with four iron centers. Also shown in Figure 1 are the calculated structures of the transitions states, TS1(2Fe) and TS2(2Fe) described in detail below. Table 1 lists the calculated As−O, Fe−O bond distances as well as the As−Fe interatomic distances of DMA complexes for the energy minimized structures OS(2Fe), MD(2Fe) and BD(2Fe) as well as the transition state structures TS1(2Fe) and TS2(2Fe). When comparing the geometries of the OS(2Fe), MD(2Fe), and BD(2Fe) complexes in Table 1 with our earlier work,19 where the same level of theory was used, it is evident that dispersion has a significant effect on the structures, especially for the OS(2Fe) and MD(2Fe) complexes. Adding dispersion changes the interatomic distances, d(As−Fe), between 0.4 and 1.0 Å for the OS and MD complexes. The bidentate structures do not differ as much, showing only a 0.1 Å difference between the structures with and without dispersion. In all three cases, adding dispersion shortens the interatomic As−Fe distance and is particularly noticeable for the outer-sphere and monodentate complexes, where the As−Fe distance is shortened by up to 20%. Dispersion adds the attractive part of van der Waals interactions between atoms that are not directly bonded and are known to have an effect on interatomic distances42 as well as on hydrogen bonds.43 Since hydrogen bonds play such an important role at the water−solid interface and are particularly important in our OS(2Fe) and MD(2Fe) complexes, great care was taken when adding the explicit water molecules to the complexes to simulate the hydration of the first solvation shell. For example, adding waters near the methyl groups was avoided because of their hydrophobicity. Instead, water molecules were added near oxygen atoms and angled in such a way that the maximum number of hydrogen bonds would form at distance between 1.6 and 1.9 Å. These dispersion corrected DFT values also compare well with EXAFS experimental results which showed that the As−Fe interatomic distances were around 3.3 Å, indicative of inner-sphere complex formation.8 The calculated As−Fe interatomic distance for the MD(2Fe) complex was 3.36 Å, and for the BD(2Fe) complex are 3.32 and 3.29 Å as per Table 1 above. Parts a and b of Figure 2 show stepwise optimization calculations along the reaction pathway of DMA complex formation to find the transition state geometries TS1(2Fe) (linking OS(2Fe) and MD(2Fe) in Figure 1) and TS2(2Fe) (linking MD(2Fe) and BD(2Fe) in Figure 1). The calculated reaction pathways in these figures show that the activation barrier from DMA OS(2Fe) to MD(2Fe) is much lower (+18.6 kJ mol−1) than the activation barrier from MD(2Fe) to BD(2Fe) (+42.2 kJ mol−1). A higher activation barrier is likely

expected to be qualitatively correct but likely overestimate energy barriers.

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RESULTS AND DISCUSSION Dispersion Effects on Calculated Geometries. A number of batch, spectroscopic, and DFT studies showed that the adsorption of DMA onto iron (oxyhydr)oxides results in simultaneous formation of outer-sphere and inner-sphere complexes via ligand exchange.5,7,20,29 Hence, Figure 1 shows

Figure 1. Optimized DMA−iron (oxyhydr)oxide complexes showing the outer-sphere, monodentate and bidentate structures with six or seven explicit water molecules and an overall charge of zero. Optimized transition state complexes between OS(2Fe) and MD(2Fe), and between MD(2Fe) and BD(2Fe) are also shown. Clusters were calculated with B3LYP/6-311+G(d,p), IEFPCM, and GD3BJ.

optimized structures of hydrated outer-sphere (OS), monodentate (MD) and bidentate (BD) DMA complexes on iron (oxyhydr)oxides clusters with two iron centers. These

Table 1. Calculated As−O, Fe−O, and As−Fe Distances in Å for DMA−Iron (Oxyhydr)oxide with Two Iron Centers Using B3LYP/6-311+G(d,p) with the IEFPCM Solvation Model and GD3BJ Dispersiona DMA complexes

As−Fe1

As−Fe2

As−O1

As−O2

As−C1

As−C2

Fe1−O1

Fe2−O2

OS(2Fe) TS1(2Fe) MD(2Fe) MD(2Fe)b TS2(2Fe) BD(2Fe)

4.81 (5.28) 4.07 3.36 (3.36) 3.34 3.35 3.32 (3.36)

4.72 (4.84) 4.74 4.05 (5.05) 4.02 3.54 3.29 (3.43)

1.72 (1.70) 1.73 1.72 (1.70) 1.71 1.72 1.71 (1.74)

1.69 (1.71) 1.69 1.70 (1.73) 1.69 1.70 1.72 (1.71)

1.93 (1.94) 1.93 1.93 (1.93) 1.91 1.93 1.93 (1.93)

1.93 (1.94) 1.94 1.93 (1.93) 1.91 1.93 1.93 (1.93)

− − 2.06 2.05 2.11 2.11

− − − − − 2.07

a

Number in parentheses are taken from ref 19 calculated using B3LYP/6-311+G(d,p) with the IEFPCM solvation model but without the dispersion correction. bOptimized using PBE0/6-311+G(d,p) with IEFPCM solvation and GD3BJ dispersion for comparison. C


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Figure 2. Electronic energies for the transition from (a) OS(2Fe) to MD(2Fe) and (b) MD(2Fe) to BD(2Fe). The MD(2Fe) complex is −33 kJ mol−1 lower in energy than the OS(2Fe) complex and there is an activation barrier of 18.6 kJ mol−1. The BD(2Fe) complex is −23.6 kJ mol−1 lower in energy than the MD(2Fe) complex and there is an activation barrier of +42.2 kJ mol−1.

Figure 3. Reaction pathway for arsenate transitioning from (a) MM to OS transition with an activation barrier of +2.5 kJ/mol relative to the OS complex, and (b) MM to BB transition showing three smaller activation barriers.

to MM transition could be more complex and could have many smaller activation barriers like the MM to BB transition with the hydrogen bonds breaking and forming as the arsenate approaches the Fe surface. The MM to BB transition shown in Figure 3b has multiple smaller activation barriers at +6.9, +12.6, and +12.9 kJ mol−1, respectively. This is in contrast to the DMA system where there is one big activation barrier for the MD(2Fe) to BD(2Fe) transition (Figure 2b). The sharp drop in the energy in the reaction pathway, from TS2(2Fe) to BD(2Fe) in Figure 2b, occurs after the formation of a covalent bond between the DMA and iron oxide, as well as the formation of new hydrogen bonds between water molecules that were rearranged after the incoming DMA molecule pushed them aside and lowered the energy even further. Reversing the reaction from BD to MD when explicit waters formed new hydrogen bonds will follow a different pathway altogether where the newly formed hydrogen bonds remain intact and the explicit water molecules orient themselves differently. However, the reorientation of waters should not affect the argument that the activation barrier is much higher when DMA goes from MD to BD compared to the Arsenate system. The barriers and energy minima in Figure 3b are attributed to the breaking and forming of new hydrogen bonds with the water molecules and hydroxyl groups of the iron (oxyhyr)oxides as the arsenate molecule moves closer to the surface. The transition of arsenate from MM to BB is also a more thermodynamically favorable reaction (−39.7 kJ mol−1) than the transition from MD(2Fe) to BD(2Fe) for DMA (−23.6 kJ mol−1). This offers further theoretical support for the observation that arsenate forms mostly bidentate complexes while DMA does not. For comparison, the activation energy for the adsorption of arsenate on synthetic goethite was calculated from experimental

the reason that DMA complex formation observed experimentally is dominated by OS and MD rather than BD on iron (oxyhyroxides) over 100 min of reaction time.5,29 The large energy barrier for formation of the BD complex may stem from the inability of the polar water molecules to stabilize the nonpolar methyl groups in the transition state geometry compared to the arsenate system. For comparison with arsenate surface complexes on iron (oxyhydr)oxides, Watts et al.44 reported that bidentate binuclear (BB) complexes are more thermodynamically favorable than monodentate mononuclear (MM) complexes, but that both could coexist because the energy differences between the two complexes are small. For consistency with the DMA calculations with dispersion reported herein, Figure S2a− c in the Supporting Information show optimized geometries of arsenate OS, MM, and BB complexes on iron (oxyhyr)oxides at the same level of theory with dispersion. The reaction pathway electronic energy calculations between these complexes are illustrated in Figure 3. It may be seen that for arsenate, the OS to MM reaction pathway has a + 2.5 kJ mol−1 barrier between the transition state and the OS complex. The reason for showing the MM to OS reaction pathway is that the energy profile for the OS to MM reaction was more challenging to compute with the transition showing more abrupt features as the arsenate approached the surface and calculations failed consistently. Thus, the calculations shown in Figure 3a were performed backward, starting with the MM complex and adding +0.1 Å to the AsO1−Fe1 distance to get to an OS complex. Hence, the OS arsenate complex reached in Figure 3a and shown in Figure S2 may be a local minimum. The true OS D


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Table 2. Electronic Energies, Electronic Energies with Thermal Corrections to Enthalpy and Electronic Energies with Thermal Corrections to Gibbs Free Energy Calculated using B3LYP/6-311+ G(d,p) with IEFPCM Solvation and GD3BJ Dispersion Models reactants

electronic energy (E0)

DMA−·4H2O DMA− ·4H2Oa H2AsO4−·4H2O [Fe2(OH)5(OH2)5]+·4H2O [Fe2(OH)5(OH2)5]+·4H2Oa

−2772.32700 −2771.39153 −2844.19050 −3595.07854 −3593.37550

electronic energy + thermal correction to enthalpy (E0 + Hcorr)


products

−2772.12954 −2772.19608 −2771.19267 −2771.25892 −2844.03976 −2844.10546 −3594.74811 −3594.84670 −3593.04252 −3593.14035 electronic energy + thermal correction to electronic energy + thermal correction to Gibbs enthalpy (E0 + Hcorr) free energy (E0 + Gcorr)

−6138.00126 −6137.55443 OS(2Fe)−DMA·6H2O[Fe2(OH)5(OH2)4] TS1(2Fe)−DMA·6H2O[Fe2(OH)5(OH2)4] −6137.99416 −6137.54850 MD(2Fe)−DMA−Fe2(OH)5(OH2)4·6H2O −6138.01393 −6137.56603 MD(2Fe)−DMA−Fe2(OH)5(OH2)4·6H2Oa −6135.63492 −6135.18383 TS2 (2Fe)−DMA−Fe2(OH)5(OH2)4·6H2O −6137.99808 −6137.55040 BD (2Fe)−DMA−Fe2(OH)5(OH2)3 ·(H2O)7 −6138.02294 −6137.57466 OS arsenate−HAsO4·3H2O[Fe2(OH)4(OH2)5] −5980.403491 −5980.08694 MM arsenate−HAsO4−Fe2(OH)4(OH2)5·3H2O −5980.419366 −5980.10272 BB arsenate−HAsO4−Fe2(OH)4(OH2)4·4H2O −5980.440010 −5980.12147 leaving group−water electronic energy electronic energy + thermal correction to enthalpy cluster (E0) (E0 + Hcorr) −229.41801 −229.15850 −458.86134

(H2O)3 (H2O)3a (H2O)6 a

electronic energy + thermal correction to Gibbs free energy (E0 + Gcorr)

−6137.67821 −6137.67400 −6137.68900 −6135.30489 −6137.67257 −6137.69862 −5980.19428 −5980.21390 −5980.22581 electronic energy + thermal correction to Gibbs free energy (E0 + Gcorr)

−229.33785 −229.07751 −458.69741

−229.37974 −229.11925 −458.75509

Optimized using PBE0/6-311+G(d,p) with IEFPCM solvation and GD3BJ dispersion for comparison.

Table 3. Values of ΔH°ads, ΔG°ads and ΔS°ads for Reactions of DMA and Arsenate with Iron (Oxyhydr)oxide Clusters at 298.15 K and 1 atma ΔH°ads (kJ mol‑1)

DMA adsorption and formation of OS, MD, and BD complexes A, C and E −

DMA ·4H2O + [Fe2(OH)5(OH2)5] ·4H2O → (R1) OS(2Fe) DMA·6H2O Fe2(OH)5(OH2)4 + (H2O)3 (R2) MD(2Fe) DMA-Fe2(OH)5(OH2)4·6H2O + (H2O)3 (R2) MD(2Fe) DMA-Fe2(OH)5(OH2)4·6H2O + (H2O)3b (R3) BD(2Fe) DMA-Fe2(OH)5(OH2)3·7H2O + (H2O)3 transition states

ΔG°ads (kJ mol‑1)

ΔS°ads (kJ mol‑1K‑1)

+

ΔH°ads

−38.4 −68.9 −68.7 −91.5 (kJ mol‑1)

ΔG°ads

−39.9 (−109) −68.2 (−132) −65.3 −93.4 (−145) (kJ mol‑1)

ΔS°ads

+0.00483 −0.00228 −0.0113 +0.00638 (kJ mol‑1K‑1)

(R4) TS1(2Fe) DMA·6H2O[Fe2(OH)5(OH2)4 + (H2O)3] (R5) TS2(2Fe) DMA−Fe2(OH)5(OH2)4·6H2O + (H2O)3] arsenate adsorption and formation of OS, MM, and BB complexes

−22.8 −27.8 ΔH°ads (kJ mol‑1)

−28.8 −25.0 ΔG°ads (kJ mol‑1)

+0.0200 −0.00937 ΔS°ads (kJ mol‑1K‑1)

H2AsO4−·4H2O + [Fe2(OH)5(OH2)5]+·4H2O → (R6) OS HAsO4·3H2O[Fe2(OH)5(OH2)5 + (H2O)6] (R7) MM HAsO4−Fe2(OH)4(OH2)5·3H2O + (H2O)6 (R8) BB HAsO4−Fe2(OH)4(OH2)4·4H2O + (H2O)6

+9.23 −32.2 (−13.1) −81.4 (−57.1)

+7.33 −44.2 (−14.1) −75.4 (−46.0)

+0.00638 +0.0402 −0.0200

a The numbers in parentheses are taken from ref 19 for DMA and ref 28 for arsenate calculated using B3LYP/6-311+G(d,p) with the IEFPCM solvation model but without dispersion. bCalculated using PBE0/6-311+G(d,p) with IEFPCM solvation and GD3BJ dispersion for comparison.

data45 to be in the range of 20−43 kJ mol−1. The value of the activation barrier reported herein for the arsenate system falls in that range, which validates our computational approach for energy barriers and gives confidence to the values reported for the DMA systems. Table S2 lists the calculated As−O, Fe−O bond distances as well as the As−Fe interatomic distances of arsenate OS, MM and BB complexes obtained with dispersion corrections. These values were compared with our earlier work without dispersion40 where the same level of theory was used. The values for the inner-sphere complexes show interatomic As−Fe distances between 3.26−3.40 Å, which is the same range of other studies (3.27−3.50 Å) using arsenate44 without dispersion, as well as studies using phosphate (3.18−3.55

Å)26 without dispersion. For arsenate complexes dispersion only seems to have a slight effect on distances. However, since arsenate does not normally form OS complexes, dispersion effects may not be as important as they are for organoarsenicals which are more likely to form outer-sphere complexes. Calculated ΔH°ads, ΔG°ads, and ΔS°ads for DMA and Arsenate Reaction with Iron (Oxyhydr)oxide Clusters. Table 2 shows the calculated electronic energies, E0, as well as the electronic energies with thermal corrections to enthalpies (E0 + Hcorr) and Gibbs free energies (E0 + Gcorr) for all reactants and products involved in the adsorption of DMA and arsenate to form inner- and outer-sphere DMA complexes, and OS, MM, and BB arsenate complexes. The ΔH°ads, ΔG°ads, and ΔS°ads are calculated using eq 1−3):46 E


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The Journal of Physical Chemistry A ° = ΔHads

∑ (E0 + Hcorr)products − ∑ (E0 + Hcorr)reactants (1)

° = ΔGads

∑ (E0 + Gcorr)products − ∑ (E0 + Gcorr)reactants (2)

° = (ΔHads ° − ΔGads ° )/T ΔSads

(3)

Table 3 lists the calculated values of ΔH°ads, ΔG°ads (in kJ mol−1) and ΔS°ads (in kJ mol−1K−1) for various hypothetical adsorption reactions with a DMA− and [Fe2(OH)5(OH2)5]+ forming the neutral OS(2Fe), MD(2Fe) and BD(2Fe) complexes, respectively (R1-R3, Table 3). The enthalpies, Gibbs free energies and entropies of the transition states, TS1(2Fe) and TS2(2Fe) are also calculated and listed in Table 3 (R4-R5) in order to derive free energy activation barriers for these reactions. The trend in the ΔG°ads values shows that the formation of the BD(2Fe) complex is the most thermodynamically favorable, followed by MD(2Fe) and OS(2Fe) at −93.4, −68.2, and −39.9 kJ mol−1, respectively. This is in agreement with previous calculations where the same trend is observed but no dispersion corrections were included.19,20 The present calculations that include dispersion differ by more than 50% in their Gibbs free energies. This is partly because the present calculations also correct the water leaving groups in order to minimize the entropy (seen in the last column in Table 3). As discussed elsewhere,40 reactions may yield more exergonic values for ΔG°ads, but they do so with a great increase in entropy unless the number of clusters on the reactants side is to equal the number of clusters on the products side. We achieve this balance by having the water leaving groups represented as a cluster rather than as individual water molecules. Figure 4a shows the difference between ΔG°ads values of OS(2Fe), MD(2Fe), and BD(2Fe) complexes of DMA relative to the OS(2Fe) complex (i.e., ΔΔGads) and includes the transition states TS1(2Fe) and TS2(2Fe). The MD(2Fe) and BD(2Fe) complexes are lower in Gibbs free energy by −28.3 and −53.6 kJ mol−1 respectively, relative to the OS(2Fe) complex, and the activation barrier from MD(2Fe) to BD(2Fe) is almost 4 times higher (+43.1 kJ mol−1) than the one from OS(2Fe) to MD(2Fe) (+11.1 kJ mol−1). A similar figure for arsenate adsorption, Figure 4b, shows the thermodynamic favorability of the MM and BB complexes with respect to the OS complex, at −51.5 and −82.8 kJ mol−1, respectively. Isolating the actual transition states proved to be more difficult for the arsenate complexes because of the multiple smaller activation barriers shown in Figure 3 for the transition from MD(2Fe) to BD(2Fe). A related study by Farrell and Chaudhary47 reported calculations for arsenate adsorption on ferric hydroxides and showed that there is a much higher activation barrier going from MM to BB than from OS to MM. Reported activation barriers ranged from +62 to +73 kJ mol−1 for OS to MM, and +79 to +112 kJ mol−1 for MM to BB. The higher activation barriers reported in their study can be explained by the exclusion of explicit water molecules. As we have argued elsewhere40 including explicit water molecules plays a major role in lowering the energies of the transition states. For the reaction enthalpies listed in Table 3 for DMA and arsenate: because careful steps were taken to minimize the entropy of the reactions, the calculated ΔHads values for the DMA adsorption reaction differ by less than 5% from ΔGads (since ΔHads = ΔGads + TΔSads) with values of −38.4, −68.9,

Figure 4. Difference in Gibbs free energies for (a) DMA and (b) arsenate adsorption reactions onto iron (oxyhydr)oxide clusters per reactions listed in Table 3.

and −91.5 kJ mol−1 for the OS(2Fe), MD(2Fe) and BD(2Fe) complexes, respectively. For arsenate, adsorption reactions forming inner-sphere complexes is also thermodynamically favorable with ΔGads values of −44.2 and −75.4 kJ/mol for the MM and BB complexes respectively and the ΔHads showing exothermic reactions and differing by less than 20% from the ΔG ads values. These values can be compared to the experimentally measured ΔHads values of −102 and −160 kJ mol−1 for the adsorption of DMA and arsenate onto hematite nanoparticles, respectively.29 These measurements were obtained from flow microcalorimetry studies at room temperature. In the same paper,29 the authors reported ΔHads values calculated from the van’t Hoff equation using ΔGads values extracted from the application of the 1-site Langmuir model and triple layer surface complexation models to temperaturedependent spectral data. The temperature-dependent studies using attenuated total internal reflectance ATR-FTIR were conducted over 5−50 °C. In these studies, it was assumed that ΔHads is temperature-independent over that range. In order to test the validity of this assumption, Table 4 lists calculated ΔHads for DMA as a function of temperature at 15, 25, and 35 °C. The data in Table 4, where ΔHads is calculated at three different temperatures, shows that ΔHads stays relatively constant for environmentally relevant temperatures with a less than 0.2 kJ mol−1 difference in the 15−35 °C range. Hence the assumption that ΔHads is temperature-independent made in the previously mentioned paper29 is valid. This section shows the importance that activation barriers play in a reaction. Although bidentate DMA is more thermodynamically favorable, the high activation barrier to go from MD to BD may explain why this complex is not the prominent one observed in experiments. F


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The Journal of Physical Chemistry A Table 4. Values of ΔHads Calculated as a Function of Temperature for the Reaction of DMA with Iron (Oxyhydr)oxide Clusters at 1 atm and at 15, 25, and 35 °Ca

As−Fe distances in the OS(4Fe) complex are more consistent with As−Fe distances >5 Å reported experimentally for arsenate outer-sphere species.48 The extra Fe-atoms also create a wider surface that inhibits an over-relaxation of the complex and does not allow the model cluster to become distorted49 as DMA is brought closer to the adsorption site. This is especially visible for the OS(2Fe) and MD(2Fe) complexes, where the DMA molecules have more freedom to tilt and wrap around the sides of the cluster to find its optimal minimum energy. It is visually observed that for the extended model surface, the OS(4Fe) and MD(4Fe) complexes in Figure 5a and b have their methyl groups sticking up whereas they are tilted to the side in Figure 1, parts A and B. The over-relaxation problem is partly responsible for the shorter As−Fe interatomic distances that are observed for the cluster with two Fe centers. The MD(4Fe) and BD(4Fe) complexes on the extended model shown in Figure 5b and c have d(As−Fe) values of 3.40 and 4.76 Å and 3.34 and 3.27 Å, respectively. The latter values are closer to those listed in Table 1 for the BD(2Fe) complex. This suggests that extending the surface may not be as important when studying BD complexes. For comparison, the trend in the thermodynamic favorability (ΔGads) of DMA complex formation on the extended model surface with four Fe centers is similar to that with two Fe: BD(4Fe) > MD(4Fe) > OS(4Fe), as listed in Table 5. Also, formation of the BD(4Fe) complex is more favorable by 55.0 kJ mol−1 relative to the OS(4Fe) complex, compared to 7.3 kJ mol−1 for the formation of the MD(4Fe) complex. The data in Table 5 shows that there is a similar energy difference between BD(4Fe) and OS(4Fe) when compared with BD(2Fe) and OS(2Fe) (−55.0 vs −53.6 kJ mol−1), but a greater difference between MD and OS when comparing the four and two iron geometries (−7.30 vs −26.3 kJ mol−1). Thus, using an extended iron model surface shows that MD(4Fe) complex formation may actually be less thermodynamically favored than MD(2Fe). A possible explanation could be linked to the over-relaxation problem noted above. When the DMA in the MD(2Fe) complex is allowed to wrap around the Fe surface, it ultimately finds a lower energy geometry. This “wrapping around” does not happen in the case with four Fe model surface because it is more rigid and less prone to over-relax. Thus, we suggest that the extended four Fe surface be used when optimizing OS and MD complexes or when using larger adsorbed molecules. Dispersion Effects on Calculated Mulliken Charges. Allocating charges to atoms is useful because they show the relative distribution of the electron density for the complexes and how charge redistribution takes place upon complex formation. This information is also useful to infer the role that electrostatics plays in the adsorption process as well as the retention of DMA by iron (oxyhydr)oxides in the environment. Table 6 shows the Mulliken population analysis50 on the DMA complexes with iron (oxyhydr)oxides clusters with two and four Fe centers. The difference in Mulliken charge (ΔMC) was calculated relative to the uncomplexed Fe surface and hydrated DMA−·4H2O and those of the complexes. Since both the extended surface model with four Fe and the surface with two Fe are assigned +1 charge in the calculations, the extended surface will have the +1 charge distributed over a larger area with a lower localized positive charge over the individual Fe atoms at the adsorption site. This distribution is seen when comparing the charge of the Fe3 and Fe4 atoms on the extended surface at +0.67 and +0.69, respectively, to the charges of the Fe1 and Fe2 atoms on the two Fe surface at

ΔHads (kJ mol‑1) as f(T) DMA adsorption reactions

15 °C

25 °C

35 °C

OS(2Fe) MD(2Fe) BD(2Fe)

−38.39 −68.91 −91.61

−38.41 −68.86 −91.53

−38.43 −68.81 −91.45

a

The numbers were calculated using B3LYP/6-311+G(d,p) with the IEFPCM solvation and GD3BJ dispersion models.

Effects of Extending the Iron (Oxyhydr)oxide Surface To Include Four Fe Centers. Calculations of DMA adsorption on extended iron (oxyhydr)oxide clusters containing four Fe centers (4Fe) were performed at the same level of theory and including dispersion to determine if (and how) the results vary when interatomic distances, Mulliken charges and relative energies are compared with those containing two Fe centers (2Fe). In all cases, the charge of the iron (oxyhydr)oxide cluster is kept at +1, which upon complex formation with the DMA−·4H2O cluster, forms neutral OS(4Fe), MD(4Fe), or BD(4Fe) complexes. Given that the point of zero charge for iron oxides is in the 7−9 pH range,17 a charge of +1 that is dispersed over four Fe centers could be more representative of a natural environment since it is unlikely to have localized high charges under neutral pH as in the case of two Fe centers. The effects of the extra Fe atoms are most noticeable when comparing the OS(4Fe) complex (Figure 5) to OS(2Fe) complex in Figure 1. The As−Fe interatomic distances, d(As− Fe), in the OS(4Fe) complex on the extended surface are 5.92 and 5.50 Å, compared to 4.81 and 4.72 Å for OS(2Fe). The

Figure 5. Optimized geometries of hydrated (a) OS(4Fe), (b) MD(4Fe), and (c) BD(4Fe) DMA−iron oxide complexes calculated with B3LYP/6-311+G(d,p), IEFPCM solvation model, and GD3BJ dispersion. G


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Table 5. Electronic Energies, Electronic Energies with Thermal Corrections to Gibbs Free Energy and Relative ΔGads for DMA Complexes on Extended Four Fe Model Surfaces Calculated Using B3LYP/6-311+G(d,p) with IEFPCM Solvation and GD3BJ Dispersion Models DMA/Fe4 complexes


electronic energy + thermal correction to Gibbs free energy (E0 + Gcorr)

rel. ΔGads (au)

rel. ΔGads (kJ/mol)

OS(4Fe) complex MD(4Fe) complex BD(4Fe) complex

−9197.3343010 −9197.3426724 −9197.3648968

−9196.91842 −9196.92120 −9196.93938

− −0.0027814 −0.0209609

− −7.30 −55.0

Table 6. Mulliken Charges for DMA/Iron (Oxyhydr)oxide Complexes with Two Fe Centers (top) and Four Fe Centers (bottom). Optimized using B3LYP/6-311+G(d,p) with IEFPCM Solvation and GD3BJ Dispersion Models atoms

Fe oxide

Fe1 Fe2 total Fe As O1 O2 total O atoms

0.72952 0.76286 1.49238

Fe1 Fe2 Fe3 Fe4 total Fe As O1 O2 total O

−0.076039 0.197875 0.669709 0.687884 1.479429

Fe oxide

DMA

OS(2Fe)

1.05340 −0.89353 −0.89355 −1.78707 DMA

0.52300 0.61023 1.13323 1.19203 −0.83128 −0.98666 −1.81794 OS(4Fe)

1.05340 −0.89353 −0.89355 −1.78707

−0.28733 −0.52471 0.61621 0.52266 0.32683 1.16710 −0.86515 −0.95627 −1.82142

ΔMCa OS(2Fe)

MD(2Fe)

ΔMCa MD(2Fe)

BD(2Fe)

ΔMCa BD(2Fe)

−0.207 −0.153 −0.359 0.139 0.062 −0.093 −0.031 ΔMCa OS(4Fe)

0.36331 0.85359 1.21690 1.32035 −0.68099 −0.87692 −1.55791 MD(4Fe)

−0.366 0.091 −0.275 0.267 0.213 0.017 0.229 ΔMCa MD(4Fe)

0.38314 0.80094 1.18408 1.22473 −0.66802 −0.59443 −1.26246 BD(4Fe)

−0.346 0.038 −0.308 0.171 0.226 0.299 0.525 ΔMCa BD(4Fe)

−0.211 −0.723 −0.054 −0.165 −1.153 0.114 0.028 −0.063 −0.034

−0.43847 −0.54318 0.59560 0.45018 0.06413 1.20060 −0.71085 −0.55242 −1.26326

−0.362 −0.741 −0.074 −0.238 −1.415 0.147 0.183 0.341 0.524

−0.33823 −0.55104 0.57869 0.46807 0.15748 1.308961 −0.357296 −0.474140 −0.83144

−0.262 −0.749 −0.091 −0.220 −1.322 0.256 0.536 0.419 0.956

ΔMC is calculated by subtracting the Mulliken charge of the atoms in the vacant Fe surface and DMA molecule from the Mulliken charge of the same atoms in the Fe-arsenical complex to show the charge redistribution after adsorption. a

However, when analyzing the ΔMC of O atoms when DMA transitions from OS to MD we see an increase in ΔMC to +0.229e− when adsorbed to two iron cluster and +0.524e− when adsorbed to four iron cluster. This trend continues as the DMA transitions into the BD complex with an increase in the ΔMC to +0.525e− when forming the BD complex with two iron cluster and +0.956e− with four iron cluster. These changes in the Mulliken charge suggest that electrostatic interactions may not play an important role for the formation of OS complexes, but may play a greater role in the formation of inner-sphere complexes. Likewise, the Fe atoms become less positively charged in the transition from bulk to OS(2Fe) to MD(2Fe) to BD(2Fe) with their total ΔMC of −0.359e−, −0.275e − , and −0.308e − , respectively, and −1.153e − , −1.415e−, and −1.322e−, respectively, in the complexes with four iron centers. The As atom becomes slightly more positively charged from +1.05e− (bulk) to +1.19e−, + 1.32e−, and +1.22e− in the OS(2Fe), MD(2Fe), and BD(2Fe), respectively. These values are compared to the ones in the four iron complexes: from +1.05e− (bulk) to +1.17e−, + 1.20e−, and +1.31e− in the OS(4Fe), MD(4Fe), and BD(4Fe), respectively. Studying Mulliken charges for the various complexes to find how the electron charge redistributes can explain what is happening at the molecular level as adsorption takes place. In this case it was observed that electrostatic attraction may play the biggest role in the transition from outersphere to inner-sphere complexes, but not in the transition from the bulk to outer-sphere complexes. Dispersion Effects on the Calculated ν(As−O). Computational chemistry studies of infrared frequencies of

+0.73 and +0.76, respectively (Table 6). The charge numbers are lower in the former case despite the fact that sum of Mulliken charges of all the Fe atoms on the two model surfaces are similar at roughly 1.48 e− and 1.49 e−, respectively. For the DMA complexes, the sum of the Mulliken charges on the Fe atoms for the extended surface with four Fe changes from +1.48 e− to +0.33, + 0.06, and +0.16 e− for the transition from the uncomplexed Fe surface to the OS(4Fe), MD(4Fe), and BD(4Fe) complexes, respectively. Similarly, the sum of the Mulliken charges on the O atoms for the extended surface with four Fe changes from −1.79 e− to −1.82, −1.26, and −0.83 e−, respectively. Also in Table 6, similar charge redistribution takes place for the clusters with two Fe atoms where the sum of the Mulliken charges for Fe atoms changes from +1.49 to +1.13 to +1.22 to +1.18 e− as the DMA transitions between the OS(2Fe), MD(2Fe), and BD(2Fe) complexes, respectively. Similarly, the sum of the Mulliken charges on the O atoms for the two Fe complexes changes from −1.79 e− to −1.82, −1.56, and −1.26 e−, respectively. The changes in the added charge values for Fe and O show how charge is redistributed within the complex as adsorption takes place and as the complex transitions from OS(2Fe) to MD(2Fe) to BD(2Fe). These values also show the role that electrostatic attraction plays in the formation of these complexes. For both model surfaces, the Mulliken charges remain relatively constant for the O atoms on the DMA molecule in the transition from the bulk to the OS(2Fe) complex with only a small difference in the Mulliken charge (ΔMC) of −0.031e− when adsorbed to two iron cluster, and −0.034e− when adsorbed to four iron cluster. H


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The Journal of Physical Chemistry A surface complexes are indispensable in the interpretation and assignment of experimental spectral data. Herein, we analyze the effects that dispersion has on vibrational frequencies and whether previously calculated scaling factors27 are still appropriate for the present calculations that include dispersion effects. Table 7 shows the calculated v(As−O) for DMA complexes (OS, MD, and BD) formed with iron (oxyhydr)oxide model clusters with two and four Fe centers. Table 7. Calculated ν(As−O) Frequencies (cm−1) for DMA/ Iron (Oxyhydr)oxide Complexes, Using B3LYP/6311+G(d,p) with IEFPCM Solvation and GD3BJ Dispersiona complex

ν(As−O)

OS(2Fe) OS(4Fe) MD(2Fe) MD(2Fe)b MD(4Fe) BD(2Fe) BD(4Fe)

757, 803 (754, 800) 789, 809 782 802 835

Figure 6. Correlation between calculated and experimental v(As−O) frequencies on DMA/hematite with anharmonic correction factor 1.0189. The solid markers are for the DMA(2Fe) complexes and the empty markers for the DMA(4Fe) complexes.

ν(As-OFe)

758, 782 790, 764, 738,

782 (739, 792) 795 781, 799 (764, 773, 788, 790) 811

vibrational frequencies. The fact remains that calculated frequencies are not quantitatively accurate. We are currently conducting work that will provide better scaling factors for systems that include Fe and As for extended surfaces while incorporating hydration and dispersion. Conclusions and Significance. The DFT calculations in this study show that the formation of inner- and outer-sphere DMA−iron (oxyhydr)oxide complexes are thermodynamically favorable, but that the activation barrier for bidentate formation from monodentate is significantly higher than that for the arsenate system. The calculations reported herein include dispersion corrections which, to our knowledge, were not included in any previous theoretical studies of arsenicals adsorption on metal oxide clusters. Also, extending the model iron (oxyhydr)oxide surface to include four Fe centers produces geometries for DMA complexes that do not overrelax and are in good agreement with experimental bond distances. However, no significant difference in the bidentate complex was obtained when modeling with two or four Fe model surfaces. The Mulliken charge distribution analysis revealed that electrostatic attraction may also play a role in the formation of monodentate complexes (in the transition from an outer-sphere complex), but the same is not observed in the formation of outer-sphere or bidentate complexes. In this paper we have shown that calculations including outer-sphere complexes, with weaker interactions between the adsorbate and the substrate, can benefit from dispersion corrections such as GD3BJ, but minimal differences were observed for inner-sphere complexes. Comparing theoretical IR spectra with experimental studies allows us to gain more insight into how adsorption takes place at a molecular level and aids in the interpretation of infrared spectra and the assignment of peaks. In particular, it was shown from the frequency calculations that using 1.89% adjustment to correct for anharmonic behavior is adequate for iron (oxyhydr)oxide and arsenic complexes when using the GD3BJ dispersion correction at the B3LYP/6-311+G(d,p) level of theory with the IEFPCM solvation model. By analyzing the Mulliken charges, it was shown that both adsorption and the transition from outersphere to inner-sphere complexes is aided by electrostatic interactions between the positively charged surface and negatively charged arsenicals. Furthermore, we recommend that extending the surface to four Fe atoms could be valuable when studying outer-sphere complexes or larger molecules that

a

Frequencies in brackets were calculated without dispersion correction.27 No scaling factor was used to correct for anharmonicity. b With PBE0/6-311+G(d,p) IEFPCM solvation and GD3BJ dispersion for comparison.

Only medium and strong intensity v(As−O) vibrations are recorded in Table 7, and vibrations below 0.3 Å in bond length displacement were omitted. ATR-FTIR adsorption studies of DMA on hematite (Fe2O3) and goethite (FeOOH) show As− O stretching frequencies at 775, 793, 840, and 877 cm−1 and 768, 787, 837, and 876 cm−1 for the DMA/hematite and the DMA/goethite complexes, respectively.20 Even without correcting for anharmonicity, the calculated values in Table 7 are in reasonable agreement with experimental values, with DMA(2Fe) complexes having As−O stretching frequencies between 757 and 803 cm−1 and DMA(4Fe) complexes having As−O stretching frequencies between 738 and 835 cm−1. Merrick et al.51 evaluated harmonic vibrational frequency scale factors for a number of DFT approaches that include B3LYP/6-311+G(d,p) and reported a value of 1.0189 for the set of molecules they tested with no solvation model. We previously reported39 that the optimal scaling factor to use for anharmonic corrections is 1.0307 when As and Fe calculations are performed at the B3LYP/6-311+G(d,p) level of theory with the IEFPCM solvation model. This scaling factor was calculated to minimize the residual between the theoretical and experimental frequencies in systems containing Fe and As. Either scaling factor will raise the value of the calculated harmonic frequencies reported in Table 7. Using the 1.0189 factor, Figure 6 shows the correlation of the scaled frequencies with experimental values. The lower frequencies (below 800 cm−1) have a better correlation with experimental values than the higher frequencies (above 800 cm−1). The experimental spectral components below 800 cm−1 may arise from both inner- and outer-sphere complexes of DMA. On the other hand, this scaling factor underestimates the values of the higher frequencies. This deviation is observed systematically for other systems that include organic molecules, small diatomic and triatomic molecules.52 For these systems, attempts have been made to correct these deviations by applying scaling factors to low (1000 cm−1) harmonic I


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tend to wrap around a smaller surface when performing energy optimizations.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.6b08367. Figures and tables showing geometries and listing structural parameters including results from IRC calculations (PDF)

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AUTHOR INFORMATION

Corresponding Author

*(H.A.A.-A.) Telephone: (519)884-0710, ext. 2873. Fax: (519) 746-0677. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge partial funding from Laurier, Compute Canada, NSERC, and an Early Researcher Award from Ontario’s Ministry of Research and Innovation.

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REFERENCES

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