Supporting Information (SI)
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1 S1 Supporting Information (SI) Theoretical Study of Small Iron-oxyhydroxide Clusters and Formation of Ferrihydrite Bidisa Das, * Technical Research Centre (TRC). Indian Association for the Cultivation of Science (IACS). 2A & 2B Raja S C Mullick Road. Jadavpur. Kolkata West Bengal. India * cambd@iacs.res.in Detailed Theoretical Methods: The molecular geometries of all Fe(III) oxyhydroxide clusters investigated in this work have been optimized using the B3LYP [1-4] hybrid density functional in vacuum along with the 6-31G** basis-set employing G09 software [5]. It has been shown earlier that B3LYP functional describes transition metal atoms with adequate accuracy to be used in large studies and has been heavily used by theoretical chemist community for organometallic systems. It is known to give results close to experimental values [6-8]. The stabilities and structures were double checked with B3PW91/6-31G**[9] methods as well and all structures were found to be stable though structural parameters like bond-distance and bond-angles differed to some extent when calculated using different functionals. To characterize the nature of the stationary points obtained from structural optimizations, harmonic vibrational frequencies were computed at the same level of theory. The stable structures were characterized by all real frequencies. The gas phase studies of Fe(III) oxyhydroxide clusters provide the important thermodynamic parameters like Enthalpies and Gibb's free energies at 298K and 1 atm pressure. The corrected Enthalpy and the Gibbs free energies were computed by adding enthalpic corrections (H corr ) and Gibbs free energy corrections (G corr ) respectively to the total energies (E(g)) from gas phase thermochemistry calculations as implemented in G09 software [5]. Past Address: Center for Advanced Materials(CAM). Indian Association for the Cultivation of Science (IACS). 2A & 2B Raja S C Mullick Road. Jadavpur. Kolkata West Bengal. India
2 S2 Following this we have conducted single point solvent phase computations on the B3LYP optimized structures using SMD and CPCM model considering water as a solvent employing the same basis functions on each atom. Single point calculations were preferred to save computational resources and to avoid complexation reactions which might sometimes take place during optimization processes. In case of studies in aqueous medium some approximations must be made to treat the solvent molecules implicitly; the first level of approximations come from treating the solvent as a continuous and homogeneous dielectric field where the solute is placed (in SMD, CPCM model) without considering explicit water molecules. The second level of approximations come while calculating solution phase enthalpies and free energies. While treating solvent as a homogeneous dielectric field has been fairly standard practice, exact predictions of free energies of ions and molecules in solution is a challenge, and no single approach is currently available which give good agreement with experimental outcome. We calculated the aqueous phase free energies form solvation free energies obtained using both SMD and CPCM methods. Solvation energy approach to obtain aqueous phase free energy The definition of solvation free energy of a solute is the difference in free energies of the solute in the solution phases [11-13] ΔG solv = G soln - G gas where G soln = (E solv + G nes ) + G corr_gas Here G corr_gas refers to the thermal correction to the free energy of the solute in the gas phase. In G09 the total free energy in solution phase using CPCM method is actually (E soln + G nes ), where G nes denotes the sum of any non-electrostatic contributions to the solvation energy, so this value is just corrected with gas-phase free energy to obtain the value of G soln. However, since corrected gas phase Gibbs free energies were computed by adding Gibbs free energy corrections (G corr_gas ) to the total energies (E(g)) (from gas phase thermochemistry calculations), hence solvation energy eventually is the just the difference in energy values as follows; ΔG solv = E soln -E gas and free energy in solution state G soln =G gas + ΔG solv Corrections for Standard States: Most tabulations of experimental and calculated free energies of solvation are based on Ben-Naim s definition [14] of solvation as the transfer of a solute from a hypothetical ideal gas at 1 M into a hypothetical ideal 1 M aqueous solution at infinite dilution. In this study, all data obtained for Fe(III) oxyhydroxide clusters in the gas phase are for 298 K and 1 atm pressure as taken in thermochemistry calculations in G09. All calculated gas-phase free energies are tabulated using an ideal gas at 1 atm as the reference state. All calculated solvation free energies are tabulated for an ideal gas at a gas-phase
3 S3 concentration of 1 mol/l dissolving as an ideal solution at a liquid-phase concentration of 1 mol/l. The relationship between these two standard states [15] is: G gas soln = RT ln(24.46) n, n = change in number of moles of products and reactants. The conversion of the 1 atm standard state to the 1 mol/l standard state can be derived from the relationship between the equilibrium constant concerning concentration, K c in 1M, and the equilibrium constant expressed in terms of pressure, K p in the 1 atm standard state. The relationship between the two constants is derived for the following general reaction: ( ) ( ) The corresponding equilibrium constants are = [ ] and [ ] = Using the ideal gas law, = T, where R is given by L atm/k mol, we can rewrite = ( / ) ( / ) =( / ) ( / )..( ) (1) Since / and / now have the units of mol/l, they can be replaced by the concentrations of A and B and simplified in terms of Kc as; = [ ] [ ] = ( ) (2) where is the change in the number of moles,. Above equation can be used to get the relationship between the Gibbs free energies in different standard states. The relationship between the 1M state and the standard state of 1 atm is = + (3) = (4) The term can be calculated from equation (2) and relations between the equilibrium constants and the free energies at the two different standard states = (5) = (6) Using equations (2), (5) and (6)we can derive the relation between the two free energies at K; = ( ) = (24:4654) (7) In equation (7) if the change in number of moles in any reaction is unity then, =1 and at T=298.15K, = ln( )=1.89 /, All the free energies reported in Table 2 of this manuscript takes into account the standard state corrections and the correction term 1.89 kcal/mol is included in the G s values.
4 S4 Although this standard state convention is fully accepted for solvated species, it still causes some confusion when water is both a solvated species and a solvent. According to the widely adopted symmetrical standard state definition, the activity of a pure solvent at standard conditions is taken as unity. For pure water [H 2 O liq ] at T =298 K, this corresponds to a concentration of M and corresponds to nrt ln[h 2 O liq ] where n is number of molecules of water used as reactant. At T =298 K, this corresponds to a correction term of 2.38*n kcal/mol. This is actually self-solvation of water leading to a free energy transfer that contains an additional term because of the difference in solute (water) concentrations between the reactant and the product phases. We use this extra correction term only in 3+ case of the four step-wise hydrolysis reactions of Fe(H 2 O) 6 reported in section "Results and Discussions" and sub-section "Formation of Fe(III) Oxyhydroxide Clusters in Aqueous Medium" to compare the free energies with experimental data [16]. Sl. No Reactions in aqueous medium using CPCM (All aqueous phase free energies calculated from G solv ) G s in aqueous medium (kcal) 1 2Fe(H 2 O) H 2 O Fe 2 (OH) 4 (H 2 O) 2+ 6 (D1) + 4H 3 O (M s =1) 30.6 (M s =11) Fe(H 2 O) 6 + 2H 2 O Fe 2 (H 2 O) 6 (OH) 2+ 4 (D2) + 4H 3 O (M s =1)* 3 2Fe(H 2 O) 3+ 6 Fe 2 (H 2 O) 8 (OH) 4+ 2 (D3) + 2H 3 O (M s =1) 11.1 (M s =11) 4 2Fe(H 2 O) H 2 O Fe 2 O(H 2 O) (D4) + H 2 O+2H 3 O (M s =1) 7.5 (M s =11) 5 2Fe(H 2 O) 3+ 6 Fe 2 OH(H 2 O) (D5) + H 3 O (M s =1) 27.3 (M s =11) 6 Fe 2 (H 2 O) 8 (OH) 4+ 2 (D3)+ Fe(H 2 O) 3+ 6 Fe 3 O(OH) 3 (H 2 O) 4+ 9 (T)+ 3H 3 O (M s =6) 19.8 (M s =16) 7 3Fe(H 2 O) 3+ 6 Fe 3 (OH) 4 (H 2 O) (L)+4H 3 O (M s =6) 29.1 (M s =16) 8 Fe 3 O(OH) 3 (H 2 O) Fe(H 2 O) 3+ 6 Fe 4 O 2 (OH) 4 (H 2 O) (TT1)+3H (M s =1) 29.6 (M s =21) 9 Fe 3 O(OH) 3 (H 2 O) Fe 2 (H 2 O) 8 (OH) 2 4+ Fe 5 O 3 (OH) 5 (H 2 O) (P) O + + 4H 3 O (M s =26) 10 Fe 3 O(OH) 3 (H 2 O) Fe 2 (H 2 O) 8 (OH) 2 4+ Fe 7 O 6 (OH) 6 (H 2 O) (M s =36)
5 S5 (H1) + 9H 3 O + 11 Fe 3 O(OH) 3 (H 2 O) Fe(H 2 O) 6 3+ Fe 7 O(OH) 12 (H 2 O) (H)+ 9H 3 O + + 3H 2 O 12 4Fe 3 O(OH) 3 (H 2 O) Fe(H 2 O) 6 3+ [FeO 4 (Fe(OH) 2 (H 2 O)) 12 ] (M s =36) (M s =66) (K δ ) + 12H 3 O + + 6H 2 O Table S1. The formation of various Fe(III) oxyhydroxide clusters in water using CPCM model within DFT. The reaction free energies calculated form solvation free energies and corrected for standard states are reported in water for spin-states mentioned in the parantheses.* No high-spin state. References: [1] A. D. Becke, Phys. Rev. A, 38, (1988). [2] A. D. Becke, Journal of Chem. Phys,, 98, (1993). [3] C. Lee, W. Yang, and R. G. Parr, Phys. Rev. B, 37, (1988). [4] J. P. Perdew, J. A. Chevary, S. H. Vosko, K. A. Jackson, M. R. Pederson, D. J. Singh, and C. Fiolhais, Phys. Rev. B, 46, (1992). [5] M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G. A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H. P. Hratchian, A. F. Izmaylov, J. Bloino, G. Zheng, J. L. Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, J. A. Montgomery, Jr., J. E. Peralta, F. Ogliaro, M. Bearpark, J. J. Heyd, E. Brothers, K. N. Kudin, V. N. Staroverov, R. Kobayashi, J. Normand, K. Raghavachari, A. Rendell, J. C. Burant, S. S. Iyengar, J. Tomasi, M. Cossi, N. Rega, J. M. Millam, M. Klene, J. E. Knox, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, R. L. Martin, K. Morokuma, V. G. Zakrzewski, G. A. Voth, P. Salvador, J. J. Dannenberg, S. Dapprich, A. D. Daniels, O. Farkas, J. B. Foresman, J. V. Ortiz, J. Cioslowski, and D. J. Fox, Gaussian, Inc., Wallingford CT, Gaussian 09, Revision A.02. [6] K. E. Riley, B. T. Op'tHolt, K. M. Merz, J. Chem. Theory Comput. 2007, 3, [7] S. Niu, M. B. Hall, Chem. Rev. 2000, 100, [8] T. R. Cundari, H. A. Ruiz Leza, T. Grimes, G. Steyl, A. Waters, A. K. Wilson, Chem. Phys. Lett, 2005, 401, [9] J. P. Perdew, in Electronic Structure of Solids 91, Ed. P. Ziesche and H. Eschrig (Akademie Verlag, Berlin, 1991) 11. [10] M. Cossi, N. Rega, G. Scalmani, V. Barone, J. Comp. Chem. 2003, 24, 669. [11] J. Ho, A. Klamt, M. L. Coote, J. Phys. Chem. A 2010, 114, [12] K. S. Alongi, G. C. Shields, Annual Reports in Computational Chemistry, 6,2010, [13] H. A. De Abreu, L. Guimaraes, H. A. Duarte, J. Phys. Chem. A 2006, 110, [14] Ben-Naim. A. Solvation Thermodynamics; Plenum: New York,1987. [15] C. P. Kelly, C. J. Cramer, D. G. Truhlar, J. Chem. Theory Comput., 2005, 1, [16] Flynn, C. M. Chem. Rev. 1984, 84, 31.
6 S6 Energies, enthalpies and free energies of various species in gas phase and in aqueous phase The two tables below show the relevant energies, enthalpies, free energies in gas phase and aqueous medium (SMD) for Fe(III) hydrolysis reactions shown in Section IV. The free energy of solvation in kcal/mol is given. Table S2 Gas phase B3LYP/6-31G**, E (H) H 2 O H (H) H corr ( ) G (H) G corr ( ) H 3 O + Fe(H 2 O) 6 3+ Fe(OH)(H 2 O) S+1=6 2S+1= ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) SMD, Solution,B3LYP/6-31G**, E (H) Gsolv (kcal/mol) Table S3 Gas phase B3LYP/ 6-31G**, E(H) H (H) H corr ( ) Fe(OH) 2 (H 2 O) 4 1+ cis Fe(OH) 2 (H 2 O) 4 1+ trans Fe(OH) 3 (H 2 O) 2 Fe(OH) 4-2S+1=6 2S+1=4 2S+1=6 2S+1=4 2S+1=6 2S+1=4 2S+1=6 2S+1= ( ) ( ) ( ) ( ) ( ) ( ) ( ) G (H) G corr ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) SMD, B3LYP/ 6-31G**, E (H) Gsolv (kcal/mol)
7 S7 Hydolysis of Fe(III) in water calculated using CPCM method Fe(H 2 O) H 2 O Fe(H 2 O) 5 (OH) 2+ + H 3 O +, G s = 1.83 kcal/mol Fe(H 2 O) 5 (OH) H 2 O Fe(H 2 O) 4 (OH) 2 + H 3 O +, G s = kcal/mol Fe(H 2 O) 4 (OH) + 2 Fe(H 2 O) 2 (OH) 3 + H 3 O +, G s = kcal/mol Fe(H 2 O) 2 (OH) 3 Fe(OH) H 3 O +, G s = kcal/mol Figure S1. The optimized structures of Fe(III) hydrolysis products
8 S8 Table S4 Species (low-spin) Gas B3LYP/6-31G** E(H) H (H) G (H) CPCM, B3LYP/ 6-31G**, E(H) D1, Fe 2 (OH) 4 (H 2 O) 6 2+ D2, Fe 2 (H 2 O) 6 (OH) (H corr : ) (G corr : ) (H corr : ) (G corr : ) D3, Fe 2 (H 2 O) 8 (OH) (H corr : ) (G corr : ) H (H) G solv = E_soln-E_gas SMD, B3LYP/ G**, E(H) G solv (kcal/mol) Table S5 Species (high-spin) Gas phase B3LYP/6-31G** E(H) H (H) G (H) CPCM B3LYP/ 6-31G** E(H) D1, Fe 2 (OH) 4 (H 2 O) (H corr : ) D2, Fe 2 (H 2 O) 6 (OH) 4 2+ D3, Fe 2 (H 2 O) 8 (OH) (H corr : ) (G (G corr : ) corr : ) No high-spin H (H) G solv =E_soln-E_gas SMD B3LYP/ G** E(H) G solv( kcal/mol)
9 S9 Table S6 Species (low-spin) Gas phase B3LYP/6-31G** E(H) H (H) G (H) CPCM, B3LYP/ 6-31G** E(H) D4, Fe 2 O(H 2 O) D5, Fe 2 OH(H 2 O) L 5+ Fe 3 (OH) 4 (H 2 O) (H corr : ) (H corr : ) ( ) (G corr : ) (G corr : ) ( ) H (H) G solv =E_soln-E_gas SMD B3LYP/ G** E(H) G solv ( kcal/mol) Table S7 Species (high-spin) Gas phaseb3lyp/6-31g** E(H) H (H) G (H) CPCM, B3LYP/ 6-31G** E(H) D4, Fe 2 O(H 2 O) D5, Fe 2 OH(H 2 O) L 5+ Fe 3 (OH) 4 (H 2 O) (H corr : ) (H corr : ) ( ) (G corr : ) (G corr : ) ( ) H (H) G solv =E_soln-E_gas SMD B3LYP/ G** E(H) G solv =E_soln-E_gas (kcal/mol)
10 S10 Table S8 Species T (low-spin), 4+ Fe 3 O(OH) 3 (H 2 O) 9 Gas phase B3LYP/6-31G** E(H) H (H) (H corr : ) G (H) (G corr : ) T (high-spin), 4+ Fe 3 O(OH) 3 (H 2 O) (H corr : ) (G corr : ) TT1(low-spin), Fe 4 O 2 (OH) 4 (H 2 O) TT1(high-spin), Fe 4 O 2 (OH) 4 (H 2 O) (H corr : ) (G corr : ) (H corr : ) (G corr : ) CPCM, B3LYP /6-31G** E(H) H (H) G solv =E_soln E_gas SMD, B3LYP /6-31G** E(H) G solv =E_soln- E_gas (kcal/mol) Table S9 Species (high-spin) P, Fe 5 O 3 (OH) 5 (H 2 O) Ms=6 Gas phase B3LYP/6-31G** E(H) H (H) H corr (H corr : ) G (H) G corr P, 4+ Fe 5 O 3 (OH) 5 (H 2 O) 11 Ms= ( ) (G corr : ) ( ) CPCM, B3LYP /6-31G** E(H) H (H) G solv =E_soln-E_gas SMD, B3LYP /6-31G** E(H) G solv =E_soln-E_gas (kcal/mol)
11 S11 Table S10 Species (high-spin) H, Fe 7 O(OH) 12 (H 2 O) K δ, [FeO 4 (Fe(OH) 2 (H 2 O)) 12 ] 7+ Gas phase B3LYP/ G** E(H) H (H) H corr ( ) ( ) G (H) G corr ( ) ( ) CPCM, B3LYP / G** E(H) H (H) G solv =E_soln-E_gas SMD, B3LYP /6-31G** E(H) G solv =E_soln-E_gas (kcal/mol) Comparison of bond-distances for dimer D3, T, P and H in different spin-states, M s (2S+1) Figure S2. D3 Complex Fe-OH (brd) Fe-OH 2 O-H(Brd) Fe-Fe <O(H2O)-Fe-O(H) D3 (Ms=1) ,95.5 D3(Ms=5) 1.88, ,94.2 D3 (Ms=11) ,97.5 Table S11
12 S Figure S3. T Complex Fe-O (brd) Fe-OH(brd) O-H(Brd) Fe-H 2 O Fe1-Fe2 Fe2-Fe3 Fe1-Fe3 T (Ms=4) 1.88,1.88, , T (Ms=6) 1.94,1.89, , T (Ms=16) 1.98,1.97, , Table S12 Figure S4. P Table S13 Bond-distances P(Ms=5) P(Ms=16) P(Ms=26) (Figure above) Fe1-Fe Fe1-Fe3, Fe2-Fe , ,3.0 Fe3-Fe4, Fe4-Fe , Fe1-O6,Fe2-O6, Fe4-O6 1.84,1.87, ,2.05, , 1.94,1.98 Fe1-O7,Fe3-O7, Fe4-O7 1.86,1.86, ,1.80, ,1.93, 2.0 Fe5-O8,Fe4-O8, Fe2-O8 1.92,1.89, ,1.95, , 2.06,1.98 Fe-OH(brd) Fe-H 2 O O-H
13 S13 Figure S5: H Table S14 Bond-distances H(Ms=36) H(Ms=26) (Fig. left) Fe1-Fe2, Fe1-Fe3,Fe , Fe4 3.43,3.42 Fe2-Fe3, Fe3-Fe5,Fe Fe5 Fe3-Fe6, Fe3-Fe5 Fe4-Fe6, Fe4-Fe7 Fe2-Fe5, Fe2-Fe Fe1-O (tetrahedral) , Fe1-O(H) (tetrahedral Fe2-O(H),Fe3-O(H), ,1.93, 2.0 Fe4-O(H) Fe5-O(H),Fe6-O(H), Fe7-O(H) , 2.00,2.03 Fe-H 2 O O-H XYZ co-ordinates of optimized structures, with corresponding energies. Figure S6: M, Fe(H 2 O) Fe(H 2 O) 6 3+ monomer M; charge: +3, spin-multiplicity(2s+1): 6 (Energies in Hartrees) B3LYP/6-31G** (3,6); E: ; H : , G : B3PW91/6-31G** (3,6); E: H ; H : H, G :
14 S14 XYZ coordinates Fe O H H O H H O H H O H H O H H O H H Figure S7: Fe 2 (H 2 O) 6 (OH) D1, Fe 2 (H 2 O) 6 (OH) 4 2+ ; charge: +2, spin-multiplicity(2s+1): 1, (Energies in Hartrees) B3LYP/6-31G** (2,1); E, ; H: , G: B3PW91/6-31G** (2,1); E, ; H: , G: XYZ co-ordinates O O O O Fe Fe O O
15 S15 H H O H H O H H O H H O H H H H H H H H Figure S8: D1, Fe 2 (H 2 O) 6 (OH) D1, Fe 2 (H 2 O) 6 (OH) 4 2+ ; charge: +2, spin-multiplicity(2s+1): 11, (Energies in Hartrees) B3LYP/6-31G** (2,11); E, ; H: ,G: B3PW91/6-31G** (2,11); E ; H :, G XYZ coordinates Fe O O O O O Fe O
16 S16 H H H H H O H O O O H H H H H H H H H H Figure S9: D3 high-spin, Fe 2 (H 2 O) 8 (OH) D3, Fe 2 (H 2 O) 8 (OH) 4+ 2 ; charge: +4, spin-multiplicity(2s+1): 11, (Energies in Hartrees) B3LYP/6-31G** (4,11); E: ;H: ,G: B3PW91/6-31G** (4,11); E ; H: , G : XYZ coordinates O O Fe Fe O O O O
17 S17 H H H H O H H O H H O H H O H H H H H H H H D3, Fe 2 (H 2 O) 8 (OH) 2 4+ ; charge: +4, spin-multiplicity(2s+1): 1, (Energies in Hartrees) B3LYP/6-31G** (4,1); E: ;H: ,G: B3PW91/6-31G** (4,1); E: ; H: , G : XYZ Co-ordinates O O Fe Fe O O O O H H H H O H H O
18 S18 H H O H H O H H H H H H H H Figure S10: D2, Fe 2 (H 2 O) 6 (OH) D2, Fe 2 (H 2 O) 6 (OH) 4 2+ ; charge: +2, spin-multiplicity(2s+1): 1, (Energies in Hartrees) B3LYP/6-31G** (2,1); E: : ; H: ; G: B3PW91/6-31G** (2,1); E: ; H: ,G: XYZ Co-ordinates
19 S D4, Fe 2 O(H 2 O) charge: +4, spin-multiplicity(2s+1): 1, (Energies in Hartrees) B3LYP/6-31G** (4,1); E: ; H: ,G: Figure S11: D4, Fe 2 O(H 2 O) XYZ co-ordinate Fe Fe O O H H O H H O H O H O H
20 S20 H O H O H O H H O H H H H H H H H O D5, Fe 2 OH(H 2 O) charge: +5, spin-multiplicity(2s+1): 1, (Energies in Hartrees) B3LYP/6-31G** (5,1); E: ; H: ,G: B3PW91/6-31G** (5,1); E: ; H: ,G: Figure S12: D5, Fe 2 OH(H 2 O) XYZ co-ordinate Fe Fe O O H H O H H O
21 S21 H O H O H H O H O H O H H O H H H H H H H H O H T, Fe 3 O(OH) 3 (H 2 O) 9 4+ ; charge: +4, spin-multiplicity(2s+1): 6, (Energies in Hartrees) B3LYP/6-31G** (4,6); E: ; H: ,G: B3PW91/6-31G** (4,6) ; E: ; H: , XYZ Co-ordinates O O Fe Fe O O O O Fe O O O H H
22 S22 H H H H H H H H O H H O H H O H H O H H H H H T, Fe 3 O(OH) 3 (H 2 O) 9 4+ ; charge: +4, spin-multiplicity(2s+1): 16, (Energies in Hartrees) B3LYP/6-31G** (4,16); E: ; H: ,G: B3PW91/6-31G** (4,16) ; E: ; H: , XYZ co-ordinate O O Fe Fe O O O O Fe O O O H H
23 S23 H H H H H H H H O H H O H H O H H O H H H H H L, Fe 3 (OH) 4 (H 2 O) ; charge: +5, spin-multiplicity (2S+1): 6, (Energies in Hartrees) B3LYP/6-31G** (5, 6); E: ; H: ,G: B3PW91/6-31G** (5, 6) ; E: ; H: , G: Figure S13: L, Fe 3 (OH) 4 (H 2 O) XYZ Co-ordinates O Fe Fe O O
24 S24 O O O O O H H H H H O H O H H O H H H H Fe O H H O H H O H H H H H H H H L, Fe 3 (OH) 4 (H 2 O) ; charge: +5, spin-multiplicity (2S+1): 16, (Energies in Hartrees) B3LYP/6-31G** (4,16); E: ; H: ,G: B3PW91/6-31G** (4,16) ; E: ; H: , G: XYZ Co-ordinates O Fe
25 S25 Fe O O O O O O O H H H H H O H O H H O H H H H Fe O H H O H H O H H H H H H H H TT1, Fe 4 O 2 (OH) 4 (H 2 O) ; charge: +4, spin-multiplicity(2s+1): 1, (Energies in Hartrees) B3LYP/6-31G** (4,1); E: ; H: , G: B3PW91/6-31G** (4,1) ; E: ; H: , G:
26 S26 Figure S14: TT1, Fe 4 O 2 (OH) 4 (H 2 O) XYZ Co-ordinates O Fe Fe Fe Fe O O O O O O O O O H H H H H H H H O H H O H H O H H O H H O H H O H
27 S27 H H H H H TT2, Fe 4 (OH) 8 (H 2 O) 8 4+ ; charge: +4, spin-multiplicity(2s+1): 1, (Energies in Hartrees) B3LYP/6-31G** (4,1); E: ; H: , G: B3PW91/6-31G** (4,1) ; E: ; H: , G: XYZ Co-ordinates Figure S15: TT2, Fe 4 (OH) 8 (H 2 O) 8 4+ O O Fe Fe O O Fe O O O O O O O O O O Fe O O H H H H H
28 S28 H H H H H H H H H H H H H H H H H H H P, Fe 5 O 3 (OH) 5 (H 2 O) ; charge: +4, spin-multiplicity(2s+1): 6, (Energies in Hartrees) B3LYP/6-31G** (4,6); E: ; H: , G: B3PW91/6-31G** (4,6) ; E: ; H: , G: XYZ Co-ordinates O Fe Fe Fe Fe O O O O O O O O O H H H H H H
29 S29 O H O H O H O H H O H O H H H H H H Fe O H H O H H O H H H H H P, Fe 5 O 3 (OH) 5 (H 2 O) ; charge: +4, spin-multiplicity(2s+1): 26, (Energies in Hartrees) B3LYP/6-31G** (4,6); E: ; H: , G: XYZ Co-ordinates
30 S H, Fe 7 O (OH) 12 (H 2 O) ; charge: +7, spin-multiplicity(2s+1): 36, (Energies in Hartrees) B3LYP/6-31G** (7,36); E: ; H: , G: B3PW91/6-31G** (7,36) ; E: ; H: , G:
31 S31 XYZ Co-ordinates O O Fe Fe Fe Fe Fe O O O Fe O O O O O O O H H H H H H H H H H H Fe O H H O H H O H H O H H O
32 S32 H H O H H O H H O O O O H H H H H O O H H H H H H Fe(III) oxyhydroxide delta Keggin ion [FeO 4 (Fe(OH) 2 (H 2 O)) 12 ] 7+ (charge=7, 2s+1=66) (Energies in Hartrees) B3LYP/6-31G** (7,66); E: ; H: , G: B3PW91/6-31G** (7,66) ; E: ; H: , G: XYZ Co-ordinates O O O O O O O Fe Fe
33 Fe O O O Fe Fe Fe O O O Fe Fe Fe O O O Fe Fe Fe O O O O O O O O O O O O H H H H H H H H H H H H H H H H H S33
34 H H H H H H H Fe O H H O H H O H H O H H O H H O H H O H H O H H O H H O H H O H H O H H S34
35 S Fe(III) oxyhydroxide delta Keggin ion [FeO 4 (Fe(OH) 2 (H 2 O)) 12 ] 7+ (charge=7, 2s+1=46) (Energies in Hartrees) B3LYP/6-31G** (7,66); E: ; H: , G: \ Figure S16: Keggin ion [FeO 4 (Fe(OH) 2 (H 2 O)) 12 ] 7+ in different spin state XYZ Co-ordinates O O O O O O O Fe Fe Fe O O O Fe Fe Fe O O O Fe Fe Fe O
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