Letter pubs.acs.org/JPCL
Why Mercury Prefers Soft Ligands Demian Riccardi,†,‡ Hao-Bo Guo,†,‡ Jerry M. Parks,† Baohua Gu,§ Anne O. Summers,∥ Susan M. Miller,⊥ Liyuan Liang,§ and Jeremy C. Smith*,†,‡ †
UT/ORNL Center for Molecular Biophysics, Oak Ridge National Laboratory, 1 Bethel Valley Road, Oak Ridge, Tennessee 37831-6309, United States ‡ Department of Biochemistry and Cellular and Molecular Biology, University of Tennessee, Knoxville, Tennessee 37996, United States § Environmental Science Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee, 37831, United States ∥ Department of Microbiology, University of Georgia, Athens, Georgia 30602-7271, United States ⊥ Department of Pharmaceutical Chemistry, University of California San Francisco, San Francisco, California 94158-2517, United States S Supporting Information *
ABSTRACT: Mercury (Hg) is a major global pollutant arising from both natural and anthropogenic sources. Defining the factors that determine the relative affinities of different ligands for the mercuric ion, Hg2+, is critical to understanding its speciation, transformation, and bioaccumulation in the environment. Here, we use quantum chemistry to dissect the relative binding free energies for a series of inorganic anion complexes of Hg2+. Comparison of Hg2+−ligand interactions in the gaseous and aqueous phases shows that differences in interactions with a few, local water molecules led to a clear periodic trend within the chalcogenide and halide groups and resulted in the well-known experimentally observed preference of Hg2+ for soft ligands such as thiols. Our approach establishes a basis for understanding Hg speciation in the biosphere.
SECTION: Environmental and Atmospheric Chemistry, Aerosol Processes, Geochemistry, and Astrochemistry
M
Hg 2+ complexation. 2,12 However, despite its very low concentrations in marine and fresh water (pM to nM), the very strong affinity of SR− makes it the primary competitor for Hg2+ in the external environment and in the thiol-rich (μM to mM) biochemistry of living cells.2,5,13 The formation of stable Hg2+ adducts with biotic sulfur ligands disrupts their biological functions.14 Most relevant for mercury speciation in the biosphere is the binding of two anionic ligands by Hg2+, converting the ionic reactants Hg2+, L1−, and L2− into the neutral product, HgL1L2
ercury occurs largely as elemental Hg0 (a liquid or monatomic vapor) or the oxidized, mercuric ion, Hg2+, with both forms undergoing redox changes in biotic and abiotic processes. Relatively unreactive, Hg0 is oxidized to Hg2+, which is highly reactive, neurotoxic, nephrotoxic, hepatotoxic, and immunotoxic.1 In addition, Hg2+ is the most immediate substrate for the microbiological synthesis of neurotoxic monomethylmercury (CH3Hg+).2−6 Consequently, the World Health Organization recommends phasing out all use of mercury and sequestering existing stocks,7 although existing anthropogenic sources will continue to disseminate thousands of metric tonnes of Hg. For example, coal burning, the main source of Hg found in the atmosphere,8 together with artisanal gold mining,9 landfills,10 and dental materials,11 directly impacts terrestrial environments, including freshwater resources. Independent of human activity, the natural release from volcanoes and deep sea vents will continue to impact terrestrial and oceanic biota. In natural aquatic systems, Hg2+ is not a free, monatomic ion complexed only by water molecules but rather is bound by inorganic or organic nucleophiles found in marine or lacustrine colloids, cellular macromolecules and small soluble molecules. In biotic aqueous solutions, in the absence of hydrosulfide (SH−) or other thiolate (SR−) ligands, OH− and Cl− dominate © 2013 American Chemical Society
Hg 2 + + L1− + L 2− ⇌ HgL1L 2
(1)
Solvation significantly affects the equilibrium in eq 1. For example, for formation of Hg(OH)SH in the aqueous phase, −623 kcal mol−1 of reactant hydration free energy15 must be overcome. Thus, contributions from hydration significantly destabilize the complex. Moreover, the equilibrium of eq 1 depends on the pH, which imposes a pKa-dependent energetic penalty on forming an anion. Thus, in the condensed phase Received: May 24, 2013 Accepted: June 27, 2013 Published: June 27, 2013 2317
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both solvent and protons compete with Hg2+ for anionic ligands. Quantification of the factors underlying differences in the affinities of diverse partners for Hg2+ is central to understanding biotic and abiotic mercury trafficking in the environment. Metal−ligand binding affinities are qualitatively rationalized in terms of the hard and soft acids and bases (HSAB) theory.16,17 From HSAB theory, the relative affinities of metals for different ligands follow the general pattern of hard metals interacting more strongly with hard ligands and soft metals with soft ligands. Thus, the interaction of Hg2+ (soft) and SH− (soft) is predicted to be stronger than that of Hg2+ and OH− (hard). However, consideration of experimental binding and hydration free energies in the comparison of the binding of two OH− versus two SH− anions to Hg2+, that is Hg(OH)2 + 2SH− ⇌ Hg(SH)2 + 2OH−
* [Hg(SH)2 , Hg(OH)2 ] ΔΔGaq ◦ * [Hg(SH)2 , Hg(OH)2 ] + ΔΔGsolv = ΔΔGgas
* [SH−, OH−] [Hg(SH)2 , Hg(OH)2 ] − 2ΔΔGsolv (3)
The computation of the difference in binding free energy between the formation of distinct neutral complexes can be performed very accurately (see SI Methods). The experimental and theoretical binding free-energy differences are shown in Table 1. Excellent agreement between calculation and experiTable 1. Binding Free Energy Differences from Gas Phase to Aqueous Phase (in kcal mol−1)a,b
(2)
leads to conclusions appearing to contradict HSAB theory. Using the experimental binding free energies of Hg(OH)212 and Hg(SH)2,5 the process in eq 2 favors the RHS (Hg(SH)2 + 2OH−) by 22.8 kcal mol−1 mol. The difference in the hydration between two SH− and two OH− also favors the right side of eq 2 by 65.2 kcal mol−1. Thus, once differences in hydration of 2OH− and 2SH− are removed, the first shell interaction between soft Hg2+ and two hard OH− ions is found to be significantly stronger than that of Hg2+ and two soft SH− ions.18 That is, in the gas phase Hg(OH)2 is expected to be more stable than Hg(SH)2. To reconcile the above considerations and to furnish a theoretical basis for Hg2+ speciation, here we use the B3PW91 density functional19,20 to calculate the aqueous binding free energy (ΔGaq * ) for a series of environmentally relevant chalcogenide and halide ligands (L1, L2 = OH−, SH−, SeH−, F−, Cl−, and Br−). All calculations were carried out with Gaussian 09.21 Geometries were optimized using a correlationconsistent basis set, aug-cc-pVDZ (abbreviated aDZ).22 For S and Cl, modified basis sets that include tight-d functions (i.e., a(D+d)Z) were used.23 Gas-phase contributions to the free energies were computed using B3PW91 augmented with DFTD3 dispersion corrections (with Becke and Johnson damping)24,25 and the correlation-consistent basis set, aug-cc-pVTZ, (abbreviated as aTZ). The corresponding small-core relativistic pseudopotentials (pp), aDZ-pp and aTZ-pp, were used for Hg, Se, and Br.26,27 We systematically investigate hydration effects using gas-phase calculations and a cluster-continuum model28−35 that has been extensively validated for group 12 divalent cations, Cu2+, and several anions.36 Details are given in the Supporting Information (SI). We report calculations for both cationic (HgL+) and neutral species (HgL1L2) but focus on the neutral complexes because these are most relevant to mercury speciation in the biosphere.37 Throughout this study, we first compare the OH− and SH− ligands and then generalize to reveal and rationalize periodic trends of mercury speciation. The calculated difference in aqueous-phase binding free energy between two ligands involves gas-phase and solvation terms (see SI Methods and Figure S1). For example, the difference in stability of Hg(SH)2 and Hg(OH)2 in eq 2 can be expressed as:
species
ΔΔG°gas
H2O
(H2O)2
ΔΔG*aq
exp
Hg(OH)2 Hg(SH)2 Hg(SeH)2 HgF2 HgCl2 HgBr2 Hg(OH)Cl
−30.5 0.0 7.1 5.6 33.0 38.5 0.7
−3.4 0.0 4.4 29.7 31.9 34.4 14.4
7.0 0.0 2.6 41.2 31.9 32.2 18.5
21.0 0.0 −1.5 52.7 32.0 27.8 26.7
22.8 0.0
33.7 27.8 27.9
Difference in free energy for gas-phase complexation (ΔΔGgas ° ) is ° with shown on the left. Stages 1 and 2, which combine ΔΔGgas solvation contributions from one and two water molecules for all species, are shown in the next two columns (labeled H2O and (H2O)2, respectively). The differences in free energy for aqueous-phase * ) computed using two explicit water molecules complexation (ΔΔGaq and a polarizable continuum (Stage 3) and the experimental values are shown in the final two columns. All values were calculated relative to Hg(SH)2. bGas-phase contributions were calculated at the B3PW91D/aTZ-pp/aTZ level of theory. The conventional rigid-rotor vibrational corrections with quasi-anharmonic corrections (see SI Methods) were calculated at the B3PW91/aDZ level of theory, which was the same level of theory used for geometry optimizations. The bulk contributions were calculated with the integral-equation formalism polarizable continuum model28,29 with atomic radii from Bondi38 scaled by 1.1 for all atoms to define the molecular cavity, and the B3PW91/SDD/6-311++G** level of theory (see SI Methods). Highlevel calculations of gas-phase free-energy differences and solvation contributions from varied relative dielectric constants for both the neutral and cationic complexes are included in Table S1 in the SI. a
ment is found in the set of ΔΔG*aq values; the mean signed error is 0.6 kcal mol−1 and the standard deviation of the mean error is 1.2 kcal mol−1 (Figure 1, filled circles). The experimental aqueous phase binding affinity trend of Hg(SH)2 > Hg(OH)2 > HgBr2 ≃ Hg(OH)Cl > HgCl2 is correctly captured by the calculations. The computed binding free energies (ΔGgas ° ) of OH− and SH− to Hg2+ show that, consistent with the above reasoning based solely on experimental numbers, in the gas phase the formation of Hg(OH)2 is ∼30 kcal mol−1 more favorable than that of Hg(SH)2. To understand why the reverse is true in aqueous solution, we examined hydration systematically by transferring the process in eq 1 from the gas phase to bulk aqueous phase in three stages. In Stage 1 and Stage 2, all of the species involved were hydrated with a single and then a second water molecule while remaining in the gas phase (cf. Figures S2, S3, and S4 in the SI). Finally, in Stage 3 the clusters with two explicit water molecules were immersed in continuum solvent. Comparisons of binding free-energy differences in each stage 2318
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ligands in the gas phase but a slightly higher affinity for two SeH− over two SH− in the aqueous phase (Figure 2). The smaller free-energy difference between Hg(SH)2 and Hg(SeH)2 (compared with Hg(OH)2) throughout the stepwise addition of hydration (compare green and black bars in Figure 2) arises from a smaller difference in the interaction strength with water molecules between SeH− and SH− (Tables S3 and S4 in the SI). The comparatively stronger hydroselenide interaction calculated here is consistent with a model of selenium protecting against Hg poisoning39,40 but being limited by eventual depletion.41,42 Recently, Korbas et al.,43 using X-ray absorption spectroscopy (XAS) to estimate Hg−Se species in five archival human brain specimens, speculated that Se depletion by Hg might not apply to that organ. There is a similar affinity ranking for Hg2+ binding to the halides. In the gas phase, HgF2 is calculated to be more stable than HgCl2 by ∼28 kcal mol−1, but in aqueous solution HgCl2 is 20.7 kcal mol−1 more stable than HgF2. Comparing HgBr2 to HgCl2, the hydration switch is again in the same direction but with reduced magnitude. Thus, in both chalcogenides and halides, weaker interactions of local waters with anions of increasing atomic number (softness16,17) led to inversion of the order of Hg2+ affinity for these ligands in the gaseous and aqueous phases. In contrast, the hydration effect is largely absent when comparing chalcogenides to halides in the same period. For example, the gas-phase formation of HgCl2 is ∼33 kcal mol−1 less favorable than that of Hg(SH)2, and this free-energy difference changes little when water is added (red bars, Figure 2). Similar trends hold for comparing Hg(OH)2 to HgF2 and Hg(SeH)2 to HgBr2. The absence of an intergroup hydration effect arises from a cancellation of small differences in the hydration free energies of the anionic reactants and neutral products. The general periodic trends revealed by the present calculations are shown schematically in Figure 3. An important practical question concerns possible modulation of the above chemistry arising from the availability of
Figure 1. Experimental and theoretical binding free-energy differences. The binding free-energy differences between neutral complexes are calculated in the gas phase (ΔΔG°gas), Stage 1 (H2O), Stage 2 * ). Linear fits for the four data sets are ((H2O)2), and Stage 3 (ΔΔGaq shown. The linear fit for the neutral complexes yields a slope [intercept] (R2) of 1.03 [−0.12] (0.99), indicating excellent agreement with the experimental binding free-energy differences. See Figure S5 in the SI for a similar plot including the cationic complexes.
with experimental binding free-energy differences are shown in Figure 1. After adding as few as two water molecules to each gas-phase species (Stage 2), the binding affinity switches from favoring Hg(OH)2 to favoring Hg(SH)2 (Figure 2). The driver of this
Figure 2. Differences in binding free energy relative to Hg(SH)2. The ° ) is difference in free energy for gas-phase complexation (ΔΔGgas shown on the left. The differences in free energy including one and two water molecules (Stages 1 and 2, respectively) are shown in the middle two sets of columns. The rightmost bars are computed using two explicit water molecules and a polarizable continuum (Stage 3). Also shown are optimized geometries for H2O·SH− and (H2O)2·SH− clusters rendered with VMD.44 See Table 1 for values.
Figure 3. Periodic trends in the formation of neutral and cationic complexes of Hg2+ and anionic ligands (L−). The cationic species formed from Hg2+ and one L− are on the left. Neutral species (HgL2) formed from Hg2+ and two identical anionic ligands (L−) are on the right. Gas-phase (black) and aqueous-phase (red) binding free energies become more favorable in the direction of the arrow. Each pair of arrows is drawn from the same origin. The length of each arrow reflects the binding free-energy difference. Each vertical arrow represents the intragroup average (hydrochalcogenides or halides) of the binding free-energy difference between the second and the fourth rows. Each horizontal arrow represents the intergroup average (rows two to four) of the binding free-energy difference between the hydrochalcogenides and the halides. Hydration contributions can be qualitatively assessed by subtracting the arrows as vectors. See Figure S6 in the SI for detailed energetics and atomic charges.
switch is the much larger interaction energy between OH− and the local H2O molecules compared with that of SH−. The two water molecules provide the majority (∼38 kcal mol−1) of the ∼52 kcal mol−1 switch in relative binding free energy between Hg(SH)2 and Hg(OH)2 on transferring from the gas phase to aqueous solution. Including continuum solvation and increasing the relative dielectric to the value of liquid water (ε = 78.4) further stabilizes Hg(SH)2 relative to Hg(OH)2, in excellent agreement with the experimental aqueous binding free-energy difference of 22.8 kcal mol−1 (Table 1). Furthermore, Hg2+ has a slightly higher calculated affinity for two SH− over two SeH− 2319
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HgSH+ and SH−. In terms of HSAB theory, the HgOH+ complex appears harder and thus more reactive than the HgSH+ complex. The same trend is observed comparing the SH− and SeH− ligands. Indeed, recent calculations49 using highlevel calculations with the Dirac-exact treatment of relativistic effects found that dissociation of the second ligand from Hg(SH)2 required 12.3 kcal mol−1 more energy than Hg(SeH)2 in the gas phase.50 The binding free energy of HgL+ is generally found to be around one-half of the binding free energy of HgL2 (Table S5 in the SI). This additivity may be expected naively, but it masks the large phase dependence of the energetics that is related to the reactivity of the complex. Furthermore, the influence of the bound ligands (see atomic partial charges in Figure S6 in the SI) will clearly affect the transformation of Hg2+ species.51 Understanding the factors that drive mercury speciation is critical for alleviating its damaging effects on the environment and on human health. We provide here the first step toward understanding the quantitative physicochemical underpinnings of the binding free-energy differences between environmentally relevant mercury complexes. Our examination of the experimental binding and hydration free energies reveals a surprising increase in local interaction strength between Hg2+ and two negatively charged ions with increasing hardness of the ions. We verified this observation using quantum chemical calculations and showed how differences in proton affinity and interactions with a very small number of local water molecules recover the experimentally well-known increasing affinity for softer ligands consistent with HSAB concepts. Analysis of the change in binding free energy from binding one ligand to two ligands allowed the source of the phase dependence to be identified as large differences in reactivity of the HgL+ complexes. The present analytical framework and systematic treatment of hydration provides a molecular explanation of the experimentally observed, robust preference of Hg2+ for soft ligands such as thiols. This framework is applicable to interactions of organic mercurials and of other metal cations52 with inorganic and organic anionic ligands, including those of cysteine and selenocysteine essential to living organisms.
protons.45 To examine this, we added two protons to each side of eq 2, that is Hg(OH)2 + 2H 2S ⇌ Hg(SH)2 + 2H 2O
(4)
In the gas phase (no water molecules), the calculated binding free-energy difference between Hg(OH)2 and Hg(SH)2 and the experimental basicities46 of OH− (383.7 kcal mol−1) and SH− (344.9 kcal mol−1) yield a free-energy change for eq 4 of −47.1 kcal mol−1. Hence, in low-dielectric environments, such as in the hydrophobic cores of proteins, the energetic contributions from proton binding mimic those of hydration, leading to Hg(SH)2 being more stable than Hg(OH)2. Moreover, enhanced stability of neutral mercury complexes (HgL1L2) buried within low dielectric media, such as in natural organic matter and biological macromolecules, may drive bioaccumulation. More generally, we can compare the periodic trends in the binding of one Hg2+ to the binding of two H+ by two anionic ligands 2H+ + 2L− ⇌ 2HL
(5) 2+
In the gas phase, similar to binding Hg to form the neutral complexes (HgL2), the binding free energy of two protons by two anions (2HL) becomes more favorable with increasing hardness.47 Furthermore, in the aqueous phase, contributions from hydration again strengthen the interaction between the anion and the proton with increasing softness of the anion. For example, comparing OH− to SH−, the difference in free energy for binding H+ is reduced from 38.8 kcal mol−1 in the gas phase to 9.5 kcal mol−1 in the aqueous phase (calculated from ΔpKa = 7). Most interestingly, the free-energy difference (gas phase and aqueous phase) between hydrochalcogenides and halides of the same period is very similar for binding two H+ compared with the binding of one Hg2+ (Figure S6 in the SI). Thus, the hardness and softness of the general acid do not appear to influence the relative basicity across groups. We can also consider the effect of pH. For the process in eq 4 occurring in high dielectric environments below pH 7, the products are favored over the reactants by 41.8 kcal mol−1.48 As the pH increases from 7 to 14, the free-energy cost of creating 2 OH− is reduced by 19.0 kcal mol−1 relative to 2 SH− yielding, again, the free-energy difference of −22.8 kcal mol−1 (Table 1). As noted, the gas-phase binding affinity of Hg2+ for two L− to form neutral HgL2 complexes increases within groups with hardness (Br− < Cl− < F−; SeH− < SH− < OH−), which is opposite of what might have been expected from HSAB principles. However, after including hydration contributions, the observed binding affinities in aqueous phase follow HSAB, increasing with the softness of L− (F− < Cl− < Br−; OH− < SH− < SeH−). In contrast, the periodic trends for HgL+ formation in both the gaseous and aqueous phases are the same as those for HgL2 in the aqueous phase (Figure 3). Thus, the phase dependence of the HgL2 binding free-energy order is associated with binding the second ligand. For both chalcogens and halogens, there is an apparent cooperative strengthening (weakening) of the HgL+ interaction with L− as the ligand becomes harder (softer), and the reactivity of the metal binding site in HgL+ depends strongly on L−. For example, because the formation of HgOH+ is less favorable than HgSH+ in both gaseous and aqueous phases, the first-shell interaction between Hg2+ and SH− is slightly stronger (∼2 kcal mol−1) than that of Hg2+ and OH−. In contrast, the first-shell interaction between HgOH+ and OH− is ∼33 kcal mol−1 stronger than that between
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ASSOCIATED CONTENT
S Supporting Information *
Detailed methods, gas-phase atomic charges, tabulated energetics, and Cartesian coordinates of all molecules. Additional comparisons of gas-phase energetics between high-level calculations and DFT and more detailed comparisons between experimental and calculated hydration and binding free energies are also included. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was conducted jointly at the University of Tennessee, Knoxville and Oak Ridge National Laboratory (ORNL) and was supported by the grant DE-SC0004895 from the U.S. Department of Energy (DOE), Office of Science, Office of Biological and Environmental Research, Subsurface 2320
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Biogeochemical Research Program. ORNL is managed by UTBattelle, LLC for the U.S. DOE under contract DE-AC0500OR22725. This research used resources of the National Energy Research Scientific Computing Center, which is supported by the Office of Science of the U.S. Department of Energy.
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The Journal of Physical Chemistry Letters
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against Methylmercury Toxicity. Biol. Trace Elem. Res. 2007, 119, 255−268. (42) Lobanov, A. V.; Hatfield, D. L.; Gladyshev, V. N. Eukaryotic Selenoproteins and Selenoproteomes. Biochim. Biophys. Acta 2009, 1790, 1424−1428. (43) Korbas, M.; O’Donoghue, J. L.; Watson, G. E.; Pickering, I. J.; Singh, S. P.; Myers, G. J.; Clarkson, T. W.; George, G. N. The Chemical Nature of Mercury in Human Brain Following Poisoning or Environmental Exposure. ACS Chem. Neurosci. 2010, 1, 810−818. (44) Humphrey, W.; Dalke, A.; Schulten, K. VMD - Visual Molecular Dynamics. J. Molec. Graphics 1996, 14, 33−38. (45) Rao, L.; Cui, Q.; Xu, X. Electronic Properties and Desolvation Penalties of Metal Ions Plus Protein Electrostatics Dictate the Metal Binding Affinity and Selectivity in the Copper Efflux Regulator. J. Am. Chem. Soc. 2010, 132, 18092−18102. (46) Burgess, D. In NIST Chemistry WebBook, NIST Standard Reference Database Number 69; Linstrom, P., Mallard, W., Eds.; National Institute of Standards and Technology: Gaithersburg MD, retrieved 2012. (47) The experimental free energies of binding one H+ to the hydrochalcogenides are −383.7, −344.9, and −335.2 kcal mol−1 for OH−, SH−, and SeH−, respectively, and those for the halides are −365.5, −328.1, and −318.3 kcal mol−1 for F−, Cl−, and Br−, respectively.46 (48) The experimental free-energy difference for binding Hg2+ to the two ligands (−22.8 kcal mol−1) combined with that of binding 2H+ to the ligands (−19.0 kcal mol−1 calculated from ΔpKa = 7 pK units per ligand). (49) Zou, W.; Filatov, M.; Atwood, D.; Cremer, D. Removal of Mercury from the Environment: A Quantum-Chemical Study with the Normalized Elimination of the Small Component Method. Inorg. Chem. 2013, 52, 2497−2504. (50) The energies of dissociating SH− from Hg(SH)2 and SeH− from Hg(SeH)2 reported in ref 49 are around 8 and 6 kcal mol−1 stronger, respectively, than those determined from Table S2 in the SI. Thus, the difference between the strength of those bonds reported here is in reasonable agreement with ref 49. (51) For example, in the addition of a carbanion to HgCl2 or Hg(SH)2, which may be central to mercury methylation,6 the larger partial atomic charge on the Hg atom in HgCl2 compared with Hg(SH)2 (Figure S6 in the SI) would enhance the formation of CH3HgCl2− compared with CH3Hg(SH)2−. (52) Other transition metals such as Fe2+, for which the spin state may depend on the ligand bound, will require more sophisticated analysis.55 (53) Fawcett, W. R. Thermodynamic Parameters for the Solvation of Monatomic Ions in Water. J. Phys. Chem. B 1999, 103, 11181−11185. (54) Kelly, C. P.; Cramer, C. J.; Truhlar, D. G. Aqueous Solvation Free Energies of Ions and Ion-Water Clusters Based on an Accurate Value for the Absolute Aqueous Solvation Free Energy of the Proton. J. Phys. Chem. B 2006, 110, 16066−16081. (55) Noodleman, L.; Han, W.-G. Structure, Redox, pKa, Spin. A Golden Tetrad for Understanding Metalloenzyme Energetics and Reaction Pathways. J. Biol. Inorg. Chem. 2006, 11, 674−694.
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