1

Supporting Information Appendix Pokrovski et al. Sulfur radical species form gold deposits on Earth

This file contains:

- SI Text,

- SI Tables S1 to S5,

- SI Figs. S1 to S10

- SI references.

2

Supplementary Text

Experimental systems. Because gold solubility is a complex function of sulfur speciation, redox

potential (fO2) and acidity (pH) of the fluid phase (1-3), the choice of model experimental

systems reflecting natural ore-bearing fluids and allowing control on these parameters is crucial.

Three types of aqueous S-bearing solutions (0.1–8.0 wt% S) used in this study satisfy this choice:

i) thiosulfate (K2S2O3 or Na2S2O3), ii) elemental sulfur (S), and iii) H2O-KCl solutions saturated

with the pyrite-pyrrhotite-magnetite (PPM) mineral assemblage (Tables S1 and S2). Acidity

(3<pH<8) was adjusted by HCl and NaOH or KOH in thiosulfate and sulfur experiments or was

buffered by an excess of quartz-muscovite-potassium feldspar (QMK) mineral assemblage in

PPM runs. Thus, these model systems provide acidity and redox buffering of the fluid phase

through equilibria between sulfate and hydrogen sulfide (±SO2 above 400°C), produced by

breakdown of thiosulfate and sulfur in aqueous solution above 150°C (4-7), and by equilibria

among the Fe-sulfide and oxide minerals yielding H2S(±SO2) in the PPM system (1-3) according

to the following reactions:

S2O32-

+ H2O = SO42-

+ H2S (1)

4 S + 4 H2O = 3 H2S + SO42-

+ 2 H+ (2)

H2S + 2 O2 = SO42-

+ 2 H+ (3)

SO42-

+ H+ = HSO4

- (4)

0.5 Fe3O4 + 2 H2S = 0.5 FeS2 + FeS + 2 H2O (5)

0.5 Fe3O4 + 1.5 FeS2 = 3 FeS + O2 (6)

In addition to these major S forms, thiosulfate and sulfur solutions (S >0.5 wt%) contain minor

amounts of molecular sulfur (Sn0) and polysulfides (Sn

2-) below ~300°C while at higher

temperatures S3- forms in significant amounts (0.001–0.2 m, depending on T, pH, and S content)

at the expense of those species and sulfide and sulfate [see refs 5-7 for details about sulfur

speciation in these systems]. Our runs were conducted at >200°C in thiosulfate and sulfur systems

and >300°C in PPM systems; these temperatures are high enough to allow the system to reach

both sulfur redox and fluid-mineral equilibrium within practical run durations, from few hours to

days (4, 7, 8). The equilibrium amounts of all S species including S3-, and the resulting pH and

redox potential at the run temperatures may accurately be calculated using the available

thermodynamic data (Table S4); this allows us to sort out the effect of S3- from that of H2S, pH,

and fO2 on Au solubility and speciation (see below).

3

In situ X-ray absorption spectroscopy (XAS) measurements. XAS spectra (including the X-

ray absorption near-edge structure region or XANES, and the extended X-ray absorption fine

structure region or EXAFS) on Au-bearing aqueous solutions were collected in both transmission

and fluorescence mode at Au L3-edge at BM30b-FAME beamline at the European Synchrotron

Radiation Facility, ESRF, Grenoble, France (9). Energy was selected using a Si(220) double-

crystal monochromator with dynamic sagittal focusing (10), yielding a beam spot on the sample

of 300 m horizontal × 200 m vertical and an X-ray flux of 1012

photons/s, allowing acquisition

of good quality EXAFS spectra at Au concentrations as low as 10-3

molal. Fluorescence spectra

were collected in the right-angle geometry using a 30-element solid-state germanium detector.

Energy calibration of each scan was checked using a gold metal foil whose L3-edge energy was

set to 11,919.0 eV as the maximum of the spectrum first derivative. Experiments were carried out

using a hydrothermal apparatus developed at the Néel Institute (11) and described in detail

elsewhere (12, 13). Most runs were conducted at pressures of 600±50 bar and temperatures from

200 to 450°C (±5°C) by allowing a piece of gold to react with a thiosulfate- or sulfur-bearing

solution in the glassy-carbon inner cell (Table S1), and following established procedures (4).

EXAFS data analysis was performed with the Athena and Artemis programs (14) according to

recommended protocols (15). Dissolved Au concentrations were determined from the amplitude

of the absorption edge height of the Au L3-edge transmission spectra using the classical X-ray

absorption relation (4, 12). Gold-sulfur-fluid equilibrium was attained within a few hours at a

given T as shown by the constancy of Au measured concentrations in multiple XAS scans and

recent in-situ Raman spectroscopy studies of similar systems (5-7). No changes in the spectra,

which might arise from X-ray beam induced photochemical phenomena or reactions with the cell

walls, were detected; this is in agreement with the stability of Au-sulfur species in well-buffered

systems (4) and the known chemical inertness of the glassy-carbon cell material (13).

Solubility measurements in a hydrothermal reactor. The XAS experiments above were

complemented by batch-reactor measurements of gold solubility at selected T-P in similar

aqueous thiosulfate solutions to check for the validity of spectroscopic determinations, and in

H2O-S-salt and PPM-saturated solutions to extend the data to more acidic pH and lower S3- and

Au concentrations (<10-3

m) not easily accessible by XAS (Table S2). Runs were conducted using

a Coretest hydrothermal reactor (16) equipped with a flexible titanium or gold cell (~100 mL) and

a rapid fluid extraction design allowing periodic samples of small portions of the fluid (2 mL) by

avoiding solute loss or degassing (17). Chemical treatment and analyses of the sampled fluid were

performed according to established protocols for S-rich systems (17). Gold concentrations were

4

analyzed in aqua-regia treated samples by ICP-AES (quantification limit ~10 ppb Au) or ICP-MS

(quantification limit ~ 0.1 ppb Au), total S contents by ICP-AES or ion chromatography after

oxidation to sulfate (>1 ppm S), and H2S (trapped as CdS) and total reduced sulfur (H2S, S3-, Sn

2-,

SO2) by iodometric titration (>10 ppm S). Steady-state Au and sulfur species concentrations

corresponding to chemical equilibrium were attained within a couple of days at T > 350°C.

First-principles molecular dynamics (FPMD) modeling. The simulations were carried out with

the CP2K code package (18) in the framework of the density functional theory (DFT) as

implemented in the QUICKSTEP module. The BLYP exchange-correlation functional (19, 20)

was used in combination with a Van der Waals correction DFT-D3 (21). A plane-wave cutoff of

600 Ry for the electronic density and a triple-zeta valence doubly polarizable (TZV2P) basis set

were chosen for all elements except Au, which was described by means of a double-zeta valence

polarizable (DZVP) basis set optimized for molecular geometries (22). The interaction between

the ionic cores and the valence electrons was treated with pseudo-potentials (23). In systems with

an odd number of electrons, spin polarization was taken into account. The Born-Oppenheimer

MD was carried out in the NVT ensemble with a time step of 0.5 fs, and the system was

thermostated at 400°C by means of a stochastic velocity rescaling algorithm (24) with a time

constant of 100 fs. The solvent density was fixed to 0.68 g/cm3, which corresponds to a pressure

of ~600 bars for heavy water (25), and some water molecules were then replaced by different Au-

S complexes, assuming equal partial molar volumes for S, HS- and H2O, and neglecting the

partial molar volume of Au+. For hydrogen, the mass of the heavy isotope deuterium was chosen,

which allows a larger time step for the integration of the equation of motion without affecting

significantly the chemistry of bonding. The cubic simulation box contained at least 126 water

molecules, and periodic boundary conditions were applied. Simulations from 10 to 50 ps duration

time were used to estimate the stability of different Au-S species; in addition they served to

calculate EXAFS spectra for the stable hydrated complexes Au(HS)S3-, Au(HS)S3

2-, Au(S3)2

-,

Au(HS)2-, and AuHS, and to compute free energy profiles for ligand exchange reactions (see

below). Note that the neutral gold hydrogensulfide complexes, AuHS(H2S) and AuHS(H2S)3,

previously suggested in some solubility studies (4, 26), were found to be unstable within 10 ps of

simulation time, breaking down to AuHS and free H2S molecules.

FPMD simulated EXAFS spectra of Au-S species. For each Au-S complex, an average EXAFS

spectrum was computed from a series of 100 snapshots extracted from the MD trajectories using

the FEFF8 code (27) as detailed elsewhere (28). For each snapshot, an individual EXAFS

5

spectrum includes contributions from single- and multiple-scattering paths whose maximal

number and path length were chosen to ensure good convergence. The scattering potentials were

obtained in the muffin-tin approximation, but it was systematically checked that the use of ab-

initio self-consistent field scheme led to results identical within errors. Since the Au-S bond

length in the DFT calculations is slightly larger than the experimental values, the EXAFS spectra

were computed from MD trajectories by rescaling all atomic coordinates by a factor of 0.96. The

amplitude reduction factor S02 was set to 0.83 as obtained experimentally (Table S1), leaving an

energy shift ΔE as the only variable parameter adjusted to minimize the mean square error

between the experimental and calculated spectra (Table S5). For all complexes with two sulfur

ligands, a good match of the experimental EXAFS amplitudes in S3-–rich solutions (where

Au(HS)S3- is dominant, see below) with comparable mean square errors was found; in contrast,

the mismatch is greater for AuHS, due to the smaller amplitude of the simulated spectrum (Fig.

S4). Minor differences in EXAFS amplitudes, persistent for all complexes at high k values (>10

Å-1

), may be due to small inaccuracies in the simulations and/or the noise intrinsic to

experimental EXAFS spectra of the fluid phase exhibiting convection in the high T-P cell.

Overall, the results from simulated MD-EXAFS spectra provide a strong support for least-square

EXAFS fits to the experimental spectra (Table S1) based on the classical EXAFS equation, which

might fail in highly disordered dynamic systems (28). The good agreement between the two

approaches indicates that disorder is not an issue for Au-S complexes with strong covalent bonds,

as also confirmed by the consistently low squared Debye-Waller factors (~0.003 Å2, Table S1)

across the whole range of solution compositions and temperatures.

FPMD simulated ligand exchange reactions. The free energy change associated with the ligand

exchange reaction (R1) in aqueous solution (main text) was computed via the potential of mean

force (29), obtained from two sets of simulations with a restraint on the reaction coordinate for

the half reactions Au(HS)2- = AuHS + HS

- (R1a) and Au(HS)S3

- = AuHS + S3

- (R1b), which are

accompanied by changes in their Gibbs free energy ΔG1a and ΔG1b, respectively; the free energy

change of the complete exchange reaction (R1) is given by ΔG = ΔG1a – ΔG1b. For reaction

(R1a), 11 MD runs of 1.25 ps were performed, with parabolic restraints on the Au-S distance as

the reaction coordinate and with target values from Rmin = 2 Å to Rmax = 5 Å. For reaction (R1b),

the distance between Au and the S atom occupying the middle position in the S3- ligand was

chosen as the reaction coordinate owing to computational convenience, and 13 MD runs were

performed with restraints on this distance ranging from 3.4 to 7.0 Å. The different choice of

reaction coordinates for the two half reactions is accounted for by including a configurational

6

entropy term (see below). For each MD run, the difference between the target value of the

reaction coordinate and its value averaged over the last picosecond allows the mean force acting

on the reaction coordinate to be calculated. The obtained mean forces were interpolated over the

range of distances by means of Akima splines (30), yielding a smooth function f(r). The free

energy profile (Fig. S5) associated with each of the half reactions was calculated as

max

( ) ( )R

rG r f r dr (7)

The difference of G(r) at the minimum of the energy profiles of the two half reactions

corresponds to an energy change of reaction (R1) of 10.9 ± 12.8 kJ/mol at 400°C (or log10KR1

(uncorrected) = -0.85±0.99; 2 SD), ignoring a contribution of configurational entropy (S1a and S1b)

related to the different definition of the Au-S pair coordinate in the two half-reactions (see

above). This entropy contribution to reaction (R1) Gibbs free energy, T(S1a – S1b), was estimated

from the effective volume, Veff

, characterizing the accessible space for S around Au for each half-

reaction (i) as:

0 22

00

0

( )ln( ) ln[1 / ( 4 exp( ))],( 1,2)

2

effi i i

i

V k r rS R R V dr r i

V RT

(8),

where V0 is an arbitrary reference volume introduced for dimensional reasons (it cancels in the

final result for the equilibrium constant), R is the ideal gas constant, ki and ri0 are regression

parameters resulting from a parabolic fit of the region of the energy profiles minima (Fig. S5) and

which account for the bond stiffness and the equilibrium distance, respectively. Equation (8)

yields Veff

= 14.5 and 60.2 Å3 for half-reactions (R1a) and (R1b), respectively, indicating that the

configurational entropy favors Au(HS)S3- over Au(HS)2

-. The final equilibrium constant of

reaction (R1) is thus log10KR1 = log10KR1(uncorrected)×Veff

(R1a)/Veff

(R1a) = -0.23±1.00 (2 SD).

This value is identical within errors to that derived from the thermodynamic analysis of gold

solubility experiments as described below.

Thermodynamic data sources and equations of state. Gold and sulfur solubility and speciation

in the fluid were modelled using available robust thermodynamic data (Table S4), and the results

were compared with the XAS and Coretest measured Au solubility. Calculations were performed

using the HCh software package and associated Unitherm database, allowing chemical

equilibrium simulations in multicomponent fluid-mineral systems based on the minimization of

the Gibbs free energy of the system (31), and accounting for non-ideality of the fluid using the

extended Debye-Hückel equation (32). The thermodynamic properties of the minerals, major

fluid components, and most sulfur aqueous species were taken from the updated SUPCRT (33)

7

and JANAF (34) databases, complemented by recent experimental data for some ion pairs and

ionic sulfur forms (35-37), including S3- (7) using the revised HKF (Helgeson-Kirkham-Flowers)

equation of state (33, 38, 39). These thermodynamic data sources were judged to be reliable

because they are either based on a large set of experimental data or on well-established

correlations among HKF parameters, allowing robust extrapolations of the resulting Gibbs free

energies over a wide T-P range, in particular for ionic species. The thermodynamic properties of

the molecular sulfur aqueous forms, H2S, SO2 and H2 and O2, were adopted according to a recent

model for aqueous non-electrolytes (40), which allows a more accurate description over a wide T-

P range than that given by the HKF model based on a more limited dataset (33). Noteworthy, the

thermodynamic data from (40) were also used in derivation of the thermodynamic properties of

Au species (see below), and thus were chosen here to maintain thermodynamic consistency. It

should be stressed, however, that uncertainties on the calculated acidity, fO2 and major S species

concentrations related to the choice of a particular data source are minor within the experimental

T-P range because of the S redox balance and acid-base constraints imposed in our thiosulfate,

sulfur and iron sulfide systems (4-7).

The thermodynamic properties of the Au+ cation, and its hydrogen sulfide (AuHS,

Au(HS)2-) and hydroxide (AuOH) species were taken from a recent compilation (3) of their HKF

parameters based on available experimental data in reduced or S-poor systems in which S3- is

negligible; these data agree with one another within better than 10 kJ/mol in terms of the species

Gibbs free energy within the investigated T-P range. The only exception is the di-chloride species

(AuCl2-) for which there is more substantial disagreement among the major experimental data

sources (3, 41); consequently we have adopted an average value of its Gibbs free energy from (3)

and (41) at each T-P point. Species such as AuCl and Au(OH)2- tentatively suggested in recent

compilations (e.g., ref. 3) were ignored in the present modeling both because their existence is not

explicitly proven by experimental data at elevated temperatures (e.g., ref. 41) and their HKF

parameters are based on estimations at ambient conditions and thus are subject to large errors at

elevated temperatures. A recently published alternative set of HKF parameters for the Au-Cl-OH-

HS species (42) based on a more limited set of experimental Au solubility data than (3) was found

to be in agreement with our choice above, yielding same within errors Gibbs free energies of Au

mono-hydroxide, hydrogen sulfide and di-chloride species over the experimental T-P range.

Another species, the neutral bis-hydrogen sulfide Au(HS)H2S, was tentatively suggested as an

alternative to AuHS and Au(HS)2- in some spectroscopic and solubility studies (4, 43) to explain

elevated Au solubilities (10-4

-10-3

m) in acidic S-H2O-NaCl-NaHSO4 solutions above 250°C

(>0.1m H2S, pH <4). However, our present measurements in similar systems using the Coretest

8

reactor (Table S2) report Au solubilities (10-6

-10-5

m Au) 1 to 2 orders of magnitude lower than

the detection limit of the XAS technique (4). Furthermore, our analysis of solubility data from

(43) is consistent with AuHS and Au(HS)2- within the experimental data scatter. If Au(HS)H2S

does form at our experimental conditions, its contribution to Au solubility is expected to be less

than 10-5

m, which is 1 to 2 orders of magnitude lower than the measured Au solubilities in S3-–

rich experiments from this study; therefore, this species was ignored in further analyses. Note that

among the species discussed above, Au(HS)2- is by far the major complex in most experimental

systems investigated in this study, so that uncertainties stemming from the other complexes are

minor.

Thermodynamic analysis of Au solubility. The systematic underestimation of the calculated Au

solubilities, using the thermodynamic data for the Au-HS-Cl-OH species above, compared to the

measured values of total dissolved Au, in experiments in which S3- concentrations exceed those of

HS- (Figs 1 and S1), provides direct evidence for the presence, in addition to those species, of

new Au complexes with the S3- ligand. The excess of Au solubility was thus modeled using a set

of species of various charge and stoichiometry formed between Au+ and S3

-, H2S and/or HS

-, and

using the constraints from XAS and FPMD results, which suggest the dominant formation of

species in which Au+ is coordinated with two S ligands. Consequently, complexes containing a

single S ligand and/or OH- or H2O (e.g., AuOHS3

-, AuS3

-) or those with more than 2 S ligands

directly coordinated to Au (e.g., AuHS(H2S)3, ref. 26) were ignored. Similarly, poly-nuclear

species having Au-(S-S)n-Au bonds (44) or Au nano-particles that may be stabilized by

surrounding thiol ligands in solution at low temperatures (45, 46) were excluded on the basis of i)

the XAS spectra showing no Au-Au signal, and ii) the solution thermodynamics suggesting that

polymeric species in aqueous solution are not favored at elevated temperatures owing to the

increasing thermal disorder.

Consequently, only species of L-Au-L stoichiometry (where L is S3-, HS

- or H2S) and

electrical charge between 0 and -3, which is typical for Au+ complexes with most organic and

inorganic ligands (3, 47), were considered. The choice among the species was performed using

two approaches based on the fundamental thermodynamics mass action law, postulating that a

stability constant (or standard molal Gibbs free energy) of a species at a given T and P is

independent of the system chemical composition. The first approach is thus based on the

statistically best match of the ensemble of Au solubility data points at each T and P with least

variation of the standard Gibbs free energy, G°T,P, of the species, and using the OptimA computer

program (48) linked to HCh (31). The different single species and their pairs were tested on the

9

basis of i) statistical criteria including least-square deviation between calculated and measured

solubility values, ii) data points weight and scatter of G°T,P values at each experimental T and P,

and iii) consistency in trends of the computed stability constants as a function of T and P. Among

the single-species sets, Au(HS)S3- was found to provide the statistically best match. Most two-

species models did not show convergence or yielded too large errors in the final G°T,P values

and/or their inconsistent T-trends. Nevertheless, caution should be taken when relying on such

statistical models applied to small experimental data sets (10 to 15 points per temperature, Table

S3). Consequently, to further support our model, a complementary approach based on an analysis

of individual stoichiometric solubility reactions was used. For example, if Au(HS)S3- is the

species accounting for the Au excess solubility, which forms according to the reaction (R2)

Au(s) + H2S(aq) + S3- = Au(HS)S3

- + 0.5 H2(aq), R2 (9),

the following relationship holds at a given T and P:

log m(Au(HS)S3-) = log KR2 + log m(S3

-) + log m(H2S) – 0.5 log m(H2), (10)

where m is molality of each indicated reaction constituent, m(Au(HS)S3-) is the difference

between measured solubility (Auexp) and calculated solubility (Aucalc) as the sum of the

concentrations of all non-S3- species of Au formed with hydrogen sulfide (+ chloride +

hydroxide) chosen as discussed above: m(Au(HS)S3-) = m(Auexp) – m(Aucalc), and KR2 is the

thermodynamic reaction constant. Consequently, a plot in the coordinates [log m(Auexp – Aucalc)]

vs [log m(S3-) + log m(H2S) – 0.5 log m(H2)] should have a slope of 1 and an intercept equal to

log KR2. Note that the activity coefficients of the -1 charged species Au(HS)S3- and S3

- are

cancelled (32) and, thus, molality may directly be used in such equations. Only data points

yielding significant positive difference were included in the analysis. It can be seen in Fig. S6 that

at all temperatures, the slope is close to 1 within errors, confirming the dominant formation of

Au(HS)S3-, and ruling out significant contributions from other species. Similar analyses were

conducted for other species of different stoichiometry and electric charge, but none of them could

have matched their corresponding slopes better than Au(HS)S3-. Furthermore, both approaches

provide identical within errors values of G°T,P of Au(HS)S3-.

The generated G°T,P values of Au(HS)S3- at each experimental T-P point, combined with

the thermodynamic properties of Au(HS)2-, HS

- and S3

- from the sources reported in Table S4,

allow the equilibrium constant KR1 of the isocoulombic exchange reaction (R1, main text) to be

calculated. This constant is close to 1 within errors between 300 and 500°C (Table S3), consistent

with the similar affinity of HS- and S3

- for Au

+ as also inferred from our FPMD modeling further

supporting our speciation scheme. Following the general properties of isocoulombic reactions,

implying that reaction thermodynamics is constant over a wide T-P range (3), this KR1 value was

10

entered in the Unitherm database (31) and used for Au solubility and speciation calculations over

the wide range of crustal conditions (Figs 2, 3, S7-S10).

Geochemical modeling and estimation of the effect of S3- on the speciation of other metals.

Calculations of fluid-mineral equilibria involving gold in model systems, pertinent to geological

settings of magmatic-hydrothermal porphyry-epithermal (Cu-Au-Mo) and metamorphic-

sedimentary (orogenic, intrusion related and Carlin) Au deposits, were performed for typical

mineralogy and fluid compositions inferred from numerous existing studies (see main text). The

common metals accompanying Au in the fluids such as Fe, Cu, Zn, and Ag were also included in

the modeling (49-51). The modeling was conducted using the HCh package and the Unitherm

database allowing chemical equilibrium calculations over a wide range of geological fluids (31,

48). The data sources for the thermodynamic properties of minerals and aqueous OH-Cl-HS

species are reported in Table S4. These sets of data arise from a large amount of experimental

studies, which are in good agreement one with another and are described by robust equations of

state such as the HKF and Ryzhenko-Bryzgalin (RB) models (48-51) enabling reasonable

extrapolations to temperatures of 700°C and pressures of 10 kbar.

In addition, the effect of S3- on the solubility of Cu, Ag and Zn was estimated using HS

- -

S3- ligand exchange reactions analogous to R1 (main text) for Au and assuming their equilibrium

constants to be equal to 1 over the whole T-P range:

(Cu,Ag)(HS)2- + S3

- = (Cu,Ag)(HS)S3

- + HS

- (11),

Zn(HS)2 + S3- = Zn(HS)S3 + HS

- (12)

It was found that Cu(HS)S3- and Zn(HS)S3 are negligible (<1% of total dissolved metal)

compared to the dominant hydrogen sulfide and chloride species of both metals in the magmatic-

hydrothermal and metamorphic settings considered in this study in Fig. 3. In contrast, while

Ag(HS)S3- is minor (<5% of total Ag, for the conditions of Fig. 3A) in saline acidic porphyry-

epithermal fluids dominated by AgCl2-, it may be a major Ag species in Cl-poor and S-rich high-

temperature (>500°C) metamorphic fluids similar to Au(HS)S3- in Fig. 3B. Similar estimations

for other metals (Pt, Mo) and metalloids are not possible at present owing to paucity of data on

their hydrogen sulfide complexes at elevated temperatures.

Uncertainties of gold solubility predictions. The uncertainties of our geochemical modeling of

Au solubility stem from experimental/analytical errors in Au solubility determination, those of the

reaction (R1) equilibrium constant derived in this study, and thermodynamic properties of S3-

itself and other major S species (in particular H2S). These sources of errors are not additive

11

because dependent one on another (e.g., the value of KR1 is dependent not only on Au measured

concentration, but also on the choice of the standard Gibbs free energies of the other reaction

constituents, necessary to calculate their equilibrium concentrations), and thus may be partially

cancelled or potentially amplified. Consequently, care was taken to accurately evaluate these

uncertainties via error propagation analyses.

Errors of experimental Au solubility measurements are independent of thermodynamic

models; they stem from scatter among multiple data points and analytical uncertainties, as was

discussed and evaluated in previous studies (4, 17). Except few data points, they usually do not

exceed a factor of 2 (~0.3 log unit) in absolute Au concentration (Tables S1 and S2).

Uncertainties of S3- concentration estimation were evaluated in a recent study (7) and do not

exceed 0.2 log unit within the experimental T-P range (200-500°C, <1 kbar). The reported values

of the reaction (R1) stability constant also include uncertainties related to calculations of

equilibrium concentrations of Au(HS)2- and H2S (and its ionized form, HS

-). These calculations

are based on numerous experimental data and their regressions obtained at T <500°C (see refs 3

and 40), which are thermodynamically consistent. For example, the stability constants of Au-HS-

Cl-OH species used in this study were derived in (3) from published raw experimental data using

the thermodynamic properties of H2S and other non-volatile electrolytes from (40); the same data

sources were used to generate the stability constant of Au(HS)S3-. Thus, errors related to the

choice of data sources for different types of species are cancelled. Our analysis suggests that

overall errors in Au solubility predictions in our model geochemical systems (e.g., Fig. 2 and 3)

do not exceed 0.5 log unit at T <500°C and P <1 kbar.

Above 500°C and ~2 kbar, in the absence of direct experimental data on H2S/HS-, S3

- and

most Au complexes, our Au solubility predictions are based on extrapolations using

thermodynamic equations of state that were all parameterized using data for these species

obtained below 500°C. Because their individual uncertainties are difficult to rigorously quantify,

the choice of accurate and consistent thermodynamic data sets is critical for reliable predictions.

This is because the modelled Au and S3- concentrations depend on those of H2S, which in turn are

determined by the choice of thermodynamic properties for this main sulfur form (3, 4, 7). For

example, it was shown (7) that the different choice of H2S thermodynamic parameters [e.g., ref.

(33) versus (40)] results in variations more than 1 log unit of the predicted S3- abundance in near-

magmatic H2S-SO2 fluids at 700°C considered in this study, whereas all data sources yield similar

S3- concentrations (±0.2 log unit) at T <500°C. In contrast, the choice of thermodynamic data for

oxidized S species (SO2 and sulfates) and other major fluid constituents (H2O-NaCl-KCl and

minerals) is far less critical both because variations between the different data sources for these

12

compounds are small, and the thermodynamic models themselves such as HKF and RB are built

in part on these data (32, 48). For ions, ion pairs and charged complexes, these two models based

on electrostatic properties of the fluid (dielectric constant) are robust enough to allow reliable

predictions to at least 700°C and 10 kbar (5, 7, 39), whereas for volatile species such as H2S,

these electrostatic models may not be reliable enough beyond the experimental data range due to

their intrinsic limitations related to the use of the Born electrostatic equation for uncharged

species (38, 40). Consequently, for H2S and other non-electrolytes (H2, O2, SO2) in this study we

have chosen the recent alternative model of Akinfiev and Diamond (40) based on well-

constrained ideal gas properties of these species and the T-P evolution of the water density

(hereafter called AD model).

We believe that this choice is the most reliable at present and allows significant reduction

in uncertainties of extrapolations above 500°C compared to other models (e.g., HKF, ref. 33) for

the following reasons: i) The AD model for aqueous H2S was parameterized using the whole set

of available experimental data, including gas-water partition coefficients, direct calorimetric and

volumetric measurements, and iron sulfide minerals-water equilibria (40). ii) This model was

used in the retrieval of the thermodynamic properties of AuHS and Au(HS)2- species from

available experimental data (3) and of Au-S3- complexes in this study, thus ensuring internal

consistency in the Au-H2S-S3- system and allowing partial error cancellation. iii) More validity to

our predictions of Au solubility in magmatic and metamorphic fluids above 600°C (~10s ppm,

Fig. 3) is brought by direct measurements of Au contents in fluid inclusions from high-

temperature porphyry and orogenic deposits (e.g., 1, 52, 53). For comparison, the use of an

alternative thermodynamic dataset for Au-HS-Cl-OH species (42) based on the HKF model

parameters for H2S and other volatile species from SUPCRT92 database (33) results in

inconsistent Au solubility predictions at conditions considered in our study (e.g., Fig. 3), ranging

from 0.01 ppm Au in the porphyry fluid at 700°C and 1.5 kbar to 1000 ppm Au in the

metamorphic fluid at 700°C at 9 kbar, whereas both data sets (3 and 42) predict similar Au

concentrations (1-10 ppm) at 500°C in a wide pressure range.

Thus, we believe that realistic uncertainties of our model predictions for Au solubility

and concentrations of Au-trisulfur ion complexes at T of 600-700°C and P of 1-10 kbar are within

one order of magnitude. It should be noted that other S3- (and potentially S2

-) – bearing gold

species may form in addition to Au(HS)S3- at such conditions. Such complexes would further

enhance Au mobility in high T-P fluids and provide additional support to our pessimistic at

present estimations of the important role of radical sulfur species in Au fate in the Earth’s crust.

13

Fig. S1. Measured Au solubility [in log10 (Au molality), m] vs S3- molal concentration (A and C), and the

difference between measured and calculated Au solubility vs the S3-/HS

- ratio (B and D) for S3

- - bearing

solutions at indicated composition, temperature, and pressure. Measured Au concentrations are from in situ XAS

(Table S1 and ref. 4) and Coretest hydrothermal reactor (Table S2) experiments; calculated Au solubility and S3-

and HS- concentrations are generated using the HCh computer code (31) and the available thermodynamic

properties of Au(HS)2- (±AuHS and AuCl2

-, which are minor in most experiments), S3

- and other S species (see

Table S4). At low S3- concentrations (<0.001 m) and/or elevated pH (>6), the difference between measured and

calculated Au solubility is close to zero within errors confirming the dominant presence of Au(HS)2-. In contrast,

at higher S3- contents and more acidic pH, the measured Au solubilities are systematically higher than those

calculated; this difference indicates the formation of other Au species, very likely with S3-. The competition

between the HS- and S3

- ligands for Au is highlighted in terms of the S3

-/HS

- ratio in the fluid (B and D): the

higher the ratio is, the larger the Au solubility difference becomes. These trends strongly support reaction (R1)

for describing Au solubilities in solutions with S3-/HS

- ratios above 1. Error bars on data points (2 SD) stem from

Au solubility measurements and calculations of Au and S3- and HS

- concentrations. Vertical and horizontal

dashed lines in (B) and (D) denote, respectively, the ideal correspondence of the measured vs calculated

solubilities and the domains of predominance of Au(HS)2- and Au-S3

- – type complexes. Note the differences in

data trends and amplitudes of data points scatter at different pH, which are due to the fact that gold solubility

also depends on pH, in addition to other factors (ligand concentrations and ratios, and redox potential).

14

Fig. S2. Gold L3-edge EXAFS spectra of representative aqueous solutions and reference compounds. (A)

Normalized k2-weighted EXAFS spectra and (B) their corresponding Fourier Transforms (not corrected for

phase shift) show the presence of 2.0±0.2 S atoms in the first coordination sphere of Au at 2.290±0.005 Å

(feature S1) of quasi-linear geometry as indicated by significant multiple scattering signals (feature MS); 2nd

shell S atoms present in the reference compounds (feature S2) could not be detected in EXAFS spectra of

experimental solutions, which are largely dominated by the first-shell S-Au-S signal. The spectral data are

consistent with the formation of Au-H2S/HS-S3- complexes with two S ligands, and allow exclusion of

complexes with a single S-ligand (e.g., H2O-Au-SH, HO-Au-S3-, H2O-Au-S3

-) as solubility-controlling species

in our solutions.

15

Fig. S3. Gold L3-edge XANES spectra of representative reference compounds and experimental aqueous

solutions dominated by Au(HS)2- or Au-S3

- complexes at indicated composition and temperature (in °C) at 600

bar pressure and the structures of the major species. Vertical dashed lines marked A, B1 and B2 reveal small but

significant differences between the spectra of Au(HS)2- – dominated solutions at neutral pH from this and

previous (4) studies and those of acidic S3- – rich solutions (above 300°C): growth in amplitude of feature A

and shift in energy position between B1 (Au(HS)2-) and B2 (Au-S3

-). The features in the S3

- – rich solutions are

similar to those observed in Au thiosulfate and thiomalate reference compounds whose structures consist of [S-

S-Au-S-S] moieties; this similarity indicates the presence of second-shell S atoms in such solutions.

16

Fig. S4. FPMD results. Calculated average EXAFS spectra (smooth black curves) of different Au-S

complexes whose ball structures (Au=pink, S=yellow, H=light grey, O=red, for a single snapshot) are

shown at the right next to the corresponding curves, and their comparison with the experimental spectrum

(red curve) from the 1.11m K2S2O3 – 0.33m HCl experiment (#4_13, Table S1) at 400°C, 600 bar in which

Au(HS)S3- is expected to be dominant according to thermodynamic solubility analyses. The spectra are

offset vertically for clarity. Each calculated spectrum represents a mean of 100 MD snapshots.

17

Fig. S5. FPMD results. Calculation of the reaction (R1) equilibrium constant. Gibbs free energy profiles at

400°C and 600 bar for the ligand exchange half reactions Au(HS)2- = AuHS + HS

- (R1a, red) and

Au(HS)S3- = AuHS + S3

- (R1b, green). These half reactions sum up to the complete ligand exchange

reaction (R1).The shaded areas indicate error bars (2 SD). The difference of 11±13 kJ/mol between the free

energy minima for the two half reactions, combined with a correction for configurational entropy

(necessary to account for the difference in the 1a and 1b reaction coordinates), yields log10KR1 = -0.2±1.0

(see SI text for details).

18

Fig. S6. Slope analysis of the measured Au solubility in terms of Au(HS)S3- at indicated temperatures and

pressures. The vertical axis displays the difference (in log scale) between Au total measured concentration

and that of Au(HS)2- (±AuHS, AuCl2

-) calculated using the available thermodynamic data (Table S4); this

difference is due to S3-–bearing Au complexes. The horizontal axis represents the calculated values of [log

m(S3-) + log m(H2S) – 0.5 log m(H2)] using the available thermodynamic data (Table S4). The solid line is

a weighted least square linear regression through the data points; its slope is close to the theoretical value of

1 (indicated by the dashed line), which stems from the theoretical relationship: log m(Au(HS)S3-) = log KR2

+ log m(S3-) + log m(H2S) – 0.5 log m(H2), where KR2 is the stability constant of the reaction Au(s) +

H2S(aq) + S3- = Au(HS)S3

- + 0.5 H2(aq), with log KR2 corresponding to the intercept of the regression line.

Errors of regression coefficients are 2 SD.

19

Fig. S7. Sulfur and gold speciation and solubility in aqueous fluids typical of porphyry-epithermal Cu-Au-

Mo deposits (A, B) and orogenic and Carlin-type Au deposits (C, D). The conditions are the same as in Fig.

3 (main text). (A, B) An Au-Fe-Cu-bearing H2S-SO2 fluid of the initial composition indicated in the figure

degasses from magma at 700°C, and cools and decompresses in a porphyry-epithermal in equilibrium with

native gold and the quartz-muscovite-K-feldspar assemblage (QMK, pH≈5-6 at all temperatures). (C, D) A

low-salinity metamorphic fluid evolves in equilibrium with native gold and the pyrite-pyrrhotite-magnetite

(PPM) and quartz-muscovite-feldspar-albite (QMKA) mineral assemblages along a typical geothermal

gradient of subduction zones (75°C/1 kbar). Pyrite breaks down to pyrrhotite at ~630°C in this system.

Curves show the concentrations of the major S (in wt% S) and Au (in ppm Au) aqueous species calculated

using the thermodynamic properties from Table S4. An oscillatory concentration pattern for Au(HS)S3-

(panel B) reflects changes in the S species abundance induced by precipitation of Cu and Fe sulfide

minerals upon the fluid cooling.

20

Fig. S8. The effect of the major fluid parameters on the equilibrium distribution of aqueous sulfur species

calculated for typical hydrothermal fluids from porphyry Cu-Au-Mo and associated deposits at the indicated T-

P-composition as a function of: (A) total dissolved S concentration at pH ~5 and fO2 buffered by H2S-SO2

equilibrium, which is very close to the HM buffer; (B) redox conditions, vertical dashed lines indicate the

oxygen fugacity corresponding to common redox buffers, QFM – quartz-fayalite-magnetite, NNO – nickel-

nickel oxide, PPM – pyrite-pyrrhotite-magnetite, and HM – hematite-magnetite; (C) fluid acidity, pH = -log10

a(H+) at fO2 between HM (acidic pH) and NNO (basic pH); (D) pressure, the grey shaded area denotes the low-

pressure region in which HKF model predictions are not reliable, P <400 bar at 500°C. In all panels, the curves

denote the concentrations of labeled species (expressed in wt% S). The thermodynamic properties of fluid

constituents are from Table S4. See also Fig. 2 in main text for the solubility of gold at the same conditions.

21

Fig. S9. The effect of fluid salinity on (A) the equilibrium distribution of major sulfur species and (B) gold

solubility in a model hydrothermal fluid representative of porphyry Cu-Au-Mo at 450°C, 750 bar, total S

concentration of 1.5 wt%, pH of ~5 as buffered by quartz-muscovite-(K)feldspar assemblage, and oxygen

fugacity of the hematite-magnetite buffer (HM). See the Fig. 2 and Fig. S7 captions for details. The slight

decrease in S3- abundance and Au(HS)S3

- solubility at high NaCl content (>20 wt%) is due to an interplay of

the change in activity coefficients for the different species at high ion strength and the growth of the amount of

alkali sulfate ion pairs (NaHSO40 and NaSO4

-) with increasing salt concentration. Note that Au-chloride

complexes remain very weak at these conditions.

22

Fig. S10. The effect of the initial SO2/H2S molal ratio in magmatic fluid on (A) sulfur species distribution and

(B) gold solubility. An aqueous fluid of 10 wt% NaCl eq. salinity containing 2 wt% total sulfur with a variable

SO2/H2S ratio is assumed to degas from magma and equilibrate with granitic rocks (Quartz-Andalusite-

(K)feldspar-Albite buffer) at 700°C and 1.5 kbar yielding pH of about 6. Oxygen fugacity (indicated in log10fO2

units relative to the Nickel-Nickel Oxide (NNO) buffer at 700°C) is controlled by equilibrium among the

major S species in the fluid. Gold solubility and S3- concentrations are maximized at the SO2/H2S ratio of 0.3

(NNO = +2) typical of magmatic fluid generation in most porphyry systems (e.g., ref. 1). Note that the gold-

trisulfur ion complex enhances by more than 10 times Au extraction from magma compared to the known Au

chloride and hydrogen sulfide complexes (shown by the green curve) in a wide range of SO2/H2S ratios (from

less than 0.001 up to ~10) corresponding to the oxygen fugacity range from NNO to NNO+2.5 typical of fluids

generated from fertile arc magmas (see main text).

23

Table S1. In-situ gold solubility and local atomic structure in Au aqueous complexes, derived from XAS

spectra of experimental aqueous solutions of the indicated composition as a function of temperature at

600 bar pressure.

Run number, composition (m, mol/kg H2O) T°C log10mAu NS, atoms

RAu-S, Å 2 (Å

2)

#1&5_11, 1.200m K2S2O3

300 350 400

-1.55±0.10 -1.47±0.15 -1.54±0.15

2.0 1.9 1.9

2.291 2.285 2.292

0.0037 0.0030 0.0036

#2_11, 0.352m K2S2O3

300 350 400 450

-2.26±0.10 -2.29±0.15 -2.30±0.10 -2.44±0.30

2.0 2.0 1.8 1.9

2.290 2.291 2.291 2.300

0.0031 0.0042 0.0035 0.0039

#4_11, 1.166m S + 1.454m NaOH 350 -2.88±0.26 2.0 2.301 0.0027

#6_11, 1.177m K2S2O3 + 0.235m HCl

275 350 400

-1.77±0.15 -1.84±0.20 -2.29±0.30

2.0 2.0 2.0

2.294 2.287 2.293

0.0025 0.0036 0.0044

#1&5_13, 0.560m K2S2O3 + 0.175m HCl

200 250 300 350

-3.18±0.22 -2.29±0.10 -2.20±0.12 -2.32±0.10

2.0 2.1 2.0 2.0

2.285 2.285 2.291 2.290

0.0018 0.0033 0.0031 0.0031

#2_13, 1.076mS + 1.114m NaOH

200 250 300 350

-2.29±0.30 -1.71±0.20 -1.69±0.20 -1.63±0.20

1.9 2.0 1.8 1.9

2.288 2.285 2.286 2.280

0.0024 0.0028 0.0032 0.0035

#3_13, 0.279m K2S2O3 + 0.066m HCl

200 250 300 350 400

-3.32±0.25 -2.61±0.10 -2.67±0.10 -2.75±0.10 -2.91±0.25

-a

2.0 2.0 2.0 2.0

- 2.290 2.286 2.296 2.283

- 0.0029 0.0035 0.0039 0.0042

#4_13, 1.110m K2S2O3 + 0.329m HCl 200 250 300 350 400 450

-2.09±0.33 -2.47±0.30 -1.76±0.10 -1.63±0.10 -1.73±0.10 -1.81±0.10

1.9 1.9 1.9 2.0 1.9 1.9

2.287 2.280 2.287 2.287 2.289 2.287

0.0019 0.0018 0.0023 0.0033 0.0030 0.0037

#6_13, 0.558m Na2S2O3 200 300 350 400 450

-2.13±0.20 -1.96±0.15 -1.84±0.15 -1.86±0.15 -1.85±0.15

2.0 2.0 1.9 1.9 1.9

2.289 2.282 2.288 2.291 2.287

0.0029 0.0031 0.0032 0.0035 0.0036

EXAFS error ±0.2 ±0.005 ±0.0010 mAu = total dissolved Au molality in solution in equilibrium with gold metal, derived from the absorption edge

height of XAS spectra as detailed in (4); RAu-S = Au-S mean distance, Ns = Au-S coordination number, 2 =

squared Debye-Waller factor. The amplitude reduction factor S02 is set to 0.83 as found from fits of model

compounds with known Au coordination. For all samples, the fitted k-and R-ranges were respectively 3.2-11.0 Å-1

and 1.3-4.8 Å (not corrected for phase shift). Multiple scattering contributions within the linear S-Au-S' cluster, Au-

S-S'-Au (Rms1 = 2×RAu-S) and Au-S-Au-S'-Au (Rms2 = 2×RAu-S) were included in all fits; their DW factors are

typically double of the first shell Au-S values, confirming a close to linear S-Au-S geometry. The number of

variables in the fit (Nvar = 5) has always been much lower than the number of independent points (Nind ~17). For all

fits, fit quality criteria, R-factor and reduced chi2 are in the range 0.01-0.03 and 10-50, respectively. All errors are 2

SD. a ‘-‘ means that structural data were not obtained because of the low signal-to-noise ratio of the EXAFS

spectrum.

24

Table S2. Gold solubility measured in experimental aqueous solutions of the indicated composition as a

function of temperature and pressure, using a Coretest flexible-cell hydrothermal reactor.

Run number, composition (m, mol/kg H2O)

T°C P, bar days Nb samples

Au, ppm log10mAu

m22, 0.543m K2S2O3+0.157m HCl, QMK 350 350 10 4 636±64 -2.45±0.08

m29, 0.199m K2S2O3+0.095m KOH 350 350 13 2 373±30 -2.70±0.04

m23/1, 0.10m KCl, PPM, QMK 350 600 17 4 0.2±0.1 -6.00±0.30

m23/2, 0.10m KCl, PPM, QMK 450 630 14 4 0.4±0.2 -5.70±0.30

m15, 0.61m S 400 670 8 3 0.24±0.10 -5.91±0.52

m17, 0.65m S+2.64m NaCl 400 750 5 2 13.4±3.0 -4.10±0.07

m14, 0.58m S+1.76m NaCl+0.59m KCl 450 630 18 3 30±15 -3.75±0.33

m16, 0.61m S+2.31m NaCl+0.59m KCl 450 700 6 3 10±2 -4.21±0.08

m18, 0.65m S+1.13m NaCl+1.18m KCl+0.067m NaOH, QMK 450 750 6 2 52±10 -4.21±0.08

m20, 0.55m S+0.051m NaCl 450 750 15 4 1.5±0.7 -5.11±0.22

M17/1, 0.65m S+2.64m NaCl 500 740 2 1 6.3±1.0 -4.42±0.07

M17/2, 0.72m S+3.01m NaCl+0.15m NaOH 500 650 6 2 77±8 -3.33±0.05 PPM = Pyrite-Pyrrhotite-Magnetite mineral assemblage; QMK = Quartz-Muscovite-K feldspar mineral assemblage.

25

Table S3. Equilibrium thermodynamic constants of the isocoulombic

exchange reaction: Au(HS)2- + S3

- = Au(HS)S3

- + HS

- (R1), derived in

this study from measured Au solubilities (at 300-500°C) and

molecular dynamics simulations (at 400°C).

T °C P, bar Number of data points

log10 KR1 Error ±2 SD

300 600 12 -0.3 0.6

350 400-600 15 0.0 0.5

400 600 12 -0.1 0.6

400 (MD)a 600 NA

a -0.2 1.0

450 600 14 -0.0 0.6

500 700 2 -0.3 0.7 a Molecular dynamics simulations of reaction (R1) using the potential of

mean force; NA = not applicable.

26

Table S4. Sources of thermodynamic data for aqueous species and minerals used in this studya.

Chemical species and phases Data source

Aqueous species H2O, H

+, OH

-, Cl

-, Na

+, NaCl

0, NaOH

0, KCl

0, K

+, KOH

0, KSO4

-, KHSO4

0, NaHSO4

0, HS

-, H2S2O3, HS2O3

-

, S2O32-

, HSO3-, SO3

2-, HSO4

-, SO4

2-, S(2 to 5)

2-, H2S2O4

0, HS2O4

-, S2O4

2-, S2O5

2-, S(3 to 5)O6

2-, S(2 to 3)O8

2-

(33)

NaSO4- (35)

S62-

, S72-

, S82-

(33, 36)b

HCl0 (37)

H2S0, SO2

0, H2

0, O2

0 (40)

NaHS0, KHS

0, NaHSO4

0 (33)

c

S80, Sn

0, S3

- (7)

Au+, AuOH

0, Au(OH)2

-, AuHS

0, Au(HS)2

-

AuCl2-

Au(HS)H2S0

Au(HS)S3-

(3) (3, 41)

d

(4) this study

f

Fe2+

, FeCl+, FeCl2

0

Cu+, CuCl

0, CuCl2

-, CuHS

0, Cu(HS)2

-

Ag+, AgCl

0, AgCl2

-, AgHS

0, Ag(HS)2

-

Zn2+

, ZnCl+, ZnCl2

0, ZnCl3

-, ZnCl4

2-

ZnHS+, Zn(HS)2

0, Zn(HS)3

-, Zn(HS)4

2-

Cu(HS)S3-, Ag(HS)S3

-, Zn(HS)S3

0

(38) (49) (49) (50) (51)

this studyg

Solids and liquids S(s), S(l), K2SO4(s), Na2SO4(s) (34) Gold, pyrite, pyrrhotite, magnetite, hematite, quartz, muscovite, microcline, sanidine, andalusite, albite, chalcopyrite, bornite, argentite Sphalerite

(33) (51)

Activity coefficient models

log i = -A zi2 I/(1+B åi I) + , for charged species

log + bi I, for neutral species (32)

e

a Thermodynamic properties of H+ are equal to 0 at all T and P; the standard states for the solid phases and H2O are unit

activity for the pure phase at all T and P; for aqueous species, the reference state convention corresponds to unit

activity coefficient for a hypothetical one molal solution whose behavior is ideal. b Values of fG°298 and S°298 of S6

2-, S72-, and S8

2- were adopted from (36), whereas HKF parameters were taken equal

to those of S52- from (33).

c Formation constant [cation + ligand = ion pair] at any T and P is assumed to be equal, respectively, to those of NaCl0,

KCl0 and KHSO40 from (33).

d Mean value at a given T-P between those from (3) and (41). e A and B are the Debye-Hückel electrostatic parameters; I is the effective molal ionic strength (I = 0.5 ∑zi

2 mi); zi and

åi are the ionic charge and the distance of the closest approach for ith species, respectively; is the mole fraction

to molality conversion factor, = log(1+0.018m*), where m* is the sum of the molalities of all solute species.

We adopted a value for åi of 4.5 Å for all charged species. For neutral species, bi is the empirical Setchenov

coefficient, which was taken as zero for all neutral species, which yields activity coefficients close to one. f From K = 1 at all temperatures and pressures for reaction: Au(HS)2

- + S3- = Au(HS)S3

- + HS- (R1). g From K = 1 at all temperatures and pressures for an exchange reaction analogous to (R1) for each metal.

27

Table S5. Energy shifts and mean square errors (MSE)a of the simulated EXAFS spectra compared to the

experimental spectrum of the 1.11m K2S2O3 – 0.33m HCl experiment (#4_13) at 400°C, 600 bar in

which Au(HS)S3- is expected to be dominant according to thermodynamic analyses of gold solubility.

Simulated complex Energy shift ΔE, eV MSE (×106)

Au(HS)S3- 9.3 3.2

Au(HS)S32-

9.5 3.0

Au(S3)22-

10.4 4.1

Au(HS)2- 9.5 5.5

(H2O)Au(HS)0 14.2 24

a Mean square error, defined as the sum of the squared differences between

simulated and experimental EXAFS data points over the k-range between 3 and

13 Å-1, divided by the number of data points.

28

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