Supplemental Information
for
“Isotopic Evidence Of Acetate Turnover In Precambrian
Continental Fracture Fluids”
Elliott P. Mueller
*
1
, Juliann
Panehal
1
,
Alexander Meshoulam
1
,
Min Song
2
, Christian T. Hansen
3
, Oliver
Warr
2
,4
, Jason Boettger
5
, Verena B. Heuer
3
, Wolfgang Bach
3
,
Kai
-
Uwe Hinrichs
3
, John M. Eiler
1
,
Victoria
Orphan
1
,
Barbara Sherwood Lollar
2,
6
, Alex L. Sessions
1
1
Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA, USA
2
Department of Earth Sciences, University of Toronto, Toronto, ON, Canada
3
MARUM Centre for Marine Environmental Sciences, University of Bremen, Bremen, Germany
4
Department of Earth Sciences, University of Ottawa, Ottawa, ON K1N 6N5, Canada
5
Department of Earth, Environmental, and Resource Sciences, University of Texas at El Paso, El Paso, Texas
,
U
S
A
6
Institut de Physique du Globe de Paris (IPGP), Université Paris Cité, 1 rue Jussieu, 75005, Paris,
France
*
Corresponding author: elliottpmueller@gmail.com
Acetate
was
purified from the high salinity matrix of fracture fluids
prior to
isotopic analysis
. To
verify that the purification scheme did not
introduce isotopic
fractionat
ion
, we spiked synthetic
solutions of Kidd Creek
fluid (Table S1) with acetate of known isotopic composition (
d
13
C =
-
19.2‰,
d
2
H =
-
127‰) and
then re
analyzed
them
after extraction from the solution. Replicates of
1 mM and 2 mM acetate solutions
yielded identical δ
13
C and δ
2
H values within analytical
uncertainty, indicating
that the extraction procedure
is
not fractionat
ing.
(Figure S1).
Small
differences <1‰ between the measured and expected values are common in ESI
-
Orbitrap
measurements, even when comparing standards of pure solutions of acetate. This i
s reported in
detail in the original method development study. The source of these minor inaccuracies are still
unclear
.
1
Table S1: Composition of synthetic solution used for validation studies on acetate purification
techniques.
Figure S1: Extracted acetate standard from a synthetic fracture fluid mixture has the same
d
13
C
and
d
2
H
values as the known composition. Error bars are one standard deviation on triplicate
analytical replicates. Dotted lines represent the
reported
value of the standard along with
uncertainties on
d
2
H
values. Uncertainties are 0.1‰ on the
reported
d
13
C
composition and
are
not visible on
this
plot.
Table S2: Acetate isotope composition and metadata from Kidd Creek and Birch
t
ree fluids.
*Taken from Warr et al. 2021
2
. **Taken from Sherwood
Lollar et al. 2021.
3
Experiment Date
Temperature (
°
C
)
Half
-
time (hr)
Half
-
time (yr)
February 2023
60
7.1 x 10
6
81
1
February 2023
60
6.5 x 10
6
742
June 2022
100
2.7 x 10
4
3.08
April 2022
150
112
0.012
June 2022
150
187
0.021
January 2023
200
3
0.00034
January 2023
200
3
0.00034
Table S
3:
Half
-
times of equilibration determined at temperatures between 60 and 200
°
C
. Data
used to make Figure 1 in the main text.
Figure S2: Exchange experiments in deuterated water (5%
2
H
2
O) with 1 mM acetate at 60
°
C
,
100
°
C
, and 150
°
C
. Acetate
incorporated deuterium from the water into its methyl
-
site in a linear
fashion. At 60
°
C
, the exchange rate is so low that deuterium incorporation is quantified as
changes in natural abundance
d
2
H
values
(10‰ is equivalent to 1 ppm absolute increase)
.
All
measurements made on an electrospray Orbitrap mass spectrometer
. Error bars represent
standard deviation of analytical triplicates.
To account for changes in exchange reaction rates due to complexation of acetate with inorganic
cations in solution, acetate was incubated in 1 mol/L CaCl
2
for 4 hours at 120
°
C
. This
experiment was done in triplicate. After the incubation, acetate was enriched by 191‰ ± 4‰.
Uncertainty represents standard deviation of experimental replicates, which was equivalent to
analytical error. This enrichment with time was converted to a reaction rate of exchange at
120
°
C
, which falls on the established Arrhenius relationship between temperature and reaction
rate based on exchange with pure water. These data suggest that complexation with calcium
cations, the major cation in Kidd Creek, does not impact exchange kinetics.
Figure S3: Arrhenius plot of exchange reaction rate with temperature (from Figure 1 in main
text) for acetate in deuterated water (5%
2
H
2
O
). Dark blue dots represent exchange with pure
water. Red dot represents exchange in 1M
CaCl
2
at 120
°
C.
The tautomerization reaction that putatively exchanges hydrogen atoms with water is shown
below (Figure S4). Tautomerization reactions are well
-
documented
isomerization
s
between
carbonyl/carboxyl and enol forms of organic ketones and acids
.
4,5
The good agreement with the
Arrhenius equation between 60
°
C
and 200
°
C
suggests that the reaction mechanism of exchange
does not change in this temperature range. Experiments at lower temperatures are not possible on
laboratory timescales due to the long time for exchange
(thousands of years). At the
in situ
temperature of Kidd Creek and Birch
t
ree (~25
°
C
), the extrapolated half
-
time of exchange is
250,000 years. If the relationship between temperature and rate were to deviate from the
regression at lower temperatures, it would represent a shift in exchange mechanism. This new
mechanism would have to have
a faster rate at 25
°
C
than the one measured at high temperatures,
Half time (yr)
otherwise this mechanism would not be rate limiting
.
If this new mechanism was
slower
, the
estimated rate of exchange
by tautomerization would not be impacted, as it would still be rate
limiting. This means that the exchange rate is a conservative, minimum estimate.
I
f another
mechanism was rate
-
limiting
, our extrapolation would be an overestimate of the exchange half
-
time in Kidd Creek and Birch
t
ree
, and f
aster exchange rates only further the conclusions drawn
in the following sections regarding acetate cy
cling rates.
Figure S4:
Proposed t
automerization
reaction mechanism for exchanging hydrogen
isotopes
between water and the
methyl group
of acetate
.
DFT Calculations of Water:
Continuum solvation models can fail to accurately reproduce
isotopic effects of H involved in hydrogen
interactions (e.g. H
2
O molecule dissolved in water)
and therefore a special treatment is required
.
6
To overcome this problem we derived the EIE
value of H
2
O in liquid water using the experimental alpha liquid/vapor and the
2
H/
1
H ratio in
H
2
O calculated in the gas phase. Using this approach, we were able to obtain
2
ε
(acetate/water)
values
which are similar to the experimental values (Fig. 2A).
Complexation of calcium and acetate: Influences on the equilibrium isotope
effect.
In CaCl
2
brines, like the Kidd Creek and Birchtree fluids, calcium cations and acetate anions can
complex to form bidentate structures. If this is
a
major
form of acetate in the fracture fluids, then
the acetate/water equilibrium isotope effect (EIE)
must
be determined for
both
the free acetate
ion and the Ca
-
acetate complex.
In the main text, the equilibrium isotope effect is calculated in
three different ways: 1.) Between free acetate and pure water, 2.) between free acetate and a 3M
CaCl
2
brine and 3.)
between a calcium
-
acetate complex and a 3M CaCl
2
brine. The first two
calculations (free acetate
-
water equilibrium and free acetate
-
brine equilibrium)
were
performed
as described in the methods section of th
e main text.
However for the
third
calculation, a molecular model of the Ca
-
acetate complex was created. To
do so, we started with a molecular geometry of the bidentate complex which was previously
determined by
Muñoz
Noval et al. (2018).
7
Their empirical structure
was used as an initial
condition to determine
the
optimized electronic structure of the Ca
-
acetate complex. The DFT
calculations used identical
methods
as in the main text
.
An
EIE value
representing a
2
H
substitution at
each of the three H atoms on the methyl group was calculated. The average value
of the three was used as the overall EIE.
During these calculations, the
following optimized atomic coordinates were determined for the
free acetate and Ca
-
acetate complex (Tables S4a and S4b, respectively).
Table S4a. Coordinates of the optimized structure for C
2
H
3
O
2
-
Atom
X
Y
Z
C
-
1.351609
-
0.039572
-
0.002275
H
-
1.750804
0.637911
-
0.762956
H
-
1.735935
-
1.04737
-
0.173155
H
-
1.722086
0.316133
0.96555
C
0.199222
-
0.000106
-
0.005931
O
0.798162
-
1.104908
0.001285
O
0.717231
1.146332
0.00119
Table S
4
b. Coordinates of the optimized structure for C
2
H
3
O
2
Ca
Atom
X
Y
Z
C
-
2.471200
-
0.000006
0.063380
H
-
2.892009
0.895852
-
0.392797
H
-
2.892007
-
0.895864
-
0.392795
H
-
2.742121
-
0.000001
1.123917
C
-
0.961595
0.000001
-
0.043604
O
-
0.340032
-
1.106705
-
0.069206
O
-
0.340037
1.106713
-
0.069063
Ca
1.728173
-
0.000001
0.032458
Acetate and the Ca
-
acetate complex
had the following calculated frequencies (Tables S5a and
S5b)
Table S5a. Calculated frequencies (cm
-
1
) for
–
C
2
H
3
O
2
-
(acetate in water)
34.3949
436.5932
611.1575
635.6974
884.2003
998.3083
1036.549
1332.708
1378.981
1454.293
1469.448
1651.552
3010.94
3069.027
3092.507
O
O
+
Ca
C
C
H
H
H
Figure S5: Diagram of the bidentate calcium
-
acetate complex that
can
form in high CaCl
2
brines, like those of Kidd Creek and Birchtree.
Bond lengths and angles are
not
to scale.
Table S5b. Calculated
frequencies for (cm
-
1
)
–
C
2
H
3
O
2
Ca
+
36.3313
102.7298
200.8444
290.1095
460.3864
614.7865
681.1430
940.0897
1023.8721
1064.3274
1368.8363
1443.1461
1446.9535
1476.3733
1554.2087
3040.1641
3106.1612
3140.4640
The optimized molecular structures
of acetate and the Ca
-
acetate complex
had the following
geometry
(Tables S6a and S6b)
:
Table S6a. Calculated molecular geometry for
–
C
2
H
3
O
2
-
C
-
O
-
C angle
127.218º
C
-
O bond length (upper/ lower)
1.258
Å
/ 1.257
Å
C
-
C bond length
1.551
Å
Dihedral angle H(lower)
-
C
-
C
-
O (lower)
-
10.21093º
Table S6a. Calculated molecular geometry for
–
C
2
H
3
O
2
Ca
+
O
-
C
-
O angle
121.319º
C
-
O bond length upper/ lower
1.2696
Å
/ 1.26956
Å
O
-
Ca bond length
2.34789
Å
/ 2.34790
Å
C
-
C bond length
1.51339
Å
Dihedral angle H(lower)
-
C
-
C
-
O (lower)
-
29.37205º
C
-
Ca length
2.69084
Å
High ionic strength solutions also
have lower
dielectric constant
s
for
water, which would
influence the force field that simulates water solvation in the DFT calculations. We tested
whether this would
change
the calculated EIE by solving for the optimized electronic structures
of free acetate and the Ca
-
acetate complex using two different dielectric constants for water: 60
and 40. However, changing the dielectric constant of water did not
shift
the calculated EIEs by
more than 1‰ at 25
°
C. Thus, our DFT models predict that the change in dielectric constant of
water does not in
fluence calculated partition function ratio of acetate or the Ca
-
acetate complex.
Supplementary
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