1
Supplementary Materials for
Theoretical and Experimental Constraints on
Hydrogen Isotope Equilibrium
in C1
-
C5
A
lkanes
The PDF file
includes:
Figure S1
–
S4
Table
S1
–
S2
Other Sup
plementary
Material
s
for this manuscript
include the following
:
A
ll
computed vibrational frequencies
A
ll computed thermodynamic properties
Optimized
cartesian coordinates for molecules (including conformers)
A
ll β values from 0 to 400°C
E
quilibrium hydrogen isotope fractionation between C
2
–
C
5
alkanes and C
1
from 0 t
o
400
°C
M
olecular and radical isotopomers for the exchange model.
Figure
S
1. Torsional
Conformers of
n
-butane,
i
-pentane and
n
-
pentane.
n
-butane
trans
gauche
i
-pentane
tg
gg
g-g+
g-g-
n
-pentane
tt
tg
Figure
S
2. Equilibrium H isotope fractionation of the H
positions, using
n
-pentane (g-g+) and
n
-butane (g) as examples.
Each molecule’s ε
are referenced to an arbitrary value (6‰ lower
than minimum β position of each conformer) for better
visualization.
Colors are used to separate hydrogens (with
different C–H orientations) on the same carbon.
n
C5 g-g+ hydrogen atoms EIE (25°C)
1
2
3
4
5
Carbon Positions
0
20
40
60
80
100
120
2
i
C5 tg hydrogen atoms EIE (25°C)
1
2
3
4
5
Carbon Positions
0
50
100
150
200
2
n
C4 g hydrogen atoms EIE (25°C)
1
2
3
4
Carbon Positions
0
20
40
60
80
100
120
2
i
C4 hydrogen atoms EIE (25°C)
1
2
3
4
Carbon Positions
0
50
100
150
200
2
Figure
S
3. Equilibrium
hydrogen isotope
fractionation for alkane pairs vs. temperature. Red
line: Thiagarajan et al. (2020); blue line: this
study.
1
2
3
4
1000/T (K
-1
)
10
-3
0
50
100
2
H
C2-C1
1
2
3
4
1000/T (K
-1
)
10
-3
0
50
100
150
2
H
C3-C1
1
2
3
4
1000/T (K
-1
)
10
-3
0
50
100
2
H
iC4-C1
1
2
3
4
1000/T (K
-1
)
10
-3
0
50
100
150
2
H
nC4-C1
1
2
3
4
1000/T (K
-1
)
10
-3
0
50
100
150
2
H
iC5-C1
1
2
3
4
1000/T (K
-1
)
10
-3
0
50
100
150
2
H
nC5-C1
-190
-180
-170
-160
-150
-140
-130
-120
-110
-100
0
200
400
600
800
δ
D
Time (h)
C1
C2
C3
Ru/Al
2
O
3
(powder)
-180
-160
-140
-120
-100
-80
-60
0
20
40
60
80
δD
Time(h)
C2
C3
iC4
nC4
iC5
nC5
Ru/Al
2
O
3
(pellet)
-190
-170
-150
-130
-110
-90
-70
0
20
40
60
80
δD
Time(h)
C2
C3
iC4
nC4
iC5
nC5
Pd/C(powder)
Figure
S
4. Examples
of unequilibrated
exchange experiments.
All experiments
here are conducted at 100
°
C.
(a)
(
b)
(
c
)
3
Table S1. Thermodynamics for stable conformers of n-alkanes, relative to the most stable
conformer.
Molecule
n
-
C
4
n
-
C
4
n
-
C
5
n
-
C
5
n
-
C
5
n
-
C
5
i
-
C
5
i
-
C
5
Conform
er
g
t (ref)
g
-
g
-
g
-
g+
tg
tt (ref)
gg
tg (ref)
ΔH (J)
4123
0
7869
15170
4161
0
4507
0
ΔS (J/K)
-
0.2618
0
-
0.6681
0.7822
0.1365
0
-
1.001
0
Table S2. Molecular composition (as a fraction of total alkanes) in the C
2
–C
5
experiment.
C2
C3
iC4
nC4
iC5
nC5
0
0.30
0.18
0.12
0.12
0.11
0.14
77
0.35
0.21
0.13
0.13
0.09
0.08
120
0.26
0.16
0.12
0.14
0.15
0.16
186
0.41
0.24
0.14
0.12
0.05
0.03
216
0.33
0.20
0.13
0.14
0.11
0.10