SUPPLEMENTARY INFORMATION for the paper entitled
A theoretical investigation of the atmospherically important reaction between
chlorine atoms and formic acid: determination of the reaction mechanism and
calculation of the rate coefficient at different temperatures
Maggie Ng,[a] Daniel K. W. Mok,*,[a] Edmond P. F. Lee,[a],[b] and John M. Dyke[b]
[a] M. Ng, D. K. W. Mok, E. P. F. Lee
Department of Applied Biology and Chemical Technology,
Hong Kong Polytechnic University, Hung Hom, Hong Kong
E-mail: Daniel@polyu.edu.hk
[b] E. P. F. Lee, J. M. Dyke
School of Chemistry, Faculty of Natural and Environmental Sciences,
University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom
Lists of figures and tables (according to the order in which they are referred to in the main
manuscript):
Figures S1 to S3: Optimized structures of various species.
Tables S1 to S3: Differences between single level and benchmark energies.
Tables S4: Computed relative energies of reaction channels (1b) and (2b).
Table S5: Available ΔHf values of HCO2.
Table S6: kCVT/kTST ratios computed at different single levels.
Figure S4: ΔG(s*) versus s plots at B3LYP and M06 single levels at 700 and 800 K.
Table S7: Recommended overall ICVT/SCT rate coefficients (kICVT/SCT; in cm3molecule-1s-1):
Table S8: Rate coefficients (in s-1) computed at the RCCSD(T)/CBS1//MP2 level for the
trans-HCOOH  cis-HCOOH isomerization.
Table S9: Rate coefficients (in s-1) computed at the RCCSD(T)/CBS1//MP2 level for the
cis-HOCO  trans-HOCO isomerization;
Supplementary Text: A section on the effect of the presence of both cis and trans HCOOH on the
overall rate of removal of formic acid from the Cl + HCOOH reaction.
Figure S1 Optimized geometries of the reactants (R) and products (P) at the MP2/6-31++G**(5D)
and M06-2X/6-31+G* (in parentheses) levels. The bond lengths are in Angstrom (Å).
Figure S2 Optimized geometries of the reactant complexes (RC) and product complexes (PC) at
MP2/6-31++G**(5D) and M06-2X/6-31+G* (in parentheses). The bond lengths are in Angstrom
(Å). (The RC for channel 1(b) could not be optimized; see text)
Figure S3 Optimized geometries of the transition states (TS) at MP2/6-31++G**(5D) and M062X/6-31+G* (in parentheses). The bond lengths are in the unit of Angstrom (Å).
Table S1. Differences of computed reaction energies (∆E0RX; in kcal/mol) and activation energies
(∆E0‡; in kcal/mol), including the zero-point energy (ZPE) corrections, as well as reaction
enthalpies (∆H298RX; in kcal/mol) from the theoretical benchmark (RCCSD(T)/CBS2//MP2) at
various single levels for channels (1a), (2a), (1b) and (2b). This table uses values from Table 2 in
the paper.
Level of Theory
Channel (1a)
Channel (1b)
Cl + trans-HCOOH
Cl + cis-HCOOH
→ HCl + cis-HOCO
→ HCl + trans-HOCO
∆E0RX ∆E0‡
B3LYP/6-31++G**(5D)
2.92
∆H298RX
-2.72 2.93
2.30
-5.04 2.31
BH&HLYP/6-31++G**(5D) 6.43
4.69
6.44
5.76
2.66
BMK/6-31+G**
3.65
-1.13 3.65
2.63
-4.21 2.64
M05/6-31+G**
1.69
-2.26 1.69
1.68
-4.61 1.68
M06/6-31+G**
3.79
-1.47 3.79
3.54
-4.22 3.54
M06-2X/6-31+G**
4.44
-0.71 4.43
3.68
-3.14 3.69
UMP2/6-31++G**(5D)
6.12
6.72
5.02
6.46
Level of Theory
Channel (2a)
Channel (2b)
Cl + trans-HCOOH
Cl + cis-HCOOH
→ HCl + HCOO (2A1)
→ HCl + HCOO (2A1)
∆E0RX ∆E0‡
a
∆H298RX ∆E0RX ∆E0‡
6.12
∆H298RX ∆E0RX ∆E0‡
5.76
5.02
∆H298RX
B3LYP/6-31++G**(5D)
-4.66
a
-2.96
-5.22
-11.42 -3.71
BH&HLYP/6-31++G**(5D)
b
1.93
b
b
0.47
b
BMK/6-31+G**
-0.35
-2.43
0.74
-1.27
-5.70
-0.19
M05/6-31+G**
c
-5.72
c
c
-9.59
c
M06/6-31+G**
c
-2.26
c
c
-9.42
c
M06-2X/6-31+G**
c
1.69
c
c
-4.12
c
UMP2/6-31++G**(5D)
4.10
13.66 4.10
3.18
9.18
3.18
Failed to locate the transition state structure.
There is a b2 mode, which has a very large and unrealistic computed frequency of 8249 cm -1, on
HCOO (2A1).
c
There is a computed imaginary vibrational frequency on HCOO (2A1).
b
Table S2. Differences of computed relative energies (kcal/mol) of the reactant complex (RC),
transition state (∆E‡), product complex (PC) and separate products (∆ERX), with respect to the
separate reactants, from the theoretical benchmark (RCCSD(T)/CBS2//MP2) at various single
levels for the Cl + trans-HCOOH → HCl + cis-HOCO reaction (channel [1a]). This table uses
values from Table 3 in the paper.
Level of Theorya
∆E‡
RC
∆Ee
∆E0
∆Ee
∆ERX
PC
∆E0
∆Ee
∆E0
∆Ee
∆E0
B3LYP/6-31++G**(5D)
1.47 0.72 -2.66 -2.72 2.81 2.88 3.11 2.92
BH&HLYP/6-31++G**(5D)
a
a
5.13
BMK/6-31+G**
a
a
-1.14 -1.13 3.85 4.23 3.89 3.65
M05/6-31+G**
1.78 1.31 -2.28 -2.26 1.19 1.97 1.86 1.69
M06/6-31+G**
1.11 0.72 -1.51 -1.47 3.02 3.61 3.86 3.79
M06-2X/6-31+G**
0.11 0.11 -0.42 -0.71 3.80 3.82 4.53 4.44
UMP2/6-31++G**(5D)
0.49 0.49 6.72
a
Fail to locate the RC structure.
4.69
6.72
6.86 6.65 6.70 6.43
5.68 5.68 6.12 6.12
Table S3. Differences of computed reaction energies (∆E0RX; in kcal/mol) and activation energies
(∆E0‡; in kcal/mol), including the zero-point energy (ZPE) corrections, as well as reaction
enthalpies from the theoretical benchmark (RCCSD(T)/CBS2//MP2), at various single levels for the
isomerizations of HCOOH and HOCO. This table uses values from Table 4 in the paper.
Level of Theory
trans-HCOOH→cis-HCOOH cis-HOCO→trans-HOCO
∆E0RX
∆E0‡
∆H298RX
∆E0RX
∆E0‡
∆H298RX
0.56
0.87
0.55
-0.05
0.55
-0.05
BH&HLYP/6-31++G**(5D) 1.01
0.64
1.01
0.33
0.54
0.33
BMK/6-31+G**
0.96
1.07
0.96
-0.07
0.65
-0.06
M05/6-31+G**
0.77
1.39
0.75
0.65
1.09
0.65
M06/6-31+G**
0.59
1.06
0.59
0.36
0.88
0.36
M06-2X/6-31+G**
0.91
0.44
0.89
0.19
0.31
0.19
UMP2/6-31++G**(5D)
0.92
1.09
0.92
-0.17
1.22
-0.17
B3LYP/6-31++G**(5D)
Table S4
Computed reaction energies (∆ERX; in kcal/mol) and activation energies (∆E‡; in kcal/mol) at
different levels of theory for the Cl + cis-HCOOH → HCl + trans-HOCO reaction (channel [1b]).
Level of Theory
∆EeRX ∆E0RX ∆Ee‡ ∆E0‡
B3LYP/6-31++G**(5D)
-3.24
-6.88
-4.48 -7.96
BH&HLYP/6-31++G**(5D) 0.36
-3.43
3.52
BMK/6-31+G**
-2.80
-6.55
-3.59 -7.13
M05/6-31+G**
-3.96
-7.50
-3.92 -7.53
M06/6-31+G**
-2.12
-5.65
-3.79 -7.14
M06-2X/6-31+G**
-1.78
-5.51
-2.47 -6.06
UMP2/6-31++G**(5D)
-0.64
-4.16
6.28
UCCSD(T)-F12/CBS//MP2
-5.72
-9.24
-1.24 -3.98
RCCSD(T)/CBS1//MP2
-5.27
-8.79
-0.26 -3.00
RCCSD(T)/CBS2//MP2
-5.66
-9.18
-0.18 -2.92
-0.27
3.53
Computed reaction energies (∆ERX; in kcal/mol) and activation energies (∆E‡; in kcal/mol) at
different levels of theory for the Cl + cis-HCOOH → HCl + HCOO reaction (channel [2b]).
Level of Theory
HCOO
TS2b
2A’
2A
1
B3LYP/6-31++G**(5D)
∆EeRX ∆E0RX ∆EeRX ∆E0RX ∆Ee‡
∆E0‡
8.74
3.46
1.99
7.93
3.50
8.37
BH&HLYP/6-31++G**(5D) 20.11
a
11.62
6.91
19.44 15.35
BMK/6-31+G**
13.13
5.94
12.74
6.75
13.85 9.18
M05/6-31+G**
8.15
b
8.14
b
10.26 5.29
M06/6-31+G**
10.17
b
10.14
3.74
10.41 5.46
M06-2X/6-31+G**
16.73
b
14.56
9.76
16.01 10.76
UMP2/6-31++G**(5D)
14.36
10.39
19.85
15.67
27.74 24.06
UCCSD(T)-F12/CBS//MP2
11.11
7.14
12.37
8.19
18.70 15.00
RCCSD(T)/CBS1//MP2
11.65
7.68
12.75
8.57
18.77 15.09
RCCSD(T)/CBS2//MP2
11.18
7.21
12.18
8.00
18.56 14.88
a
There is a b2 mode, which has a very large and unrealistic computed frequency of 8249 cm-1, on
HCOO (2A1).
b
There is a computed imaginary vibrational frequency on HCOO (2A1).
Table S5
A summary of available ΔHf(HCO2) values (in kcal/mol).
ΔHf
Remarks
Experimental
Year Reference
AE (CH3+)
-40±6
(Holmes 1991: AE inaccurate)
1987 Nishimura
AE (CH3)3C+
-37.7±3.0
Previous works discussed
1991 Holmes
Pes of HCO2-
-31±3
EA=3.498(15) eV and ΔHf(HCO2-)=
1995 Kim
-111 kcal/mol from JANAF,1988
Photodisso.
(-28.6±0.7) 0 K value using D0=111.7(3) kcal/mol 1997 Langford
of HCOOH
(as above)
-29.3±1.0
298 K value (thermal correction by
(as above)
Haworth 2000)
Computation
RCCSD(T)/CBS -30.1±1.0
+CV+SR; G2: -31.9; G3:-31.1
2000 Haworth
RCCSD(T)/CBS -30.4
+CV+SO+SR
2003 Dixon
RCCSD(T)/CBS -30.2±0.4
+CV+SO+SR; G2: -28.6; G3: -31.2;
2003 Feller
CBS-Q: -45.2
W1U
-30.4
Energies computed w.r.t. OH + CO
2005 Fabian
References for Table S5 (for earlier works, see Holmes 1991):
T. Nishimura, Q. Zha, G. G. Meisels, J. Chem. Phys. 1987,87, 4589.
J. L. Holmes, F. P. Lossing, P. M. Mayer, J. Am. Chem. Soc. 1991, 113, 9723.
E. H. Kim, S. E. Bradforth, D. W. Arnold, R. B. Metz, D. M. Neumark, J. Chem. Phys. 1995, 103,
7801.
S. R. Langford, A. D. Batten, M. Kono, M. N. R.Ashfold, J. Chem. Soc., Faraday Trans. 1997, 93,
3757.
N. L. Haworth, M. H. Smith, G. B. Bacskay, J. C. Mackie, J. Phys. Chem. A 2000, 104, 7600.
D. A. Dixon, D. Feller, J. S. Francisco, J. Phys. Chem. A 2003, 107, 186.
D. Feller, D. A. Dixon, J. S. Francisco, J. Phys. Chem. A 2003, 107, 1604.
W. M. F. Fabian, R. Janoschek, Journal of Molecular Structure: THEOCHEM 2005, 713, 227.
S. G. Lias, J. E. Bartmess, J. F. Liebman, J. L. Holmes, R. D. Levin, W. G. Mallard, J. Phys. Chem.
Ref. Data 17, Suppl. No. 1 (1988).
Table S6 kCVT/kTST ratios computed at different single levels
Level of Theory
Temperature
ΔE0‡
ωi
%HF exchange
300 K 1500 K
B3LYP
0.41
0.40 -0.95
415i
20
M05
0.19
0.28 -0.49
556i
28
M06
0.89
0.43
0.30
375i
27
BMK
0.34
0.45
0.64
441i
42
M06-2X
0.13
0.24
1.06
915i
54
BH&HLYP
0.45
0.23
6.46 1211i
50
MP2
0.07
0.20
8.49 1348i
100
Figure S4: ΔG(s*) versus s plots at B3LYP and M06 single levels at 700 and 800 K.
B3LYP
M06
Table S7. Recommended overall ICVT/SCT rate coefficients (kICVT/SCT; in cm3molecule-1s-1):
k1aICVT/SCT was obtained for reaction 1a with a barrier of 3.14 kcal.mol-1 (including SO in Cl) at the
ICVT/SCT
RCCSD(T)/CBS2//MP2 level. k1b
was obtained using the RCCSD(T)/CBS2//MP2 computed
ICVT/SCT
+ k1bICVT/SCT * K eq is the total rate coefficient for removal of formic
surface for reaction 1b. k1a
acid by chlorine atoms, which includes allowance for the presence of both trans and cis HCOOH at
ICVT/SCT
+ k1bICVT/SCT * K eq values are the final recommended values for the
a given temperature. These k1a
overall rate coefficients.
Temperature (K)
/ SCT
k1ICVT
a
ICVT/SCT
k1b
k1aICVT/SCT + k1bICVT/SCT * K eq
200
250
300
350
400
450
500
550
600
650
700
750
800
850
900
950
1000
1050
1100
1150
1200
1250
1300
1350
1400
1450
1500
8.17E-14
1.31E-13
2.00E-13
2.89E-13
3.98E-13
5.24E-13
6.67E-13
8.26E-13
1.00E-12
1.19E-12
1.39E-12
1.60E-12
1.83E-12
2.06E-12
2.31E-12
2.57E-12
2.84E-12
3.13E-12
3.42E-12
3.72E-12
4.03E-12
4.36E-12
4.69E-12
5.03E-12
5.38E-12
5.75E-12
6.12E-12
6.93E-13
1.07E-12
1.48E-12
1.93E-12
2.40E-12
2.88E-12
3.36E-12
3.85E-12
4.35E-12
4.83E-12
5.33E-12
5.82E-12
6.32E-12
6.82E-12
7.32E-12
7.83E-12
8.35E-12
8.87E-12
9.39E-12
9.92E-12
1.05E-11
1.10E-11
1.16E-11
1.21E-11
1.27E-11
1.33E-11
1.39E-11
8.17E-14
1.31E-13
2.02E-13
2.96E-13
4.14E-13
5.60E-13
7.33E-13
9.35E-13
1.17E-12
1.43E-12
1.72E-12
2.05E-12
2.40E-12
2.79E-12
3.21E-12
3.65E-12
4.13E-12
4.63E-12
5.17E-12
5.73E-12
6.32E-12
6.93E-12
7.58E-12
8.25E-12
8.94E-12
9.66E-12
1.04E-11
Table S8 Rate coefficients (in s-1) computed at the RCCSD(T)/CBS1//MP2 level for the transHCOOH  cis-HCOOH isomerization; computed forward and reverse equilibrium constants are
also shown.
RCCSD(T)/CBS1//MP2 (forward rate coefficients)
T (K)
TST
CVT
ICVT
TST/ZCT
CVT/ZCT
ICVT/ZCT
TST/SCT
CVT/SCT
ICVT/SCT
200
1.75E0
1.75E0
1.75E0
4.20E0
4.21E0
4.21E0
4.92E0
4.92E0
4.92E0
300
3.41E+4
3.41E+4
3.41E+4
4.86E+4
4.87E+4
4.87E+4
5.11E+4
5.12E+4
5.12E+4
500
1.04E+8
1.04E+8
1.04E+8
1.18E+8
1.18E+8
1.18E+8
1.19E+8
1.20E+8
1.20E+8
1000
4.84E+10
4.84E+10
4.84E+10
4.99E+10
4.99E+10
4.99E+10
5.01E+10
5.01E+10
5.01E+10
1500
3.89E+11
3.88E+11
3.88E+11
3.94E+11
3.94E+11
3.94E+11
3.94E+11
3.94E+11
3.94E+11
RCCSD(T)/CBS1//MP2 (reverse rate coefficients)
T (K)
TST
CVT
ICVT
TST/ZCT
CVT/ZCT
ICVT/ZCT
TST/SCT
CVT/SCT
ICVT/SCT
200
3.91E+4
3.90E+4
3.91E+4
9.39E+4
9.40E+4
9.40E+4
1.10E+5
1.10E+5
1.10E+5
300
2.65E+7
2.64E+7
2.64E+7
3.78E+7
3.78E+7
3.78E+7
3.97E+7
3.97E+7
3.97E+7
500
5.34E+9
5.33E+9
5.33E+9
6.03E+9
6.03E+9
6.03E+9
6.13E+9
6.13E+9
6.13E+9
1000
3.14E+11
3.14E+11
3.14E+11
3.24E+11
3.24E+11
3.24E+11
3.25E+11
3.25E+11
3.25E+11
1500
1.26E+12
1.26E+12
1.26E+12
1.27E+12
1.27E+12
1.27E+12
1.28E+12
1.28E+12
1.28E+12
RCCSD(T)/CBS1//MP2 Equilibrium Constants (unitless)
T (K)
Forward
Reverse
200
4.48E-5
2.23E+4
250
3.35E-4
2.99E+3
300
1.29E-3
7.76E+2
350
3.39E-3
2.95E+2
400
7.01E-3
1.43E+2
450
1.24E-2
8.09E+1
500
1.95E-2
5.13E+1
550
2.83E-2
3.53E+1
600
3.87E-2
2.58E+1
650
5.04E-2
1.98E+1
700
6.33E-2
1.58E+1
750
7.71E-2
1.30E+1
800
9.16E-2
1.09E+1
850
1.07E-1
9.37E0
900
1.22E-1
8.18E0
950
1.38E-1
7.24E0
1000
1.54E-1
6.49E0
1050
1.70E-1
5.88E0
1100
1.86E-1
5.37E0
1150
2.02E-1
4.95E0
1200
2.18E-1
4.59E0
1250
2.34E-1
4.28E0
1300
2.49E-1
4.01E0
1350
2.65E-1
3.78E0
1400
2.80E-1
3.57E0
1450
2.95E-1
3.40E0
1500
3.09E-1
3.24E0
Table S9
Rate coefficients (in s-1) computed at the RCCSD(T)/CBS1//MP2 level for the cis-HOCO  transHOCO isomerization; computed forward and reverse equilibrium constants are also shown.
RCCSD(T)/CBS1//MP2 (forward rate coefficients)
T (K)
TST
CVT
ICVT
TST/ZCT
CVT/ZCT
ICVT/ZCT
TST/SCT
CVT/SCT
ICVT/SCT
200
2.75E+5
2.74E+5
2.74E+5
7.82E+5
8.20E+5
8.20E+5
9.69E+5
1.02E+6
1.02E+6
300
9.68E+7
9.67E+7
9.67E+7
1.50E+8
1.55E+8
1.55E+8
1.64E+8
1.69E+8
1.69E+8
500
1.17E+10
1.17E+10
1.17E+10
1.35E+10
1.38E+10
1.38E+10
1.40E+10
1.42E+10
1.42E+10
1000
4.66E+11
4.66E+11
4.66E+11
4.82E+11
4.86E+11
4.86E+11
4.85E+11
4.90E+11
4.90E+11
1500
1.63E+12
1.63E+12
1.63E+12
1.65E+12
1.66E+12
1.66E+12
1.65E+12
1.66E+12
1.66E+12
RCCSD(T)/CBS1//MP2 (reverse rate coefficients)
T (K)
TST
CVT
ICVT
TST/ZCT
CVT/ZCT
ICVT/ZCT
TST/SCT
CVT/SCT
ICVT/SCT
200
4.98E+3
4.98E+3
4.98E+3
1.42E+4
1.49E+4
1.49E+4
1.76E+4
1.85E+4
1.85E+4
300
6.77E+6
6.76E+6
6.13E+6
1.05E+7
1.08E+7
1.08E+7
1.15E+7
1.18E+7
1.18E+7
500
2.38E+9
2.38E+9
2.38E+9
2.76E+9
2.81E+9
2.81E+9
2.85E+9
2.90E+9
2.90E+9
1000
2.11E+11
2.11E+11
2.11E+11
2.18E+11
2.20+11
2.20+11
2.20E+11
2.22E+11
2.22E+11
1500
9.61E+11
9.61E+11
9.61E+11
9.73E+11
9.79E+11
9.79E+11
9.76E+11
9.82E+11
9.82E+11
RCCSD(T)/CBS1//MP2 Equilibrium Constants (unitless)
T (K)
Forward
Reverse
200
5.51E+1
1.82E-2
300
1.43E+1
6.99E-2
500
4.90E0
2.04E-1
1000
2.21E0
4.52E-1
1500
1.69E0
5.91E-1
Supplementary Text:
The effect of the presence of both cis and trans HCOOH on the overall rate of removal of
formic acid from the Cl + HCOOH reaction
The overall rate of removal of formic acid from the Cl + HCOOH reaction at a selected temperature
needs to take into account the presence of both cis and trans HCOOH. The equilibrium constant K
for this isomerisation can be expressed in terms of the forward and reverse rate coefficients for this
process as:
Keq = cis-HCOOH/ trans-HCOOH = kf/kr
The net loss rate of formic acid can be conveniently expressed as the net rate of HCl production:dHCl/dt = k1a Cl trans-HCOOH + k1b Cl cis HCOOH
= Cl trans-HCOOH ( k1a + k1b.kf/kr)
= Cl trans-HCOOH ( k1a + k1b.Keq)
Values of k1a and k1b obtained at the ICVT/SCT level are listed in Table S8 and the computed
values of (k1a + k1b.Keq ) in the temperature range are shown in column 4 of this Table. It can be
seen from this Table that the k1b.Keq correction to the overall rate coefficient is negligible in the
temperature range 200-300 K (the atmospherically significant region), and small at higher
temperatures. The biggest change is at 1500 K where k1a is 6.12 x10-12 cm3molecule-1s-1 and (k1a +
k1b. Keq ) is 10.4 x10-12 cm3molecule-1s-1.