Tunneling effects in Bimolecular Nucleophilic Substitution (SN2)
Reactions
Wan-Chen Tsai and Wei-Ping Hu*
Department of Chemistry and Biochemistry, National Chung Cheng University, Chia-Yi,
Taiwan 621
Abstract
Tunneling effects on the bimolecular rate constants of three SN2 reactions have been
studied theoretically using dual-level dynamics approach with variational transition state
theory including multidimensional tunneling. The three reactions, (1) gas-phase CN + CH3F,
(2) gas-phase OH(H2O) + CH3F microsolvated reaction, and (3) OH + CHF in bulk water
solvent represented models of S2 reactions with positive energy barrier heights and with
various degrees of solvation. The calculated results indicated that the tunneling effects cannot
be ignored in evaluating the reaction rate constants of the S2 reactions with even modest
barrier heights (> 5 kcal/mol) at room temperature, and they contribute significantly to the
rate constants at lower temperature. The calculation also suggested that, regardless of the
levels of solvation, the tunneling effects resulted mostly from the motion of central carbon
atom, not from the primary hydrogen atoms, through the sharp energy barriers. The heavy
atom tunneling contributed importantly to the calculated carbon kinetic isotope effects (KIEs)
at low temperature, and the 13C and 14C KIEs as large as 7 and 40 have been predicted.
Introduction
The ion-molecule nucleophilic substitution (SN2) reactions, which usually involve an
alkyl halide and an anion (the nucleophilie), are ubiquitous and very important in organic and
interstellar chemistry.13 Most methyl and ethyl halides can only undergo the SN2 pathway.
However, for i-propyl or higher branched alkyl halides, the SN2 and E2 reactions may be
competitive with the same reactants and produce the same ionic products.4,12,14,16,1921 This
makes it difficult to distinguish these two pathways by experiments, especially in the gas
phase. Therefore, measurement of the bimolecular rate constants and kinetic isotope effects
(KIEs) can be very useful for investigating the reaction mechanisms. In the last three decades,
there have been significant amount of experimental and theoretical studies on gas-phase SN2
reactions. Due to the experimental techniques employed and the rate of molecular collisions,
the gas-phase rate constants could be measured in the range of 109 to 1012 cm3 molecule
s1. This translates to the ion-molecule reactions with no barriers to with barrier heights of ~5
kcal/mol. It has been known that SN2 reactions usually show lightly inverse deuterium KIEs
(kH/kD ≈ 0.71.0),412,1517,2022 while the E2 reactions show strong normal deuterium
KIEs at room temperature (kH/kD ≈ 26).4,12,13,16,18,20,21,23
The SN2 reactions often proceed much efficiently in the gas phase than the in the
solution. Due to the strong ion-dipole interaction, most exoergic SN2 reactions have very low
energy barriers in the gas phase. However, in the solution phase, the strong solvation effects
usually raise the energy barriers significantly.21 The SN2 reactions in the gas phase with
small or negligible energy barriers are very fast with bimolecular rate constants approaching
that of those of ion-dipole collisions. Recently, there have been some experimental and
theoretical studies on the microsolvated systems (added one or a few solvent molecules) in
attempt to connect the gap of our understanding between the gas phase and solution phase
reactions.5,8,9,11,13,17,18,22,23 For example, Truhlar have evaluated the microsolvated system
of Cl(H2O)n (n = 02) + CH3Cl reactions.5 As the microsolvated H2O molecules increase,
the barrier heights were raised from 3.1 kcal/mol (n = 0), 5.4 kcal/mol (n = 1) to 10.7
kcal/mol (n = 2). Simultaneously, the rate constants were predicted to be 2.36 × 1014 cm3
molecule1 s1 (n = 0), 6.38 × 1018 cm3 molecule1 s1 (n = 1), and 2.07 × 1020 cm3
molecule1 s1 (n = 1), respectively. The predicted KIEs due to the CD3 substitutions were
0.96, 0.95, and 0.93 for n = 0, 1, and 2, and the KIEs from the D2O substitutions were 1.04
and 1.26 for n = 1 and 2, respectively. According to the results, we could inference the
number of the microsolvated H2O molecules had no significant effects on the deuterium
KIEs.
Scheme 1 revealed the potential energy surface of the common gas-phase and
solution-phase SN2 reactions. In the gas-phase, ion and molecule formed an ion-dipole
complex with ~ 20 kcal/mol energy released before the transition state. The ion-dipole
complex had high internal energy so that the reaction could easy overcome the transition state
and form another ion-dipole complex before it separated into the products. Therefore, most
gas-phase SN2 reactions have low barrier heights and fast reaction rate constants. For the
solution-phase SN2 reactions, the negative charges were usually much more localized in the
reactants than in the transition states, the solvation effects were usually stronger on the
reactants, and thus the energy barriers were significantly higher in polar solvent than in the
gas phase.2427 For example, Tanaka had measured the rate constants of several SN2
reactions in the gas phase and in solution.24 For the CH3Br + Cl reaction, the rate constants
were 2.1 × 1011 cm3 molecule1 s1 and 8.2 × 1027 cm3 molecule1 s1, respectively. The
solvation energies significantly raised the barrier height and decreased the reaction rate
constants. There may be some differences of the kinetic isotope effects in the gas phase and
in solution. The comparison of the CN + CH3I in the gas phase and in solution has been
reported.21 In the gas phase, the computational KIE due to the CD3 substitution was 0.83 is in
excellent agreement with the experimental KIE of 0.84 at 298 K. In the solution phase, the
experimental KIE from the CD3 substitution was 0.902 in the 40% CH3OH/60% DMSO (v/v)
solution at 293 K.
As the solvation effects raising the energy barriers of the SN2 reaction, the tunneling
effects may dramatic influence the rate constants and KIEs at low temperature due to the
motion of hydrogen and α-carbon atoms. In the past, the rate constants of the high-barrier
SN2 reactions were too slow that can’t be measured experimentally, and most theoretical
studies on the SN2 rate constants and KIEs were based on the transition state theory (TST).
However, the TST theory was only feasible for the small barrier (4 ~ 3 kcal/mol) systems.
For the high barrier cases, the tunneling contribution to the rate constants and KIEs needed to
be calculated accurately. In this research, we performed theoretical studies on three
exothermic SN2 reactions, (1) gas-phase CN + CH3F, (2) gas-phase OH(H2O) + CH3F
microsolvated reaction, and (3) OH + CH3F in bulk water solvent, which have positive
energy barriers. We used the variational transition state theory with multidimensional
tunneling (VTST/MT)2833 correction to calculate the dynamics behaviors of reaction rate
constants and KIEs from the various isotope substitutions over a wide range of temperature.
The energetics, geometries, reaction rate constants, kinetic isotope effects, solvent kinetic
isotope effects, and tunneling effects of reactions were discussed in this report.
Computational Methods
Electronic Structure Calculations. The geometry and vibrational frequencies of
stationary points and transition states were calculated using the B3LYP34 hybrid functional
with the 6-311+G(d,p)35,36 basis set and MP237 theory with the 6-311+G(d,p), aug-cc-pVDZ,
and aug-cc-pVTZ38,39 basis sets. Single-point energies were calculated at the
CCSD(T)40/aug-cc-pVTZ
level.
Additionally,
MLSE(C1)-M06-2X41
and
CCSD(T)/aug-cc-pVQZ single point energies were also calculated for the gas-phase CN +
CH3F reaction. Bulk solvation in water was modeled using the polarizable continuum model
(PCM)4244 for the OH + CH3F reaction. All the electronic structure calculations were
performed using the Gaussian 09 program.45
Dual-level VTST/MT Dynamics Calculations. The dual-level46,47 variational
transition state theory with multidimensional tunneling (VTST/MT) correction was used in
the present study to calculate the thermal rate constants over the temperature range of 35 K to
600 K. The method requires a qualitatively correct “low-level” potential energy surface (PES),
and a set of “high-level” geometry and energy data on the stationary points along the reaction
path for the interpolated corrections to the low-level PES. We selected the MP2/aug-cc-pVDZ
to calculate the low-level PES as required for the VTST/MT calculation. The reaction path
was calculated from 6.5 to 5.5 bohrs for gas-phase CN + CH3F reaction, 5.5 to 5.5 bohrs
for gas-phase OH(H2O) + CH3F reaction, and 9.0 to 5.0 bohrs for OH + CH3F in bulk
water solvent reaction with a gradient step size of 0.006 bohr and a hessian step size of 0.03
bohr using the Page-McIver method48,49 in the mass-scaled coordinates with a scaling mass
of 1 amu. Redundant internal coordinate systems5053 were used in the vibrational analysis
along the reaction path. The interpolated correction was based on the ion-dipole complexes
for the gas-phase CN + CH3F and OH(H2O) + CH3F reactions, and was based on the
reactants and products for the OH + CH3F in bulk water solvent. The high-level geometries
were obtained at the MP2/aug-cc-pVTZ level, and the high-level energies data were obtained
at CCSD(T)/aug-cc-pVTZ (CCSD(T)/aug-cc-pVQZ for gas-phase CN + CH3F reaction. The
SIL-1 interpolated correction scheme54 was applied in the dual-level calculation using the
CCSD(T)/aug-cc-pVTZ energies along the low-level reaction path geometries to estimate the
barrier widths. Thermal rate constants as a function of temperature were calculated at the
conventional transition state theory (TST), canonical variational theory (CVT),28,29 canonical
variational theory with small-curvature tunneling approximation (CVT/SCT),30,33,55 and
canonical variational theory with microcanonical optimized multidimensional tunneling
correction (CVT/μOMT)33 levels. Since the SCT tunneling probabilities were larger than
LCT, the CVT/μOMT rate constants were identical to the CVT/SCT rate constants of these
three SN2 reactions in this research. Thus, we only showed the CVT/SCT rate constants in the
results. The rotation symmetry number of CH3F (C3v) is three. For CN + CH3F, the rotation
symmetry number of transition state (C3v) is three, so the overall symmetry numbers of
reaction were set to one. For OH(H2O) + CH3F, the transition state structure (C1) is chiral,
so the overall symmetry numbers of reaction were set to six. For OH + CH3F, the symmetry
of transition state is Cs, therefore the overall symmetry numbers of reaction were set to three.
The dual-level VTST/MT calculations were performed using the Gaussrate 8.4H program,
which is a locally modified version of Gaussrate 8.2 program56 to work with the new
Gaussian 09 program. The Gaussrate program primarily served as an interface between the
Gaussian 09 and Polyrate 8.2 programs.57
Results and Discussion
Gas-phase CN + CH3F reaction
(a) Geometry and Energetics
Figure 1 shows the calculated geometries of the CN + CH3F → F + CH3CN reaction
at the MP2/aug-cc-pVTZ level.
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Table 1. Calculated reaction energeticsa (in kcal/mol) of the gas-phase CN + CH3F → F +
CH3CN reaction.
Erxnb
B3LYP/6-311+G(d,p)
MP2/6-311+G(d,p)
3.2
5.2
MP2/aug-cc-pVDZ
MP2/aug-cc-pVTZ
7.2
5.9
1.2
1.4
1.2
CCSD(T)/aug-cc-pVTZc
CCSD(T)/aug-cc-pVQZc
MLSE(C1)-M06-2Xc
energies relative to CN + CH3F
bEnergy of reaction
cUsing MP2/aug-cc-pVTZ structures
aAll
ion-dipole complex ion-dipole complex
barrier height
CN...CH3F
F…CH3CN
8.9
8.3
28.9
14.5
9.5
28.1
9.2
9.5
31.0
11.3
9.1
29.9
11.7
9.1
25.6
12.0
8.9
25.7
12.1
9.2
25.7
Table 2. Calculated rate constants (in cm3 molecule1 s1) by the TST and CVT/SCT methods of the gas-phase CN + CH3F reaction.
CN + CH3F
CN + CD3F
CN + 13CH3F
CN + 14CH3F
CN + 13CD3F
T(K)
TST
CVT/SCT
TST
CVT/SCT
TST
CVT/SCT
TST
CVT/SCT
TST
CVT/SCT
35
50
70
6.43(90)a
4.15(67)
6.36(52)
1.03(32)
7.79(33)
7.38(33)
3.13(89)
1.17(66)
1.24(51)
1.39(32)
1.05(32)
9.93(33)
4.17(90)
3.03(67)
5.02(52)
1.94(33)
1.48(33)
1.43(33)
2.86(90)
2.30(67)
4.09(52)
4.30(34)
3.32(34)
3.28(34)
1.91(89)
8.18(67)
9.58(52)
2.71(33)
2.07(33)
1.99(33)
90
100
150
200
250
300
400
1.73(43)
1.56(40)
1.22(31)
3.86(27)
2.15(24)
1.58(22)
4.01(20)
9.10(33)
1.15(32)
1.81(30)
1.07(26)
3.80(24)
2.27(22)
4.71(20)
2.77(43)
2.33(40)
1.50(31)
4.33(27)
2.31(24)
1.66(22)
4.17(20)
1.24(32)
1.55(32)
2.17(30)
1.19(26)
4.05(24)
2.37(22)
4.87(20)
1.43(43)
1.31(40)
1.08(31)
3.50(27)
1.98(24)
1.47(22)
3.79(20)
1.84(33)
2.41(33)
1.10(30)
8.82(27)
3.33(24)
2.05(22)
4.38(20)
1.21(43)
1.12(40)
9.65(32)
3.21(27)
1.84(24)
1.38(22)
3.61(20)
4.39(34)
6.01(34)
7.65(31)
7.56(27)
3.00(24)
1.88(22)
4.12(20)
2.25(43)
1.93(40)
1.31(31)
3.92(27)
2.12(24)
1.55(22)
3.94(20)
2.59(33)
3.38(33)
1.34(30)
9.84(27)
3.57(24)
2.15(22)
4.54(20)
500
1.29(18)
1.44(17)
1.38(18)
1.46(17)
1.34(18)
1.50(17)
1.43(18)
1.51(17)
1.23(18)
1.38(17)
1.30(18)
1.38(17)
1.18(18)
1.33(17)
1.24(18)
1.33(17)
1.28(18)
1.44(17)
1.35(18)
1.44(17)
600
a6.43(90)
means 6.43 × 1090
Table 3. Calculated KIEs by the TST and CVT/SCT methods of the gas-phase CN + CH3F reaction.
KIE(CD3)
KIE(13CD3)
KIE(13C)
TST
CVT/SCT
KIE(14C)
TST
CVT/SCT
TST
CVT/SCT
T(K)
TST
CVT/SCT
35
50
70
0.205
0.356
0.511
0.744
0.743
0.743
1.541
1.370
1.265
5.322
5.258
5.144
2.244
1.802
1.554
24.009
23.478
22.492
0.337
0.507
0.664
3.810
3.769
3.698
90
100
150
200
250
300
400
0.624
0.668
0.815
0.890
0.930
0.950
0.962
0.737
0.740
0.832
0.902
0.937
0.957
0.967
1.210
1.191
1.134
1.104
1.085
1.073
1.058
4.947
4.763
1.645
1.213
1.140
1.107
1.075
1.430
1.388
1.266
1.204
1.167
1.142
1.112
20.732
19.112
2.362
1.414
1.268
1.204
1.144
0.768
0.807
0.930
0.986
1.011
1.019
1.018
3.521
3.401
1.352
1.087
1.063
1.055
1.037
500
600
0.963
0.962
0.965
0.963
1.049
1.044
1.060
1.051
1.095
1.085
1.114
1.098
1.010
1.005
1.021
1.011
Table 4. Calculated reaction energeticsa (in kcal/mol) of the gas-phase OH(H2O) + CH3F reaction.
F(H2O) +
CH3OH
Erxnb
F +
CH3OH(H2O)
ion-dipole complex
F + H2O +
CH3OH
OH(H2O)...CH3F
F(H2O)...CH3OH
barrier
height
11.4
12.5
44.1
45.1
1.9
6.8
12.7
11.9
12.2
44.4
42.9
43.5
2.9
6.1
5.1
B3LYP/6-311+G(d,p)
MP2/6-311+G(d,p)
21.3
22.1
1.3
7.3
5.3
MP2/aug-cc-pVDZ
MP2/aug-cc-pVTZ
21.2
19.9
20.0
0.6
1.7
1.8
5.6
7.7
7.8
CCSD(T)/aug-cc-pVTZc
energies relative to OH(H2O) + CH3F
bEnergy of reaction
cUsing MP2/aug-cc-pVTZ structures
aAll
1.2
Table 5. Calculated rate constants (in cm3 molecule1 s1) by the TST and CVT/SCT methods of the gas-phase
OH(H2O) + CH3F reaction.
OH(H2O) + CH3F
OH(H2O) + CD3F
OD(H2O) + CH3F
OH(D2O) + CH3F
T(K)
TST
CVT/SCT
TST
CVT/SCT
TST
CVT/SCT
TST
CVT/SCT
35
50
1.31(59)a
7.35(46)
1.65(25)
1.20(25)
1.20(58)
3.05(45)
2.26(25)
1.71(25)
1.90(58)
4.49()
2.53(25)
1.84(25)
6.69(57)
5.55(44)
8.35(25)
6.18(25)
70
90
100
150
200
250
300
1.03(36)
1.24(31)
7.51(30)
1.79(24)
9.93(22)
4.90(20)
7.20(19)
1.14(25)
1.49(25)
1.96(25)
1.38(23)
2.36(21)
8.05(20)
9.91(19)
2.58(36)
2.37(31)
1.31(29)
2.40(24)
1.19(21)
5.52(20)
7.86(19)
1.69(25)
2.25(25)
2.99(25)
1.85(23)
2.82(21)
9.04(20)
1.08(18)
3.53(36)
3.08(31)
1.66(29)
2.82(24)
1.33(21)
5.98(20)
8.30(19)
1.75(25)
2.29(25)
3.04(25)
2.11(23)
3.17(21)
9.88(20)
1.15(18)
2.21(35)
1.33(30)
6.32(29)
7.36(24)
2.86(21)
1.14(19)
1.46(18)
5.99(25)
7.90(25)
1.04(24)
5.64(23)
6.86(21)
1.89(19)
2.03(18)
400
500
600
2.48(17) 2.90(17)
2.43(16) 2.64(16)
1.24(15) 1.30(15)
OD(D2O) + CH3F
2.63(17) 3.07(17)
2.56(16) 2.78(16)
1.30(15) 1.36(15)
OH(H2O) + 13CH3F
2.68(17) 3.16(17)
2.55(16) 2.79(16)
1.28(15) 1.35(15)
OH(H2O) + 14CH3F
4.21(17) 4.96(17)
3.69(16) 4.04(16)
1.74(15) 1.83(15)
OH(H2O) + 13CD3F
T(K)
TST
CVT/SCT
TST
CVT/SCT
TST
CVT/SCT
TST
CVT/SCT
35
50
8.23(56)
3.02(43)
1.28(24)
9.36(25)
8.76(60)
5.48(46)
5.84(26)
4.30(26)
6.19(60)
4.24(46)
2.18(26)
1.62(26)
7.51(59)
2.18(45)
8.13(26)
6.21(26)
70
90
100
150
6.89(35)
3.04(30)
1.29(28)
1.08(23)
8.92(25)
1.17(24)
1.54(24)
8.06(23)
8.26(37)
1.04(31)
6.36(30)
1.59(24)
4.18(26)
5.72(26)
7.92(26)
9.99(24)
6.81(37)
8.86(32)
5.50(30)
1.43(24)
1.61(26)
2.32(26)
3.38(26)
7.61(24)
2.02(36)
1.95(31)
1.09(29)
2.12(24)
6.26(26)
8.76(26)
1.21(25)
1.33(23)
200
250
300
400
500
600
3.57(21)
1.31(19)
1.58(18)
4.27(17)
3.63(16)
1.68(15)
a1.31(59) means
8.58(21)
2.17(19)
2.20(18)
5.06(17)
4.00(16)
1.78(15)
1.31 × 1059
9.03(22)
4.53(20)
6.73(19)
2.35(17)
2.32(16)
1.19(15)
2.01(21)
7.18(20)
9.06(19)
2.71(17)
2.51(16)
1.24(15)
8.31(22)
4.23(20)
6.35(19)
2.24(17)
2.23(16)
1.15(15)
1.75(21)
6.49(20)
8.37(19)
2.56(17)
2.39(16)
1.19(15)
1.08(21)
5.10(20)
7.34(19)
2.49(17)
2.44(16)
1.25(15)
2.39(21)
8.05(20)
9.85(19)
2.88(17)
2.64(16)
1.30(15)
Table 6. Calculated KIEs by the TST and CVT/SCT methods of the gas-phase OH(H2O) + CH3F reaction.
KIE(CD3)
KIE(OD(D2O))
KIE(OD)
TST
CVT/SCT
TST
CVT/SCT
TST
CVT/SCT
KIE(D2O)
T(K)
TST
CVT/SCT
35
50
70
0.110
0.241
0.399
0.728
0.702
0.676
0.069
0.164
0.292
0.651
0.651
0.651
0.002
0.013
0.047
0.197
0.194
0.190
0.000
0.002
0.015
0.129
0.128
0.128
90
100
150
200
250
300
400
0.524
0.574
0.745
0.837
0.888
0.917
0.942
0.660
0.657
0.743
0.839
0.890
0.919
0.944
0.404
0.452
0.635
0.747
0.820
0.868
0.924
0.650
0.646
0.652
0.745
0.815
0.862
0.918
0.093
0.119
0.243
0.347
0.428
0.492
0.588
0.188
0.189
0.244
0.344
0.425
0.489
0.584
0.041
0.058
0.166
0.278
0.376
0.457
0.580
0.128
0.128
0.171
0.275
0.371
0.451
0.573
500
0.950
0.952
0.953
0.948
0.658
0.654
0.669
0.661
600
0.954
0.956
0.970
0.965
0.713
0.709
KIE(13CD3)
0.737
0.729
KIE(13C)
KIE(14C)
T(K)
TST
CVT/SCT
TST
CVT/SCT
TST
CVT/SCT
35
50
70
1.493
1.342
1.249
2.819
2.790
2.727
2.113
1.731
1.515
7.537
7.392
7.072
0.174
0.336
0.512
2.025
1.933
1.821
90
1.199
2.600
1.404
6.419
0.638
1.700
100
150
200
1.182
1.128
1.100
2.481
1.377
1.174
1.366
1.253
1.195
5.812
1.807
1.352
0.688
0.846
0.923
1.618
1.034
0.989
250
300
400
500
600
1.082
1.070
1.055
1.047
1.042
1.121
1.094
1.067
1.054
1.047
1.159
1.135
1.106
1.090
1.081
1.239
1.185
1.131
1.105
1.090
0.962
0.981
0.993
0.995
0.994
1.000
1.006
1.007
1.003
1.000
Table 7. Calculated reaction energeticsa (in kcal/mol) of the
OH + CH3F → F + CH3OH reaction in bulk water solvent.
B3LYP/6-311+G(d,p)
MP2/6-311+G(d,p)
MP2/aug-cc-pVDZ
MP2/aug-cc-pVTZ
CCSD(T)/aug-cc-pVTZb
Erxnb
25.7
27.0
25.7
barrier height
24.3
24.2
16.9
16.2
13.3
19.0
14.6
to OH + CH3F in bulk water solvent. Solvation
energies in water were calculated using the PCM model.
bEnergy of reaction
cUsing MP2/aug-cc-pVTZ structures.
aRelative
Table 8. Calculated reaction energeticsa (in kcal/mol) of the
OH + CH3F → F + CH3OH reaction in bulk water solvent.
Erxnb
barrier height
B3LYP/6-311+G(d,p)
MP2/6-311+G(d,p)
MP2/aug-cc-pVDZ
25.7
27.0
25.7
13.3
19.0
14.6
MP2/aug-cc-pVTZ
24.3
24.2
16.9
16.2
CCSD(T)/aug-cc-pVTZb
to OH + CH3F
bEnergy of reaction
cUsing MP2/aug-cc-pVTZ structures
aRelative
Table 9. Calculated rate constants (in cm3 molecule1 s1) by the TST and CVT/SCT methods of the OH + CH3F
reaction in bulk water solvent.
OH + CH3F
T(K)
35
50
TST
CVT/SCT
1.11(119)a 6.80(45)
1.53(87) 1.24(44)
70
90
100
150
200
250
300
3.56(66)
2.49(54)
3.45(50)
9.12(38)
1.57(31)
9.31(28)
3.26(25)
400
500
600
5.65(22) 7.25(22)
5.66(20) 6.50(20)
1.34(18) 1.45(18)
OH +13CH3F
2.26(43)
1.18(41)
8.99(41)
5.85(36)
6.51(31)
2.03(27)
5.37(25)
OH + CD3F
OD + CH3F
OD + CD3F
TST
CVT/SCT
TST
CVT/SCT
TST
CVT/SCT
7.90(119)
5.50(87)
1.12(44)
2.12(44)
4.12(118)
1.62(86)
2.62(46)
1.83(45)
3.05(117)
6.00(86)
4.14(46)
3.06(45)
8.23(66)
4.51(54)
5.74(50)
1.19(37)
1.85(31)
1.04(27)
3.52(25)
3.92(43)
1.96(41)
1.47(40)
8.03(36)
7.67(31)
2.26(27)
5.78(25)
1.68(65)
7.56(54)
9.00(50)
1.54(37)
2.18(31)
1.17(27)
3.82(25)
1.26(43)
1.46(41)
1.43(40)
1.00(35)
9.16(31)
2.56(27)
6.34(25)
3.94(65)
1.38(53)
1.51(49)
2.04(37)
2.58(31)
1.30(27)
4.15(25)
2.19(43)
2.53(41)
2.43(40)
1.38(35)
1.08(30)
2.86(27)
6.85(25)
6.20(22) 7.97(22)
6.00(20) 6.90(20)
1.39(18) 1.51(18)
OH +13CD3F
6.56(22)
6.29(20)
1.45(18)
8.40(22)
7.21(20)
1.57(18)
5.96(22) 7.62(22)
5.91(20) 6.77(20)
1.39(18) 1.50(18)
OH + 14CH3F
T(K)
TST
CVT/SCT
TST
CVT/SCT
TST
CVT/SCT
35
50
7.52(120)
1.14(87)
1.02(45)
2.09(45)
5.34(120)
8.90(88)
1.74(46)
3.97(46)
1.59(118)
1.25(86)
5.24(45)
1.03(44)
70
90
100
150
2.87(66)
2.09(54)
2.93(50)
8.11(38)
4.75(44)
2.85(42)
2.35(41)
3.28(36)
2.37(66)
1.79(54)
2.54(50)
7.32(38)
1.06(44)
7.50(43)
6.79(42)
2.08(36)
2.04(65)
1.18(53)
1.52(49)
3.34(37)
2.22(43)
1.29(41)
1.05(40)
1.30(35)
200
250
300
400
500
600
1.43(31)
8.63(28)
3.05(25)
5.37(22)
5.41(20)
1.28(18)
a1.11(119) means
5.38(31)
1.80(27)
4.89(25)
6.79(22)
6.16(20)
1.38(18)
1.11 × 10119
1.32(31)
8.07(28)
2.88(25)
5.12(22)
5.20(20)
1.24(18)
4.61(31)
1.63(27)
4.52(25)
6.41(22)
5.88(20)
1.33(18)
5.32(31)
3.04(27)
1.04(24)
1.79(21)
1.79(19)
4.22(18)
1.94(30)
6.22(27)
1.65(24)
2.24(21)
2.02(19)
4.53(18)
Table 10. Calculated KIEs by the TST and CVT/SCT methods of the OH + CH3F reaction in bulk water solvent.
KIE(CD3)
KIE(OD + CD3)
KIE(OD)
TST
CVT/SCT
TST
CVT/SCT
TST
CVT/SCT
TST
CVT/SCT
TST
CVT/SCT
KIE(13C)
KIE(14C)
KIE(13CD3)
T(K)
TST
CVT/SCT
35
50
70
0.141
0.277
0.433
0.608
0.586
0.578
0.027
0.094
0.212
25.983
6.812
1.791
0.004
0.025
0.091
16.428
4.069
1.033
1.483
1.334
1.243
6.686
5.961
4.764
2.086
1.714
1.502
39.182
31.330
21.385
0.070
0.122
0.174
1.298
1.204
1.016
90
100
150
200
250
300
400
0.553
0.601
0.763
0.849
0.897
0.925
0.948
0.600
0.610
0.729
0.849
0.900
0.928
0.952
0.330
0.383
0.590
0.719
0.799
0.852
0.911
0.807
0.630
0.583
0.711
0.793
0.847
0.909
0.180
0.228
0.448
0.608
0.715
0.785
0.862
0.466
0.369
0.425
0.601
0.711
0.783
0.863
1.194
1.177
1.124
1.096
1.079
1.068
1.054
4.127
3.831
1.783
1.209
1.129
1.097
1.068
1.394
1.357
1.246
1.189
1.154
1.131
1.104
15.683
13.234
2.817
1.413
1.250
1.187
1.131
0.212
0.226
0.273
0.295
0.307
0.312
0.316
0.914
0.853
0.451
0.335
0.327
0.326
0.323
500
600
0.957
0.961
0.960
0.964
0.942
0.960
0.942
0.961
0.900
0.921
0.902
0.925
1.046
1.041
1.055
1.048
1.089
1.080
1.105
1.092
0.316
0.316
0.321
0.320
0
ΔV≠
Reactants
Y + RX
TS
[Y∙∙∙R∙∙∙X]
-10
-20
-30
30
Y∙∙∙RX
X∙∙∙RY
20
ΔV≠
-40
-50
Products40
X + RY
gas-phase
10
solution-phase
0
Reaction Coordinate
-10
Scheme 1. Potential energy diagram of a typical gas-phase (black) and solution-phase (red)
SN2 reactions.
C3v
C∞v
C3v
(a)
(b)
C3v
(c)
C3v
Cs
(d)
Figure 1. Calculated structures by the MP2/aug-cc-pVTZ method of the gas-phase CN +
CH3F reaction. Bond lengths are in Å (blue). Experimental values are in the parentheses. (a)
Reactants (b) Products (c) Transition state (d) Ion-dipole complex.
log k(T) (cm3 molecule1 s1)
-20
CN + CH3F
CN + CD3F
CN + 13CH3F
CN + 14CH3F
-25
-30
-35
-40
-45
0
5
10
15
20
25
30
1000/T (K1)
Figure 2. The Arrhenius plots of the calculated rate constants of the gas-phase CN + CH3F
reaction. The broken and solid lines indicate results calculated at TST and CVT/SCT levels,
respectively.
3.0
KIE(CD3)
KIE(13C)
KIE(14C)
2.5
KIE
2.0
1.5
1.0
0.5
0.0
0
5
10
15
1000/T
20
(K1)
25
30
Figure 3. Calculated temperature dependence of the KIEs of the gas-phase CN + CH3F
reaction. The broken and solid lines indicate results calculated at TST and CVT/SCT levels,
respectively.
(a)
(b)
(c)
(d)
Figure 4. Calculated structures by the MP2/aug-cc-pVTZ method of the gas-phase OH(H2O)
+ CH3F reaction. Bond lengths are in Å (blue) and bond angles in degrees (red). (a)
Reactants (b) Products (c) Transition state (d) Ion-dipole complex.
Relative Energy (kcal/mol)
10
OH(H2O) + CH3F
0
-20 -∞
-15 -10 -5
Transition state
0
5
10
15
20
25
30
35
∞
-10
Ion-dipole complex
-20
F(H2O) + CH3OH
-30
-40
Ion-dipole complex
-50
s (Bohr)
Figure 5. Calculated potential energy curves along the reaction path of the gas-phase
OH(H2O) + CH3F reaction at the MP2/aug-cc-pVDZ level.
log k(T) (cm3 molecule1 s1)
-17
-19
-21
-23
-25
-27
-29
-15
log k(T) (cm3 molecule1 s1)
OH(H2O) + CH3F
OH(H2O) + CD3F
OH(H2O) + 13CH3F
OH(H2O) + 14CH3F
-15
-17
-19
-21
-23
-25
-27
-29
-31
-31
-33
-33
-35
-35
0
5
10
15
20
1000/T (K1)
25
30
OH(H2O) + CH3F
OD(H2O) + CH3F
OH(D2O) + CH3F
OD(D2O) + CH3F
0
5
10
15
20
1000/T (K1)
25
30
Figure 6. The Arrhenius plots of the calculated rate constants of the gas-phase OH(H2O) + CH3F reaction. The broken and solid lines indicate
results calculated at TST and CVT/SCT levels, respectively.
KIE(CD3)
KIE(13C)
KIE(14C)
9.0
8.0
0.9
0.8
7.0
0.7
KIE
6.0
KIE
KIE(OD(H2O))
KIE(OH(D2O))
KIE(OD(D2O))
1.0
5.0
0.6
0.5
4.0
0.4
3.0
0.3
2.0
0.2
1.0
0.1
0.0
0.0
0
10
20
1000/T (K1)
30
0
10
1000/T
20
(K1)
30
Figure 7. Calculated temperature dependence of the KIEs of the gas-phase OH(H2O) + CH3F reaction. The broken and solid lines indicate
results calculated at TST and CVT/SCT levels, respectively.
(a)
(b)
(c)
Figure 8. Calculated structures by the MP2/aug-cc-pVTZ method of the OH + CH3F
reaction in bulk water solvent. Bond lengths are in Å (blue) and bond angles in degrees (red).
(a) Reactants (b) Products (c) Transition state.
log k(T) (cm3 molecule1 s1)
-25
-30
-35
-40
-45
-50
-20
log k(T) (cm3 molecule1 s1)
OH + CH3F
OH + CD3F
OH + 13CH3F
OH + 14CH3F
-20
-25
-30
-35
-40
-45
-50
-55
-55
-60
-60
0
5
10
15
20
1000/T (K1)
25
30
OH + CH3F
OD + CH3F
OD + CD3F
0
5
10
15
20
1000/T (K1)
25
30
Figure 9. The Arrhenius plots of the calculated rate constants of the OH + CH3F reaction in bulk water solvent. The broken and solid lines
indicate results calculated at TST and CVT/SCT levels, respectively.
KIE(CD3)
KIE(13CH3F)
KIE(14CH3F)
KIE(OD)
KIE(OD + CD3)
4.0
3.5
KIE
3.0
2.5
2.0
1.5
1.0
0.5
0.0
0
10
1000/T
20
(K1)
30
Figure 10. Calculated temperature dependence of the KIEs of the OH + CH3F reaction in
bulk water solvent. The broken and solid lines indicate results calculated at TST and
CVT/SCT levels, respectively.
CN + CH3F
OH(H2O) + CH3F
OH + CH3F (PCM, solvent=water)
20
VMEP (kcal/mol)
16.2
15
1.4, 8.2
1.1, 6.1
12.0
10
1.2, 8.1
5.1
1.2, 6.0
5
0.8, 2.5
0.8, 2.5
0
-5
-3
-1
-5
1
3
5
-10
-15
-20
s (bohr)
Figure 11. The calculated dual-level energy profiles along the reaction path. The VMEP(s) of
the half-width and the barrier heights are indicated in the figure.
3.5
3.0
2.5
2.0
t12C / tH
t13C / tH
t12C / tD
t13C / tD
3.5
3.0
ratio
ratio
4.0
t12C / tH
t13C / tH
t12C / tD
t13C / tD
4.5
t12C / tH
t13C / tH
t12C / tD
t13C / tD
4.0
3.5
3.0
2.5
ratio
4.0
2.5
2.0
2.0
1.5
1.5
1.5
1.0
1.0
0.5
0.5
0.0
0.0
0
50 100 150 200 250 300
T(K)
(a)
1.0
0.5
0.0
0
50 100 150 200 250 300
T(K)
(b)
0
50 100 150 200 250 300
T(K)
(c)
Figure 12. Temperature dependence of the calculated contributions from the tunneling effects of the rate constants for the 12C, and 13C of the (a)
gas-phase CN + CH3F, (b) gas-phase OH(H2O) + CH3F, (c) OH + CHF in bulk water solvent.