Dynamics of Competitive Reactions: Endothermic Proton Transfer and Exothermic Substitution

Article abstract of DOI:10.1021/ja030006z

Dynamics of an endothermic proton-transfer reaction, F^- with dimethyl sulfoxide, and an endothermic proton-transfer reaction with a competing exothermic substitution (S_N2) channel, F^- with borane-methyl sulfide complex, were investigated using a Fourier transform ion cyclotron resonance mass spectrometer (FT-ICR) and kinetic modeling. The two proton-transfer reactions have slightly positive and a small negative overall free energy changes, respectively. Energy-dependent rate constants were measured as a function of F^- ion translational energy, and the resulting kinetics were modeled with the RRKM (Rice-Ramsperger-Kassel-Marcus) theory. The observed rate constants for the proton-transfer reactions of F ^- with dimethyl sulfoxide and with borane-methyl sulfide complex are identical, with a value of 0.17 × 10^-9 cm³ molecule^-1 s^-1; for the S_N2 reaction, k = 0.90 × 10-9 cm³ molecule^-1 s^-1 at 350 K. Both proton-transfer reactions have positive entropy changes in the forward direction and show positive energy dependences. The competing S_N2 reaction exhibits negative energy dependence and becomes less important at higher energies. The changes of the observed rate constants agree with RRKM theory predictions for a few kcal/mol of additional kinetic energy. The dynamic change of the branching ratio for the competing proton transfer and the substitution reactions results from the competition between the microscopic rate constants associated with each channel.

Full text of DOI:10.1021/ja030006z

Published on Web 02/06/2004
Dynamics of Competitive Reactions: Endothermic Proton
Transfer and Exothermic Substitution
Jianhua Ren1 and John I. Brauman*
Contribution from the Department of Chemistry, Stanford UniVersity,
Stanford, California 94305-5080
Received January 6, 2003; Revised Manuscript Received November 21, 2003; E-mail: brauman@stanford.edu
Abstract: Dynamics of an endothermic proton-transfer reaction, F- with dimethyl sulfoxide, and an
endothermic proton-transfer reaction with a competing exothermic substitution (SN2) channel, F- with
borane-methyl sulfide complex, were investigated using a Fourier transform ion cyclotron resonance mass
spectrometer (FT-ICR) and kinetic modeling. The two proton-transfer reactions have slightly positive and
a small negative overall free energy changes, respectively. Energy-dependent rate constants were measured
as a function of F- ion translational energy, and the resulting kinetics were modeled with the RRKM (Rice-
Ramsperger-Kassel-Marcus) theory. The observed rate constants for the proton-transfer reactions of F-
with dimethyl sulfoxide and with borane-methyl sulfide complex are identical, with a value of 0.17 × 10-9
cm3 molecule-1 s-1; for the SN2 reaction, k ) 0.90 × 10-9 cm3 molecule-1 s-1 at 350 K. Both proton-
transfer reactions have positive entropy changes in the forward direction and show positive energy
dependences. The competing SN2 reaction exhibits negative energy dependence and becomes less
important at higher energies. The changes of the observed rate constants agree with RRKM theory
predictions for a few kcal/mol of additional kinetic energy. The dynamic change of the branching ratio for
the competing proton transfer and the substitution reactions results from the competition between the
microscopic rate constants associated with each channel.
Introduction
term (∆H°) would allow. More interestingly, some of the
reactions appeared to reach collision rates at higher temperatures.
A variety of endothermic ion-molecule reactions have been
observed and studied with mass spectrometry.2-6 Most endo-
thermic reactions proceed slowly in the gas phase, although
some endothermic reactions are observed to be fast.7-10 These
fast reactions often involve large entropy gains in the forward
direction and hence have negative overall free energy changes.
Such reactions are referred to as “entropy-driven” reactions.11,12
A series of entropy-driven reactions, charge transfer (eq 1a)13
and proton transfer (eq 1b),12,14 for example, have been observed
and studied with ion cyclotron resonance and high-pressure mass
spectrometers at variable temperatures. Equilibrium constants
were observed in favor of product formation, and the forward
reactions were found to occur much faster than the enthalpy
These results lead to conclusions that fast endothermic reactions
are best characterized by a barrierless single well potential
energy surface and the kinetics are determined by the free energy
changes.12,13
A large positive entropy change can significantly reduce the
free energy for a reaction, especially at higher temperatures
(∆G° ) ∆H° - T∆S°). When the magnitude of T∆S° is large
enough, ∆G° and ∆H° can have opposite signs, that is, ∆H° >
0 and ∆G° < 0. A positive entropy change in a reaction can
occur for many reasons; the most familiar is an increase in
translational entropy in a reaction because of a larger number
of particles on the product side.7,8,15 Other cases involve
increases in vibrational and rotational entropy, for example, on
the release of a hydrogen bonding interaction in the product
with ring opening,9,16-18 a change in conformation, or an
increase in rotational degrees of freedom, from an atomic ion
to a diatomic molecule.12 All of these reactions are characterized
by favorable entropy changes. The observed rate constants,
however, are macroscopic quantities, an integration of energy-
dependent microscopic counterparts weighted according to the
energy distribution.
(1) Current address: University of the Pacific.
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9
2640
J. AM. CHEM. SOC. 2004, 126, 2640-2646
10.1021/ja030006z CCC: $27.50 © 2004 American Chemical Society

Dynamics of Competitive Reactions
A R T I C L E S
determined from trajectory calculations of ions undergoing reversible
rf acceleration.25
Entropy effects have been observed as an important factor
affecting dynamics of gas-phase reactions involving a double
well potential energy surface, such as a substitution reaction
(SN2, eq 1c).19 The efficiency of an SN2 reaction is a result of
the competition between a complex dissociating to reactants,
which has a positive entropy change, and the conversion to
products, which can have a lower energy but is less favorable
entropically.20
All chemicals were purchased from Aldrich and were used without
further purification. Multiple freeze-pump-thaw cycles were applied
to all of the gaseous and liquid chemicals prior to introduction into the
vacuum chamber. The reactant ion, F-, was generated by electron
impact on NF3. The neutral reagents, dimethyl sulfoxide (1) and
borane-methyl sulfide complex (2), were introduced into the vacuum
chamber through leak valves. The pressure of the neutral reagents was
in the range of (2-5) × 10-7 Torr. To determine rate constants at
different translational energies of F-, the intensities of F- were
measured as a function of time while an on-resonance rf signal (in the
range of 1-2 V/m)26 was applied to the F- ion. Data were fit to eq 2
A+ + B f A + B+
A- + BH f AH + B-
X- + RY f XR + Y-
(1a)
(1b)
(1c)
(where C is a constant and n is the number density, in molecule cm-3
,
of the neutral reactant). Control experiments show that the relative ion
loss as well as the intensity of the irradiated ions are not affected
significantly by this procedure. The absolute uncertainty of the
experimental results was estimated to be about 10%. Mass balance was
examined by measuring the total ion intensity (reactant + product) with
acceleration of F- and by comparing the total ion intensity with that
measured without the acceleration signal.23 For H/D exchange experi-
ments, neutral CH3OD was introduced into the ICR cell to react with
hydrogen-containing ions. If H/D exchange occurs, new peak(s) with
one mass unit higher would show up. The numbers of new peaks
represent the numbers of H/D exchanges.27,28
Dynamic analysis of isoergic proton-transfer reactions
(A- + AH) suggests that the observed kinetics are influenced
by several dynamic factors involved in the association and
the dissociation of the ion-molecule complex.21 A study of
the dissociation of a proton-transfer intermediate complex
[(NC)2CH2‚Cl]- at two widely separated energy regimes (about
30 kcal/mol) indicated that the branching ratio of (NC)2CH-
versus Cl- is qualitatively consistent with a statistical RRKM
(Rice-Ramsperger-Kassel-Marcus) model. In this study, the
higher energy proton-transfer intermediate was generated via
an SN2 reaction, CN- + NCCH2Cl, and the proton-transfer
channels were found to compete with the SN2 channel.
ln[F-] ) n‚k‚t + C
(2)
Quantum Calculations.29 The structures and vibrational frequencies
for the neutral molecules, ions, and ion-molecule complexes were
calculated using the B3LYP/6-31G(d) and the MP2/6-31+G(d) meth-
ods. The transition state was located on the B3LYP potential energy
surface using the QST3 method. True energy minima and the saddle
point were confirmed by frequency analysis and by viewing the motion
of the structure corresponding to each vibrational mode. For all of the
structures at the energy minima, no imaginary frequency was found.
For the transition state structure, one imaginary frequency was found.
Relative energies were obtained at the MP2/6-311+G(2d,p)//B3LYP/
6-31G(d), B3LYP/6-311+G(3df,2p)//MP2/6-31+G(d), and G2MP2
levels of theory. The calculated results were compared with the available
experimental data.
In this study, we chose a reaction that has an endothermic
proton-transfer channel competing with an exothermic SN2
reaction. As a comparison, we also studied an endothermic
proton-transfer reaction independently. We investigated the
dynamics of these reactions by measuring rate constants as a
function of reactant ion translational energy, and we model the
reaction kinetics with statistical RRKM theory.
Experimental Section
Statistical Modeling. The reaction kinetics were modeled with the
RRKM program, HYDRA.30 A detailed statistical model and the
modeling procedure are described in a previously published paper.31
Briefly, the RRKM theory predicted rate constant can be described as
the collision rate constant (kcoll) multiplied by the macroscopic reaction
efficiency (Φ),32 eq 3. The macroscopic efficiency is the integration
Experiments. Experiments were carried out in an IonSpec OMEGA
Fourier transform ion cyclotron resonance mass spectrometer (FT-ICR)
equipped with an ion kinetic energy controller.22,23 Briefly, the
instrument is operated at a 0.6 T magnetic field with a background
pressure of 3 × 10-9 Torr. The temperature in the ICR cell was
estimated to be 350 K.24 Neutral reagents were added to the vacuum
chamber through variable leak valves. The pressure of the neutral
reagents was measured with a Varian ionization gauge calibrated against
a MKS Baratron capacitance manometer. The primary ions were
generated by electron impact, and the unwanted ions were removed
by using ejection pulses. Impulse excitation was used to excite the ions
prior to detection. On-resonance excitation of the selected ion was
achieved using an ion kinetic energy controller.23 The ion kinetic energy
controller supplies 180° phase-shifting radio frequency (rf) with variable
voltage to the selected ion, so that the ion can be alternately accelerated
and decelerated. On average, the ion kinetic energy is higher than the
thermal energy. The average center-of-mass kinetic energy was
(25) Craig, S. L.; Brauman, J. I. J. Phys. Chem. A 1997, 101, 4745-4752.
(26) Ren, J.; Brauman, J. I. J. Phys. Chem. A 2002, 106, 3804-3813.
(27) DePuy, C. H.; Bierbaum, V. M.; King, G. K.; Shapiro, R. H. J. Am. Chem.
Soc. 1978, 100, 2921-2922.
(28) Stewart, J. H.; Shapiro, R. H.; DePuy, C. H.; Bierbaum, V. M. J. Am.
Chem. Soc. 1977, 99, 7650-7653.
(29) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M.
A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J. A.; Stratmann,
R. E.; Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kudin,
K. N.; Strain, M. C.; Farkas, O.; Tomasi, J.; Barone, V.; Cossi, M.; Cammi,
R.; Mennucci, B.; Pomelli, C.; Adamo, C.; Clifford, S.; Ochterski, J.;
Petersson, G. A.; Ayala, P. Y.; Cui, Q.; Morokuma, K.; Malick, D. K.;
Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Cioslowski, J.; Ortiz,
J. V.; Baboul, A. G.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.;
Komaromi, I.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham,
M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.;
Johnson, B.; Chen, W.; Wong, M. W.; Andres, J. L.; Gonzalez, C.; Head-
Gordon, M.; Replogle, E. S.; Pople, J. A. Gaussian 98; Gaussian, Inc.:
Pittsburgh, PA, 1998.
(19) Shaik, S. S.; Schlegel, H. B.; Wolfe, S. Theoretical Aspects of Physical
Organic Chemistry. The SN2 mechanism; Wiley: New York, 1992.
(20) Craig, S. L.; Zhong, M.; Brauman, J. I. J. Am. Chem. Soc. 1999, 121,
11790-11797.
(30) Wladkowski, B. D.; Lim, K. F.; Brauman, J. I. HYDRA: Calculation of
ion-molecule reaction rate coefficients using Variational transition state
theory; 1991, unpublished.
(31) Wladkowski, B. D.; Lim, K. F.; Allen, W. D.; Brauman, J. I. J. Am. Chem.
Soc. 1992, 114, 9136-9153.
(32) Moylan, C. R.; Brauman, J. I. AdV. Classical Trajectory Methods 1994, 2,
95-114.
(21) Lim, K. F.; Brauman, J. I. J. Chem. Phys. 1991, 94, 7164-7180.
(22) Wilbur, J. L. Ph.D. Dissertation, Stanford University, 1993.
(23) Boering, K. A.; Rolfe, J.; Brauman, J. I. Int. J. Mass Spectrom. Ion
Processes 1992, 117, 357-386.
(24) Han, C. C.; Brauman, J. I. J. Am. Chem. Soc. 1989, 111, 6491-6496.
9
J. AM. CHEM. SOC. VOL. 126, NO. 8, 2004 2641

A R T I C L E S
Ren and Brauman
Table 1. Enthalpy and Free Energy at 298 K, in kcal/mol34
Table 2. Experimental Rate Constants, Collision Rate Constants,
and Efficiencies Obtained at 350 K
reaction
∆H°
∆G°
kobs
k
coll
(CH3)2SO f CH3SOCH2- + H+
(CH3)2SBH3 f CH3S(BH3)CH2- + H+
HF f F- + H+
373.5a
372.5b
371.3c
366.4a
364.3b
365.5c
(10-9 cm3
(10-9 cm3
reactants
channel
molecule-1 s-1
)
molecule-1 s-1
)
Φ
(CH3)2SO + F-
(CH3)2SBH3 + F-
PT
0.17
4.8
5.0
0.035
(CH3)2SO + F- f CH3SOCH2- + HF
+2.2d
+0.9d
(CH3)2SBH3 + F- f CH3S(BH3)CH2- + HF
+1.2d
-1.2d
total
SN2
PT
1.1
0.90
0.17
0.21
0.18
0.034
a Reference 40 (value altered from reference due to change in acidity
scale).34 b Reference 41. c Reference 42. d Values derived from the previous
three reactions in Table 1.
of the microscopic counterparts weighted according to the thermal
equilibrium energy and angular momentum distribution of the ion-
molecule complex. RRKM theory is incorporated into the microscopic
efficiency calculation. The corresponding collision rate constants are
calculated using the Su trajectory model, in which the relative kinetic
energy of the system is a variable.33 At thermal condition (350 K), the
theoretically predicted efficiency is fit to the experimentally observed
efficiency, eq 4. This can be achieved by adjusting the barrier height
(the energy difference between the transition state and the intermediate
complex) of the product formation channel. To model a system at
increased translational energy, the added translational energy is assumed
to be incorporated into the internal modes of the reactant complex.
Therefore, the average total energy of the system is equal to the average
thermal energy (350 K) of the reactants plus the center-of-mass collision
energy. The temperature is replaced with an effective temperature
corresponding to a temperature at which the collision complex has a
Boltzmann distribution of total internal energy, and the theoretical
efficiency is calculated with increasing effective temperature.
Figure 1. Experimental (2) and RRKM (-) rate constants versus relative
kinetic energies for the reaction of CH3SOCH3 + F-.
proton-transfer reaction is endothermic by 1.2 kcal/mol, but with
a free energy change of -1.2 kcal/mol at 298 K (-1.6 kcal/
mol at 350 K). The SN2 reaction is exothermic by 19.8 kcal/
mol.34 We measured rate constants as a function of increasing
F- translational energy, and we modeled the kinetic results with
RRKM theory.
When F- ion was undergoing collision with a neutral molecule, the
kinetic energy added to the F- was assumed to be incorporated into
the internal energy of the system. Therefore, the average total energy
of the reaction system is a combination of the center-of-mass collision
energy and the average thermal internal energy (350 K) of the reactants.
The temperature of the system is replaced with an effective temperature.
3 + F- f CH SOCH - + HF
(5)
CH3SOCH
3
2
kRRKM ) kcoll‚Φ
Φ ) kobs/kcoll
(3)
(4)
1
+ F- f CH S(BH )CH - + HF (6a)
CH3S(BH3)CH3
3
3
2
2
The proton-transfer reactions of F- with both 1 and 2 were assumed
to have a single well potential energy surface, and the SN2 reaction of
F- with 2 was assumed to have a conventional double well potential
energy surface. The transition state of the proton-transfer channel was
treated as product-like with one 2D-rotor associated with H-F
formation (the 20 cm-1 of the rotational constant for H-F was treated
as an active rotational mode for energy redistribution in the proton-
transfer transition state). The relative energies of relevant species on
the potential energy surfaces were taken from energy calculations, and
the vibrational frequencies and rotational constants were obtained from
the frequency calculations at the B3LYP/6-31G(d) level.
f CH3SBH3- + CH3F
(6b)
The reaction of F- with 1 produced only one ionic product,
CH3SOCH2-. The proton-transfer rate constant was determined
by measuring the decay of F- as a function of time, and a value
of 0.17 × 10-9 cm3 molecule-1 s-1 was obtained at 350 K.
The collision rate constant was calculated to be 4.8 × 10-9 cm3
molecule-1 s-1 by using the Su trajectory model,33 giving an
efficiency of 0.035 (Table 2). When F- was accelerated with
an on-resonance radio frequency, the reaction rate was observed
to increase as a function of F- translational energy. The results
are plotted in Figure 1.
Results
Experimental Results. We studied reactions of F- with
dimethyl sulfoxide (1) and borane-methyl sulfide complex (2).
Thermochemical quantities of these reactions can be derived
from thermochemical cycles, involving the gas-phase acidity
of 1, 2, and HF (Table 1). Proton transfer (PT) from 1 to F-
(eq 5) is endothermic by 2.2 kcal/mol, while the free energy
change for this reaction is 0.9 kcal/mol at 298 K (0.7 kcal/mol
at 350 K). The reaction of F- with 2 proceeds via two competing
channels, proton transfer (eq 6a) and SN2 (eq 6b). The
The reaction of F- with 2 generated two product ions,
-
-
CH3SBH3 (SN2, m/z 61) and CH3S(BH3)CH2 (PT, m/z 75),
-
in a ratio of 5:1 at 350 K. Borane transfer from 2 to CH3SBH3
would give CH3SBH3BH3- (m/z 75), which would overlap with
the peak of CH3S(BH3)CH2-. Boron isotope patterns show the
-
percentage of CH3SBH3BH3 (two borons) as compared to
-
CH3S(BH3)CH2 (one boron). We examined the formation of
(34) NIST Chemistry Webbook, NIST Standard Reference Database Number 69;
(33) Su, T. J. Chem. Phys. 1994, 100, 4703.
National Institue of Standards and Technology; March, 2003.
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Dynamics of Competitive Reactions
A R T I C L E S
bonding has also been found in the calculated structure of
dimethyl sulfoxide-hydroxide complex.36
Figure 2. Experimental (b total, 9 SN2, 2 PT) and RRKM (-)
rate constants versus relative kinetic energies for the reaction of
CH3S(BH3)CH3 + F-.
-
CH3SBH3BH3 as a function of reaction time and found
-
that the intensity of CH3SBH3BH3 was less than 5% within
Relative energies for reaction 5 were calculated using the
MP2/6-311+G(2d,p)//B3LYP/6-31G(d) and the B3LYP/
6-311+G(3df,2p)//MP2/6-31+G(d) procedures. Complex 3 was
calculated to be 28.2 kcal/mol (MP2/6-311+G(2d,p)//B3LYP/
6-31G(d)) and 29.3 kcal/mol (B3LYP/6-311+G(3df,2p)//MP2/
6-31+G(d)) below the separated reactants. A proton-transfer
product complex, corresponding to the structure of [(CH3SOCH2-)
HF], was calculated to have an energy about 12 kcal/mol higher
than 3. A search for a transition state between 3 and the product
complex was unsuccessful at the B6LYP/6-31G(d) level,
suggesting that the proton-transfer transition state structure is
unstable. The proton-transfer products, CH3SOCH2- + HF, were
calculated to be 6.2 kcal/mol (MP2/6-311+G(2d,p)//B3LYP/
6-31G(d)) and 6.4 kcal/mol (B3LYP/6-311+G(3df,2p)//MP2/
6-31+G(d)) higher in energy than the reactants, CH3SOCH3 +
F-.
We calculated relative energies for reaction 6 at both the MP2/
6-311+G(2d,p)//B3LYP/6-31G(d) and the G2MP2 levels of
theory. The proton-transfer reaction 6a was calculated to be
endothermic by 5.8 kcal/mol (MP2/6-311+G(2d,p)//B3LYP/
6-31G(d)) and 4.4 kcal/mol (G2MP2), and the SN2 reaction 6b
was calculated to be exothermic by 24.4 kcal/mol (MP2/
6-311+G(2d,p)//B3LYP/6-31G(d)) and 25.7 kcal/mol
(G2MP2). Complex 4 was found to be 30.9 kcal/mol (MP2/
6-311+G(2d,p)//B3LYP/6-31G(d)) and 31.5 kcal/mol (G2MP2)
below the separated reactants. The proton-transfer product
complex, [(CH3S(BH3)CH2-) HF], was calculated to be about
10 kcal/mol above 4, and the SN2 product complex, [(CH3SBH3-)
CH3F], was calculated to be 1.6 kcal/mol below 4 at the MP2/
6-311+G(2d,p)//B3LYP/6-31G(d) level. A SN2 transition state,
5, was located at 18.4 kcal/mol (MP2/6-311+G(2d,p)//B3LYP/
6-31G(d)) above 4. The geometry of the transition state has a
normal SN2 transition state structure, except that the methyl
group has a slightly nonplanar geometry. Because the calculated
energy of the transition state was not important for kinetic
modeling, we did not perform further energetic calculations.
For the SN2 reaction to reach transition state 5, intermediate
4 has to rearrange to a formal SN2 reactant complex with the
F- attached to the backside of the reaction center, the methyl
carbon. This reactant complex is likely to have an energy
between that of 4 and 5. We performed an energy scan procedure
1 s. We collected all kinetic data at 0.6 s with negligible
CH3SBH3BH3-. Furthermore, hydrogen-deuterium exchange
reactions between CH3OD and the ion with m/z 75 showed a
maximum of five H/D exchanges, suggesting that the ion with
m/z 75 corresponded to the structure of CH3S(BH3)CH2 .
- 35 The
overall rate constant for reaction 6 was determined by measuring
the decay of F- as a function of time, and a value of 1.1 ×
10-9 cm3 molecule-1 s-1 was obtained. The collision rate
constant was calculated to be 5.0 × 10-9 cm3 molecule-1 s-1
,
giving an overall efficiency of 0.21. Combined with the product
branching ratio of 5:1 (SN2 to PT), we obtained rate constants
for the SN2 and the proton transfer of 0.90 × 10-9 and 0.17 ×
10-9 cm3 molecule-1 s-1, and efficiencies of 0.18 and 0.034 at
350 K, respectively (Table 2). As the F- was accelerated, the
overall rate constant was insensitive to the energy change. The
rate constant of the SN2 reaction is decreased, and the rate
constant of the proton transfer is increased. The results are
plotted in Figure 2.
Computational Results. To obtain vibrational frequencies
for kinetic modeling and qualitative energetic information, we
performed quantum calculations with Gaussian 98.29 We
optimized structures of the neutral molecules and intermediate
complexes for the two reaction systems using the B3LYP/6-
31G(d) method. Corresponding vibrational frequencies and
rotational constants were evaluated at the same level of theory.
For comparison, we also optimized structures using the MP2/
6-31+G(d) method. The two methods give similar geometries
for reactants and products, and slightly different bond lengths
between F- and the neutral moiety in intermediate complexes.
Stable ion-molecule complexes were found for both reactions
5 and 6. In the complex of F- with 1, [(CH3SOCH3) F-] (3),
the distance between the F- and the two methyl carbons was
calculated to be 2.74 Å with B3LYP and 2.93 Å with MP2.
Similarly, the MP2 method predicts a longer (by 0.2 Å) distance
between the F- and the two methyl carbons in the complex of
F- with 2, [(CH3S(BH3)CH3) F-] (4). In both complexes 3 and
4, the F- is apparently hydrogen bonded to one hydrogen on
each of the two methyl groups. This type of nonlinear hydrogen
(35) Ren, J.; Workman, D. B.; Squires, R. R. Angew. Chem., Int. Ed. Engl.
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Chem. 1996, 100, 16137-16140.
9
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A R T I C L E S
Ren and Brauman
to locate the reactant complex, starting from 5 and ending with
complex 4. The potential energy falls smoothly, and no
additional intermediate complex was found at the B3LYP/
6-31G(d) level. The SN2 reactant complex is probably located
in a shallow well and is insensitive to this computational
procedure. Apparently complex 4 serves as a common inter-
mediate for both the proton transfer and the SN2 reactions.
Statistical Modeling. The reaction of F- with 1 (eq 5) was
modeled with a single well potential energy surface with ion-
molecule complex 3 associated with the well (Discussion
section). Complex 3 can either dissociate back to the reactants
(kB) or give the proton-transfer products (kPT). The entrance and
the exit channels were assumed to have reactant-like and
product-like transition states, respectively.37 The efficiency for
the overall reaction is described using eq 7. The efficiency of
reaction 5 was measured to be 0.035 at 350 K. Statistical
modeling gives the barrier height, the energy difference between
the transition state and the complex, of the product channel to
be 30.9 kcal/mol, corresponding to a 2.7 kcal/mol endother-
micity for the overall proton-transfer reaction. By using the
energetic quantities obtained at 350 K, we calculated a series
of theoretical efficiencies at higher system energies (associated
with increasing effective temperature). We also calculated the
corresponding collision rate constants using the Su trajectory
model. The collision rate constant decreases slowly as a function
of increase in collision energy. With an additional 5 kcal/mol
of kinetic energy, the collision rate constant decreases by 20%.
Combining the efficiencies obtained with statistical modeling
and the calculated collision rate constants, we obtained RRKM
rate constants (eq 3) as a function of kinetic energy. The RRKM
rate constants show positive energy dependence (Figure 1).
is 0.18, and that for the proton transfer is 0.034. Statistical
modeling gives the central barrier height for the SN2 channel
as 23.9 kcal/mol, corresponding to 7 kcal/mol below the
separated reactants. The modeling gives a barrier height for the
proton-transfer channel of 33.7 kcal/mol, corresponding to 2.8
kcal/mol of endothermicity for the proton-transfer reaction. With
increasing system energy (corresponding to increasing the
effective temperature), the efficiency for the SN2 channel is
decreased, and the efficiency for the proton transfer increased.
The corresponding RRKM rate constants at different system
energies were obtained by multiplying the theoretical efficiencies
by the calculated collision rate constants (eq 3). The SN2 rate
constants show negative energy dependence, and the proton
transfer shows positive energy dependence (Figure 2).
Discussion
We have investigated the dynamics of endothermic proton-
transfer reactions and the proton-transfer reaction with a
competing SN2 channel by measuring the rate constants as a
function of reactant ion translational energy and modeling the
kinetic results with RRKM theory. Proton transfer from 1 to
F- has a rate constant of 0.17 × 10-9 cm3 molecule-1 s-1 and
an efficiency of 0.035 at 350 K. The observed rate constant
increases as the F- translational energy is increased. The changes
of the rate constants agree with RRKM theory predictions
(Figure 1). The reaction of F- with 2 has an overall rate constant
of 1.1 × 10-9 cm3 molecule-1 s-1 and an efficiency of 0.21 at
350 K. The proton transfer and the SN2 channels have rate
constants of 0.17 × 10-9 and 0.90 × 10-9 cm3 molecule-1 s-1
,
corresponding to efficiencies of 0.034 and 0.18, respectively.
The overall rate constant is insensitive to energy change, while
the proton-transfer channel shows positive energy dependence
and the SN2 channel shows negative energy dependence. The
observe rate constants agree with RRKM theory predictions in
the energy range examined, although theory predicts a larger
change at higher energies (Figure 2).
kPT
ΦPT
)
(7)
kB + kPT
The reaction of F- with 2 (eq 6) was modeled with two
competing channels, the SN2 and the proton transfer (PT). The
SN2 channel was treated as a double well, and the proton transfer
was treated as a single well potential energy surface (Discussion
section). The ion molecule complex 4 was assumed to be the
common intermediate for the two channels. Because the SN2
reaction is highly exothermic, the rate-determining step would
be the crossing of the SN2 central barrier. The efficiency for
each exit channel is associated with the branching over the three
pathways, dissociation back to the reactants (kB), crossing the
SN2 central barrier (kSN2), and formation of the proton-transfer
products (kPT). The efficiency for the SN2 channel can be
described using eq 8, and the efficiency for the proton-transfer
channel can be described using eq 9.
The ion molecule complex 3 has a calculated association
energy of about 28 kcal/mol. The strong binding between F-
and dimethyl sulfoxide is apparently a result of the hydrogen
bonding between the F- and the hydrogens on the two methyl
groups in dimethyl sulfoxide in addition to an ion-dipole
interaction.31 Our calculations show that the corresponding
proton-transfer product complex, [(CH3SOCH2-)HF], is higher
than 3 by 12 kcal/mol, and is located in a shallow well. No
transition state structure can be located between 3 and
[(CH3SOCH2-)HF]. Complex 3 is likely a stable intermediate
for the proton-transfer reaction. The energy profile for the
reaction of F- with 1 may well be represented using a single
well potential energy surface with 3 associated with the well32
(Figure 3). A single well potential energy surface has been
employed to characterize a large number of fast proton-transfer
and charge-transfer reactions, including a series of entropy-
driven endothermic reactions.12,38 Complex 3 can exit the
well by either forming the proton-transfer products (the PT
kSN2
ΦSN2
ΦPT
)
(8)
(9)
kB + kSN2 + kPT
kPT
)
kB + kSN2 + kPT
(38) Wilbur, J. L.; Wladkowski, B. D.; Brauman, J. I. J. Am. Chem. Soc. 1993,
115, 10823-10829.
The experimentally measured overall efficiency for reaction
6 is 0.21 at 350 K. The measured efficiency for the SN2 reaction
(39) Bohme, D. K.; Mackay, G. I.; Schiff, H. I. J. Phys. Chem. 1980, 84, 4976-
4986.
(40) Bartmess, J. E.; Scott, J. A.; McIver, R. T., Jr. J. Am. Chem. Soc. 1979,
101, 6046-6056.
(37) Moylan, C. R.; Brauman, J. I. Annu. ReV. Phys. Chem. 1983, 34, 187-
(41) Ren, J.; Workman, D. B.; Squires, R. R. J. Am. Chem. Soc. 1998, 120,
10511-10522.
215.
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Dynamics of Competitive Reactions
A R T I C L E S
Figure 4. Potential energy surface for the reaction of CH3S(BH3)CH3 +
F-.
Figure 3. Potential energy surface for the reaction of CH3SOCH3 + F-.
equilibrium constant.12,13,39-42 Because K is finite, the efficiency
in either direction alone cannot be unity. This elegant analysis
assumed both a single well potential and also that the collision
rate constants for the forward and back reactions were the same,
which was quite reasonable given the reactions under consid-
eration. For complex reactions, however, in which the entropy
changes are large, even if the reaction proceeds on a single well
potential, the collision rate constants may not be same for the
forward and back reactions. Thus, both the collision rates and
the efficiencies must be taken into account in understanding
the rate constants.
The reaction of F- with 2 has two competing channels, proton
transfer and SN2. The potential energy surface for the proton-
transfer reaction has features similar to those for reaction 5,
with a deep single well of 31 kcal/mol connected to the entrance
(B) and the exit (PT) channels (Figure 4). The intermediate
complex (4) associated with the well also has features similar
to that of 3, where a hydrogen-bonding interaction is involved
in stabilizing the complex. The PT channel is about 2 kcal/mol
higher than the B channel. In addition, a double well potential
energy surface is employed to describe the SN2 reaction. Stable
structures, 4 and [(CH3SBH3-)CH3F], associated with the two
wells were determined from quantum calculations, and a SN2
transition state structure (5) was located along the reaction path
from complex 4 to [(CH3SBH3-)CH3F]. The SN2 reaction shares
the same entrance channel (B) and intermediate complex (4)
with the proton-transfer reaction. Because the SN2 reaction is
highly exothermic (20 kcal/mol), the reactivity is mainly
determined by the first well. The ion-molecule complex (4)
can exit the well via three pathways, dissociation back to the
reactants (B), formation of the proton-transfer products (PT),
and crossing the SN2 barrier (SN2). Among the three pathways,
the PT channel has the highest energy and also the highest
density of quantum states. The high density of states is mainly
due to the formation of H-F from F-, which increases the
rotational entropy. The SN2 channel has the lowest energy and
also the lowest density of states.
channel) or dissociating back to the reactants (the B channel).
The PT channel has a higher energy, but a higher density of
quantum states above the transition state. The higher density
of states is mainly the result of the increase in rotational degrees
of freedom (increase in rotational entropy), from the atomic ion
F- in the reactants to the diatomic molecule H-F in the
products.
The proton-transfer efficiency is determined by the competi-
tion between the B and the PT channels. The observed efficiency
of 0.035 at 350 K means that about 3.5% of the collision
complex reacts via the PT channel, while the majority of the
complex dissociates back to reactants. The low efficiency of
this reaction suggests that most of the collisions have an energy
below the critical energy of the PT channel at 350 K. If we
assume that the reactants have a Boltzmann distribution of
energy upon collision, then about 4% of the collisions would
surmount the 2.2 kcal/mol of endothermicity at 350 K. This is
comparable to the observed efficiency of 3.5% at 350 K.
The observed rate constants as a function of increase in F-
translational energy in Figure 1 reflect the dynamic change of
the efficiency at different energies. The PT channel is statisti-
cally favored at higher energies, because of the higher density
of states at the transition state. A graphical description of density
of states (shown as sum of states) versus total energy for the
two dissociation channels of the PT intermediate complex is
similar to that of dissociation of [(NC)2CH2‚Cl]-.38 With
increasing system energy, more and more collision complexes
will dissociate via the PT channel. As a result, the efficiency
becomes larger at higher energies. Because the collision rate
constants decrease slowly with increasing collision energy, the
change of the observed rate constant will mainly be determined
by the change of efficiency. Positive energy dependence for
the overall proton-transfer reaction is expected. Indeed, we
observed larger rate constants at higher F- translational energies
(Figure 1).
On the basis of studies with high-pressure mass spectrometry,
Sieck and Mautner13 suggested that fast bimolecular reactions
can be characterized by a single well potential, so that Φ )
K/(1 + K) and Φf + Φr ) 1, where Φ is the efficiency (Φf,
forward reaction, and Φr, reverse reaction) and K is the
The efficiencies for the SN2 and the proton-transfer reactions
are determined by the competition among the three pathways
(42) Blondel, C.; Delsart, C.; Goldfarb, F. J. Phys. B.: At. Mol. Opt. Phys.
2001, 34, L281-L288.
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J. AM. CHEM. SOC. VOL. 126, NO. 8, 2004 2645

A R T I C L E S
Ren and Brauman
(eqs 8, 9). The efficiencies observed at 350 K show that about
18% of the collision complexes dissociate via the SN2 channel,
and about 3% via the PT channel. The majority of the complexes
(79%) dissociate back to the reactants. The low efficiency
observed for the proton-transfer reaction suggests that a small
fraction of the collisions occur above the critical energy of the
PT channel, and most of the collisions occur at or below the
PT channel. The SN2 channel has the lowest critical energy,
but is least favored entropically. It is not surprising that only
about 18% of the collisions lead to the SN2 products, although
the SN2 channel is about 7 kcal/mol lower than the B channel.
Statistical modeling shows that the observed proton-transfer
rate constants in reaction 5 agree with RRKM theory predictions
(Figure 1). The apparent statistical behavior may be due to the
strong binding energy of the complex, which results in a longer
lifetime of the complex for statistical redistribution of the
additional kinetic energy. For reaction 6, the observed overall
rate constants agree with RRKM calculations, and both the SN2
and the proton-transfer reactions agree with theory within an
additional 2.5 kcal/mol of kinetic energy (Figure 2). The
agreement between experiment and theory is consistent with
the statistical partitioning of the additional kinetic energy, which
may also result from the relatively long lifetime of the
intermediate complex. For the SN2 reaction to occur, complex
4 has to rearrange to a SN2 reactant complex with a backside
orientation of the F- relative to the leaving group, just like that
in [(NC)2CH2‚Cl]- system.38 The lifetime of the complex has
to be long enough for this rearrangement. At higher energy,
theory predicts a larger difference of the rate constants between
the PT and the SN2 channels. This may be due to the choice of
the frequencies in the transition states and the use of an
approximate statistical model; that is, an effective temperature
is used based on the total system energy.
The efficiency observed for the SN2 reaction is comparable to
that for the reaction of Cl- + NCCO2CH3 giving NCCO2
+
-
CH3Cl.26 The latter reaction has an efficiency of 0.19 and a
potential energy surface with the central barrier 6.3 kcal/mol
below the separated reactants. According to eqs 8 and 9, if kPT
is very small, the forward reaction would be dominated by the
SN2 channel, and the overall efficiency (ΦSN2 + ΦPT) would
be determined by ΦSN2. In fact, we observed the overall
efficiency of 0.21 as compared to 0.18 for the SN2 reaction at
350 K.
The relative densities of states associated with the three
pathways connected to the well associated to 4 determine the
dynamic changes of the microscopic rate constants and efficien-
cies. With increasing system energy, the changes of microscopic
Conclusion
We have investigated the dynamics of an endothermic proton-
transfer reaction of F- with dimethyl sulfoxide and a competitive
reaction system of F- with borane-methyl sulfide complex, an
endothermic proton transfer competing with an exothermic SN2
channel. We measured rate constants as a function of F-
translational energy and modeled reaction kinetics with RRKM
theory. Both proton-transfer reactions have positive entropy
changes in the forward directions and show positive kinetic
energy dependences. The competing SN2 reaction shows nega-
tive energy dependence and becomes less important at higher
energies. The observed kinetics agree with RRKM theory
predictions within a few kcal/mol of additional kinetic energies.
Dynamic analysis indicates that an endothermic reaction must
have less than unit efficiency and must be slower than the
collision rate at thermal condition, even though the reaction has
an overall negative free energy change. The branching ratio for
the two competing channels results from the competition of a
combined factor of relative critical energy and density of states.
The changes of the branching ratio as a function of system
energy reflect the dynamic change of the microscopic rate
constants associated with each channel.
rate constants would be in the order of ∆kPT > ∆kB > ∆kSN2
.
The efficiencies for the PT channel would increase, and for the
SN2 channel they would decrease. Similar to reaction 5, the
collision rate constant for F- with 2 decreases slowly with
increasing collision energy. Therefore, changes of the observed
rate constants would be determined by efficiencies. Positive
energy dependence is expected for the proton-transfer reaction,
and negative energy dependence is expected for the SN2 reaction.
We indeed observed the increase in proton-transfer rate constants
and the decrease in SN2 rate constants at higher F- translational
energy (Figure 2).
Can we expect 100% proton-transfer products at even higher
energy? Using an analysis similar to that applied to reaction 5,
there is always a nonzero fraction of collisions whose total
energy is below the critical energy of the PT channel under
thermal condition. This fraction of collisions does not have
enough energy to access the PT channel. Therefore, the
endothermic proton-transfer reaction must have less than unit
efficiency and less than 100% product branching ratio. The
experimentally observed overall rate constants appear to be
insensitive to energy change. This may be due to the fact that
the SN2 and the proton-transfer reactions have opposite effects
on the overall rate constants, and the effects happen to have
similar magnitudes within the energy range examined.
Acknowledgment. We are grateful to the National Science
Foundation for support of this work.
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2646 J. AM. CHEM. SOC. VOL. 126, NO. 8, 2004