Internal excitation in the products of nucleophilic substitution from the dissociation of metastable ion complexes

Article abstract of DOI:10.1021/ja9730775

The relative kinetic energy distributions for the products of the dissociation of four metastable gasphase ion clusters have been analyzed by means of ion kinetic energy spectroscopy, and the results modeled using statistical phase space theory. The systems studied represent reaction intermediates in bimolecular nucleophilic substitutions (S(N)2). These studies build on previous investigations that demonstrated vibrational excitation in the products of the substitution reactions of halide ions with methyl halides. The present studies explore the effects of molecular structure, reaction exothermicity, and nucleophile and leaving group variation. The experimental kinetic energy distributions are compared with theoretical distributions calculated for statistical partitioning of energy among internal modes and relative kinetic energy of the products. In each reaction, the calculated distributions agree with the experimental distributions only if a significant fraction of the energy released in the exothermic reactions is assumed to be unavailable for randomization in the dissociation. The results suggest that the products of these S(N)2 reactions are internally excited.

Full text of DOI:10.1021/ja9730775

J. Am. Chem. Soc. 1998, 120, 6785-6796
6785
Internal Excitation in the Products of Nucleophilic Substitution from
the Dissociation of Metastable Ion Complexes
,
‡
†
†
Susan T. Graul,* Catherine J. Carpenter, John E. Bushnell,
†
,†
Petra A. M. van Koppen, and Michael T. Bowers*
Contribution from the Departments of Chemistry, Carnegie Mellon UniVersity, 4400 Fifth AVenue,
Pittsburgh, PennsylVania 15213, and UniVersity of California, Santa Barbara, California 93106
ReceiVed September 2, 1997
Abstract: The relative kinetic energy distributions for the products of the dissociation of four metastable gas-
phase ion clusters have been analyzed by means of ion kinetic energy spectroscopy, and the results modeled
using statistical phase space theory. The systems studied represent reaction intermediates in bimolecular
nucleophilic substitutions (SN2). These studies build on previous investigations that demonstrated vibrational
1
excitation in the products of the substitution reactions of halide ions with methyl halides. The present studies
explore the effects of molecular structure, reaction exothermicity, and nucleophile and leaving group variation.
The experimental kinetic energy distributions are compared with theoretical distributions calculated for statistical
partitioning of energy among internal modes and relative kinetic energy of the products. In each reaction, the
calculated distributions agree with the experimental distributions only if a significant fraction of the energy
released in the exothermic reactions is assumed to be unavailable for randomization in the dissociation. The
results suggest that the products of these SN2 reactions are internally excited.
kinetics and dynamics of these reactions.1
6-20
A major as-
Introduction
sumption in these statistical theories is that energy is rapidly
randomized due to strong coupling among the modes of the
reacting molecules. As a result, properties such as reaction rates
and product energy deposition can be predicted by using only
densities of states of the reactants, products, and transitions
states.
Bimolecular nucleophilic substitution (SN2) reactions are
2
some of the most widely studied reactions in solution, and have
1
-8
been the object of a number of gas-phase studies as well. In
this latter case, statistical theories, such as RRKM and phase
space theory,9
-15
have often been invoked as models for the
Recently, however, there has been theoretical and experi-
‡
Carnegie Mellon University.
University of California.
mental evidence that some SN2 reactions may not behave
†
1,21-26
statistically.
For example, quantum dynamical and reac-
(
1) (a) Graul, S. T.; Bowers, M. T. J. Am. Chem. Soc. 1991, 113, 9696-
tion path Hamiltonian calculations show nonstatistical behavior
9
3
697. (b) Graul, S. T.; Bowers, M. T. J. Am. Chem. Soc. 1994, 116, 3875-
883.
-
-
for X + CH3F f F + CH3X (X ) H, F, OH), including
(2) Shaik, S. S.; Schlegel, H. B.; Wolfe, S. Theoretical Aspects of
23,24
formation of vibrationally excited products.
Hase and co-
Physical Organic Chemistry. The SN2 Mechanism; Wiley-Interscience: New
York, 1992.
workers have performed trajectory calculations for the reactions
a
-
b
b
-
a
-
-
(
3) (a) Bohme, D. K.; Mackay, G. I.; Payzant, J. D. J. Am. Chem. Soc.
974, 96, 4027-4028. (b) Tanaka, K.; Mackay, G. I.; Payzant, J. D.; Bohme,
D. K. Can. J. Chem. 1976, 54, 1643-1659.
4) (a) Lieder, C. A.; Brauman, J. I. J. Am. Chem. Soc. 1974, 96, 4029-
030. (b) Brauman, J. I.; Olmstead, W. N.; Lieder, C. A. J. Am. Chem.
Cl + CH3 Cl f Cl + CH3 Cl and Cl + CH3Br f Br +
1
(12) Chesnavich, W. J.; Bowers, M. T. In Gas-Phase Ion Chemistry;
Bowers, M. T., Ed.; Academic Press: New York, 1979; Vol. 1, pp 119-
151.
(
4
Soc. 1974, 96, 4030-4031. (c) Olmstead, W. N.; Brauman, J. I. J. Am.
Chem. Soc. 1977, 99, 4219-4228. (d) Asubiojo, O. I.; Brauman, J. I. J.
Am. Chem. Soc. 1979, 101, 3715-3724. (e) Pellerite, M. J.; Brauman, J. I.
J. Am. Chem. Soc. 1980, 102, 5993-5999. (f) Wilbur, J. L.; Wladkowski,
B. D.; Brauman, J. I. J. Am. Chem. Soc. 1993, 115, 10823-10829. (g)
Wladkowski, B. D.; Wilbur, J. L.; Brauman, J. I. J. Am. Chem. Soc. 1994,
(13) Pechukas, P.; Light, J. C.; Rankin, C. J. J. Chem. Phys. 1966, 44,
794-805.
(14) Nikitan, E. Theor. Exp. Chem. (Engl. Transl.) 1965, 1, 285.
(15) (a) Chesnavich, W. J.; Bowers, M. T. J. Am. Chem. Soc. 1976, 98,
8301-8309. (b) Chesnavich, W. J.; Bowers, M. T. J. Chem. Phys. 1978,
68, 901-910. (c) Chesnavich, W. J.; Bowers, M. T. Prog. React. Kinet.
1982, 11, 137-267.
(16) (a) Dodd, J. A.; Brauman, J. I. J. Phys. Chem. 1986, 90, 3559-
3562. (b) Wladkowski, B. D.; Lim, K. F.; Allen, W. D.; Brauman, J. I. J.
Am. Chem. Soc. 1992, 114, 9136-9153.
(17) Pellerite, M. J.; Brauman, J. I. J. Am. Chem. Soc. 1983, 105, 2672-
2680.
1
16, 2471-2480.
(
5) (a) DePuy, C. H.; Gronert, S.; Mullin, A.; Bierbaum, V. M. J. Am.
Chem. Soc. 1990, 112, 8650-8655. (b) Gronert, S.; DePuy, C. H.; Bierbaum,
V. M. J. Am. Chem. Soc. 1991, 113, 4009-4010.
(6) Cyr, D. M.; Posey, L. A.; Bishea, G. A.; Han, C.-C.; Johnson, M. A.
J. Am. Chem. Soc. 1991, 113, 9697-9699.
7) Cyr, D. M.; Baily, C. G.; Serxner, D.; Scarton, M. G.; Johnson, M.
A. J. Chem. Phys. 1994, 101, 10507-10520.
8) Li, C.; Ross, P.; Szulejko, J. E.; McMahon, T. B. J. Am. Chem. Soc.
996, 118, 9360-9367.
9) Forst, W. Theory of Unimolecular Reactions; Academic Press: New
York, 1973.
(
(18) Caldwell, G.; Magnera, T. F.; Kebarle, P. J. Am. Chem. Soc. 1984,
106, 959-966.
(
(19) Barlow, S. E.; Van Doren, J. M.; Bierbaum, V. M. J. Am. Chem.
Soc. 1988, 110, 7240-7242.
1
(
(20) Viggiano, A. A.; Morris, R. A.; Su, T.; Wladkowski, B. D.; Craig,
S. L.; Zhong, M.; Brauman, J. I. J. Am. Chem. Soc. 1994, 116, 2213-
2214.
(10) Robinson, P. J.; Holbrook, K. A. Unimolecular Reactions; Wiley-
Interscience: New York, 1972.
(21) (a) Bergsma, J. P.; Gertner, B. J.; Wilson, K. R.; Hynes, J. T. J.
Chem. Phys. 1987, 86, 1356-1376. (b) Gertner, B. J.; Whitnel, R. M.;
Wilson, K. R.; Hynes, J. T. J. Am. Chem. Soc. 1991, 113, 74-87.
(11) Pechukas, P. In Dynamics of Molecular Collisions, Part B; Miller,
W. H., Ed.; Plenum Press: New York, 1976.
S0002-7863(97)03077-1 CCC: $15.00 © 1998 American Chemical Society
Published on Web 06/26/1998

6786 J. Am. Chem. Soc., Vol. 120, No. 27, 1998
Graul et al.
CH3Cl.22 The results are indicative of nonstatistical dynamics,
-
F + C H OCH f
6
5
3
including vibrational state-specific rate enhancement, multiple
crossings of the transition state (TS) dividing surface, and
nonstatistical product energy distributions. Reaction path
-
C H O + CH F
∆H ) -12.7 kcal/mol (3)
Cl + C H I f I + C H Cl ∆H ) -15.0 kcal/mol
2 5 2 5
6
5
3
-
-
-
Hamiltonian calculations for the Cl + CH3Br reaction indicate
(4)
weak coupling between the intramolecular and intermolecular
modes of the ion-dipole complex, which inhibits rapid energy
randomization.
This set of reactions allows us to explore the effects of molecular
structure of the neutral reactant, the strength of the nucleophile,
overall reaction exothermicity, and the effects of substitution
at the inverting carbon center. The experimental approach taken
involves generating an ion-molecule complex of each pair of
reactants in eqs 1-4 and analyzing the dissociation of this
complex. Experimental KERDs are reported and compared with
statistical phase space theory predictions to obtain deeper insight
N
2
7
Experimental evidence also supports the view that some SN2
reactions may not behave statistically. Viggiano et al. have found
-
-
that the rate constant for Cl + CH3Br f Br + CH3Cl does
not depend on the internal temperature of CH3Br between 207
and 564 K,25 whereas RRKM theory predicts a positive
28
temperature dependence over the same temperature range. The
a
-
b
b
-
a
rate constant for Cl + ClCH2CN f Cl + ClCH2CN has
into dynamics of the S 2 reaction.
20
also been measured versus ClCH2CN temperature. In contrast
to what they observed for the Cl + CH3Br reaction, Viggiano
-
Experimental Section
et al. found that the rate constant does depend on the internal
energy of the neutral reactant, and obtained reasonable agree-
ment for both the relative kinetic energy dependence and
temperature dependence with RRKM theory. They suggest the
statistical behavior of the Cl + ClCH2CN reaction is due to
the longer lifetime of the ion-dipole complex, which allows
These experiments were carried out in a reverse-geometry double-
focusing sector mass spectrometer (V.G. ZAB-2F) with a temperature-
-
-
-
and pressure-variable ion source. The Cl
were generated by dissociative electron attachment to CCl
HCN, respectively. The adduct species were then formed by associative
collisions with CF CO CH , CH OC , or C I with the neutral gas
, F
, and CN
reactant ions
4
, CH F, and
3
-
3
2
3
3
H
6 5
2 5
H
pressure maintained as low as possible to minimize stabilization by
secondary collisions. The neutral gas pressures were typically 20-40
mTorr and the source temperature approximately 270-300 K. Under
these conditions, the collision frequencies for these reactants are
for statistical energy exchange.
In addition to the kinetics studies, possible nonstatistical
behavior in SN2 reactions has been investigated by measuring
the energy partitioned into the relative translation of the
products. In an experiment with kinetic energy-ion cyclotron
resonance (KE-ICR) spectroscopy, the CH3F product of the SN2
5
6
-1
approximately 10 -10 s , corresponding to 1 to 50 collisions for
typical source residence times.
The adduct ions were accelerated into the magnetic sector for mass
selection. The adduct ion beam was focused such that its energy spread
in an ion kinetic energy scan was about 2 eV fwhm for a typical beam
energy of 8010 eV. Product ions resulting from dissociation of
-
-
reaction F + CH3Cl f Cl + CH3F was found to be
2
6
vibrationally cold compared to the statistical prediction. In
contrast, kinetic energy release distribution (KERD) experiments
on the SN2 reactions X + CH3Yf Y + CH3X (X ) Cl, Br;
Y ) Br, I) show, in all cases, that the products are internally
30
metastable adduct ions in the field-free region between the magnetic
-
-
and electrostatic sectors were energy analyzed in the electrostatic sector.
The flight time from the ion source to the second field-free region of
1
-5
excited relative to statistical predictions.
the instrument is about 10 s, which means that the metastable
dissociation experiments probe the reactions of adduct ions with
lifetimes of about 10 µs. Kinetic energy release distributions were
derived from the laboratory-energy-analyzed product ion peak shape
by a method described previously.31 The metastable experiments were
repeated several times to verify reproducibility. To ensure that
collisional effects were not contributing to the metastable peak shapes,
collisional activation studies were carried out by leaking helium gas
into the collision cell located in the second field-free region. This
experimental configuration does not allow the direct measurement of
metastable dissociation rate constants, so only metastable branching
ratios were measured.
For theoretical modeling of these reactions, experimental heats of
formation and spectroscopic data were used where available. When
such data were not available or were incomplete, the molecular and
ionic species required for the modeling were studied theoretically with
ab initio molecular orbital theory to obtain the energetic and spectro-
scopic parameters needed. The ab initio calculations were performed
with the Gaussian 92 suite of programs.32
In this paper we expand the range of SN2 reactions studied
to include the following.29
-
Cl + CF CO CH f
3
2
3
-
CF CO + CH Cl
∆H ) -13.4 kcal/mol (1)
3
2
3
-
CN + CF CO CH f
3
2
3
CF CO2- + (CH CN, CH NC)
3
3
3
∆
H ) (-47.6, -24) kcal/mol (2)
(
22) (a) Vande Linde, S. R.; Hase, W. L. J. Am. Chem. Soc. 1989, 111,
2
6
7
349-2351. (b) Vande Linde, S. R.; Hase, W. L. J. Phys. Chem. 1990, 94,
148-6150. (c) Vande Linde, S. R.; Hase, W. L. J. Chem. Phys. 1990, 93,
962-7980. (d) Cho, Y. J.; Vande Linde, S. R.; Zhu, L.; Hase, W. L. J.
Rate coefficients for the bimolecular reactions have been measured
Chem. Phys. 1992, 96, 8275-8287. (e) Hase, W. L.; Cho, Y. J. J. Chem.
Phys. 1993, 98, 8626-8639. (f) Wang, H.; Peslherbe, G. H.; Hase, W. L.
J. Am. Chem. Soc. 1994, 116, 9644-9651. (g) Peslherbe, G. H.; Wang, H.;
Hase, W. L. J. Chem. Phys. 1995, 102, 5626-5635.
by Olmstead and Brauman4 and Grabowski and Owusu.
33
These
(30) Cooks, R. G.; Beynon, J. H.; Caprioli, R. M.; Lester, G. R.
Metastable Ions; Elsevier: Amsterdam, 1973.
(23) Basilevsky, M. V.; Ryaboy, V. M. Chem. Phys. Lett. 1986, 129,
7
1-75.
(31) Jarrold, M. F.; Illies, A. J.; Kerchner, N. J.; Wagner-Redeker, W.;
Bowers, M. T.; Mandich, M. L.; Beauchamp, J. L. J. Phys. Chem. 1983,
87, 2213-2221.
(32) Gaussian 92, Revision A.; Frisch, M. J.; Trucks, G. W.; Head-
Gordon, M.; Gill, P. M. W.; Wong, M. W.; Foresman, J. B.; Johnson, B.
G.; Schlegel, H. B.; Robb, M. A.; Replogle, E. S.; Gomperts, R.; Andres,
J. L.; Raghavachari, K.; Binkley, J. S.; Gonzalez, E.; Martin, R. L.; Fox,
D. J.; DeFrees, D. J.; Baker, J.; Stewart, J. J. P.; Pople, J. A. Gaussian,
Inc.: Pittsburgh, PA, 1992.
(
24) Ryaboy, V. M. Chem. Phys. Lett. 1989, 159, 371-375.
(25) Viggiano, A. A.; Morris, R. A.; Paschekewitz, J. S.; Paulson, J. F.
J. Am. Chem. Soc. 1992, 114, 10477-10482.
26) VanOrden, S. L.; Pope, R. M.; Buckner, S. W. Org. Mass Spectrom.
(
1
991, 26, 1003-1007.
(27) Wang, H.; Hase, W. L. Chem. Phys. 1996, 212, 247-258.
(28) Wang, H.; Hase, W. L. J. Am. Chem. Soc. 1995, 117, 9347-9356.
(29) Lias, S. G.; Bartmess, J. E.; Liebman, J. F.; Holmes, J. L.; Levin,
R. D.; Mallard, W. G. J. Phys. Chem. Ref. Data 1988, 17, Suppl. 1.
(33) Grabowski, J. J.; Owusu, D. Private communication.

Internal Excitation in the Products of Nucleophilic Substitution
J. Am. Chem. Soc., Vol. 120, No. 27, 1998 6787
Table 1. Branching Ratios and Average Kinetic Energy Releases
for Metastable and Collisionally Activated Dissociation of
-
-
-
Cl (CF
3
CO
CH
2
CH
3 3 2 3 3 6 5
), CN (CF CO CH ), F (CH OC H ), and
-
Cl (CH
3
2
I)
collisionally
activated
metastable
product
ion
ratio,
%
〈E
meV
t
〉,
ratio, 〈E
〉,a
t
complex
%
meV
-
Cl-
Cl (CF
3
CO
2
CH
3
)
4
96
2
98
5
95
<2
>98
22 ( 6
38 ( 1
29 ( 10
66 ( 3
59 ( 5
60 ( 2
80
20
90
10
60
40
25
75
68
67
68
73
68
77
68
66
-
CF
3
-CO
2
-
CN (CF
3
CO
2
CH
3
)
CN
CF
-
3
CO
2
F-(CH
OC
H
5
)
F
-
3
6
C
6
H
5
O-
-
-
b
Cl (CH
3
CH
2
I)
Cl
-
I
46 ( 1
a
Error bars for CAD average kinetic energy release measurements:
b
(
4 meV. Product not detected; branching ratio is the upper limit.
kinetics are modeled with statistical phase space theory, to estimate
the energies of the substitution transition state. These values were then
used in the statistical phase space models for the kinetic energy release
distributions (KERDs). Internal excitation in the products was modeled
by calculating a series of KERDs assuming between 0 and 100% of
the energy released was unavailable for randomization in the product
orbiting transition state. Details of the statistical phase space model
are given in the Appendix and the parameters used are available as
Supporting Information.
Results
The metastable adduct species are represented in this paper
-
as the reactant complexes X (RY) formed by simple association
Figure 1. Experimental kinetic energy release distributions for
-
reactions of X + RY. As will be seen, both the experimental
results and the phase space theoretical modeling indicate that
if any rearranged complexes Y (RX) are formed in the ion
metastable (heavy solid line) and collisionally activated (dashed line)
-
-
dissociation of Cl (CF
CO CH
3
CO
2
CH
3
): (a) back-dissociation to Cl + CF
3
-
-
-
2
3
; (b) nucleophilic displacement to CF
3
CO
2
3
+ CH Cl.
source, they do not contribute to the metastable signal.
Metastable Dissociation and Collisional Activation. For
the purpose of modeling the kinetic energy release data, it is
important that the dissociations observed arise from metastable
ions and not from collisional activation by residual background
gases in the second field-free region (2FFR). To verify that
the experiment is probing true metastable dissociation, the
KERDs and branching ratios measured are compared to those
obtained with helium added to the 2FFR collision cell to result
in about 50% depletion in the main beam. The branching ratios
and average kinetic energy releases for metastable and colli-
sionally activated dissociation are collected in Table 1, and
further details for the specific systems are given below.
A representative example of this comparison for the KERDs
similar KERDs would be expected for both experiments.
Additional evidence that the experiment probes true metastable
dissociation can be found in the branching ratios observed for
metastable dissociation vs CAD. Metastable dissociation of
-
Cl (CF CO CH ) strongly favors channel 5b over 5a by a factor
3
2
3
of 25. In contrast, CAD reverses the preference, and favors 5a
over 5b by a factor of 4 (for target gas pressures that result in
an increase of product ion signal of more than 10×). For the
-
production of CF3CO2 , the ion kinetic energy analysis for the
metastable KERDs was repeated twelve times over the course
of several days, and showed a highly reproducible average
-
kinetic energy release of 38 ( 1 meV. The KERD for the Cl
product from metastable dissociation was narrower, with an
average release of 22 ( 6 meV.
-
is shown in Figure 1 for the dissociation of Cl (CF3CO2CH3).
(Plots of the experimental KERD data for metastable dissocia-
Significant differences in KERDs and branching ratios
for metastable vs CA dissociation were observed for all
four reactions, with one exception: the KERDs for the
tion and CAD for the remaining three reactions are available
as Supporting Information.) Two ionic products are observed,
corresponding to cleavage of the electrostatic bond (eq 5a) and
nucleophilic displacement (eq 5b). Equation 5b represents a
half-reaction for the gas-phase SN2 process, starting from the
intermediate adduct species.
-
CF3CO2 product from metastable and CA dissociation of
-
CN (CF3CO2CH3) were similar. In this case, the relatively
broad metastable KERD is probably a consequence of the large
-
exothermicity of this reaction. The KERDs for the CN product
-
-
in the two experiments were clearly different (with CAD giving
a much broader KERD), and the branching ratios were very
different for metastable dissociation vs CAD. Therefore we
conclude that in all four systems, we are observing true
metastable dissociation.
Cl (CF CO CH ) f Cl + CF CO CH
3
(5a)
(5b)
3
2
3
3
2
f CF CO2- + CH Cl
3
3
It can be seen that for both products, the KERD for collisionally
activated dissociation (CAD) is significantly broader. This result
is evidence that the dissociations leading to the narrower KERDs
do not result from CAD with background gases, in which case
-
The metastable adduct from the reaction of CN with CF3-
-
-
CO2CH3 dissociated to yield both CN and CF3CO2 (eq 6),
with a branching ratio of 50:1 in favor of channel 6b.

6788 J. Am. Chem. Soc., Vol. 120, No. 27, 1998
Graul et al.
-
-
CN (CF CO CH ) f CN + CF CO CH
(6a)
3
2
3
3
2
3
f CF CO2-
+
3
(
CH CN, CH NC) (6b)
3 3
For CAD, however, when the target gas pressure was high
enough to produce an increase in the product ion signal of about
3
0×, channel 6a was favored over channel 6b by 9:1. The vast
majority of this increase corresponds to dissociation into channel
a. This result demonstrates that CAD and metastable dis-
sociation are distinct processes.
The dissociation of the metastable adduct of F with CH3-
6
-
-
-
OC6H5 yielded F and C6H5O (eq 7), with a branching ratio
of about 20:1 in favor of eq 7b.
-
-
F (CH OC H ) f F + CH OC H
5
(7a)
(7b)
3
6
5
3
6
Figure 2. Calculated reaction coordinate for S
CF CO CH . Relative energies shown are determined from MP2/6-
2 reaction of Cl-
+
N
-
f C H O + CH F
6
5
3
3
2
3
3
1+g(d) single-point energies calculated at the HF/6-31+G(d) opti-
Collisional activation results in channel 7a dominating by about
:2, with an increase in total product ion signal of more than a
mized geometries and corrected for zero-point vibrational energy.
Literature thermochemistry is shown in parentheses and adjusted to 0
K. Energies are given in kcal/mol.
3
29
factor of 40 for the target gas pressure used. In this system,
-
the KERD for the F product is significantly broader than
observed for eqs 5a and 6a, although it is still narrower than
the corresponding KERD for collisional activation.
The adduct of Cl with CH3CH2I was difficult to generate
searches for structures at local minima were made at the
Hartree-Fock level by using the 3-21G basis set. Further
optimization was performed for all degrees of freedom by using
the 6-31+G(d) basis set. Frequency analysis was performed
for these optimized geometries, and single point energies were
then calculated at the MP2 level. At this level, good agreement
was found with experiment for the overall 0 K enthalpy of the
-
in abundance and the signals for the product ions from
metastable dissociation were correspondingly weak. Only one
-
fragment ion, I , was observed. We attribute this ion to the
substitution reaction (eq 8a) rather than the elimination reaction
-
-
(eq 8b), which is slightly endothermic (∆H ) 1.6 kcal/mol).
reactions of Cl and CN with CF3CO2CH3. The agreement
-
The latter channel would not be expected to compete effectively
with the thermoneutral reversion to reactants or with the
exothermic substitution reaction in metastable dissociation.
was less satisfactory for the reaction of F with CH3OC6H5.
For this reaction, the single-point MP2 calculations were
performed with a larger basis set, 6-311+G(d,p), which yielded
-
better agreement with the literature. For the reaction of Cl
-
-
Cl (CH CH I) f I + CH CH Cl
(8a)
(8b)
with CH3CH2I (eq 4), full geometry optimizations were
performed at the HF and MP2 levels by using the LANL1DZ
basis set. Frequency analyses were performed at the HF level.
For this reaction, the MP2 level gave better agreement with the
overall experimental thermochemistry. Detailed structural
information (in the form of z-matrixes), total energies (hartrees),
and zero-point vibrational energies (kcal/mol) are provided in
The Supporting Information.
3
2
3
2
-
f I + C H + HCl
2
4
On the basis of the observed signal-to-noise ratio of the
-
experiments, the branching ratio for Cl produced by metastable
dissociation must be less than 2%. The experiment was repeated
nine times and KERD analysis gave an average kinetic energy
release of 46 ( 1 meV. When helium was admitted to the
collision cell in the 2FFR for CAD experiments to give an
On the basis of the results of these calculations, schematic
reaction coordinates were constructed for each of the reactions
at 0 K. These are shown in Figures 2-4 for reactions 1-3.
The relative energies are evaluated from the MP2 single point
energies with zero-point vibrational energy included. For
reaction 4, the relative energies are evaluated from the geometry-
optimized MP2 values and corrected for the HF zero-point
vibrational energies (Figure 5). Also shown are literature values
-
increase of about 40× in the total product ion signal, both Cl
-
and I were detected, in approximately 1:3 ratio favoring the
I product. In the CAD experiments, eq 8b may also figure in
-
-
the formation of I .
For these reactions, the ion source conditions (temperature
and reactant pressure) under which the clusters could be
generated were fairly limited. However, over the range avail-
able, no systematic variation in the average kinetic energy
releases or the shapes of the KERDs could be observed.
Molecular Orbital Calculations. Although the overall
thermochemistry for the bimolecular reactions studied is avail-
able from the literature, information about the relative energies,
structures, and vibrational frequencies of the intermediate
complexes and the transition states were lacking. Because such
information is needed for the modeling of the KERDs by
statistical phase space theory, ab initio molecular orbital
calculations were performed. The possibility of isomeric species
was also a concern for some of the ion-molecule complexes
and transition states. For three of the reactions (eqs 1-3), initial
2
9,34,35
for the overall reaction thermochemistry.
These reaction
coordinates were used for the statistical phase space theoretical
modeling described in the next section.
For the reactions with CF3CO2CH3, the optimized geometry
for the reactant complex showed the nucleophile X bound at
the methyl group approximately in line with the C-O bond,
slightly closer to the hydrogen anti to the carboxyl group, as
(34) The heat of formation of CF3CO2CH3 is estimated by using the
additivity method of Benson (ref 35), by taking the difference between the
known values of ∆Hf (ref 29) for CH3CO2CH3 and CH3COOH as an
estimate for the incremental change in ∆Hf between CF3CO2CH3 and CF3-
COOH. The estimated uncertainty is (3 kcal/mol.
(35) Benson, S. W. Thermochemical Kinetics; John Wiley & Sons: New
York, 1968.

Internal Excitation in the Products of Nucleophilic Substitution
J. Am. Chem. Soc., Vol. 120, No. 27, 1998 6789
Figure 4. Calculated reaction coordinate for S
CH OC . Relative energies shown are determined from MP2/6-
11+G(d,p) single-point energies calculated for the HF/6-31+G(d)
2 reaction of F-
+
N
3
6 5
H
3
optimized geometries and corrected for zero-point vibrational energy.
The proton-transfer channel is shown as a dashed line and is
endothermic overall. Literature thermochemistry is shown in parentheses
and adjusted to 0 K.29 Energies are given in kcal/mol.
-
Figure 3. Calculated reaction coordinates for S
CF CO CH
N
2 reaction of CN +
3
2
3
. Relative energies shown determined as in Figure 2. The
solid line corresponds to nucleophilic attack by the carbon atom of
-
CN , and the dashed line is for attack by the nitrogen atom. Literature
thermochemistry is shown in parentheses and adjusted to 0 K.29 Energies
are given in kcal/mol.
shown in Figure 2. The X-C-O angle in this species is nearly
linear: 165-170°. Two analogous isomeric structures were
-
found for the reactant complex in the reaction of CN with CF3-
CO2CH3, corresponding to attack by the carbon or nitrogen atom
-
of CN . The latter structure is the more stable of the two by
about 0.8 kcal/mol. No evidence was found for a tetrahedral
intermediate resulting from nucleophilic addition at the carbonyl
group.
-
In the reactant complex for the reaction of F with CH3-
-
OC6H5, the F nucleophile was found to form a bridge between
an ortho hydrogen of the phenyl ring and one of the hydrogens
on the methyl group. This complex was bound by 23.5 kcal/
mol, almost twice as strongly as the reactant complex species
-
-
found for Cl and CN with CF3CO2CH3. A second isomer
-
was found in which the F was bound at the phenyl hydrogen
para to the methoxy group. This structure was bound by about
1
6 kcal/mol at the highest level of theory used.
Coarse transition state searches were performed by starting
with the optimized reactant complex structures and gradually
decreasing the distance between the nucleophile and the carbon
of the methyl group. That degree of freedom was fixed and all
others were optimized. This process was repeated until the
energy reached a maximum, at which point a transition state
optimization was performed for all degrees of freedom. Fre-
quency analysis confirmed for each optimized transition state
that only one vibrational mode was imaginary, and this mode
corresponded to the asymmetric stretch mode for the X-C-Y
Figure 5. Calculated reaction coordinate for S
CH CH I. Relative energies shown are determined from MP2/
LANL1DZ optimized geometries and corrected for zero-point vibra-
tional energy. Literature thermochemistry is shown in parentheses and
adjusted to 0 K.29 Energies are given in kcal/mol.
2 reaction of Cl-
+
N
3
2
group, where X is the attacking atom of the nucleophile and Y
the atom of the leaving group that is bound to the transferring
methyl group. An interesting feature of the transition states

6
790 J. Am. Chem. Soc., Vol. 120, No. 27, 1998
Graul et al.
98 Y + CH X (9)
kcoll
k1
for the reactions involving CF3CO2CH3 is that the methyl group
rotates by 60° from its optimal position in the reactant complex,
such that in the transition state a CH bond is eclipsed with the
carboxyl group (see Figure 2). This rotation was observed to
occur within the last 0.05 Å change in distance between the
nucleophile and the methyl carbon, and the eclipsed conforma-
tion is retained in the product complexes. For reactions 1-3,
the SN2 transition states were found to be 1-3 kcal/mol below
the energy of the separated reactants when zero-point energy
was included. As can be seen in Figures 2-5, for all the
transition states, the transferring methyl or ethyl group is nearly
planar in the transition state.
It is interesting to compare the reactions of Cl- and CN-
with CF3CO2CH3. The cyanide reaction is significantly more
exothermic, but the central barrier height (the transition state
energy relative to the separated reactants) calculated for the
carbon attack in the cyanide reaction is only slightly lower than
that of chloride. The unimolecular substitution barrier, as
measured by the energy difference between the reactant complex
and the transition state, is about 9.6 kcal/mol. This is smaller
than the chloride barrier of 12.8 kcal/mol (at the highest level
of theory used), but is significantly greater than the substitution
barrier for another SN2 reaction of comparable exothermicity,
F
only 2.8 kcal/mol at 0 K, at the G2(+) level of theory.
According to Marcus theory as applied to gas-phase substitution
reactions, this would suggest a greater intrinsic substitution
barrier for cyanide as compared to the halides. (The intrinsic
barrier is the difference between the reactant complex and the
transition state for the symmetric reaction *X + CH3X f
CH3*X + X ). A greater intrinsic barrier would be consistent
-
-
-
X + CH Y { } X (CH Y)
3
3
3
k-1
This allows the reaction probability, defined as kexpt/kcoll, to be
related to the ratio of the rates of unimolecular dissociation of
the reactant complex to the reactants vs SN2 products. Thus,
kexpt
k1
)
(10)
kcoll
k1 + k
-1
where k1 is the rate constant for passage through the SN2
transition state. Reaction probabilities were calculated for a
range of central barrier heights. These probabilities were then
compared to the experimental efficiency, which was taken as
the experimental rate coefficient divided by the collision rate
constant. These calculated reaction probabilities are most
sensitive to the central barrier height and the values of the lowest
frequency vibrational modes of the SN2 transition state. The
uncertainty in the calculated barrier heights was estimated by
varying the lowest five frequencies of the transition state by
3
9
(
25% and assuming error bars for the experimental rate
coefficients of (30%. The resulting fitted barrier heights are
collected in Table 2, along with the calculated transition state
energies from the ab initio calculations. Also shown are the
experimental reaction coefficients and the calculated collision
rate constants that were used in the fitting.
-
+ CH3Cl, which has been calculated to have a barrier of
3
6
The median calculated barrier heights from modeling the
reaction kinetics were used in phase space modeling of the
branching ratios for the metastable dissociations. If the
metastable species is assumed to be the unstabilized ion-
molecule collision complex (i.e., no stabilizing third-body
collisions occur during the lifetime of the complex), the
predicted branching ratio for metastable dissociation strongly
favors dissociation to the reactants (channel a in eqs 5-8). In
contrast, the calculated metastable branching ratios for fully
thermally stabilized 270 K clusters strongly favor the SN2
products. Taken together, these calculations suggest that the
metastable species have undergone at least partial stabilization.
The stabilization mechanism is probably low-energy collisions
in the ion source, which should serve to relax the nascent internal
energy distribution of the ion-molecule collision complex
toward a thermal Boltzmann distribution. It therefore seems
reasonable to assume that the true internal energy E and angular
momentum J distributions of the metastable clusters will fall
between these two extremes (nascent collision complex and
thermally equilibrated), and that calculations assuming the two
extreme cases may be used to “bracket” the experimental KERD
results. It should be noted that these E and J distributions are
further modified by the inclusion in the calculations of the
probability of dissociation within the experimental time window.
The effect of including this factor is to truncate the high-energy
portion of the energy distributions. For simplicity, the E and J
distribution functions for the two cases will hereafter be referred
to as “CC” for the nascent collision complex and “Th” for a
270 K thermalized species, and the resulting KERDs will be
labeled as such.
4
e
-
-
with the 30-40 kcal/mol greater energy of a C-C bond vs a
C-Cl bond for both homolytic and heterolytic dissociation.
2
9,37
-
The calculations for the reaction of Cl with CH3CH2I
reproduce the literature value for overall reaction enthalpy quite
well (Figure 5).29 However, the central barrier height is
somewhat lower than might be expected by comparison with
the Cl + CH3I reaction, for which high-level calculations give
-
38
the central barrier as -2.7 (MP2/PTZ+) and -3.3 kcal/mol
(
G2+),36 and a PST model of bimolecular kinetics gives -4.6
1
(
0.4 kcal/mol. The MP2 optimized geometries with the
unaugmented LANL1DZ basis set give a central barrier of -7.2
-
kcal/mol (corrected for zero-point energy) for the Cl + CH3-
CH2I reaction. This reaction is only slightly more exothermic
than the Cl + CH3I SN2 reaction, and the reaction efficiencies
are about equal (∼10%), which would suggest comparable
central barriers. As is shown below, the PST-ADO calculations
give a central barrier of -3.5 ( 1.8 kcal/mol for reaction 4.
Theoretical Phase Space Calculations. Central barrier
heights for the SN2 reactions were evaluated by modeling the
experimental reaction rate coefficients using statistical phase
space theory with the average dipole approximation (PST-ADO).
The details of the PST-ADO model are described in the
Appendix, and only the results are presented here. The reaction
kinetics were modeled with the assumption of steady-state
conditions for a reactant complex that is formed at the collision
rate (eq 9).
-
5b
With use of these E and J distribution functions, statistical
PST-ADO calculations were performed to predict kinetic energy
release distributions for the metastable dissociations of the ion
complexes. To test the sensitivity of the results to the values
of the parameters used in the PST-ADO calculations, the central
(
36) Glukhovtsev, M. N.; Pross, A.; Radom, L. J. Am. Chem. Soc. 1996,
18, 6273-6284.
37) McMillen, D. F.; Golden, D. M. Annu. ReV. Phys. Chem. 1982, 33,
1
4
1
(
(39) Su, T.; Chesnavich, W. J. J. Chem. Phys. 1982, 76, 5183-5185.
See also: Chesnavich, W. J.; Su, T.; Bowers, M. T. J. Chem. Phys. 1980,
72, 2641-2655. Chesnavich, W. J.; Su, T.; Bowers, M. T. NATO ASI Series
BsPhysics; Ausloos, P., Ed.; Plenum: New York 1979; Vol. 40, p 31ff.
93-532.
(
38) Hu, W.-P.; Truhlar, D. G. J. Am. Chem. Soc. 1995, 117, 10726-
0734.

Internal Excitation in the Products of Nucleophilic Substitution
J. Am. Chem. Soc., Vol. 120, No. 27, 1998 6791
Table 2. Comparison of Central Barrier Heights for the Following Reactions: Cl- + CF
CO
CH
, CN- + CF
CO
CH
, F- + CH
H
5
,
3
2
3
3
2
3
3
OC
6
-
and Cl + CH
3
2
CH I
a
3
3
q
b
q
c
q
d
reactants
k
coll, cm /s
k
expt, cm /s
∆E (kinetics), kcal/mol
-1.4 ( 1.6
∆E (ab initio), kcal/mol
-1.16
∆E (KERD), kcal/mol
-
-9
-10 e
Cl + CF
3
CO
2
CH
3
2.79 × 10
3.09 × 10
2.63 × 10
2.11 × 10
1.29 × 10
-2.0
-
10 f
0
.45 × 10
[0.0 to -5.3]
-3.7
-
-9
-9
-9
-10 e
10 f
CN + CF
3
CO
2
CH
3
1.05 × 10
-2.3 ( 1.6
-3.3 ( 1.6
-3.5 ( 1.8
-3.26
-1.09
-7.22
-
0
.3 × 10
[-1.8 to -4.6]
-3.7
F- + CH
H
0.8 × 10
5.7 × 10
-10 f
10 e
3
OC
6
5
-
g
(
)
[-3.1 to -4.6]
-4.6
-
-10 e
Cl + CH
3
CH
2
I
2.07 × 10
[
-1.7 to -7.0]
a
Collision rate constant calculated by using the variational transition state method, ref 39. b Central barrier heights determined from fitting
experimental kinetics by using statistical phase space theory (PST-ADO). c Central barrier heights from ab initio calculations. Central barrier
height from fitting KERD. In brackets are shown the ranges of barrier heights considered for fitting. Grabowski and Owusu, flowing afterglow
results, private communication. Reference 4c. Not used in modeling; third-body enhancement of rate suspected based on observation of clustering
of reactants.
d
e
f
g
barrier heights were varied over the complete range given by
the ab initio calculations plus the PST-ADO modeling of the
bimolecular reaction kinetics. In addition, the binding energies
for the complexes were varied from the ab initio values by
(
25% and the lowest five vibrational frequencies of the
transition states were varied by (25%. Although the experi-
mental KERDs for the simple back-dissociation could be
bracketed by the calculated KERDs for the CC and Th
distribution functions, the experimental KERDs for the SN2
products were always considerably narrower than both the
calculated KERDs, indicating that products were translationally
cold and internally hot relative to the predictions of statistical
theory. The effect of internal excitation in the SN2 products
was modeled by decreasing the reaction exothermicity and
calculating the effective KERD, and the best fits are presented
below. For clarity of presentation, the experimental and
calculated KERDs are scaled to the same maximum.
In Figure 6a are shown calculated and experimental KERDs
-
-
for the dissociation of Cl (CF3CO2CH3) to give Cl and CF3-
CO2CH3. This calculation was found to be most sensitive to
the value of complex binding energy and the central barrier
height. Increasing the binding energy or raising the central
barrier had the effect of broadening the calculated KERD, due
to an increased complex lifetime, such that higher energy
complexes move into the metastable time window. The results
shown were obtained for a binding energy of 14.0 kcal/mol
(from the ab initio calculations) and a central barrier height of
-
2.0 kcal/mol, a value that was found by trial and error to give
the best fits for the SN2 dissociation (see below). The CC and
Th KERDs bracket the experimental result at relative kinetic
energies below about 0.04 eV. The high-energy “tail” in the
experimental distribution at relative kinetic energies greater than
Figure 6. Experimental and theoretical KERDs for metastable dis-
-
sociation of Cl (CF
3
CO
2
CH
3
). (a) KERDs for products from back-
: experimental data (heavy solid line);
-
dissociation to Cl + CF
calculated with CC distribution (light solid line); calculated with Th
3
CO
2
CH
3
0
.04 eV is probably due to the occurrence of a small amount of
CAD, which strongly enhances this dissociation channel (Table
distribution (dashed line). (b) KERDs for displacement products
-
-
1
). As can be seen in Figure 1, the KERD for the Cl product
CF
3
CO
2
3
+ CH Cl: experimental data (heavy solid line); statistical
from CAD extends well beyond 0.15 eV relative energy.
The same parameters were used to calculate the KERD for
the CF3CO2 product, and the CC (solid line) and Th (dashed
dissociation calculated with CC distribution (light solid line); statistical
dissociation calculated with Th distribution (dashed line); CC with
internal excitation Efix ) 0.25 eV (open circles); dissociation from a
thermalized product complex (dotted line).
-
line) KERDs are shown in Figure 6b along with the experimental
result. Both calculated curves are clearly broader than the
experimental KERD. For the CC distribution, decreasing the
central barrier height over the range shown in Table 2 results
in broadening of the calculated KERD and a shift of the energy
of maximum probability to higher energies. The Th KERD is
wider than the experimental data and does not reproduce the
energy dependence well, showing a maximum probability at
satisfactory fits. (An example of the variation of the calculated
KERDs with barrier height is included in the Supporting
Information.) The open circles in Figure 6 show the calculated
KERD that is obtained with the CC distribution by decreasing
the exothermicity of the reaction from -13.4 kcal/mol to -7.6
kcal/mol, a change of +5.8 kcal/mol. The agreement with
experiment is excellent. For the Th distributions, the fit of the
calculated KERDs to the experimental data was not improved
greatly by changing the reaction exothermicity. Although the
calculated KERDs narrowed somewhat as the exothermicity was
0.00 eV and higher probabilities for large kinetic energies than
in the experimental distribution. Lowering the barrier height
narrowed the calculated KERD, but did not result in any

6792 J. Am. Chem. Soc., Vol. 120, No. 27, 1998
Graul et al.
complex binding energy of 12.9 kcal/mol. These values
compare favorably with both the results of the ab initio
calculations (Figure 3), and the central barrier height falls within
the range calculated with PST-ADO theory for the bimolecular
reaction (Table 2). In this case, the effect of the internal energy
distribution is more noticeable, and the CC and Th curves
bracket the experimental result, as might be expected if the
experiment probes a partially stabilized species. The long tail
of the experimental curve is most likely due to a small amount
of collisional activation. As mentioned previously, CAD not
only results in a much broader KERD for the simple back-
dissociation process but also strongly favors that channel.
Calculation of the SN2 KERD for this reaction is complicated
by the possible competition between carbon and nitrogen attack.
At the highest level of theory employed, the N-attack transition
state is about 3.3 kcal/mol higher in energy than the C-attack
transition state and 0.7 kcal/mol higher than the separated
reactants. For these central barrier heights, the predicted
branching ratio from PST-ADO is essentially 100% carbon
attack, both for the bimolecular reaction and for the metastable
reaction. On the basis of this branching ratio, we conclude that
the nitrogen attack channel can be neglected for the purposes
of calculating the KERD. The KERDs shown in Figure 7b were
calculated for statistical dissociation with the CC (solid line)
and Th (dashed line) distribution. Both curves are significantly
broader than the experimental result. The KERD plotted with
open circles is the result obtained with the CC energy distribu-
tion and assuming that the exothermicity of the reaction is only
-
26.7 kcal/mol instead of the -47.6 kcal/mol given by literature
thermochemistry (corrected to 0 K). The fourth set of data
Figure 7. Experimental and theoretical KERDs for metastable dis-
(
dotted line) corresponds to metastable dissociation of a
-
sociation of CN (CF
dissociation to CN + CF
3
CO
2
CH
3
). (a) KERDs for products from back-
CH : experimental data (heavy solid
-
thermalized (300 K) product complex CF3CO2 (CH3CN), and
is clearly much narrower than the experimental result. This
KERD was calculated by using a complex binding energy of
13.6 kcal/mol relative to separated products, as given by the ab
initio calculations.
-
3
CO
2
3
line); calculated with CC distribution (light solid line); calculated with
Th distribution (dashed line). (b) KERDs for displacement products
-
CF
3
CO
2
3
+ CH CN: experimental data (heavy solid line); statistical
CC (light solid line); statistical Th (dashed line); CC with Efix ) 0.9
eV (open circles); dissociation from a thermalized product complex
In Figure 8, the results for the metastable dissociation of the
(dotted line).
-
F (CH3OC6H5) complex are shown. The experimental KERD
for back-dissociation to F and CH3OC6H5 can be reproduced
(
-
reduced, they all peaked at 0.0 eV and the probability fell off
less steeply with energy than the experimental curve does. For
this reaction, the change required in the reaction thermochem-
except for the high-energy tail) by using the CC energy
distribution with a complex binding energy of 23.5 kcal/mol,
as given by the ab initio calculations, and a central barrier height
of -3.7 kcal/mol (Figure 8a), in good agreement with the value
determined by fitting the bimolecular kinetics (Table 2). The
calculated KERD for the 270 K Th distribution, however, is
considerably narrower than the experimental result, which
suggests that a large fraction of the metastable complexes has
not undergone significant stabilization. The same input param-
eters were used for the SN2 dissociation with the CC and Th
distributions, and yielded the curves shown in Figure 8b. As
with the other systems, these two curves are broader than the
experimental results. The curve plotted with open circles was
obtained with the CC distribution and an effective exothermicity
of -9.7 kcal/mol, rather than the -22.4 kcal/mol from the
literature (corrected to 0 K). The KERD calculated for
dissociation of a thermally equilibrated 270 K product complex
istry is about the same as the estimated uncertainty of (5 kcal/
mol in the reaction thermochemistry.34
Because these ion complexes are formed under conditions
where partial collisional stabilization may occur, it is possible
that the experimental KERD results from dissociation of a
species trapped in the product complex well and partially
thermalized. To determine whether this could yield the narrow
experimental KERD, the KERD expected for such a situation
was calculated. The very narrow curve shown as a dotted line
in Figure 6b corresponds to the dissociation of a 300 K product
-
complex CF3CO2 (CH3Cl). This result is only very weakly
sensitive to the assumed temperature of the internal energy
distribution and depends most strongly on the binding energy
of the complex. The distribution shown was calculated for a
product complex binding energy of 14 kcal/mol, and is clearly
much narrower than the experimental result. The binding energy
parameter had to be increased to more than 35 kcal/mol to
reproduce the width of the experimental KERD. However, this
is unreasonably large for an ion-dipole complex.2
-
C6H5O (CH3F) is much narrower than the experimental KERD.
In Figure 9 are shown KERDs calculated for the dissociation
-
of Cl (CH3CH2I) with the CC distribution (solid line) and the
9
Th distribution (dashed line) for a central barrier height of -4.6
kcal/mol relative to the separated reactants. Both calculated
curves are clearly broader than the experimental KERD, but
the CC distribution more nearly reproduces the shape. The open
circles in Figure 9 show the calculated KERD that is obtained
The experimental and calculated KERDs for dissociation of
-
-
CN (CF3CO2CH3) to give CN and CF3CO2CH3 are shown in
Figure 7a. The KERDs shown were calculated for a central
barrier height of -3.7 kcal/mol (relative to reactants) and a

Internal Excitation in the Products of Nucleophilic Substitution
J. Am. Chem. Soc., Vol. 120, No. 27, 1998 6793
field-free region. Therefore, no curve is shown for the dis-
sociation of a stabilized product complex.
Discussion
As mentioned in the Introduction, our goal is to study the
unimolecular dissociation of the chemically activated intermedi-
ate complexes of a bimolecular nucleophilic substitution reac-
tion. Of particular interest is the dissociation that corresponds
to passage through the SN2 transition state, and whether this is
a statistical process. In our earlier study of metastable dis-
1
sociation of halide-methylhalide complexes, statistical phase
space modeling of the experimental results led to the conclusion
that the neutral species were vibrationally excited well beyond
what would be predicted by statistical partitioning of the
available reaction energy. The present study considers four
relatively disparate examples of carbon-centered nucleophilic
substitution, with widely different reaction exothermicities,
polyatomic nucleophiles, and leaving groups, many more
internal degrees of freedom than in the methylhalide reactions,
and, in one case (eq 3), a hydrogen-bonded reactant complex,
which is significantly more strongly bound and therefore longer
lived than any of the other complexes (Figure 4). Yet the results
of the theoretical modeling again indicate that the products of
nucleophilic substitution are internally excited.
In Table 3, the amounts of unavailable (fixed) energy, Efix,
that had to be deducted from the reaction exothermicities to
produce the fits shown in Figures 6-9 are listed and compared
to various reaction parameters. There is a good correlation of
Efix with overall reaction exothermicity ∆Hrxn and no apparent
correlation with the number of vibrational degrees of freedom
Nvib of the intermediate complexes. In all cases, the value of
Efix is a significant fraction (>40%) of the reaction exother-
micity, and is moreover large enough to accommodate several
vibrational quanta in modes such as the umbrella motion of the
CH3 group and the stretch of the newly formed C-X bond (X
being the nucleophile). One conclusion that may be drawn from
this observation is that there is relatively little randomization
of the energy stored in these modes after passage through the
transition state region.
Figure 8. Experimental and theoretical KERDs for metastable dis-
-
sociation of F (CH
dissociation to F + CH
calculated with CC distribution (light solid line); calculated with Th
distribution (dashed line). (b) KERDs for displacement products C
3
OC
3
6
H
5
). (a) KERDs for products from back-
H
6 5
-
OC : experimental data (heavy solid line);
-
6 5
H O
+
CH
3
F: experimental data (heavy solid line); statistical CC (light
solid line); statistical Th (dashed line); CC with Efix ) 0.55 eV (open
circles); dissociation from a thermalized product complex (dotted line).
-
In the X (RY) complexes, several low-frequency vibrational
modes are associated with stretching and bending about the
-
-
electrostatic X -RY bond. For the case of Cl (CH3Br) or
-
Cl (CH3Cl), these modes are significantly lower in frequency
than the modes associated primarily with the CH3Br or CH3Cl
moiety. For the purpose of this discussion, these two sets of
vibrational modes will be called “intermoiety” and “intramoi-
ety”, respectively. Hase and co-workers have suggested that
poor coupling between the low-frequency intermoiety and higher
frequency intramoiety vibrational modes of the intermediate
complexes in halide-methylhalide reactions causes incomplete
22
randomization of energy. The noncorrelation of Efix with Nvib
would support this conclusion; the number of intramoiety modes
in the intermediate complex has no discernible impact on the
internal excitation of the products. However, the energy gap
between the inter- and intramoiety modes for these complexes
Figure 9. Experimental and theoretical KERDs for metastable dis-
-
-
sociation of Cl (CH
3
CH
2
3
I) to give the displacement products I + CH -
CH Cl: experimental data (heavy solid line); statistical CC (light solid
2
line); statistical Th (dashed line); CC with Efix ) 0.45 eV (open circles).
-
is considerably smaller than in the case of Cl (CH3Cl) and
-
with the CC distribution by decreasing the exothermicity of the
reaction from the literature value of -15.0 kcal/mol to -4.6
kcal/mol. The agreement with experiment is quite good.
However, this exothermicity is well outside the combined
uncertainty of the reaction thermochemistry. Under the condi-
tions of our experiment, the PST-ADO calculations predict that
Cl (CH3Br). The fifth column of Table 3 shows the vibrational
frequencies corresponding to the intermoiety modes and, in
parentheses, the lowest two intramoiety modes for the product
complexes. For all four reactions, the energy gap between the
-
1
inter- and intramoiety modes is less than 200 cm , but for the
first two reactions listed, the lowest frequency vibrational mode
-
-1
product complexes I (CH3CH2Cl) with internal energy above
(6 and 8 cm ) corresponds to an intramoiety mode, rotation
the dissociation threshold dissociate before reaching the second
of the CF3 group.

6794 J. Am. Chem. Soc., Vol. 120, No. 27, 1998
Graul et al.
Table 3. Internal Excitation in Substitution Products and Various Experimental and Fitted Parameters
c
ν, cm-1 intermoiety (intramoiety)d
e
reactants
E
fix,a kcal/mol
∆Hrxn,b kcal/mol
-13.4
N
vib
τ, s
-
-12
Cl + CF
3
CO
CO
OC
Cl + CH CH
2
CH
3
5.8 (43%)
30
33
45
21
14, 29, 52, 60, 74, 90
2.1 × 10
(
8, 247)
14, 28, 31, 60, 80, 106
6, 248)
4, 10, 11, 76, 81, 82
194, 419)
42, 47, 71
249, 302)
-
-12
CN + CF
3
2
CH
3
20.8 (44%)
12.7 (57%)
10.4 (69%)
-47.6
-22.4
-15.0
1.5 × 10
(
F- + CH
-10
3
6
H
5
1.8 × 10
(
-
-12
3
2
I
7.5 × 10
(
a
Energy that is unavailable for randomization, as determined from fitting experimental KERDs by using statistical phase space theory (PST-
b
c
N
ADO). The values in parentheses show the unavailable energy as a percent of reaction exothermicity. Overall S 2 reaction enthalpy, 0 K. Number
d
of vibrational degrees of freedom for intermediate ion-molecule complexes. Intermoiety and (lowest two intramoiety) vibrational frequencies for
product complexes. See text of Discussion for explanation of “intermoiety” and “intramoiety”. e PST-ADO lifetime of product complexes after
passage over TS.
The last column of Table 3 shows lifetimes calculated with
PST-ADO for the product complexes formed by passage over
the substitution barrier for reactions 1-4. These lifetimes
correspond to statistical dissociation of metastable complexes
with the CC distribution, and therefore reflect the lifetimes for
the population observed in the MIKES experiment. It might
be expected that the shortest-lived product complexes would
show the greatest deviations from statistical energy partitioning,
but such a correlation is not apparent. However, in all cases,
the predicted lifetime for statistical dissociation is quite short.
In the SN2 reactions described here, the transition state structures
are significantly distorted from the product geometry. The
distorted structure of the SN2 transition state and the very short
lifetime of the product complex result in significant amounts
of energy being stored in vibrational modes of the products,
with the result that the experimental kinetic energy distributions
are narrower than predicted by theory.
We have shown that statistical dissociation of the reactant
complexes formed in reactions 1-4 cannot lead to the observed
KERDs for the SN2 products unless the products are assumed
to be internally excited. As outlined in the Results section, we
have considered the possibility that the narrow KERDs result
from dissociation of complexes trapped in the product well by
low-energy collisions in the ion source, and have found that
the statistical dissociation of such complexes would yield
KERDs very much narrower than the observed results (Figures
modeling the bimolecular kinetics or by the ab initio calcula-
tions. As is shown in Table 2, the optimized SN2 barrier heights
from PST-ADO modeling of the metastable dissociation KERDs
are slightly lower than those derived from modeling the
bimolecular reaction rate coefficients, but in all cases are well
within the uncertainties. The agreement with ab initio calcula-
tions is not as good, but the level of calculation used here is
only moderate and we consider the PST-ADO results to be more
reliable. The KERD analysis indicates clearly that partitioning
of energy in these metastable dissociations is not statistical. The
time scale of the metastable experiment guarantees that the
vibrational energy in these complexes is randomized, so the
nonstatistical dissociation dynamics must be associated with
passage through the SN2 transition state. If the bimolecular
reaction kinetics are correctly described by the steady-state
model shown in eqs 9 and 10, then the good agreement between
the energies of the SN2 barriers derived for these two experi-
ments (bimolecular reaction vs metastable unimolecular dis-
sociation) suggests that the vibrational energy in intermediate
complexes in the bimolecular reactions is also largely random-
ized.
Conclusions
The kinetic energy release distributions (KERDs) for meta-
stable dissociation of four ion-molecule complexes have been
measured by mass-analyzed ion kinetic energy spectroscopy and
modeled with a combination of ab initio molecular orbital
calculations and statistical phase space theory with the average
dipole orientation approximation. The complexes correspond
to intermediates in bimolecular SN2 reactions. In each case,
the experimental KERD is significantly narrower than would
be predicted by phase space theory. A model for metastable
dissociation that includes an adjustable parameter for internal
excitation in the products is able to account for the nonstatistical
experimental KERDs. There is a strong correlation between
the magnitude of the internal excitation (Efix) and the overall
exothermicity of the reaction, and an inverse correlation with
the lifetime of the product complex that is formed after passage
over the SN2 barrier.
6-8), or would yield no metastable signal (Figure 9), thus ruling
out contributions from trapped product complexes. Recently,
Viggiano and Hase and co-workers proposed that tunneling
through the SN2 barrier is implicated in the unimolecular
dissociation to Br- and CH3Cl of Cl-(CH3Br) formed by the
endothermic solvent-switching reaction of CH3Br with
-
40
Cl (H2O). Although our results indicate that some collisional
stabilization occurs in the ion source, we are confident that
tunneling does not contribute significantly to the KERDs we
observe for these metastable dissociations. Phase space calcula-
tions show that even fully thermalized complexes have adequate
internal energy for classical passage over the barrier, with
-
3
-6
probabilities on the order of 10 to 10 that this dissociation
-
5
occurs on the metastable time scale (∼10 s), consistent with
experimental observation of a metastable dissociation signal.
Acknowledgment. This work was supported in part by the
National Science Foundation through grants CHE-9502038
An important feature of the PST-ADO calculations is that a
self-consistent set of input parameters could be identified that
reproduced the KERDs for both the back-dissociation and
nucleophilic substitution (with the caveat that the reaction
exothermicity is a variable parameter), and that these parameters
were moreover in acceptable agreement with those given by
(S.T.G.) and CHE-9421176 (M.T.B.). S.T.G. also gratefully
acknowledges support from the American Chemical Society
Petroleum Research Fund in the form of a Type G grant (27088-
G6) and a research award from the American Society for Mass
Spectrometry. We are very grateful to Prof. J. J. Grabowski
and Mr. Daniel Owusu for measuring the bimolecular rate
coefficients for these reactions and communicating the results,
(40) Seeley, J. V.; Morris, R. A.; Viggiano, A. A.; Wang, H.; Hase, W.
L. J. Am. Chem. Soc. 1997, 119, 577-584.

Internal Excitation in the Products of Nucleophilic Substitution
J. Am. Chem. Soc., Vol. 120, No. 27, 1998 6795
and we thank Dr. A. Viggiano and Prof. W. Hase for useful
discussion. S.T.G. is grateful to Dr. L. M. Bass for helpful
discussion in modifying the phase space theory computer code
to incorporate the ADO potential.
literature when available or from the ab initio relative energies,
corrected for zero-point vibrational energies. The SN2 transition
state energy is evaluated by three different methods: ab initio
calculations, PST-ADO modeling of the bimolecular kinetics,
and PST-ADO fitting of the experimental KERDs. For the
product orbiting transition states, the relative heats of formation
comes from the literature. The relative heats of formation for
the reactant and product complexes were taken from the ab initio
calculations.
Appendix
The PST-ADO Method. For these phase space calculations,
we used the formalism developed by Bass and Bowers for the
average dipole orientation (ADO) potential for long-range ion-
41
Experimental vibrational frequencies are used where avail-
dipole interactions. In this formalism, the long-range potential
is given by eq 11 for a point charge interacting with a point
dipole,
4
3
able. For other species, the vibrational frequencies are taken
from the ab initio calculations at HF/6-31+G(d) and scaled by
0.89. The rotational constants used in the phase space calcula-
2
2
2
qµD
tions are the geometric mean of the rotational constants yielded
by the ab initio calculations. Molecular polarizabilities were
L p
q R
Veff(L,r,θ) )
-
-
cos θ
(11)
2
4
2
2r
2r
r
44
taken from the literature or estimated by using the method of
4
5
Miller and Savchik.
where L is the orbital angular momentum quantum number, r
is the separation between the charge and dipole, q is the charge
on the ion, R is the polarizability of the dipole, µD is the dipole
moment, and θ is the angle between the charge-dipole line of
centers and the dipole orientation. For this effective potential,
there is a maximum referred to as the centrifugal barrier located
at rk, defined by:
Tables of the parameters used in these calculations are
provided as Supporting Information.
Internal Energy and Total Angular Momentum Distribu-
tions. For an ensemble of nascent ion-molecule complexes
formed by thermal energy capture collisions at temperature T,
the probability distribution of internal energy E and total angular
momentum J may be expressed by eq 16:
dV (L,r)
eff
)
rk
0
(12)
P (E,J;T) dE dJ )
(
)
CC
dr
E
E-Et
orb
1
∫
dE
t
exp(-E
t
/k
B
T)
∫
dE
v
P(E
v
,E
r
) dJ2JF
(E,J)
0
0
As was shown by Bass and Bowers, the minimum translational
∞
∞
Jmax
orb
q
energy Et required to surmount the centrifugal barrier for this
potential can be expressed as:
∫
dE exp(-E /k T)
∫
dE P(E ,E )
∫
dJ2JF1 (E,J)
16)
t
t
B
v
v
r
0
0
0
(
2
qµ d cos θ(r)
2
q
q R
2
D
where E is zero for the separated reactants at 0 K, Et is the
relative translational energy of the reactants, Er and Ev are the
reactant rotational and vibrational energy, respectively, and
E (r ) )
-
(13)
t
k
(
)
4
rk
dr
rk
orb
The maximum orbital angular momentum quantum number L*
for which passage over the centrifugal barrier is possible can
be expressed as:
F1 (E,J) is the flux through the orbiting transition state for
total energy E and angular momentum J. In this expression,
P(Ev,Er) is the probability for the reactants having vibrational
energy Ev and rotational energy Er:
2
1/2
2
q
q Rµ
2 2
L*(r ) ) 2r µE (r ) +
+ D p cos θ(r )
k
k
k
t
k
P(E ,E ) ) 2F(E )[(E - E - E )/B ]
2
[
]
v
r
v
t
v
r
rk
(14)
exp[-(E - E - E )/k T] (17)
t v B
where
where F(Ev) is the density of vibrational states for reactant
vibrational energy Ev and Br is the reduced rotational constant
of the reactants. The function in eq 16 is referred to in the text
as the CC distribution, for “collision complex”.
2
µqµD
2
D )
(15)
2
p
If the complex formed by association in the ion sorce is
brought to thermal equilibrium by low-energy collisions, the
probability distribution of internal energy E and total angular-
momentum J may be expressed by:
An average value 〈cos θ〉 for the dipole orientation term and its
derivative are calculated numerically for the appropriate tem-
perature of the dipole and as a function of the separation between
the dipole and charge, r.42 By evaluating eqs 13 and 14 for a
q
series of rk values, a set of {Et , L*} is obtained for the orbiting
P (E,J;T) dE dJ )
Th
transition states at separation r. These values are then used to
determine the limits of integration for the calculation of available
phase space.
Parameters. Depending on the specifics of each calculation,
several species enter into the model. In general, the important
species include the orbiting transition states for association of
the separated reactants or products, the reactant and product
complexes (ion-dipole complexes), and the SN2 transition state.
The relative heats of formation at 0 K are taken from the
E
2
∫
dE P(E ,E ) dJ2J exp(-B J /k T)
v
v
r
RC
B
0
(18)
∞
Jmax
2
∫
dE
v
P(E
v
,E
r
)
∫
dJ2J exp(-BRCJ /k T)
B
0
0
where the zero of energy is now taken as the zero point of the
(43) Shimanouchi, T. Tables of Molecular Vibrational Frequencies;
National Bureau of Standards: Washington, DC, 1972; Consolidated Vol.
1.
(44) Radzig, A. A.; Smirnov, B. M. Reference Data on Atoms, Molecules,
(
(
41) Bass, L. M.; Bowers, M. T. J. Chem. Phys. 1987, 86, 2611-2616.
42) Bass, L. M.; Su, T.; Chesnavich, W. J.; Bowers, M. T. Chem. Phys.
and Ions; Springer-Verlag: Berlin, 1985.
(45) Miller, K. J.; Savchik, J. A. J. Am. Chem. Soc. 1979, 101, 7206-
7213.
Lett. 1975, 34, 119-122.

6796 J. Am. Chem. Soc., Vol. 120, No. 27, 1998
Graul et al.
reactant complex and BRC is the rotational constant of the pre-
reaction complex. The functional form of P(Ev,Er) is given by
eq 19 for Ev + Er ) E.
for dissociation of the reactants complex by eq 10. The optimal
value of ∆H is then determined by comparison of the
q
experimental efficiency with the calculated efficiencies for a
q
series of values of ∆H .
E - Ev
Branching Ratios and KERDS. Metastable branching ratios
were calculated with eq 21, for the fraction of dissociation into
channel i for an ion with n dissociation channels. The
probability of dissociation in the experimental time window,
Pdiss(E,J), is given by eq 20.
c
v
P(E ,E ) ) F (E )2
exp[-(E - E )/k T]
v B
v
r
v
( B
)
RC
(19)
c
In this equation, Fv (Ev) is the density of vibrational states for
the ion cluster at vibrational energy Ev. The function given in
eq 18 is referred to in the text as the Th distribution for a
thermalized ion cluster.
∞
Jmax
∫ ∫ dE dJP(E,J;T)Pdiss(E,J)F (E + ∆H ,J)
i
i
0
0
fi )
n
Each of these energy distributions is further modified by a
factor that accounts for the probability of dissociation within
the experimental time window of about 10-20 µs. This factor
is calculated by using eq 20,
∞
Jmax
(
∫ ∫ dE dJP(E,J;T)Pdiss(E,J)F (E + ∆H ,J))
∑
i
i
0
0
i)1
(21)
Branching ratios were calculated for P(E,J;T) given by eq 16
and eq 18. The quantity ∆Hi is defined as the 0 K heat of
formation of the appropriate transition state, relative to the
separated reactants, as in Figure 1.
Pdiss(E,J) ) exp(-k(E,J)t ) - exp(-k(E,J)t ) (20)
1
2
where k(E,J) is the calculated rate of dissociation of the
metastable complex of internal energy E and total angular
momentum J, and t1 and t2 are the times of entry to and exit
from the second field-free region of the mass spectrometer.
The KERDs for metastable dissociation were calculated as
12,41
described previously.
Internal excitation of the products was
modeled by assuming different values for the overall bimolecular
reaction enthalpy. The optimal fit of the calculated KERDs to
the experimental data was determined by a visual inspection of
the data.
q
q
Calculation of ∆H . For the calculation of ∆H , it is
assumed that the pre-reaction complex is formed in the
bimolecular reactions at the collision rate kcoll, as given by the
variational method of Su and Chesnavich.39 It is also assumed
that the experimental rate coefficients correspond to the low-
pressure limit, such that eq 16 is the appropriate form for the
distribution function for internal energy and angular momentum.
Under the assumption of transition state theory, the complex
subsequently dissociates back to reactants or forms the substitu-
tion products in an irreversible process. In this way, the
efficiency of the bimolecular reaction (kexpt/kcoll) can be related
to the ratio of the thermally averaged unimolecular rate constants
Supporting Information Available: Plots of metastable vs
CAD experimental KERDs for eqs 2-4; z-matrixes with
optimized geometries; tables of absolute energies from ab initio
calculations; tables of calculated vibrational frequencies; tables
of parameters for PST-ADO calculations (19 pages, print/PDF).
See any current masthead page for ordering information and
Web access instructions.
JA9730775