Thermochemistry is not a lower bound to the activation energy of endothermic reactions: A kinetic study of the gas-phase reaction of atomi-chlorine with ammonia

Article abstract of DOI:10.1021/jp056406l

The rate constant for Cl + NH₃ → HCl + NH₂ has been measured over 290-570 K by the time-resolved resonance fluorescence technique. Ground-state Cl atoms were generated by 193 nm excimer laser photolysis of CCl₄ and reacted under pseudo-first-order conditions with excess NH₃. The forward rate constant was fit by the expression k₁ = (1.08 ± 0.05) × 10^-11 exp(-11.47 ± 0.16 kJ mol^-1/RT) cm³ molecule^-1 s^-1, where the uncertainties in the Arrhenius parameters are ±1 σ and the 95% confidence limits for k₁ are ±11%. To rationalize the activation energy, which is 7.4 kJ mol ^-1 below the endothermicity in the middle of the 1/T range, the potential energy surface was characterized with MPWB1K/6-31++G(2df,2p) theory. The products NH₂ + HC1 form a hydrogen-bonded adduct, separated from Cl + NH₃ by a transition state lower in energy than the products. The rate constant for the reverse process k_-1 was derived via modified transition state theory, and the computed k_-1 exhibits a negative activation energy, which in combination with the experimental equilibrium constant yields k₁ in fair accord with experiment.

Full text of DOI:10.1021/jp056406l

6844
J. Phys. Chem. A 2006, 110, 6844-6850
Thermochemistry Is Not a Lower Bound to the Activation Energy of Endothermic
Reactions: A Kinetic Study of the Gas-Phase Reaction of Atomic Chlorine with Ammonia†
Yide Gao,‡ I. M. Alecu,‡ P-C. Hsieh,‡ Brad P. Morgan,§ Paul Marshall,*,‡ and
Lev N. Krasnoperov|
Department of Chemistry, UniVersity of North Texas, P. O. Box 305070, Denton, Texas 76203-5070,
Department of Physical Sciences, Morehead State UniVersity, 123 Lappin Hall, Morehead, Kentucky 40351,
and Department of Chemistry and EnVironmental Science, New Jersey Institute of Technology,
Newark, New Jersey 07102
ReceiVed: NoVember 6, 2005
The rate constant for Cl + NH3 f HCl + NH2 has been measured over 290-570 K by the time-resolved
resonance fluorescence technique. Ground-state Cl atoms were generated by 193 nm excimer laser photolysis
of CCl4 and reacted under pseudo-first-order conditions with excess NH3. The forward rate constant was fit
by the expression k1 ) (1.08 ( 0.05) × 10-11 exp(-11.47 ( 0.16 kJ mol-1/RT) cm3 molecule-1 s-1, where
the uncertainties in the Arrhenius parameters are (1 σ and the 95% confidence limits for k1 are (11%. To
rationalize the activation energy, which is 7.4 kJ mol-1 below the endothermicity in the middle of the 1/T
range, the potential energy surface was characterized with MPWB1K/6-31++G(2df,2p) theory. The products
NH2 + HCl form a hydrogen-bonded adduct, separated from Cl + NH3 by a transition state lower in energy
than the products. The rate constant for the reverse process k-1 was derived via modified transition state
theory, and the computed k-1 exhibits a negative activation energy, which in combination with the experimental
equilibrium constant yields k1 in fair accord with experiment.
1. Introduction
reaction
A standard assumption is that, for an endothermic gas-phase
reaction of the kind A + B f C + D, a lower bound to the
activation energy Ea for the rate constant k is set by the overall
enthalpy change ∆H°.1,2 That is, Ea ) -R d(ln k)/d(1/T) g ∆H°.
However, the phenomenon of negative activation energies for
apparently elementary gas-phase reactions is now well-
known.3-6 Some of these have been interpreted in terms of
formation of an intermediate bound complex in the entrance
channel, followed by a tight transition state (TS) whose energy
lies below that of the reactants.7-9 Because the overall reaction
enthalpy equals the difference between the activation energies
for the forward and reverse reactions,10 a consequence is that
the activation energy for the reverse of a process with a negative
temperature dependence is less than its endothermicity. This
may be important in cases where the observed Ea is used to set
an upper limit to ∆H°, or in estimation of upper limits to rate
constants where an assumed preexponential factor is combined
with an Ea equal to ∆H°. There is little information in the
literature concerning the validity of the assumption Ea g ∆H°
for this kind of reaction where complexes might be involved in
the exit channel. Here, we present the first determination of the
temperature dependence of the rate constant k1 for the endo-
thermic reaction
Cl + CH4 f HCl + CH3
(2)
As will be seen, Ea is significantly below ∆H° for reaction 1,
while Ea exceeds ∆H° for reaction 2. An important difference
between the two reactions is that strong hydrogen bonding is
only possible between the products of reaction 1. This stabilizes
the TS and leads to a negative Ea for the reverse of reaction 1.
A computational investigation of the potential energy surface
(PES) confirms that the TS is followed by a hydrogen-bonded
complex between HCl and NH2, and this PES is analyzed via
transition-state theory for quantitative comparison with the
measurements.
2. Experimental Technique
Details of the apparatus and its operation have been given
previously.11,12 Briefly, ground-state atomic chlorine was pro-
duced by 193-nm excimer laser (MPB PSX-100, beam cross-
section 7 × 8 mm2) photolysis of CCl4 precursor and monitored
by time-resolved resonance fluorescence at 134-140 nm ((4s)2P
f (4p)2P1/2,3/2).13 This fluorescence was excited by a microwave
discharge through a separate flow of Cl2 (0.2% in Ar, 0.2 mbar
pressure). The experiments were conducted in a large excess
of Ar bath gas to thermalize the system and to slow diffusion
of Cl to the reactor walls. Low photolysis energies F were
employed, to minimize secondary chemistry involving photoly-
sis or chemical products. Above 570 K, so many H atoms were
produced from NH3 photolysis that their fluorescence, excited
by trace hydrogen impurities in the resonance lamp, interfered,
despite the use of calcium fluoride optics. The initial atom
concentration [Cl]0 was estimated from the laser fluence and
the room-temperature absorption cross-section of CCl4.14 It does
Cl + NH3 f HCl + NH2
(1)
and compare it with the isoelectronic and also endothermic
† Part of the special issue “David M. Golden Festschrift”.
* Corresponding author: marshall@unt.edu.
‡ University of North Texas.
§ Morehead State University.
| New Jersey Institute of Technology.
10.1021/jp056406l CCC: $33.50 © 2006 American Chemical Society
Published on Web 03/09/2006

Thermochemistry and Ea of Endothermic Rxn
J. Phys. Chem. A, Vol. 110, No. 21, 2006 6845
Figure 2. Arrhenius plot for Cl + NH3. Open circles, present
measurements with 1 σ statistical error bars; solid square, measurement
by Westenberg and deHaas.15
Figure 1. Plot of kps1 vs [NH3] obtained at 357 K. The error bars are
1 σ. The inset shows the fluorescence signal plus background
corresponding to the filled point.
molecule-1 s-1 at room temperature.15 As may be seen from
Figure 2, this earlier result lies in the range of our measurements.
not need to be known for the kinetic analysis, but verifies that
the pseudo-first-order condition [Cl]0 , [NH3] was attained.
The ammonia concentration is effectively constant, so that
Figure 2 also shows that most of the measurements at room
temperature lie slightly above the linear Arrhenius fit. This could
indicate slight curvature in the Arrhenius plot or that a second
channel becomes important at low temperatures. A possible
adduct is discussed in the next section. However, we note that
there is no systematic pressure influence on the room-temper-
ature data, over a variation of more than a factor of 5. This is
evidence against an addition pathway, which would be expected
to be pressure-dependent. If such a path was at its high-pressure
limit under our conditions, then rate constants of around 10-10
cm3 molecule-1 s-1 would be expected. Most likely, the adduct
is thermodynamically unstable, as discussed in the following
section.
d[Cl]/dt ) -k1[NH3][Cl] - k′[Cl] ) -kps1[Cl] (3)
and exponential decays of the fluorescence signal were obtained.
An example is shown in Figure 1. Nonlinear least-squares fitting
provided the first-order decay coefficient kps1, and plots of kps1
vs [NH3], such as that shown in Figure 1, have slopes equal to
k1. Typically, five values of [NH3] were employed at each set
of conditions, from zero to [NH3]max. The intercept k′ arises
from diffusional loss of Cl and any reaction with photolysis
fragments of CCl4 and NH3. The experimental parameters
pressure p, [Cl]0, F, and the residence time of gases in the heated
reactor τres were varied to check for any influence on the
measured k1 values.
The thermochemistry of reaction 1 is well-established. The
spectroscopic measurements of Mordaunt et al. yield a precise
bond strength for ammonia of 444.0 ( 0.2 kJ mol-1 at 0 K,16
and the bond strength of HCl from Gurvich et al. is 427.8 (
3. Results and Discussion
Eighty-three measurements over 290-570 K are summarized
in Table 1. It may be seen that there is no systematic variation
of k1 with p, [Cl]0, F, and τres, which indicates that the reaction
is effectively bimolecular, has been successfully isolated from
any secondary chemistry, and is unaffected by decomposition
of the reactants inside the heated reaction cell. Potential
interference might arise from condensation of HCl product with
NH3 to form solid NH4Cl, but no obvious light scattering
problems were encountered. The kinetic data are plotted in
Arrhenius form in Figure 2. A weighted linear fit was based on
the 1 σ uncertainties in the slopes of plots such as Figure 1,
listed in Table 1, combined with an estimated σT/T ) 2%, and
yielded
0.1 kJ mol-1 17 The difference is ∆H° ) 16.2 ( 0.2 kJ mol-1
. ,
0
and via tabulated temperature dependences of the enthalpies,17
at the approximate center of the T-1 range, ∆H° ) 18.9 kJ
400
mol-1, significantly larger than the measured activation energy.
Because, as noted in the Introduction, ∆H° ) Ea(k1) - Ea(k-1),10
the activation energy of the reverse process must be negative.
Reaction 1 can be compared with the isoelectronic reaction
2. The measured variation of k2 with temperature yields a curved
Arrhenius plot,18 and near the middle of the same temperature
range as here yields average Arrhenius parameters of about A
) 1.9 × 10-11 cm3 molecule-1 s-1 and Ea ) 13.1 kJ mol-1
.
These parameters and the corresponding k2 values are similar
to those determined here. The activation energy for reaction 2
is slightly larger than for 1, but by contrast to the latter case, it
k1 ) (1.08 ( 0.05) ×
10-11 exp(-11.47 ( 0.16 kJ mol-1/RT) cm3 molecule-1 s-1
exceeds the endothermicity, where for reaction 2, ∆H° ) 7.5
298
( 0.3 kJ mol-1 and ∆H° ) 8.4 ( 0.3 kJ mol-1 17,19,20
.
400
(4)
Quantitative analysis of reaction 2 includes no role for bound
intermediates,21 and we would expect no strong interaction
between CH3 and HCl. Their reaction, the reverse of reaction
2, has a positive temperature dependence.22 The electronegativity
of nitrogen makes hydrogen bonding feasible between NH2 and
HCl, which, apart from leading to a bound intermediate, also
stabilizes the transition state for the reaction. This idea, and
where the uncertainties in the Arrhenius parameters are (1 σ.
Together with the covariance and a 10% allowance for potential
systematic errors, these yield 95% confidence limits of (11%
for k1. The only prior measurement of reaction 1 was made by
Westenberg and DeHaas with flash lamp photolysis of the same
CCl4 precursor, and they obtained (1.23 ( 0.02) × 10-13 cm3

6846 J. Phys. Chem. A, Vol. 110, No. 21, 2006
Gao et al.
TABLE 1: Summary of Measurements of the Rate Constant k1 for Cl + NH3
τres
s
F
mJ
p
[CCl4]
[NH3]max
[Cl]0
k1 ( σk1
T K
mbar
1015 molecule cm-3
1015 molecule cm-3
1012 molecule cm-3
10-13 cm3 molecule-1 s-1
290
292
294
294
294
295
295
295
295
295
326
326
326
326
326
326
326
327
327
327
327
327
357
357
357
357
357
357
357
357
357
357
357
402
402
402
404
404
404
404
404
404
452
452
452
456
456
456
456
456
456
508
508
509
509
509
509
510
510
510
510
510
510
510
511
511
511
511
512
512
512
562
1.2
0.9
2.2
6.9
1.6
4.9
3.6
3.6
3.4
3.5
1.4
1.4
1.4
1.4
1.6
1.6
1.6
3.0
3.0
3.0
2.3
2.3
2.7
2.7
2.7
1.4
1.4
1.4
2.1
2.1
1.3
1.3
1.3
0.7
0.7
0.7
1.3
1.3
1.3
0.6
0.6
0.6
0.6
0.6
0.6
0.5
0.5
0.5
1.1
1.1
1.1
0.5
0.5
0.9
0.9
0.9
0.9
0.3
0.3
0.6
0.6
0.6
0.6
0.6
0.5
0.5
0.5
0.8
1.0
1.0
1.0
0.5
0.41
0.18
0.21
0.20
0.11
0.15
0.30
0.19
0.14
0.09
0.79
0.59
0.36
0.25
0.59
0.35
0.25
0.49
0.29
0.19
0.29
0.19
0.49
0.29
0.19
0.69
0.44
0.29
0.44
0.29
0.69
0.44
0.29
0.62
0.39
0.19
0.65
0.50
0.20
0.60
0.42
0.18
0.79
0.58
0.24
0.63
0.45
0.28
0.73
0.54
0.26
0.34
0.23
0.69
0.37
0.24
0.18
0.43
0.20
0.36
0.17
0.83
0.34
0.16
0.64
0.51
0.28
0.41
0.59
0.25
0.17
0.67
28
43
49
147
36
155
80
80
76
79
35
35
35
35
71
71
71
73
73
73
148
148
72
72
72
72
72
72
148
148
36
36
36
59
59
59
61
61
61
29
29
29
59
59
59
29
29
29
57
57
57
57
57
71
71
71
71
22
22
45
45
44
44
44
30
30
30
63
59
59
59
45
2.72
1.80
4.05
5.54
3.77
5.45
5.93
5.93
5.64
5.94
2.09
2.09
2.09
2.09
2.32
2.32
2.32
2.90
2.90
2.90
2.75
2.75
2.59
2.59
2.59
2.91
2.91
2.91
2.51
2.51
2.34
2.34
2.34
1.69
1.69
1.69
2.01
2.01
2.01
1.53
1.53
1.53
1.46
1.46
1.46
1.61
1.61
1.61
1.65
1.65
1.65
1.27
1.27
1.76
1.76
1.76
1.76
0.98
0.98
1.38
1.38
1.32
1.32
1.32
1.22
1.22
1.22
2.02
1.54
1.54
1.54
1.42
3.47
1.51
1.27
2.05
1.48
3.09
2.19
2.19
1.42
1.24
1.31
1.31
1.31
1.31
1.46
1.46
1.46
1.56
1.56
1.56
1.16
1.16
1.13
1.13
1.13
1.16
1.16
1.16
1.25
1.25
1.13
1.13
1.13
1.73
1.73
1.73
1.18
1.18
1.18
1.57
1.57
1.57
1.22
1.22
1.22
1.13
1.13
1.13
1.21
1.21
1.21
1.50
1.50
1.29
1.29
1.29
1.29
1.86
1.86
1.95
1.95
1.69
1.69
1.69
1.45
1.45
1.45
1.31
2.12
2.12
2.12
1.73
0.9
0.3
0.7
0.9
0.3
0.7
1.5
0.9
0.6
0.4
1.4
1.0
0.6
0.4
1.1
0.7
0.5
1.2
0.7
0.5
0.7
0.4
1.1
0.6
0.4
1.7
1.1
0.7
0.9
0.6
1.3
0.9
0.6
0.9
0.6
0.3
1.1
0.8
0.3
0.8
0.5
0.2
1.0
0.7
0.3
0.8
0.6
0.4
1.0
0.7
0.4
0.4
0.2
1.0
0.5
0.4
0.3
0.4
0.2
0.4
0.2
0.9
0.4
0.2
0.7
0.5
0.3
0.7
0.8
0.3
0.2
0.8
1.25 ( 0.08
0.94 ( 0.05
0.91 ( 0.02
1.19 ( 0.02
1.01 ( 0.04
1.25 ( 0.12
1.32 ( 0.07
1.11 ( 0.04
1.24 ( 0.03
1.08 ( 0.07
1.77 ( 0.12
1.72 ( 0.11
1.41 ( 0.10
1.32 ( 0.05
1.71 ( 0.07
1.54 ( 0.03
1.43 ( 0.07
1.92 ( 0.10
1.63 ( 0.05
1.48 ( 0.08
1.54 ( 0.04
1.51 ( 0.04
2.04 ( 0.09
1.82 ( 0.04
1.92 ( 0.04
2.42 ( 0.10
2.21 ( 0.03
2.06 ( 0.03
2.12 ( 0.04
1.99 ( 0.02
2.15 ( 0.11
2.14 ( 0.10
2.13 ( 0.09
3.14 ( 0.11
3.11 ( 0.11
3.19 ( 0.08
3.77 ( 0.17
3.68 ( 0.21
3.80 ( 0.12
3.29 ( 0.11
3.23 ( 0.15
3.38 ( 0.09
5.05 ( 0.04
5.44 ( 0.22
5.16 ( 0.24
5.41 ( 0.24
5.63 ( 0.21
5.52 ( 0.13
5.10 ( 0.14
5.21 ( 0.13
5.31 ( 0.18
6.97 ( 0.06
7.26 ( 0.13
6.50 ( 0.40
7.24 ( 0.38
7.46 ( 0.26
7.54 ( 0.21
6.60 ( 0.47
7.09 ( 0.52
6.74 ( 0.62
7.47 ( 0.28
7.33 ( 0.35
7.13 ( 0.32
7.75 ( 0.18
6.64 ( 0.19
6.98 ( 0.20
7.85 ( 0.39
7.94 ( 0.27
6.96 ( 0.20
7.91 ( 0.26
8.05 ( 0.37
9.28 ( 0.79

Thermochemistry and Ea of Endothermic Rxn
J. Phys. Chem. A, Vol. 110, No. 21, 2006 6847
TABLE 1 (Continued)
τres
s
F
mJ
p
[CCl4]
[NH3]max
[Cl]0
k1 ( σk1
T K
mbar
1015 molecule cm-3
1015 molecule cm-3
1012 molecule cm-3
10-13 cm3 molecule-1 s-1
562
562
563
563
563
563
563
563
566
566
566
0.5
0.5
0.5
0.5
0.5
0.9
0.9
0.9
0.5
0.5
0.5
0.44
0.22
0.59
0.37
0.27
0.76
0.38
0.24
0.61
0.39
0.19
45
45
22
22
22
44
44
44
43
43
43
1.42
1.42
1.35
1.35
1.35
1.84
1.84
1.84
1.85
1.85
1.85
1.73
1.73
1.47
1.47
1.47
1.48
1.48
1.48
1.06
1.06
1.06
0.5
0.3
0.7
0.4
0.3
1.2
0.6
0.4
0.9
0.6
0.3
9.36 ( 0.51
9.43 ( 0.40
8.21 ( 0.27
9.24 ( 0.40
9.66 ( 0.32
8.00 ( 0.14
9.61 ( 0.31
9.83 ( 0.24
10.20 ( 0.27
10.50 ( 0.45
10.80 ( 0.61
TABLE 2: Enthalpies at 0 K of Stationary Points on the Potential Energy Surface Relative to Cl + NH3, Derived by Various
Methods
Cl-NH3
2c-3e adduct
transition
state
H2N-HCl
intermediate
method
NH2 + HCl
CBS-QB3
G3B3
15.1
14.0
26.2
19.0
17.5
17.2
17.0
20.9
-40.3
-36.6
-52.5
-50.2
-49.1
-47.7
-47.7
-51.3
-48.3
-47.2
9.4
11.2
12.8
9.8
8.1
9.0
8.8
9.0
7.3
8.4
-1.7
-1.9
1.5
-0.3
-1.6
-1.3
-1.4
-2.2
-1.9
-2.5
MPWB1K/6-31+G(d,p)
MPWB1K/6-31+G(2d,p)
MPWB1K/6-31++G(2d,2p)
MPWB1K/6-31+G(2df,2p)
MPWB1K/6-31++G(2df,2p)
MPWB1K/6-311+G(d,p)
MPWB1K/6-311++G(2df,2p)
MPWB1K/6-311++G(3d2f,2df,2p)
experiment
15.1
14.6
16.2 ( 0.1
the prediction of a negative activation energy for k-1, is explored
quantitatively in the next section.
K is 1.2 × 10-24 exp(BDE/RT) cm3 molecule-1, where BDE is
the 0 K bond dissociation enthalpy. With a DFT value of 48 kJ
mol-1, Kc ≈ 5 × 10-16 cm3 molecule-1, which implies that
under the most favorable conditions (maximum [NH3] and
lowest T) up to two-thirds of the initial atomic Cl could be
complexed by NH3. Most of the room temperature runs would
have a smaller fraction of Cl potentially complexed. The lack
of observed p-dependence suggests that the two-center/three-
electron species is not significantly formed in our experiments.
The implication is that the BDE is probably slightly smaller
than 48 kJ mol-1 and more in line with the ab initio values
listed in Table 2. Lower-temperature experiments would check
this proposition.
The potential energy diagram shown in Figure 4 reveals a
TS with an energy below that of the final products, with an
intervening complex bound by about 18 kJ mol-1 relative to
NH2 + HCl. The structure and energy of this complex are
consistent with hydrogen bonding, and no barrier was found
for dissociation to NH2 + HCl. Energy optimizations starting
with other Cl-H-N arrangements did not lead to new bound
species. We now analyze this PES to derive rate constants for
comparison with experiment, through consideration of the
reverse process
4. Theoretical Analysis
The Gaussian 03 program suite23 was employed to calculate
geometries, vibrational frequencies, and energies of stationary
points on the PES. Several approaches were used. The composite
G3B3 and CBS-QB3 ab initio methodologies were applied24,25
and also the MPWB1K density functional developed by Zhao
and Truhlar for systems involving hydrogen bonding and
reaction barriers.26 These DFT calculations were applied with
a variety of basis sets, and the vibrational frequencies were
scaled by a factor of 0.955.26 G3 theory includes a spin-orbit
correction of -3.5 kJ mol-1 to the energy of atomic Cl, and
this correction was applied to the other levels of theory. Spin
contamination was negligible, with S2 spin expectation values
for the open-shell species of at most 0.757, cf. the ideal value
of exactly 0.75. Table 2 summarizes the results.
The two composite ab initio approaches are in good accord
with the overall reaction enthalpy, although they underestimate
∆H° by up to 2 kJ mol-1 (which is within their target
0
accuracies). The DFT results show systematic variation with
the size of the basis set, with errors ranging from +10 kJ mol-1
with the smallest 6-31+G(d,p) basis set considered to -2 kJ
mol-1 with the largest 6-311++G(3d2f,2df,2p) basis set. These
two basis sets were denoted DIDZ and MG3 by Zhao and
Truhlar.26 The trend suggests that an intermediate-sized basis
NH2 + HCl f Cl + NH3
(-1)
and then derive k1 via microscopic reversibility: k1/k-1 ) Keq
where the equilibrium constant was obtained from tabulated
data17 and the ∆H° derived above. This yields, to within 6%,
set may give close accord with the experimental ∆H°, and
0
0
Keq ) 27.3T-0.049 exp(-2248/T) over 200-2000 K.
accordingly, we focus on MPWB1K/6-31++G(2df,2p) results
which give the best agreement with ∆H°. Corresponding
k-1 is derived via modified transition state theory
(MTST). The standard TST result for the microcanonical rate
constant is k(E) ) Wq(E+)/hFR(E),28 where FR(E) is the density
of states of the reactants at energy E, Wq(E+) is the total number
of states of the TS with an energy below E+ ) E - E0, count-
ing from the ground state of the TS, and E0 is the barrier
height relative to the reactants. In the case where this
0
geometries of stationary points are shown in Figure 3.
A molecule with a long (∼2.4 × 10-10 m) two-center/three-
electron Cl-N bond has been characterized previously, and our
calculations are in general accord with those of McKee et al.27
MPWB1K/6-31++G(2df,2p) geometries and frequencies imply
that the equilibrium constant Kc for Cl-NH3 formation at 290

6848 J. Phys. Chem. A, Vol. 110, No. 21, 2006
Gao et al.
Figure 3. Geometries and frequencies (scaled by 0.955) of stationary points on the Cl + NH3 potential energy surface, computed via MPWB1K/
6-31++G(2df,2p) theory: 1. C3V NH3, 977, 1610 (2), 3440, 3576 (2) cm-1. 2. HCl, 2932 cm-1. 3. C2V NH2, 1475, 3332, 3427 cm-1. 4. C3V Cl-NH3
adduct, 297, 342 (2), 817, 1570 (2), 3466, 3614 (2) cm-1. 5. Cs transition state, 622i, 391, 400, 677, 984, 1180, 1502, 3376, 3481 cm-1. 6. C2V
H2N-HCl complex, 153, 156, 185, 556, 577, 1472, 2568, 3358, 3461 cm-1
.
barrier is positive, k(E+ < 0) ) 0, and thus
1
QR
k(T) )
)
∞ exp(-E/kT)FR(E)k(E+) dE
∫
E0
exp(-E0/kT)
∞ Fq(E+) exp(-E+/kT) dE +
kT
h
∫
0
QR
kT Qq
h QR
)
exp(-E0/kT)
(5)
where Q‡ and QR are the partition functions for the TS and
reactants, respectively. This is the usual TST result for k(T).
For a reaction such as -1, where E0 < 0, eq 5 is not
applicable. At normal pressures, collisions are not rapid enough
to thermalize the energy levels of the TS, and therefore, energy
levels below the reactants are inaccessible (except in solution
or at very high gas density). Thus, E g 0, and the lower bound
of the first integration of eq 4 must be zero, which leads to
Figure 4. Potential energy diagram for Cl + NH3 computed at the
MPWB1K/6-31++G(2df,2p) level of theory.
further by Krasnoperov et al.30 They noted that the latter integral
of eq 6 is smaller than Qq because the lower limit of integration
is greater than zero, and so, k(T) is reduced over the value
derived via eq 5. Here, we also took into account angular
momentum conservation (the J quantum number) and conserva-
tion of the energy of the K rotor at the TS, and quantum
mechanical tunneling/reflection through the barrier. The latter
effect is relatively small and only increases the rate constant
by 9% at 300 K, 7% at 500 K, and 5% at 700 K. The interaction
between NH2 and HCl was calculated from a relaxed MPWB1K/
k(T) )
∞ exp(-E/kT)FR(E)k(E+) dE
1
QR
∫
0
dE+
kT
kT exp(-E0/kT)
∞
)
Wq(E+) exp(-E+/kT)
(6)
∫
-E0
hQR
This result was noted by Garrett et al. in the context of improved
canonical variational TST29 and has recently been explored

Thermochemistry and Ea of Endothermic Rxn
J. Phys. Chem. A, Vol. 110, No. 21, 2006 6849
to the common assumption that, for an endothermic process,
Ea g ∆H°. This result can be rationalized in terms of a PES
based on density functional theory, where for the reverse process
there is a bound complex in the entrance channel, followed by
a transition state lying below the energy of NH2 + HCl.
Modified transition-state theory yields a negative temperature
dependence for the NH2 + HCl reaction and, through micro-
scopic reversibility, fair accord with k1.
Acknowledgment. The UNT work was supported by the
Robert A. Welch Foundation (grant B-1174), the National
Science Foundation (grant CTS-0113605), and the UNT Faculty
Research Fund. B.P.M. was supported through UNT’s NSF
Research Experience for Undergraduates program (grant CHE-
0243795), and computer facilities were purchased with funding
from the NSF (grant CHE-0342824).
References and Notes
Figure 5. Comparison of theoretical and measured rate constants. Solid
line, k-1(MTST) for NH2 + HCl; dashed line, k1(MTST) for Cl + NH3;
dash-dot line, experimental k1 for Cl + NH3.
(1) Daniels, F.; Alberty, R. A. Physical Chemistry, 2nd ed.; John
Wiley: New York, 1961.
(2) Laidler, K. J.; Meiser, J. H. Physical Chemistry; Benjamin/
Cummings: Menlo Park, CA, 1982.
6-31++G(2df,2p) scan. This revealed that the energy dropped
rapidly enough as the separation decreased for centrifugal
barriers (at relevant J values) to be absent in the entrance valley
leading to formation of the initial hydrogen-bonded intermediate,
and thus, the reaction bottleneck is controlled by the TS. The
full analytical expressions for this modified TST are given
elsewhere.30
An Arrhenius plot of the computed k-1 is shown in Figure 5.
Over 250-750 K, the theoretical rate constant is summarized
by
(3) Fontijn, A.; Zellner, R. Influence of Temperature on Rate Coef-
ficients of Bimolecular Reactions. In Reactions of Small Transient Species;
Fontijn, A., Clyne, M. A. A., Eds.; Academic: New York, 1983.
(4) Russell, J. J.; Seetula, J. A.; Gutman, D. J. Am. Chem. Soc. 1988,
110, 3092.
(5) Kalinovski, I. J.; Gutman, D.; Krasnoperov, L. N.; Goumri, A.;
Yuan, W.-J.; Marshall, P. J. Phys. Chem. 1994, 98, 9551.
(6) Nicovich, J. M.; Van Dijk, C. A.; Kreutter, K. D.; Wine, P. H. J.
Phys. Chem. 1991, 95, 9890.
(7) Golden, D. M. J. Phys. Chem. 1979, 83, 108.
(8) Mozurkewich, M.; Benson, S. W. J. Phys. Chem. 1984, 88, 6429.
(9) McEwen, A. B.; Golden, D. M. J. Mol. Struct. 1990, 224, 357.
k-1(MTST) )
(10) Benson, S. W. The Foundations of Chemical Kinetics; McGraw-
Hill: New York, 1960.
(11) Shi, Y.; Marshall, P. J. Phys. Chem. 1991, 95, 1654.
(12) Ding, L.; Marshall, P. J. Phys. Chem. 1992, 96, 2197.
(13) Okabe, H. Photochemistry of Small Molecules; Wiley: New York,
4.08 × 10-13 T0.343 exp(+622/T) cm3 molecule-1 s-1 (7)
and clearly, the predicted temperature dependence is negative
below 800 K. The deviation from the results of incorrect
application of eq 5 is a factor of 3 at 298 K and increases with
lower temperatures, so that the incorrectly derived k-1 would
be too large and the temperature dependence too negative, as
discussed by Krasnoperov et al.30 There are no measurements
of this NH2 + HCl reaction for direct comparison with eq 7.
Combination of k-1 with the equilibrium constant implies
1978.
(14) Hanf, A.; La¨uter, A.; Volpp, H.-R. Chem. Phys. Lett. 2003, 368,
445.
(15) Westenberg, A. A.; deHaas, N. J. Chem. Phys. 1977, 67, 2388.
(16) Mordaunt, D. H.; Dixon, R. N.; Ashfold, M. N. R. J. Chem. Phys.
1996, 104, 6472.
(17) Thermodynamic Properties of IndiVidual Substances, 4th ed.;
Gurvich, L. V., Veyts, I. V., Alcock, C. B., Eds.; Hemisphere: New York,
1989; Vol. 1.
(18) Bryukov, M. G.; Slagle, I. R.; Knyazev, V. D. J. Phys. Chem. A
2002, 106, 10532.
(19) Thermodynamic Properties of IndiVidual Substances, 4th ed.;
Gurvich, L. V.; Veyts, I. V.; Alcock, C. B., Eds.; Hemisphere: New York,
1992; Vol. 2.
k1(MTST) )
1.11 × 10-11 T0.294 exp(-1626/T) cm3 molecule-1 s-1 (8)
for Cl + NH3 over 250-750 K. The agreement between k1-
(MTST) and experiment is quite good, as seen in Figure 5,
considering the exponential dependence on computed barrier
height. The theoretically derived rate constant is around a factor
of 3 too large. This might reflect an error in the barrier of a
few kilojoules per mole, or the computed TS may be too tight.
Nevertheless, the approximate magnitude and temperature
dependence of k1 are rationalized in terms of a TS whose energy
lies below that of the final products (Figure 4). The role of
hydrogen bonding between the products is to stabilize the TS,
and details of the subsequent bound complex do not enter into
the analysis.
(20) Litorja, M.; Ruscic, B. J. Chem. Phys. 1997, 107, 9852.
(21) Corchado, J. C.; Truhlar, D. G.; Espinosa-Garcia, J. J. Chem. Phys.
2000, 112, 9375.
(22) Russell, J. J.; Seetula, J. A.; Senkan, S. M.; Gutman, D. Int. J.
Chem. Kinet. 1988, 20, 759.
(23) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb,
M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K.
N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.;
Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.;
Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.;
Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li,
X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.;
Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.;
Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.;
Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich,
S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A.
D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A.
G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.;
Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham,
5. Conclusions
The measured rate constant k1 for Cl + NH3 f NH2 + HCl
exhibits an activation energy more than 7 kJ mol-1 below the
endothermicity. The reaction is therefore a clear counterexample

6850 J. Phys. Chem. A, Vol. 110, No. 21, 2006
Gao et al.
M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.;
Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian
03, revision C.02; Gaussian, Inc.: Wallingford, CT, 2004.
(24) Baboul, A. G.; Curtiss, L. A.; Redfern, P. C.; Raghavachari, K. J.
Chem. Phys. 1999, 110, 7650.
(25) Montgomery, J. A., Jr.; Frisch, M. J.; Ochterski, J. W.; Petersson,
G. A. J. Chem. Phys. 1999, 110, 2822.
(27) McKee, M. L.; Nicolaides, A.; Radom, L. J. Am. Chem. Soc. 1996,
118, 8, 10571.
(28) Truhlar, D. G.; Garrett, B. C.; Klippenstein, S. J. J. Phys. Chem.
1996, 100, 12771.
(29) Garrett, B. C.; Truhlar, D. G.; Grev, R. S.; Magnuson, A. W. J.
Phys. Chem. 1980, 84, 1730.
(30) Krasnoperov, L. N.; Peng, J.; Marshall, P. J. Phys. Chem. A 2006,
110, 3110.
(26) Zhao, Y.; Truhlar, D. G. J. Phys. Chem. A 2004, 108, 6908.