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Statistical
Thermodynamics and
Chemical Kinetics
Lecture 10
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Chapter 10 Transition State Theory
10. 1 Motion on the Potential Surface
The potential energy surfaces are based on the BornOppenheimer separation of nuclear and electronic motion.
A justification for this separation is the disparity in the
electron and nuclear masses, which results in very slow
nuclear motion compared to electronic motion. With the
Born-Oppenheimer separation, each electronic state of the
chemical reactive system has a potential energy surface.
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For a chemical reaction involving N atoms there are
3N-6 vibrational degrees of freedom at the saddle point.
One of these degrees of freedom corresponds to
infinitesimal motion along the reaction path. The
remaining 3N-7 degrees of freedom define vibrational
motion orthogonal to the reaction path.
To study properties of the saddle point in more detail,
consider a potential energy contour diagram for a collinear
chemical reaction (e.g., H + H-H). This collinear system
has two orthogonal internal degrees of freedom, for which
the coordinate are  =r1+ r2 and s=r2-r1. The saddle point
has a symmetric configuration at which r1= r2 = r0,  =2r0
and s=0.
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E0
U
0
S
0
U
E0

2r0
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The first and second derivatives of the potential at the
saddle point are
U
U
U
U
s
 0,
2
s 2
 0;

 0,
2
 2
0
Therefore the vibrational frequency for motion along the
reaction path will be imaginary (negative). The vibrational
frequency for the  coordinate will be positive.
In the vicinity of the saddle point, a Taylor’s series
expansion of the potential is
(10-1)
U ( , s)  12 C (  2r0 )2  12 Cs s 2  E0
The transition state theory is based on the postulate that
the rate of transformation of systems from reactants to
products is given solely by passage in the forward
direction from coordinates s< 0 to s > 0.
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10.2 Basic postulates and standard
derivation of TST
Transition state theory, introduced by Eyring and by
by Evans and Polyani in 1935, provided the first
theoretical attempt to determine absolute reaction rates.
In this theory, a transition state separating reactants and
products is used to formulate an expression for the
thermal rate constant. The relationship between transition
state theory and dynamical theories was first discussed
by Wigner who emphasized that the theory was a model
essentially based on classical mechanics.
A number of assumptions are made in deriving the
TST rate expression.
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The two most basic are the separation of
electronic and nuclear motions, equivalent
to the Born-Oppenheimer approximation in
quantum mechanics, and the assumption that
the reactant molecules are distributed
among their states in accordance with the
Maxwell-Boltzmann distri-bution.
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However, the following additional assumptions,
which are unique to the theory, are also required.
1) Molecular systems that have crossed the TS in
the direction of products cannot turn around and
reform reactants.
2) In the TS, motion along the reaction coordinate
may be separated from the other motions and
treated classically as a translation.
3) The TSs that are becoming products are
distributed among their states according to the
M-B laws.
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• It is customary to derive TST by postulating a quasiequilibrium between TS species and reactants. This
approach focuses on the third assumption listed.
• Another approach follows the dynamical formulation of
Wigner and uses the first assumption, which is considered
the “fundamental assumption” of TST.
• Both derivations are given here, and they use the
conventional transition state theory model in which the
transition state is located at the saddle point on the
potential energy surface. Later in this chapter, variational
TST, a more accurate method for choosing the TS, is
discussed.
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The third assumption, the “quasi-equilibrium
hypothesis”, is based on a simple physical interpretation.
Suppose we have an elementary reaction
A + B  X‡  C
(10-2)
where X‡ is a TS. Suppose also that it is possible to define
a small region at the top of the potential energy barrier
such that all systems entering a small region from the left
pass through to products without turning back, and
similarly all products entering from the right must pass
through to reactants. This small region is often referred to
as the dividing surface and is orthogonal to the reaction
pathway. Systems within this small distance are by
definition transition states, to the right are products, to the
left reactants. (See Fig. 10-2)
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Vs
TS
React
Prod.
-/2 0 /2
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Consequently, for a system in which reactants are in
equilibrium with the products, there are two types of
transitions states: those moving from reactant to products,
and those moving in the opposite direction. We designate
the concentration of these by Nf‡ and Nb‡, respectively. At
equilibrium the rate of the forward reaction must be the
same as the backward reaction; accordingly, the concentrations of the TSs moving toward reactants and toward
products must be equal. Hence,
Nf‡ + Nb‡ = N‡ = K‡[A][B]
(10-3)
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Now, if all the products are suddenly removed from
equilibrium, that is, if Nb‡ =0 , then, since the forward rate
of reaction must be the same regardless of the back reaction
rate, it follows that the concentration of the forwardmoving transition states is the same as it would be for full
equilibrium; hence,
Nf‡ = K‡[A][B]/2
(10-5)
This is the “quasi-equilibrium hypothesis” of transition
state theory.
To calculate the net rate of reaction, the rate at which
transition states pass over the barrier to products is needed;
i.e.,
(10-6)
dN
N
(reactants  products ) 
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The number of transition states per unit volume having
velocity between v and v+dv in one direction is presented
by determining N‡. The average time t for the N‡
transition states to cross the barrier is equal to the thickness
 of the dividing surface divided by the average velocity vs
at which the transition states traverse the dividing surface;
that is, t   / vs
(10-7)
dN
‡ vs
 N
Hence,
(10-8)
dt

From equation 10-5, the number of transition states
crossing the dividing surface in the direction of products is
one-half the total number of transition states, i.e.,
N‡= N‡/2
(10-9)
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Therefore, the number of transition states crossing the
barrier per unit volume in unit time is,
(10-10)
dN N ‡ v
dt

s
2 
On the assumption that there is an equilibrium distribution
of velocities, the average velocity of the transition state
moving in one direction, e.g., the forward direction, is

vs



0
(  m s vs2 / k BT )
1/ 2
 2k BT 

 
 ( m v2 / 2k T )
e s s B dvs  ms 
vs e
dvs
(10-11)
0
Where ms is the reduced mass for motion through the
dividing surface.
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Inserting this value into equation (10-10) gives
1/ 2
dN N  2k BT 



dt
2  ms 
‡
(10-12)
1

Since the transition state is in equilibrium with the
reactants, it is possible to obtain N‡ from equilibrium
statistical mechanics, namely, through
‡
(10-13)
N
‡
KC 
[ A][ B]
This statement of equilibrium does not imply that the TS is
long-lived. This equilibrium constant can be expressed in
terms of partition functions as
‡
‡
Q
N
(10-14)
K‡ 
 tot e  E / k T
0
C
[ A][ B]
B
QAQB
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Combining equation 10-12 and 10-14, we have, for the
reaction rate, dN  2k T 1/ 2 1 Q ‡  E / k T
tot
  B 
e
[ A][ B]
(10-15)
dt  ms  2 QAQB
In the approaches of Eyring and Evans and Polyani,
the partition function for the reaction coordinate in the
transition state is considered to be a translational function.
Since this motion is assumed to be separable, the
translational partition function is therefore separable as
‡
‡
Qtot  QsQ
(10-16)
where Qs is the partition function for the reaction
coordinate motion and Q‡ is the partition function for all
other 3N-1 degrees of freedom in the transition state.
0
B
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The translational partition function for motion in one
dimension in a system of length  is
Qs  (2mS k BT )1/ 2  / h
(10-17)
This Qs is not divided by 2, since it is the partition function
for all the transition states. Substituting this expression into
equation 10-16 and the result into equation 10-15 gives
‡
Q
(10-18)
dN k BT
E / k T
dt

h QAQB
e
0
B
[ A][ B]
From chapter 1, we know that the experimental rate
equation for a bimolecular reaction is
dN
(10-19)
 k[ A][ B]
dt
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Comparison of equations 10-18 and 10-19 gives the
absolute rate coefficient for A + B  products,
‡
k BT Q
(10-20)
k k 
eE / k T
0
abs
B
h QAQB
Note that the artificial constructs  and ms, as well as the
factor 1/2, have cancelled out of the absolute rate theory
expression. The ratio kBT/h, having the units of frequency
and the magnitude 6.25x1012 sec-1 (for T=300K), is
frequently termed the frequency factor.
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In order to be able to evaluate equation 10-20, we
must be able to calculate the transition state partition
function Q‡ , using the statistical mechanical techniques
discussed before. To do that, we need to know the
structural parameters of the transition state (specifically,
the moment of inertial I‡ ) , as well as its 3N-7
vibrational frequencies {v‡ }. In practice, such
parameters can only be estimated approximately. With
detailed information about potential surface now
becoming available from ab initio theory, however, we
may expect to see more precise calculations of rate
coefficients from transition state theory.
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The energy E0 is the difference in zero-point energy
between the transition state and the reactants. It is useful
to point out the relationship between E0 and the
experimental activation energy Ea. As shown by Tolman
et al.
Ea  Er (T )  E(T )
(10-21)
where <Er(T)> is the average energy of molecules
undergoing reaction and <E (T)> is the average energy of
all reactant molecules. In transition state theory, <Er(T)>
is given by the average energy of the transition states
plus E0.
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10.3 Quantum mechanical effects in TST
A basic difficulty in generalization of classical
transition state theory to quantum mechanics is that the
reaction criterion cannot be formulated as the condition
that a trajectory pass through a critical surface. This is
connected with the fact that, in a quantum mechanical
observation, the coordinates and momenta of a system
con not be assigned simultaneously. Consider the
Heisenberg uncertainty relations,
DpDq  
and
DEDt  
For the reaction coordinate. If Dp is replaced by ħ/l,
where l is the de Broglie wavelength, we have the
relation Dq > l.
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Thus the uncertainty in the value of the reaction
coordinate at the transition state must be larger than the
wavelength associated with motion along the reaction
coordinate. In other words, quantum mechanically, the
transition state is not localized. The uncertainty relation
DEDt  ħ may be analyzed in a similar way. For the
thermal averaging in TST to have a meaning, it is
necessary that the translational energy E in the reaction
coordinate be much less than kBT. As a result, the
lifetime Dt of the transition state must be larger than
ħ/kBT. Therefore, in the quantum case, the transition
state can not be considered a definite configuration of
nuclei during an infinitesimal interval of time.
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Thus, for the calculation of the reactive flux in the
quantum case, it is necessary to consider explicitly the
dynamics of the trajectories’ motion in the region Dq or to
follow the eolution with time of the system for time Dt.
In classical TST, the potential energy is constant and the
reaction coordinate motion is separated from the
remaining internal motions at the localized position along
the reaction coordinate which defines the transition state.
Quantum mechanical delocalization of the transition state
along the reaction coordinate can lead to two problems.
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First, if the potential is not flat in the region Dq, so that
the system is not freely moving, it is incorrect to treat the
reaction coordinate as being a classical translation motion.
Rather, the potential will usually have a concave-down
shape, and quantum mechanical tunneling will be occur
through the potential.
The second problem is more critical. If there is curvature
along the reaction coordinate in the region Dq, the reaction
coordinate is not separable from the remaining internal
degrees of freedom. Thus, the rate constant expression can
not be factored into a frequency kBT/h for the reaction
coordinate and a partition function for the remaining
degrees of freedom.
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Also, since the curvature couples the reaction
coordinate with the remaining modes, tunneling can not be
treated as a one dimensional reaction coordinate barrierpenetration problem. Instead, there will be a multitude of
tunneling paths which involve all the coordinates.
To correct the tunneling, we have to consider the
problem of crossing the barrier quantum mechanically
rather classically as done in previous sections. According
to quantum mechanics, there is a probability that a particle
finds its way from reactants to products, and that
probability varies continuously with energy; for E<E0
there is a finite nonzero probability, and for E > E0, it
approaches unity.
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The probabilities can be calculated for any barrier from
the Schrödinger equation  2  8 2 m
 2 [ E  V ( s)]  0
2
(10-23)
x
h
We have assumed a one-dimensional barrier, which is
allowable since, with the separable approximation, there is
reaction only long one coordinate, that is, the reaction
pathway. A solution of equation 10-23 is obtained for a
suitable choice of potential V(s) to describe the barrier.
The resulting expression for the probability of tunneling
through the barrier is given by
(10-24)
 4 m s

1/ 2
G ( E )  exp  


h

2
s1
(V ( s )  E ) ds 


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where G(E), called the permeability function, depends on
the exact shape of the barrier along the reaction coordinate,
and s1 and s2 are turning points, i.e., the coordinates of the
reaction path for which V(s)=E. The tunneling correction
is obtained by integrating over a M-B distribution, i.e.,
(10-25)
E /k T  1
E / k T
Qtunnel  e
0
B

0
k BT
e
B
G ( E )dE
Even for simple barrier shapes, a closed solution for the
permeability function is difficult to obtain; and, in any case,
the integration over all energies must be carried out
numerically.
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However, one barrier shape for which an exact expression
for G(E) is known and is physically meaningful is the
symmetrical Eckart barrier. The potential for this barrier
has the form
V(s) = E0 sech2(s/l)
(10-26)
The permeability function for this barrier is
cosh( 4)  1
(10-27)
G( E ) 
cosh( 4)  cosh( 2 )
where
1
  (2mE)1/ 2
h
1/ 2
1
h 
and    8mE0  2 
h
4 
2
And where l is the width of the barrier.
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For small barrier heights and widths, the tunneling
correction approaches an asymptotic form given by
1 h s 2
k BT
(10-28)
Qtunnel  1  (
) (1 
)
24 k BT
E0
Where s is the imaginary frequency of the transition
state at the top of the barrier.
The experimental evidence for tunneling comes from
Arrhenius plots of lnk versus 1/T. If the Arrhenius show
significant nolinearity, then tunneling may be the cause.
The curvature in the Arrhenius plots of lnk vs. 1/T tends
to be concave upward when tunneling is important,
because the calculated reaction rate deviation is positive
and increases for large values of 1/T.
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10.4 Thermodynamic formulation of TST
The transition state derived rate constant can be
reformulated in thermodynamic terms, since it is
sometimes more useful to work with the rate constant in
this form than with partition functions. The rate constant
expression given by equation 10-20, viz.,
‡
k BT Q
k
e  E0 / k B T
h QAQB
can be rewritten as
where
K c‡ 
Q‡
Q A QB
k BT ‡
k
KC
h
e  E0 / k BT
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(10-29)
(10-30)
which is the equilibrium constant for formation of the
transition state. If the equilibrium constant is expressed
in terms of the molar Gibbs standard free energy using
the van’t Hoff relation
DG0‡   RT ln K c‡
(10-31)
Then equation 10-20 can be written as
k BT  DG / RT
(10-32)
k
e
‡
0
h
 DG0‡  DH 0‡  TDS0‡
k BT DS0‡ / R  DH 0‡ / RT
k 
e
e
h
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(10-33)
(10-34)
Equation 10-34 is similar to the Arrhenius equation
 E a / RT
(10-35)
k  Ae
and the thermodynamic parameters can be related to the
Arrhenius parameters. The Arrhenius activation energy is
defined by
Ea
d (ln k )

dT
RT 2
(10-36)
Taking the logarithm of equation 10-29 and differentiating
with respect to T gives
d (ln k ) 1 d (ln K c‡ )


(10-37)
dT
T
dT
(10-38)
d (ln K c‡ ) DE0
dT

RT 2
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Inserting 10-38 into equation 10-37 and comparing the
Ea  RT  DE0
result with 10-36 gives
(10-39)
The relationship between the standard thermodynamic
energy and enthalpy for a constant-pressure process is
DH 0‡  DE0  P(DV0‡ )
(10-40)
since H=E + PV. The quantity DV0‡ is known as the
standard volume of activation. With equation 10-40,
equation 10-39 becomes Ea  DH 0‡  RT  P(DV0‡ ) (10-41)
For a unimolecular reaction, there is no change in the
number of molecules, so the volume maintains. Therefore,
(10-42)
Ea  DH 0‡  RT
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Inserting 10-42 into equation 10-34 leads to
k BT DS0‡ / R  Ea / RT
k  e
e
e
h
Hence,
k BT DS0‡ / R
Ae
e
h
(10-43)
(10-44)
For gas phase reactions other than unimolecular, the
relationships between the Arrhenius parameters and
thermodynamica terms different from the relationships just
given. If the ideal gars relation is assumed, i.e.,
Dn‡ RT  P(DV0‡ )
(10-45)
then, from equation 10-41, one obtains
Ea  DH 0‡  RT  Dn‡ RT  DH 0‡  (1  Dn‡ ) RT (10-46)
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And the Arrhenius pre-exponential factor is
Ae
 ( Dn ‡ 1)
k BT DS0‡ / R
e
h
(10-47)
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10.5 Applications of TST
• 10.5.1 Evaluating partition functions
Determining rate constants from the canonical level of
TST is an invaluable aid in both elucidating mechanisms
and evaluating rate constants. Calculating the rate
constant for a reaction requires calculating the partition
functions. The total partition function associated with the
internal motion for each molecule is given as follows,
Q  QrotQvibQelecQtrans
(10-48)
To calculate the individual partition functions, one needs
to know moments of inertia, vibrational frequencies, and
electronic states. Such information can be obtained by
quantum chemical calculations.
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• 10.5.1.1 Electronic partition function.
Qelec   gi e  Ei / k BT
(10-49)
where gi is the degeneracy and Ei is the energy above the
lowest state of the system. In most reactions, few electronic
energy levels other than the ground state must be
considered. For reactions involving doublet and triplet
systems, the degeneracy factor is the corresponding spin
degeneracy which would contribute a factor of two or more
to the calculated rate constant.
• 10.5.1.2 Translational partition function.
i
(2mkBT )3 / 2 l 3
Qtrans 
h3
Qtrans (2mkBT )3 / 2

3
V
h
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(10-50)
(10-51)
• 10.5.1.3 Vibrational partition function.
A polyatomic molecule has s=3N-6 vibrational modes
if it is nonlinear and 3N-5 modes if it is linear; the
vibrational partition function for a polyatomic molecule is
s
1
i 1 1  exp( hc i / k BT )
Qvib  
(10-52)
• 10.5.1.4 Rotational partition function.
For a polyatomic molecule with moments of inertia Ia, Ib,
and Ic about its principal axes. The rotational partition
function is
Qrot  
1/ 2
1/ 2
 8 I a k BT 


2
h


2
1/ 2
 8 I b k BT 


2
h


2
1/ 2
 8 I c k BT 


2
h


2
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(10-53)
10.5.2 Symmetry and Statistical Factors
If molecules involved in a reaction have elements of
symmetry, then in calculating the rate expression, the
symmetry must be accounted for in the partition
functions. For molecules which have rotational system, it
is customary to divide the rotational partition function for
each molecule by its appropriate symmetry number ,
defined as the number of equivalent arrangements that
can be obtained by rotating the molecule. For example,
consider H2. The number of identical atoms in the
molecule is 2, and by rotating we get two equivalent
arrangements: H1-H2 and H2-H1. Therefore, the
symmetry number is 2. For planar NO3 radical, the
symmetry number is 6.
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In taking into account the symmetry numbers in the
rotational partition function, the standard procedure is to
divide by the symmetry number. This procedure is correct
when calculating rate constants, but it has some
limitations. A good example which illustrates this is the
reaction, H + H2  [H · · · H-H]‡  H2 + H. The
symmetry number is 2 for H2, and so is the symmetry
number of the complex; consequently, the rate constant is
‡
Q‡ / 2
Q
k BT
k
T
k1 
e  E0 / k B T  B
e  E0 / k B T
h (QH / 1)(QH 2 / 2)
h QH QH 2
If we compare the rate obtained for the reaction
D + H2  [D · · · H-H]‡  DH + H.
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(10-54)
we see that the symmetry number for the complex is 1;
therefore,
Q‡ / 1
k BT
k1 
e  E0 / k B T
h (QD / 1)(QH 2 / 2)
‡
2
Q
k BT

e  E0 / k B T
h QDQH 2
(10-54)
The conclusion is that the second reaction is favored over
the first by a factor of 2. However, since both reactions
are extracting hydrogen atoms from H2, the rates can not
differ by a factor of 2; this factor should appear in both
equations!
The best way to resolve this dilemma is by using a
statistical factor, defined as the number of different
transition states that can be formed if all identical atoms
are labeled to distinguish them from one another.
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Thus the above reactions both have a statistical factor of 2.
In general, with this definition, we can omit symmetry
numbers from the partition functions and multiply the rate
expression by the statistical factor L‡, i.e.,
‡
Q
‡ k BT
k1  L
eE / k T
h QAQB
(10-55)
0
B
Great care must be used in the choice of a transition state
with the correct degree of symmetry.
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10.5.3 Application: The F + H2 Reaction
The reaction H2 + F  H + HF has been of
particular interest in chemical kinetics because it is the
rate-limiting step in the chain reaction H2 + F2  2HF,
which plays an important role in the kinetics of the HF
chemical laser. It is also of special theoretical interest,
because it is one of the simplest examples of an
exothermic chemical reaction. The expression for the rate
constant can be written as
‡

Q
k T
k  L‡ B 
h  QF QH 2
  Q‡
 
  QF QH
2
 vib 
 
  Q‡
(Q‡ / V )
 
 
  (QF / V )(QH / V )   QF QH
2
2
 rot 
trans
These rations can be evaluated separately.
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
 e  E0 / RT

 elec
• Properties of the reactants and transition state.
Parameters
R2(F-H) Å
R1(H-H) Å
F…H-H
1.602
0.756
1, cm-1
2, cm-1
3, cm-1
4007.6
397.9
397.9
4, cm-1
E0 (kJ/mol)
m(amu)
I(amu Å2)
310.8i
6.57
21.014
7.433
gelec
4
F
H2
0.7417
4395.2
18.9984
2.016
0.277
4
1
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We note that the electronic degeneracy for the fluorine
atom in its ground electronic state (2P3/2) is 4, and that for
the linear FH2 complex(2P) is the same. We neglect
contributions from the (2P1/2) spin-orbit state of F at 404
cm-1. The degeneracy for H2 in its ground state (1Sg+) is 1.
Consequently, the electronic partition function
contribution is unity. The translational partition function
3/ 2
3/ 2
‡
ratio is 

 mF  mH   h 2 
(Q / V )
2 





 (QF / V )(QH / V ) 
 mF mH   2k BT 
2
2

trans 

And inserting the values given in the table gives


(Q‡ / V )


 4.16 10 31 m3
 (QF / V )(QH / V ) 
2

trans
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The rotational and vibrational partition functions are
dimensionless, and contain no contribution from the
mono-atomic F species. The rotational partition function
ratio is
 Q‡ 
 8 2 k BTI ‡ / h 2  I ‡

 

 26.8
2
2
 QH 
 8 k BTI H / h  I H
2
2
 2  rot 

In evaluating the vibrational partition function ratio we
obtain the expression
 Q‡

 QH
 2

1  exp( h H 2 / k BT )
 
3

 vib  [1  exp( h i‡ / k BT )]
i 1
Thus
 Q‡

 QH
 2

  1.39

 vib
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The statistical factor L contributes a factor of 2. Thus we
obtain for the rate constant
k  (1.95 10
16
3 1
m s ) exp(  E0 / k BT )
1
3 1
 1.17 10 exp( 6570 / 8.31T ) mol m s
8
1
 1.17 10 exp( 790 / T ) liter mol s
11
1
The experimental data are best represented by
1
k (T )  2 10 exp( 800 / T ) liter mol s
11
1
This is very reasonable agreement, for such a simple
model.
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10.6 Variational TST
Classical TST gives the exact rate constant if the net
rate of reaction equals the rate at which trajectories pass
through the transition state. These two rates are equal,
however, only if trajectories do not recross the transition
state: any recrossing makes the reactive flux smaller than
the flux through the transition state. Thus the classical
transition state theory rate constant may be viewed as an
upper bound to the correct classical rate constant.
The effect of recrossing on the reaction rate can be
taking into account by means of the variational
transition state theory. In the canonical approach, the
minimum in the canonical transition state theory constant
given by equation 10-20 is found along the reaction path
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dk (T )
0
‡
dq
(10-56)
Since the canonical rate constant is related to the free
energy according to equation 10-32, i.e.
k BT  DG / RT
k
e
h
the canonical variational transition state will be located
at the maximum in the free energy along the reaction
path. To apply canonical variational TST, the transition
state’s partition function (or free energy) must be
calculated as a function of the reaction path. These
calculations require values for the classical potential
energy, zero-point energy, vibrational frequencies, and
moments of inertia as a function of the reaction path.
‡
0
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Variational TST is particularly important for
reactions without saddle points, e.g., H + CH3  CH4.
Results of a canonical variation TST calculation for this
reaction are listed in the following Table.
T (K)
R‡ (Å)
rock ‡
E0
k
200
3.54
95
-0.51
1.24
400
3.33
138
-1.05
1.56
600
3.19
173
-1.62
1.70
800
3.09
204
-2.22
1.78
1000
3.00
233
-2.84
1.83
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A particular interesting result is the shorter H-CH3
bond length and thus “tighter” transition state as the
temperature is increased. The vibrational frequency
for the degenerate H-CH3 rocking motions increases
as the transition state tightens. A tightening of the
transition state with increase in temperature is a
common result for reactions without potential energy
barriers. The calculated rate constant for H+CH3 
CH4 reaction is in good agreement with the
experimental value of 2.8 × 108 m3 mol-1 s-1 for T =
300-600 K.
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Assignment
The following reaction was done experimentally at
various temperatures in order to obtain rate constants:
O + HO2  OH + O2
T1=298 K, k1 = 6.1 x 10-11 cm3 molecule-1 s-1
T2=229 K, k2 = 7.57 x 10-11 cm3 molecule-1 s-1
(a) Using the experimental data, find the activation
energy Eact;
(b) Calculate the following thermodynamic properties
at T = 298 K using transition state theory: DE‡, DH‡,
DS‡, DG‡, A.
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