United States
                    Environmental Protection
                    Agency
 Atmospheric Sciences
 Research Laboratory
 Research Triangle Park NC 27711
                    Research and Development
EPA/600/S3-86/072 Apr. 1987
&EPA          Project  Summary
                    Structure-Reactivity
                    Relationships  for
                    Predicting  Environmentally
                    Hazardous  Chemicals
                   Norman Cohen
                     A method previously developed for
                    extrapolating rate coefficients by con-
                    ventional transition-state theory was
                    applied to reactions of hydroxyl  (OH)
                    radicals with 10 halomethanes and 18
                    haloethanes.  For each  reagent, the
                    entropy  of activation  AS* was calcu-
                    lated. That value, together with an ex-
                    perimental value of the rate of reaction
                    at 298 K, k(298), was used to calculate
                    k(T) at higher temperatures. The calcu-
                    lated values for all the haloalkanes dif-
                    fered  from experimental values by no
                    more  than 25%, except that of (OH +
                    CHCI3), for which the possibility of ex-
                    perimental errors was considered.
                     Those calculations were then used to
                    develop a simpler, approximate scheme
                    that can be applied to any haloalkane. For
                    a-hydrogen abstraction reactions,
                    AS*(298) can be fitted, with a maximum
                    error of 1.4 and an average error of 0.3
                    cal mor1 K~1 (entropy units, or eu), by
                     AS*(298) = -2.2 In M -18.0 + R In nH
                    where M = molecular weight of the
                    haloalkane and nH =  the number of
                    abstractable a-hydrogen  atoms. The
                    activation energy at 298 K, E(298). can
                    be fitted, with an average error of 0.3
                    and a  maximum error of 1.1 kcal/mol,
                    by
                     E(298)/R=2100-85nF-51nc1 -
                               950nCH3 - 600cH2X -
                               650nCHx2 - 250nCX3
                    where the n, indicate the number of H
                    atoms on CH4 replaced with the in-
                    dicated substituents, and X is either Cl
                    or F. The above relations for AS*(298)
                    and E(298) are  used to generate a
                    "universal" rate coefficient expression
that  depends only on the molecular
weight and the number of abstractable
H atoms in the reagent haloalkane:
             k(T) =
         nH 10" M-1 T1 6
      exp[-[E(298)/R-450]/T]
where E(298)/R  is given by the pre-
ceding equation.  For most reagents,
this expression predicts rate coefficients
within a factor of 3 of  experimental
data  and provides a  useful predictive
tool if no reliable data are available.
  This Project Summary was developed
by EPA's Atmospheric Sciences  Re-
search Laboratory, Research Triangle
Park, NC, to announce key findings of
the research project that Is fully docu-
mented In a separate report of the same
title (see Project  Report ordering In-
formation at back).
Introduction
  The aim of this research has been to
develop the means for predicting reac-
tivities of potential man-made pollutants
in the stratosphere and troposphere.
Although it is possible to measure re-
activities in the laboratory, the number of
possible species of concern is enormous,
and the cost of studying each one in
detail would be prohibitive. The assess-
ment of the atmospheric fate of pollutants
can, for the most part, be satisfied by a
procedure that enables prediction of re-
activities to within a factor of 3 to 5,
without requiring  the higher  accuracy
attainable by  elaborate laboratory
measurements.

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  Consideration of the important oxidizing
species in the atmosphere and their rela-
tive reactivities leads to the conclusion
that for almost all reagents, the species
that determines the lifetime of an atmo-
spheric pollutant is the  hydroxyl (OH)
radical. Consequently, any program con-
cerned with  predicting reactivities  of
potential pollutants should concern itself
first with the reactions of OH  radicals.
For this reason, the work under this con-
tract focused on OH reactions.
  The  initial  efforts proceeded in two
phases: The first addressed the problem
of calculating in detail the temperature
dependence of the reaction rate  coef-
ficients;  the second explored  the pos-
sibility of developing simplified procedures
for estimating, with sufficient accuracy,
the rate  coefficients of OH reactions at
any temperature. The second phase re-
quired  estimating  both  the  entropy  of
activation (AS*), and, with  more dif-
ficulty, the energy of  activation  (E).
These  two parameters  determine the
rate of reaction  at any temperature, in
accordance with  the general equation
    k(T) = C exp(ASVR) exp(-Ea/RT)   (1)
   Finally, the  problem  of developing a
universal rate  coefficient  expression
that can  predict  with reliability the rate
coefficients, at  various  temperatures,
for reactions of OH radicals  with  im-
portant  atmospheric  pollutants  was
addressed.

Procedure

Transition-State  Theory
Calculations
  The  procedure follows  our  previous
studies. Here, the general reaction  is
              XN          ,0,
  XYZCH + OH - Y--C--H'    'H-
              Z'
  XYZC + HOH
where X, Y, and Z are each either H, C1,
F, CH3,  or a halomethyl radical. The
principal problem is how to calculate the
entropy of the activated complex, S*. The
calculation involves using the haloalkane
reagent RH itself as a model compound,
then making  suitable corrections to the
various degrees  of freedom as  indicated
below. The entropy S* is then given by
       S* = SS,H + AS, + Av + ASr +     .,,
           AS,r + ASe + AS<, + ASn     ' '
where the  AS terms represent the cor-
rections  required in replacing the pro-
perties (translation, vibration,  rotation,
internal  rotation, electronic, symmetry,
optical isomerism,  respectively) of  the
model  compound by those of  the acti-
vated complex.
  It was assumed that the C-H, H-O,
and 0-H bond  lengths and  C-H-0 and
H-O-H  bond  angles  are  approximately
the same as those calculated by Walch
and Dunning1 for the reaction  of (OH +
CH4):  1.2,  1.3, 1.0  A  and  160° and
110°, respectively. From this information,
the product of moments of inertia of the
complex I* can be calculated, whence  AS,
= R In (l*/l), where I is the product of the
moments of inertia of the reagent RH.  AS,
is given  by  (3/2) R ln(M'/M).  The
electronic degeneracy  of the  activated
complex  is assumed to be  2, whence
AS8 = R In 2 - 1.38 eu (entropy units, or
cal mol"1 K'1). AS0 =  R  Info/a"), where a
abd at  are  the external symmetry num-
bers of the alkane and complex, respec-
tively, calculated assuming rigid rotation.
ASn = R In (nt/n), where n and n* are the
numbers of optical isomers in the alkane
and complex,  respectively.  Only  the
vibrational frequencies and internal rota-
tions of the activated complex remain to
be determined.
Vibrational Frequencies
  For each halomethane XYZCH, where
X, Y,  and Z are either H, Cl, or F, we
estimated the vibrational frequencies in
the activated complex by using those in
the molecule XYZCF as guides, on the
assumption that the C-H-OH portion of
the activated complex is similar to the C-
F portion of a real molecule. The vibra-
tional-frequency changes in the activated
complexes for all the halomethanes are
summarized in the full report.
  For the haloethanes, it was not possible
to examine each reaction in detail because
there are more frequencies, fewer mode
identifications, and fewer molecules for
which detailed spectra are available. In-
stead, the  vibrational  frequencies  of
CH3CH3, CH3CH2F, CH3CHF2,  and CH3CF3
were compared, the change in the first
pair representing the reaction of OH with
all  haloethanes with  only  /3-hydrogen
atoms (i.e.,  no H atoms on the same C
atom as F or Cl atoms), and the changes
between the second and third pairs repre-
senting  reactions with  a-H  atoms.
Because the experimental data indicate
that a reaction  with  haloethanes  con-
taining  only /?-H atoms is at least  an
order  of  magnitude  slower than for
haloethanes with some a-H atoms,  it
was assumed that in those reagents con
taining both a- and y-H atoms, the re
action  with the  /J-H atoms could bi
neglected. In both kinds of reactions,  i
was assumed that the newly formed C H-(
and H-O-H bonds  have the same value:
that were used in the halomethane re
actions (1000cm1 each).
Internal Rotations
  The properties of the internal rotation;
must be  evaluated accurately, because
considerable entropy is associated  witr
these two degrees of freedom.  The
moments of inertia for the internal  rota-
tions are calculated by the procedure 01
Herschbach  et  al.2 The entropy of free
rotation is given by Sf = R(ln 0 + 1/2),
where Q = 0.35(lrT)'/2/a for lr, the reduced
moment of inertia, in dalton-A. Here o is
the symmetry of  the internal rotation,
which  is  1  for most of the  reagents
considered in this report but 3 for rotation
about the C-H bond in CH4, CHC13, and
CHF3. For rotation about the C-H bond, Q
«= 6.2/a for all halomethanes and 1.8 for
CH4. For  rotation about the  0-H bond, Q
» 5.9 for all  halomethanes and 5.1 for
CH4. The corrections to the entropy due
to the barrier to  rotation,  S( - Sh> are
interpolated from  tables developed  by
Pitzer and coworkers where SH = entropy
of hindered rotation.
  For all the haloethanes,  the reduced
moment of inertia lr for rotation about the
C-H bond is approximately 1.1 dalton-A,
which  makes  the partition  function Q
equal to 6.5,  and the entropy of free
rotation Sf, 4.7 eu. For rotation about the
H-O bond, I, =  0.95, Q = 6.0, and Si =
4.6 eu.
  Unlike  the halomethanes, the halo-
ethanes already have one internal  rota-
tion — about the C-C bond. In a previous
study involving transition-state  theory
calculations for reactions of oxygen (0)
atoms with  alkanes, reasonable agree-
ment with experiment was obtained by
assuming that the barrier to internal rota-
tion was  lowered  by 1 kcal/mol in the
activated complex. The same assumption
was made here. The contributions to AS*
are shown in the full report. There is a
qualitative difference between the re-
actions abstracting a-H atoms and those
abstracting /3-H atoms, because the OH
adduct makes a much greater change in
the moment of inertia of a CH3 group
than it does when added to a halomethyl
group.
 'Walch, S. P., and T H Dunning, Jr J. Chem. Phys ,
  72:1303, 1980.
 2 Herschbach, D R., H S Johnston, K S Pitzer, and
 R F. Powell. J. Chem Phys., 25 736, 1956

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Empirical Correlations
  The results of the detailed transition-
state theory calculations outlined above
were used to establish simple empirical
correlations  between activation entropy
and activation energy for an arbitrary (OH
+ haloalkane) reaction with readily deter-
mined  molecular  parameters.  The fol-
lowing  procedure  generates  simple,
approximate expressions for  ASt(298)
and for E(298) without requiring  more
information  than  the  molecular weight
of the reacting haloalkane and its  gross
structural details.

Entropy of Activation
  The entropy of the activated  complex,
S*, is calculated from the entropy of the
reacting  haloalkane RH by a series  of
corrections terms:
  S* = SttH + AS, + ASV + ASr + AS,r +  .01
      ASe + AS0 + ASn              IJ'
where  the AS terms represent the cor-
rections required  in replacing  the pro-
perties (translation, vibration,  rotation,
internal rotation,  electronic, symmetry,
optical  isomerism, respectively) of the
haloalkane by those  of  the activated
complex. The translational contribution
AS,  is given  by  (3/2)R  In(MVM);
therefore, it will decrease to zero as the
mass  M of the reagent RH  increases
(since  M* = M + MOH). The  rotational
contribution AS, is  given  by (1/2)R
ln[(la'blc)*/(lalblc)]. where the three I factors
are the principal moments of inertia. Each
I depends approximately on M; hence ASr
too will decrease to zero as the size of the
reagent haloalkane (and hence  its mole-
cular weight) increases. The vibrational
contribution, ASV, is the sum of contribu-
tions from each vibrational mode, each of
which  varies approximately with vibra-
tional frequency. In this procedure, several
vibrational  modes,  all  of  comparable
frequencies  in different  reagents, are
replaced by other modes in the activated
complexes, for which the frequencies are
comparable  for  different reactions.  A
similar  argument,  though  somewhat
weaker, can be made for internal rota-
tions. The remaining three terms on the
right-hand side of Eq. (3) are independent
of mass. These arguments suggested that
there might be some correlation between
AS*(298) and M, a suggestion borne out
by graphic display of the data.
Activation Energy
  Previously, workers attempted to cor-
relate activation energies with bond dis-
sociation energies  (BDEs)  of  the dis-
sociating bond. This approach was tried
with moderate success for (OH + halome-
thane)  reactions.  However, the  same
could  not  be done profitably for the
haloethanes  because BDEs are known
for very few of the compounds. Instead,
an empirical correlation was made of the
activation energies with a set of six struc-
tural  parameters;  each  parameter de-
scribes the correction to the activation
energy of CH4 that  must be made as H
atoms  are substituted  by  F,  Cl,  CH3,
CH2X,  CHX2,  or CX3, where X = F or Cl.
(At present  there  are temperature-
dependent rate data for only  one bro-
minated haloalkane; hence, attention was
confined to fluorinated  and chlorinated
compounds  until  more data  become
available.) In other words,
E(298)/R = E(CH4)/R - aFnF  -
           aC1nC1 - aCH3nCH3 - acH2Xr>CH2X
           - aCHx2ncHX2 - acx3ncx3     (4)
The calculated activation energies for all
halomethanes and  haloethanes (except
CHF3 and  CHsCFs,  which  pose unique
problems),  which are derived  from the
experimental values of k(298), were used
in deriving the values of the various a,.
The results of this effort are given in the
following section.

Results and Discussion

Transition-State  Theory
Calculations

OH +  Haloalkanes
  Transition-state  theory  calculations
were  carried  out using  the vibrational-
frequency changes and the entropies of
activation listed in the full report. There it
was shown  that the temperature ex-
ponents n for all the a-hydrogen abstrac-
tions  are 1.6 to  1.7, whereas for the
three ^-hydrogen abstraction reactions n
= 1.1. For the halomethanes, two models
were  used for each reaction: one with
hindered internal rotation, and one with
free internal  rotation. The  two models
were otherwise identical. On the average,
the free internal rotation model appears
to give slightly better agreement with the
data. For all but one reagent, agreement
with experimental data is within the ex-
perimental uncertainties, and  discrep-
ancies  between experimental  and cal-
culated rate coefficients  are no greater
than 25%.
  The single puzzling exception  is CHCI3,
for which both models greatly underpre-
dict the activation energy and hence the
rate coefficients at T > 300 K. To obtain
agreement with the  data  requires a
greatly increased  AS*(298) —  from
                                                                                 -28.7 to —25.3 eu — for the free internal
                                                                                 rotation case. One way to achieve this is
                                                                                 by lowering the four low-frequency vibra-
                                                                                 tions in the activated  complex to  150
                                                                                 cm"1. However, there is no a priori reason
                                                                                 for making the frequencies of this one
                                                                                 complex so much lower than those of all
                                                                                 the others.
                                                                                   The discrepancy between the calculated
                                                                                 and experimental values  of k(T) for this
                                                                                 halomethane suggests either that k(300)
                                                                                 is  really larger than the measured value
                                                                                 or, more  likely, that at higher tempera-
                                                                                 tures (400-500 K), another process re-
                                                                                 moving OH radicals is occurring. Because
                                                                                 of  the possible serious consequences for
                                                                                 the applications  of the thermochemical
                                                                                 approach to conventional transition-state
                                                                                 theory as we  have been using it,  we
                                                                                 recommend  that the (OH + CHCI3) re-
                                                                                 action rate be carefully remeasured over
                                                                                 a temperature  range sufficiently wide to
                                                                                 eliminate any  doubts concerning both
                                                                                 the absolute value of the rate coefficients
                                                                                 and the activation energy.
                                                                                 Empirical Correlations

                                                                                 Activation Entropies
                                                                                   In the full report, AS*(298) for the free
                                                                                 internal rotation model is plotted against
                                                                                 the molecular weight M of the reacting
                                                                                 haloalkane  for all  the  a-hydrogen ab-
                                                                                 stractions. The least-squares fit through
                                                                                 all the points is described by
                                                                                         AS*(298) (eu/H atom) =
                                                                                            -2.2 In M -18.0
                                                                                 or
                                                                                              AS'(298) =
                                                                                        -2.2 In M- 18.0 + RlnnH
                                                                                 where  S is in eu  (entropy units, or cal
                                                                                 mol"1 K"1), M is in daltons, and nH is the
                                                                                 number of abstractable a-H atoms.  This
                                                                                 expression fits all the data with a maxi-
                                                                                 mum error of 1.4 eu and an average error
                                                                                 of 0.3  eu.  [The   values  of  AS* for
                                                                                 CH3CC13,  CH3CF3,  and  CH3CF2CI,
                                                                                 which have only 0-H atoms, are all 2 to 3
                                                                                 eu larger than Eq.  (2) predicts.] When M
                                                                                 becomes large  enough (approximately
                                                                                 220 daltons), the contributions to AS,
                                                                                 and ASr will  be  close to  zero,  and
                                                                                 AS*(298) per H atom  should  reach  a
                                                                                 minimum value of —-30.3 eu.
                                 (5a)
                                 (5b)
Activation Energies
  Using the approach outlined above, a
least-squares fitting program was applied
to activation  energies  for  28 (OH +
haloalkane) reactions to solve for the
parameters a, of Eq. (4). The derived

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values, based on E(CH4)/R = 2100 at 298
K, are:
         a, = 85     aCH2x = 600
         aa = 515    aCHx2 = 650
       aCH3 = 950     aCX3 = 250
The values of E(298)/R  predicted with
Eq.  (4) are compared with the  experi-
mentally derived values in the full report.
The discrepancy between predicted and
derived values is never worse than 570,
i.e., an error in E of 1.1 kcal/mol, and in
most  casts is considerably smaller: The
average error is 150, i.e., 0.3 kcal/mol.
  This approach to calculating the en-
ergetics of a reaction is not novel: It relies
on what is essentially a  bond additivity
argument.  Heicklen3 explored  a similar
approach to predicting BDEs, from which
he predicted rate coefficients for reactions
of OH radicals with a wide variety of
organics. The difference here is the use
of the approach directly  for calculating
activation energies, rather than BDEs.
This shortcut circumvents the problem of
the uncertainties in many BDEs  — gen-
erally 1 to 2 kcal/mol. These uncertainties
may  introduce  errors  into  the  bond
additivity expressions for predicting un-
measured BDEs and hence in activation
energies. Since the correlation factor in
the equation relating activation energies
with  BDEs is approximately 0.4,  a  2-
kcal/mol error in BDE imparts an error to
k(298) of a factor of 3.8.
A "Universal" Rate Coefficient
Expression
  Equation (4) for E(298)/R and Eq. (5)
for AS*(298) can be substituted in the
general expression for k(T) from transi-
tion-state theory  to yield a general  rate
coefficient expression  for  (OH + halo-
alkanes)  that  depends  only on  the
molecular weight of  the reagent  and
the number of various substituents. We
can force a T1 5pre-exponential tempera-
ture  dependence  to  agree  with  the
results of the calculations. The A factor
is determined by requiring the expres-
sion to yield the proper values of k(298)
and E(298). The result is
    k(T) = nH 106 s M-' T15 exp(-B/T)  (6)
where M is in daltons and T is in kelvins.
The  pre-exponential factors have been
modified slightly to round off the ex-
ponent of the molecular-weight factor M.
3Heicklen, J. Int. J. Chem. Kinet, 13 651, 1981
The term B is calculated from E(298)/R
obtained from Eq. (4): B = [E(298)/R -
450]. The rate coefficients resulting from
Eq. (6) are shown for several typical re-
actions in figures given in the full report.
[Equation  (6) does not apply to halo-
ethanes  with only  /3-hydrogens.]  For
CH2CICHCI2  and CH2FCHF2,  Eq. (6) was
applied separately to the two different
kinds of H atoms and the results summed
together. In general, the rate coefficients
calculated by Eq. (6) disagree with experi-
mental data (where  they exist) by less
than a factor of 3.
Conclusions
  Four principal conclusions emerge from
the present study.  The first is that  a
reasonable set of assumptions can be
applied consistently to all but one of the
reactions considered  here to obtain
transition-state models that lead to cal-
culated  rate coefficients in good agree-
ment with experimental data. This is true
even though the A factors at 298 K are
not in particularly good agreement with
experimental values. The good agreement
is a result of the tendency of activation
entropies and energies to compensate
one another.
  The second conclusion is that one of
the reactions — that of (OH + CHCI3) — is
anomalous. Either the experimental data
are flawed or there is something unusual
about the dynamics of this reaction, re-
quiring a qualitatively different activated
complex to obtain agreement between
calculations and experiments. A new ex-
perimental investigation is recommended.
  Third,  the above two conclusions to-
gether demonstrate that, while one might
be able to tailor a model for the activated
complex to force reasonable agreement
with a particular set of experimental data
for one reaction, simultaneous agreement
with  data for several  homologous re-
actions  is by  no means  a fortuitous
achievement. The  greater  constraints
imposed by treating an entire family  of
reactions together rather than  a single
reaction give greater confidence that the
model and the resulting calculations are
physically meaningful.
  Finally, we used the calculations just
discussed as a  guide for  generating
empirical expressions for AS*(298) and
E(298)  for a-hydrogen  abstraction re-
actions of OH radicals from fluorinated
and chlorinated  methanes and  ethanes.
The calculated entropies and energies of
activation were then applied to generate
a "universal" rate coefficient that depends
only on the molecular weight and the
number of abstractable a-hydrogen atoms
of the reagent haloalkane. This expression
predicts rate coefficients within a factor
of about 3 of the experimental data for all
26 reactions for which data were available
(and generally much better), and offers
promise as a predictive  tool  when  no
reliable experimental data are available.

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      Norman Cohen is with Aerospace Corporation, EIS eg undo, CA 90245.
      Bruce W. Gay, Jr.. is the EPA Project Officer (see below).
      The complete report, entitled "Structure-Reactivity Relationships for Predicting
        Environmentally Hazardous Chemicals," (Order No. PB87-140 497/AS; Cost:
        $9.95, subject to change) will be available only from:
              National Technical Information Service
              5285 Port Royal Road
              Springfield, VA 22161
              Telephone: 703-487-4650
      The EPA Project Officer can be contacted at:
              Atmospheric Sciences Research Laboratory
              U.S. Environmental Protection Agency
              Research Triangle Park, NC 27711
United States
Environmental Protection
Agency
Center for Environmental Research
Information
Cincinnati OH 45268
Official Business
Penalty for Private Use $300

EPA/600/S3-86/072
                   OCOC329    PS
                                                   *G£NCr

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