Time-resolved studies of CN radical reactions and the role of complexes in solution

Article abstract of DOI:10.1021/jp8064079

Time-resolved studies using 100 fs laser pulses generate CN radicals photolytically in solution and probe their subsequent reaction with solvent molecules by monitoring both radical loss and product formation. The experiments follow the CN reactants by transient electronic spectroscopy at 400 nm and monitor the HCN products by transient vibrational spectroscopy near 3.07 μm. The observation that CN disappears more slowly than HCN appears shows that the two processes are decoupled kinetically and suggests that the CN radicals rapidly form two different types of complexes that have different reactivities. Electronic structure calculations find two bound complexes between CN and a typical solvent molecule (CH₂Cl₂) that are consistent with this picture. The more weakly bound complex is linear with CN bound to an H atom through the N atom, and the more strongly bound complex has a structure in which the CN bridges Cl and H atoms of the solvent. Fitting the transient absorption data with a kinetic model containing two uncoupled complexes reproduces the data for seven different chlorinated alkane solvents and yields rate constants for the reaction of each type of complex. Depending on the solvent, the linear complex reacts between 2.5 and 12 times faster than the bridging complex and is the primary source of the HCN reaction product. Increasing the Cl atom content of the solvents decreases the reaction rate for both complexes.

Full text of DOI:10.1021/jp8064079

J. Phys. Chem. A 2008, 112, 12081–12089
12081
Time-Resolved Studies of CN Radical Reactions and the Role of Complexes in Solution
Andrew C. Crowther, Stacey L. Carrier, Thomas J. Preston, and F. Fleming Crim*
Department of Chemistry, UniVersity of Wisconsin - Madison, Madison, Wisconsin 53706
ReceiVed: July 21, 2008; ReVised Manuscript ReceiVed: August 31, 2008
Time-resolved studies using 100 fs laser pulses generate CN radicals photolytically in solution and probe
their subsequent reaction with solvent molecules by monitoring both radical loss and product formation. The
experiments follow the CN reactants by transient electronic spectroscopy at 400 nm and monitor the HCN
products by transient vibrational spectroscopy near 3.07 µm. The observation that CN disappears more slowly
than HCN appears shows that the two processes are decoupled kinetically and suggests that the CN radicals
rapidly form two different types of complexes that have different reactivities. Electronic structure calculations
find two bound complexes between CN and a typical solvent molecule (CH2Cl2) that are consistent with this
picture. The more weakly bound complex is linear with CN bound to an H atom through the N atom, and the
more strongly bound complex has a structure in which the CN bridges Cl and H atoms of the solvent. Fitting
the transient absorption data with a kinetic model containing two uncoupled complexes reproduces the data
for seven different chlorinated alkane solvents and yields rate constants for the reaction of each type of
complex. Depending on the solvent, the linear complex reacts between 2.5 and 12 times faster than the bridging
complex and is the primary source of the HCN reaction product. Increasing the Cl atom content of the solvents
decreases the reaction rate for both complexes.
I. Introduction
in the gas phase. For example, Samant and Hershberger have
measured a rate constant of (5.4 ( 0.3) × 108 M-1 -1
s
for the
Bimolecular reactions in solution are ubiquitous in chemistry,
but there are relatively few studies that explore their mechanisms
and dynamics on a time scale comparable to the time between
encounters. In addition to the inherent interest of these processes,
understanding the properties of thermal bimolecular reactions
in solution is a prelude to using vibrational excitation to
influence them.1 Reactions in which CN radicals abstract
hydrogen atoms from chlorinated hydrocarbons are particularly
attractive candidates for such ultrafast studies, and, indeed, one
of the two pioneering studies2,3 addresses the reaction of CN
with chloroform (CHCl3). Photodissociating ICN with 267 nm
light generates CN radicals efficiently in solution, and transient
absorption using the strong B r X electronic transition near
388 nm can monitor their evolution.4 It is also possible to probe
the HCN reaction products using transient infrared absorption
by the C-H stretching transition near 3.07 µm.2 Because the
C-H stretching transition lies at higher energy in HCN than in
alkanes, it is relatively well isolated from interfering transitions
in many solvents. The strong C-H bond in the product also
makes typical hydrogen abstraction reactions exothermic by
about 10 000 cm-1,5 which is enough energy to populate C-H
stretching vibrations as high as VCH ) 3 in the HCN product
and makes CN radical reactions suitable for studying product
vibrational energy distributions as well.
loss of CN radicals in reaction with CHCl3 in the gas phase,8 a
value that agrees well with the corresponding rate constant of
(4.2 ( 0.4) × 108 M-1 -1
s
for the appearance of HCN in
solution.2 However, the populations of the vibrational states of
the products show differences that seem to arise from the
presence of the solvent. The energy available in gas-phase
reactions of CN radicals with hydrocarbons primarily appears
as internal excitation of the products,6,9 in apparent contrast to
condensed-phase reactions. The most direct comparison is for
the reaction of CN radicals with CHCl3.6 In the gas phase, it
produces an inverted vibrational distribution for the HCN
product, with more population in the VCH ) 2 level than in VCH
) 1. However, reaction of CN with CDCl3 in solution produces
primarily ground-state DCN with only 20% of the products in
VCD ) 1.2
Complexes often play an important role in condensed phase
reactions. Neta and co-workers have observed complexes of Br
in a variety of alkanes and haloalkanes following pulsed
radiolysis or laser flash photolysis.10,11 These complexes are
stable for microseconds and can control much of the subsequent
chemistry because the reacting entity is a complex rather than
a free Br atom.12 Similarly, Cl radicals form complexes in
solution. Chateauneuf has found a strong charge-transfer transi-
tion of chlorine complexes with a variety of solvents,13-15 and
Elles et al. have observed a shift of the transient absorption in
the first few picoseconds following photolytic production of Cl
in CH2Cl2 that is consistent with the formation of a Cl
complex.16 There are no comparable studies of CN in solution,
but it would be surprising if complexes were not important.
Gas-phase studies of CN radical reactions with simple hydro-
carbons find negative activation energies that suggest that the
reaction proceeds through a weak complex,7,17-23 and Heaven
and co-workers have observed ground electronic state van der
Waals complexes of CN with H2 and Ar in molecular beams.24-27
Detailed studies of gas-phase reactions of CN potentially
provide a reference point for comparing reactions in gases and
liquids, which can differ substantially because interactions with
solvent molecules can change energy barriers and modify the
motion along the reaction coordinate. Reactions of CN radicals
with most alkanes occur on nearly every gas-phase collision,6,7
suggesting that there is essentially no barrier to the reaction.
The reaction is slower for chloromethanes both in solution and
* To whom correspondence should be addressed. E-mail: fcrim@
chem.wisc.edu.
10.1021/jp8064079 CCC: $40.75
2008 American Chemical Society
Published on Web 11/06/2008

12082 J. Phys. Chem. A, Vol. 112, No. 47, 2008
Crowther et al.
or a broadband continuum, and we probe the HCN product with
infrared light near λprobe ) 3.07 µm. All of the pulses for the
experiment come from applying nonlinear optical techniques
to a 2.5 mJ, 100 fs pulse of 800 nm light from a Ti:sapphire
oscillator and regenerative amplifier operating at 1 kHz. Using
this approach, we study CN radical dynamics in seven different
solvents (chloroform, dichloromethane, 1,2-dichloroethane, 1,4-
dichlorobutane, 2-chloropropane, 2-chlorobutane, and 1-chlo-
robutane).
A. Photolysis Light. We generate 267 nm photolysis light
using two different schemes. For transient UV absorption
experiments, a previously described low-power 267 nm ar-
rangement delivers 0.75 µJ pulses to the sample.33 However,
because the HCN infrared transition is about an order of
magnitude weaker than the electronic transition of CN, the
infrared transient absorption experiments require higher energy
photolysis pulses in order for reaction of CN to form enough
HCN products. In these experiments, we generate 400 nm light
by sending 700 µJ of p-polarized 800 nm light through a 3:1
telescope and into a ꢀ-barium borate (BBO) crystal (0.3 mm, θ
) 29°, type I, ooe) and mixing that pulse with 440 µJ of 800
nm light in a second BBO crystal (0.3 mm, θ ) 42°, type I,
ooe), a process that generates 95 µJ of 267 nm light. A grating
pair stretches this pulse to 3.25 ps to minimize burning of the
sample cell, an arrangement that also minimizes the possibility
of multiphoton background signals. The stretcher, which uses
1200 grooves/mm ruled gratings blazed at 250 nm, has an
overall efficiency of 25%. In both arrangements, a double
Fresnel rhomb rotates the 267 nm pulse to magic-angle
polarization (54.7°) with respect to the probe pulse to suppress
the effects of anisotropic decay. The energy of the photolysis
pulse reaching the sample is 8 µJ.
B. Probe Light. We use three different probe techniques for
these experiments. Electronic probing of the CN reactant uses
either 400 nm light obtained by doubling 800 nm light from
the regenerative amplifier or by generating a broadband
continuum. Vibrational probing of the HCN uses 3.07 µm
infrared light from a potassium niobate (KNbO3) optical
parametric amplifier (OPA). We block half of the photolysis
pulses using either a chopper or shutter for active background
subtraction, and a computer-controlled translation stage estab-
lishes the delay between the photolysis and probe pulses in all
of the probe schemes.
Figure 1. Experimental approach for transient absorption studies of
CN reactions. A λphot ) 267 nm photolysis pulse dissociates the ICN
precursor, and probe pulses at either λprobe) 400 nm or λprobe) 3.07
µm interrogate the CN reactant or the HCN product respectively, at
time delays of ∆tCN or ∆tHCN following the photolysis pulse. Hydrogen
abstraction from CH2Cl2 is exothermic by 9700 cm-1, and chlorine
abstraction from CH2Cl2 is exothermic by 6000 cm-1
.
There are also time-resolved studies that use transient
absorption to monitor the evolution of photolytically generated
CN radicals in CHCl3 solution. Two potential pathways for the
abstraction reaction of CN radicals with CHCl3 produce either
HCN or ClCN. The hydrogen abstraction channel, producing
HCN and CCl3, is exothermic by 11 300 cm-1, and the chlorine
abstraction channel, producing ClCN and CHCl2, is exothermic
by 7000 cm-1.5 Wan et al.28 and Moskun and Bradforth29 have
followed the isotropic CN radical decay in CHCl3 using the B
r X electronic transition near 388 nm to observe two distinct
timescales. They assign the fast component of a few picoseconds
to recombination of the CN radical with I and the slower
component of about 70 ps to reaction of the CN radical, results
that are consistent with a molecular dynamics simulation of ICN
photodissociation in CHCl3.30 In addition, Moskun et al. have
observed the decay of the CN radical anisotropy in several
solvents.29,31
The goal of the work described here is to use transient
absorption to probe the reactions of CN radicals with a range
of chlorinated alkane solvents by monitoring both the decay of
the absorption in the vicinity of the electronic transition of the
CN radical and the growth of the infrared absorption of the HCN
reaction product. In an earlier study of the reaction of chlorine
radicals, we found that the decay rate of the chlorine radical
matched the appearance rate of the HCl reaction product,
consistent with simple kinetics.32 The striking result in the study
described here is that the decay and appearance rates are not
commensurate for the reaction of CN with seven different
solvents. The transient absorption on the CN radical transition
decays between a factor of 2.5 and 12 more slowly than the
transient absorption of the HCN product grows. Detailed kinetic
analysis and electronic structure calculations point to the critical
role of rapidly formed complexes that react at different rates.
The frequency doubling scheme generates 400 nm probe light
using a BBO crystal (0.3 mm, θ ) 29°, type I, ooe). We separate
the pulses into a probe beam and a reference beam that we detect
with integrating silicon photodiodes, and we average 1000 pulses
for each position of the delay stage to achieve a noise level of
50 µOD. At the sample, the diameters of the photolysis and
probe beams are 200 and 80 µm full width at half-maximum
(fwhm) intensity, respectively. The broadband UV-vis scheme
generates a continuum between 350 and 650 nm by focusing a
small amount of 800 nm light into a 6 mm thick piece of UV-
grade CaF2. After recollimation and focusing by off-axis
parabolic mirrors, both the probe and reference continuum
beams enter a modified Czerny-Turner spectrometer. Each
beam passes through a polarizer, strikes a 600 grooves/mm
grating blazed at 400 nm, and passes through a 50 mm focal
length lens before striking separate 512 pixel, 12.5 mm wide
silicon photodiode arrays (Hamamatsu, S3904-512Q). We
calibrate the arrays using a holmium perchlorate solution (15%
w/v) in 10% perchloric acid and use two shutters (Vincent
Associates Uniblitz-LS6, Uniblitz-VMM-D4) to obtain the
transient signal with and without the photolysis pulse present.
II. Experimental Approach
The key feature to our approach is generating CN radicals
by 267 nm photolysis of ICN with a short pulse of light and
probing transient absorption using either the electronic transition
of the CN radical reactant or the fundamental C-H stretching
transition of the HCN reaction product. Figure 1 illustrates our
excitation and detection scheme for the case in which CH2Cl2
is the solvent. Following λphot ) 267 nm photolysis, we probe
the CN radical at λprobe ) 400 nm with either a fixed wavelength

CN Radical Reactions
J. Phys. Chem. A, Vol. 112, No. 47, 2008 12083
We typically integrate 300 pulses on the photodiodes with and
without the photolysis light present and subsequently average
20 to 30 such pairs of data to achieve a noise level of about 1
mOD. At the sample, the diameters of the photolysis and probe
beams are 100 and 45 µm (fwhm), respectively.
The continuum-seeded, two-pass OPA that generates infrared
light for probing HCN uses a KNbO3 crystal (2 mm, θ ) 41.5°,
type I). Beginning with 750 µJ of 800 nm light, we generate
up to 30 µJ of mid-infrared idler light that we separate into
probe and reference beams. The reference beam strikes a single
lead-selenide integrating photodiode, and the probe beam
passes through the sample and into a 0.25 m monochromator
having a 300 grooves/mm grating blazed at 2 µm. The
monochromator disperses the probe pulse onto a 32 pixel, 6.7
mm wide mercury cadmium telluride array (Infrared Associates,
MCT-10-2 × 32). We calibrate the arrays using 25% by
volume solutions of CHCl3 and CH2Cl2 in CCl4. Averaging 10
traces of 5000 pulses for each position of the delay stage
produces a noise level of 40 µOD. We focus the photolysis and
probe pulses to diameters of 80 and 40 µm fwhm at the sample,
respectively.
C. Sample. We use a modified version of the procedures
described by Moskun and Bradforth29 and by Larsen et al.34 to
synthesize ICN. The most important change is an additional
recrystallization in cyclohexane.35 Because purification of the
ICN by sublimation does not change the UV-vis spectrum or
the time evolution, we use it without further purification. For
CN radical detection, we make 0.1 M ICN solutions (OD ≈
0.9 at 267 nm), and for HCN detection, we make 0.2 M ICN
solutions (OD ≈ 1.7 at 267 nm). A Teflon gear pump circulates
each 50 mL sample through a 1 mm thick Teflon cell that has
2 mm thick UV-grade MgF2 windows. We only use a sample
for about an hour, when a light-purple color from accumulation
of I2 appears, and find that the observed time evolution at the
beginning and end of the sample lifetimes are the same. We
use 99.9% CH2Cl2 from Mallinckrodt Chemicals. All other
solvents come from Sigma-Aldrich: CHCl3, >99.9%; 1,2-
dichloroethane, 99.8%; 1,4-dichlorobutane, 99.0%; 2-chloro-
propane, 99.0%; 2-chlorobutane, 99+%; and 1-chlorobutane,
99.5%.
Figure 2. Top Panel: The UV-vis transient spectrum of CN radical
in CH2Cl2 at a delay of ∆tCN ) 5 ps. The structure in the panel is that
of the bridging complex to which we primarily attribute this spectrum.
The arrow for λprobe marks the wavelength we use for monitoring the
time evolution. Bottom Panel: The transient spectrum of HCN in CH2Cl2
at ∆tHCN ) 1 ns. The open circles are the transient spectrum obtained
from the infrared photodiode array, and the solid line is a conventional
infrared spectrum obtained after a one-hour irradiation of the sample.
The arrow for λprobe marks the point we use for monitoring the time
evolution, and the error bar shows the typical uncertainty for the
measurements.
III. Results
A. Transient Absorption. Photolysis of ICN with 267 nm
light creates a transient population of I and CN, and our goal is
to probe the evolution of the CN radical and adducts or products
that it forms. In general, the radicals can have transitions similar
to those of the isolated species but slightly perturbed by the
presence of the solvent, and they can also have transitions to
excited states in which there is charge transferred between the
solvent and the radical. A weakly bound, ground-state complex
might have a transition to a charge-transfer state that is strongly
bound by the Coulomb interaction between the separated
charges. Consequently, these charge-transfer transitions of the
complexes can have a substantially lower energy than those of
the isolated species. The transition energy increases as the
difference in the ionization energy of the electron donor and
the electron affinity of the electron acceptor grows, as illustrated
by the Cl complexes in which the transition shifts to higher
energy as the ionization energy of the solvent increases.13 These
considerations help identify the transition responsible for the
transient electronic absorption we observe.
all of the solvents we study. In addition, a density functional
theory calculation and molecular dynamics simulation finds the
CN B r X transition to be centered at 344 nm in water.36 The
top panel in Figure 2 is the transient UV-vis absorption
spectrum that we obtain by introducing the broadband con-
tinuum probe at a delay of ∆tCN ) 5 ps after the photolysis
pulse in the solvent CH2Cl2. Its prominent maximum near 380
nm is likely the B r X electronic transition that occurs at 388
nm for isolated CN radicals,4 although the sharp decrease of
the continuum probe intensity at shorter wavelengths prevents
our locating the maximum precisely. The spectra for all of the
other solvents have maxima at essentially the same location.
We rule out the transition to a charge-transfer state of a
CN-solvent complex because it should appear at a much longer
wavelength than the transition we observe. The 550-nm transi-
tion of the CN-H2O complex29 would occur at even longer
wavelengths in our more easily ionized solvents. Adjusting the
transition energy for the water complex for the ionization energy
Moskun and Bradforth29 identify the transition near 380 nm
as the B r X transition of the CN radical, a conclusion that is
consistent with the transition we observe in the same region in

12084 J. Phys. Chem. A, Vol. 112, No. 47, 2008
Crowther et al.
of our solvents predicts that the charge-transfer transitions lie
beyond 1.2 µm.
It is also unlikely that the transition we observe arises from
the I atom produced in the photolysis. The transient electronic
absorption decays within a few nanoseconds, a time that is too
short for the endothermic reaction of I with the solvent and too
long for complexation dynamics. In addition, a rough estimate
of the location of the charge-transfer transition for I, obtained
by adjusting the λ ) 340 nm transition for the Cl-CH2Cl2
complex33 for the electron affinity of I and the ionization energy
of the solvents,13 predicts that all of these charge-transfer
transitions are below 364 nm. Another potential origin of the
absorption we observe is excitation of a charge-transfer transition
in a complex of the solvent with an electronically excited I atom.
A similar estimate of the transition energy in which we increase
the electron affinity by the spin-orbit splitting of iodine predicts
transitions for the I*-solvent complex in the range of 360 to
480 nm for our solvents. However, Moskun et al. showed that
the I* channel is likely to be energetically inaccessible for 267
nm photolysis of ICN in water, and they did not observe the
I*-H2O complex in photodetachment studies of I- in water.37
Because we also observe no transitions at wavelengths greater
than 400 nm in any solvent, it is unlikely that I*-solvent
complexes contribute significantly to our signals.
Using a fixed wavelength 400 nm probe (marked with a
vertical arrow in Figure 2) to monitor the time evolution gives
the best signal-to-noise ratio, and the top panel of Figure 3 shows
the resulting transient absorption. The 1 ps coherent response
of the neat solvent determines the time resolution of the
measurement. The signal rises to a maximum in about 1 ps38
and has two, well-separated decays of about 4 and 1500 ps.
We identify the initial, rapid decay as both cage and diffusive
geminate recombination, and we assign the subsequent, slow
decay to reaction of CN with the solvent. In the first few
picoseconds after photodissociation, solvent reorganization can
cause the features to shift, but we observe no spectral changes
during that time.
Figure 3. Top Panel: The time evolution of the λprobe ) 400 nm signal
in CH2Cl2 following photolysis of ICN. Bottom Panel: The time
evolution of the λprobe ) 3.07 µm (3261 cm-1) signal in CH2Cl2
following photolysis of ICN. The solid lines in the figures are the fits
of the kinetic model to the data using the parameters in Table 1.
The complementary observation to the time evolution of the
reactive CN radical is the appearance of the HCN reaction
product, which we detect by transient infrared absorption in the
region of the fundamental C-H stretching transition. The open
points in the bottom panel of Figure 2 are the transient
absorption spectrum of HCN formed in CH2Cl2 at a delay of
∆tHCN ) 1 ns, and the solid line is the conventional infrared
spectrum obtained after irradiating a 3 mL sample of 0.2 M
ICN in CH2Cl2 with 55 µJ pulses of 267 nm light for one hour.
The bottom panel in Figure 3 shows the transient infrared signal
at the maximum in the absorption at 3261 cm-1 (marked with
a vertical arrow in Figure 2) following photolysis of ICN in
CH2Cl2. In all seven solvents we study, there is an early
multiphoton signal that we remove by subtracting the back-
ground signal at the edge of the array (∼3200 cm-1) from the
maximum. The data shown in Figure 3 for CH2Cl2 have the
poorest signal-to-noise ratio of all the solvents we study.
where the decay times of the chlorine electronic absorption and
the rise of the HCl vibrational transition are commensurate.32
The slow loss of the reactants compared to the appearance of
the products suggests that the two probes are observing species
that are kinetically decoupled from each other. One possibility
is that CN radicals rapidly complex with the solvent to form
two species that react at different rates but have similar
electronic spectra. As described below, a kinetic scheme that
incorporates that possibility describes the measurements quan-
titatively, and we have performed electronic structure calcula-
tions on isolated complexes as a rudimentary test of the
plausibility this picture.
B. Electronic Structure Calculations. We use the Gaussian
03 suite of programs to perform electronic structure calculations
of isolated CN-solvent complexes.39 Including the effects of
the bulk solvent, which may stabilize isolated complexes
differently, would change our quantitative results but not the
qualitative picture, as shown by test calculations where we
include a continuum solvent. Density functional theory calcula-
tions on the CN + CH2Cl2 system at the B3LYP level of theory
with the 6-31+G* basis set find the two geometry minima
shown in Figure 4. There is a linear complex with the nitrogen
of the CN radical positioned next to a hydrogen atom of CH2Cl2,
and there is a bridging complex with the CN radical spanning
an H atom and a Cl atom of CH2Cl2 with the carbon atom of
Comparison of the decay of the CN radical absorption with
the growth of the HCN product absorption in Figure 3 shows
that their timescales differ by about a factor of 7, indicating
that the two experiments are not probing simple loss of a reactant
and formation of the corresponding product. Every solvent we
studied shows this disparity with differences ranging from about
a factor of 2.5 for 1-chlorobutane to a factor of 12 for 1,2-
dichloroethane. This situation contrasts drastically with the
behavior we have observed previously for the reaction of
chlorine radicals with pentane in some of the same solvents,

CN Radical Reactions
J. Phys. Chem. A, Vol. 112, No. 47, 2008 12085
TABLE 1: Fitting Parameters
Fixed Parameters
A/ns-1/2
Adjustable Parameters
kbr/ ns-1
k
lin/ ns-1
flin
flin
CN
HCN
Solvent
φ
1-chlorobutane
2-chlorobutane
2-chloropropane
1,4-dichlorobutane
1,2-dichloroethane
dichloromethane
chloroform
0.82
0.81
0.79
0.80
0.87
0.82
0.84
0.0055
0.0045
0.0063
0.0045
0.0035
0.0065
0.0083
4.05 ( 0.84
3.52 ( 0.34
2.17 ( 0.21
2.72 ( 0.33
1.00 ( 0.07
0.67 ( 0.14
0.45 ( 0.12
10.5 ( 1.3
11.9 ( 1.8
16.1 ( 4.3
11.4 ( 2.0
12.4 ( 2.2
4.8 ( 1.4
3.2 ( 1.9
0.21 ( 0.21
0.03 ( 0.10
0.05 ( 0.07
0.03 ( 0.10
0.00 ( 0.04
0.03 ( 0.10
0.00 ( 0.09
1.00 ( 0.16
0.94 ( 0.15
0.83 ( 0.15
1.00 ( 0.18
0.72 ( 0.11
1.00 ( 0.50
1.00 ( 0.50
the radical positioned near a Cl atom of the solvent. Including
zero-point energies in the calculations gives stabilities of the
complexes relative to separated CN and CH2Cl2 of 430 cm-1
for the linear complex and 1540 cm-1 for the bridging complex.
There is a transition state between the two that lies 220 cm-1
below the energies of the separated reactants but far enough
above the energies of the complexes that there is a barrier to
interconversion. (Analysis using a kinetic scheme that includes
interconversion of the two complexes also suggests that it is
unimportant in this system.40) The minima that this simple
density functional theory calculation predicts are certainly not
quantitatively correct because of both the level of theory and
the neglect of solvent interactions. Because our kinetic analysis
finds that the two complexes interconvert slowly, it is likely
that the complexes are more strongly bound than our calculations
suggest.
The relative population at room temperature of the two states
with these energies favors the lower energy bridging complex
by a factor of 250 over the linear complex. Solvation can change
these relative populations substantially, and the B r X transition
probability of the CN radical may be different in the two
complexes. However, the greater stability of the bridging
complex suggests that it is the more abundant species and, thus,
responsible for most of the absorption at 400 nm. By contrast,
the difference in the observed decay times, described below,
and the calculated structure of the linear complex suggest that
it is responsible for most of the products whose infrared
absorption we observe. The weaker binding of the linear
complex and the proximity of carbon of the CN radical to
adjacent solvent molecules from which it can abstract a
hydrogen atom make it more likely to form HCN than the
bridging complex.
38 cm-1 with the H2 located on the nitrogen of the CN
radical,24,27,41 and they have also detected a bent complex
between Ar and CN bound by 102 cm-1 with an Ar-C-N angle
of 140°,25 qualitatively similar to the 132° Cl-C-N angle that
we calculate for the bridging complex. There are also electronic
structure calculations for the CN-H2O complex that find a
hydrogen bond-like linear conformation with a well depth of
about 600 cm-1 36
These experiments and calculations are all
.
consistent with the CN radical forming two complexes with
characteristically different geometries. There are also gas-phase
kinetics studies that suggest that complexes are important in
CN radical reactions with saturated hydrocarbons. These experi-
ments obtain negative activation energies of several hundred
wavenumbers.7,17-23 Because negative activation energies are
often the kinetic signature of complex formation, it appears that
even the relatively weak interactions between the radicals and
hydrocarbons give complexation a role in CN radical chemistry.
IV. Kinetic Analysis
Our observation of two different timescales for CN loss and
HCN formation along with experiments and calculations
implicating complexes in CN radical chemistry motivate our
use of the kinetic scheme shown in Figure 5. In this scheme,
rapid complexation forms two CN containing species that react
at different rates following photolytic production of CN radicals.
Figure 5 illustrates the kinetic scheme for the reaction with
CH2Cl2, but we use it for all of the solvents we study. In this
scheme, the complexation occurs in a few picoseconds and is
much faster than any of the subsequent kinetics. Thus, the
kinetics are essentially those of two independent species, the
linear and bridging complexes, that react with rate constants
klin and kbr, respectively. Both complexes contain the CN
chromophore that we interrogate by transient absorption with
λprobe ) 400 nm. They do not interconvert during the measure-
ment, and both can potentially react to form the HCN product
whose transient absorption we probe with λprobe ) 3.07 µm.
The kinetic scheme shows the formation of HCN and ClCN
explicitly, but our analysis only determines the total rate
constant, klin or kbr, for the parallel reactions from each complex.
Although the complexes could react to form other products, such
as HNC, the formation of other products does not change the
rate constants we extract. In fact, gas-phase studies of the
reaction of CN radicals with hydrocarbons and CHCl3 find
negligible formation of HNC.7,42
Heaven and co-workers have studied CN radical van der
Waals complexes experimentally and theoretically.24-27,41 They
have observed a linear complex between H2 and CN bound by
These two rate constants and the fraction of the signal that
comes from each complex are the important adjustable param-
eters for fitting the data. To fit data such as those shown in
Figure 3 with this simple model, we also include a term in the
transient absorption that accounts for the fast recombination of
the initially formed CN radical. This term influences the fit to
the rapid initial decay in the CN signal that is obvious in the
data, but it does not influence the longer time behavior from
Figure 4. The calculated structures and energies of the CN-solvent
complexes and the transition state for isomerization.

12086 J. Phys. Chem. A, Vol. 112, No. 47, 2008
Crowther et al.
Figure 5. Kinetic scheme for photolysis of ICN, complex formation, and reaction of CN. Each complex reacts to form HCN or ClCN with
different pseudo-first-order rate constants of klin for the linear complex (top) and kbr for the bridging complex (bottom). Fitting the transient absorption
data shows that linear complex abstracts both H and Cl more rapidly than the bridging complex, which primarily abstracts Cl. The sizes of the
vertical arrows for the probe transitions qualitatively indicate the relative contribution of each species to the transient absorption signal.
which we extract the rate constants and fractional contributions.
The reactive loss of CN complexes and the formation of the
HCN products follow the usual simple exponential decay and
growth. Thus, we simultaneously fit the transient signals for
CN, SCN(t), and for HCN, SHCN(t), to the expressions,
The solid lines in Figure 3 show the quality of fits that this
model produces, and Table 1 collects the fitting parameters and
associated uncertainties. The uncertainties are the amounts by
which it is possible to change the parameters without an
observable change in the quality of the fit. The recombination
decay is essentially complete in 10 ps for all solvents, in
agreement with previous measurements and molecular dynamics
simulations of ICN photodissociation in CHCl3.28-30 The crucial
results in the table are the rate constants and fractional
contributions of the different complexes to the CN signal and
the HCN signal, which we fit simultaneously. The fits yield a
rate constant for the bridging complex, kbr, that is between a
factor of 2.5 and 12 smaller than that for the linear complex,
klin, depending on the solvent. This result is consistent with the
more stable bridging complex giving up CN more slowly than
the linear complex. The difference in the fractional contributions
of the linear complexes to the CN signal and the HCN signal is
particularly striking. The very small fractional contribution of
linear complex to the evolution of the CN signal, flinCN ≈ 0,
suggests that the more stable bridging complex dominates, fbrCN
) 1 - flinCN ≈ 1, and determines the transient electronic
absorption signal we observe. This behavior is again consistent
with the more stable bridging complex being the most abundant
species. By contrast, the linear complex is primarily responsible
for the HCN time evolution, flinHCN ≈ 1, consistent with the
more weakly bound complex reacting more readily and having
a favorable geometry for hydrogen atom abstraction from the
surrounding solvent.
CN
br
brt
SCN(t) ) ACN[1 - φerfc(A ⁄ t)][flCinNe-k t + f e-k ] + Aoffset
lin
√
(1)
SHCN(t) ) AHCN[flHinCN(1 - e-k ) + fbHrCN(1 - e-k )] (2)
lint
brt
The first term in brackets in eq 1 accounts for the removal of
CN radicals by recombination using the Smoluchowski theory
of diffusive recombination.43,44 The parameter φ is the fractional
recombination of the CN radical with its original partner radical
I, and A comes from the rate of recombination. The second set
of brackets in eq 1 contains the important terms that describe
the bimolecular reaction of the complexes. In this expression,
flinCN is the fraction of the CN transient absorption arising from
the linear complexes, and fbrCN ) 1 - flinCN is the fraction
from the bridging complexes. The coefficient ACN is an arbitrary
amplitude, and Aoffset accounts for a slowly decaying background
signal that is essentially constant during the measurement.
The terms for the HCN transient absorption signal are
analogous. The rate constants are the same in the two equations,
and the fractional contributions of the linear and bridging
complexes to the production of HCN are flinHCN and fbrHCN
) 1 - f linHCN. Again, the coefficient AHCN is an arbitrary
amplitude, and there is no contribution of the recombination to
the HCN signal during the times we analyze. Thus, the four
essential fitting parameters are the two global rate constants,
klin and kbr, and the fractional contribution of the linear
complexes to the signal for CN and for HCN, flinCN and flinHCN.
The reaction rate constant data are insensitive to the details
of recombination, and we are able to fix the φ and A terms. We
use the φ ) 0.84 from a molecular dynamics simulation of
IV. Discussion
Our observation of different times for the disappearance of
the CN reactant absorption and the appearance of the HCN
product absorption motivates our kinetic model incorporating
two different CN complexes. Using this model to analyze the
time evolution of the CN reactant and HCN product allows us
to extract the reaction rate constants for CN complexes with
seven different solvents. The rate constants for the complexes
differ by as much as a factor of 10 among the solvents, a
variation that appears to arise from a competition between
differences in the number of labile atoms and differences in
the transition states.
A. Complexes and Reaction Rates. The two previous
studies of the decay of the CN transient absorption in CHCl3
following photolysis of ICN28,29 both fit the decay to a rapid
component lasting a few picoseconds and a slower component
lasting about 70 ps. Wan et al.28 fit their data to a double
30
CHCl3 and scale it according to the viscosity of the solvent
for the other systems we study.45 Similarly, we take advantage
of the insensitivity of the fits to the exact value of the parameter
A to hold it constant at a value from an initial fit for each solvent.
The offsets are Aoffset ) 0.9 mOD and Aoffset ) 0.5 mOD for
the slowly reacting CH2Cl2 and CHCl3 solvents respectively as
determined in measurements with a 9 ns delay. The offset term
is zero for all other solvents. We fit the HCN signal beginning
with points at a delay of ∆tHCN ) 50 ps to prevent imperfections
in subtracting the multiphoton solvent response from affecting
the results.

CN Radical Reactions
J. Phys. Chem. A, Vol. 112, No. 47, 2008 12087
exponential form with time constants of τ1 ) (2.5 ( 0.4) ps
and τ2 ) (76 ( 10) ps, and Moskun and Bradforth29 use a
similar scheme to obtain τ1 ) 4.0 ps and τ2 ) 72 ps. In the
latter case, they also include a long time, constant signal and
find that the three components have amplitudes of A1 ) 31%,
A2 ) 27%, and A∞ ) 42%. These fitting parameters reproduce
our data rather well over the first 200 ps but do not agree at the
longer times where we observe a continuing decay rather than
the constant asymptote of their fit. Their experiments also
observe a rapid rise of about 600 fs that is consistent with the
rise we observe. Thus, all three measurements observe very
similar decays over the time range that they have in common
and find that the initial rapid decay comes from recombination
of I and CN. However, our analysis of the longer time
component shows that the decay does not simply reflect reaction
to form HCN but involves the fate of the different complexes
described above. Both of these previous studies focused on the
short-time behavior and, in the case of Moskun and Bradforth,
on the rotational dynamics of the initially formed CN radical.
By contrast, we concentrate on the longer time behavior and
possible reaction pathways.
ClCN + CH2Cl products. Thus, we expect that the bridging
complex primarily reacts to form ClCN because formation of
HCN within the complex is unlikely and the CN radical is poorly
positioned to abstract a hydrogen atom from the surrounding
solvent. By contrast, the relatively weakly bound linear complex,
in which the CN is bound to hydrogen through its nitrogen atom,
is ideally positioned to react with surrounding solvent molecules
by abstracting either a hydrogen atom to form HCN or a chlorine
atom to form ClCN. In this picture, the linear complex forms
both products, and the rate constant klin reflects those two parallel
processes, whose relative probability we do not know. Perhaps
coincidentally, the activation energy of 420 cm-1 that Raftery
et al.2 obtain from the temperature dependence of the production
of HCN from the reaction of CN with CHCl3 is close to the
binding energy we calculate for the linear complex.
Our analysis finds that the two complexes have different
reaction rates, product pathways, and stabilities. We can use
the transient absorption of HCN that we measure in CH2Cl2 to
make a rough estimate of the relative concentration of the
complexes. Using the infrared extinction coefficient of ꢀHCN
)
326 cm-1M-1 for HCN,2 a path length of 1 mm, and our
measured HCN absorption of 0.31 mOD, we calculate a
concentration of 10 µM for HCN. Using the approximation that
the amount of ClCN produced by the linear complex is
comparable to the amount of HCN, we estimate an initial
concentration of linear complexes of about 20 µM. Using our
measured extinction coefficient for ICN at 267 nm, ꢀCN ) 86
cm-1M-1, and our beam conditions, we calculate that the initial
concentration of CN that escapes the solvent cage after
photolysis is 520 µM.46 Assuming that all of those CN radicals
form one of the two complexes, we estimate that the concentra-
tion of bridging complexes is 500 µM, a 25 fold excess over
the concentration of linear complexes. Thus, both our calculation
of the relative energies of the isolated complexes and our
experimental estimate of the relative amounts show that the
bridging complex is the dominant species in solution. Our
picture of the reaction is that the CN radicals rapidly form two
different complexes with the solvent. Most of the complexes
have a relatively stable bridging structure and react relatively
slowly to form primarily ClCN but a few of them have a less
stable linear structure and react relatively rapidly to form, in
part, the HCN products that we observe.
The first time-resolved study of the reaction of CN radicals
following photolysis of ICN in CHCl3 used transient infrared
absorption to monitor the production of HCN and ClCN. It
showed that HCN appeared with an exponential time constant
of τHCN ) (194 ( 20) ps and that ClCN appeared with a time
constant of τClCN ) (140 ( 36) ps.2 By comparison, a similar
fit to our data in Figure 3 yields a time constant of τHCN
)
(313 ( 93) ps. The time constant corresponding to our more
-1
elaborate model, klin ) (312 ( 185) ps, is the same with a
larger uncertainty owing to the more complicated model. The
appearance time of ClCN measured in those experiments is also
consistent with reaction of the linear complex, which forms both
HCN and ClCN in our kinetic scheme. The slower reaction of
the bridging complex should also produce a slower rise over a
period of a few nanoseconds that may be present in the data
but is difficult to discern over the 1 ns observation window.2
Although our analysis consistently obtains a slightly longer
reaction time to produce HCN, the results agree satisfactorily
in light of our uncertainties. The most important point is that
the model illustrated in Figure 5, which involves two complexes
reacting a different rates, reproduces both the slow decay of
the transient electronic absorption and the rapid growth of the
transient vibrational absorption.
B. Correlation of Solvent Structure and Reactivity. Our
measurements and analysis for seven different solvents provide
the pseudo-first-order reaction rate constants for the reaction of
CN complexes with those solvents. They have different extents
of chlorine substitution and range from methane derivatives
(chloroform and dichloromethane) to butane derivatives (chlo-
robutane and dichlorobutane). This range of sizes and substitu-
tions allows us to search for correlations of the structure of the
solvent with its reactivity. Studies of hydrogen abstraction by
chlorine radicals have established a correlation between chlorine
atom substitution and a change in the rate of abstraction of R
and ꢀ hydrogens.47-49 These correlations are the basis of
quantitative structure activity relationships that predict the
reaction rate constant from the number and positions of the
chlorine substitutents.48,50 The structure activity relationships
empirically predict the rate of hydrogen abstraction by chlorine
from any chlorinated alkane by assigning a rate constant to each
primary, secondary, and tertiary hydrogen based on its position.
Weighting each contribution by a factor that depends on the
neighboring substituents and summing all of the contributions
gives the predicted rate constant. Sheps et al. have shown that
these relationships correctly predict the relatiVe rates for the
The key to our analysis is linking the absorptions to two
different complexes. Fitting the data for all seven solvents using
the kinetic scheme with two complexes (Figure 5) yields the
results in Table 1. The fractional contributions of each of the
complexes to the signal show that one complex, which we assign
as the bridging complex, is responsible for the transient
electronic absorption, and that another complex, which we assign
as the linear complex, is responsible for production of the HCN
that we observe by transient vibrational absorption. Calculations
of the energies of the isolated complexes find that the bridging
complex is more stable and, thus, likely less reactive than the
linear complex. The relative reactivity of the complexes is not
built into the model but is an inference from the fits. The
negligible contribution of the bridging complex to the production
of HCN implies that it primarily reacts to form other products
(or decays by a nonreactive pathway). The calculated structure
of the bridging complex, in which the CN spans a chlorine atom
and a hydrogen atom with the carbon of the CN adjacent to
chlorine, suggests that a likely reaction path is abstraction of
chlorine within the complex and subsequent separation of the

12088 J. Phys. Chem. A, Vol. 112, No. 47, 2008
Crowther et al.
TABLE 2: Second-Order Rate Constants and Fractional Cl
Content
labile hydrogen atoms by less reactive chlorine atoms. The
variation in the rate constants that we found previously for
chlorine atom reactions31 reflects changes in the transition state
for hydrogen abstraction,33,47-49 and those same effects seem
important in the analogous reactions of CN radicals.
solvent
fCl Csolvent/M kb2r/109 M-1s-1 kl2in/109 M-1s-1
1-chlorobutane
2-chlorobutane
2-chloropropane
1,4-dichlorobutane 0.20
1,2-dichloroethane 0.33
0.10
0.10
0.13
9.6
9.4
11
9.1
12.7
15.6
12.4
0.42 ( 0.09
0.37 ( 0.04
0.20 ( 0.02
0.30 ( 0.04
0.079 ( 0.006
1.1 ( 0.1
1.3 ( 0.2
1.5 ( 0.4
1.3 ( 0.2
1.0 ( 0.2
V. Summary
Time-resolved studies of the reaction of CN radicals with a
series of chlorinated alkanes using transient absorption to
observe the evolution of the reactants and of the products
indicate that CN radicals rapidly form two different types of
complexes with the solvent. One of the complexes is linear with
CN bound to a hydrogen atom of the solvent through its nitrogen
atom, and the other complex is bent with the CN bridging a
chlorine atom and a hydrogen atom of the solvent with its carbon
atom connected to the chlorine. The experiments probe the CN
radical by its electronic absorption near 400 nm and interrogate
the HCN product by the infrared absorption of the C-H stretch
near 3.07 µm. The observation that the CN signal disappears
more slowly than the HCN signal appears suggests that the two
species are decoupled from each other kinetically, as would be
the case if the CN radical rapidly formed complexes with the
solvent. Electronic structure calculations on isolated complexes
of CN with CH2Cl2 find that there are two complexes with
different stabilities. The relatively weakly bound linear complex
is likely to abstract either hydrogen or chlorine atoms readily
from the solvent to form HCN ClCN, and the more strongly
bound bridging complex is likely to react more slowly to
produce primarily ClCN. Fitting the transient signals, we observe
to this kinetic model shows that the linear complex reacts up to
12 times faster than the bridging complex. The analysis also
shows that the bridging complex is responsible for the slow
decay of the CN transient absorption and that the linear complex
is responsible for the rapid formation of the HCN product. The
details of the structure of the reacting solvent molecules
influence the reaction rates of both complexes. Increasing the
fractional Cl content of the solvent slows the reaction rate for
both complexes, reflecting both the different reactivities of the
H and Cl atoms and the changes that chlorine substitution makes
in the transition state for the reaction.
dichloromethane
chloroform
0.50
0.75
0.043 ( 0.009 0.31 ( 0.09
0.036 ( 0.010 0.26 ( 0.15
reactions of chlorinated alkanes in solution.33 They also found
that the abstraction rate decreased with increased chlorine
content in a series of chlorinated butanes, in accord with the
structure activity relationships and consistent with chlorine
substitution changing the stability of the transition state to
increase the activation energy.
Our measurements of the reactivity of the CN complexes
show some of the same qualitative trends as chlorine atom
abstraction of hydrogen atoms in gases and liquids. To compare
the rates for the different solvents, we divide the pseudo-first-
order rate constants for the two complexes in Table 1, klin and
kbr, by the concentration of the neat solvent to obtain the
corresponding second-order rate constants, k2lin and kb2r. Table 2
lists these rate constants along with the fraction of the labile
atoms that are chlorine, fCl, for each solvent. Figure 6, which
gives the second-order rate constants for the solvents in order
of increasing chlorine content, shows that the reaction rate
constants for both the linear and bridging complexes decrease
as the fraction of the labile atoms that are chlorine increases.
The second-order rate constant for the linear complex, k2lin, is
roughly the same for all the butanes and perhaps slightly larger
for 2-chloropropane, but it decreases noticeably for 1,2-
dichloroethane, dichloromethane, and chloroform. These three,
which have Cl fractions ranging from fCl ) 0.33 to 0.75, are
clearly less reactive than the other four, which have fractions
between 0.10 and 0.20. The second-order rate constant for the
bridging complex, k2br, follows a similar pattern with the rate
constant falling sharply for 1,2-dichloroethane. There is a general
correlation of slower reaction with greater Cl content, but it is
likely that this trend does not solely reflect the replacement of
Acknowledgment. We thank the National Science Founda-
tion for supporting this work, and A.C.C. gratefully acknowl-
edges an NSF predoctoral fellowship. We thank Professor Frank
Weinhold for many useful discussions concerning electronic
structure calculations, and we are grateful to Professor Martin
Zanni for the use of his infrared photodiode array.
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CN Radical Reactions
J. Phys. Chem. A, Vol. 112, No. 47, 2008 12089
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