Photodissociation of HCN at 157 nm: Energy disposal in the CN(A2Π) fragment

Article abstract of DOI:10.1063/1.481504

Photodissociation of HCN at 157 nm was found to produce only H and CN(A²Π) through analysis of laser-induced fluorescence experiments. The CN(A²Π) vibrational populations decrease monotonically from v=0 to 3, represent 19±1% of the available energy and are in good agreement with a prior distribution of 9500 cm^-1 of energy. The rotational distributions of the four vibrational levels are very similar, represent 6.5% of the available energy and are approximately Boltzmann with temperatures near 900 K. The rotational distribution of CN(A²Π,v=0) is compared to several highly simplified reference distributions and approximate agreement is found with a phase space calculation.

Full text of DOI:10.1063/1.481504

Photodissociation of HCN at 157 nm : Energy disposal in the CN (A 2 Π) fragment
Jingzhong Guo, R. Eng, Tucker Carrington, and S. V. Filseth
Citation: The Journal of Chemical Physics 112, 8904 (2000); doi: 10.1063/1.481504
View online: http://dx.doi.org/10.1063/1.481504
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JOURNAL OF CHEMICAL PHYSICS
VOLUME 112, NUMBER 20
22 MAY 2000
Photodissociation of HCN at 157 nm: Energy disposal
in the CN„A 2⌸… fragment
Jingzhong Guo, R. Eng, Tucker Carrington, and S. V. Filsetha)
Department of Chemistry, York University, 4700 Keele Street,
Toronto, Ontario M3J 1P3, Canada
͑Received 16 December 1999; accepted 28 February 2000͒
Photodissociation of HCN at 157 nm was found to produce only H and CN(A 2⌸) through analysis
of laser-induced fluorescence experiments. The CN(A 2⌸) vibrational populations decrease
monotonically from ϭ0 to 3, represent 19Ϯ1% of the available energy and are in good agreement
v
with a prior distribution of 9500 cmϪ1 of energy. The rotational distributions of the four vibrational
levels are very similar, represent 6.5% of the available energy and are approximately Boltzmann
with temperatures near 900 K. The rotational distribution of CN(A 2⌸, ϭ0) is compared to several
v
highly simplified reference distributions and approximate agreement is found with a phase space
calculation. © 2000 American Institute of Physics. ͓S0021-9606͑00͒00220-8͔
I. INTRODUCTION
sible at wavelengths lower than 144 nm and Davis and
Okabe6 have observed a threshold wavelength for emission
of the CN(B 2⌺ϩ –X 2⌺ϩ) violet system at 148 nm. A
threshold of 149 nm is reported by West and Berry,7 and
Lee8 reports significant quantum yields ͑у10%͒ only for
wavelengths shorter than 144 nm. Energy disposal in the
CN(B 2⌺ϩ) fragment has been investigated by dispersal of
the violet system emission following excitation of HCN at
several discrete wavelengths below 150 nm.9
The threshold wavelength for production of CN(A 2⌸)
is 189 nm and this is lowered to 185 nm if the calculated5
3200 cmϪ1 barrier is included. There have been several re-
ports of the observation of CN(A 2⌸) as a product of HCN
photodissociation. Mele and Okabe10 report red system,
CN(A 2⌸–X 2⌺ϩ), emission, when Kr and Xe, but not Hg,
resonance lamps were employed as light sources, consistent
with the wavelength thresholds given above. A lower limit of
180 nm for the wavelength threshold for production of red
system emission was determined by West and Berry7 using a
synchrotron source with a wavelength resolution of 0.4–0.8
nm. Flash photolysis at wavelengths longer than 155 nm led
to chemical laser emission in the red system suggesting that
little CN(X) is produced in dissociation at these wave-
lengths. Red system emission has also been observed in pho-
tofragment emission excitation spectra at wavelengths as
long as 147 nm.8,11
The technique of H(D) atom photofragment transla-
tional spectroscopy has been employed recently to study the
dissociation of HCN(DCN) at 121.6 nm.12 The CN fragment
is found to be formed almost exclusively in the A 2⌸ state
with little vibrational energy but a bimodal rotational distri-
bution extending to values of NϾ100. This work permits a
determination of the bond dissociation energy of HCN of
43 740Ϯ150 cmϪ1, a value adopted in this paper. Finally,
and very recently, Bucher and Lehmann13 report an investi-
gation of the vibrationally mediated HCN dissociation. In
this work single rotational states of HCN(X,004) are pro-
Hydrogen cyanide is a prominent constituent of the in-
terstellar and cometary media. Optical absorption is negli-
gible at wavelengths longer than 200 nm but is very signifi-
cant at shorter wavelengths. Vacuum ultraviolet excitation
followed by dissociation is a prominent loss process and its
description has been of fundamental interest in chemical
physics. The pseudo-halogen character of the CN free radical
makes the investigation of HCN dissociation a natural exten-
sion of the study of the dissociation of the simple hydrogen
halides. The many degrees of freedom available for fragment
energy disposal ensure that HCN dissociation will provide an
important test of both its computed potential-energy surfaces
and of the scattering calculations carried out upon them.
The ground state of the CN free radical is 2⌺ϩ and there
are two fairly low-lying excited states, A 2⌸ at 1.1 eV and
B 2⌺ϩ at 3.2 eV. Each of these three states has been ob-
served as a product of the HCN dissociation depending upon
the wavelength region of excitation. Analysis by Herzberg
and Innes1 of HCN absorption in the 150–200 nm region
indicated that the lowest-lying excited singlet state of HCN
1
is A A and bent at 125°. The (000)1Ϫ(00°0) origin was
˜
Љ
found at 52 278 cmϪ1 ͑191.29 nm͒. Weak absorption via hot
bands permitted Eng et al.2 to study disposal of ϳ9500 cmϪ1
of excess energy amongst the rovibrational states of
CN(X 2⌺ϩ) after excitation at 193 nm. No production of
3,4
CN(A 2⌸) ͑T0ϭ9116 cmϪ1 ͒ was detected which could
suggest the existence of a barrier in the dissociation coordi-
nate. However, the process is only barely possible energeti-
cally. Ab initio calculations by Peric et al. are in agreement
5
´
1
˜
with the Herzberg and Innes assignment, finding the A A
Љ
state to lie at 54 000 cmϪ1 with a bond angle of 123° and a
barrier to dissociation to CN(A 2⌸) of 3200 cmϪ1
.
Dissociation of HCN with the production of the first
electronically excited ⌺ϩ state of CN is energetically pos-
2
a͒
Electronic mail: sfilseth@yorku.ca
0021-9606/2000/112(20)/8904/6/$17.00
8904
© 2000 American Institute of Physics
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J. Chem. Phys., Vol. 112, No. 20, 22 May 2000
Photodissociation of HCN
8905
duced and then dissociated with 220 nm radiation. The re-
sulting CN(A) fragments are detected by laser induced fluo-
rescence in the B–X violet system after excitation in the
B–A LeBlanc system. The total energy involved in this se-
quential two-photon process is equivalent to a single photon
wavelength of 172 nm and represents about 5300 cmϪ1 of
energy above the energy of the 189 nm threshold. Despite
the available energy, only CN(A, ϭ0) was detected and
v
that only with low-rotational energy.
In the present work we report the first detailed measure-
ments of the rovibrational population distribution of
CN(A 2⌸) formed in the dissociation of HCN at an energy
1
1
˜
˜
above the barriers to dissociation on the A A and B A
Љ
Ј
1
˜
surfaces but below the origin of the C A surface. Consid-
Љ
FIG. 1. Sections of experimental and computed LIF spectra in the ͑2,0͒ band
of the CN(B
Population parameters derived from a multivariate linear regression analysis
of the full experimental LIF spectrum are employed to generate the com-
puted LIF spectrum.
erable excitation of both vibrational and rotational levels is
observed and we compare our results to those for production
of other CN states at other wavelengths.
2
⌺
ϩ –A 2⌸) LeBlanc system beginning at the P22 bandhead.
II. EXPERIMENT
band and extend from the P22(6,5,7) bandhead at 479.49 nm
to the Q11(11) line at 477.76 nm.
The apparatus and data analysis procedure have been
described previously.14 Only an abbreviated description is
given here. Experiments were carried out in a 27 L alumi-
num gas cell. Unpolarized photolysis radiation was provided
at 157 nm by an excimer laser operating on mixtures of F2
A number of preliminary experiments were completed
before LIF spectra of the nascent distribution were acquired.
In experiments carried out with 300 mTorr of HCN in static
or flowing configurations it was found that the LIF signal at
80 ns delay was linear in the 157 nm excimer energy be-
tween about 1 and 10 mJ/cm2. Our experiments were carried
out in that interval. The dependence of the LIF signal on
probe laser energy between pulse energies of 10 and 150 ␮J
was investigated on a series of P, Q, and R lines in the ͑2,0͒
band. Mild saturation behavior was observed and correction
factors were computed based upon an average of the behav-
ior for the several lines. These ͑2,0͒ band factors were ap-
plied to the LIF spectra section by section resulting in cor-
rections of a few percent depending upon the variation in dye
laser energy across a single section of the spectrum.
and He at 25 Hz. Product CN(A, ,N) populations were de-
v
termined, as described previously, from the intensities of
fluorescence in the CN(B–X) system excited by absorption
of tunable dye laser radiation in the CN(B–A) system be-
tween 482 and 460 nm. Laser induced fluorescence ͑LIF͒
spectra were scanned in overlapping sections and joined to-
gether with the aid of repetitive scans over selected lines
taken at the beginning and end of single sections. The probe
laser beam was passed through a wedge depolarizer and
crossed the excimer beam direction at right angle. LIF was
collected on an axis normal to the plane of the two laser
beams. Two complete scans of the CN(A, ,N) product dis-
The time dependence of the CN(A) production and re-
moval was investigated with a fast transient digitizer. The
resolution of this experiment was found to be about 20–25
ns by recording the time dependence of the red atomic fluo-
rine laser light that precedes15 the 157 nm vacuum ultraviolet
͑VUV͒ radiation. This measurement effectively provides a
convolution of the laser pulse waveform and the red-
sensitive photomultiplier tube ͑EMI 9558͒ response function.
Fluorescence from the CN(A) photofragment in the red sys-
tem was separately viewed through color filters at wave-
lengths longer than 710 nm. In experiments with 300 mTorr
of HCN, the red system signal was found to have a rise time
of 20–25 ns and a single-exponential decay time constant of
about 1 ␮s. This decay time is consistent with removal of
CN(A) in collisions with HCN if the rate constant for this
process is comparable to that found by Taherian and
Slanger16 for removal in collisions with C2N2 .
v
tributions were recorded at pressures and probe delay times
of 260 mTorr, 60 ns, and 77 mTorr, 170 ns corresponding to
products of pressure and delay time of 16 and 13 Torr ns,
respectively. Based upon measurements of the population ra-
tio for Nϭ7 and 18 as a function of delay time, we find that
collision-induced relaxation of the nascent distribution has
less than a 5% effect on that distribution under our measure-
ment conditions.
We have previously given a detailed description of a
powerful computer-based multivariate linear regression pro-
cedure developed for the purpose of determining
CN(A, ,N) population distributions from LIF data.14 The
v
complex CN(B–A) LeBlanc system consists of 12 branches
comprising some 2000 separate spectral lines in the wave-
length region covered by our experiment. We recover ϳ200
population parameters through the regression procedure
without resolution of spin or lambda doublets. For the pur-
pose of comparison, Fig. 1 shows a section of the experimen-
tal spectrum ͑ϳ8%͒ together with the corresponding section
of a synthetic spectrum computed from the values of the
fitted population parameters. The sections are from the ͑2,0͒
The LIF detector is a UV ͑ultraviolet͒ photomultiplier
tube ͑EMI 6256͒ and the system time resolution is the same
as that determined for the Red System fluorescence. A weak
background signal was observed with this UV detector in the
absence of probe laser radiation. Measurements with the
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8906
J. Chem. Phys., Vol. 112, No. 20, 22 May 2000
Guo et al.
FIG. 3. Rotational population distribution for the four lowest vibrational
states of CN(A 2⌸) formed in the 157 nm photodissociation of HCN. The
solid line is a result of a phase space calculation for the disposal of 4000
FIG. 2. Dependence of LIF excited in the R(4) line of the ͑0,0͒ band of the
CN(B
photodissociation pulse and the tunable dye laser pulse, PHCNϭ200 mTorr.
2
2
⌺ ⌺
ϩ –X ϩ) violet system on the delay time between the 157 nm
cmϪ1 of energy into CN(A, ϭ0) as described in the text. The dashed line
v
is a Boltzmann function fitted to the CN(A, ϭ0) data.
v
transient digitizer showed that it is formed promptly within
the time resolution of the detector and decays with a time
constant of about 80 ns. Although too weak to be dispersed
for assignment, the time dependence is consistent with
CN(B) fluorescence as the source of this signal. Since pro-
duction of CN(B) in a single photon process is excluded on
energetic grounds, it was expected that this signal would
display a nonlinear dependence on excimer laser energy but
this is not the case. The origin of this signal was not inves-
tigated and it represents a small constant background which
is corrected for in the data analysis procedure.
sis of a sample of the gas showed no detectible contamina-
tion due to C2N2 . In our experiments HCN flowed slowly
through the gas cell and pressures were measured with ca-
pacitance pressure gauges.
III. RESULTS
In initial analyses of the data, F1 , F2 spin–orbit resolu-
tion for ϭ0 was preserved in the fitting procedure but led
v
The LIF from the CN(A) photoproduct is generated in
to distributions for the two components which were not dis-
tinguishable within their precisions. Therefore, this resolu-
tion was not retained in the final data analysis and the results
reported here represent those for the combined spin–orbit
states. As a consequence the number of lines available for
the determination of individual rotational state populations is
doubled. However, for the highest rotational states, and par-
ticularly in the higher vibrational levels, where many lines
lie at wavelengths shorter than the 460.75 nm limit men-
tioned above, there are too few transitions from levels of
very low populations to prevent the return of erratic values
for populations. We have, therefore, limited the population
parameter set employed in the fitting procedure to values of
scans of the probe laser over the ⌬ ϭϩ2 bands of the Le-
v
Blanc system. The long wavelength limit lies at 480.41 nm
corresponding to the O12 branch bandhead of the ͑2,0͒ band.
Data acquisition ends at a short wavelength limit in the ͑5,3͒
band because of interference from overlapping excitation of
the CN(X, ϭ2) LIF at the P-branch bandhead of the violet
v
system at 460.75 nm. Since it is thus evident that CN(X) is
present in these experiments, several time-resolved measure-
ments were made of its production. CN(X) was detected by
tuning the probe laser to the violet system ͑0,0͒ band R(4)
line at 387.32 nm. A typical result is given in Fig. 2 for a
sample of 200 mTorr of HCN flowing slowly through the gas
cell. A single exponential growth function fitted to this data
is characterized by a time constant of about 2 ␮s. Several
experiments are consistent with a zero intercept and we in-
trepret this result as indicating that there is no significant
production of CN(X) as a primary fragment at 157 nm. We
suggest that its observation at later times is a result of radia-
tive decay from the CN(A) state combined with fast
collision-induced rotational energy transfer.
In our experiments HCN was prepared on a separate
vacuum system by dropwise addition of a concentrated aque-
ous solution of KCN into a continuously stirred 1:1 mixture
of concentrated H2SO4/distilled water maintained at 80 °C.
The HCN produced was swept out of the reaction flask and
through a 40 cm column of anhydrous CaCl2 by a slow flow
of N2 gas and collected in a chilled trap at Ϫ78 °C. The HCN
was transferred to the experimental vacuum system as a liq-
uid and stored as a gas in an evacuated flask. Infrared analy-
NϽ63, 50, 45, and 35 for ϭ0 through 3, respectively.
v
The rotational distributions obtained in the analysis de-
scribed above are given in Fig. 3. A Boltzmann function
provides a reasonable description of the distribution, particu-
larly for the bulk of the distribution which lies at values of
NϽ30. We have fitted Boltzmann functions to the two indi-
vidual data sets and to a scaled and merged set. These tem-
peratures are given in Table I. Also given are the vibrational
distributions of the two sets and their average. As is evident
from Table I and Fig. 3 the rotational distributions are very
similar to one another. To further expose this similarity, the
merged data sets for ϭ0, 1, and 2 have been scaled so that
v
the summed rotational populations up to Nϭ45 are equal for
all three levels and then displayed together in Fig. 4. Only
the distribution for ϭ1 departs moderately from those for
v
ϭ0 and 2. Evidently, the mechanism͑s͒ responsible for en-
v
ergy disposal into product vibration and rotation are effec-
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J. Chem. Phys., Vol. 112, No. 20, 22 May 2000
Photodissociation of HCN
8907
TABLE I. CN(A, ,N) distribution from the 157 nm HCN photodissocia-
v
tion.
ϭ0
ϭ1
ϭ2
ϭ3
v
v
v
v
Vibrational distribution ͑%͒
Dataset 1
Dataset 2
Average
39.7
35.6
38Ϯ3
27.3
26.2
27Ϯ1
22.6
24.6
24Ϯ1
10.3
13.6
12Ϯ2
a
Rotational temperature ͑K͒
Dataset 1
Dataset 2
Merged setb
911 ͑24͒
842 ͑31͒
876 ͑20͒
723 ͑22͒
675 ͑18͒
698 ͑14͒
881 ͑25͒
893 ͑20͒
887 ͑19͒
839 ͑52͒
916 ͑65͒
877 ͑42͒
aStandard deviations of the Boltzmann fits are given in parentheses.
bThe summed rotational populations for Dataset 2 were scaled to equal those
for Dataset 1 for each vibrational level and a Boltzmann distribution was
fitted to the merged set.
FIG. 5. A cartoon of several HCN potential-energy surfaces along the C–H
dissociation coordinate. The abscissa gives the displacement in atomic units
1
relative to the equilibrium separation in the ground state, X
⌺
ϩ. The loca-
tion of minima and barriers along the ordinate reflect literature estimates as
described in the text.
tively decoupled from one another and in the discussion
which follows we consider the two separately.
for its existence. Peric et al.21 find that calculated absorption
intensities are inconsistent with the exclusive involvement of
IV. DISCUSSION
A. Energetics
1
˜
transitions to A A . They propose that absorption in the vi-
Љ
cinity of 63 000 cmϪ1 includes contributions from transitions
1
˜
The spectroscopy and photochemistry of HCN have
to the B A state. This is the energy region reached by ab-
Ј
been reviewed by Ashfold et al.17,18 The ground state of
sorption at 157 nm as indicated in Fig. 5. In this cartoon, the
abscissa gives values of the C–H dissociation coordinate in
atomic units relative to the equilibrium separation in the
ground state. The curves themselves are illustrative only and
the vertical scale incorporates experimental values for disso-
ciation limits and barrier heights from ab initio calculations.5
Recent photofragment TOF ͑time-of-flight͒ measure-
ments on DCN dissociation12 have permitted a determination
of the H–CN dissociation energy of 43 740Ϯ150 cmϪ1. With
a value of 9116 cmϪ1 for T0 of CN(A 2⌸),3,4 an energy
threshold for production of CN(A 2⌸) may be calculated of
52 856Ϯ150 cmϪ1. The principal output of the excimer laser
operating on an F2–He mixture consists of a single narrow
͑р1 cmϪ1͒ feature at 157.63 nm with a weaker line at 157.52
nm.22 We may then calculate that the energy available for
disposal in the H and CN(A 2⌸) fragments is 10 600Ϯ150
cmϪ1 ignoring internal energy in HCN.
1
ϩ
˜
HCN is linear X ⌺ while several of the excited states
populated in the vacuum ultraviolet are bent. As a conse-
quence the absorption spectrum is dominated by long pro-
gressions in bending modes. Analysis of the rotationally re-
solved near VUV absorption spectrum by Herzberg and
Innes1 indicates that the first excited singlet is a bent A
Љ
state. A recent ab initio calculation19 in combination with the
experimental value for T0 gives
ϭ53 266 cmϪ1 for the A A state. At wavelengths below
150 nm, preparation of the bent C state is possible and an
extensive bending progression has been observed and ana-
lyzed. The number and identity of states which contribute to
absorption at wavelengths longer than 150 nm has been ex-
tensively debated. Ab initio calculations indicate the pres-
a
value of Te
1
˜
Љ
˜
1
˜
ence of a bent state of A symmetry, B A , in this energy
Ј
Ј
interval but Meenakshi et al.20 find no experimental evidence
It is of interest to determine what fraction of the avail-
able energy lies above the barrier͑s͒ which separate the prod-
ucts from the excited HCN state͑s͒ produced in absorption. If
1
˜
A A is the principal state produced in absorption, two esti-
Љ
mates are possible. Peric et al.5 have found a barrier of 3200
cmϪ1 for dissociation on the A A surface and a value of
1
˜
Љ
2100 cmϪ1 for the separation between the minimum of this
curve and the dissociation limit. Thus we find that the top of
the barrier lies 1100 cmϪ1 above the dissociation limit. More
recent large scale ab initio calculations2,19 have yielded val-
ues between 4400 and 4900 cmϪ1 for the barrier height rela-
1
˜
tive to the A A minimum. This minimum has been located
Љ
at an energy of 53 226 cmϪ1 in the same work and, when
combined with the 52 586 cmϪ1 threshold given above for
2
˜
production of CN(A ⌸) and the HCN(X) zero-point en-
ergy, it permits a calculation of 1600–2100 cmϪ1 for the top
of the barrier relative to the dissociation limit. Alternatively,
FIG. 4. Normalized rotational populations for the three lowest vibrational
states of CN(A 2⌸). The summed populations in the interval 0ϽNϽ45 for
1
˜
ϭ1 and 2 are individually scaled to equal those for ϭ0.
if B A is the excited state reached in absorption at 157 nm,
v
v
Ј
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8908
J. Chem. Phys., Vol. 112, No. 20, 22 May 2000
Guo et al.
where ⑀ and fv are the available energy and the fraction of it
found in vibration of CN(A), respectively. In our calculation
the Franck–Condon factors are integrals, over the interval
R
CNϭ0.5–2.0 Å, of Morse functions generated from spectro-
1
˜
scopic constants for CN( ϭ0,1) in HCN(A A and
v
Љ
26
3,4
B A ) and in CN(A 2⌸). The density of translational
˜
1
Ј
energy states is calculated for an available energy of 10 600
cmϪ1 and the model distributions are included in Fig. 6. It is
clear that the golden rule model is only in reasonable accord
with the measured vibrational distribution when CN(A 2⌸)
1
˜
is produced by dissociation of HCN(B A ) with one quan-
Ј
˜
tum of CN vibration, 3 , excited. We have no basis for
v
preferring this description of the observed vibrational distri-
bution to that provided by the prior distribution. The identity
of the dissociative upper state͑s͒ of HCN at 157 nm cannot
be inferred from our results.
FIG. 6. Vibrational population distribution for the four lowest states of
CN(A 2⌸) produced in the 157 nm photodissociation of HCN. Experimen-
tal distribution, ͑᭺͒. The results of model calculations described in the text:
1. Prior distribution of 9500 cmϪ1 of available energy, ͑᭞͒, 2. Fermi’s
golden rule/FC model with 6600 cmϪ1 of energy available to HCN(A 1A )
˜
Љ
without vibrational excitation ͑᭝͒, 3. Fermi’s golden rule model with 4000
C. Rotational distribution
cmϪ1 of energy available to HCN(B 1A ) with one quantum of CN stretch
˜
Ј
excited ͑ᮀ͒.
As shown in Fig. 3, the rotational distributions for all
vibrational levels are approximately Boltzmann and very
similar to one another. This suggests that the mechanism
responsible for disposal of available energy into fragment
rotation is decoupled from that which determines the vibra-
tional distribution. Elementary arguments based on purely
classical conservation of parent rotation and bending motions
cannot provide the high level of rotational excitation which
we find in the CN(A) distribution. Beswick and Gelbart,27
however, have shown on the basis of zero-order distorted-
wave calculations that the contribution of parent bending to
CN product rotation can be substantial for HCN dissociation
from the ground electronic state. For example, at JHCNϭ10,
even zero-point bending leads to a CN rotational distribution
peaked at Nϭ9 and extending to Nϭ14 at half-maximum.
The CN(A) distributions found in the present work, where
use of the Peric et al.21 calculation permits an estimate of
almost 6600 cmϪ1 for the top of the barrier relative to the
dissociation limit.
B. Vibrational distribution
The dissociation of HCN at 157 nm is accompanied by
the release of 10 600Ϯ150 cmϪ1 of available energy into
fragment degrees of freedom. A substantial amount of this
energy lies above the barriers which separate the fragments
from the A 1A and B 1A states which are candidates for the
Љ
Ј
excited states reached in absorption. With modest available
energy it has often been found that energy disposal can be
described by a prior distribution or some version of phase
space theory.23 Accordingly we have compared our experi-
mental distribution to the prior distribution computed for an
available energy of 9500 cmϪ1. This is the amount of energy
which lies above an 1100 cmϪ1 barrier to dissociation on the
bending levels as high as 2ϭ11 are energetically possible in
v
excited HCN, are peaked near Nϭ12 and extend to NϾ20 at
half-maximum. Even higher levels of rotational excitation
have been found in CN(B) by Ashfold et al.9 when the avail-
able energy is 9700 cmϪ1, which is somewhat lower than
that available in our work.
A 1A surface. As is evident from Fig. 6, reasonable agree-
Љ
ment is found with experiment.
The rotational energy of product CN is evidently not
consistent simply with carry over of the rotation and bending
motions of the parent HCN state according to conservation
principles. This conclusion encourages the consideration of
other descriptions of both dynamical and statistical character
and these have been discussed at length.28 The modified im-
pulse model of Busch and Wilson29 has often been found to
provide reasonable agreement with measured rotational dis-
tributions. In the present case however, the low mass of the
H atom fragment provides little excitation of rotational mo-
tion due to impulsive energy release. Elementary calcula-
tions suggest low-energy, narrow distributions quite unlike
our measured distributions.
An alternative approach is suggested by the good agree-
ment found between a simple golden rule model24 and the
CN(B 2⌺ϩ) vibrational distribution produced by photodisso-
ciation of HCN at wavelengths below 150 nm.10 In such a
model, relative transition probabilities for the formation of
different vibrational states, f, of a diatomic fragment, CN(A)
in this case, from a given initial state, i, of the electronically
*
excited parent, HCN , are calculated from Fermi’s golden
rule as
2
k ϭ 4␲2/h͒
͉
Vif
͉
␳.
͑1͒
͑
if
2
In this expression
͉
Vif
͉
is approximated as a Franck–
Condon vibrational overlap integral between the bound ini-
The contribution to product rotation arising from statis-
tical partitioning between rotation, vibration and translation
of the remaining available energy which lies above the bar-
rier can also be calculated in various ways. The energy-
conserving prior distribution for rotation can be written30 as
tial state wave function i, taken to be the CN oscillator
*
within HCN , and the fragment CN(A) wave function f. The
translational density of states factor ␳ is given25 by
3/2
␳ ⑀͒ϰ ⑀ 1Ϫf ͒
͓ ͑
,
͔
͑2͒
͑
v
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J. Chem. Phys., Vol. 112, No. 20, 22 May 2000
Photodissociation of HCN
8909
1/2
P0 ,N ͒ϰ 2N ϩ1͒ EϪE ϪE
͑v
͒
N
.
͑3͒
find only approximate agreement between the experimental
͑
͑
Ј
Ј
Ј
v
Ј
Ј
rotational distribution for CN(A, ϭ0) and one of several
v
This distribution will peak at a value of N which provides for
equipartition between rotation and translation of the avail-
able energy other than vibrational energy. For the available
energies involved in this work the distributions peak at much
higher values of N than observed in the experiment. In order
to incorporate angular momentum conservation into the sta-
limiting-case models for energy disposal, namely a phase-
space model in which 4000 cmϪ1 of energy is distributed
from a Boltzmann distribution of parent HCN molecules
subject to a constraint on the total angular momentum. The
agreement is not so satisfactory as to encourage application
to other vibrational states.
A more satisfactory understanding of the mid-VUV pho-
todissociation of HCN awaits further theoretical and experi-
mental progress on the roles of the two excited singlet states
of HCN which can be reached at these energies.
tistical model, we have compared our CN(A 2⌸, ϭ0,N)
v
distribution with that predicted by the simple phase space
theory ͑PST͒ of Pechukas and Light.31 We test our imple-
mentation of PST by reproducing the distribution reported by
Pechukas and Light for OH(A) formed in the 121.6 nm pho-
todissociation of H2O. A constraint to a maximum value of
total angular momentum is achieved by our choice of the
value for the C6 coefficient in a Lennard-Jones potential.
Based upon literature values for dipole moments, ionization
potentials and polarizabilities, we compute32 a value of 8.3
eV Å6 for C6 . Calculations were carried out at six values of
ACKNOWLEDGMENTS
This research has been supported by the Natural Sci-
ences and Engineering Research Council of Canada and by
York University.
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J
HCN in the interval Jϭ0–24 and for two values of available
energy: ͑a͒ 9500 cmϪ1 corresponding to dissociation from
HCN(A A ) with a reverse barrier of 1100 cmϪ1, and, ͑b͒
1
˜
3 D. Cerny, R. Bacis, G. Guelachvili, and F. Roux, J. Mol. Spectrosc. 73,
154 ͑1978͒.
Љ
4000 cmϪ1 for dissociation from HCN(B A ) with a reverse
1
˜
Ј
4 A. J. Kotlar, R. W. Field, J. I. Steinfeld, and J. A. Coxon, J. Mol. Spec-
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At., Mol. Clusters 5, 65 ͑1987͒.
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8 L. C. Lee, J. Chem. Phys. 72, 6414 ͑1980͒.
energy, the PST distributions for rotation in CN(A, ϭ0) are
v
broadly flat-topped for all JHCN which is not in agreement
with our experimental distribution shown in Fig. 3. When the
energy available for disposal is limited to 4000 cmϪ1, rather
better agreement is achieved with experiment when a
weighted distribution over JHCN is taken for comparison.
9 See for example, M. N. R. Ashfold, M. T. Macpherson, and J. P. Simons,
Chem. Phys. Lett. 55, 84 ͑1978͒ and references therein.
10 A. Mele and H. Okabe, J. Chem. Phys. 51, 4798 ͑1969͒.
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v
13 C. R. Bucher and K. K. Lehmann, Chem. Phys. Lett. 294, 173 ͑1998͒.
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ment is only approximate, however, and overemphasizes
populations in the Nϭ15–30 interval at the expense of those
for NϾ30. Klippenstein and Marcus33 have observed that,
for energies well above threshold, PST is expected to over-
estimate the distribution of excess energy into rotation.
15 M. Takahashi, K. Maeda, T. Kitamura, M. Takasaki, and S. Horiguchi,
Opt. Commun. 116, 269 ͑1995͒.
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V. SUMMARY
18 M. N. R. Ashfold, D. H. Mordaunt, and S. H. S. Wilson, Adv. Photochem.
21, 217 ͑1996͒.
We report the first measurements of the rovibrational
population distribution of the CN(A 2⌸) product of the 157
nm photodissociation of HCN in a gas cell experiment. We
find reasonable agreement between the experimental vibra-
tional distribution and, ͑a͒ a prior distribution based upon the
availability of 9500 cmϪ1 of energy as would be the case if
energy disposal was determined by statistical release of the
energy above a reverse barrier of 1100 cmϪ1 as has been
19 P. Botschwina, M. Horn, M. Matuschewski, E. Schick, and P. Sebald, J.
Mol. Struct.: THEOCHEM 400, 119 ͑1997͒.
20 A. Meenakshi, K. K. Innes, and G. A. Bickel, Mol. Phys. 68, 1179 ͑1989͒.
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͑1988͒.
22 T. J. McKee, Phys. Can. 36, 41 ͑1980͒.
23 T. Baer and W. L. Hase, Unimolecular Reaction Dynamics ͑Oxford Uni-
versity, New York, 1996͒, Chap. 9.
24 M. J. Berry, Chem. Phys. Lett. 29, 329 ͑1974͒.
25 M. J. Berry, Chem. Phys. Lett. 29, 323 ͑1974͒.
1
˜
computed for dissociation from HCN(A A ), or, ͑b͒ a
Љ
26 J. F. Stanton and J. Gauss, J. Chem. Phys. 100, 4695 ͑1994͒.
27 J. A. Beswick and W. M. Gelbart, J. Phys. Chem. 84, 3148 ͑1980͒.
28 R. Schinke, Photodissociation Dynamics ͑Cambridge University Press,
Cambridge, 1993͒.
simple Franck–Condon golden rule model in which the full
10 600 cmϪ1 exoergicity is available to products from disso-
1
˜
ciation of HCN(B A ) with a single quantum of CN stretch
excited. We find no basis for preferring one of these models
to the other.
The rotational distributions of three of the four vibra-
tional levels are very similar to one another and approxi-
mately Boltzmann with temperatures near 900 K. The tem-
Ј
29 G. E. Busch and K. R. Wilson, J. Chem. Phys. 56, 3626 ͑1972͒.
30 R. D. Levine and R. B. Bernstein, Molecular Reaction Dynamics and
Chemical Reactivity ͑Oxford University Press, New York, 1987͒.
31 P. Pechukas and J. C. Light, J. Chem. Phys. 42, 3281 ͑1965͒; P. Pechukas,
J. C. Light, and C. Rankin, ibid. 44, 794 ͑1966͒.
32 J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird, Molecular Theory of
Gases and Liquids ͑Wiley, New York, 1954͒.
perature found for CN(A, ϭ1) is about 200 K lower. We
33 S. J. Klippenstein and R. A. Marcus, J. Phys. Chem. 92, 5412 ͑1988͒.
v
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