NO μ-v-j correlations in the photofragmentation of 2-chloro-2-nitrosopropane

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NO ␮-v-j correlations in the photofragmentation

of 2-chloro-2-nitrosopropane

Radoslaw Uberna,^a⁾Robert D. Hinchliffe,^b⁾and Joseph I. Cline

Department of Chemistry and Chemical Physics Program, University of Nevada, Reno, Nevada 89557-0020

͑

Received 16 August 1996; accepted 9 September 1996͒

2

The trajectory of NO X ⌸_⍀_ϭ₁_/₂_,₃_/₂(vϭ0) produced after excitation of 2-chloro-2-nitrosopropane

˜

1

S₁A AЉ is studied by polarized 1ϩ1Ј resonance-enhanced multiphoton ionization with

time-of-ﬂight mass spectrometry detection. The correlations among the NO velocity v, angular

˜

1

˜

0

1

momentum j, and the S A AЉ←S X AЈ ͓n͑N͒,␲*͑NvO͔͒ transition dipole ␮ of the parent

1

molecule are measured. The dissociation occurs by internal conversion to the ground S state or

0

˜

intersystem crossing to the T₁a AЉ state and the observed speed distribution of the NO fragments

3

is bimodal. There is no evidence for ␮-v-j correlations for the products associated with the slow

component of the speed distribution. For the higher speed component, the v-j correlation is a

0

function of the NO rotational state, j, and is described by the bipolar moment ␤ ͑22͒. The average

0

value of ␤ ͑22͒ is Ϫ0.17͑Ϯ0.02͒ at jϷ11.5–22.5, more than ﬁve times larger than predicted by

statistical phase space theory for dissociation on the S X AЈ surface, indicating a moderate

˜

1

0

preference for a perpendicular orientation of the NO rotational angular momentum and velocity

vectors. The v and j vectors are nearly uncorrelated for low NO rotational states ͑jр6.5͒. The ␮-v

2

correlation described by the ␤ ͑20͒ bipolar moment does not change with j and its average value is

0

2

0

Ϫ0.04͑Ϯ0.01͒ at jϷ12.5–19.5. The average value of the ␤ ͑02͒ bipolar moment describing ␮-j

correlation is 0.04͑Ϯ0.02͒ at jϷ7.5–24.5. These results are consistent with a mechanism involving

3

both impulsive force due to a barrier along the reaction coordinate on the T₁

˜

a AЉ surface and

Institute of Physics. ͓S0021-9606͑96͒03546-5͔

I. INTRODUCTION

kanes is dominated by dissociation to nitric oxide and an

alkyl radical. More recent photodissociation studies of ni-

2

The reaction dynamics of large molecules is commonly

assumed to be typiﬁed by statistical energy distributions.

When the reaction mechanism is truly statistical its dynamics

is expected to be sensitive only to the gross features of the

molecular potential. Recent studies of the photodissociation

of some relatively complex molecules show that, even in the

presence of apparently statistical populations of energy lev-

els, correlations among the vector properties of the dissocia-

tion dynamics can be clearly nonstatistical. These correla-

tions offer additional information about the potential surface

and reaction mechanism. Since the mapping of potential sur-

faces by spectroscopic measurement of eigenstates is gener-

ally infeasible for large molecules, the inversion of such dy-

namical data may provide a practical means to probe

chemically interesting regions of the potential surface.

Here we report on our continuing study of the photo-

fragmentation dynamics of 2-chloro-2-nitrosopropane ͑here-

trosoalkanes in the gas phase show that simple dynamical

models, based on energy conservation, cannot accurately

4

model the observed rotational distributions. The optically

˜

1

prepared S A AЉ state of the nitrosoalkanes diabatically

1

correlates to excited state products; an avoided crossing pro-

duces a high barrier to dissociation to the alkyl radical and

nitric oxide in their ground electronic states. It is generally

agreed that the dissociation mechanism involves internal

˜

1

conversion or intersystem crossing from S X AЉ electronic

1

˜

1

state followed by predissociation on the S X AЈ or T₁

0

3

˜

a AЉ electronic surfaces.

Experiments at low excess energy

3

–5

͑less than about

200 cm above the ground-state dissociation limit͒ show

1͒ that fragmentation lifetimes are on the microsecond time

scale; ͑2͒ that the NO X ⌸₁_/₂_,₃_/₂(vϭ0) rotational distribu₆-

tions can be well modeled by statistical phase space theory;

͑3͒ that spin–orbit ratios are nearly always nonstatistical,

with an anomalously high ⍀ϭ1/2 population; and ͑4͒ the

Ϫ1

1

͑

2

˜

1

˜

1

after abbreviated CNP͒ following S₁A AЉ←S X AЈ

0

͓

n͑N͒,␲*͑NvO͔͒ excitation. This molecule provides a trac-

dissociation energies, D , required for consistency between a

table system for the study of vector correlations in large mol-

ecule reactions. We have discussed elsewhere the unique fea-

tures making CNP, and the chloronitrosoalkanes in general,

0

statistical model and experimentally observed NO rotational

Ϫ1

distributions range from 13 500 to 14 500 cm . At higher

1

excess energies the dissociation lifetime decreases to the

nanosecond time scale and the NO rotational distribution be-

of special utility in such experiments. Early work showed

the 600–700 nm, n→␲* photochemistry of the nitrosoal-

3,7

comes slightly nonstatistical. In ͑CH ͒ CNO, the largest

3

nitrosoalkane for which gas-phase dynamics have been re-

ported to date, this nonstatistical behavior appears above a

distinct energy threshold with a concomitant decrease in dis-

a͒

Present address: JILA, University of Colorado, Boulder, CO 80309-0440.

Present address: Technical Visions, Inc., 14000 S.W. Karl Braun Drive,

Beaverton, OR 97077.

b͒

J. Chem. Phys. 105 (22), 8 December 1996

0021-9606/96/105(22)/9847/12/$10.00

9847

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9848

Uberna, Hinchliffe, and Cline: NO ␮-v-j correlations

7

˜

1

˜

1

sociation lifetime. Noble et al. attribute this effect to the

length within the continuum S₁A AЉ←S X AЈ

0

opening of a dominant dissociation channel on the T sur-

͓n͑N͒,␲*͑NvO͔͒ absorption of CNP. ͑2͒ The polarized

1

˜

1

3

face. Both the S X AЈ and T

˜

a AЉ surfaces of the ni-

probe laser is tuned to a single resolved rotational line in the

0

1

2

ϩ

2

trosoalkanes correlate to the same product electronic states at

inﬁnite product separation. The T₁

have a low barrier to dissociation and this energy barrier

must be overcome for dissociation to occur by the T

A ⌺ ←X ⌸ (vЉϭvЈϭ0) band of the nascent NO. ͑3͒

⍀

3

2

ϩ

˜

a AЉ state is believed to

These NO A ⌺ molecules, originating from the probed NO

2

X ⌸ (vЉϭ0,jЉ) product, are ionized and the one-

dimensional projection of NO X ⌸ ͑vЉϭ0, jЉ) velocity dis-

tribution onto a detection axis is obtained from the NO

arrival transients measured in pulsed-extraction TOF mass

spectrometry. ͑4͒ The pump and probe laser polarizations are

varied to study their effect on the shapes of the NO TOF

⍀

2

1

⍀

3

,7

ϩ

channel.

Our recent measurements¹^,⁸^,⁹of NO translational and ro-

tational distributions produced in the photodissociation of the

gem-nitrosoalkane CNP are at relatively high excess energies

ϩ

and are sensitive to products appearing on a relatively short

These studies revealed bimodal

product speed distributions that are correlated with the NO

transients.

time scale ͑Ͻ20 ns͒.¹

,10,11

A. Sample delivery and vacuum system

rotational quantum number, j. Given the previous work on

Our two-chamber molecular beam vacuum apparatus

and the preparation of 2-chloro-2-nitrosopropane ͑CNP͒

have been previously described,¹but we have since made

several improvements to the sample delivery system. In the

present experiments He carrier gas was bubbled through the

CNP sample held in a Teﬂon sample cell maintained at 0 °C.

With the exception of the stainless steel pulsed nozzle, the

CNP sample was only exposed to glass, Teﬂon, and polyeth-

ylene materials. This procedure allows a chloronitrosoalkane

sample to be used with little decomposition over many days

of experiments. The gas mixture of He and CNP was ex-

panded into the source chamber through a pulsed solenoid

valve source with a 0.5 mm diameter nozzle. Careful studies

of the stagnation pressure dependence of experimental sig-

nals showed the presence of some clustering in the molecular

beam. Evidence for contamination by cluster species was the

appearance of a large fraction of low velocity NO photodis-

sociation products. At stagnation pressures less than 350

Torr there was no evidence for cluster formation at any time

during the valve pulse. As a further test the observed signal

was compared to that obtained from a glass capillary effusive

source as well as that obtained from a pulsed nozzle expan-

sion with 1000 Torr of backing pressure. Based upon a com-

parison to these two limits, and with no evidence for delay-

dependant structural differences, it was clearly established

that the nozzle operating conditions used in this experiment

were sufﬁcient to achieve expansion cooling of the CNP with

no or very little condensation.

͑

CH ͒ CNO, it is natural to assign the two velocity groups as

3 3

,10

arising from the S and T dissociation channels of CNP. In

0

1

Refs. 1 and 10 we proposed a qualitative model for the CNP

dissociation mechanism involving both surfaces that is con-

1

sistent with the experimental data. In this model, dissocia-

tion across the T barrier generates impulsive recoil forces

1

resulting in correlated distributions of NO translation and

rotation ͑scalar v-j correlation͒. Such a mechanism would

produce a characteristic NO vЌj vector correlation inconsis-

11

tent with a simple statistical fragmentation mechanism. In a

8

recent communication we reported a vЌj correlation of NO

͑

jϭ18.5 and 22.5͒ from CNP photodissociation at 650 nm.

Here we report the complete measurements and analysis

of the vector properties of the nuclear trajectories of nascent

NO from CNP dissociation. The experiments are performed

in a molecular beam and the rotational alignment of indi-

vidual NO rotational states is probed by polarized, two-color,

resonance-enhanced multiphoton ionization ͑1ϩ1Ј REMPI͒

with coincident velocity analysis by pulsed-extraction time-

of-ﬂight ͑TOF͒ mass spectrometry. The experiments de-

scribed in this study investigate CNP photochemistry at

wavelengths shorter than 670 nm and are sensitive only to

those molecules which dissociate on a time scale shorter than

20 ns. We describe several improvements in the experimen-

tal technique which, when coupled with a semiclassical

method to obtain the bipolar moments of the correlated v-j

distribution from this data,¹²allow the measurement of even

the very small ␮-v and ␮-j vector correlations of the NO

product. Finally, we discuss the interpretation of these vector

correlations in terms of our previous dynamical model for

CNP fragmentation, the expectations of PST constrained by

the conservation of vectorial angular momentum, and the

general features of large molecule photofragmentation dy-

namics.

The CNP sample was found to contain very small

amounts of NO, presumably from sample decomposition. In

TOF measurements this impurity NO appears as a narrow

peak having a width corresponding to the instrumental speed

resolution and typically contributes a few percent of the total

intensity, though on weaker NO transitions the contribution

can reach 10%.

II. EXPERIMENT

B. Lasers and optics

The experiments are of the pump–probe type using po-

larized nanosecond pulsed lasers and are conducted in a mo-

lecular beam. The velocity dependence of the angular mo-

mentum polarization, which contains the measurable

signature of NO v-j correlation, is measured by the following

scheme: ͑1͒ The photolysis laser is set at a ﬁxed wave-

Figure 1 shows a schematic representation of the optical

components of the experiment. Each measurement cycle

contained a sequence of three light pulses: A dissociation

pulse at 650 nm, a probe pulse at approximately 226 nm, and

an ionization pulse at 308 nm. All light pulses were ulti-

mately derived from a single Nd:YAG laser ͑6 ns pulses, 10

J. Chem. Phys., Vol. 105, No. 22, 8 December 1996

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Uberna, Hinchliffe, and Cline: NO ␮-v-j correlations

9849

laser pulses present and in the correct temporal sequence. In

some cases a weak background signal from NO impurities is

observed in the absence of the dissociation pulse; this impu-

rity signal is readily identiﬁed because it has a TOF width

corresponding to the speed resolution of our apparatus.

The dissociation and probe pulses were linearly polar-

ized and the laboratory orientation of their polarization axes

were controlled either by half-wave plates or a photoelastic

modulator ͑Hinds model PEM-90͒. The laboratory-frame po-

larization angle of one pulse was ﬁxed and the polarization

angle of the other pulse varied by the data acquisition com-

puter. This was achieved by synchronizing the data acquisi-

tion process with the 50 kHz resonant frequency of the PEM.

A data acquisition cycle was initiated every 5000 PEM os-

cillations for a data acquisition rate of 10 Hz. The relative

timing of the molecular beam pulse, ﬁring the Nd:YAG laser

ﬂashlamps and Q-switch, and TOF extraction pulse were

constant. The computer selected the temporal phase shift of

FIG. 1. Optical system for pump–probe studies of CNP photodissociation

with 1ϩ1Ј REMPI-TOFMS detection of the NO photoproduct. Pump and

probe dye lasers: DL1, DL2; polarization rotator: ␭/2; vacuum chamber:

VC; multichannel ion detector D; molecular beam: MB; photoelastic modu-

lator: PEM; Pellin–Broca prism PB; wavelength separator/combiner: WSC.

the laser Q-switch pulse within a PEM oscillation cycle to

13,14

achieve the desired polarization angle.

In most experi-

ments this polarization angle was alternated between two

values on successive laser pulses, allowing temporally inter-

leaved acquisition of signals at multiple laser polarizations

and thereby minimizing signal variation due to drifts in

source conditions, laser power, and other experimental pa-

rameters that are difﬁcult to control.¹⁴The variable polariza-

tion angle was ﬁxed immediately before the photolysis

chamber and laser pulses enter the chamber nearly orthogo-

nal to a fused silica window.

Hz repetition rate͒ which was frequency doubled and tripled.

A tunable dye laser pumped by the Nd:YAG 532 nm second

harmonic produced the linearly polarized, 7 mJ dissociation

pulse at 650 nm. The Nd:YAG 355 nm third harmonic was

split into two beams. The minor fraction ͑20%͒ was directed

into a second tunable dye laser to produce a linearly polar-

ized pulse at approximately 450 nm. The 450 nm pulse was

frequency doubled in ␤-barium borate to produce the tun-

able, Ͻ50 ␮J probe pulse at 224–227 nm. The probe pulse

was separated from the dye laser fundamental using four

Brewster angle prisms in a mirror image conﬁguration such

that the spatial location of the isolated probe beam axis is

independent of its wavelength. The spectral resolution of our

probe dye laser is sufﬁciently low to cover the whole Dop-

pler width of the probe transition. This is necessary in order

C. Physical and polarization geometry

As in our previous experiments on CNP dissociation, the

propagation direction of the molecular beam, the laser

beams, and the axis of the TOF mass spectrometer were

mutually orthogonal. The formal mathematical description of

the experimental geometry is deﬁned using the convention of

12

our previous theoretical analysis of ␮-v-j correlation mea-

ϩ

that the NO TOF transient is uniformly sensitive to all NO

velocities.

The major fraction ͑80%͒ of the 355 nm light was di-

rected into a 60 cm long stainless steel tube with fused silica

surements by REMPI/TOF mass spectrometry and is not

given here. Three laboratory-frame polarization geometries,

labeled cases 2, 3, and 4 in Table III of Ref. 12, were used in

the present experiments. For case 2 the dissociation pulse

windows containing H gas at 60 psi. The ﬁrst-order anti-

ˆ

2

polarization ⑀ is parallel to the detection axis k ͑along the

d

D

Stokes stimulated-Raman pulse at 308 nm was separated

from the 355 nm pump pulse and the other Stokes and anti-

Stokes Raman frequencies by a Pellin–Broca prism. The 308

nm ionization pulse energy was approximately 1 mJ and had

a poorly deﬁned polarization state. The probe and ionization

beams are spatially overlapped using a harmonic separator

made of four Brewster prisms. The probe/ionization beam

was weakly focused in the photolysis vacuum chamber, in-

tersecting the 650 nm dissociation beam at a very small

angle. This spatial intersection deﬁned a volume where CNP

molecules can be dissociated and the NO fragments probed.

Simple optical delay lines were used to control the temporal

sequence of the three pulses. Within a given acquisition

cycle, tϭ0 is deﬁned by the dissociation laser pulse. The

probe and ionization pulses were delayed by 10 and 15 ns,

respectively. No dissociation signal was obtained without all

TOF mass spectrometer͒, and the probe pulse polarization ⑀_p

ˆ

is orthogonal: ⑀_d

ʈ

k Ќ⑀ . For cases 3 and 4 the polarization

D p

ˆ

D

geometries are ⑀_d

ʈ

⑀ Ќk and ⑀ k Ќ⑀ , respectively. Tem-

ʈ

p

D

p d

porally interleaved data sets were collected for cases 2 and 3

by alternating the dissociation pulse polarization angle and

for cases 3 and 4 by alternating the probe pulse polarization

angle.

D. Time-of-ﬂight mass spectrometry

ϩ

The NO ions were accelerated from the interaction re-

gion by a high-voltage extraction pulse delayed tϭ2 ␮s from

the dissociation laser pulse. The extracted ions traveled

through a standard Wiley–McLaren time-of-ﬂight mass

spectrometer with a 66 cm long ﬁeld-free ﬂight path and

were subsequently detected by a large area microchannel

J. Chem. Phys., Vol. 105, No. 22, 8 December 1996

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9850

Uberna, Hinchliffe, and Cline: NO ␮-v-j correlations

plate ͑Galileo model TOF-2003͒. The time-of-ﬂight distribu-

tion of these ions was measured by a 300 MHz digital oscil-

loscope ͑LeCroy model 9361͒ with an effective temporal

resolution of 1 ns/sample. Each ion arrival transient was ana-

lyzed using a discrimination threshold and individual ion de-

tection events were assigned to a single 1 ns wide bin. Signal

pulse energy. In our data analysis we assume the full satura-

ϩ

1

ϩ

2 ϩ

tion of the NO X ⌺ ←NO A ⌺ ionization transition.

The two-color, 1ϩ1Ј REMPI NO detection scheme de-

scribed here and ﬁrst reported in Ref. 8, has additional ad-

vantages over the more common 226 nm, one-color 1ϩ1

REMPI probing of NO. The 308 nm ionization wavelength

ϩ

1 ϩ

averaged NO TOF transients were constructed by summing

more efﬁciently produces the continuum X ⌺ state of

ϩ

the results from 5000–30 000 laser shots. The amplitude of

these summed ion arrival transients has units of absolute ion

counts and the summed transients have nearly zero back-

ground.

NO . Chloronitrosoalkanes have no signiﬁcant absorbance

at 308 nm and there is no detectable probe induced dissocia-

tion of CNP in our 1ϩ1Ј scheme. Such probe-induced dis-

sociation is a common problem when high energy 226 nm

ϩ

5,8

The NO TOF can be expressed as an analytic function

pulses are used for 1ϩ1 REMPI probing. A similar two-

of ␯ , the projection of the NO fragment velocity along the

color REMPI scheme using a 280 nm ionization wavelength

has been developed by Kolodney et al. We believe the

ZЉ

ˆ

5

TOF detection axis, ZЉ. The TOF is a parametric function of

ϩ

the NO ion charge, its mass, and instrumental voltages and

method reported here is signiﬁcantly easier to implement us-

ing with Nd:YAG pumping. Another NO 1ϩ1Ј REMPI de-

tection scheme was recently reported¹⁷that is essentially

equivalent to one used here and in previous experiments in

1

ϩ

dimensions. We transform the raw NO TOF transients ob-

tained when probing the NO product rotational j, and using

geometry case n, into a distribution function, D (j,␯ Љ), of

n

Z

8

the NO product velocity projection, ␯ Љ. The D (j,␯ ) are

our lab, but the 308 nm ionization pulse is produced by an

Z

n

ZЉ

directly analogous to Doppler proﬁles and can be analyzed

by application of the standard tools of Doppler spectroscopy.

The transformation is performed using the procedure de-

scribed in the Appendix of Ref. 1. Finally, the amplitude of

excimer laser.

III. RESULTS

the D (j,␯ ) distributions is scaled to account for ␮-j cor-

n

ZЉ

A. Parametrization of correlated probability

distribution

relation ͑rotational alignment͒ using the procedure described

in Sec. III B.

Information about the correlated distribution function of

v and j, F͑v,j͒, for the NO fragment is obtained from a

simultaneous measurement of the projection of the NO ve-

E. 1؉1Ј REMPI probe of NO

ˆ

Saturation of the resonant transition is a common difﬁ-

culty that limits the utility of 1ϩ1 REMPI techniques for

detailed dynamical measurements.¹⁵In particular, saturation

diminishes observed anisotropy of the correlated photofrag-

ment v-j distribution. To minimize this effect it is necessary

to use low probe pulse energy and this can greatly decrease

the quality of the experimental signal. Therefore single-

color, 1ϩ1 REMPI techniques are unsuitable for measure-

ments of the fragment vector correlations. The probe and

ionization steps of the detection process are separated in

multiple-color techniques, such as 1ϩ1Ј REMPI. This per-

mits very low probe pulse energies. To avoid saturation of

locity distribution onto the TOF-MS detection axis k , and

D

the projection of the NO angular momentum distribution

onto the polarization vector of the probe laser ⑀ . In practice,

p

this is obtained by a study of the polarization dependence of

the shape of D (j,␯ ) transients. Extracting the F͑v,j͒ dis-

n

ZЉ

tribution from these data is a challenging inverse problem

12,18,19

that has been discussed elsewhere.

The techniques of

can, in principle, be used to invert

the D (j,␯ ) data to extract the underlying correlated dis-

Doppler spectroscopy²

0–22

n

ZЉ

tribution of v and j, making no assumptions about the func-

tional form of F͑v,j͒. Unfortunately, relatively small uncer-

tainties in the measured D (j,␯ ) result in a large

n

ZЉ

2

ϩ

2

the NO A ⌺ ←X ⌸ (vЉϭvЈϭ0) transition, the energy

uncertainty in the distribution function obtained in an uncon-

strained inversion procedure. This is the case for the present

data.

⍀

of the 226 nm probe pulse was less than 15 ␮J. Data ob-

tained with the probe pulse energy higher than 50 ␮J pro-

duced approximately 50% lower values of the v-j correlation

moment for a Q-type transition in the NO photoproduct than

for the P- or R-type transitions. The Q-type transitions satu-

rate more easily than other transition types with correspond-

ing value of j due to the higher values of the line strength

factors. In a present experiment the results produced for R-

and Q-type transitions are identical, indicating the probe step

is free of saturation.

We instead assume a functional form for F͑v,j͒ which

depends on a set of adjustable parameters and incorporates

physically realistic simpliﬁcations and constraints. The pa-

rameters are optimized to obtain the best ﬁt to the experi-

mental data in a forward convolution procedure. The result-

ing distribution function is not a rigorously unique solution

to the inversion problem; it is merely consistent with the

experimental data.

1

6

To remove alignment effects from the intermediate reso-

Ignoring the possibility of quantum interference among

the product states, we expand the semiclassical NO product

distribution function F͑v,j͒ into a sum of distributions

2

ϩ

nant NO A ⌺ state, a high energy, unpolarized ionization

1

2

pulse is desired. Our ionization pulse is weakly polarized

Ͻ50% of linear polarization͒ and its average power is ap-

ˆ

͑

F ͑v,j͒ for each rotational state, j, of the NO product, aver-

j

proximately 1 mJ. There was no detectable correlation of the

REMPI signal intensity with ﬂuctuations in the ionization

aged over the coincident internal states of the chloropropyl

fragment

J. Chem. Phys., Vol. 105, No. 22, 8 December 1996

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Uberna, Hinchliffe, and Cline: NO ␮-v-j correlations

9851

ˆ

^F^͑^v^,^j^͒^ϭ͚_j

b F ͑v,j͒.

͑1͒

j

In Eq. ͑1͒, b is the fractional population of rotational state j,

j

1,9

previously measured elsewhere. In Ref. 1 the bimodal NO

speed distribution was interpreted as arising from distinct

dissociation channels on the S and T electronic surfaces of

0

1

CNP. In this previous model the lower speed group arises

from S dissociation and the higher speed group from T₁

0

dissociation. Extending the model of Ref. 1, the functional

form of our product distribution function includes terms for

both dissociation channels

1

₆_␲2

ˆ

͓c^͑^S^͒f^͑^S^͒͑␯͒P^͑^S^͒͑ vˆ ,j͒ϩc f^͑^T^͒͑␯͒

ˆ

͑T͒

F ͑v,j͒ϭ

j

1

ϫP^͑͑ vˆ ,j͔͒.

T͒

ˆ

͑2͒

In Eq. ͑2͒, c⁽^S⁾and c⁽^T⁾are the fractional populations of the

S and T dissociation channels, respectively, and satisfy the

0

1

(

S)

(T)

constraint c ϩc ϭ1. In addition, Eq. ͑2͒ assumes the dis-

tribution function for channel ␨ can be written as a separable

product of component distributions for NO product speed,

FIG. 2. One-dimensional velocity distributions, D (j,␯ ) measured prob-

͑␨͒

ˆ

n

ZЉ

f

͑␯͒, and spatial anisotropy, P ͑ vˆ ,j͒. The simpliﬁcations

ing the Q₂₂ϩR₁₂branch transitions of nascent NO using ͑a͒ geometry case

3 and ͑b͒ geometry case 4. The D (j,␯ ) functions for different j are offset

due to this important assumption of separability have been

n

ZЉ

discussed elsewhere.²

0,23

Since the slower speed component

Ϫ5

Ϫ1

by 4.0ϫ10 ͑m/s͒ . The photodissociation wavelength was ␭ ϭ650 nm.

d

in D (j,␯ ) exhibits no measurable dependence on the po-

n

ZЉ

larization geometry, we assume there are no vector correla-

(

S)

ˆ

f^͑^␨^͒͑␯͒ϭk₁exp͓Ϫk₂͑␯Ϫ␯^͑₀^␨^͒͒²͔,

͑␨͒

tions for the S dissociation channel ͓i.e., P ͑ vˆ ,j͒ϭ1͔.

0

ˆ

Given the functional form of F ͑v,j͒ in Eq. ͑2͒, we use

j

1

/2

␲

Eq. ͑3͒ of Ref. 12 for the case of linearly polarized probe

light to obtain the velocity projection distribution function

͑␨͒

^ϭ⁴^k2

͑␨͒

͑␨͒ ͑␨͒2

k

²^␯0 ^e^x^p^͑^Ϫ^k2

␯

͒ϩ

1

ͭ

0

ͩ

͑␨͒

2

ͪ

k

D ͑ j,␯ ͒ϭc^͑^S^͒D ^͑^j^,^␯Z ͒ϩc^͑^T^͒^D ^͑n^T^͒^͑^j^,^␯Z

͑S͒

͒

͑

␨͒ ͑␨͒2

͑␨͒

2

n

Z

n

ϫ͑1ϩ2k

␯

͓͒1ϩerf͑␯₀

ͱ

k

͔͒ ,

Љ

2

0

ͮ

ϱ

␯

1

ϭ

͵

ͩ

c^͑^S^͒f^͑^S^͒͑␯͒ϩc^͑^T^͒f^͑^T^͒͑␯͒

4 ln͑2͒

͑

␨͒

2

␯

͉

k

ϭ

,

͑4͒

ZЉ

2

_␯͑␨͒

⌬

1

͑

␨͒

͑␨͒

ϫ A ͑ j,␯ /␯͒Ϫ h^͑²^͒͑ j͓͒A ͑ j,␯ /␯͒

0

2

0

^w^h^e^r^e^␯0 is the center speed and ⌬ ␯ is the FWHM.

ͭ

Z

Љ

2

The P⁽^T⁾͑ vˆ ,j͒ distribution gives the angular vector cor-

ˆ

relations of the T channel NO product and is most naturally

written using the bipolar harmonic formalism of Dixon.

bipolar harmonic parametrization of the vector correlations

1

2

␯²d␯,

18

Ϫ3A₂_ϩ͑ j,␯ /␯͔͒

ͪ

͑3͒

A

ZЉ

ͮ

k

where the A (j,␯ ) are the spherical tensor moments of the

q

ZЉ

angular distribution of j in the frame of the probe beam and

is a depolarization factor depending upon j and the

branch of the probing transition. For probe transitions of

͑

2͒

h

12

͑2͒

mixed R/P and Q character, h is replaced by the effective

͑

2͒

(2)

Q

(2)

quantity h ϭS h ϩS_Rh_R, where S and S are the rela-

eff

Q

R

tive H o¨ nl–London factors.²⁴Having now obtained

ˆ

D (j,␯ ) for F ͑v,j͒, we next consider the detailed form of

n

ZЉ

j

its speed and vector correlation components.

Reference 1 shows that the NO speed distribution is bi-

modal and that the contribution of the higher speed group

increases with NO angular momentum, j. The bimodal speed

distribution is clearly evident in the D (j,␯ ) distributions

n

ZЉ

(

T)

in Fig. 2 and Fig. 3 shows the j-dependence of c . We

FIG. 3. The j dependence of the high speed component of the NO popula-

tion distribution assigned to the T₁dissociation of CNP at 650 nm. Error

bars are 95% conﬁdence limits.

͑␨͒

write each component, f ͑␯͒, of the speed probability den-

sity as a normalized Gaussian function⁹

J. Chem. Phys., Vol. 105, No. 22, 8 December 1996

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9852

Uberna, Hinchliffe, and Cline: NO ␮-v-j correlations

imposes no loss of generality, as the nature of the probing

process naturally restricts the amount of information in the

experiment to a speciﬁc set of bipolar harmonics.¹²However,

the assumption of separability does not allow for speed de-

pendence of the bipolar moments.¹

2,25

In the present experi-

ment, as in related Doppler experiments,²⁶the data can be

very closely modeled without consideration of any speed de-

pendence of the bipolar moments.

The bipolar moments are most conveniently obtained

from the difference between D (j,␯ ) measured at two dif-

n

ZЉ

ferent polarization geometries as discussed in Ref. 12. Ex-

pressing the spherical tensor moments in Eq. ͑3͒ in terms of

bipolar moments, the difference function for polarization ge-

ometries 2 and 3 is

Q₂_–₃͑ j,␯_Z_Љ͒ϭD ͑ j,␯_Z_Љ͒ϪD ͑ j,␯_Z_Љ

͒

2

3

ϱ

1

6

5

ϭc^͑

T͒

f^͑^T^͒͑␯͒

Ϫ

h

͑2͒

␤ ͑02͒

2

͵

ͫ

eff

0

FIG. 4. One-dimensional velocity distributions, D2(j,␯Z ) and D3(j,␯Z ),

Љ Љ

2

␯

͉

␯

͉

and Q₂_–₃(j,␯_Z) difference functions, probed on the R₂₂͑12.5͒ and

ZЉ

Љ

Q₂₂ϩR₁₂͑12.5͒ transitions of the NO photofragment ͑␭ ϭ650 nm͒. The

d

9

5

symbols ᭺ and ᭹ indicate geometry cases 2 and 3, respectively. The solid

line in the lower panel is a ﬁt to Eq. ͑5͒. Error bars are 95% conﬁdence

2

0

͑2͒

2

0

ϩ3␤ ͑20͒P ͑␯ /␯͒Ϫ

␤ ͑42͒

2

ZЉ

eff

limits obtained from Poisson counting statistics for a single point. Errors

2

associated with ␤ ͑20͒ are 95% conﬁdence limits obtained from the ﬁt.

0

ϫP ͑␯_Z_Љ/␯͒

ͬ

␯²d␯,

͑5͒

4

For the R₂₂branch the sign is positive at ␯ ϭ0 and negative

ZЉ

and for geometries 3 and 4 it is

for large ͉␯ ͉; the opposite is observed for the Q ϩR

ZЉ

22

12

2͒

͑

Q₃_–₄͑ j,␯_Z_Љ͒ϭD ͑ j,␯_Z_Љ͒ϪD ͑ j,␯_Z_Љ

͒

branch. This effect is expected due to the sign of the heff

3

4

depolarization factor for different probe transitions. The ob-

ϱ

1

6

5

_ϭ_c͑

T͒

_f͑T͒͑␯͒

͑2͒

eff

2

served sign of Q₃(j,␯ ) indicates a vЌj correlation

–4 ZЉ

͵

ͫ

h

␤ ͑02͒

0

2

͉

ZЉ

␯

͓␤ ͑22͒Ͻ0͔. We ﬁrst reported this vЌj preference in Ref. 8.

0

͉

v

Note that the shape of D (j,␯ ) in Fig. 4 is different

3

ZЉ

9

͑

2͒

0

͑2͒

eff

2

0

from that in Fig. 5. The reason for this difference is that the

overlap angle between the dissociation and probe/ionization

Ϫ3h ␤ ͑22͒P ͑␯ /␯͒Ϫ

h

␤ ͑42͒

eff

2

ZЉ

5

ϫP ͑␯_Z_Љ/␯͒

ͬ

␯²d␯.

͑6͒

4

B. Qualitative data analysis

Figure 4 shows D (j,␯ ) distributions ͑nϭ2,3͒ and the

n

ZЉ

Q₂_–₃(j,␯ ) difference functions measured when probing

ZЉ

the R ͑12.5͒ and Q ϩR ͑12.5͒ transitions of NO

2

22

12

2

⌸₃_/₂

͑␯ϭ0͒. These geometry cases correspond to the disso-

ciation pulse polarized either parallel or perpendicular to the

TOF detection axis ͑see Sec. II C and Ref. 12.͒ In Fig. 4 the

sign of Q₂_–₃(j,␯ ) is positive at ␯ ϭ0 and negative at

ZЉ

large ͉␯ ͉, a qualitative indication of a ␮Ќv correlation

ZЉ

2

0

͓

␤ ͑20͒Ͻ0͔ that is consistent with the perpendicular charac-

˜

1

˜

0

1

ter of the S A AЉ←S X AЈ ͓n(N),␲*͑NvO͔͒ transition

1

of CNP. Note that the sign and the amplitude of Q₂(j,␯ )

–3

ZЉ

are independent of the rotational branch of the probe transi-

tion.

The D (j,␯ ) ͑nϭ3,4͒ distributions and the

n

ZЉ

^Q³–4(j,␯ ) difference function in Fig. 5 were obtained for

ZЉ

FIG. 5. One-dimensional velocity distributions, D (j,␯ ) and D (j,␯ ),

3

ZЉ

4

ZЉ

the R ͑12.5͒ and Q ϩR ͑12.5͒ transitions of NO

and Q₃_–₄(j,␯ ) difference functions, probed on the R₂₂͑13.5͒ and

2

22

12

ZЉ

2

^Q22^ϩ^R12͑12.5͒ transitions of the NO photofragment ͑␭ ϭ650 nm͒. The

⌸₃_/₂

͑␯ϭ0͒. These geometry cases correspond to the probe

d

symbols ᭹ and ᭺ indicate geometry cases 3 and 4, respectively. The solid

line in the lower panel is a ﬁt to Eq. ͑6͒. Error bars are 95% conﬁdence

pulse polarized either perpendicular or parallel to the TOF

detection axis ͑see Sec. II C and Ref. 12͒. The sign of

limits obtained from Poisson counting statistics for a single point. Errors

0

Q₃_–₄(j,␯ ) depends on the branch of the probe transition:

associated with ␤ ͑22͒ are 95% conﬁdence limits obtained from the ﬁt.

ZЉ

J. Chem. Phys., Vol. 105, No. 22, 8 December 1996

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Uberna, Hinchliffe, and Cline: NO ␮-v-j correlations

9853

components,²²the D (j,␯ ) distributions in Figs. 4 and 5

TABLE I. Measured bipolar moments for NO ͑vϭ0͒, averaged over mea-

surements on different probe branches, from the 650 nm photodissociation

of 2-chloro-2-nitrosopropane.

3

ZЉ

are different. In Figs. 4 and 5, the fractions of the higher

speed NO component are c⁽ϭ0.90 and 0.99, respectively.

However, since the slow component shows no polarization

dependence, it does not contribute to the difference functions

used to extract vector correlations.

T)

2

0

j

␤ ͑20͒

␤ ͑22͒

0

3

5

6

7

8

9

0.5

1.5

2.5

3.5

6.5

8.5

9.5

0.5

1.5

2.5

.5

Ϫ0.015 ͑Ϯ0.014͒

Ϫ0.037 ͑Ϯ0.012͒

0.025͑Ϯ0.040͒

Ϫ0.006͑Ϯ0.050͒

Ϫ0.048͑Ϯ0.018͒

Ϫ0.106͑Ϯ0.026͒

Ϫ0.107͑Ϯ0.020͒

Ϫ0.114͑Ϯ0.016͒

Ϫ0.112͑Ϯ0.015͒

Ϫ0.144͑Ϯ0.010͒

Ϫ0.171͑Ϯ0.011͒

Ϫ0.190͑Ϯ0.019͒

Ϫ0.159͑Ϯ0.018͒

Ϫ0.188͑Ϯ0.014͒

Finally, the integrated amplitudes of the D (j,␯ ) for

n

ZЉ

nϭ2,3, and 4 are nearly the same, but a quantitative analysis

shows small, consistent differences which indicate a slight

2

0

preference for a ␮

ʈ

j correlation ͓␤ ͑02͒տ0͔.

1

2

Ϫ0.037 ͑Ϯ0.010͒

Ϫ0.040 ͑Ϯ0.024͒

Ϫ0.047 ͑Ϯ0.010͒

Ϫ0.047 ͑Ϯ0.012͒

Ϫ0.037 ͑Ϯ0.018͒

C. Quantitative description of vector correlations

The procedure for the quantitative analysis of the data

consists of the following steps: ͑1͒ the proper amplitude scal-

ing of the raw TOF transients; ͑2͒ determination of the speed

parameters for each photodissociation channel, ␨; and ͑3͒

Ϫ0.155͑Ϯ0.040͒

Ϫ0.158͑Ϯ0.028͒

ﬁtting experimental Q

(j,␯ ) difference functions to ex-

m–n

ZЉ

Ϫ0.049 ͑Ϯ0.022͒

2

0

tract the ␤ ͑02͒ and ␤ ͑22͒ moments. We now consider each

0

step in detail.

1

. Scaling the amplitude of the TOF transients

beams in the experimental setup used to collect the data in

Fig. 4 ͑ϳ2.5°͒ is larger than the overlap angle used in Fig. 5

2

In the absence of ␮-j correlation ͓␤ ͑02͒ϭ0͔ the inte-

0

͑ϳ1°͒. Because of the reduced spatial overlap of the two

grated amplitudes of two distributions, D (j,␯ ) and

n ZЉ

laser beams in the data of Fig. 4, the intensity of the true NO

signal from CNP photodissociation is a smaller fraction of

the total NO intensity than in Fig. 5. This effect is due to the

background NO signal mentioned in Sec. II A which appears

as a slow component in the NO speed distribution. Since the

D (j,␯ ), obtained in a single set of experimental measure-

m ZЉ

27

ments ͑e.g., nϭ2, mϭ3 or nϭ3, mϭ4͒ are unity. Thus, ␮-j

correlation is present if raw TOF transients collected for ge-

ometry cases n and m on a single rotational transition have

different integrated intensities S and S . By integrating Eq.

n

m

qualitative shape of the D (j,␯ ) distribution is very sensi-

tive to even small variations in the fraction of the slow NO

͑3͒ and using Eqs. ͑A3͒–͑A6͒ of Ref. 12, the integrated am-

plitude of D (j,␯ ) for linearly polarized probing is

n

ZЉ

n

ZЉ

ϱ

S_n

N

͑

eff

2͒

2

0

ϭ

͵

D ͑ j,␯ ͒d␯ ϭ1ϩh ͑ j͒a ␤ ͑02͒,

͑7͒

n

Z

n

Љ

Ϫϱ

where a is a constant which depends on the geometry case

n

n (a ϭa ϭϪ4/5,a ϭ2/5), and N is an instrumental scal-

2

4

3

ing parameter. Measurement of TOF transients at two or

2

0

more geometries allows N and ␤ ͑02͒ to be obtained by the

solution of simultaneous equations of the form of Eq. ͑7͒.

The raw TOF transients are then scaled by N to obtain the

properly normalized D (j,␯ ). The NO ␮-j correlation ob-

n

ZЉ

served from CNP dissociation is very small: The average

2

0

value of ␤ ͑02͒ measured for jϭ7.5–24.5 is 0.04Ϯ0.02.

2. Speed parameters

The ﬁve parameters of the speed function, ␯ ^S⁾, ␯

(

(T)

,

0

⌬ ⁽

␯

S)

, ⌬␯ , and c , are optimized by ﬁtting Eq. ͑3͒ to the

(T)

experimental D (j,␯ ) distribution using nonlinear least

n

ZЉ

squares optimization. In the ﬁrst iteration physically reason-

able values of the bipolar moments are used. Later, after

2

0

optimization of ␤ ͑02͒ or ␤ ͑22͒, the speed parameters are

reoptimized. The speed parameters are quite insensitive to

the values of the bipolar moments over a wide range of

2

0

2

0

FIG. 6. Measured NO bipolar moments ␤ ͑20͒ and ␤ ͑22͒ as a function of j

␤ ͑02͒ and ␤ ͑22͒, and self-consistency is usually achieved

0 0

for the 650 nm photodissociation of CNP. Data points labeled ᭺ were mea-

sured on NO R₂₂branch transitions and ᭹ indicates Q₂₂ϩR₁₂probe transi-

tions. Error bars are 95% conﬁdence limits. Phase-space theory ͑PST͒ pre-

dictions and quantum mechanical ͑QM͒ and classical limits are shown for

comparison.

after two iterations.

The central speed ␯₀_a_n_d_t_h_e_w_i_d_t_h_⌬_␯(T) of the NO

(T)

product speed distribution for the T channel are nearly in-

1

dependent of j and their average values obtained for 12 dif-

J. Chem. Phys., Vol. 105, No. 22, 8 December 1996

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Uberna, Hinchliffe, and Cline: NO ␮-v-j correlations

ferent transitions at jϷ3.5–22.5 are respectively 1202͑Ϯ73͒

IV. DISCUSSION

(

S)

m/s and 472͑Ϯ125͒ m/s. The average values of ␯ and

0

A. Critical evaluation of the measured bipolar

moments

(

S)

⌬␯

are respectively 17͑Ϯ15͒ m/s and 492͑Ϯ133͒ m/s. The

(

S)

low precision of ␯₀arises from its small value. As noted by

Gordon and Hall,²²the shape of the Doppler proﬁle for a

Gaussian speed distribution is not very sensitive to the cen-

The focus of this study is to use the vector properties of

the NO product trajectory to infer a dissociation mechanism

for CNP. Several phenomena complicate the interpretation of

the measured bipolar moments that parameterize the vector

properties. Some of these effects are related to fundamental

deﬁciencies in our probing scheme: ͑1͒ unresolved hyperﬁne

structure in the probe spectrum of NO will diminish the ap-

parent rotational polarization and ͑2͒ our data analysis

scheme ͑Ref. 12͒ assumes semiclassical dynamics of the NO

product. Other phenomena, though integral components of

the CNP dissociation dynamics, obscure the mechanistic in-

formation we seek: ͑3͒ the contribution of the initial CNP

angular momentum to the rotational excitation of the prod-

ucts and ͑4͒ motion of the energized CNP molecule during

its ﬁnite dissociation lifetime. Here we consider each of these

phenomena for the experimental results obtained in Sec. III.

tral speed ␯ when the ratio of the central speed to the

0

FWHM is less than unity. The fractional population of the T

1

(

T)

dissociation channel, c , depends on j, in accord with our

1

(T)

earlier study. Figure 3 shows c as a function of j for the

D (j,␯ ) distributions ͑nϭ3,4͒ shown in Fig. 2. For mod-

n

ZЉ

erate and high j the fraction of the S dissociation channel

0

becomes insigniﬁcant. This effect further diminishes the sen-

sitivity of D (j,␯ ) to the parameters associated with the

n

ZЉ

lower speed group.

Our preliminary studies of NO v-j correlation in CNP

photodissociation were reported in a previous communica-

8

tion for jϭ18.5 and 22.5. That paper used a simpliﬁed form

for f͑␯͒ which included only one dissociation channel and

assumed only v-j correlation was present, ignoring the bimo-

dal character of the NO speed distribution and the very small

velocity and rotational alignment. In addition, as discussed in

Sec. II A, the earlier data was found to include a stagnation-

pressure dependent contribution, apparently due to CNP

clusters, which is not present in the data reported here. The

0

1. Quantum restrictions on ␤ (22)

The bipolar harmonic treatment of vector correlations

from Ref. 8 is based on Dixon’s semiclassical formulation of

the correlated angular v-j probability distribution. Quantiza-

tion of the angular distribution of j is severe for low NO

product angular momenta and the semiclassical approxima-

measured v-j correlations in Ref. 8 were diminished by these

0

effects: The analysis of the newer data gives a ␤ ͑22͒ value

about 30% larger than that reported previously.

tion becomes poor. The quantum mechanical limits on

0

␤

͑22͒, calculated using Eq. ͑8͒ of Ref. 29, are indicated by

the dotted line in Fig. 6. Our values are do not exceed this

physical restriction. Carleton and co-workers²⁹have shown

that Doppler proﬁles calculated using the quantum mechani-

2

0

3

. Determination of the ␤ (20) and ␤ (22) moments

0 0

30

cal density matrix method of Hall, et al. and the semiclas-

The optimized speed parameters are used to ﬁt experi-

18

sical method of Dixon are nearly identical even for the

2

mental difference Q

␤

(j,␯ ) functions to obtain ␤ ͑20͒ or

m–n

ZЉ 0

lowest values of j. Thus we expect the semiclassical analysis

0

͑22͒. The amplitude of Q (j,␯ ) gives the velocity

alignment, ␤ ͑20͒. The amplitude of Q (j,␯ ) gives the

lowest order moment of the v-j correlation, ␤ ͑22͒. The

͑42͒ moment, associated with the fourth-order Legendre

0

2–3

ZЉ

to introduce relatively little error into the ␤ ͑22͒ determina-

2

0

3–4

ZЉ

tion.

0

2

0

␤

function, P (␯ /␯), is expected to be very small. An F-test

4

ZЉ

2

. Hyperﬁne structure depolarization

28

signiﬁcance analysis conﬁrms the data is not sensitive to

2

0

␤

͑42͒.

Nuclear spin coupling will depolarize j measured on a

hyperﬁne-unresolved probe transition.¹

tion effect reduces the apparent values of ␤ ͑22͒ and ␤ ͑02͒

by a factor of 1/

hyperﬁne splitting ␻ , and the time ␶ between CNP dis-

8,31,33

This depolariza-

The best ﬁt to the experimental Q₂_–₃(j,␯ ) and

ZЉ

0

2

Q₃_–₄(j,␯ ) is represented by the solid line in Figs. 3 and 4.

ZЉ

0 0

2

0

2

g (j). The quantity g (j) depends upon the

¯ ¯

(2)

Table I and the upper panel of Fig. 6 show ␤ ͑20͒ as a

function of NO j. The values of ␤ ͑20͒ are, within experi-

2

0

FFЈ

p

mental error, independent of j and the probed branch for

sociation and absorption of the probe photon. Expressions

2

(2)

Ϫ1

jϭ7.5–22.5. The average value of ␤ ͑20͒ measured for

for

been given₃previously for probing by natural

¯

g (j) in the limits ␻ Ӷ␶_pand ␻ ӷ␶_phave

0

FFЈ FFЈ

seven different transitions is Ϫ0.04͑Ϯ0.01͒. The fact that

1,32

quite strong polarization effects in Fig. 4 correspond to very

ﬂuorescence.

For large j the effect of nuclear spin cou-

2

0

small values of ␤ ͑20͒ demonstrates the high sensitivity of

pling is negligible.

The ¹⁴N O molecule has nuclear spin Iϭ1. For low j

16

our method to this moment₀.

The j dependence of ␤ ͑22͒ is shown in Table I and the

the ground electronic state of NO is well described by

0

Hund’s case ͑a͒³

3,34

and I couples directly to j according to

lower panel of Fig. 6. At low j the NO v and j vectors are

35

uncorrelated or show a slight preference for v

ʈ

j correlation.

the ͑a ͒ coupling scheme of Townes and Schawlow to

form FϭIϩj. In our experiment ␻ is on the order of ␶_p

¯

͑␶ ϳ10 ns͒. We have calculated g (j) for the NO jу3.5

p

␤

0

Ϫ1

At moderate to high j the value ␤ ͑22͒ is negative ͑vЌj

0

FFЈ

36

(2)

correlation͒, reaching an average value of Ϫ0.17͑Ϯ0.02͒ at

eleven different transitions in the 11.5рjр22.5 range.

levels probed in this experiment. The depolarization effects

J. Chem. Phys., Vol. 105, No. 22, 8 December 1996

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Uberna, Hinchliffe, and Cline: NO ␮-v-j correlations

9855

resulting from nuclear spin coupling are very small and

much less than the experimental uncertainty of the measure-

ment.

uct is predominately due to the torque applied in the disso-

ciation dynamics and not parent angular momentum.

The tangential relative velocity of the fragments associ-

ated with the orbital angular momentum l in case ͑ii͒ above

will contribute to the measured ␮-v correlation. Within this

idealized parent molecule model, the center-of-mass frame

velocity of fragment 1 is ͉v ͉ϭ͉l͉/m R and is directed perpen-

3. Partitioning of parent angular momentum between

the products

1

dicular to the orientation of the symmetry axis at the instant

Product rotational state population distributions are com-

2

0

of dissociation. The measured ␤ ͑20͒ moment is diminished

monly used to probe the torques applied in dissociation dy-

namics. If the parent molecule is nonrotating, or if its rota-

tional state is completely speciﬁed, the interpretation of

product rotational distributions is relatively straightforward.

If there is a distribution of parent molecule rotational states

the analysis is greatly complicated by the partitioning of par-

ent molecule angular momentum among the rotational de-

grees of freedom of the products and orbital angular momen-

tum. For large parent molecules, even at the low rotational

temperatures attained in supersonic molecular beams, the ini-

tial rotational distribution is quite broad. In such a case it

may become difﬁcult to cleanly connect measured fragment

v-j and ␮-j correlations to torques that are characteristic of

the dissociation mechanism. Here we use kinematic argu-

ments to show the NO product angular momentum in the

dissociation of CNP is only slightly inﬂuenced by the initial

parent angular momentum: The measured NO rotational

population distribution is overwhelmingly determined by

torques applied in the dissociation process. This result is a

general feature of the kinematics of dissociation processes

giving two products with greatly disparate moments of iner-

tia.

from that for the nonrotating parent molecule by a factor f,

which can be roughly approximated using the diatomic

model of Jonah.³⁸In rotationally cold molecular beams the

magnitude of this effect is small³⁹͑fϷ0.98 for CNP͒.

4. Dissociation lifetime

In an instantaneous photodissociation event the product

␮-v, ␮-j, and ␮-v-j correlations are clear indications of the

directionality of recoil forces developed in the fragmentation

process. This mechanistic information is reduced if the dis-

sociation lifetime of the energized parent molecule is on the

2

0

order of its rotational period. The ␤ (k k ) moments are

1 2

functions of the rotational reorientation of the parent mol-

ecule.

Yang and Bersohn showed how the velocity alignment

depends on the parent molecule angular frequency and dis-

sociation lifetime.³⁹Unfortunately we have no reliable mea-

surement of the CNP lifetime and Yang and Bersohn do not

provide an analytic expression for the rotational reorientation

dependence of the velocity alignment in asymmetric top

molecules such as CNP ͑asymmetry parameter ␬ϭ0.47͒. An

Consider the dissociation of an idealized parent mol-

ecule with angular momentum J consisting of two rigid

spherical top components initially separated by a distance R.

The components have masses m and m , and rotational mo-

upper limit on the magnitude of this effect can be made using

the pseudodiatomic model,³

8–40

in which the departing frag-

1

2

ments of inertia I and I . Angular momentum conservation

ments are treated as point masses connected by the dissoci-

ating bond.

1

2

in the dissociation requires that Jϭj ϩj ϩl, where j and j

1

2

1

2

are angular momenta of the two fragments and l is the orbital

angular momentum.

Within this diatomic model the velocity alignment can

2

be expressed as ␤ ͑20͒ϭ␤ ͑20͒* D͑␶͒, where ␶ is the disso-

0

To focus on the contribution of J to j and j , we assume

ciation lifetime.⁴¹The function D͑␶͒ depends upon the angu-

1

2

no torques are imparted in the dissociation process: All prod-

uct angular momentum arises from simple conservation con-

straints. We consider the two limiting orientations of J

within the body-ﬁxed frame of the idealized parent molecule:

lar frequency of the rotating molecule and has been given by

St. Pierre and Steele⁴⁰and others.

38,39

The function D͑␶͒ de-

creases with ␶ and D͑0͒ϭ1. In analogy with the deﬁnition of

2

␤ ͑20͒, ␤ ͑20͒*ϭ͗P ͑ ␮ˆ ͓tϭt*͔• vˆ ͓tϭϱ͔͒͘ corresponds to the

0

2

velocity alignment in an idealized frame speciﬁed by the

orientation of the rotating CNP molecule at the instant of

fragmentation, t*. The quantity ␤ ͑20͒* is more directly

͑i͒

If J is parallel to the symmetry axis, the angular mo-

mentum of fragment i is j ϭJ I /(I ϩI ) and the

i

1

2

42

2

0

orbital angular momentum l is zero. Note that for

I ӶI , j ϳ0.

2

0

related to the dissociation mechanism than ␤ ͑20͒ since it is

1

2

1

ideally free of the effects of parent molecule rotational reori-

entation.

͑ii͒

If J is perpendicular to the symmetry axis, the angular

2

momentum of fragment i is j ϭJ I /(I ϩI ϩ␮R ),

i

1

2

In the ␶→ϱ limit, D͑␶͒ asymptotically approaches 1/4

where ␮ϭm m /(m ϩm ), and the orbital angular

1

2

1

2

0

for the diatomic model. The average value of ␤ ͑20͒ for NO

2

momentum is lϭJ ␮R /(I ϩI ϩ␮R ). Note that for

1

2

from CNP photodissociation in an effusive 293 K ﬂow is

2

I ӶI ϩ␮R , j ϳ0.

1

2

1

43

only 5% less than in a supersonic expansion. This implies

2

0

Using this simple kinematic analysis to treat the frag-

the ␤ ͑20͒ measurements are nearly independent of the rota-

mentation of CNP to chloroisopropyl radical and NO prod-

ucts, the angular momentum of CNP at 40 K contributes on

average approximately one ប of angular momentum to the

tional temperature, so that D͑␶͒ is near the limit of 1/4. With

this assumption of inﬁnite lifetime, we have the bound

2

0

2

0

␤ ͑20͒*р4␤ ͑20͒ϭϪ0.16͑Ϯ0.02͒. This value is indicative

3

7

NO product. Thus the angular momentum of the NO prod-

of a preference for ␮(tϭt*)Ќv correlation and is consistent

J. Chem. Phys., Vol. 105, No. 22, 8 December 1996

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9856

Uberna, Hinchliffe, and Cline: NO ␮-v-j correlations

with the perpendicular orientation of the CNP S →S tran-

sive recoil picture for the excitation of NO translation and

rotation as the dissociating molecule accelerates from the T₁

barrier.

1

0

sition dipole and the C–N bond.

This procedure can be extended further to obtain a

2

angular

momentum

alignment

moment, ␤ (02)*

Even within a statistical dissociation model, angular mo-

mentum constraints associated with the orbital angular mo-

0

ˆ

ϭ

͗

2

P ͑ ␮ˆ [tϭt*]•j͓tϭϱ͔͒͘, in an idealized frame at the in-

44

11,49

stant of dissociation. Docker et al. used the azimuthally

mentum will result in a ͑generally weak͒ vЌj correlation.

45

averaged addition theorem

to show that the ratio

͑02͒/␤ ͑20͒ is unaffected by rotational reorientation and

Klippenstein and Cline studied this source of NO vЌj corre-

2

0

2

0

␤

lation for the ‘‘barrierless’’ dissociation of CNP within a

1

depends only on the fragmentation dynamics. Following Ref.

statistical PST model for dissociation on the S surface.

0

2

0

4

4, we have ␤ ͑02͒*ϭ␤ ͑20͒*͓␤ ͑02͒/␤ ͑20͔͒. This proce-

The PST value of ␤ ͑22͒ from Ref. 11 is shown in Fig. 6͑b͒

0

2

dure gives the limit ␤ ͑02͒*у0.16͑Ϯ0.09͒, indicative of a

as a function of j. For the most probable NO rotational state

the experimentally measured magnitude of the v-j correlation

is more than ﬁve times greater then the PST prediction. This

discrepancy provides a good evidence for a presence of

strong dynamical effects in the dissociation of CNP and is a

signature of mechanistic information. Again, the most likely

origin of these effects is the dynamical constraints imposed

0

preference for ␮(tϭt*)

j. This value is consistent with a

ʈ

dissociation mechanism corresponding to impulsive recoil

from a transition state that retains some memory of the CNP

S →S transition dipole being initially perpendicular to the

1

0

C–N–O plane.

in the barrier crossing on the T surface exit channel.

B. ⌳-doublet states of NO

1

Any preference for NO product rotation in the C–N–O

plane of CNP suggests a selective population of the

D. Summary: A model for the CNP dissociation

mechanism

⌳

-doublet states of the NO product.⁴⁶Nonstatistical NO

-doublet populations have been observed for other, more

3,47

As outlined in Sec. I and described in detail in Ref. 1,

the extensive previous literature on the S1←S0 photodisso-

ciation of the nitrosoalkanes provides the basis for under-

standing the detailed scalar and vector correlation measure-

ments we have made of the photodissociation of CNP. The

earlier literature focussed primarily on the appearance times

and rotational distributions of the NO product, and the con-

sensus of those studies is that ͑1͒ the dissociation occurs on

direct, photodissociations,

but not in the slow fragmenta-

_t_i_o_n_s_o_f_n_i_t_r_o_s_o_a_l_k_a_n_e_s_.3

The NO vector correlations from CNP were measured by

probing the R and Q ϩR branches of the NO

2

22

12

2

ϩ

2

A ⌺ ←X ⌸₃_/₂(vЉϭvЈϭ0) band. The R₂₂branch transi-

tions probe the ⌸͑AЈ͒ ⌳-doublet state and Q ϩR branch

22

12

46,48

transitions probe the ⌸͑AЉ͒ ⌳-doublet state of NO.

As

shown in Figs. 6͑a͒ and 6͑b͒ there is no difference in the

vector correlations of the two ⌳-doublet states within experi-

mental error. We examined the population ratio

Rϭ⌸(AЉ)/⌸(AЈ) of the two NO ⌳-doublet states obtained

from the total intensity of Q ϩR (j), R (j), R (j), and

Ϫ9

Ϫ6

the 10 to 10 s time scale, ͑2͒ the optically prepared S₁

state decays by intersystem crossing to T or internal conver-

1

sion to S , ͑3͒ dissociation near the energy threshold occurs

0

mainly on the S surface with NO rotational distributions

0

22

12

22

21

well modelled by statistical PST, and ͑4͒ at higher energies

the NO rotational distributions show some deviation from

PST predictions and the dissociation lifetime decreases, pre-

R ϩQ (j) transitions divided by appropriate H o¨ nl–

1

21

London factors. The results did not show any systematic

-doublet preference ͑Rϭ1.1Ϯ0.8͒. The large conﬁdence

⌳

sumably due to the opening of the T channel for dissocia-

1

limits on R is an indication of the unsuitability of 1ϩ1Ј

REMPI spectroscopy for the measurement of absolute inten-

sity on different transitions and branches.

tion. The gross features of the NO product state distributions

from CNP are similar to those seen in the earlier studies for

other nitrosoalkanes. The broad rotational and translational

distributions reported in Ref. 1 are consistent with extensive

and essentially statistical distribution of the available energy

C. vЌj correlation within statistical models for CNP

dissociation

following decay of the S state and prior to fragmentation.

1

We previously measured NO rotational distributions and

The present, more detailed measurements of the NO scalar

and vector correlations show that, for CNP at 650 nm, the

deviations from a purely statistical dissociation mechanism

are substantial. As discussed in Sec. I, the bimodal transla-

tional energy distribution is consistent with the participation

of both the S and T dissociation channels and that the T

bimodal scalar speed distributions and scalar v-j correlations

1

from CNP dissociation. Though the rotational distributions

are qualitatively consistent with a statistical dissociation

mechanism, the bimodal speed distributions are not. In Ref.

we proposed a crude statistical phase space theory ͑PST͒

1

0

1

model for the fragmentation process that accounts for the

channel is the predominate source of the more highly excited

rotational states of the NO product. We have no meaningful

information about stereodynamical preferences of the low

potential barrier in the exit channel of the T surface. The

1

most important feature of that model is that the T barrier

1

energy is not available for vibrational excitation of the chlor-

oisopropyl radical and NO products and instead predomi-

nately appears in their rotational and translational excita-

tions. Our initial vector vЌj correlation for NO reported in

Ref. 8 was interpreted to be consistent with a simple impul-

speed NO assigned to the S channel because of the limited

speed resolution in our experiment.

The process of ‘‘inverting’’ the measured NO trajectory

to further constrain the CNP dissociation mechanism is a

formidable challenge. In Sec. V A we considered a number

0

J. Chem. Phys., Vol. 105, No. 22, 8 December 1996

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Uberna, Hinchliffe, and Cline: NO ␮-v-j correlations

9857

of complicating phenomena and showed that, despite the

slow dissociation lifetime, wide range of parent molecule

initial states, and limitations in the probing process, the NO

product vector correlations must indeed be sensitive to the

recoil forces developed during the CNP fragmentation. As

discussed in Sec. V A there is a very small, but measurable

NO ␮Ќv correlation. This result is consistent with both the

perpendicular character of the S ←S transition and the ex-

barrier is responsible for generating the observed

j-dependent vЌj vector correlation and positive v-j scalar

correlation. We ﬁnd that the details ͑e.g., j dependence͒ of

the vЌj correlation do result from the interplay of the recoil

force from the T₁barrier and the restoring force of the

C–N–O angle bending potential at the transition state.

We conclude by suggesting it may be generally possible

to use the vector correlations of a product molecule to extract

at least limited mechanistic information about large molecule

reactions, even when the gross features of the product state

distributions are apparently statistical. In examining the im-

portant angular momentum properties of a fragmentation

process, the study of the smaller product molecule is advan-

tageous not only due to the practical simplicity of its probing

but also due to the general kinematics of the breakup of the

transition state.

1

0

pected slow dissociation rate of CNP. The NO v-j correlation

is not concealed by rotational reorientation of the energized

CNP molecule prior to fragmentation and it provides the

most useful mechanistic information. In an absolute sense

the observed preference for vЌj is only moderate. For the

0

higher NO rotational states ␤ ͑22͒ is only about 34% of the

0

minimal value of ␤ ͑22͒ϭϪ1/2. However, this degree of vЌj

correlation is much larger than that expected for a simple

statistical dissociation mechanism and some underlying

mechanistic phenomena must generate this stereodynamical

preference. The vЌj correlation is consistent with a impul-

sive recoil force applied to the nitrogen atom as the nascent

ACKNOWLEDGMENTS

The authors wish to thank Kazuhiko Fukui for many

helpful discussions on dissociation dynamics of nitrosoal-

kanes, Patrick Pisano for several improvements to the data

acquisition software, and Walt Weaver for technical support.

Acknowledgment is made to the Donors of the Petroleum

Research Fund, administered by the American Chemical So-

ciety, for the support of this research. Financial support from

the National Science Foundation is gratefully acknowledged

under Cooperative Agreement OSR-9353227.

NO molecule recoils from T barrier. An alternative expla-

1

nation is that extensive excitation of C–N–O angle bending

motion at the transition state is efﬁciently coupled to NO

product rotation. It is even more difﬁcult to provide a quali-

tative interpretation for the increase of the vЌj correlation

with j shown in Fig. 6, though one might expect large rota-

tional excitation to accompany highly directional torques that

establish the vЌj correlation. The ␮-j correlation is also sen-

sitive to CNP reorientation. The measured ␮

indeed very weak, but is clearly nonzero. As discussed in

Sec. IV A, this implies the ␮ j correlation is signiﬁcant in a

frame attached to the rotating, energized CNP molecule. The

ʈ

j correlation is

1

J. L. Tomer, M. C. Wall, B. P. Reid, and J. I. Cline, J. Chem. Phys. 102,

6100 ͑1995͒.

ʈ

2

J. G. Calvert and J. N. Pitts, Photochemistry ͑Wiley, New York, 1966͒,

Chap. 5-5G; The Chemistry of the Nitro and Nitroso Groups edited by H.

Feuer ͑Interscience, New York, 1969͒; B. G. Gowenlock, J. Pfab, and G.

Kresze, J. Chem. Soc. Perkin Trans. II 1974, 511; D. Forrest, B. G. Go-

wenlock, and J. Pfab, ibid. 1978, 12.

H. Reisler, M. Noble, and C. Wittig, in Molecular Photodissociation Dy-

namics, edited by M. N. R. Ashfold and J. E. Baggot ͑Royal Society of

Chemistry, London, 1987͒, Chap. 5.

0

simultaneous vЌj ␮ correlation implied by ␤ ͑22͒Ͻ0 and

͑20͒Ͼ0 suggests the CNP transition state retains some

memory of the torsional conﬁguration about the C–N bond

at the instant of photon absorption. Nonetheless, we do not

see strong evidence of nonstatistical ⌳-doublet populations

ʈ

0

2

0

␤

3

4

R. W. Jones, R. D. Bower, and P. L. Houston, J. Chem. Phys. 76, 3339

2

that would indicate the NO X II state retains the polarization

͑

1982͒; R. D. Bower, R. W. Jones, and P. L. Houston, ibid. 79, 2799

͑1983͒; M. R. S. McCoustra, J. A. Dyet, and J. Pfab, Chem. Phys. Lett.

36, 231 ͑1987͒; J. A. Dyet, M. R. S. McCoustra, and J. Pfab, Faraday

3

of the CNP T₁

˜

a AЉ state during the fragmentation process.

1

The overall conclusion we reach is that the product state

distributions in the 650 nm photodissociation of CNP are

consistent with a mechanism dominated by energy random-

Discuss. Chem. Soc. 84, 463 ͑1988͒; J. A. Dyet, M. R. S. McCoustra, and

J. Pfab, J. Chem. Soc. Faraday Trans. 86, 2049 ͑1990͒.

E. Kolodney, P. S. Powers, L. Hodgson, H. Reisler, and C. Wittig, J.

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5763 ͑1986͒.

R. Uberna and J. I. Cline, J. Chem. Phys. 102, 4705 ͑1995͒. Note that the

polarization geometries used in this reference correspond to geometry

cases 1 and 2 of Ref. 12.

M. C. Wall, Ph.D. thesis, University of Nevada, 1995.

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216, 286 ͑1993͒.

S. J. Klippenstein and J. I. Cline, J. Chem. Phys. 103, 5451 ͑1995͒.

R. Uberna, R. D. Hinchliffe, and J. I. Cline, J. Chem. Phys. 103, 7934

5

6

7

8

ization following decay of the optically prepared S state, but

1

a dynamical bottleneck imposed by a potential barrier on the

predominate T₁channel results in ‘‘exit channel interac-

tions’’ that induce characteristic NO product state correla-

tions.

In order to clearly establish the connection between

these dynamical measurements and speciﬁc features of the

potential surface and speciﬁc motions in the transition state,

we have completed classical dynamics studies of nitrosoal-

kane fragmentation. These calculations will be fully de-

scribed elsewhere,⁵⁰but it is satisfying to mention some of

the results here. It is possible to reproduce all the major

trends in energy distributions and correlations using a single,

physically realistic, potential surface obtained from a combi-

nation of ab initio and experimental data. These trajectory

calculations unambiguously conﬁrm the suspicion that the T₁

9

0

1

2

͑

1995͒.

1

3

4

M. A. O’Halloran, H. Joswig, and R. N. Zare, J. Chem. Phys. 87, 303

1987͒.

J. F. Black, J. R. Waldeck, and R. N. Zare, J. Chem. Soc. Faraday Trans.

85, 1312 ͑1989͒.

͑

2

15

D. C. Jacobs, K. Kolasinski, R. J. Madix, and R. N. Zare, J. Chem. Soc.

Faraday Trans. 2 85, 1325 ͑1989͒.

J. Chem. Phys., Vol. 105, No. 22, 8 December 1996

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132.174.255.116 On: Mon, 22 Dec 2014 21:03:18

9858

Uberna, Hinchliffe, and Cline: NO ␮-v-j correlations

1

6

33

D. C. Jacobs, R. J. Maddox, and R. N. Zare, J. Chem. Phys. 85, 5469

1986͒.

M. Hippler and J. Pfab, Chem. Phys. Lett. 243, 500 ͑1995͒.

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C. A. Taatjes, J. I. Cline, and S. R. Leone, J. Chem. Phys. 93, 6554

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Reinhold, New York, 1950͒, Vol. I, Chap. 5.

C. H. Townes and A. L. Schawlow, Microwave Spectroscopy ͑Dover,

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See Ref. 34, Chap. 8.

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͑1954͒.

͑

1

2

7

8

9

0

34

35

36

͑1990͒.

21

37

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Using the average rotational constants for CNP and the chloroisopropyl

radical. The rotational constants were provided by K. Fukui in an ab initio

Ϫ1

UHF 6-31G** Fopt Freq calculation. For CNP: Aϭ1.041ϫ10 cm

,

Ϫ2

Ϫ1

Ϫ2

Ϫ1

Bϭ9.607ϫ10 cm and Cϭ7.405ϫ10 cm . For chloroisopropyl

radical: Aϭ0.275 cm , Bϭ0.159 cm and Cϭ0.105 cm . The NO

rotational constant of 1.695 cm was obtained from spectroscopic data.

2

3

Ϫ1

38

͑1990͒.

C. Jonah, J. Chem. Phys. 55, 1915 ͑1971͒.

S. Yang and R. Bersohn, J. Chem. Phys. 61, 4400 ͑1974͒.

2

4

5

39

40

R. N. Zare, Angular Momentum ͑Wiley, New York, 1988͒, Table 6.6.

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41

2

0

͑1996͒.

We equate ␤ ͑20͒* with ͑4␲/5͒g . The quantity g₀₀is a rotation-

00

2

6

7

S. W. North and G. E. Hall, J. Chem. Phys. ͑to be published͒.

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K.-H. Gericke, S. Klee, and F. J. Comes, R. N. Dixon, ibid. 85, 4463

independent ‘‘geometry factor’’ described in Ref. 39.

The z axis of this idealized frame is determined by a body-ﬁxed vector

␮͑tϭt*͒ that correlates to the transition dipole at the instant of dissocia-

42

͑

1986͒.

tion photon absorption.

R. Uberna, G. N. Fickes, and J. I. Cline ͑in preparation͒.

M. P. Docker, A. Ticktin, U. Br u¨ hlmann, and J. R. Huber, J. Chem. Soc.,

Faraday Trans. 2 85, 1169 ͑1989͒.

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2789 ͑1983͒.

M. H. Alexander et al. J. Chem. Phys. 89, 1749 ͑1988͒.

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NO μ-v-j correlations in the photofragmentation of 2-chloro-2-nitrosopropane

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