Double-resonance overtone photofragment spectroscopy of trans-HONO. I. Spectroscopy and intramolecular dynamics

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JOURNAL OF CHEMICAL PHYSICS

VOLUME 112, NUMBER 20

22 MAY 2000

Double-resonance overtone photofragment spectroscopy of trans-HONO.

I. Spectroscopy and intramolecular dynamics

F. Reiche and B. Abel

Institut f u¨ r Physikalische Chemie, Universit a¨ t G o¨ ttingen, Tammannstrasse 6, D-37077 G o¨ ttingen, Germany

a)

R. D. Beck and T. R. Rizzo

´

Laboratoire de chimie physique mol e´ culaire, Ecole Polytechnique F e´ d e´ rale de Lausanne,

1015 Lausanne, Switzerland

͑

Received 29 December 1999; accepted 28 February 2000͒

Using the technique of double-resonance overtone photofragment spectroscopy ͑DROPS͒, we have

measured rotationally resolved vibrational overtone transitions to the previously unobserved 5v₁,

6

v₁, and 7v₁levels of gas-phase trans-nitrous acid ͑HONO͒ in its electronic ground state.

Observing the onset of dissociation from different rovibrational states of 5v₁near threshold

Ϫ1

determines the HO–NO bond energy to be D ϭ16 772Ϯ14 cm . Observed spectral splittings and

0

broadening of individual rovibrational transitions provide quantitative data on the rate and extent of

collision free vibrational energy redistribution that would result after coherent ultrashort pulse

excitation. In parallel with these frequency domain measurements, we determine the unimolecular

dissociation rates directly in time for trans-HONO molecules excited to several rotational states near

threshold. The combination of time- and frequency-resolved data allows us to estimate the linewidth

contributions from the ﬁnite dissociation lifetime of the molecule. Our results reveal intramolecular

dynamics that are clearly not a simple function of the vibrational energy but rather depend

sensitively upon speciﬁc couplings and, in turn, on the vibrational character of the individual states

I. INTRODUCTION

IVR phenomena in which one laser pre-selects a single rota-

tional state of a molecule via a well characterized infrared or

electronic transition followed by a second excitation that pre-

pares the molecules in a highly excited state of the ground

electronic potential-energy surface. Techniques implement-

ing this general strategy include high resolution infrared

double resonance absorption spectroscopy of larger mol-

A complete description of unimolecular dissociation pro-

cesses requires a fundamental understanding of intramolecu-

lar vibrational energy redistribution ͑IVR͒ which precedes

the chemical transformation.¹Experimental measurements

of IVR dynamics can be performed either in the time

domain or in the frequency domain. In the latter case,

information on the time scales, extent, and mechanisms of

intramolecular energy ﬂow can be obtained from analysis of

spectral splittings and broadening and their dependence on

vibrational and rotational quantum numbers. Unambiguous

interpretation of such information requires rovibrational

spectra that are free from spectral congestion arising from a

distribution of initial states, isomers, or isotopes. For vibra-

tional fundamentals and low overtones of larger molecules,

–3

4

–6

1–3

2

,18–21

ecules in supersonic jets,

ﬂuorescence- or ion-depletion techniques,

and stimulated emission pumping ͑SEP͒.

double resonance overtone

pumping,²

2–31

32,33

3

4–37

Over the last several years we have developed and

implemented an excitation scheme that we call double

resonance

͑

overtone

photofragment

spectroscopy

DROPS͒.⁶^,²²^–²⁵^,²⁷^–²⁹This approach uses an infrared laser

pulse to pre-excite reactant molecules to single, well deﬁned

rovibrational states of an assigned fundamental or low-

overtone vibrational level. The state-selected molecules are

then further excited by a second laser to single rovibrational

states of a high vibrational overtone level above the disso-

ciation threshold, and the resulting fragments are detected by

laser induced ﬂuorescence ͑LIF͒. Scanning the frequency of

the second laser results in a simpliﬁed vibrational overtone

excitation spectrum from the intermediate state. For small

molecules, the selectivity of double resonance excitation of-

ten allows one to obtain fully resolved spectra at room tem-

perature. This has the advantage of providing access to a

large range of rotational states, allowing the study of the

rotational effects on the IVR and dissociation dynamics.

In principle, fully resolved spectra contain information

both on IVR processes and on unimolecular dissociation

this can be achieved using cold molecular beams and single

resonance excitation by a narrow band laser.²

,7–15

For high

vibrational overtone levels of small molecules, high-

resolution single-laser techniques such as intra-cavity laser

absorption spectroscopy ͑ICLAS͒¹

6,17

can often distinguish

individual rovibrational transitions in a thermal sample.

However, as molecules become slightly more complex, spec-

tral congestion becomes sufﬁciently high that different rovi-

brational transitions overlap within their natural linewidth,

making it impossible to resolve homogeneous structure by

single resonance excitation. This problem has stimulated the

development of double resonance spectroscopic probes of

^a^͒Electronic mail: thomas.rizzo@epﬂ.ch

0021-9606/2000/112(20)/8885/14/$17.00

8885

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1

8886

J. Chem. Phys., Vol. 112, No. 20, 22 May 2000

Reiche et al.

rates.³⁸Resolvable splittings or clump structures in the spec-

tra can be directly interpreted in terms of IVR, where the

largest splittings or the clump-widths correspond to the fast-

est redistribution timescale if the system were to be coher-

ently excited by a short-pulse laser. If rather than discrete

splittings, the observed transitions show broad, unresolved

line shapes, frequency resolved measurements alone cannot

distinguish whether the broadening results from vibrational

coupling to a large number of background states or from the

ﬁnite lifetime for unimolecular dissociation. In this case,

time-resolved measurements of the dissociation rate from the

prepared initial state become invaluable in that they reveal

directly the lifetime broadening contribution and allow one

to extract unambiguous information on IVR time scales from

the frequency-resolved data.³⁹^–⁴³In this work, we report

both time- and state-resolved measurements of the unimo-

lecular dissociation dynamics of trans-HONO.

4

4–51

and the less stable cis- isomer⁴⁴^,⁴⁵^,⁵¹of

52

Both trans-

HONO have been the subject of many previous spectro-

scopic investigations. The microwave and IR spectra of

trans-HONO have provided accurate determinations of the

equilibrium structure, the dipole moment, and all six funda-

mental vibrational frequencies.⁴

4–51

Matrix studies,

monic force ﬁeld calculations, and ab initio calculations

53,54

har-

5

5–58

suggest a barrier for cis–trans isomerization of about 3500

Ϫ1

cm . Holland et al. have observed several combination

bands of trans-HONO by FTIR spectroscopy and have mea-

FIG. 1. Schematic of energy levels and pump and probe scheme involving

sured the 3v₁and 4v₁bands using the method of vibra-

tionally mediated photodissociation. Herman and co-

two separate double resonance excitation steps ␭1 ͑IR laser͒ and ␭2 and a

5

9

product detection step (␭ ).

3

workers have measured FTIR ͑Fourier-transform infrared͒

Ϫ1

spectra from 600–12 000 cm , and in combination with pre-

II. EXPERIMENT

vious data, have produced a complete set of rovibrational

4

9–51

parameters.

isolated perturbations, analysis of the band contours of the

v and 4v levels obtained by Holland et al. suggest that

While the lower bands seem to exhibit only

Figure 1 shows an energy level schematic for the

DROPS experiment on trans-HONO. Individual rovibra-

tional transitions to the v1 or 2v1 levels are excited by

narrow-band ͓full width at half maximum ͑FWHM͒ϭ0.02

3

1

they are more extensively perturbed by coupling to various

zeroth-order dark states. Intramolecular energy transfer and

cis–trans isomerization in HONO has also been investigated

via classical trajectory calculations on simple ab initio

_p_o_t_e_n_t_i_a_l_-_e_n_e_r_g_y_s_u_r_f_a_c_e_s_.₆0 Moreover, trans-HONO has

Ϫ1

cm ͔͒ infrared laser pulses. For simplicity, we use symmet-

ric top notation for HONO, an asymmetric top close to the

prolate limit ͑␬ϭϪ0.96͒.⁴⁴We denote ground-state rota-

tional quantum numbers with a double prime and those for

molecules in the intermediate state of the double resonance

scheme with a single prime. We use the IR transition fre-

been the subject of many experimental and theoretical stud-

6

1–64

ies of ultraviolet photodissociation on the S surface.

1

50

quencies for the v and 2v bands provided by Herman to

1

In this study we use double resonance overtone photo-

fragment spectroscopy to investigate the previously unob-

served 5v , 6v , and 7v levels of gas-phase trans-HONO

prepare trans-HONO molecules in well deﬁned intermediate

states. A second tunable dye laser excites the molecules from

the pre-selected intermediate level into states above the dis-

sociation threshold with v ϭ5, 6, or 7. The energies of the

predissociative levels are determined from the term values

1

in its electronic ground state. After a brief review of our

experimental technique, we present double resonance spectra

for each band, extracting spectroscopic constants and analyz-

ing perturbations arising from vibrational coupling. We also

report time-resolved measurements of the unimolecular dis-

1

50

for the intermediate state given by Herman, together with

the measured wave number of the visible overtone excitation

laser. A time-delayed ultraviolet pulse from a frequency

doubled dye laser detects the resulting OH fragments by la-

ser induced ﬂuorescence via the A–X(0,0) band.

The apparatus used in the present study is similar to that

used in our previous work.⁶Pulsed infrared light for state

selection is generated by mixing the output of a narrow-band

tunable dye laser ͑Scanmate 2E, Lambda Physik͒ and the

fundamental output of a single mode Nd:YAG laser ͑GCR-

sociation rate for HONO excited to 5v . These measure-

1

ments enable us to distinguish between the contributions of

intramolecular energy transfer and unimolecular dissociation

,27

to the homogeneous linewidths in 5v . Finally, we combine

1

our time- and frequency-resolved data to give an overall pic-

ture of the intramolecular dynamics of trans-HONO as a

function of vibrational energy.

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J. Chem. Phys., Vol. 112, No. 20, 22 May 2000

Spectroscopy of trans-HONO. I

8887

190, Spectra Physics͒ in a lithium niobate crystal ͑INRAD,

Autotracker II͒ to generate the difference frequency. This

Ϫ1

produces 0.8–1.5 mJ pulses at 3600 cm for excitation of

Ϫ1

v₁and up to 4 mJ at 7000 cm for excitation of 2v . The

1

absolute wave number of the infrared light is measured by

recording photoacoustic spectra of H O and comparing it

2

with the HITRAN database. For excitation to the vibrational

overtone levels above the dissociation threshold in the sec-

ond step of the double resonance scheme, we use the 25–80

mJ output of a second dye laser directly ͑either a Scanmate

Ϫ1

2

E, Lambda Physik with 0.1 cm bandwidth or a Lumonics

Ϫ1

HD-500 with 0.04 cm bandwidth͒ or pump an H Raman

2

shifter and use the ﬁrst Stokes beam. For highest-resolution

measurements of selected transitions, an intracavity etalon is

inserted into the Scanmate 2E dye laser which improves its

Ϫ1

bandwidth to 0.02 cm . Wavelength calibration of the vis-

FIG. 2. Photofragment spectrum of the 5v₁band of HONO, recorded by

ible lasers is veriﬁed by a pulsed wave meter ͑WA 4500,

_p_r_e_-_e_x_c_i_t_i_n_g_t_h_eQQ₇branch of the v₁fundamental at 3590.16 cm and

Ϫ1

Burleigh͒ with an absolute accuracy of 0.02 cm . The laser

scanning the overtone excitation wave number. The wave number scale

beams are introduced into the gas cell through bafﬂed side-

arms equipped with Brewster windows. A quartz f/1 con-

denser lens of 50 mm focal length collects the OH ﬂuores-

cence at 90 degrees to the incident laser beams and images it

onto a slit in front of a UV sensitive photomultiplier ͑EMI

represents only that of the overtone excitation in the second step.

energy will appear in the photofragment excitation spectrum.

Because these are near-threshold experiments, we detect the

9635QB͒. A UG11 UV-transmitting ﬁlter rejects the scat-

OH product in its lowest rotational state via the Q (1) tran-

1

tered light from the intense overtone excitation laser. A gated

integrator collects the signal from the photomultiplier tube

and averages it for 10–50 laser shots.

sition.

Figure 2 shows an excitation spectrum of the 5v level

in which we ﬁrst populate a large number of J states in the

1

In the frequency-resolved experiments, the delay be-

tween the three lasers is ﬁxed and the total OH ﬂuorescence

is collected as a function of the overtone excitation laser. For

the time resolved experiments, the laser frequencies are all

ﬁxed on appropriate transitions and the total OH ﬂuores-

cence is collected as a function of the delay time between the

overtone excitation laser an the UV probe laser.

intermediate level by tuning the infrared state-selection laser

Q

wave number to the Q branch of the v fundamental at

7

1

Ϫ1

3

590.16 cm . Compared to the spectra of lower OH

50,59

overtones,

this spectrum appears to be missing many

transitions. While it contains a central Q branch as well as P

and R branches characteristic of a parallel band of a nearly

prolate symmetric top, transitions to states with low J do not

deposit enough energy into the molecule to cause it to dis-

sociate and hence are not detected. Using the state selectivity

provided by the DROPS technique, one can determine ex-

actly which states are located below the dissociation thresh-

old and which lie above. Promoting the HONO molecules in

the ﬁrst step to a single rotational state of the intermediate

vibrational level leads to photofragment excitation spectra

with a simple structure, since the number of transitions from

Trans-HONO is prepared by mixing equimolar amounts

of gaseous H O, NO , and NO at a total pressure of ϳ50

2

Torr in a 5 l glass bulb. The sample mixture is allowed to

equilibrate for at least 24 h before use. With an equilibrium

Ϫ1

59

constant of K ϭ1.36 bar at room temperature, the total

p

͑

pressure dependent͒ HONO concentration is ϳ5%, with the

3

7,44,59

trans- and cis-isomer in a 2:1 ratio.

During the experi-

ments, the sample mixture ﬂows through the LIF cell at a

total pressure of 30–100 mTorr as measured by a capaci-

tance manometer. We expect the concentration of HONO in

the sample cell to be unchanged from the higher pressure

the intermediate JЈ, KЈ levels to the 5v band is limited by

1

the optical selection rules. The ability to fully assign this

structure allows us to prepare molecules in single, well-

reservoir due to its short residence time and the slow rate at

characterized rotational states of the 5v level and permits

_w_h_i_c_h_t_h_e_s_u_r_f_a_c_e_c_a_t_a_l_y_z_e_d_e_q_u_i_l_i_b_r_i_u_m_i_s_r_e_a_c_h_e_d_.59,65

1

the precise determination of the reactant energy and hence

the dissociation threshold. Figure 3 contains two series of

double resonance spectra where intermediate states in 2v₁

with KЈϭ6 and 10 and various JЈ quantum numbers are

III. RESULTS

A. The 5v region

1

accessed in route to excitation of 5v . In Figs. 3͑a͒ and 3͑d͒

1

1. Determination of the dissociation threshold

one can see the P, Q, and R branch structure characteristic of

a parallel band of a near prolate symmetric top. The other

small features in the spectra result from accidental overlap in

the infrared state-selection step and not from vibrational

mixing at the 5v₁level. We verify this by accessing the

same ﬁnal state via different intermediate states, in which

case the structure due to accidental overlap will change

whereas the target transition will not.

Our investigation of the 5v level of trans-HONO uses

1

rovibrational levels of both the v fundamental ͑in a 1� 0,

1

5

� 1 excitation scheme͒ as well as the ﬁrst overtone 2v ͑in

1

a 2� 0, 5� 2 scheme͒ as intermediates to access the highly

excited state. The vibrational band origin of the 5v level is

1

6

below the dissociation energy of the HO–NO bond, and

thus only transitions to 5v states with sufﬁcient rotational

1

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J. Chem. Phys., Vol. 112, No. 20, 22 May 2000

Reiche et al.

TABLE I. Spectroscopic constants of OH overtones of trans-HONO.

v₁/cm^Ϫ¹

Ϫ1a

Ϫ1

5

6v /cm

7v /cm

1

A

B

C

v₀

3.037͑2͒

0.4173͑3͒

0.3663͑3͒

3.036͑8͒

0.4164͑15͒

0.3650͑11͒

2.99͑5͒

0.421͑5͒

0.366͑3͒

16 327.73͑5͒

19 110.05͑5͒

21 740.1͑1͒

a

The values for 6v₁represent those for the observed band before depertur-

bation.

products of this ground-state dissociation process, we cannot

rule out the possibility of the presence of such a barrier.

2. Spectroscopic parameters

Although we use symmetric top notation for assigning

the HONO overtone spectra, a quantitative description re-

quires an asymmetric top treatment, especially at the high J

values accessed in these experiments. In order to extract the

rotational constants and band origin of the 5v₁state, the

observed line positions were ﬁt to an asymmetric rotor Wat-

r

70

son A-type Hamiltonian in I representation. A total num-

ber of 60 lines were included in the ﬁt, yielding the 5v band

1

FIG. 3. Rotationally resolved spectra of the 5v₁band using intermediate

states in 2v₁with KЈϭ6 ͑left panel͒ and KЈϭ10 ͑right panel͒ and JЈ

denoted in the ﬁgure. The difference in the wave number scale from Fig. 2

arises from the difference in the intermediate state.

origin and rotational constants shown in Table I. The limited

data set restricts the number of meaningful spectroscopic

constants that we could extract and thus we constrain all

higher order constants to their ground state values.⁵⁰

3

. Linewidths and perturbations

In the spectra of Figs. 3͑b͒ and 3͑c͒, the transitions that

access the Jϭ30, Kϭ6 ﬁnal state are missing from their

Thus far, we have interpreted the rotationally resolved

6

7

Q

predicted positions ͓i.e., P (31) in Fig. 3͑b͒ and Q (30)

vibrational overtone spectra as if the HONO molecule were

bound in the upper state. The assignability of these spectra to

zeroth-order J and K quantum numbers indicates that the

lifetimes of the highly excited states are long compared to

the rotational period of the molecule. To get information on

intramolecular energy transfer and unimolecular dissociation

dynamics of highly excited trans-HONO in these quasi-

bound states, one must examine splittings, linewidths, and

degree of fractionation of the zeroth-order rovibrational tran-

sitions.

6

in Fig. 3͑c͔͒, while the transitions to the Jϭ31, Kϭ6 ﬁnal

state are present. From this we conclude that the effective

dissociation threshold, E (Jϭ30), falls in the energy inter-

0

Ϫ1

val between 16 787.65 and 16 812.6 cm , respectively. In

an analogous manner, one can see from Figs. 3͑d͒–3͑f͒ that

the transitions to the Kϭ10, Jϭ21 level are missing but

those to the Kϭ10, Jϭ22 level appear. This indicates that

Ϫ1

E (Jϭ21) falls between 16 772.9 and 16 790.1 cm , re-

0

spectively. Determining the rotationless dissociation thresh-

old, E (Jϭ0), from this data requires knowledge of the cen-

The double resonance spectra of the 5v level shown in

0

1

trifugal barrier. As will be described in detail in a

forthcoming publication,⁶⁸we estimate this barrier as a func-

tion of J using a model potential associated with a statistical

adiabatic channel model ͑SACM͒ calculation that is adjusted

to agree with experimental data for the high pressure rate

constants and the product state distributions. Together with

Fig. 3 exhibit no obvious fragmentation from coupling of the

zeroth-order bright states to other zeroth-order vibrational

levels. Because strong anharmonic resonances arise largely

from low-order terms in the vibrational Hamiltonian,⁷¹the

number of such resonances is relatively sparse, despite a cal-

Ϫ1

culated density of states of 15 per cm at this energy. Nev-

our spectroscopic data, this allow us to estimate the dissocia-

ertheless, there are a few states in or near this region that

Ϫ1

tion threshold, E (Jϭ0), to be 16 772Ϯ14 cm . The un-

could be coupled to 5v via third- or fourth-order terms that

0

1

certainty in this value comes from the uncertainty in estimat-

ing the centrifugal barrier and not from the spectroscopic

accuracy of our measurements. Nevertheless, our determina-

tion of the dissociation threshold of HONO decreases the

error limits of the previously accepted value⁶⁶by more than

an order of magnitude. While simple bond ﬁssion reactions

do not usually exhibit a static barrier in the potential, it is

possible for small barriers to exist as the nature of bonding

changes along the dissociation coordinate.⁶⁹Because we can-

not measure the small amount of translation excitation in the

we do not observe. In particular, the 4v ϩ2v ϩv , 4v

1

3

5

1

ϩv ϩ2v and 4v ϩv ϩv states predicted to be 39, 53,

2

5

1

2

3

Ϫ1

and 78 cm , respectively below the 5v band. One should

1

note that our experimental approach could bias against ob-

serving certain resonances from states to the low-energy side

of 5v . For HONO pre-selected with a certain value of J and

1

K, dark perturbing states to the low energy side of 5v may

1

lie below the dissociation threshold and hence be invisible to

photofragment detection. If such a situation were to occur,

the bright state would be shifted, but we would see no evi-

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J. Chem. Phys., Vol. 112, No. 20, 22 May 2000

Spectroscopy of trans-HONO. I

8889

FIG. 4. Time and frequency resolved measurements of selected rotational

states in the 5v₁band of HONO at energies near the dissociation threshold.

See Table II for the corresponding linewidths and dissociation rates.

dence of the perturber itself in the spectrum. While this is

certainly possible, there are two factors that rule against this

possibility. First, as shown in Fig. 3, no perturbing states

FIG. 5. Linewidths of individual rovibrational transitions in 5v , 6v , and

1

7

v₁as a function of J. For 5v , transitions to states with both Kϭ0 and

1

Ϫ1

Q

appear within 60 cm to the low energy side of the R (32)

6

Kϭ7 are shown. For the other bands, all transitions terminate on states with

Kϭ0.

transition which accesses the Kϭ6 Jϭ33 level at an esti-

Ϫ1

mated energy of at least 52 cm above the centrifugal bar-

Ϫ1

rier. This implies that any perturbing states within 52 cm

higher range of J investigated, the dependence is not strong.

Moreover, the linewidths show no systematic dependence

upon K. These observations rule out the possibility of rota-

tionally induced IVR being the primary factor responsible

for the linewidths. It remains to distinguish the contributions

of purely vibrational coupling to the bath of dark background

states from that of lifetime broadening due to unimolecular

dissociation. As described below, we do this by direct time-

resolved measurements of the unimolecular dissociation

rates.

of this level should appear in the photofragment spectrum.

Second, we observe no substantial displacement of the band

origin from its zeroth-order position. Thus, there appears to

be no strong perturbations in the region of the 5v level.

1

Despite the lack of strong vibrational coupling, higher

resolution measurements of the spectral line shapes reveal

Ϫ1

widths that range from 0.15 cm to more than 0.92 cm

,

Ϫ1

which is signiﬁcantly broader than either the 0.022 cm

Ϫ1

Doppler width ͑for 5� 1 excitation͒ or the 0.02 cm laser

linewidth. As shown on the left hand side of Fig. 4 for sev-

eral representative cases, the line shapes appear to be well ﬁt

by Lorentzian proﬁles. Lorentzian line shapes can arise ei-

ther from coupling of the bright state to a sufﬁciently large

number of dark background states or from lifetime broaden-

ing due to the ﬁnite unimolecular dissociation rate. Deter-

mining the difference between these two possibilities is dif-

ﬁcult on the basis of frequency resolved data alone. One clue

to the broadening mechanism might come from the J or K

dependence of the linewidths, which could reﬂect Coriolis or

centrifugal coupling to a manifold of background states. The

linewidths extracted from Lorentzian ﬁts to the data are

shown for a larger number of lines in Fig. 5͑a͒ as a function

of J. While there seems to be a slight J dependence at the

4. Unimolecular dissociation rate measurements

To measure the unimolecular dissociation rate of reac-

tant molecules from well deﬁned initial states, we ﬁx the

wavelengths of the three lasers at known transitions of the

HONO molecule and the OH fragment and measure the OH

ﬂuorescence intensity as a function of the time delay be-

tween the overtone dissociation laser and the UV probe laser.

While our time resolution of ϳ10 ns is limited by the pulse

lengths and relative jitter of the Nd:YAG pump lasers, this is

sufﬁcient to measure the unimolecular dissociation rate for a

number of states close to the dissociation threshold. The

right hand side of Fig. 4 shows, for several initial states of

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8890

J. Chem. Phys., Vol. 112, No. 20, 22 May 2000

Reiche et al.

TABLE II. Unimolecular dissociation rate constants and linewidths of se-

lected rotational states of the 5v₁level close to the dissociation threshold.

Ϫ1a

7

Ϫ1

⌫/cm^Ϫ¹

J

K

E–E /cm

␶/ns

k/10 s

0

2

7

4

9

3

5

2

10

8

1

7

3

18.1

20.7

25.3

26.0

26.2

29.1

36.6

Ͼ37

8.6

21

Ͻ4

11

4.2

Ͻ4

8.3

Ͻ4

12

0.20

0.14

0.15

0.12

0.26

0.16

0.18

2

3

2

3

4.8

Ͼ25

9.1

24

Ͼ25

12

0

5

all others

Ͼ25

^aE–E₀carries an uncertainty of Ϯ14 cm^Ϫ¹arising from the uncertainty of

the dissociation threshold, E . However, the uncertainty in the difference

0

Ϫ1

in the excess energies of these states is on the order of 0.04 cm , deter-

mined by the accuracy with which we measure the laser wave number.

the HONO molecule, the rise in laser induced ﬂuorescence

intensity of the OH dissociation product as a function of the

delay between the overtone excitation laser and UV probe

laser. To the left of the time resolved data in Fig. 4 we show

the high-resolution frequency resolved data for the same re-

actant state. We extract the unimolecular dissociation rate

from the time-resolved data by deconvoluting a 10 ns Gauss-

ian for the effective laser time resolution, determined in a

separate experiment, from the rise of the laser-induced ﬂuo-

rescence signal. This procedure allows us to determine rise-

times as short as 4 ns. The rise-times and unimolecular dis-

sociation rates are displayed in Table II together with the

corresponding linewidth for a number of states near the dis-

sociation threshold. The lowest trace in Fig. 4 shows OH

product formation after excitation to the Jϭ34, Kϭ1 level

FIG. 6. Rotationally unresolved spectrum of the 6v₁vibrational band of

Q

HONO, via a 2� 0, 6� 2 excitation scheme using the Q branch of the ﬁrst

2

Ϫ1

OH-overtone at 7016.33 cm . The wave number scale represents only that

of the overtone excitation in the second step. As described in the text, the

Ϫ1

smaller satellite signals marked with arrows at 12 120.3 and 12 153.0 cm

are splittings caused by anharmonic coupling.

process. As is evident from Fig. 4 and discussed more fully

below, the rates for these particular rotational states in 5v₁

indicate that lifetime broadening from unimolecular dissocia-

tion would make a negligible contribution to the correspond-

ing spectral linewidths.

These rate measurements conﬁrm that the observed line-

widths are determined primarily by coupling of the bright

state to the manifold of dark background states. Our investi-

gation of the J and K dependence ͑or lack thereof͒ of the

linewidths imply that this coupling occurs primarily via vi-

brational ͑anharmonic͒ terms in the Hamiltonian, although

Coriolis coupling appears to contribute to the overall spectral

width at the highest values of J. With a vibrational density of

in 5v , a state that dissociates faster than the time resolution

1

of the system. All states that we investigated with excess

Ϫ1

energies larger than ϳ37 cm dissociate with a rate that is

too fast for us to resolve.

One can see from Table II that the unimolecular disso-

ciation rates do not monotonically increase with energy. For

example, the Jϭ34, Kϭ1, and Jϭ29, Kϭ7 states, which lie

Ϫ1

states of 15 per cm , the individual rovibrational features

are likely to consist of a few components that are overlapped

within the laser limited linewidth. Although not the primary

factor in determining the linewidths, Coriolis coupling be-

tween states of different K can increase the rovibrational

density of states and hence smooth out the spectral proﬁles.

Ϫ1

within 1 cm of each other, exhibit dissociation rates that

differ by more than a factor of 2.5, with the higher energy

state exhibiting the slower of the two rates. This type of

behavior has also been observed in our recent work on

HOCl, where dissociation rates from the 6v level show a

1

wide variation and no simple correlation with the excess en-

ergy or with J. Such statistical rate ﬂuctuations seem to be

B. The 6v region

1

6

1. Spectroscopic parameters

the rule rather than the exception in eigenstate speciﬁc mea-

surements of unimolecular dissociation rates.⁶^,⁷²^–⁷⁴Statisti-

cal theories of unimolecular dissociation, which predict

smooth trends in the rates with increasing energy, can only

expected to be accurate ‘‘on average’’ and will not reproduce

such ﬂuctuations in the eigenstate speciﬁc rates.⁷⁴

All the measurements on the 6v band that we report

1

here use a 2� 0, 6� 2 double resonance excitation scheme.

Figure 6 shows an excitation spectrum of the 6v level ob-

1

q

tained with the IR state-selection laser ﬁxed on the Q₂

branch of the 2v band to access a large number of interme-

1

At the 100 mTorr pressure employed in these experi-

ments, the collisional contribution to the rates in Table II

diate rotational states. Unlike the corresponding 5v spec-

trum of Fig. 2, one observes the entire rotational contour,

1

should be negligible. With a hard sphere collision rate of 1

since the rotationless 6v level lies well above the dissocia-

1

Ϫ1

␮s

, even a rotational state changing collision, which may

tion threshold. Without using the state selection capabilities

of the ﬁrst step, the individual rovibrational transitions of the

6v₁band are heavily overlapped, making it impossible to

extract information on molecular constants and perturba-

tions. We do observe, however, several weak satellite bands

occur as much as 10 times the hard-sphere rate, would not

signiﬁcantly inﬂuence the measured rise times. The fact that

we measure identical dissociation rates at 40–50 mTorr pres-

sure conﬁrms the collision free nature of the dissociation

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J. Chem. Phys., Vol. 112, No. 20, 22 May 2000

Spectroscopy of trans-HONO. I

8891

FIG. 7. Rotationally resolved spectrum of the 6v₁vibrational band of

HONO, via a 2� 0, 6� 2 excitation scheme using different intermediate

rotational states in the ﬁrst overtone of HONO. In the left series of spectra

KЈ is ﬁxed at 0 and JЈ varied, while JЈ is held constant at a value of 5 and

KЈ changed for the spectra displayed on the right side.

which, as discussed more fully below, arise from strong vi-

brational coupling between 6v₁and speciﬁc dark back-

ground states.

^F^I^G^.⁸^.^S^p^lⁱ^t^tⁱⁿ^gⁱⁿ^t^h^e⁶^v1 double resonance spectra due to strong anhar-

monic coupling with 2 dark background states. The double resonance spec-

tra originate from intermediate states with JЈϭ8, 9, 10, and 11 and KЈ

Figures 7͑a͒ and 7͑b͒ show simpliﬁed double resonance

Q

spectra of the 6v band in which we ﬁrst use the R(JЉ)

Q

1

ϭ0. A double resonance spectrum measured by pre-excitation of the Q₂

Ϫ1

lines of the 2v band for state selection and scan the second

branch of the ﬁrst OH-overtone at 70 16.33 cm is shown on the bottom for

1

comparison.

laser over the 6� 2 band. The two major features in each

Q

spectrum of Fig. 7͑a͒ correspond to P and R branch tran-

sitions originating from the JЈ, KЈϭ0 intermediate level for

the value of JЈ indicated. Figure 7͑b͒ shows a second series

of spectra with JЈϭ5 and values of KЈ ranging from 0 to 3.

In addition to the P- and R-branch transitions, Q-branch tran-

sitions appear for KЈÞ0 with an intensity that increases with

respectively. Because the same pattern is found for excitation

through different intermediate states, we exclude accidental

overlap in the state selection step as the source these extra

features. The fact that the intensities of these satellite peaks

do not depend upon J and K suggests that they arise from

7

5

K. The spectroscopic assignments of the observed transi-

zeroth-order dark states that couple to the 6v state via an-

1

tions in the overtone spectra are straightforward using as-

harmonic terms in the vibrational potential. While in prin-

ciple these features could arise from combination bands that

carry a small amount of intrinsic oscillator strength, the fact

that they do not appear in the region of other vibrational

overtone levels implies that they borrow oscillator strength

signments of the lines in the 2v intermediate level from

1

5

0

Guilmot et al. Fitting the spectra using an asymmetric rotor

7

0

Hamiltonian and known lower state rotational constants al-

low us to determine the spectroscopic constants for the 6v₁

level shown in Table I. As in the previous ﬁt, the limited

number of lines in our double resonance spectra lead us to

constrain all higher order constants to the ground state

by being coupled to the pure 6v level.

1

The linewidths at the 5v level discussed in the previous

1

section revealed that each rovibrational transition is split by

coupling to a large number of zeroth-order dark states, and

5

0

values.

one expects the same behavior at 6v . However, the appear-

ance of the satellite peaks at 26.6 and 59.3 cm with sub-

1

2. Linewidths and perturbations

Ϫ1

In addition to the spectroscopically assignable features

stantial intensity indicates that coupling between the 6v₁

zeroth-order bright state and two particular zeroth-order dark

states is substantially stronger than the weaker couplings that

contribute to the linewidths of the individual features. Such a

hierarchy of vibrational coupling strengths is commonly ob-

in the 6v band, small satellite features appear in each spec-

1

trum in this region shifted to the high-frequency side of the

main band. These are perhaps most evident in the rotation-

ally unresolved 6v₁spectrum of Fig. 6 ͑marked with ar-

rows͒, but as shown in Fig. 8, these same features can be

observed in the rotationally resolved double resonance spec-

tra as well if one looks over a sufﬁciently wide energy range.

Each P or R branch transition in Fig. 8 shows two satellite

served in highly resolved vibrational overtone spectra of

small polyatomic molecules.⁷

6–80

Because of this separation

of coupling strengths, we treat the interaction of the 6v₁

level with the two dark states as a simple three state problem.

Even with this simplifying approximation, the deperturbation

of the spectrum to yield the zeroth-order state energies and

Ϫ1

peaks, shifted by 26.6 and 59.3 cm from the main band,

carrying ϳ12% and 8% of the total intensity of the band,

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8892

J. Chem. Phys., Vol. 112, No. 20, 22 May 2000

Reiche et al.

selves may shift their positions away from their zeroth-order

energies. Nevertheless, one can see that the number of states

available for low-order couplings is rather limited, providing

us with a reasonable chance of assigning the two perturbing

states that appear in the spectrum. Figure 9 shows that there

are only four dark states in the energy range of the observed

satellite peaks that can couple to the 6v₁bright state by

Ϫ1

terms of fourth order or less: 5v ϩv ϩ2v at 19 116 cm

,

1

2

6

Ϫ1

5

v ϩ2v ϩv at 19 132.4 cm , 5v ϩv ϩv ϩv at

9 167.7 cm and 5v ϩv ϩv at 19 169.6 cm . Compari-

1 3 6 1 2 5 6

Ϫ1

1

2

3

son of these predicted levels with the deperturbed positions

of the two measured satellite bands suggests that 5v ϩ2v₃

1

FIG. 9. Predicted positions for zeroth-order states in the energy range close

to 6v₁from a Dunham expression.

ϩv and 5v ϩv ϩv are the most likely candidates. We

6

1

2

3

assign the higher energy of the two satellite bands, with its

Ϫ1

deperturbed position of 19 165.1 cm

to 5v ϩv ϩv

1 2 3

rather than the nearby 5v ϩv ϩv ϩv since the former is

coupled to 6v₁in third order while the latter requires a

fourth-order term in the vibrational Hamiltonian. Although

1

2

5

6

_t_h_e_c_o_u_p_l_i_n_g_m_a_t_r_i_x_e_l_e_m_e_n_t_s_i_s_n_o_t_u_n_i_q_u_e_.₄2 One can further

simplify the situation by neglecting the coupling matrix ele-

ment between the two dark states. It is not at all clear if such

an approximation is justiﬁed, particularly without speciﬁc

information on the vibrational assignment of the zeroth-order

dark states. However, whether or not these two dark states

are themselves coupled simply affects our interpretation of

their zeroth-order energies and hence their vibrational as-

signments. The coupling among these two levels will not

change their center of gravity, and thus it will have no effect

^t^h^e^c^o^u^p^lⁱⁿ^g^b^e^t^w^e^eⁿ⁶^v1 and 5v ϩ2v ϩv requires a

1

3

6

fourth-order term, this state can couple to the 5v ϩv ϩv

1

2

3

level in third order and thus might be coupled indirectly to

6

v .

1

One should note that both perturbers (5v ϩ2v ϩv ,

1

3

6

5

v ϩv ϩv ) have quanta in the v -͑H–O–N bend͒ vibra-

1

2

3

^tⁱ^oⁿ^.^Aⁿ^e^f^f^e^c^tⁱ^v^e^c^o^u^p^lⁱⁿ^g^b^e^t^w^e^eⁿ^t^h^e^v1 ͑O–H stretch͒

^aⁿ^d^t^h^e^v3 ͑H–O–N bend͒ mode of HONO is not unex-

pected in that the v /v combination bands in the IR spectral

on their perturbation of the 6v bright state.

1

3

1

region show signiﬁcant anharmonicity which manifests itself

Within the above mentioned approximations, the deper-

turbation process consists of diagonalizing a 3ϫ3 matrix

containing the zeroth-order energies and the coupling matrix

elements W_A_Band W_A_Bwhere state A is the bright state and

states B and C are the lower and higher frequency dark

states, respectively. The matrix diagonalization procedure

was performed iteratively until acceptable values for the po-

sitions and intensities of the observed bands were obtained.

Ϫ1

ⁱⁿ^a^l^a^r^g^e^D^uⁿ^h^a^m^p^a^r^a^m^e^t^e^r^x13 of Ϫ24.36 cm . The cou-

pling between stretching and bending modes in HONO has

5

9

also been pointed out in recent studies of 3v and 4v and

1

in classical trajectory studies.⁶⁰In addition, strong couplings

between a stretch and a bend mode have been found for a

variety of other molecules such as substituted

methanes⁸

1,84,85

and benzene. High-level ab initio calcula-

86

tions like those recently performed on CHD OH should be

This procedure yields zeroth-order energies of 19 117.8,

2

Ϫ1

1

9 133.0, and 19 165.1 cm for the bright and two dark

able to identify the most important coupling terms in HONO

and test our simple arguments based upon coupling order and

states, respectively, with coupling matrix elements W and

AB

Ϫ1

87

W_A_Cof 9.7 and 14.3 cm

.

calculations of zeroth-order energies.

To identify the vibrational assignment of the zeroth-

order dark states, one might in a ﬁrst approximation consider

In addition to the strong couplings that give rise to the

satellite peaks discussed above, the intramolecular dynamics

of the highly excited molecule are also reﬂected in the line-

widths of individual rovibrational transitions. As displayed

in Fig. 5, these linewidths do not depend upon J over the

range investigated, and similar comparison reveals no sys-

tematic dependence upon K. This rules out the possibility

that rotationally induced IVR ͑i.e., Coriolis or centrifugal

coupling͒ makes a signiﬁcant contribution to the observed

line proﬁles. The observed linewidths must, therefore, arise

from either vibrational state mixing or from unimolecular

dissociation or a combination thereof. The contribution of

only states that can couple to the 6v bright state by low-

1

order anharmonic terms in the vibrational Hamiltonian, since

a number of studies have clearly indicated the central role of

such low-order couplings for controlling the vibrational en-

ergy redistribution dynamics.¹

–3,71,78,79,81–83

Of particular rel-

evance to the present work are the recent spectroscopic re-

sults on vibrationally excited methanol.⁷

1,79

Despite the

relatively high density of states in this molecule ͑ϳ120 per

Ϫ1

cm in this region͒, the 5v₁level selectively couples to

only a small number of states. We use the Dunham-

parameters given by Herman et al.⁵⁰to predict all vibrational

dissociation broadening at the 6v level is not nearly as clear

1

levels of HONO that are energetically close to the 6v level

and could couple to it by third- and fourth-order terms in the

as in the case of the 5v level since the unimolecular disso-

ciation rate is too fast for us to resolve directly.

1

vibrational Hamiltonian. We show these states in Fig. 9 for

As will be discussed more fully below, the line proﬁles

Ϫ1

an energy interval of Ϯ100 cm about the 6v position. The

at 7v reveal clumps of individual lines at sufﬁciently high J.

1

Ϫ1

calculated energies are likely to be several cm too high,

The individual members of those clumps exhibit widths that

since the only off-diagonal anharmonicities available are x₁₃

and x₁₄. Moreover, coupling among the dark states them-

are on the same order as those at 6v . If the widths of these

1

components at 7v reﬂect entirely lifetime broadening from

1

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J. Chem. Phys., Vol. 112, No. 20, 22 May 2000

Spectroscopy of trans-HONO. I

8893

FIG. 11. Rotationally unresolved spectrum of the 7v₁vibrational band of

q

FIG. 10. Magniﬁcation of the 6v₁band showing the difference in line-

widths for the different members of the coupled set of states.

HONO, via a 2� 0, 7� 2 excitation scheme using the Q branch of the ﬁrst

3

Ϫ1

OH-overtone at 7016.52 cm . The wave number scale represents only that

of the overtone excitation in the second step.

unimolecular dissociation, then we would expect the corre-

sponding contribution to the 6v line proﬁles to be signiﬁ-

sociation laser. While this spectrum contains a sharp Q

branch and clear P and R branch structure characteristic of a

parallel band of a prolate symmetric top, we detect a broad,

unstructured background signal underlying these features.

This background arises from OH ﬂuorescence, since it re-

quires the UV probe laser to be precisely tuned to an OH

transition, and thus it must result from the dissociation of

HONO. Moreover, it requires the presence of three laser

pulses in the same order as the DROPS scheme and is lin-

early related to the power of the overtone laser. One possible

explanation ͑as discussed more fully below͒ would be that

we are observing transitions from the intermediate 2v1 level

to the tail of a dissociative electronic state that overlaps the

7v1 band.

1

cantly smaller. It is likely that the 6v proﬁles are qualita-

1

tively similar to those of 5v in consisting of a number of

1

components arising from vibrational coupling to the bath,

each of which is broadened by the ﬁnite lifetime of the mol-

ecule.

Further insight on the dynamics of the molecule at this

level is provided by a comparison of the linewidths of indi-

vidual rovibrational transitions arising from the different

members of the strongly coupled triplet of states, 6v , 5v₁

1

ϩ2v ϩv and 5v ϩv ϩv . Figure 10 shows the spectrum

3

6

1

2

3

from the JЈϭ8, KЈϭ0 intermediate level to the 6v region

1

in which the small peaks are magniﬁed for comparison of

their linewidths. The linewidths of the intense components,

which consist primarily of 6v character are on the order of

Figure 12 shows a series of fully state-resolved double

resonance spectra using individual rotational states in 2v1

with KЈϭ0 as intermediates. We observe sharp transitions

that we assign to the 7v1 band of HONO, but the back-

ground signal discussed above remains, causing individual

rovibrational transitions to exhibit slightly asymmetric line

1

Ϫ1

1

cm , while those of the smaller components having

mostly character of the 5v ϩ2v ϩv and 5v ϩv ϩv

1

3

6

1

2

3

states are roughly two times broader. While this difference

could arise from either differences in the coupling strengths

of these ‘‘ﬁrst-order states’’ to the rest of the bath⁷¹or from₈

state-speciﬁc differences in unimolecular dissociation rate,²

we expect the former to be more likely in light of our sug-

gestion that anharmonic coupling is major source of the

spectral width. In either case, the differences in width clearly

proﬁles. Asymmetric proﬁles have been observed in the elec-

tronic photofragment yield spectra of FNO,⁸

8,89

and in this

case they have been attributed to the interference between

the oscillator strength of bound and continuum levels. This

effect was ﬁrst described by Fano,⁹⁰and the line shapes are

usually called Fano-type line proﬁles. Although the signal-

to-noise ratio in our HONO spectra is not sufﬁcient to permit

careful modeling of these line shapes, we believe that this is

the ﬁrst report of such line proﬁles appearing in vibrational

overtone spectra. The asymmetry of the lines thus conﬁrms

our speculation that the background arises from the presence

of a dissociative electronic state.

indicate that IVR from the 6v state is not complete on the

1

time scale of unimolecular dissociation. This will be dis-

cussed more fully in Sec. IV.

C. The 7v region

1

1. Spectroscopic parameters

We use a 2� 0, 7� 2 excitation scheme to access the

7

v level of HONO and detect the absorption of the disso-

A ﬁt of the line positions of the 7v band using an asym-

1

ciating photon by monitoring the OH fragment by LIF via

metric top Hamiltonian gives considerably less satisfactory

the Q (4) line. Figure 11 shows a rotationally unresolved

results than our ﬁt of 5v and 6v , and this is reﬂected in the

1

excitation spectrum of the 7v band of HONO, recorded by

uncertainties of the rotational constants shown in Table I.

One source of difﬁculty lies in the extraction of precise line

positions without proper modeling of the asymmetric line

1

pre-exciting a large number of intermediate J states via the

q

Q branch of the 2v band and scanning the overtone dis-

3

1

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8894

J. Chem. Phys., Vol. 112, No. 20, 22 May 2000

Reiche et al.

FIG. 13. Line proﬁles of transitions to several 7v₁rotational states with

Kϭ0 and J as noted in the ﬁgure. The bold lines represent Lorentzian ﬁts to

the data.

FIG. 12. Rotationally resolved double resonance spectra of the 7v₁state of

HONO originating from various intermediate levels with KЈϭ0 and JЈ

denoted in the ﬁgure.

strongly on the J quantum number. While low J double reso-

nance spectra exhibit smooth, near Lorentzian proﬁles, at

high J the features become much broader and begin to show

distinct clump structure. These partially resolved clumps im-

ply that the dominant contribution to the overall width is

intramolecular coupling and not lifetime broadening due to

dissociation of the molecule, since the latter would lead to

smooth Lorentzian line shapes. The J dependence of the

clump widths illustrated by Fig. 5 indicate that at high J,

Coriolis coupling plays the dominant role in redistributing

the energy deposited in the OH stretch to the rest of the

vibrational bath states.

proﬁles. Nevertheless, within the quoted error limits there is

a smooth trend in the rotational constants from 5v to 7v .

1

2. Linewidths and perturbations

Unlike the case for 6v , we detect no distinct satellite

1

bands due to strong coupling of dark background states with

the 7v level. The lack of obvious vibrational splitting in this

1

region is consistent with our assignment of the resonance in

the 6v region. Using the coupling matrix elements deter-

1

mined from deperturbation of the 6v₁spectrum together

with the Dunham parameters,⁵⁰we predict that the corre-

sponding coupling between 7v₁and the dark states, 6v₁

ϩ2v ϩv and 6v ϩv ϩv would be sufﬁciently out of

Ϫ1

The ϳ1 cm width of the individual components of the

clump puts a lower limit on the lifetime of the excited mol-

ecule and hence an upper limit on the contribution of lifetime

broadening to the line proﬁles. Moreover, assuming that

3

6

1

2

3

resonance that we would not see evidence of them in the

spectrum. This underlines the rather selective nature of the

strong vibrational coupling in highly excited HONO. Despite

HONO molecules excited to 6v will dissociate more slowly

1

Ϫ1

than at 7v , we suggest that vibrational coupling to back-

the fact that there are ϳ50 states per cm in this energy

1

^g^r^o^uⁿ^d^s^t^a^t^e^sⁱ^s^t^h^e^m^a^j^o^r^s^o^u^r^c^e^o^f^t^h^e^lⁱⁿ^e^wⁱ^d^t^h^s^a^t⁶^v1 ^.

region, the lack of certain doorway states allows the 7v₁

band to retain its vibrational integrity.

Despite the lack of strong splittings in this energy re-

gion, information on the intramolecular dynamics of the dis-

sociating HONO molecules is contained in the homogenous

line shapes. The left panel of Fig. 13 shows the line shapes

D. Birge–Sponer analysis

The extraction of information on the dynamics of highly

excited molecules from splittings and broadening of the fre-

quency domain data requires a proper understanding of the

zeroth-order basis in which to describe the molecular motion.

Fitting the observed overtone levels to an expression for a

Morse oscillator and comparing the extracted fundamental

frequency and anharmonicity with other molecules provides

insight into the nature of the vibrational motion responsible

for the oscillator strength. The energy levels of a Morse os-

cillator can be written in the form

for a number of 7v rotational levels with Kϭ0 and several

1

different J values. These spectra, which were recorded at

Ϫ1

0

.04 cm resolution, were ﬁtted by Lorentzian proﬁles to

obtain a rough estimate of the linewidth. Although the line

shapes are not well represented by a Lorentzian, particularly

at high J, we use this ﬁt as an estimate of the overall enve-

lope width. One can see from Figs. 5 and 13 that the mea-

sured lineshapes and corresponding envelope widths depend

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J. Chem. Phys., Vol. 112, No. 20, 22 May 2000

Spectroscopy of trans-HONO. I

8895

␯ϭAvϩBv²,

where B is the anharmonicity, x₁₁, and ␻ ϭAϪB is the

͑1͒

˜

e

harmonic frequency. A Birge–Sponer plot of ␯/v vs v will

˜

yield an intercept of A and a slope of B. Application of this

approach using the vibrational band origins of lower OH

stretch overtone levels of t-HONO, in combination with our

Ϫ1

data on 5v Ϫ7v yields Aϭ3670.2Ϯ1.8 cm

and Bϭ

1

Ϫ1

Ϫ80.8Ϯ0.4 cm , slightly different from the values of Hol-

land et al. based solely upon the lower overtone data.

5

9

These values are close to those found for the OH diatomic

molecule ͑3735, Ϫ82.8͒ and the HONO molecule ͑3628,

2

Ϫ79͒, suggesting that the zeroth-order bright state consists

almost entirely of OH stretch character. A good ﬁt of the

energies of light atom stretch vibrations to this Morse ex-

pression has been often erroneously cited as evidence for the

‘

‘local’’ or isolated nature of the vibrational mode. We em-

FIG. 14. Time-dependent survival probability of the initially prepared 6v₁

state. The oscillatory behavior on the early time scale of IVR can be de-

duced from the spectral splittings and the overall exponential decay is de-

termined by the spectral linewidths.

phasize that it is the energy range over which the zeroth-

order bright state character is spread and not the linearity of

a Birge–Sponer plot that determines the degree of isolation

of a particular vibrational mode.

of intramolecular dynamics. The survival probability P(t) of

IV. DISCUSSION

an initially prepared state ͉␾(0) ϭ⌺c ⌿ coherently pre-

͘

i i

3

,9

pared by a short pulse laser is given by

Having presented the rotationally resolved vibrational

overtone spectra of HONO in the 5v , 6v , and 7v re-

1

2

P͑t͒ϭ

p ϩ2

p p cos͑␻ t͒ exp͑Ϫt/␶͒,

͑2͒

ͩ

͚_i

i

͚

i

j

ij

ͪ

gions, we discuss here the overall picture of intramolecular

dynamics implied by these spectra. Given a certain bright

state, the dynamics are determined on short time scales by

the strong couplings that give rise to wide splittings ͑e.g., the

iϾj

with ␻ ϭ2␲(E ϪE )/h and p ϭI /͚I .

The coefﬁcients p and p are proportional to the mea-

sured line intensities, ␻ ϭ2␲(E ϪE )/h can be obtained

ij

i

j

i

j

ij

i

j

satellite peaks that we observe near 6v ) and on the longer

1

from the observed splittings in 6v . The function P(t) ex-

1

time scales by weak couplings that causes a single rovibra-

pressed in Eq. ͑2͒ and displayed in Fig. 14 shows the peri-

odic energy ﬂow between the zeroth-order bright state and

the restricted number of dark states. As discussed more fully

below, the overall exponential decay with ␶Ϸ6 ps ͑deter-

mined from average linewidths͒, reﬂects draining of the en-

ergy into the remaining dark states and the coupling to the

dissociative continuum.

At the 7v₁level, the states perturbing 6v₁appear to

have tuned out of resonance, leaving this state to appear

largely unperturbed. Thus, for times up to ϳ5 ps ͑determined

by the width of the individual features͒, energy appears to

remain entirely in the OH stretch after coherent excitation.

tional feature to appear as a clump of lines and by broaden-

_i_n_g_f_r_o_m_t_h_e_ﬁ_n_i_t_e_l_i_f_e_t_i_m_e_o_f_t_h_e_d_i_s_s_o_c_i_a_t_i_n_g_m_o_l_e_c_u_l_e_.₇1

We emphasize throughout this discussion that the dynamics

to which we refer are those that would occur if the bright

state were coherently excited by a short pulse laser at time

tϭ0.

A. Short time scale dynamics implied by strong

couplings

The short time dynamics of HONO molecules excited to

high OH stretching overtone levels are dominated by a few

speciﬁc strong couplings that tune in and out of resonance as

a function of the OH stretch level. The dynamics at the 5v₁

level is relatively simple insofar as it shows no splittings

Ϫ1

B. Longer time scale dynamics implied by the

homogeneous linewidths

within at least Ϯ50 cm from the band origin. This implies

that upon coherent excitation of the 5v band, energy would

1

remain in the OH stretch mode for on the order of 5–10 ps as

determined by the ϳ0.5–1.0 cm width of individual rovi-

brational features.

While the short time vibrational dynamics are reﬂected

by strong spectral splittings ͑or lack thereof͒, the longer time

scales of IVR will appear as either ﬁner splittings or, if cou-

pling is to a sufﬁcient number of levels, simply as a broad-

ened spectral lines. In addition to IVR dynamics, unimolecu-

lar dissociation imposes a width upon each eigenstate that

reﬂects the ﬁnite lifetime of the molecule. The difﬁculty in

inferring the longer time intramolecular dynamics of predis-

sociating molecules from frequency resolved data is in dis-

tinguishing such lifetime broadening from the apparent

broadening that comes from vibrational coupling ͑i.e., IVR͒

Ϫ1

The situation in 6v is different from that of 5v in that

1

relatively strong anharmonic resonances with two particular

dark states, 5v ϩ2v ϩv and 5v ϩv ϩv , appear, and

1

3

6

1

2

3

these will dominate the short time intramolecular dynamics.

Upon coherent excitation of the 6v level, energy will rap-

1

idly oscillate from the pure OH stretch state to these combi-

nation states. We can use the splittings and relative intensi-

ties of features in 6v to illustrate the early time dependence

1

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8896

J. Chem. Phys., Vol. 112, No. 20, 22 May 2000

Reiche et al.

to a dense manifold of levels.⁹¹The proper interpretation of

the long time dynamics requires an understanding of the rela-

tive importance of these two factors. To distinguish them,

one must compare the linewidths with direct measurements

of the unimolecular dissociation rates, or if such measure-

ments are not available, with theoretical predictions of the

limit on the lifetime of the excited HONO molecules of

about 5 ps.

V. SUMMARY AND CONCLUSIONS

In the present study we use double resonance excitation

via single assigned rovibrational states (v or 2v levels͒ to

1

dissociation rate. The HONO molecule represents one of

investigate individual rotational states belonging to the 5v₁,

only few examples⁶

,28,29,39–43

where time-resolved and fre-

6v , and 7v₁OH stretch overtones of trans-nitrous acid

1

quency resolved measurements exist for the same reactant

states, although in the present case the rates are only resolv-

͑HONO͒ in its electronic ground state. The absorption into

these quasi-bound states above the dissociation limit has

been detected by laser induced ﬂuorescence of the OH frag-

ment. The principal ﬁndings and conclusions are summa-

rized below:

able in rotational levels of the 5v band very close to the

1

dissociation threshold.

The interpretation of the linewidths in the 5v₁region

where we have direct measurements of the unimolecular dis-

•

Spectroscopic constants and homogeneous linewidths

sociation rate is clear. At energies close to E , rates on the

0

for 5v , 6v , and 7v levels of trans-HONO have been

1

order of 1–10 ns indicate that the contribution to the line-

width from the ﬁnite lifetime of the molecule is three orders

of magnitude smaller than the measured widths. This indi-

reported. The 6v band has been found to be split into at

1

Ϫ1

least three components over a range of 60 cm due to an-

harmonic coupling.

cates that the line proﬁles ͑which exhibit widths in the range

•

From the onset of dissociation from different rovibra-

Ϫ1

0

.15–1.0 cm ͒ are determined by coupling of the bright

tional states of the 5v level near threshold we determine the

1

state to a dense bath of dark states and hence represents a

time scale of ϳ5–30 ps for vibrational energy ﬂow. The lack

of J and K dependence indicates that this energy redistribu-

tion is controlled primarily by anharmonic terms in the vi-

brational potential. Although IVR is as much as 1000 times

faster than unimolecular decomposition, complete energy re-

distribution to all of the energetically accessible bath states

may occur on a much longer timescale, giving rise to unimo-

lecular dissociation rates that depend upon the precise eigen-

Ϫ1

HO–NO bond energy to be D ϭ16 772Ϯ14 cm

.

0

•

Direct determination of the dissociation rates of HONO

molecules excited to 5v levels near the dissociation thresh-

1

old enable us to extract the lifetime broadening contributions

to the homogeneous linewidth contributions from the ﬁnite

lifetime of the molecule in 5v . These results show that at

1

this level, dissociation occurs on a nanosecond time scale

while IVR occurs on a picosecond time scale.

•

Detailed examination of the linewidths and line shapes

2

8,29

state composition.

The observed ﬂuctuations in the mea-

in the 5v , 6v , and 7v overtone levels of HONO and

1

sured rates between close lying states suggest that the IVR

process is not complete on the time scale of dissociation.

The interpretation of the longer time dynamics of HONO

comparision with measured rate constants for 5v indicates

1

that in all cases the line proﬁles contain only small contri-

butions from lifetime broadening and, therefore, reﬂect

mostly intramolecular processes and not unimolecular de-

cay.

excited to the 6v level is not nearly as clear as in the case of

1

the 5v level since the unimolecular dissociation rate is too

1

fast for us to resolve directly. All the rovibrational transitions

• Studies of the rotational state dependence of the line

proﬁles of individual rovibrational transitions indicate that

that we observe at 6v have widths in the range of 1–1.5

1

Ϫ1

cm with no obvious dependence on J and K and seem to

for 5v₁and 6v , the primary mechanism responsible for

1

exhibit Lorentzian proﬁles. Based upon the behavior at the

IVR from the bright state to the bath of dark states is anhar-

5

v and 7v levels, we suggest that the primary broadening

monic coupling. At the 7v level, sharply increasing clump

1

mechanism at this level is vibrational coupling to the mani-

fold of dark states. This implies that IVR, which occurs on a

3

widths with increasing J indicates that Coriolis coupling be-

gins to play an important role in the energy redistribution

dynamics.

–5 ps time scale ͑as determined from the linewidths͒, is

faster than unimolecular dissociation, although the relative

magnitudes of these two processes are likely to be much

• A strong resonance between 6v and what appear to be

1

the 5v ϩ2v ϩv and 5v ϩv ϩv levels would lead to

1

3

6

1

2

3

closer than at 5v . The fact that the different components

fast vibrational energy oscillation between a restricted num-

1

resulting from the strong mixing of 6v , 5v ϩ2v ϩv and

ber of states if the band were coherently excited.

1

3

6

5

v ϩv ϩv exhibit linewidths that differ by a factor of 2

• Differences in linewidths between members of the

coupled 6v ⇔5v ϩ2v ϩv ⇔5v ϩv ϩv levels indicate

1

2

3

reinforces the notion that vibrational state-mixing is not

complete on the time scale of unimolecular dissociation.

1

3

6

1

2

3

that vibrational energy redistribution is not ‘‘statistical’’ but

rather depends upon zeroth-order character of the prepared

states.

The intramolecular dynamics of 7v appears to be some-

1

what different from the others discussed above in that IVR

seems to be governed mostly by Coriolis interactions to the

bath states. Overall clump widths of 0.5–3 cm over the

• State-to-state ﬂuctuations in the rates at the 5v level

indicate that IVR is not complete on the time scale of uni-

1

Ϫ1

range of J investigated imply an IVR time scale in the range

molecular dissociation.

1

.7–10 ps, strongly dependent on the J of the reactant state.

ACKNOWLEDGMENTS

The breakup of single rovibrational transitions into clumps

of lines with widths on the order of 1 cm imposes an upper

Ϫ1

´

We gratefully acknowledge the support of the Ecole

limit on the degree of lifetime broadening and hence a lower

Polytechnique F e´ d e´ rale de Lausanne ͑EPFL͒, the Fonds Na-

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J. Chem. Phys., Vol. 112, No. 20, 22 May 2000

Spectroscopy of trans-HONO. I

8897

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D. Luckhaus for providing us with the program used to ﬁt

the spectra. We also enjoyed stimulating discussions of vari-

ous aspects of this work with J. Troe. F.R. thanks the Stif-

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BMFT for ﬁnancial support.

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1

Article Doi

Double-resonance overtone photofragment spectroscopy of trans-HONO. I. Spectroscopy and intramolecular dynamics

DOI: 10.1063/1.481502

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Full text of DOI:10.1063/1.481502

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