3944
J. Phys. Chem. 1993,97, 3944-3955
FEATURE ARTICLE Stimulated Emission Pumping Studies of Energy Transfer in Highly Vibrationally Excited Molecules X. Yang,? J. M. Price, J. A. Mack, C. G. Morgan,* C. A. Rogaski, D. McGuire, E. H. Kim,$ and A. M. Wodtke’*ll-L9# Department of Chemistry, University of California, Santa Barbara, California 93106 Received: October 20, 1992; In Final Form: January 15, 1993
The stimulated emission pumping (SEP) technique has made the study of highly vibrationally excited molecules increasingly appealing, enabling sophisticated spectroscopic probes to be converted to preparation techniques. With such an approach even relatively improbable processes, such as vibrational energy transfer and chemical reactivity, may be studied. This article describes studies of the vibrational quantum number dependence of the vibrational relaxation of highly vibrationally excited nitric oxide and oxygen. The NO experiments are one of the first data sets on bimolecular energy transfer for molecules with several hundreds of kJ/mol of internal energy. Information is obtained showing to what extent energy transfer theories designed for low vibrational energy can be applied in this case. Strong evidence is also obtained suggesting that qualitatively different mechanisms such as “transient chemical bond formation” can influence the rate of vibrational energy transfer at high vibrational energy. Analogous experiments on 02 have also been carried out. Compelling evidence for 03 0 has been obtained. The the vibrationally enhanced endothermic chemical reaction 0&) 0 2 possible relevance of these results to the stratospheric ozxone budget is also discussed.
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Introduction During the last fifty years, the field of high-resolution spectroscopy has made an immense contribution to the understanding of molecular structure and interaction, evolving into one of the most mature and sophisticated fields in physical chemistry. Resolved rotational spectra routinely provide themost precise measure of molecularbond lengths for ground and excited electronic states. Atomic bonding within molecules has been extensively understood by infrared and Raman spectroscopy. High-resolution spectroscopy of molecular clusters is revealing the detailed nature of solute-solvent interactions. The understanding of vibrational energy flow within polyatomicmolecules, which is at the root of chemical reaction rate theory, has been and continues to be strongly influenced by high-resolution spectroscopy. Furthermore, the theoretical roots of molecular spectroscopy are deep and secure, linking experiment to the most fundamental level of molecular understanding, quantum mechanics.’ In recent years, significant progresshas been made in the study of molecules containing large quantities of internal energy.24 This is a spectroscopic subject of clear chemical relevance, since chemical reactions often involve either the consumption or production of highly excited species. For example,an exothermic reaction such as F + Hz HF(v) + H,5 often produces highly vibrationally excited products. Photochemistry, which in one sense is the process of converting ultraviolet photon energy into photoproductinternal (as well as kinetic) energy,is another arena for highly excited molecules. For example, it now appears clear that stratospheric ozone photodissociation,03 + hv 0 2 + 0,
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Present address: Department of Chemistry, Princeton University, Princeton, NJ 08544. IBM Graduate Student Research Fellowship Recipient. s Present address: Department of Chemistry, University of California, Berkeley, CA 94720. !I Camille and Henry Dreyfus Teacher-Scholar. 1. Alfred P. Sloan Research Fellow. # National Science Foundation Presidential Young Investigator. f
0022-365419312097-3944$04.00/0
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is an efficient means for producing vibrationally excited O2in quantum levels at least as high as v = 22.6 The role of highly vibrationally excited molecules is also important to endothermic chemical reactions, which are often strongly enhanced by vibrational excitation. In fact, it has been shown experimentally that control of vibrational excitation can be equivalentto control of chemical and photochemical reaction rates and branching rati0’s.~-I6 Another area of chemical interest is isomerization. Completelystable, closed-shell molecules may undergo chemical isomerization when enough vibrational energy is available. Consequently,even the chemical identity of a molecule might be controlled by state-specific control of a molecule’s vibrational excitation. For example, it appears that vibrational excitation of HCCH can lead to a totally chemically distinct isomer HzCC:.17 The same is true for HCN CNH’*J9and HCP CPH.*O Such studies are also leading to the experimental determination of chemical reaction potential surfaces, the most fundamental property of a chemical reaction.21 Most studies of highly vibrationally excited molecules have been sophisticated spectroscopicstudies designed to unravel the intramolecular properties of highly vibrationally excited molecules. A far smaller number of investigationshave attempted to use spectroscopic techniques as a means of preparing highly vibrationally excited molecules for study in bimolecular or gas/ surface collisions. New methods including stimulated emission pumping4(SEP) which will be described later, are efficient enough that experiments along these lines are becoming increasingly feasible. This is one of the most exciting new developments in the study of the chemistry of high-energy species. Our technological ability is advancing rapidly and we are now entering a period where it will become quite standard to prepare molecules in the “Boltzmann energy tail” with complete quantum state specificity and high enough efficiency to unravel the chemistry and collision dynamics of these highly energized species! Experiments such as these are the subject of this article, which describes work to investigate the vibrational energy transfer of
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0 1993 American Chemical Society
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The Journal of Physical Chemistry, Vol. 97, No. 16, 1993 3945
Feature Article molecules containing a very large amount of internal energy. SEP has been used to prepare large quantities of highly vibrationally excited NO as well as 0 2 . The self-relaxation rate constants could then be determined for an unprecedented range of vibrational quantum numbers using laser-inducedfluorescence as a probe. In both experiments a dramatic increase in the relaxation rate constant is found when the vibrational energy exceeds the lowest bimolecular reaction threshold. For NO: For 0,:
NO(u) + NO 02(u)
+ 0,
--
N 2 0+ 0
0, + 0
A2X
1
In the case of NO, this occurs despite the fact that the reaction rate constant remains quite small. This is the first time that the vibrational enhancement of vibrational relaxation has been observed to be related to the energy threshold for a bimolecular reaction. This observation may be evidence for new and unique energy transfer mechanisms that are possible only for highly vibrationally excited molecules. In the case of 02, bimolecular reaction appears to take place as soon as the vibrational energy exceeds the reaction threshold. This reaction may have importance in the stratospheric ozone budget, since the role of highly vibrationally excited molecules has always been neglected in atmospheric models. A comparison between NO and 0 2 also leads to some simple predictions about the reactive transition state.
/
/
/+--/
/ /
T
IO,OOO cm-I
Energy Transfer in Highly Vibrationally Excited NO Exothermic chemical reactions, ultraviolet photodissociation, and electrical discharges are three common and naturally occurring examples of means by which highly vibrationally excited molecules are produced. Such excited states may have unique and interesting chemicaland physical properties. Slow, normally unimportant chemical reactions may become rapid when large amounts of vibrational energy are found in the reaction ~oordinate.~-’6J2 Infrared emission may be stronglyaffected due to the fact that vibrationally excited molecules may sample a different part of the dipole moment functi0n.2392~Photochemical activity of highly vibrationally excited molecules can also be significantly altered. One physical phenomenon that is related to all of these issues is the rate of vibrational energy transfer for highly vibrationally excited molecules. How long does chemically active energy stay in a molecule? We would like to know, for example, if our understanding of molecular energy transfer, which has been derived from the study of molecules in v = 1, also applies to molecules with enough internal energy to undergo endothermic chemical reaction or isomerization. Although the field of molecular energy transfer is well developed, there have been very few investigationsof energy transfer for molecules with chemically signi’cant energy, largely due to the lack of good methods for preparing such species. Overtone excitation of H F into v = 3, 4, and 5 has shown that vibrational energy transfer may be greatly enhanced in comparison to u = 125.26 when vibrational energy is converted to translational energy (V-T).
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V-T HF(u) HF(0) HF(u - 1) HF(0) In cases where near resonant vibration-to-vibration(V-V) energy transfer is important, for example,
02(u) + O2(0)
-
+
v-v O,(u - 1) O,(1) there is reason to believe that vibrational excitation should slow down thevibrational energy transfer by many orders of magnitude since the energy resonance “detunes” with increasing vibrational quantum number due to anharmonicity.6 One of the most significant advances in this field is the development of stimulated emission pumping (SEP). Consider Figue 1 which shows the SEPmethod appliedto the NO molecule.
X211 Figure 1, Schematic representation of the potential curves for NO which are of relevance to the stimulated emission pumping of this molecule. A tunable argon fluoride laser was used to access the B state which has particularly good Franck-Condon factors, as is indicated by the wave functions. This approachcan be used to prepare essentially any vibrational level of NO up to u = 25. A third laser can be used to probe thecollisional consequences using laser induced fluorescence through either the B or A states.
SEP uses two lasers for vibrational pumping. The first ‘PUMP” photon is absorbed by molecules in a single thermally populated quantum state producing an electronically excited molecule, similarly, in a single well-resolved quantum state. The second ‘DUMP” photon stimulatesemission back to the ground electronic state. The beauty of this method is manifold. First, the overall transition probability is related to the molecular Franck-Condon factors for allowed electronic transitions. Compare this to direct overtone excitation, which relies on the deviation of molecular oscillators from the simple harmonic oscillator approximation and one will immediately realize that SEP transitions are, in general, much stronger and easier to saturate. Overtone pumping often relies on the large anharmonicity of hydride stretching motions, while SEP can allow access to many different kinds of vibrationally excited states. Finally, SEP is a double resonance spectroscopicmethod. The first laser prepares a single quantum state and the second laser, in essence, takes the spectrum of this single level. Typically, this means that complicated spectra can be unraveled much more easily than by other methods. The SEP method also has limitations. Conventional wisdom holds that the intermediate “stepping-stone”state must be long-lived so that during the time of the SEP process (typically 20 ns) this state does not decay. We will see below that SEP can also be carried out when the “stepping stone” state’s lifetime is as short as 10 ps! One particularly favorable application of SEP is to the preparation of highly vibrationally excited nitric oxide (NO).27-29 SEP allows quantum state specific control of the preparation of
Yang et al.
3946 The Journal of Physical Chemistry, Vol. 97, No. 16, 1993 V = 23 by SEP
Ercimcr Pumped
PUMP
DUMP ... .
J
Collectins k n s e 0 193nm Mirror 1=3
’’N
0
Vibrational Q u a n t u m Number
v
“N
“0
-
= 23 by SEP
Vibrational Quantum Number
Figure 2. Calculation of the actual vibrational population distribution created by stimulated emission pumping and the accompanying FranckCondon pumping. See text.
vibrationally excited NO for nearly every vibrational state up to u = 25, which contains more than 440 kJ/mol of vibrational energy. Figure 1 shows a potential curve diagram for the NO molecule. Excitation to the B state is accomplishedusing a tunable argon fluoride laser, and deexcitation back to high vibrational levels of the ground electronic state is performed with a XeCl excimer pumped dye laser. The large difference in equilibrium bond lengths between the X and B states means that many high vibrationallevels of the X state have good Franck-Condon overlap with the “stepping stone” state and can easily be produced using SEP. This approach provides an experimental capability that is the equivalent of a dial for the vibrational quantum number of NO! Actually, one must consider the situation a bit more carefully. Imagine that one can saturate both transitions in the SEP process. Then after the laser pulses are over (20 ns), one has a third of the initial population in each of the three radiatively coupled states. The excited electronic state then begins to radiate spontaneously,with a lifetime of about 1 MS, producing a range of vibrationally excited levelsof the ground electronicstatedictated by the Franck-Condon factors, qvTvft. This “Franck-Condon pumping” background tends to destroy the vibrational state specificity of the SEP method. However, spontaneous emission rates are proportional to the Franck-Condon factor times the third power of the emission frequency, qv,vtwv+,J.Consequently, low vibrational states which are formed by spontaneousradiation with the largest values of wv,vf,are favored by the Franck-Condon pumping and a high degree of specificity is obtained after all. Figure 2 shows the results of an examplecalculation of the actual state distribution produced by SEP including the effect of FranckCondon pumping for SEP preparation of u = 23. One can see that specific vibrational states can indeed be prepared with a high degree of selectivity. It should also be mentioned that a very new and elegant method called STIRAP (stimulated Raman scattering with rapid adiabatic passage) avoids the problem of
Figure 3. Experimental setup for measuring vibrational relaxation rate constants with stimulated emission pumping. The outputs of a tunable ArF laser and two excimer pumped dye lasers were overlapped in a standard low pressure sample cell. A gated photomultiplier tube blocks the light flash from the SEP and gates-on to detect the LIF probe signal resulting from the evolving population of vibrationally excited molecules.
spontaneousemission.3u1 This approach uses Fourier transform limited laser pulses and the phase relationship of the PUMP and DUMP lasers to coherently transfer all of the population from the initial state to the final state. It will certainly become the method of choice as Fourier transform limited lasers become more readily available. Figure 1 also suggests an experimental approach to the study of energy transfer in highly vibrationally excited NO. A high power pulsed ultraviolet laser is used to excite single rovibronic transitions in the B X system. A pulsed dyelaser subsequently stimulates downward transitions to the desired X211vibrational level on a time scale shorter than the gas kinetic collision time. After a variable delay comparable to the vibrational relaxation lifetime, a third laser can be used to probe the remaining population of the prepared vibrational level using LIF detection through either the A22 or B211 excited electronic states. Pressuredependent pseudo-fust-order lifetimes of the individual vibrational levelscan be obtained and from them thevibrationalstatespecific relaxation rate constant^.^^,^^ A schematic diagram of the experimental setup can be seen in Figure 3. Two millijoules of light from a tunable ArF laser (Model EMG 15OTMSC) was used to pump NO from U” = 0 of the XzIIstate to u‘= 7 of the B211state. This unique laser system is ideally suited for deep UV excitation of rovibronic transitions in diatomic molecules. Although originally somewhat difficult to use, we have had reliable results from a slightly modified commercial system.44 An excimer pumped dye laser served as the DUMP laser to stimulate transitions to the high vibrational levels of the ground state. A precise description of the pulse energies necessary for efficient SEP of this molecule can be found in our previous Another XeCl excimer pumped dye laser was used to probe either the prepared vibrational state or the collisionally populated ones. Laser-inducedfluorescence was detected through the A X or B X systems by a time-gated photomultiplier tube (Thorn-EM198 16B/GB 1001B) to eliminate detector saturation from the SEP spontaneous fluorescence background. Diffusionoutof the beam was controlledby focusing the pump beam and expanding the probe beam. One quite subtle difficulty that must be overcome in these experiments derives from the state-specific nature of the preparation and thedetection method. It is well-known that rotational relaxation is much faster than vibrational relaxation and, for that matter, most chemical reactions. Consequently,rotational equilibration will take place before most processes of interest. Since state-specific laser probes cannot be used to probe more than one rotational state at a time, the initially prepared population +
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Feature Article
The Journal of Physical Chemistry, Vol. 97, No. 16, 1993 3941
-
L
20-
:
.J
15-
> v
c
>
10-
Y
Y
504.0
508.0
506.0
PROBE laser wavelength ( n m )
-
5-
t*----
o ~ " " ' " " " " " " " '
Figure 4. Laser-induced fluorescence spectrum of B(u' = 1) X ( u = 16) band of NO after a specific rovibronic level of u = 16 was prepared with SEP. The spectrum was taken 8 ws after the SEP and at a cell pressureof0.4 Torr. Onecan seeclearly that thespin-rbit and rotational states come to local equilibrium by this time.
5
0
10
15
20
"
'
"
25
'
"
'
30
Vibrational Quantum Number (v)
Figure 6. Plot of the quantity of total decay rate constant divided by vibrational quantum number versus vibrational quantum number. This picture shows the two regions of vibrational dependence of total decay rates.
TABLE I: Inner and Outer Turning Points for Selected Vibrational States of NO. vibrational quantum number (u)
> -
-
0 5 10 15 20 25 30
,OOt 200 -
h
>
r
m
100-
,m.s 8
*f
e .* -
0 * " " " " " " " " " " " " " " ' 0 5 10 15
20
25
30
Vibrational Q u a n t u m Number ( v )
Figure 5. Vibrational quantum number dependence of the vibrational relaxation rate constants for two isotopes of NO.
will be diluted over all of the thermally populated rotational, and in this case, spin-orbit levels. One must therefore count on a significant loss of signal before any measurements can be made, unless one is expressly interested in spin-orbit and rotational energy transfer. For high vibrational states of diatomics there is no evidence that rotational energy transfer is significantly different than for low vibrational states. Our interest was in the vibrational relaxation. Despite these problems, due to the high efficiency of the SEP method andour ability to saturate thedouble resonance transitions, this experiment actually yields avery large signal. Figure 4 shows the fully rotationally relaxed laser-induced fluorescencespectrum of the (1, 16) B-X band obtained by scanning the probe laser wavelength at a pressure of 0.4 Torr, 8 ps after SEP. The timed decay of these spectral features can be used to measure the pressure-dependent collisional lifetime. Pressure studies are then used to extract rate constants for the decay of every individual vibrational state. These vibrational state dependent self-relaxationrate constants are displayed in Figure 5 for two isotopes (I4NI6Oand I5Nl8O). This figure shows one of the only completesets of data on molecular collisional properties over a wide range of internal energy. The dependence of the relaxation rate on vibrational excitation is quite obvious. For example, it increases by about 200 times for the highest vibrational level in comparison to u f f = 1. One can also see a large region at low energy (0 < u < 15) where the vibrational enhancement of the relaxation rate constant is rather modest. In comparison,when u > 15the vibrational enhancement is much stronger. Figure 6 shows that upon closer inspection, the rate constant in the low energy region is linearly proportional to its vibrational quantum number. This figure showsthe measured rate constants divided by the vibrational quantum number as a function of vibrational quantum number. The region of vibrational quantum number over which the curve is constant indicates
inner turning point (r< (u))~ 1.lO5(Oc) 1.018(4).087) 0.980(4. 125) 0.955(4150) 0.936(4.169) 0.921 ( 4 . 1 8 4 ) 0.9 lO(4.195)
outer turning point (r> (u))~ 1.203(od) 1.353(0.150) 1.458(0.255)p 1.558(0.355) 1.659(0.456) 1.769(0.566) 1.901(0.698)
Results of RKR analysis. Units are angstroms. In parentheses the deviation of r(O) is shown. e As a point of comparison, the equilibrium bond length of the B211 excited electronic state, where an electron has been promoted to an antibonding orbital, is displaced only 0.26 A from that of the ground state.
the linear part of the vibrational quantum number dependence. This linear region is thought to be dominated by Au = -1 collisional propensity rules. In the high-energy region above u = 15, we have been able to observethe presence of multiquantum relaxation, that is Au = -2 relaxation. Detailed experimentation on u = 18 showed that multiquantum relaxation is as important as Au = -1 relaxation in the high-energy region. Table I shows the inner and outer classical turning points of the vibrational motion for a few selected vibrational levels as derived from RKR analysis. One can easily see that the displacements are indeed large. As a point of comparison, bear in mind that the equilibrium bond length for the excited B211 electronic state, where an electron has been promoted to an antibonding orbital, is 1.4167 A, only 0.260 A displaced from the ground state equilibrium bond length. If 0.26 A is the bond length change associated with promotion of an electron to an antibonding orbital, then it is reasonable to assume that the electronic structure of the NO diatomic at the outer classical turning point of high vibrational states where the displacement is larger than 0.26 A away from the outer classical turning point of u = 0 is also strongly distorted from that of vibrationless NO. One might therefore expect that the vibrational energy transfer will be much different if the electronic structure distortions lead to significantly different interactions with the collision partner. Indeed as will be discussed further below, we believe that the vibrational states above u = 15 have stronger, transient chemicalbond-like interactions with the collisional partner NO. This hypothesis and the evidence for it will be discussed in more detail below. The Low-Energy Region One of the most notorious problems encountered in theories of molecular energy transfer is that of the NO-NO system. No
3948 The Journal of Physical Chemistry, Vol. 97, No. 16, 199‘3 one has been able to explain why NO self-vibrationalrelaxation out of v = 1 is about 105 times faster than that of other comparable molecules such as CO in u = 1. Additionally, the temperature dependence is highly unusual in this example. We have found that the SchwartzSlawsky-Herzfeld (SSH)theory,4547one of the simplest one-dimensional quantum mechanical theories of vibrational energy transfer, can be applied in a modified but logical fashion to provide a realistic if qualitative understanding of the low-energy region of our e ~ p e r i m e n t .It~appears ~ that the simple picture provided by this theory may be applicable up to about v = 14. The following is a simple description of the SSH theory. As the molecules approach one another, the oscillating,vibrationallyexcited bond feels a time-dependent force due to the collision, Fcoll(r).In classical mechanics we recall that a driven harmonic oscillator absorbs energy most rapidly when it is driven at its “resonant frequency”. For vibrational energy transfer, this means that Fcoll(t) must try to drive the vibrating bond at its resonant frequency. Since vibrations typically occur on the 10-14 s timescale while Fcoll(r) would be expected to fluctuate on the timescale of the molecular collision, 10-12 s,one way of understanding the energy transfer is in terms of a frequency mismatch problem; the vibrational frequency is much larger than the Fourier frequency components of Fcoll(t). It is also clear that if we can find the region of the classical collision’s trajectory where the Fourier frequency components of Fmll(t) are the largest, we will have found where the frequency mismatch is the smallest and where the V-T energy transfer is the most efficient. Let us follow a collision’s trajectory. At first as the collision’s trajectory samples the long range attractive part of the potential, FcOil(t) varies only very slowly in time because thegradient of the interaction potential is small at long range and the thermal collision energy is also low. In addition, the long range potential is an interaction with both atoms of the diatomic bond and probably does not exert a large force inducing one atom of the diatomic bond to move relative to the other. The collision proceeds until it reaches the repulsive wall, where the gradient of the interaction potential is by far the largest and where one can most accurately say that the collision is with one of the two atoms in the diatomic bond. It is in this region of the trajectory that Fcoll(r) has the highest Fourier frequency components and, according to the above arguments, where V-T energy transfer should be most efficient. The essence of this classical argument carriers over into quantum mechanics. Hence, SSH theory starts with the Ansatz that it is the repulsive wall, where the high-frequency vibration experiencesthe most rapidly varying collision-inducedforce, that allows vibrational-to-translational energy transfer to take place. For simplicity, SSH theory models the repulsive wall as an exponential fall-off. In light of the last paragraph, the steepness of this fall-off has an extremely strong influence on the relaxation rate. The collision velocity also plays a very important role and, consequently, SSH theory always predicts that V-T energy transfer is strongly enhanced by increased temperature. SSH theory does a good job reproducing the V-T energy transfer probabilities for many diatomics, such as CO/M for example. However, NO/NO V-T energy transfer is lo5times faster than CO/CO and it exhibits a very weak temperature dependence? This problem has yet to be explained in the literature. We give here a simpleexplanationwithin the frameworkof theSSH theory. Figure 7 compares a Lennard-Jones potential for CO/CO with a Lennard-Jones potential for NO/NO which is based on experimental bond energies and bond lengths.48-51 It is obvious that one of the principal differences between NO/NO and other molecules is the magnitude of the attractive well’s depth, and some have guessed that it is the attractive part of the potential that enhances V-T energy transfer in NO/NO. However, Yang was the first to realize that because of an anamolously large well depth in the NO dimer, the repulsive wall is also much steeper
Yang et al. 2000r
No-No
co-co
I
\
t
-1000’ 1
W 2
3
4
Intermolecular Distance
5
6
(A)
Figure 7. Potential curves for NO-NO interaction and CO-CO interaction. The dashed line represents the thermal energy level, &T(T = 300 K).
than for CO/CO. Yang carried out SSH-like calculationsusing the increased steepness and larger collision velocity due to the attractive well to show that SSH theory could predict the correct order of magnitude for the N O relaxation rate.42 Yang also compiled numerous relaxation rate data and showed that there is a direct correlation between the magnitude of the well depth and the relaxation rate constant for a number of closed-shell hydrogen bonded speciesas2 This early success still does not explain the temperature dependence. We have increased the sophistication of the SSH theory to includethe possibility of long range trapping in molecular collisions. This will be especially important for NO/NO at low temperature. This has been done by including the osculating sphere model for trapping with the SSH theory for V-T energy transfer. In the osculating sphere model for a given collision energy, there will be a maximum value of the impact parameter, b,,,, that creates a centrifugal barrier and prevents the forming collision complex from feeling the attraction between the two N O monomers. That is the centrifugal force, which tears the dimer apart, exactly balances the attractive interaction. Our model makes the simple assumption that all collisions at impact paramters smaller than b,,, will be trapped; that is, they will suffer an SSH-like collision with the repulsive wall. Therefore, we can use this maximum impact parameter as an estimate of the trapping cross section.
Next we imagine that the vibrational relaxation probability is proportional to the product of the trapping probability and the SSH relaxation probability that occurs on the repulsive wall.
This includes two processes that have opposite temperature dependencies. Trapping becomes more important at low temperature while SSH relaxation becomes less important. The expressionscan easily be derived as a function of collision energy. The thermal averaging was done by a Monte Carlo sampling program. Figure 8 shows the results of such calculations for CO/CO and NO/NO. The CO/CO is a control case where the attractive well is extremely shallow, and therefore no trapping can take place and one can see that we reproduce this example well, as one would expect from a normal SSH approach. Over the narrow temperaturerange shown here CO V-T energy transfer speeds up by almost 3 orders of magnitude. On the other hand, due to the competing influences of trapping and SSH-like V-T energy transfer, the NO/NO V-T energy transfer is hardly influenced at all by the change in temperature. The results of this comparison strongly suggest that the SSH/osculating sphere model is at least a qualitatively correct approach to the problem.
Feature Article
The Journal of Physical Chemistry, Vol. 97, No. 16, 1993 3949 c2v
-8
h
3
czv
11.00 1.218
9.00
6.00
Experimental NOiNO
I
Ni
-NZ
E =
200
7 \
04
03
1.398
1.322
L(ONO)
3.00
Nz
NI-
10.00
v
s“
Dzh
=
108.2
E = 16600 em-‘
27200cm-‘
E = zzsoo
cm-’
I ~
l
400
~
I
600 600 Temperature (K)
1
1000
~
~
1200
Figure 8. Temperature dependence of vibrational relaxation, experiment and theory. Model calculations o f N O ( u = 1) relaxation by Noincluding long range trapping followed by SSH-like relaxation (see text). Experimental data for NO self-relaxation was taken from the l i t e r a t ~ r e . ’ ~ The same model was also applied to the case of C O ( u = 1) relaxation by CO, which is known to be well described by SSH theory. Experimental data were also taken from the l i t e r a t ~ r e . ’ ~
When we consider the vibrational quantum number dependence of the relaxation rate constant, further support for the simple SSH approach is found since a linear dependence on vibrational quantum number is one of the central predictions of the SSH theory. Additionally, the direction of the isotope effect is correctly predicted by the SSH theory. It is easy to notice that the vibrational relaxation of 15Nt80is always slower than that of l4Nl6O for the same vibrational quantum level. This behavior isstillobservedeven if the rateconstants areplottedvsvibrational energy instead of vibrational quantum number. This is the opposite behavior one would expect for an exponential energy gap law, since heavy N O has more closely spaced vibrational quantum levels. On the other hand, this is precisely the direction of the isotope effect predicted from SSH theory. All of these considerations taken together provide evidence that some of our simplest and most insightful ideas about vibrational energy transfer can be used a t higher energy. Our results show that the “linear region” extends up to as high as u = 15 and it is reasonable to surmize that below this level of excitation the mechanism for energy transfer described above is the correct one. This is the first experimental information which sheds light on the question of applying existing energy transfer theories to highly vibrationally excited molecules.
The High-Energy Region Inspection of Figures 5 and 6 show clearly that above about u = 14, vibrational energy enhances the relaxation rate constant more than linearly. Indeed, there is a threshold for enhanced vibrational relaxation which occurs close to u = 14. It is quite interesting to note that this is precisely where the bimolecular chemical reaction NO NO -* N 2 0+ 0 becomes energetically accessible. On the other hand, if this threshold were to be due to the onset of chemical reaction, how is it that we are able t o perform our experiment even for such high vibrational states as u = 23, where one might suspect that the prepared vibrational state would disappear too rapidly to be detected? Furthermore, how is it to be explained that we could prepare u = 19 and detect the collisionally quenched u = 18 and 1742 if chemical reaction is important? A series of experiments was carried out in order to prove that bimolecular chemical reactions were not contributing to the collisional lifetime.29 These experiments used a small-volume photolysis cell. If the observed rate constants were indeed due to bimolecular chemical reaction
+
~
~
(a)
(b)
t
(c)
Figure 9. Calculated structures of NO-NO from the work of Mark Gordon’s group. 500-
SSH-type Collision
“Chemical” Interaction
K
h 3
Lh
400Weak Interaction
4 0
-0
7
300-
-i 200h
P
& N
n
Linear Region A V
= -1
v
4:
100-
” 0
0
10000
J
20000
30000
40000
Vibrational Energy (cm-1)
Figure 10. Apparent correlation of the calculated energies for the D2h and Cla(N0)z complexes with energies at which relaxation accelerates.
of vibrationally excited NO, it would have been possible to photolyze the sample with the SEP lasers. Mass spectral analysis of the samples showed that the N O was not consumed by the SEP process, implying that relaxation was the dominant collisional loss process. Nevertheless, we are faced with the observation that the vibrational energy transfer experiences an acceleration when we come above the reaction threshold. This observation led us to hypothesize that trajectories which pass near to the transition state for bimolecular chemical reaction may lead to enhanced vibrational energy transfer efficiency. This hypothesis was dubbed “transientchemical bondformation”. Another possible way that transient chemical bondformation could play a role was suggested by ab initio calculations of high-energy forms of the N O dimer, carried out by Gordon and his Three such complexes are shown in Figure 9 along with their energies. These forms of NO dimer are remarkable in the simplicity of their valence bond structures. They all apparently exist at the bottom of a local minimum in the potential surface. Figure 10 shows how the energies of two of these high-energy NO dimers apparently coincide with acceleration of the vibrational relaxation rate. Our experiments do not allow us to determine which of these two different forms of transient chemical bond formation, if any, is responsible for the acceleration of the vibrational energy transfer. However, it is quite reasonable to expect that trajectories that pass near to a chemical reaction’s transition states will experience a stronger Fcoll(t). This mechanism implies that, in comparison to the low-energy region, the high-energy collisions will be characterized by a significantly stronger and more anharmonic deviation of the interaction potential along the vibrating N O coordinate from its asymptotic (nearly harmonic) form. Consequently one might expect to see the change in mechanism manifested, not only in the magnitude of the rate but also in the vibrational quantum
Yang et al.
3950 The Journal of Physical Chemistry, Vol. 97, No. 16, 1993 number changing propensity rules. Detailed state-to-state measurements have, in fact, shown that Av = 2 is as important as Av = 1 relaxation in the high-energy region above u = 15.42 This is to be contrasted with the observed linear dependence of relaxation rate on vibrational quantum number, which implies the dominance of single quantum relaxation in the low-energy region. We believe this is consistent with the idea of transient chemical bond formation. It should be pointed out that efficient multiquantum relaxation has been observed when the perturbation approximationinherent to the SSH theory is invalid, for example in I2 where thevibrational spacing is significantlyless than kT.s4+ss However, for NO even at these high energies the vibrational spacing is still much bigger than kT. For example, thevibrational spacing in 14N16O between u = 18 and u = 19 is 1350 cm-I while kT is 208 cm-I. The idea of transient chemical bond formation suggests that at high vibrational energy, the electronicstructure of NO is much different than that of NO at its equilibrium geometry. Table I shows that the magnitude of the bond distention is indeed large and we have suggested that this implicates a distortion of the electronic structure of NO in high vibrational states. Ab initio calculations of the vibrational state specific dipole moments also show strong evidence of the electronic distortion of the vibrationally excited NOSZ3All diatomics that separate to neutral atoms must asymptotically have a zero dipole moment. This means that NO’S dipole moment, which is essentially zero at its equilibrium geometry, rises slowly and turns over going back to zero at infinite separation. Although this interesting effect has not yet been observed experimentally,this t u n over is theoretically predicted to occur near the outer classical turning point of u = 20.23 Furthermore the orbital occupation analysis of the ab initio calculations shows much more excited state character at these large NO separations. One should not think that the dipole moment for these high vibrational levels is particularly large and likely in itself to have a major impact on thevibrational relaxation. It is not. However, in the region of intenuclear separationswhere the dipole derivative is zero, it is also likely that this “NO molecule’s” interactions with another NO(u = 0) reflect a part of the four-atom-potentialenergy surface that is nothing like the well-known (NO)z van der Waals molecule. In this experiment it was observed that vibrational excitation can strongly enhance vibrational relaxation, and it was suggested that this is due to trajectories which pass near to the transition statesof chemicalreactions. Let us now consider another example. Vibrational Energy Transfer of Highly Vibrationally Excited 0 2
The depletion of the stratospheric ozone layer due to halogencatalyzed, gas-phase chemistry has made its way into the cultural knowledge of the modem American. Due to its obvious importance, a great deal of effort has gone into developing a chemical and meteorological model that can accurately predict the outcome of assumed pollution scenarios. The complexity of this undertaking is daunting and it comes as no surprise that even the “best” models have significant failings. One of the most difficult problems has been thedevelopmentof a model that can accurately reproduce the experimentallydetermined ozone altitude profile. In point of fact, no existing model can accomplish this seemingly simple requirement. This has led some to suspect that one or more of the underlying assumptions of all of the models might be in error. Surprisingly, these suspicions turn out to implicate highly vibrationally excited molecules! One of the most fundamental simplificationsused in nearly all atmospheric models is the assumption of local thermodynamical equilibrium (LTE).s6 According to this assumption, theinternal quantum state distribution of all atmospheric constituents can be described by an equilibrium distribution characterized by a local temperature. Because atmospheric temperatures are
relatively low (ca. 200-300 K), assuming LTE means assuming that nearly all atmospheric constituents are in their lowest vibrational quantum state. In order to see the importance of the LTE assumption, imagine the modeling complexities if it were not applicable. It is well-known that individual quantum states of molecules, especially excited electronic and vibrational states, can exhibitstartlinglygreater reactivity than thelowest vibrational quantum state. Consequently if one cannot assume LTE, each quantum state of an atmospheric constituent would have to be treated as if it were a unique atmospheric species with its own rate constants for chemical and photochemical production and destruction. Similarly, if one were to attempt a concentration retrieval from infrared emission data collected from a satellite, it would be necessary to know the nonequilibrium, steady-state distribution of emitting vibrational levels, a distribution governed by many state-to-state collisional processes. On the other hand, if the LTE assumption is valid, an enormous simplification obtains. For example, all of the detailed statespecific reactivity information can be averaged out and replaced by the Arrhenius law and an activation energy. Even a photochemical process can be described simply by a temperature dependence. Similarly, a molecule’s infrared radiance can be theoretically interpreted using the Planck law of radiation in order to determine concentration profiles from satellite data. In essence, for the cases where the LTE assumption holds, quantum states of molecules “do not count“. Traditional chemical kinetics will be a sufficient conceptual framework for atmospheric modeling. A priori, if the production rate of a nonequilibrium quantumstate distribution of a given atmospheric constituent is large in comparison to the rate of return to equilibrium, the atmosphere will establish a nonequilibrium, steady-state distribution of molecular quantum states. If this nonequilibrium distribution of quantum states were toexhibit specialchemicalor photochemical behavior, no amount of modeling within the LTE assumption would accurately reproduce the actual atmospheric events. Indeed, “fiddling” with an LTE model to fit an inherently nonLTE set of data would bequite a dangerous undertaking, possibly leading to very erroneous conclusions. Consequently, it is of the utmost importance to determine if LTE models are being applied inappropriately and, if so, to determine what non-LTE properties are of importance. It has been recognized recently that the mid-latitude stratosphere is a likely region to find non-LTE phenomena since (1) ultraviolet photochemistry, which can produce highly energized photoproducts, is important and (2) the total pressure is low, meaning the return to equilibrium may be slow. One of the most important examples was suggested by Slangeret a1.6 to help explain the inability of LTE models of the stratosphere to reproduce measured ozone altitude profiles.57 After considering the unexpected laboratory observation that 248-nm irradiation of pure 0 2 leads to ozone formation, Slanger was able to show that UV photodissociation of 0 3 produces highly vibrationallyexcited 0 2 , which can absorb light at much longer wavelengths than LTE distributions of 0 2 vibrational states. This implies that vibrationally excited 02 may be much more easily photodissociated than 0 2 in u = 0 and that this could be a non-LTE source of ozone. Steps 1-3 characterize the “Slanger mechanism“ for nonLTE ozone formation. Since there is much more solar photon
0, + hv (A
-
- + + - +
250 nm)
0,(3Z,u)
+ hv (A > 300 nm) 20(3P) + 2 0 , 2M 2 0 ,
02(3Z,u)
O(3P)
(1)
20(3P)
(2)
2M
(3)
flux at wavelengths longer than 300 nm in the stratosphere, this mechanism a l l o ~ s O ~ ( ~ 2to, ubecomeanozoneprecursor. ) Again,
Feature Article
The Journal of Physical Chemistry, Vol. 97, No. 16, 1993 3951
cc
eV
2.4 W21) P(19
10 8
\
\ \ \\
;wpUMp PROBE
x3x
’
51bO
’
51680 ’ 51720 ’ Excitation Frequency (cm-1)
51760
’
5 l h
Figure 12. 02 Schumann-Rungeexcitation spectrum. When the tunable argon fluoride laser is scanned while observing the gated fluorescence from a cell containing 100 Torr of 02 as 190 OC,the spectrum shown is recorded. Hot band transitionsare easily assigned from well-established 02 spectral studies as shown in the figure.
Figure 11. Electronic states of 0 2 and the PUMP-DUMP-PROBE scheme. This figure shows the stimulated emission pumping scheme for measuring the collisional properties of highly vibrationally excited 0 2 . The PUMPlaser induces population transfer from the X3Z,- to the B3Z,-. The DUMP laser induces emission back to high vibrational levels of the X3Z,- state. A third PROBE laser observes the time evolution of the prepared state. The experimental approach is quite effective, despite the facts that nanosecond pulsed lasers areused and that all of thevibrational levels of the B3Xu- state predissociate on the picosecond time scale.
if we had assumed LTE, this source of ozone would not have appeared in the model. What evidence is there that O3photodissociation leads to highly vibrationally excited 02? Photofragmentation translational energy measurements of O(3P) atoms resulting from ozone photodissociation at 226 nm gave strong albeit low resolution evidence for efficient production of highly vibrationally excited 02 in vibrational levels as high as u = 28.58 Recently, the distribution of vibrationally excited 02 resulting from ozone photolysis at 248 nm has been measured in Slanger’s laboratory using high-resolutionLIF methods, showing efficient production of 0 2 ( u )up to and including u = 22.59This measurementconfirms the hypothesizedproductionmechanism for high vibrationallevels of 0 2 . A photochemicalmodel of the upper atmosphere60v61was used to include the Slanger mechanism and it was found that the presence of highly vibrationally excited 02 was a possible way to improve the altitude profiles of 0 3 as well as a means to model recent 6.9-pm infrared emission measurements from the LIMS.62 A very recent model c a l c ~ l a t i o nidentified ~~ the important areas for experimental measurements to be (I) the vibrational distribution of 0 2 ( u ) from ozone photodissociation as a function of photolysis wavelength and (11) the determination of vibrational relaxation rate constants. The stimulated emission pumping technique is clearly suited to investigation of the collisional propertiesof highly vibrationally excited molecules, as can be appreciated for the case of the NO molecule discussed above.27-29.42*43.64,65 One complication arises when considering application of the same methodology to 02. Figure 1 1 shows a potential curve diagram for 02.Unlike NO (shown in Figure 1) the intermediate “stepping stone” state used for the SEP is far above the ground state dissociation limit and predissociation is much more important for 0 2 than for NO. Indeed the predissociation rates are about loll s-I. No conventional SEP experiment has ever been done on a molecule with such a short lifetime as this.66 In fact it is conventional wisdom that the “stepping stone” state must have a nanosecond timescale lifetime in order to perform SEP. Therefore SEP on 02 poses an excitingtechnical questionin addition to the atmospheric ones: Is it possible to use the SEP method when the intermediate state predissociates so rapidly?
Figure 1 1 also shows the experimental approach that was applied. A pulsed tunable argon fluoride PUMP laser is used to pump 02 from u = 0, 1, or 2 of the X32,- ground electronic state to u’ = 4, 7, or 10, respectively, of the B32,- excited electronic state by way of the well-known Schumann-Runge system. A powerful DUMP laser stimulates emission, inducing population transfer back to a specific vibrationallevel of the ground electronic state. As will be seen stimulated emission is efficient enough to compete with the rapid predissociationof 0;s B state. A third tunable PROBE laser detects the vibrationally excited 02 by laser induced fluorescence. By varying the time delay between the DUMPand the PROBE, the time dependenceof the prepared vibrational level can be followed, data that contains the relevant information necessary to deriving the vibrational state specific relaxation rate constants. The experimental arrangement is nearly identical to that used for NO. 02 flows rapidly through a cell at a well-controlled pressure and temperature. The tunable argon fluoride laser is overlapped carefully in space and time with the output of an excimer pumped dye laser, the DUMP. A second excimer pumped dye laser is spatially overlapped but variably delayed to give the PROBE signal. The PROBE signal is averaged on a boxcar and plotted out on a digital plotter or collected by a PC-286 clone. Figure 12 shows the results of the one laser experiment where the tunable argon fluoride laser’s wavelength is scanned over its 1 nm tuning range. Many 0 2Schumann-Runge bands are readily observed and assigned, mainly to rotational structure in the 10 2 and 7 1 vibronic bands.67 In order to enhance the hotband signal, the cell is heated to 465 K. Under these conditions very high quality data are obtained. Figure 13 shows the results of the next most complicated experiment, where the PROBE laser’s wavelength is scanned at a fixed delay with respect to the PUMP laser, while the PUMP laser excites one of the rovibronic transitions of Figure 12. In this figure one sees the results of the experiment are a high signal-to-noise spectrum of the 0 21 LIF band. The u = 21 population has been created in this experiment by the small fraction of 02 B state which has spontaneously emitted to u 1 21, rather than undergone predissociation-the fate of the vast majority of molecules that were excited to the B state. This creates a time evolving population in u = 21 as the molecules cascade back down the vibrational ladder. This experiment is performed in order to find the correct laser frequency at which the u = 21 target state can be detected with the PROBE laser. Once this has been accomplished, the PROBE laser is tuned to a strong feature of the 0 21 spectrum. Figure 14 shows the results of the three laser experiments, scanning the wavelength of the DUMP laser while observing the LIF signal from the PROBE. One can see that when the DUMP laser hits a resonance
- -
-
-
,:
Yang et al.
3952 The Journal of Physical Chemistry, Vol. 97, No. Id, 1993
data points
1
3
5
7
9
11
13
Figure 15. Time dependence of the SEP signal. The natural log of the SEP induced population of u = 24 plotted vs time. The data are shown as squares. The straight line is the best fit to the data from which a pressure-dependent lifetime can be derived. This experiment was carried out at 190 O C and 50 Torr. R(13)
P(151
DUMP v ' :
10
-
v"=20
PUMP v ' = l O - v " = 2
P(151
I P(191
PUMP
1
"':10+-"":2
Rl17)
I02
FCP Contribution
L 4 I
354 100
L
355 900
APUMP
(nm)
Figure 14. Stimulated emission pumping of 02. The PROBE signal described in Figure 4 is dramatically enhanced at specific frequencies of the DUMP laser. This is shown in this figure. The two transitions are the P and R branch emission transitions of the PUMP-laser-prepared quantum state. The two traces show the dependence of the positions of the SEP transitions on the choice of the PUMP transition. The contribution of the Franck-Condon pumping is indicated.
transferring population from the single rovibronic level prepared by the PUMP laser, a large enhancement of the PROBE signal results. These features can readily be assigned to specific stimulated emission transitions with well-known frequencies.68 Predissociationhas long been thought to preclude the possibility of performing SEP on a molecule. It is a great success of the SEP method that this experiment is possible, euen though the intermediate "stepping-stone state" predissociates on the picosecond time scale! In Figure 15the collisional lifetimeof the prepared vibrational s t a t e is measured. This is accomplished by repeatedly scanning the DUMP laser over the stimulated emission transition and recording the magnitude of this signal as a function of DUMPPROBE delay. This method of acquiring the data guarantees that the time dependence of the contribution to the prepared vibrational state's population which is due to SEP is independent of the time evolution of the population due to Franck-Condon pumping. These data are fit to an exponential function and the exponentialtime constant is derived. Similar measurements are made at a series of pressures. In Figure 16 the inverse of the exponential time constant for a representative vibrational state was plotted against the pressure and linear regression analysis was carried out to determine the fitted straight line. Oneobserves the expected linear dependence on pressure. The slope of this
01
Figure 16. The derived relaxation rate constant. The inverse of the derived pressure-dependent collisional lifetime for u = 24 (prepared by SEP) is plotted vs pressure. The slope gives the relaxation rate constant.
TABLE Ik Relaxation Rate Constants for Specific Vibrational Levels of O2 --
0
0
k(u)" (T = 300 K)
k(u)" (T = 465 K)
19 20 21 22 23 24 25 26 27
(4.7 0.3) x 10-15 (3.2 f 0.3) X 10-15 (5.8 f 1.2) x 10-15 (5.4 f 0.8) X (12 f 4) x 10-15 (8.4 & 0.4) X (18 0.5) x 10-15 (47 i 0.2) x 10-15
(2.3 0.1) x 10-14 (3.1 0.08) X lO-I4 (2.2 0.9) x 10-14 (3.7 0.3) x 1044 (4.1 0.6) X l&14 (6.9 f 0.5) X lO-I4 (1 1.7 0.2) x 10-14 (16.4 & 2) X (83.0 f 5 ) x 1 0 4 4
* * *
cm3 molecule-' s-1.
straight line is used to derive the vibrational state specific rate constant for disappearance from the prepared state. Table I1 and Figure 17 show vibrational self-relaxation rate constants for 19 I u I 27, high vibrational states of 0,which are thought to be produced by atmospheric ozone photodissociation. These experimentswere carried out at two temperatures, 465 and 300 K. Up to u = 26 the rate constants were determined as described above. However, it was found that u = 27 disappeared much too rapidly to be observed directly with the PROBE laser in this experiment, strongly suggestingtheonset of a new relaxation channel. This is a very interesting result since u = 27 is the first vibrational level studied that is within kTof the chemicalreaction energy threshold.69
0,+ 0,---L 0,+ 0 Although we could not observe u = 27 directly, Figure 18 shows the measured time dependence of u = 26 and 25 obtained after
Feature Article
The Journal of Physical Chemistry, Vol. 97, No. 16, 1993 3953
I
18
22
21
Ku(465KI I KuIZ95KI
24
26
I
-2,’OO -1.’50 -1,’OO -0.50 0.00 0.50 1.00 1.50 Differencefrom Calc. Frequency (“1)
28
ulbratlonal quantum number
Figure 17. Vibrational state specific relaxation rate constants for highly 2 being relaxed by collisions with 02. vibrationally excited 0
O,gi 1,
I
0.8
2.00 2.50 3.00
Figure 19. “Trickle down spectroscopy” of u = 27 and u = 28. The PROBE laser is tuned to detect the presence of u = 26 which was observed 26 band, 2 ps after the SEP. The DUMP laser is through the 2 scanned over the DUMP transition producing u = 27 (upper trace) which is easily detected after the u = 27 “trickles down” to u = 26, the identical experiment for production of u = 28 (lower trace) from which one observes almost no ”trickle-down” signal in u = 26. The u = 27 data are at least 1OX larger than that of u = 28. This is strong evidence that u = 28 reacts 2 to form 0 and 03.See text. with 0
-
:;K\,\ 0.1
0
0
1000 2000 3000 4000 5WO 6OOO 7000 8000 9000 10000
Delay time Dumpprobe (ns)
Figure 18. Observation of the time dependence of u = 26 and 25 after preparation of u = 27. The open squares are the data for the time dependence of u = 26 while the x’s are that for u = 25. The solid lines are the results of a model calculation that assumes single quantum relaxation. The solid line which appears as an early time exponential fall-off is the model calculation results for the prepared state, u = 27.
preparing u =: 27. Obviously, someof the prepared u = 27 “trickles down” to the longer lived u = 26 and 25 levels. By probing the u = 26 population 1 ps after SEP, the 7 27 DUMP resonances could be observed, leaving no doubt that we do, in fact, prepare u = 27. The fit to the data in Figure 18 assumes a model which only allows single quantum relaxation, that is: 27 26 25 24. This decision was made after considering the fact that the NO vibrational self-relaxation proceeded by single quantum relaxation as long as the vibrational excitation was below the first bimolecular reaction threshold. Further evidence for the use of a single quantum relaxation model is found in the theoretical calculations of Billing.70 These calculations give reasonable agreement with experiment for u I 20 and imply the importance of single quantum relaxation by both V-T and V-V energy transfer.
-
-
0,(4+ O,(O)
0,w
--
O,(U - 1) + O,(O)
--
0,+ 0 ’0, + 0,
V-T
v-v O,(U - 1) + 0,(1) Finally, the good fit to the data in Figure 18 is suggestive that single quantum relaxation dominates the disappearance of u = 26 and 25. From the analysis of the data in Figure 18 it was possible to derive the collisional removal rate constant for u = 27 which is also shown in Table I1 and Figure 17. As expected from the fact that it could not be observed directly due to its short lifetime, the derived relaxation rate constant for u = 27 is much larger than for u I26. We believe that the large jump in the + O,(O)
removal rate constant for u = 27 means that a significant fraction of the prepared u = 27 reacts forming ozone. This interpretation is further supported by an observation made when we apply the method of “trickle-down spectroscopy” to u = 28. Figure 19 makes a comparison between two experiments where the DUMP laser is tuned over the resonances for preparation of u = 28 and 27. The transfer of population to either u = 27 or 28 is detected by probing the longer lived u = 26 vibrational state with the PROBE laser set at a 2-3 ps delay. While it is clear that a fraction of the SEP prepared u = 27 population “trickles down” to u = 26, there is no evidence that u = 28 “trickles down” at all. This is consistent with the dominance of bimolecular chemical reaction forming ozone for u = 28. By comparing the intensities of these two signals, we can estimate the reaction rate constant for u = 28 to be about lo-” cm3/s. These experiments tend to confirm the suspicion that highly vibrationally excited molecules can play an important role in the stratospheric ozone budget. However, it also appears that the original Slanger mechanism for ozone formation may not be the only possible hypothesis to explain the discrepancies between reality and existing LTE ozone models. It is clearly of great atmospheric interest to know to what extent photolysis of O3 leads to02vibrational states where u 1 27,vibrational states that appear to react. Such measurements should be carried out as a function of photolysis wavelength over the entire O3absorption spectrum. Before concluding, one is curious to ask why oxygen might react while NO experiences only enhancedvibrational relaxation. It turns out that this is exactly what one would expect based on simple arguments concerning the nature of the transition state. First consider the oxygen case. The reverse reaction
E, = 4.6 kcal/mol
AH = -93.7 kcal/mol
-
is a classic example of a strongly exothermic reaction with a small activation energy analogous to the F + H2 HF H reaction. In contrast, the reaction
N,O
+ 0 -NO
+NO
+
E, = 28 kcal/mol
AH = -36 kcal/mol is significantly less exothermic and has a much larger activation
Yang et al.
3954 The Journal of Physical Chemistry, Vol. 97, No. 16, 1993
energy. Hammond was apparently the first to realize that the activation energy correlates with the similarity or dissimilarity between the transition state and the reactant^.^',^^ The so-called Hammond postulate states that if the activation energy is high, the transition state differs greatly from the reactants in energy and structure, while if the activation energy is low, the transition state resembles the reactants both in energy and structure. This line of reasoning suggests that in the oxygen case the transition state could be very similar to 0 03, while the transition state for NO + NO N20 + 0 is not very similar to N2O + 0. In other words from the point of view of the possible reactions in the SEP experiment one would expect the following:
-
0,+ 0, 0,+ 0 NO + N O + N , O + 0 --+
+
LATE BARRIER EARLIER BARRIER
It is well-known that reactions with the late barriers are strongly enhanced by reactant vibrational energy while those with earlier barriers require reactant translation e n e r g ~ . ~ 3This 3 ~ ~is consistent with our observations that suggest the ozone-forming reaction is fast, while no evidence of N2O formation has been found. It would be a very valuable contribution if ab initio calculations could be carried out on these two chemical reaction potential energy surfaces.
below the bimolecular reaction threshold. Above the reaction threshold a dramatic increase in the collisional removal rate constant was observed, similar to theNO experiments. However in contrast to NO, the oxygen experiments provided strong evidence for the dominanceof bimolecular reaction for vibrational states above the reaction threshold. The similarities and differences between NO and 0 2 are consistent with simple concepts of early and late barriers to reaction, and a comparison of the two experiments reinforces the concept of transient chemical bond formation in the NO relaxation system. Acknowledgment. This work was partially supported by the donors to the Petroleum Research Foundation, administered by the American Chemical Society, National Science Foundation Presidential Young Investigator Award CHE-8957978, and National Science Foundation Atmospheric Chemistry division ATM-8922214. In addition, a small grant from the Universitywide Energy Research Group from the University of California is gratefully acknowledged. This work was also made possible by the Santa Barbara Laser Pool under NSF Grant CHE841 1302. The Camille and Henry Dreyfus as well as the Alfred P. Sloan foundations are gratefully acknowledged. Specialthanks go to Professor J. William Rich at the Ohio State University for his help with models of vibrational energy transfer as well as many useful discussions.
Summary Vibrational energy transfer dynamics of very highly vibrationally excited NO and 0 2 were studied by the PUMP-DUMPPROBE method. These studies show two of the best examples of how modern laser methods can be used to transform spectroscopic techniques into preparative methods. Vibrational selfrelaxation of NO was studied for vibrational energies as high as 440 kJ/mol. Several important observations came out of these experiments. First, it was found that below u = 15 the V-T energy transfer exhibited a linear dependence on vibrational quantum number. The magnitude of the vibrational relaxation rate constant, the direction and magnitude of the isotope effect between I4Nl6Oand I5Ni8O,the temperature dependence, and the vibrational quantum number dependence all point to a simple mechanism where long range trapping is followed by vibrationalto-translational energy transfer on the repulsive wall of the interaction potential. The onset of the higher than linear dependence of vibrational energy transfer came at the energy threshold of the lowest accessibleendothermic bimolecular reaction: N O NO N2O 0. This as well as calculations by Gordon et al., which showed the presence of stable high-energy collision complexes,suggested that a qualitatively different relaxation mechanism may be important in these studies at high vibrational energy. This hypothesized mechanism was named transient chemical bond formation and means simply that trajectories which pass near to the transition states of chemical reactions or collision complex formation channels may give rise to much more efficient vibrational energy transfer. This hypothesis indicates a fundamentally stronger and less harmonic interactionat high vibrational excitation. Further evidence for this line of reasoning was found in the third important experimental observation. It was found that for high vibrational levels, Au = 2 relaxation was about as important as Au = 1 relaxation. This result obtained, despite the fact that the energy separation between vibrational levels was 5 to 10 times kT. Such behavior has not been previously observed. The same experimental method has also been applied to the important atmospheric problem of highly vibrationally excited 0 2 . The experimental approach works well even though the intermediate state used in the SEP preparation predissociated on a picosecond time scale. In this example, a single quantum relaxation model was able to reproduce the time evolution of the vibrational states even for relaxation of the last vibrational state
+
+
-
References and Notes (1) The number of volumes dedicated to high-resolution spectroscopy is far too large to reference here. One excellent and representative publication is: Steinfeld, Jeffrey I. Molecules and Radiation; M.I.T. Press: Cambridge, MA, 1985. (2) A representative collection of recent work can be found in a special issue devoted to stimulated emission pumping: J . Opt. SOC.Am. 1990, 87. (3) Crim, F. F. Annu. Rev. Phys. Chem. 1984, 35, 657. (4) Hamilton, C. E.; Kinsey, J. L.; Field, R. W. Annu. Rev. Phys. Chem. 1986, 37, 493. ( 5 ) Neumark, D. M.; Wodtke, A. M.; Robinson, G. N.; Hayden, C. C.; Lee, Y. T. Resonances in Electron-Molecule Scattering, Van der Waals Complexes and Reactive Chemical Dynamics; ACS Symposium Series No. 263; Truhlar, D. G., Ed.; American Chemical Society: Washington, DC, 1984, and references therein. (6) Slanger, T. G.; Jusinski, Black, G.; Gadd, G. E. Science 1988, 241, 945. (7) Crim, F. F.; Hsiao, M. C.; Scott, J. L.;Sinha, A.; Vander Wal, R. L. Philos. Trans. R . Soc. London A 1990, 332, 259. (8) Crim, F. F.; Sinha, A.; Hsiao, M. C.; Thoemke, J. D. Proceedings of the 24th Jerusalem Symposium in Quantum Chemistry and Biochemistry, 1992. (9) Hsiao, M. C.; Sinha, A.; Crim, F. F. J . Phys. Chem. 1991,95,8263. (10) Sinha, A. J . Phys. Chem. 1990, 94,4391. (1 1) Sinha, A.; Hsiao, M. C.; Crim, F. F. J . Chem. Phys. 1990,92,6333. (12) Sinha, A.; Thoemke, J. D.; Crim, F. F. J . Chem. Phys. 1992,96,372. (13) Vander Wal, R. L.; Crim, F. F. J. Phys. Chem. 1989,93, 5331. (14) Vander Wal, R. L.;Scott, J. L.; Crim, F. F. J. Chem. Phys. 1991, 94, 3548-3555. (15) Vander Wal, R. L.; Scott, J. L.; Crim, F. F.; Weide, K.; Schinke, R. J . Chem. Phys. 1991.95, 3548. (16) Bronikowski,M. J.; Simpson, W. R.; Girard, B.; Zare, R. N. J . Chem. Phys. 1991, 95, 8467. (17) Chen, Y.; Jonas, D. M.; Kinsey, J. L.; Field, R. W. J . Chem. Phys. 1989, 91, 3976-3987. (18) Yang, X . ; Rogaski, C. A.; Wodtke, A. M. J . Chem. Phys. 1990,92, 21 11. (19) Yang, X.; Rogaski, C. A.; Yang, X.J.Opt. SOC.Am. 1990,87,1835. (20) Chen, Y.-T.; Watt, D. M.; Field, R. W.; Lehmann, K. K. J . Chem. Phys. 1990, 93, 2149-2151. (21) Gazdy, B.; Bowman, J. M. J . Chem. Phys. 1991, 95,6309. (22) Kleinermanns, K.; Wolfrum, J. Appl. Phys. 1984, 834, 5 . (23) Billingsley, F. P., I1 J . Chem. Phys. 1975, 62, 864. Billingsley, F. P., I1 J. Chem. Phys. 1975, 63, 2267. (24) Amiot, C. J . Mol. Spectrosc. 1982, 94, 150. (25) Dzelzkalns, L.S.; Kaufman, F. J . Chem. Phys. 1983,79 (8), 3836. (26) Dzelzkalns, L. S.;Kaufman, F. J . Chem. Phys. 1982,77 (7), 3508. (27) Yang, X.; Wodtke, A. M. J. Chem. Phys. 1990, 92, 116. (28) Yang, X.; McGuire, D.; Wodtke, A. M . J . Mol. Spectrosc. 1992, 154, 361. (29) Yang, X.;Kim, E. H.; Wodtke, A. M. J . Chem. Phys. 1990.93.4483. (30) Becker, M.; Gaubatz, U.; Bergmann, K.;Jones, P. L. J . Chem. Phys. 1987,87, 5064. (31) Coulston, G.; Bergmann, K. J . Chem. Phys., submitted.
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