J. Phys. Chem. 1993,97, 8 116-8 127
8116
FEATURE ARTICLE Diode Laser Studies of Collisional Energy Transfer George W. Flynn' Department of Chemistry and Columbia Radiation Laboratory, Columbia University, New York, New York 10027
Ralph E. Weston, Jr.' Brookhaven National Laboratory, Upton, New York I1973 Received: March 1, 1993; In Final Form: May 4, I993
Time-resolved infrared diode laser absorption spectroscopy has proven to be a remarkably sensitive probe for the study of collisional energy transfer processes. The high spectral resolution makes it possible to determine the rovibrational states, as well as the translational energy content, of small molecules excited in collisions. We illustrate this technique with studies of "hot" atom collisions and show that in the case of H C02 encounters the experimental results can be explained by a simple "breathing ellipsoid" model. Recently, we applied diode laser spectroscopy to studies of collisional energy transfer from highly vibrationally excited molecules, containing chemically interesting amounts of energy. Our results indicate that most of the energy loss from the donor molecule results in rotational and translational, rather than vibrational, excitation of the "bath" gas species. The small number of collision events which lead to vibrational excitation of the bath molecule states appears to be dominated by long-range forces in which donor vibrational energy is exchanged for acceptor vibrational energy with little or no excitation of the rotational and translational degrees of freedom.
+
I. Introduction Energy transfer from molecules excited to high vibrational levels plays an important role in the reaction kinetics of many chemical systems. A particularly striking example is presented by a gas-phase unimolecular reaction, with the mechanism in its simplest form given by:
+ M -,Rt + M, Rt + M R + M, R
Rt
-
-
k,
(1)
k-,
(2)
products, k,
(3) Here, R is the reactant molecule; M is any molecule, including the reactant, products, or added inert species, and the dagger indicates reactant molecules with enough energy to overcome the barrier between reactants and products. The reaction mechanism outlined above is greatly simplified because the rate constants, k,,are written as if they were independent of energy, i.e., did not depend on the internal states of the molecules involved. One of the goals of our workover the past few years has been to determine this dependence. Energy removal from moleculesexcited to low vibrationallevels has been extensively studied over the past two decades.1.2 Experiments in which global energy loss is measured have been superseded by techniques that make it possible to excite molecules into specificvibrational modes and to monitor the transfer of this energy into other vibrational modes, as well as into rotational or translational energy. The theoretical treatment of these processes is also well advanced, and reasonable agreement between experiment and theory is found for many small-moleculesystems. Unfortunately, there is a large gap in the energy range between this type of study and the energy domain relevant to molecules capable of undergoing chemical reaction. Only recently have methods been developed for studying energy transfer from molecules (especially large polyatomics) excited to well-defined 0022-365419312097-8116$04.00/0
energies. In the approach we have adopted, a "donor" molecule is excitedto a singletstate that either undergoesinternal conversion back to the ground electronic state or is strongly mixed with the ground state. In either case, a pulsed laser excitation source produces ground electronic state molecules with large but welldefined amounts of vibrational energy. The mechanism of energy loss is then examined by observing the vibrational, rotational, and translational energy distributions in the "acceptor" molecule using infrared diode laser absorption spectroscopy as the probe. The spectral resolutionof this technique (- 3 X 1(r cm-1) permits the ready assignment of specific vibration-rotation transitions, and, from the Doppler broadening of absorption lines, the translational energy of the acceptor molecule can also be determined. Such studies provide information that leads to a better understanding of the features of potential energy surfaces that govern the interactions of molecules containing "chemically interesting" amounts of vibrational energy. Both the first and second steps in the above mechanism involve an energy transfer process, which in the case of the first step is the conversion of collisional energy into vibrational energy of the reactant molecule. At room temperature, the average translational energy is only about 300 cm-I, low compared to the spacing of typical vibrational energy levels (500-3OoO cm-1). Therefore, the necessary excitation of the reactant requires higher temperatures, many collisions, or both. In order to increase the probability of this translational-vibrational (T-V) energy exchange, we have utilized "hot" atom methods, in which the collisional energy is of the order of 20 000 cm-1 and corresponds to temperatures as high as 10000-25000 K. All of these experiments have employed "hot" H atoms produced by the laser photolysis of substrates such as a hydrogen halide or hydrogen sulfide. In the course of our experiments in which diode laser spectroscopy is used as the probe, we have obtained information about the final quantum state and translational energy distributions in small molecules excited by collisions with hot H atoms. 0 1993 American Chemical Society
Feature Article Dlwc UICR
The Journal of Physical Chemistry, Vol. 97,No. 31, 1993 8117
n
150 cm-l), spectrally pure (10.0003 cm-1 linewidth), cw (continuous wave), commercially available, low-power (- 1 mW/ cm2) diode laser. By selectively tuning to, and monitoring, transitions such as
\
LEN8
/.u*l*./
OOOO,J-OOO1,Jf
1;
01'0,J-+01'1,Jf
1
10°0,J-lOO1,Jf
1;
0200,J-+0201,Jf 1
01'1,J-+01'2,Jf
1;
0220,J-O221,J*
LIALQY
-
..
A LENS
Figure 1. Diagram of a typical arrangementfor the experimentsdescribed in this article. The UV photolysis or excitationsource is either a pulsed excimer laser or an excimer-pumped dye laser. The IR probe source is a tunable diode laser, operating at temperatures of 10-50 K, mounted in a closed-cycle helium cryostat that provides both temperature and current tuning of the diode laser. The excimer and diode laser beams are made collinear by a dichroic mirror that transmits IR and reflects UV light; a similar mirror removm the UV beam before the IR beam is reflected into a monochromator for mode selection. After a monochromator, the IR beam is focused on an InSb (77 K) detector, and the resulting signal is amplified and stored in a digital oscilloscope. A small fraction of the incident IR beam is split off to pass through either a gas-filled reference cell or a scanningetalon. The signal from the detector viewing this beam controls the current through the diode laser in order to fix the wavelength.
This information, in turn, has led to the development of a classical model which explains the results of H* + C02 scattering semiquantitatively.
II. Experimental Section-The Diode Laser hobe Technique Almost all studies of dynamic processes in molecules begin with an initiating pulse that pushes the system away from equilibrium. The interesting dynamical information (kinetic rate constants, cross sections, and quantum state lifetimes) is then obtained by following the return of the molecular system to equilibrium with some probe technique. In our experiments, the time origin is established by a light pulse from an excimer laser or an excimer laser-pumped dye laser; in either case, the pulse duration of 10-20 ns is instantaneous on the time scale of the collision processes being monitored. The diode laser probe method, which we and others have developed over the past few years, is an extraordinarily powerful, very high resolution, highspeed, sensitive method for, following the dynamic events that occur following the initial dye or excimer laser pulsed excitation. Like all really useful experimental methods, the technique is essentially a simple one and, although novel in its application to the types of processes we are investigating, makes use of wellknown ideas and commercially available equipment. Figure 1 shows a diagram of the basic apparatus used in these experiments. The essence of the diode absorption method is the realization that any vibration-rotation level in a variety of small gas-phase molecules can be monitored through an absorption transition, as illustrated below for C02, of the following type: C02(mn'p,J,v,)
+ hu( -4.3
Fm)
-
CO,(mn[p+l,Jfl,v,)
where m is the u1 (1388 cm-l) mode quantum number, n the u2 (667cm-l) mode quantum number, p the u3 (2349 cm-l) mode quantum number, J the rotational angular momentum quantum number, 1 the vibrational angular momentum quantum number, and VL the translational velocity along the laser probe direction. The source of infrared light is a continuously tunable (over 5 0 -
1
the entire behavior of the populations in these states can be followed during and after a collision or photofragmentationprocess which produces COz(mn'p,J) as the result of an optical pulse.3-16 The combination of small anharmonicities, which separate the mn'p mn'p 1 transitions for different values of m, n, 1, and p byO.l-10cm-1, and thehighspectralpurityofthedioderadiation allow us to separate with ease these different absorption feature^.^^^.'^ Moreover, since such transitions "ride" the very strong v3 absorption coefficient and have essentially the same oscillator strength as the OoOO-OOol transition, even the infrared inactive vl symmetric stretch (1oO0) and the u2 bending fundamental (01lo), whose emission at 15 pm is relatively difficult to detect (us factor plus detectorlimitations), can be easily observed and probed. We have used this techniqueto probe all three normal modes of N20, C02, and OCSL7produced as a result of collisions, photodissociation, or chemical reactions. Very recently, we extended the technique to probe molecules such as H20, NO2, CD4, CDF3, CF3D, and CS2, and we are setting up experiments to monitor other polyatomic molecules such as CHCD and S02. Although the amount of diode laser light absorbed depends on the difference between the lower and upper state populations (e.g., N(0110) - N(0l'l) for the 01'0 01'1 transition), there are a variety of ways to test for the significanceof an upper level population in such experiments (time behavior of the observed signals, gap laws, etc.). The most direct method, however, is simply to measure the absorptionof successively higher transitions until there is no significant absorption. In practice, for the systems which we have studied so far the determination of individuallevel populations is s t r a i g h t f o r ~ a r d . ~ - ~ ~ A key feature of the diode probe technique, which we have exploited with considerable success in recent experiments, is the ability to probe the nascent Doppler line width of molecules which have undergone a collision with a highly energetic species. The laser line width is only about one-tenth as large as the room temperature (- 300 K) Doppler line width of a typical molecule absorbing in the infrared spectral region. We have been able to resolvecollision processes which produce an increase in the Doppler profile of a recoiling molecule that corresponds to as little as a 50 K increase in the translational temperature.28 This amounts to a recoil energy of only about 50 cm-l per molecule (0.14 kcal/ mol)! Although our initial use of the diode laser probe technique was to study collisions between high-velocity ("hot") hydrogen atoms and C02, this experimental method has become remarkably diverse in its application to a number of different problems in chemical dynamics. Thus, we have used diode laser probing to investigate the quantum state and velocity recoil profiles of fragments produced in bimolecular chemical reactions19 and to study the vibrational, rotational, and translational energy distributions of bath molecules 'heated" by collisions with highly vibrationallyexcited molecules.16J8.m*21 In addition,we have used this same technique to follow the transfer of energy from electronically excited atoms3-s-5.2z and hot electrons23.24 to cold quencher molecules, to determine the energy disposition in photodissociation,8*12and to study V-V energy transfer,lo as well as to study interactions between translationally hot atoms and cold molecules.2~39
-
+
-
-
8118 The Journal of Physical Chemistry, Vol. 97, No. 31, 1993 The remarkable resolution of the diode laser probe method has several advantages. First, specificquantum-state-resolveddetails of kinetic processes such as photodissociation,inelastic collisions, or chemical reactions can be probed at a previously unattainable level. This will improve our understanding of these very fundamental processes. Second, the high-resolution absorption method provides an almost unambiguous probe for a given molecule, or a specific state of a molecule, in the presence of many molecules or molecules distributed in hundreds of different quantum states. Thus, in a complex reacting mixture of gases, the diode laser absorption probe allows us to follow a single "interesting" molecule or a single "interesting"state of a molecule without interference from a very large number of "uninteresting" processes. It is a very specific probe for the proverbial "needle in a haystack".
Flynn and Weston
TABLE I: Cross Sectionsafor Excitation of Various Vibrational States of Cor Due to Collisions with Hot H and D Atoms atom, final C02 cross energy (eV)* state, mdp section, A2 ref 0001 H,2.30 0.54 34 0001 D,2.16 0.32c 34,9 0002 H,2.30 0.026 38 01'1 H,2.30 0.12 36 H,2.30 1000/0200 (upper) 0.34 31 tOO0/02'% (lower) H,2.30 49 0.26 0220 H,2.30 0.20 31 a Theabsolutecrosssectionsdetermined in these experimentsareknown with an accuracy of *25%. Relative translational energy. C Calculated from the rotational population of C02(0001) excited by H atoms and the relative probability of exciting individual rotational levels by H and D atoms.
III. Hot Atom Excitation of Vibrational States of Polyotomic Molecules
A key idea which we set out to test in these experiments is whether the rotational and/or translational energy profiles of different final vibrational states of COZ,produced by collisions The photochemical production of atoms with translational with hot H atoms, could give clues as to which H/CO2 collision energy much greater than that of their surroundings at ambient trajectories were the most effective in excitinga given vibrational temperature was discovered almost 50 years a g ~ "Hot" . ~ atom ~ ~ ~ level. This is one of the main reasons for studying collision kinetic studies were an active field of research for some time processes of polyatomic as opposed to diatomic molecules. The before interest gradually diminished. The availability of intense increased complexity that goes with unraveling collision data for pulsed light sources in the form of excimer lasers and dye lasers three different vibrational modes is richly compensated by the made it possible to study hot atom processes in real time, instead remarkable information enhancement that goes with studying of relying on analyses of reaction products. As a result, interest the effects of collisions on the different vibrational motions. To in this field has been renewed, and scientific activity in the area illustrate these ideas, we consider the collision processes that has been intense for roughly the past decade. produce the three different vibrational states C02(0110), In our own laboratories,the infrared diode laser probe technique C02(00°1), and CO;!(OIOl): for following high translational energy collisions has produced a truly stunning variety of experimental data, revealing for the first time unexpected and unheard of details about collisions between "hot" hydrogen atoms and carbon dioxide molecules.6179111.13-15,1735-3* The experimentalstudy of this hot H atom collision process has produced a large amount of data which can be used to test potential energy surfaces for the H COScollision system as well as to compare fully quantum, quasiclassical trajectory, and classical calculations of the collisional excitation probabilities and energy distributions for the final states of
+
c02.424
+
A. H* Cor. The basic experiment in these studies can be described by the equations
H
- + +
CO,(mn'p,J,v,)
+ hv(4.3 pm)
H,S
+ hv( 193 nm)
HS H*
(hot atom production)
H*+ C0,(0Oo0,J',v')
CO,(mn'p,J,v)
-
CO,(mn'p+ 1 , J f 1 ,vL)
(collisional excitation)
(diode laser probing)
The hydrogen atoms, H*,produced in the first step have approximately 2.3 eV of translational energy, corresponding to a "temperature" of nearly 24 QOO K. Upon collision with carbon dioxide, an arbitrary final vibration-rotation state of the C 0 2 molecule is produced. The pressure and laser beam geometry conditionsare such that the majority of the nascent hot H atoms leave the laser probe region without suffering any collisions, and less than 10%of the hot H atoms suffer two collisions within the observation region. High-energy collision data have been obtained for C02 final states oo00 (pure rotational scattering), 0110,1OOO, 0200,020,OOOl, 01'1, and 0002. These data are far too extensive to cover in detail here, but we will highlight some of the more interesting results and summarize the major findings.
The form of the vibrationalmotion for each of the final vibrational states is shown to the right. As noted above, an intriguing feature of these experiments is the hope that the different vibrational modes, reflecting as they do different atomic motions of the C02 molecule, will act as indicators of the relative efficiencies of "endon" versus "broadside" collisions in producing translational, rotational, and vibrational excitation of the molecule. This hope has been at least qualitatively borne out in the data obtained so far, although more precise theoretical computations will be required before quantitative comparisons between the experimental data and these simple ideas are possible. For example, optimum antisymmetric stretch excitation (0001) should occur for hits out near the 0 atom ends of the molecule, while bend excitation (0110) should peak for hits near the C atom center of the molecule. It is worth noting that such expectationswould not be reasonable if H and C02 formed a tight, long-lived complex. So far there is no evidence in our data of the influenceof a collision complex, and early theoretical scattering calculations on the H + CO;!system4 also indicate that complex formation has little effect on the probability of excitation for C02 vibrational states lower in energy than -4000 cm-l, which includes all of the states which we have studied so far. Thus, the simple mechanical ideas expressed above are a reasonable starting point from which to look at the H* + COz scattering data. We shall see below that these concepts go a long way toward explaining the observed data. To illustrate the kind of information obtained from these experiments, consider collisions that excite the antisymmetric
Feature Article
The Journal of Physical Chemistry, Vol. 97, No. 31, 1993 8119
co2(00'0, O'O'O
J') +
H* -+
CO, (00'1, J) + H
w
C02(0000;J)tH*
+ CO2(0Oo1;J)t H
C02(OOoO;J')tH*
CO2(O1'1;J) t H
01'1 x 4 1.0. 0
0.5-
0
0
0
Off
/
\
0
,
9'
WOI
\
' ~ ~ ~ ~ ' ~ ~ ~ " " " ' ~ " ' " " ' ~ ' ' ' ' ' 10 20 30 40 50 60 70
J
Figure 2. Solid line, best polynomialfit to data (opencircles) represcnting the rotational population of C02(OOO1,J)resulting from collisionsof C02 with H atoms of 2.3-eV transiational energy (data from ref 34). The area under the H atom curve is normalized to unity. The dashed line is correspondingpopulation distribution produced by collisionswith D atoms (2.1 eV). This distribution is calculated from that produced in H atom
collisions, combined with the relative probability of exciting specific rotational levels with D atoms compared with H atoms (ref 9).
stretchingvibrational state 0001?,79956J8.31*33-35 Figure 2 illustrates the rotational population distribution for this state, produced by H* collisions. The population peaks at about J = 39, well above the most probable room temperature thermal value of J' = 16 in which the molecules started. Typical changes in angular momentum correspond to A J = 30-40 units of h/2u, and the fall-off in population for J > 39 is almost certainly due to the conservation of angular momentum. A simple calculation shows that J values up to 200 are allowed based on energy constraints but that the total angular momentum available in the collision (orbital angular momentum of the H*/C02 collision plus initial angular momentum, J', of the C02 ground state) limits the final J to the range 0-75. In fact, the maximum J is actually limited by the molecular dimensions of COZsince the orbital angular momentum in a collision is L = pv6. Here, p is the reduced mass of H/C02, v is the H atom-CO2 relative velocity, and 6 is approximately the distanceof closest approach of H to C02 during a collision that produces excitation. The maximum value of 6, which determines the maximum value of L since p and v (essentially the H atom velocity) are fixed in these experiments, is set by the dimensions of the C02 molecule to be about 2 A. This results in a maximum L of around 50 units of h/27r. For initially nonrotating C02 molecules, the final angular momentum J cannot exceed L. Somewhat larger final J values can result from collisions between initially rotating C02 molecules and H atoms. Thus, H* COz collisions can be thought of here as being "starved" for angular momentum, with thelimits of available angular momentum set by the dimensions of the C02 molecule and the H* atom momentum. Figure 2 also shows the rotational population distribution for C02(0001) excited by collisions with hot D atoms. The difference between the distributions for excitation by H and D atoms is attributed to the increased orbital angular momentum in D atom collisions. The available energy of D is changed only slightly from that of H (due to the zero-point energy difference between H2S and D2S), but the change in mass lowers the D atom velocity by a factor of - 4 2 . Because the reduced mass for D-CO2 collisions is roughly twice as great as that of H-COZ collisions, there is an overall increase of - 4 2 in the orbital angular momentum of the D atoms. At low J levels ( J 0), the H atoms are more efficient by a factor of about 4 in exciting C02, but the ratio approaches unity at J 70, because the maximum possible AJ for D atom collisions is larger than that for H atom collisions.9 The differences in the rotational population distributions for
+
-
-
J
Figure 3. Data for collisions between hot H atoms (2.3-eV translational energy) and C02(oooO): filled circles, rotationally resolved populations for the even rotational levels of COz(O1l l ) ; open circles, corresponding values for C02(OOO1). The solid line represents the rotationally resolved population distribution for the 01'1 state predicted by the breathing ellipsoid model (see text). Each data set has been normalized for the purpose of comparison by setting the maximum of each distribution to unity; the total population in the 01'1 state is about one-fourth that in the 0001 state. (Data from refs 34 and 36.)
\ I
I Force I 1 to OCO axis
a = 1.94A
1 Force +Bend ll Force +Stretch
Figure 4. Breathing ellipsoid model for H atom collisionswith C02, with the dimensions of the molecule used as the major and minor axes of the prolate ellipsoid taken from ref 46 for an energy of 2.3 eV. Excitation of the 0001 stretching mode is taken to be proportional to the square of the component of the force parallel to the major (04-0) axis, while excitation of the 01'0 bend is taken to be proportional to the square of the component perpendicular to this axis. One can see that the parallel component drops off rapidly as the point of impact moves toward the center of the molecule, due to the change in curvature of the ellipsoid. the threeverydifferent vibrationalmotions,OllO, 0001, and01'1, are extremely revealing. The pure antisymmetric stretch state 0001 shows the broadest rotational excitation profile with a peak near J = 39-41, while bending states show a significantly cooler rotational distributi~n.l~q~~J~ The bend-stretch combination state 01'1 shows a rotational profile36which mimics that of the pure antisymmetric stretch state 0001, as shown in Figure 3. This initially surprising result can be understood in terms of an H*/ C 0 2interaction which has been successfullyapproximated using a very simple "breathing" ellipsoid model coupled with an infinite order sudden (10s) scaling approximation.33.35 Figure 4 shows a simple representation of an ellipsoid potential for C02 with typical forces acting during an H*/C02 collision. In this model, the probability for exciting the 0001 stretching mode is taken to be proportional to the square of the force along the 0-C-O axis,
Flynn and Weston
8120 The Journal of Physical Chemistry, Vol. 97, No. 31, 1993 1.o2.
a m
0.8-
CO,(OOoO)
+ H' + C02(00°2) + H
C02(O0°0)
+ H'
CO2(0Oo1) + H
-$
r)
g 0.6a
0.012-
.
C
.-
0.4-
'
e 0092 0 wo1
C v1
g
0.010-
0.20.0-
'
0.5
0.0
I.o
1.5
x (4
Broadside
0.008-
2.0
3 -0 0
End-on
2
f
0.006-
I,,
;
0.25-
0.004
.-%
0
0.20-
1
0
.
I
,
I
,
,
,
2
0
3
0
4
0
5
, 0
,
6
i300" 0
J
r)
Figure 6. Rotationally resolved transient line widths (fwhm in cm-I) for COz(oOO2) (filled circles) and CO2(oOOl) (open circles). The solid line is a linear least-squaresfit to both sets of data. (Data from refs 34 and
Bend-Stretch
0.15C 0
.-.z 0.10-
38.)
C
0.05-
0.00.
0.5
0.0
1.o
1.5
2.0
x (4 Figure5. (a, top) Breathingellipsoid model predictionsof the probabilities for the excitationof the bending and antisymmetricstretchingvibrational modes of COz by H atom collisions. The probability is shown as a function of the point of impact for a normal incidence collision at a distance X from the center of the molecule. (b, bottom) The probabilityof exciting the combined bend-stretch vibrationalmode, given by the product of the probabilities shown in (a). (From ref 36.) while the probability for exciting the 0110 bending mode is taken to be proportional to the square of the force perpendicular to the 0-C-0 axis. This approach correctly predicts the rotational profiles for all states observed so far. In particular for the 0111 level, the model shows that the probability for bending excitation (0110) from H atom impacts normal to the H/C02 ellipsoid surface is about the same for impacts at the C atom as those a t the 0 atom end of the molecule. In contrast, the probability for antisymmetricstretch excitation (OOO1) peaks rather sharply near the 0 atom end of the C02 molecule. Figure 5 shows how the bend and stretch probabilities vary along the length of 04-0 axis, as derived from this model. The combination bend-stretch excitation probability is thus dominated by the sharply peaked probability for 0001 excitation.36 This result is, of course, very sensitive to the curvature chosen for the H/C02 interaction potential (cf. Figure 4). For the ellipsoid potential used in our model, where the ratio of the major to minor ellipsoid axes is about 2 (consistent with the C02 geometry), stretching excitation is most probable only out near the end of the molecule. The experimental results for all vibrational levels, coupled with the simple "breathing ellipsoid" model calculations, strongly suggest that the rotational profiles produced by collisions are heavily influenced by the geometry of the vibrational motions excited. Those modes (bends) which are expected to be produced most efficiently by broadside collisions near the C02 center of mass (C atom) have relatively little rotational excitation, while stretching motions, which are expected to be excited mostefficiently by collisions out near the 0 atom end of the molecule (far from the center of mass), show significantly more rotational excitation. The rigid ellipsoid model also predicts a roughly linear increase of theaverage C02(0001) linear recoil momentum with increasing AJ, beyond AJ 20. This is in qualitative agreement with the observed increase in Doppler line width (proportional to molecular velocity) with increasing rotational level observed for the C02(0001) and C02(0002) final states, shown in Figure 6. The
-
model reproduces the rotational profiles nearly quantitati~ely~3J"~ and gives the correct qualitative results for the velocity recoils, but it cannot beused to predict the relativeexcitation probabilities for thedifferent vibrational levels. Amoresophisticated treatment of the vibrational coupling,39 one which involves a detailed potential surface, will be required to get thevibrational excitation probabilities correct. It will also be interesting to see if the simple physical picture for rotational excitation and its dependence on vibrational mode, which has emerged from the ellipsoid model, will hold up for more sophisticated, exact potential surfaces. Initial indications are that it will,39but substantially more theoretical work will be required to prove this point. The data produced here should serve as an excellent test for the accuracy of any ab initio potential energy surface which can be constructed for the H C02 sy~tem.3~vW* In particular, the rotational profiles predicted for scattering into different final vibrational states, when compared to the data, should give clues to any corrections that might be needed in the potential surfaces themselves. The translationally and rotationally resolved population distribution has also been measured for C02(0002) produced by collisions of COz with hot hydrogen atoms. The magnitude of the populationscattered into 0002 is -21 times smaller than that scattered into 0001. A simple repulsive force quantum scattering model predicts a much smaller probability for the excitation of 00°2 compared to OOol than that determined experimentally. The 00°2 rotational population distribution and rotationally resolved line widths (Figure 6) are remarkably similar to those previously obtained for 0001. Within the context of the "breathing ellipsoid" model, the similar rotational distributionsand translational recoils for OOol and 0002 suggest that these two states are excited by similar collision trajectories, wherein antisymmetric stretching excitation is optimized when H strikes near the end of the 04-0 molecule. It appears that the rotational and translational degrees of freedom of COz can be treated classically for H*-C02 collisions which produce either the one-quantum 0001 state or the twoquantum 0002 state. The overall probability for excitation of one or two quanta of antisymmetric stretching vibration, however, requires a quantum mechanical approach with a proper potential energy surface. Interesting isotope effects are observed when D replaces H as the hot atom. The differences in rotational distributions have been discussed above. In addition, the excitation of v2 compared to that of v3 is about 2.5 times greater for D atoms than for H atoms with comparable translational energies but different velocities.14 This velocity effect has been qualitatively explained on the basis of the Born approximation model discussed in section IV.
+
The Journal of Physical Chemistry, Vol. 97, No. 31, 1993 8121
Feature Article
C02 + H*
+ C02 (Ol'l;J,V)+ H
i'
I'
to the true eigenfunctions can be formed by taking linear combinations ofjust the harmonicoscillator basis functions (11OOO) and )0200)), where the expansion coefficients indicate the harmonic "purity" of the true eigenstates. The high-energy state (1388 cm-1) of the Fermi doublet of W 0 2 can thus be represented by
'
9, = (11000)
Similarly, the corresponding low-energy state (1288 cm-I) can be represented by
0
o
0
o
p
o
0
O D
0.004 0
"
10
"
20
9,= (110OO) - 1020O))/d2
e
O*
e
0
"
"
40
30
+ 1020O))/d2
"
50
"
60
J Figure 7. Rotationally resolved distribution of COz(Olll) produced by
collisions of CO~(00oo)with 2.3-eV H atoms at a sample temperature of 292 K: filled circles, populations of even J levels derived from R branch transitions;open circles, populations of odd J levels derived from R branch transitions; squares, odd J level populations derived from P branch transitions. Note that for J = 11 and 19,the populations derived from the R branch transitions are substantiallyhigher than those derived from the P branch transitions. (From ref 36.)
B. Quantum Interference and Symmetry Effects in Scattering hocesses. The diode probe technique has been used to observe two interesting phenomena which can be expected to be important in a number of polyatomic molecule scattering studies. The first is a variation in the probability of excitation of odd and even J states in the two C02 levels 0110 and 0111,27,36a phenomenon which was predicted in theoretical studies by Alexander and Clary47before our experimental work. The effect is most evident in the hot H atom excitation of the C02(0111) vibrational leveP6 shown in Figure 7. The bending or combination levels with I > 0 in C02 contain both odd and even J levels (unlike the I = 0 levels which have either the even or odd J levels missing). Collisions of H* with C02 preferentially excite either the odd or even J levels when 1 > 0, and the preferred levels change with the symmetry of the vibrational state. Thus, in the 0111 level, even J levels are preferentially excited, while in 01'0, odd Jlevels are favored.27336 This scattering phenomenon has a somewhat complicated but in its simplest terms it may be thought of as a breaking of the C02 symmetry during the collision, with a preference being maintained for those processes that preserve the overall vibration-rotation symmetry without consideration of the symmetry effects arising from the presenceof thevibrational angular momentum 1. A second quantum effect which has been observed with diode laser probing is the preferential excitation of one of the two C02 Fermi mixed 02°0-1000 vibrational levels by both hot H or D collisions and by hot (1-3 eV) electron c0llisions.4~ In both cases, the upper energy Fermi level is excited with higher probability than the lower energy member of the pair. For H or D scattering, the effect is only about 30% but in the case of hot electrons, the upper energy member of the Fermi pair is excited 10 times more effectively than the lower energy member! This observation can be explained as a simple and clear cut case of quantum interference in the scattering process. In COz, the symmetric stretch harmonic oscillator vibrational state ( 10°O) and the first overtone of the bending harmonic oscillator state (0200) are of the same vibrational symmetry and lie extremely close in energy; therefore, the anharmonic mixing of these two states (Fermi resonance) is very strong.50 In such cases, the vibrational quantum numbers conventionally attached to the molecular levels are only a crude guide to the true nature of the states. Reasonable approximations
In the 12C02 species these two energy eigenstates are almost exactly equal mixtures of the two harmonic oscillator states with a very slight excess of 11000) in PL. For T O z , this state has a very slight excess of 102°0).51It is, at first sight, surprising that there is such a dramatic difference in the vibrational excitation probability of these mixed states in view of the strong Fermi resonance and the "indistinguishability" of the symmetric stretching "fundamental" from the "overtone" of the bending mode. However, the observed results can be simply explained in terms of a strong quantum mechanical interference in the electronscattering experiments. The collisional excitation probability Pgu or P g ~from , the ground vibrational state to the Fermi coupled vibrational levels is proportional to I( OOoO1qq)12or to Pg"
+ - 1 oooolq ooo ooool
PgL
~ ( o o o o ( ~ l o o o (00°0~q0200)p ) (qU upper energy state) (
1
)-(
Jqo2Oo ) I2 (9,lower energy state)
-
where Vdefines the interaction potential. When (00001~0200) (OOoO)~lOoO), PgL 0 is assumed here). This might be referred to as the strong coupling limit, since it implies that two-quantum harmonic oscillator transitions are about as likely as one-quantum transitions in thescattering process. For e-/COz scattering,where a strong perturbation of the neutral, linear C02 structure can be expected through the transient formation of bent C02- negative ion52 and where large cross sections for vibrational excitation have been o b ~ e r v e d ,strong ~ ~ . ~ coupling ~ with ( O O o O ~ ~ l O o O ) (00°01T40200) is not surprising and nicely explains the results observed here. The reverse limit, ( O O o O ~ ~ l O o O>> ) (00001~0200),in which one-quantum harmonicoscillator transitions are strongly favored over two-quantum transitions, predicts Pgu P g and ~ can be thought of as the weak coupling limit. Such coupling is typical of vibrational energy transfer or excitation in neutral-neutral collisions a t moderate to low collision e n e r g i e ~ . ~Even ~ - ~in~ hot H atom collisions, two-quantum excitation of C02 from the 0000 ground state to either 01 l l or 00°2 (essentially pure two-quantum harmonic oscillator states) is smaller by factors of 4 and 21, respectively,36J8thanone-quantumexcitation toOOol . (This weak coupling limit and the concomitant improbability of multiplequantum transitions also appears to apply to collisional energy transfer from highly excited molecules, described in section IV). Nearly equal excitation probabilities (Pgu 1. 3 P g ~are ) observed for hot H(D) scattering from the C02 ground state to PUand PL, in marked contrast to the results for electron/COz scattering. The slight preference for PU over PL( P , u / P g ~ 1.3) indicates that two-quantum harmonic oscillator transitions are indeed much less probable than one-quantum transitions for H(D)/C02 excitation. Note that the present experiments, which are sensitive only to the absolute value of the differences in the harmonic oscillator matrix elements, cannot distinguish which term, (0000ltIlOOO) or (0000ly10200),is larger. While the assumption that the one quantum matrix element dominates is quite safe in
-
-
-
-
8122 The Journal of Physical Chemistry, Vol. 97, No. 31, 19’93
the case of hot H(D) atom s~attering,36.3~,5*,59 the situation for hot electron scattering is less clear. The key point, however, is that the two matrix elements are comparable in the electron/ C02 encounter but not in the H(D)/C02 encounter. The above experimentalresults lead to three conclusionswhich seem to be general. First, quantum mechanical interferences can reduce the overall matrix element for excitation from the ground state to the lower energy state of a mixed pair to well below the values of individual terms in the expansion based on harmonic oscillator wave functions. Second, the upper energy state of a mixed pair always exhibits higher excitation probability than thelower energy statesinceit sumsupall thematrixelements. Note that this conclusion assumes a positive interaction potential, V > 0. Finally, the excitation probability of the Fermi coupled levels depends on a subtle combination of the intermolecular dynamics and the vibrational force field of the C02 molecule itself with differences to be expected when the identity of the collision partner is varied. Our descriptionof the Fermi doublet excitation by hot H atoms, being based entirely on a quantum formulation, provides no information about the types of collision that excite the upper and lower members of the doublet. The quasi-classical trajectory calculations of Schatz et ~ 1 . give ~ 6 an upper/lower ratio of 1.4, in good agreement with our measurements. Their results also indicate that broadside collisions are about 50% more effective than end-on collisions in exciting both upper and lower states of the doublet. The studies described here are only one aspect of experimental work being pursued on the four-atom H CO2 system. While we have studied the vibrationally, rotationally, and translationallyinelastic channelsdescribedabove,others have investigated the reactive channel
+
H*
+ CO,
-
OH(v,N)
+ CO(o,J)
by studying the quantum states produced in both OH and CO. The number of experimental studies is particularly rich, encompassing bimolecular reaction experiments,us nanosecond and picosecond studies of the breakup of HCO2 complexes prepared by supersonic expansion techniques,6675 and studies76.77 of the reverse reaction OH + CO C02 H. Taken together, these studies present an astonishingly detailed picture of the collision dynamics for the H + C02 and OH CO reactions. C. H* OCS. The basic idea that collisions with different parts of a molecule might be reflected in the final rotational and translational energy profiles of different final vibrational states has been tested further by studying the two processes17
-
+
+
+
H* + OCS(OO’O,J’,v’) H*
+ OCS(OOoO,J’,v’)
-+ -+ H
OCS(OOo,l,J,v)
H
OCS( 10°O,J,v)
The experiments proceed in a manner analogous to those for the H* C 0 2system. In the OCS case, the two ends of the molecule are quite different, leading to two very different stretching frequencies: 2062 cm-1 for the 1000 level, essentially a C-O stretch, and 859 cm-l for OOol, a C S stretch. The cross section for 1000 excitation is -0.4 A2, similar to the value of 0.54 A2 for C02(0001) given in Table I. The 0001 cross section is 1.0 AZ, about twice as large. The rotational energy is lower in the 0001 state; the two rotational populations can be fit to Boltzmann distributions with temperatures of 840 K (CO stretch) and 510 K (CS stretch). The typical linear dependence of line width on J is observed for both vibrational states. The vibrational and mass assymmetry of OCS can be taken into account in breathing ellipsoid calculations of the type described above, by adjusting the excitation probabilities for the amplitude of vibration of the atoms in each mode and the fact that the center of mass of ellipsoid isnotthesameas thecenter ofthechargedistribution. Adistorted ellipse was used to describe the charge distribution. The results for this collision system again suggest that the rotational
+
-
Flynn and Weston distributions of different final vibrational states reflect ‘hits” between the H atom and different parts of the OCS m01ecule.l~ Collisions in which H strikes the 0 end of OCS are further from the center of mass than those where H strikes the S end of the molecule! Thus, we expect more rotational angular momentum to be imparted to the CO stretch (rotational temperature = 840 K) than to the CS stretch (rotational temperature = 510 K), as observed! IV. Energy Transfer from Highly Vibrationally Excited Molecules We have discussed above one of the possible mechanisms for vibrational excitation of molecules, Le., the conversion of translational energy into internal energy. This may be thought of as the initiating step (reaction 1) of a unimolecular reaction. The other important energy transfer process in this scheme (reaction 2), in which a highly vibrationally excited molecule loses energy in collisions with a cold “bath” gas, has been extensively investigated. Earlier kinetic methods relied upon studies of the decrease in the unimolecular rate constant with decreasingpressure to determine collision efficiencies and amounts of energy transferred per collision. These experimentshave been extensively reviewed.’8-82 More direct methods of determining collisional energy loss have been developed recently, and a summary of the results is discussed in various reviews.78.82-85 We have also carried out experiments, using the diode laser technique, to study energy loss from highly vibrationally excited molecules. To prepare the highly excited energy donor molecule, we have utilized the technique pioneered by Troe8”9 and Barker.90 This method takes advantage of the photophysics of these molecules, which can be excited in the near UV to an SI or S2 state that undergoes very rapid internal conversion to the ground electronic state. The excitation energy, defined by the choice of excitation wavelength, is converted to intemal energy of the aromatic species. Our approach differs from that of other workers, who have used ultraviolet absorption or infrared emission spectroscopyto follow collisional energy loss of the “donor”molecule. Instead,weobserve the energy gain in the ‘acceptor’) or bath gas molecule, using diode laser absorption spectroscopy. The motivation for this approach is very simple. A detailed knowledge of the vibrationrotation energy levels of small molecules such as COz or N20 is available, but the aromaticdonor moleculesare excited to energies such that the density of states is as high as 1020/cm-1, and the spectroscopy is terra incognita. A variation on this method of photoexcitationfollowed by internal conversion makes use of the fact that strong perturbations in some small molecules (such as NO2, CS2, and S02) mix the ground electronicstate with excited states which can be populated by UV or visible excitation. Thus, photoexcitation leads to states that are predominantly ground electronic state in character, with large amounts of vibrational energy. The infrared diode laser probe technique has been applied so far to experiments in which the energy of the donor molecule is well defined, but its internal quantum states are not. On the other hand, essentially completequantum-state distributions and the velocity recoil profile of the acceptor molecule are obtained with this technique. The dynamics of the relaxation of the highenergy donor are thus viewed through the window supplied by the nearly total state-resolved behaviorof the acceptor. The initial, fully quantum state resolved experimental approach was demonstrated with highly excited NO2 as the donor species and C02 as the bath acceptor molecule,20 but the general technique is a development of the method that was employed to investigate energy transfer from azulene to C02 several years ag0,16.91 an experiment in which only the vibrational energy of the C02 bath could be probed. Key improvements in the technique since these initial experiments have been the ability to operate at low enough pressures to observe only the first collision of the excited donor with the bath and the ability to probe the velocity recoil of the
The Journal of Physical Chemistry, Vol. 97, No.31, 1993 8123
Feature Article bath acceptor molecule28 as well as its vibrational and rotational states. Not only does this experimentalmethod supply data about the partitioning of energy between vibrational and rotational degrees of freedom, it also allows for a determinationof thedivision of energy between rotational and translational degreesof freedom! This technique can be illustrated by consideringthe relaxation of highly excited C6F6 in collisions with C02.92 Excited C6F6 molecules (C6F&Q)are produced at energy E = 40 650 cm-I by an excimer laser (-20-11s pulse width, 248 nm), followed by internal conversion: C6F6
+ hv(248 nm)
-
C,jF,(E)
Collisions of C6F40 with CO2 cause translational, rotational, and vibrational excitation of the first antisymmetric stretching vibrational state (u3,OO01, 2349 cm-I) as well as rotational and translational excitation in the vibrationless (0000)level:
-
+ c o ~ ( o o o o ) c6F6(E-m)+ co,(oool,J,V) C6F6(E)+ CO,(OOoO) C6F6(E-u) + CO,(OOoO,J',v') C6Fla
-
J and J' represent rotational angular momentum quantum numbers and v and v' the recoil velocities for the corresponding ro-vibrational states. A tunable diode laser operatingcontinuously at 4.3 pm is used to probe the P and/or R branch bands of the following transitions:
+
C02(OOo1,J,vL) hv(4.3 pm) CO,(OOoO,J',v,')
+ hv(4.3 pm)
-
-
CO,(OO~~,J~I,V,) CO,(OOol ,J'f 1, v i )
Velocity recoils are measured by probing the nascent Doppler profiles for different spectral lines. The initially excited molecules may lose energy to produce species, such as C6F6(E-m,that can still excite CO2. In these experiments,however, the C02 excitedstate populations and Doppler velocity profiles are measured at such a short time after the initial laser excitation pump pulse and at such low sample pressures that these channels are minimized. The population of a given C02(0001,J,v~)level can be derived from the simple standard kinetic equation d[CO,(OOO1,J,vL)]/dt = k,(J) [C,jF,Q] [ c o ~ ( o o o o ) ] (4) At short times (typically correspondingto one-tenth to one-third of a gas kinetic collision interval), the nascent population of bath molecules in a specific state is given by the expression A[C02(00°1~J,~JI~, = k,(J) [C6F,(E)I0[C0,(00~0)1 At (5) where [C6F&"]o is the initial concentrationof [CaF&E)]produced by the pump laser. In addition to nascent distributions of the CO2(O001,J,vL)product, which reveal many aspects of the energy transfer mechanism, these experiments provide values for the energy transfer rate constants, k R ( J ) , since the initial concentration of excited donor, [C6F&@]olis easily determined from absorption measurements and all other parameters in eq 5 are known in the experiments. Some extremely interesting results have been obtained using this technique. Perhaps most surprising is the fact that the vibrationally excited bath molecules, CO2(oOOl,J,v),are produced with a rotational distribution that approximates the initial room temperature distribution of the unexcited CO2(OooO,J,v) groundstate molecules, present before laser excitation of C6F6. Thus, energy-transfer events that produce C02(OO01,J,v) are accompanied by almost no increase in rotational energy of the acceptor molecule, despite the fact that the vibrational energy of the acceptor for these events increasesby 2349 cm-I, more than 1 0 k F An examinationof thevelocity recoil profiles for these same events tells a similar story. The vibrationally excited molecules are produced with a translational energy distribution that is near
TABLE II: Energy Transfer from Highly Excited NO,(@ Small Molecules (M)
NO,(E)
+ M(00'0)
molecule (model E, cm-1 v, cm-1
-
NO,(E-GE)
C02(0001l
to
+ M(mn'p)
N20(00"1)
N20(10%l
20 200 22 200 22 200 2349 2223 1285 2.7 0.9 3.1 0.9 kvP 3.9 0.7 147 h 42 128 38 ZWb 102* 18 (A&), cm-' e 23 4 15*4 10*3 (hEmt),cm-ld 0.30*0.10 0.18*0.09 0.22+0.12 0.51 & 0.35 0.41 & 0.35 (bE,,),cm-l * 0.41 0.21 Rate constants in units of cm3molecule-' s-I for excitation of vibrational state mn'p due to collisions with N02(E). Z is defined as k u / k W , and the Lennard-Jonescollision rate coefficients ku are 3.98
*
*
* *
*
cm3molecule-1s-l for both N O A 0 2 and NOrNzO collisions. Vibrationalenergy transferred per collision, defined as v/Zw. Energy transferred per collision, calculated from the translationalor rotational temperature and ZW. X
e
TABLE IIk Energy Transfer from Highly Excited Aromatic Molecules to CO2(OOOl) AH(E)
E, cm-l
+ CO,(OOoO)
-
AH(E4E)
+ CO,(OOol)
C6H6
C6F6
C4N2H4
40 690 480 A 170 4.9 1.8
41 860 760 A 340 3.1 1.4
40 640 100 A 30 23 7 320 30 310 A 30
Z(V3) (A&b),'cm-l Tt" K 340 25 Tmt,K 360 30 Energy transferred to COz(v3) per collision defined as in Table 11: k u values (in units of W O cm3 molecul& s-l) are 5.0,5.0,and 3.0for collisions of CO2 with C6H6, C&, and C4N2H4, respectively.
*
* *
**
that of the original Boltzmann distribution of the sample. These observations are not limited to the C6F6/C02 collision system. Similar results have been obtained with hot NO2 (E = 22 OOO cm-1) as the donor and C02 as the acceptor'* or with N2O as the acceptor93 and hot pyrazine as the donor94 (Table 11). In the case of N20 as the acceptor with NO2 (E = 22 000 cm-') as the both the loo0 and 00O1 vibrational states (VI and v3 modes) are excited with almost equal probability and with almost no excitationof the translational or rotationaldegrees of freedom, as shown in Figure 9. When hot pyrazine (C6bN2) is the donor (E = 40 322 or 32 470 cm-I), similar results are again obtained with C02, N20, or OCS as the acceptor m0lecules,9~as shown in Figure 10. Probabilities for vibrational excitation are rather small for these systems,with values running from 0.01 per collision for NO2 as the donor18 to 0.002 per collision with C6F6 as the donor92 (Table 111). Thus, even though a large quantum of energy is transferred in events leading to bath vibrational excitation, the probability of energy transfer is so small that these processes account for very little loss of energy from the donor. The inefficiency of energy uptake from highly excited molecules by thevibrational modes of small bath acceptors is in agreement with trends observed in a number of earlier experimental studies performed with lower energy resolution. The observationof bath vibrational excitation without rotational or translational excitationin the quenchingof highly vibrationally excited donors is, however, quite startling! The data obtained so far, while on a limited subset of donors and acceptors, are consistent with a long-range vibrationally resonant energy transfer mechanism in which vibrational energy loss in the donor is matched almost exactly by vibrational energy gain in the acceptor. The small rotational and translational energy transfer that accompanies vibrational excitation of bath states such as C02(0001), N20(1000), N20(0001), and OCS(W1) in these systems is reminiscent of long-range, resonant energy transfer processes which are known to be of great importance in
8124 The Journal of Physical Chemistry, Vol. 97, No. 31, 1993
Flynn and Weston Pyrazine(E=40300cm-*)+CO~(OO~O; J', VI)+ Pyrazine(E.AE)+CO~(OO~O;3 x 6 2 , V)
Pyrazine-Carbon Dioxide Energy Transfer
0.025
It
Q)
0.020
'0 1
:
4
0.015
0.010
0.005 0.000 -0.01 0
0.000
0.01 0
cm-' from line center
0005
P J r azin e (Ex403 0 Oc m -1) + C 0 2( 0000; J', V*)+ PyrazIne(E-AE)+CO~(OO~l;3117, V) 0004
0Oo1+0O02 P(17)
0.06
0003
0.05 0.04 c
0002
I
-7
-*-I
I
I
/
COZ Rotation
0.03
0.01
i co2 Translation
e
a 0.02
I 't I
0.00
0 cm"
Pyrazine*
Figure 8. Schematic energy level diagram for collisions of highly vibrationallyexcited pyrazinewith C02. The excited pyrazineis produced by pumping the SIstate, which rapidly undergoes internal conversion to the SO state with the same energy. Translational, rotational, and vibrational excitation of the CO2 by collisionswith pyrazine are probed with an IR diode laser. The translational energy distribution of the recoiling C02 is representedby the dense manifold of states with a spread of 0.005 cm-l (the 300 K Doppler width of a C02(OO01) C02(OOO2) transition). -+
vibration-vibration energy transfer mechanismsinvolving small, weakly excited molecules.95-g7 Indeed, Toselli and Barker98have recently performed model calculations in which they use a longrange force mechanism to calculate the probability for excitation of C02 bending and stretching modes by collisions with benzene and toluene as the donors. The role of collision complexes in the quenching processes producing vibrationally excited bath molecules, however, is not yet clear, but it should not be ignored at this early stage of the quantum-state-resolved investigation^.^^ This is particularly true given the small size of the cross section for producing vibrationally excited molecules. A mechanism involving a very small fraction of collision events (for example, those at very low velocity) with very large cross sections for vibrational excitation1OO-105 would still be in agreementwith these observations. Indeed, there have been a number of reports of very large vibrational energy transfer cross sections for collisions of very cold molecules in supersonic expansion, molecular beam experiments. Further experiments will be required to establish definitely the mechanism for thesevibrational excitationprocesses, but the dominant signaturefor these events seems to be low angular and linear momentum transfer. In collisions between highly energetic benzene (E = 40 690 cm-1) and C02, the very small amount of energy collisionally transferred to the antisymmetricstretching mode of C02 is much less than the total energy loss per collision from the benzene (270 cm-l).lO6 Therefore, a substantial amount of this total energy loss from the excited aromatic must appear as translational and rotational excitation of carbon dioxide molecules in the ground vibrational level. Is this an example of d2ja us( all over again?
cm-' from line center
Figure 9. Nascent Doppler line shapes for C02 excited in collisionswith pyrazine ( E = 40 300 cm-l). The upper figure is for pure rotational excitationproducing C02 in the OO%, J = 62 level; the lower figureshows the line shape for molecules in the 0001, J = 17 level. (Reproduced, with permission, from the Annual Review of Physical Chemistry, Vol. 43, @ 1992 by Annual Reviews, Inc.)
Lin and Rabinovitch,107 following an earlier suggestion by Stevens,108carried out calculations of energy transfer from CH3NC using a model that stressed the importance of "transitional modes" of the collision complex, which replace translations and rotations of the individual collision partners. Their calculations showed that efficient energy transfer can take place even if the internal vibrational modes of the bath molecule are inactive. In this case, the energy transferred to the transitional modes would, perforce, revert to translational and rotational energy upon separation of the collision partners. Several modifications of this model have been proposed and are discussed in the reviews cited earlier.78v79 For all donors and acceptors studied so far, the behavior of the ground (OOOO) state of the acceptor is dramatically different than that of thevibrationally excited states, as described above. In the case of C6Fs or pyrazine as a donor with C02 as an acceptor, excitation to high J levels is readily observed, and the recoil line widths for these high rotational levels are substantially broader than room temperature Doppler widths. Typical translational recoil energies are a few kT at room temperature. Complete rotational energy distributions for these ground vibrationless molecules have not yet been reported; however, preliminary data indicate that the rotational energy increase of the bath molecule is the same order of magnitude as the translationalenergy increase. Figure 9 illustratesthe dramatic difference in the velocity recoil profiles for the ground level C02(OOOO,J=62)and thevibrationally excited level C02(0001,J= 17) produced by collisions between hot pyrazine (E = 40 300 cm-l) and cold (300 K) C02 bath molecules, with the most populated initial rotational level at J = 16. A determination of the rotational energy populations at high J for these ground vibrationless COz molecules indicates that the average amount of rotational energy transferred per collision is about the same as the average gain of translational energy. Because the angular momentum imparted to the bath molecule is AJ = pvb, where p is the collision reduced mass, v the center-of-mass recoil velocity, and b the impact
The Journal of Physical Chemistry, Vol. 97,No.31, I993 8125
Feature Article
0 008 0 008 0 004
00'1
0 002
R18
Firtl Atymmelric Slrolchinp Slate
0 000
.O 0 0 8
.O 0 0 4
0 000
0 004
0 000
10'0
R15
most of this average energy uptake by the bath must go into the translationaland rotational degrees of freedom. Thus, the average energy lost by the donor per collision must be approximately equal to the sum of the translational and rotational energy of excitation of the ground (vibrationless) state as measured in the quantum-state-resolved studies. The exciting feature of these data is the possibility of correlating specific rotational energy changes with specific translational energy changes, correlations that can be expected to appear over the next few years. The results presented abovegiveclear evidence for the existence of two quite distinct mechanisms for energy loss by highly vibrationally excited molecules.93 Both mechanisms can be understood in the context of a simple semiclassicalpicture based on time-dependent perturbation theory. In this model, the probability of vibrational energy loss to the translational degrees of freedom is optimized when the Fourier transformof the potential acting during the collision has significant amplitude at the frequency Au = AEAblhu correspondingto thevibrational energy loss &!7yib.1159*121-126 The probability for a transition from state i to state j is given in this semiclassical picture by
Firs1 Symmilrlc SlreIChmp Slate
.O 0 0 8
.O 0 0 4
o ooo
o
004
0 008
Wavenumben lrom line Cenler
N02[E1tN20(0000,J',V*)+ N02[E-AE1tN20(0000,J,V)
where Kj(t) is the matrix element for the interaction potential and Auij = A E A b / h is the change in vibrational frequency during thevibration to translation energy transfer process. This transition probability is optimized when V,,(t) changes on a time scale t < l/Aui,, since the term in exp[2dAvi,t] oscillates on a time scale t l/Auij. The rate of change of V,,(t) is in turn controlled by the relative collision velocity and the steepness,or rate of change with distance, of the intermolecular potential. The most rapidly changing part of the intermolecular potential, the short-range repulsive region, gives rise to the highest frequency Fourier componentsfor K,(t). For heavy molecules such as NO2 or C6F6 as donors and COZor N2O as acceptors at room temperature, the relatively low average collision velocities preclude large energy loss to translational or rotational degrees of freedom, even for collisions that sample the steep repulsive potential wall of the intermolecular potential. The line widths observed for the vibrationless(OOOO) level correspondto a mean vibrational energy loss to translation of -200-700 cm-l per collision. This is just the magnitude of vibration-translation (V-T) energy transfer predicted by the above simple impulsive force/Fourier transform argument for heavy molecules at rmm temperature, whoseshortrange interaction potential can be described as exponentially repulsive with a characteristic range of -0.2 A, typical of many small polyatomic molecules.1J2G126Note that enough energy is contained in the donor molecules to transfer much more energy than observed,but the dynamics of the collision process limit the magnitude of the energy transfer. The approach outlined above is very different from that of the "transition mode" model,107 which depends upon the formation of a collision complex. However, our semiclassical model is not inconsistent with later modifications of the transition mode model that reduce thevolume of phase space sampled by the acceptor molecule due to the impulsive nature of the collisions between donor and acceptor. In contrast to the ground vibrationless state, energy transfer from pyrazine*, C&*, or N02* donors which produchp vibrational excitation in the C02, OCS, or N2O bath occurs by a mechanism in which almost no energy is transferred to the translational degrees of freedom as reflected by the narrow line widths observed for recoiling N2O(OOol,J), N20(1OOO,J), C02(0001,J), or OCS(O001,J).With the same Fourier transform argument given above, these results suggesta resonant vibrational energy transfer mechanism in which vibrational energy in the donor is exchanged for vibrational energy in the acceptor with Au,, = A E ~ b / h 0. Such a transfer can be brought about by the long-range attractive part of the intermolecular potential, which changes only slowly with distance, yielding Fourier components of the interaction force which are near zero frequency.
-
. i : "1 " 2J
j
WK
OOoO
R62
Vibfllbnlesa Qrcund State
Wawn~mDertliom ttnv cenivi
Figure 10. Nascent Doppler line s h a p for N20 excited in collisions with NO2 (E = 22 200cm-9: (a, top) the antisymmetricstretchingstate OOO1 0002 R(18), (b, middle) the symmetric stretching state loo0 lo01 R( 1 S), (c, bottom) the vibrationless ground state oo00 OOO1 R(62). The circles are data points and the solid lines are best fits to a Gaussian function. The dashed lines are room temperatureDoppler profiles. (From -+
-. -
ref 85.)
parameter (distance from the center of mass of the bath acceptor molecule to the point of 'push-off" by the vibrating atoms of the donor), some scalingof rotational energy with translational recoil is e~pected.~sThus, in the case of pyrazine-carbon dioxide collisions the translational temperature (and energy) of the C02 is found to scale approximatelywith the rotational energy content for high rotational levels. This is not found to be the case for C6Fs-CO2 collisions, and the difference in results between these two donor molecules is presently being explored. The dependenceof the energy transfer probability on the initial energy of the donor is a topic of considerable current interest8"90~98.1"1'1~.'22 and has been studied using diode laser probing in only a few cases. For example, vibrational excitation of the Wl state of C02 as a bath gas due to collisions with NO2(@ donors has been found to be independent of donor energy in the range 16000-22000 cm-l. Similar results have been found at the two initial energies 40 3OOcm-1 and 32 500 cm-l for pyrazine as the donor producing C02(0001)excitation. However, significantly different energy transfer distributions and probabilities have been observed at these same two energies for collisions between pyrazine and C02 which produce translationally and rotationally hot COz molecules in the vibrational ground state
(009). The results obtained for the ground vibrationless state of the acceptor are quite consistent with earlier studies8690JMJ1@122 showing that the mean energy transferred per collision is on the order of a few kT. Since little energy goes into the vibrationally excited states of the bath for these small acceptor molecules,
-
8126 The Journal of Physical Chemistry, Vol. 97, No. 31, 1993
Indeed, the weak recoil for the vibrationally excited species also suggests energy transfer at a distance, indicating a long-range force mechanism for the excitation of the bath vibrational modes.95-97 The rotational profiles observed for the excited states of the bath acceptor molecules, which show only small changes in J upon vibrational excitation, are also consistent with an energy transfer process mediated by long-range forces. Such a longrange potential of interaction, which can be represented to first order by a dipoledipole would have “collisionalselection rules” with AJ = f l , completely consistent with the above experimental data. Finally, changes in the rotational energy for the ground vibrationless state of the acceptors are comparable to the changes in translational energy for this same state implying that AJ >> 1. This observation is again completely consistent with a short-range force mechanism for the translationalrotational (V-T/R) excitation of the ground level. The shortrange repulsive part of the potential can only be described reasonably well by a multipole expansion which includes rather high-order terms, which, of course, can give rise to changes in AJ which are significantly larger than 1. Although the simple explanation for the observed data given above must be viewed with some caution (particularly for the vibrationallyexcitedstateswhere thecrosssectionsarevery small), the excitation of bath vibrational modes clearly occurs by a different mechanism than the rotational-translational excitation of the ground vibrationless state. The situation for quenching of high-energy donors by acceptors such as C02, OCS, and N20 can be described as “vibrationallycrisp”. The energy of the bath vibrationalmodes (typically 1200or 2300 cm-I) is large compared to the mean bath translational energy (kT 200 cm-I), which controls the donor/acceptor collision velocity. In such a case, excitation of the high-frequency bath modes by a short-range repulsive force mechanism is essentially ruled out due to the low velocity and the high-mode frequencies. Nevertheless, as the bath mode frequencies drop, or the bath translational energy increases,such that hAv kT, vibrational excitation could occur by more than one mechanism. Finally, although a long-range force mechanism seems to dominatethe bathvibrational excitation process, short-range forces can be expected to play some role, even a small role, and properly designed experiments should be capable of detecting the effects of these forces.
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V. Conclusions In this feature article, we have described experiments carried out during the past several years in which time-resolved diode laser absorption spectroscopy has been used to explore the dynamics of collisional energy transfer process. The hot atom experiments have expanded our knowledge of the dynamics of atom-small molecule collisions,providing information about the potential energy surface which is also relevant to reactivecollisions. When compared to the initial classical experiments,Iz7which provided only energy threshold data and approximate cross sections, they show the dramatic advances in chemical kinetics that have been brought about by laser techniques in just the past several years. The availability of data for rotationally, vibrationally, and translationally inelastic scattering channels, which compete with the reactive events, adds a degreeof insight hitherto unavailable in the field of collision dynamics for atom/polyatomic molecule encounters. It is perhaps not too much to expect that the H* + COZsystem may, in the near future, become the first fully characterized four-atom kinetic system in which precise comparisons between theory and experiment will be the norm rather than the exception. The results seem certain to deepen our understanding of chemical reaction mechanisms and ultimately to improveour control of the rates and products of chemical reaction processes. Energy transfer from highly vibrationally excited molecules has been a subject of intense interest to chemical kineticists for
Flynn and Weston the past 70 years, ever since Lindemann p r o p o d the activation/ deactivation mechanism generally accepted as describing unimolecular reactions. The experiments we have described above make it possible to determine populations of molecules in welldefmedvibrationaland rotational states and with specificamounts of translational energy. We hope that the detailed information obtained in this work will lead to increased interaction between theory and experiment, which will, in turn, lead to a better understanding of the detailed collision dynamics that govern these energy transfer events. Perhaps the most surprising, but encouraging, observation is that many of the concepts which have been used to model energy transfer processesfor molecules in low energy, low quantum number states form a useful framework for understanding the relaxation of highly vibrationally excited molecules.
Acknowledgment. Work described here and performed at Columbia University was supported by the Department of Energy under Grant DE-FG02-88-ER13937. Equipment support was provided by the National Science Foundationunder Grants CHE88-16581 and CHE-91-18782 and the Joint Services Electronics Program (U.S. Army, U.S. Navy, and U.S.Air Force) under Contract DAAL03-91-C0016. Work performed at Brookhaven National Laboratory was carried out under Contract DE-ACO276CH00016 with the U.S. Department of Energy and supported by its Division of Chemical Sciences, Office of Basic Energy Sciences. References and Notes (1) Yardley, J. T. Introduction to Molecular Energy Transfer, New York Academic Press, 1980. (2) Weitz, E.; Flynn, G. W. Annu. Rev. Phys. Chem. 1974,25, 275. (3) Brady, B. B.; Spector, G. B.; Chia, L.;Flynn, G. W. J. Chem. Phys. 1987,86, 3245. (4) Harding, D. R.; Weston, R. E., Jr.; Flynn, G. W. J. Chem. Phys. 1988,88, 3590.
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