Molecular beam chemistry: magnetic deflection analysis of monoxide

2113

J . Phys. Chem. 1993,97, 21 13-2122

Molecular Beam Chemistry: Magnetic Deflection Analysis of Monoxide Electronic States from Alkali-Metal Atom + Ozone Reactions X. Shit and D. R. Herschbach’ Department of Chemistry, Harvard University, Cambridge, Massachusetts 021 38

D. R. Worsnop and C. E. Kolb Center for Chemical and Environmental Physics, Aerodyne Research, Inc., Billerica, Massachusetts 01821 Received: August 12, 1992; In Final Form: November 20, 1992

Magnetic deflection analysis of the alkali-metal monoxide products from reactions of alkali-metal atoms (Na,

K, Rb) with ozone in crossed molecular beams indicates that the monoxides are produced predominantly in their lowest 22+electronic state. This occurs despite the existence of a nearby low-lying *lIelectronic state, which for NaO is the ground state and for KO and RbO an excited state that could be populated by utilizing

+

a small fraction of the reaction exoergicity. The finding that N a 0 3 yields predominantly N a O in the 22+ state has important implications for interpretation of the mesospheric sodium airglow and the luminescence of meteor trails. Since NaO 0 produces the airglow chemiluminescence, the emission may depend on the electronic state of NaO produced in the upper atmosphere. This aspect is discussed as well as properties that might foster the strong selectivity for forming alkali-metal monoxide *Z+ states.

+

Introduction

The reaction of alkali-metal atoms with ozone to form alkalimetal monoxide and oxygen molecules, ki

M + 03+MO + 0,

(1) is a highly exothermic process. From the ozone dissociation energy’ for O A of 101.4 kJ/mol and the monoxide bond energies,2 the M + 0,reaction exoergicity is 171.7,174.6,and 176.5 kJ/mol for M = Na, K, and Rb, respectively. Since the low ionization potential of the alkali-metalatom and high electron affinity of ozone foster an electron-jump or “harpooning” mechanism,3the reaction cross section or rate constant is expected to be very large. The Na + O3 reaction rate has indeed been found to bevery fast, even at very low temperatures.”’ The most recent measurement7of this rate gives kl = (8.9f 4) X 1O-Io exp[(dO f 140/T ) ] cm3molecule-’ s-I for temperatures between 216 and 293 K. A molecular beam study of the Na + O3reaction by Covinsky et aL8has found the angular and velocity distributions of NaO likewise have the form typical for reactions of alkalimetal atoms with electrophilic target molecules such as diatomic halogen^.^ The alkali-metal monoxide bonding is quite ionic, essentially M+O-, and the open-shell structure of the oxygen anion gives rise to low-lying 211and 2Z+electronic s t a t e ~ . The ~ J ~ground ~ ~ state has been shown to be 2 I I for NaO from both experimentI4and theory,2 and to be 22+for RbO and probably for KO also.2J’J5 The energy separations, A = E ( 2 2 + )- E(2II), have not yet been measured, but Langhoff et al. have recently calculated values of 22.5,-0.55, and -7.8 kJ/mol for NaO, KO, and RbO, respecti~e1y.l~Similar small values of A were obtained in earlier theoretical calculations by So and RichardsI2 and by Allison et al.I3 Given that A is a small fraction of the M + O3 reaction exoergicity, and that no obvious spin or orbital selection rules dictate the predominant population of either MO product state, both the22+ and 2 I I states might be expected to be produced with comparable yields. In this paper we report a test of this notion by means of a crossed molecular beam study of M + O3reactions, Present address: Department of Earth, Atmospheric, and Planetary Sciences. Massachusetts Institute of Technology, Cambridge, MA 021 39.

0022-365419312097-2113$04.00/0

using magnetic deflection analysis to identify the electronic state of the MO product. Our motivation stems from an unresolved question concerning sodium chemistry in the upper atmosphere. Large amounts of atomic sodium are deposited by ablating meteorites at altitudes of -85-95 km,in the lower thermosphere and upper mesophere. Reactions involving atmospheric 0 3 and 0 are believed to form excited Na(2P) atoms which emit the yellow D-line doublet, observed in the sodium nightglow and the luminescence of meteor trails. These emissions are attributed to a reaction sequence16J7 first proposed in 1939 by Chapman,

€ k2

Na +

NaO

+ 0

O3

k3b

Na(’P)

k4

+ O2

(2)

Na(2P) + O2

(3a)

Na(2S) + O2

(3W

NaO

Na(’S) + hv

(4)

In the late 1970s analyses of atmospheric data using theoretical estimatesofrateconstantsfor theNa+ 03andNaO+Oreactions indicated that these processes were sufficiently fast to sustain Chapman’s mechani~m.~J8 Recent measurements find the rate constantsare even somewhat larger than the previous e ~ t i m a t e s . ~ J ~ However, the branching ratio to form excited Na atoms, A = k3,/(k3,+ k3b), must be quite large to account for the observed nightglow intensity; f3 1 0.3 is required by current models.20q21 In contrast, from a slow-flow study of the NaO + 0 reaction, Plane and Husain19estimated thatf3 I0.01. In their experiment, Na + N 2 0 rather than Na 0,was used to prepare NaO, so the nascent electronic state populations might differ. Since the experiment was performed at atmospheric pressure, however, it is safe to assume that the NaO is collisionally relaxed to the ground electronic state, 2 I I . This prompted the question whether the reaction of Na with mesospheric O3might produce a significant yield of NaO in the excited 22+state. If so, the low limit of f3n reported by Plane and Husain19 need not conflict with the high branching ratio required for nightglow models20J to match the observed emission

+

0 1993 American Chemical Society

2114 The Journal of Physical Chemistry, Vol. 97, No. 10, 1993

levels. At the low ambient pressure of the mesosphere, collisional quenching of the excited %+ state is likely to be slow. Also, r a n t infrared spectroscopic studies by Yamada et ai. indicate that the radiative lifetime for the zZ+ 2 l l transition of NaO is very long.I4 Thus, we conclude that a definitive test of the Chapman mechanism requires determination of two branching ratios. One ratio, f2 = kza/(kza + k z b ) , pertains to formation of the NaO electronic states:

Shi et al. To 2' D.P

-

Na +

03

€

NaOtZ') +

0 2

(5a)

NaO('ll) + 02

(5W

k a

The other ratio, denotedhZ, pertains to atomic excitation arising from NaO in the 22+ state:

NaO(*Z*) + O(3P)

€

Na('P) + Na('S)

0 2

+ 0 2

(sa) (W

To 6" DP

To 6

DP

Figure 1. Schematic drawing (top view) of the apparatus. In the source chamber, M designates the alkali-metal oven, G the gas oven, F the gas beam flag, and T the cold shield attached to the liquid nitrogen trap. The pair of ovens and their enclosing cold shields and collimating slits (not shown) are suspended from a rotatable frame which is turned about the scattering center R to scan the angular distribution over a range of 0, the laboratory scattering angle; the beams intersect at 90'. In the detector chamber, C designates the collimator, H the deflecting magnet, and D the surface-ionization detector.

k3Zb

In the work reported here we find the ozone reaction yields predominantly NaO(?Z+), with f2 > 0.8 and most likely near unity. Photoelectron spectroscopy by Wright, Ellis, and DykeZZ has recently given independent evidence for Na0(22+) as the major product. Elsewherez3we consider the atomic excitation mechanism and present correlation diagrams derived from the electron-jump model which indicate that f 3 n 0 but 2/3.

-

Experimental Design and Procedures

The method and apparatus are similar to those used in previous magnetic deflection studies of other alkali-metal atom reacti0ns.~~+24 The detector is a surface-ionizationfilament, which is equally sensitive to any alkali-metal species, unreacted alkalimetal atoms or product molecules. An inhomogeneous magnetic field deflects paramagnetic species of sufficiently low kinetic energy, comprising both unreacted M atoms and product MO molecules in the 22+ state, but transmits higher kinetic energy components of these species as well as virtually all the MO moleculesin the 211state. Thelattercomprisea 2111/~component, which is diamagnetic because the spin and orbital magnetic moments nearly cancel, and a 'II3/2 component, for which the net electronic magnetic moment couples strongly to the internuclear axis and hence exhibitsonly a weak rotation-averagedinteraction with the deflecting field. The effective magnetic moments are evaluated in Appendix A. Because the scattering at wide angles is almost entirely product MO molecules, the deflection analysis enables us to place a lower bound on the fractional yield of the 22+ state. Figure 1 gives a schematic view of the apparatus. There are two separately pumped vacuum chambers: the source chamber (pumped by a 6411. diffusion pump, HS-6 Varian with Dow 704, through a liquid nitrogen trap) and the detector chamber (pumped by a 6-in. diffusion pump, HS-6 Varian with Santovac 5, through a water-cooled trap). The twochambersare linked by a collimator tube 20 mm in diameter and mounted on the shared bulkhead. Thelengthofthis tube,or thedistancebetweenthetwocollimating slits, can be adjusted by sliding an outer collar along an inner one. The volume enclosedwithin the tube is evacuated from the detector chamber only, through openings in the cylindrical wall of the tube (as shown in Figure 1). To reduce the background pressure in the source chamber, an auxiliary pump (2-in. diffusion pump, HS-2 Varian with Santovac 5) is mounted on the back wall of the source chamber and connected to the cabinet enclosing the gas oven via a flex tube 2 in. in diameter. The pair of molecular beam ovens and their enclosing cabinets are mounted on a rotatable frame which is suspended from the roof of the source chamber by a stainless steel pipe 0.5 in. in

diameter. This pipe extends through the vacuum wall via a pair of O-ring sealed connectors and serves as the rotation shaft for the frame, which can be scanned over an angular range of about 105" by means of a worm gear attachment. The pipe also provides a channel for the gas line which feeds the ozone oven. To suppreas secondary scattering of alkali-metal atoms and condensable gas molecules, the source chamber is lined with a copper shield (l/4 in. thick) attached to a liquid nitrogen trap. The alkali-metal and gas ovens were similar to those described previ~usly.~ In this work, the alkali-metal oven was heated by two separate resistance wirings. The temperatures of the exit slit and the alkali-metal reservoir could be adjusted independently and were monitored with thermocouples. The alkali-metalvapor pressure in theoven was typically 5-10 Torr. For theexperiments reported here, the oven temperatures for Na, K, and Rb were 720, 670, and 580 K, respectively. The gas oven was equipped with a Zacharias slit (many-channel "crinkly foil" array, 0.005cm hole radius, 0.5 cm long, estimated porosity 50%) and its own thermocouple. The ozone was generated by a commercial electric dc discharge ozonizer and trapped on silica gel cooled by dry ice (to 196 K). Any untrapped gas was pumped off to purify the ozone before connecting the storage flask to the oven feed line and allowing it to warm to room temperature. A stainless steel needle valve in the feed line held the ozone pressure in the oven at about 1Torr. The oven temperature was 298 K. This produced an ozone beam flux sufficient to attenuate the alkali-metal beam by about 10% at the collision zone. Thedistance from the oven exit slit to the center of the collision zone, located on the axis of the rotatable frame, is 7 cm for the alkali-metal beam and 5 cm for the ozone beam. The flight path from the center of the collision zone to the deflecting magnet entrance is 11 cm, to the magnet exit 18 cm, and to the detector 21 cm. The electromagnet when energized with a dc current of about 100 A, the maximum used in this work, provided a field of -12 kG within its barrel (0.3 cm wide, 7 cm long), with a transverse gradient of -30 kG/cm. The detector is a surfaceionization filament of single-crystal tungsen (0.0076-cm diameter, heated with 0.5 A) which converts essentially 100%of the incident alkali-metal atoms and alkali-metal oxide molecules to atomic cations. Signals were recorded as the difference in readings with the alkali-metal beam flag open and the gas beam flag first open and then closed. Angular distributions were measured by turning the rigid oven frame about its rotation axis. With the parent alkali-metal beam direction designated as Oo and the gas beam direction 90°, this provided an angular range extending from -40" to +65". For comparison purposes, auxiliary runs were made with gases other than ozone or with the magnetic field off.

The Journal of Physical Chemistry, Vol. 97, No. 10, 1993 2115

Molecular Beam Chemistry

-1

00%

M+O+Op

Na (8.3) K (5.9)

101.4

/

x2z+

KO

NaO

I

I

I

I

x2z+

I

RbO

1

Figure 2. Energetic relationships (kJ/mol) for reactions of Na, K, or R withozone. At theleft areindicated theozonedissociationenergy, reaction exoergicity to form MO2 + 0 or M O 02,and relative translational energy corresponding to the most probable reactant beam velocities in M 0 3 collisions (cf. Figure 3). At the right are indicated energies to form M O in the 211 or 22+ electronic state with the accompanying 02 in various states (X,a, or b).

+

+

The data acquisition and beam flagging were controlled and actuated by an IBM PC-XT computer.

Results and Analysis Before presentingour magnetic deflection data and its analysis, we note energetic and kinematic aspects that are prerequisite for describing and interpreting the experimental results. Figure 2 displays the energetic relationships for the M 0 3 reactions. The relative kinetic energies corresponding to the most probablebeamvelocities are 8.3,5.9,and 3.9 kJ/mol, for theNa, K,and Rb reactions, respectively. Although these reactionscould form M02 + 0,this apparently does not occur to a detectable extent.5 The Berkeley study of theNa reactions found no evidence of Na02; despite likely fragmentation in the mass spectrometer, the time-of-flight distributions would have revealed its presence. Likewise, at least for the Rb reaction our magnetic deflection analysis indicates there is no appreciable yield of RbO2, which would be purely diamagnetic whereas the rubidium oxide product appears to be entirely paramagnetic. Thus, we assume the reactions with ozone yield practically only MO + 02. However, in addition to the possibility of forming MO in either the *llor 2Z+ state, these reactions can produce 0 2 in any of three states: X2n, alAg, or blZB+. Figure 3 shows velocity vector diagrams exhibiting the range of product scattering angles and velocities accessible in our experiments. The parent beam velocity vectors represent the maxima of Maxwell-Boltzmann distributions. Also shown are the corresponding vectors for the relative collision velocity and the centroidvelocityand the circular locus of elastically scattered M atoms. Dashed arcs indicate the region of reactant or product scattering directions that can enter the barrel of the deflecting magnet as the angular distribution is scanned. The radius of these arc8 indicates the region in which the velocity of a paramagnetic M atom or MO molecule (with magnetic moment

+

+

Figure 3. Kinematic diagrams for M 03 reactions, drawn for the most probable thermal velocities in the reactant beams. The horizontal and vertical arrows show the lab velocity vectors for M and 03, respectively; V denotes the initial relative velocity vector and C the center-of-mass velocity vector, directed at a lab angle of Bc = 4 2 O , 36O, or 2 8 O (from the alkali-metal beam) for M = Na, K, or Rb,respectively. The inner dotted circle is the locus for elastically scattered alkali-metal atoms. The heavy dashed arc (cf. Appendix B) indicates the velocity above which the paramagnetic alkali-metal monoxide product (Le., in the 2Z+ state) would be transmitted by our deflecting magnet; the angular spread of the arc shows the range of observable lab scattering angles. The solid circles are loci of the M O product with indicated percentages of reaction exothermicity in relative translational energy.

of 1 pa) is low enough so that practically all will be deflected by the magnet (at its maximum field strength). The calculations providing this estimate of the resolving power of the defection analysis are presented in Appendix B. This sets an approximate upper limit on the laboratory kinetic energy of the M atoms or MO molecules that can be deflected. Appreciably faster atoms or molecules will be transmitted to the detector without regard to their paramagnetic or diamagnetic character, in which case our experiment gives no information about the electronic state. Data for Comparable RWC~~OIM. Figures 4-6 present our magnetic deflection results in terms of the percent transmission as a functionof the laboratory scattering angle. The transmission ratio for a given angle is just the signal recorded at the maximum field strength divided by that for zero field. In order to provide comparisons useful in interpreting our ozone data, Figures 4 and 5 include data for interactions of alkali-metal atoms with other gases previously subjected to magnetic deflection a n a 1 y ~ i s . l ~ ~ ~ ~ These offer four pertinent comparisons. (1) No reaction occurs for Ar and CpHs. Practically none occurs for N 2 0 since the activation energy (-13 kJ/m017) is substantially higher than our mean relative kinetic energy (cf. Figure 2). Thus, for these systems the detector observes only paramagnetic alkali-metal atoms. The transmission ratio is therefore quite low over the whole range of scattering angles, less

Shi et al.

2116 The Journal of Physical Chemistry, Vol. 97, No. 10, 1993 Soil

a,

I

'

; '

I

'

'

'

'

I

T.

r&

+

B I

1

* I a

K

a

-30'

30'

O0

-

10-

o

a

-

. * e - -

O

,,: "

0

0 0

-4

701

CH,NO,

0 '

30'

-30'

90'

60'

LAB SCATTERING ANGLE Figure 4. Angular variation of the observed transmission (ratioof signals recorded with deflecting magnet on and off) for Na and various gases: N20 ( 0 ) ;NO2 (A);03 (0);CH3N02 (0);halogens (- -,from ref 24). Data pertain to total scattering: unreacted alkali-metal atoms and any alkali-metal-containing reaction products. The solid curve was fit to elastic scattering from N 2 0 as described in Appendix B.

60'

4

90'

LAB SCAlTERING ANGLE M p r e 5. Transmission data (cf. Figure 4) for K and Rb various gases: Ar ( 0 ) ;C3H8 (V);N 2 0 ( 0 ) ;NO2 (A);0 3 (0);CH3N02 ( 0 ) ;halogens (- -,from ref 24). The solid curves were fit to elastic scattering as described in Appendix B.

+

-

than about 10% for the Na case and even lower for the K case. These residual transmissions represent the fraction of atoms traveling too fast to be deflected. Our residuals are lower than in previous ~ o r k ' 0because , ~ ~ improved beam collimation makes weaker deflections observable. (2) For NO2 reaction to produce alkali-metal monoxide has a large cross sectionlo but is energetically inhibited. Since the +NO bond strength (305 kJ/moP) is larger than that for M-O, under singleallision conditionsthe reaction must utilize the initial collision energy (cf. Figure 2). In the sodium case, this precludes an appreciable yield of NaO in the paramagnetic 22+state. Any NaO must be formed almost solely in the zIIground state, so it is diamagnetic or only very weakly paramagnetic. Most of this NaO thusshould pass through the magnet without being deflected. In Figure 4 the observed transmission ratio at wide angles for NO2 is indeed appreciably higher than the residual transmission. Essentiallyonly the residual transmission appears at narrow angles (within - S O 0 of the alkali-metal beam), since there most of the scattered signal still comes from the nonreactively scattered,

0 '

30'

60'

I

goo

LAB SCATTERING ANGLE Figure 6. Comparison of the magnetic deflection analysis (cf. Figures 4 and 5) for reactions of Na, K,and Rb with ozone. The bars a t the right indicate the transmission calculated (cf. Appendix B) assuming that at wide angles the scattering signal is due entirely to the alkali-metal monoxide product in the 2E+electronic state with laboratory translational energy distributions shown in Figure 7.

paramagnetic alkali-metal atoms. In Figure 5 for the potassium case, however, even at wide angles the transmission ratio is quite similar to the residual transmission. This is consistent with forming KO predominantly in the paramagnetic 22+state and with relatively low translational energy, which would allow practically all the product to be deflected. Again, our data agree with previous results.10 (3) For CHsN02 reaction a u r s to produce a large yield of alkali-metal nitrite.I0 This is diamagnetic, so the transmission climbs high above the residual level. Since the yield increases for Na K,the transmission also rises further at wide angles. Despite the diamagnetic character of the product, however, the transmission remains well below 100%. This is because for CHsNO2 much of the flux at wide angles is paramagnetic, as it comes from nonreactively scattered alkali-metal atoms. (4) Diatomic halogen molecules, such as Br2 or ICI, react to form an extremelylarge yield of alkali-metal halide.9 Accordingly, this diamagnetic product is the dominant component of the scattering over most of the angular range. The paramagnetic nonreactive scattering is almost completely quenched at wide angles. The transmission thus is practically loofxb outside M O O . We did not perform a magnetic analysis for a diatomic halogen case, but include for comparison in Figures 4 and 5 dashed curvcs from previous work.24 As noted below, we expect the laboratory angular and translational energy distributions of alkali-metal monoxides from the ozone reactions to resemble those for alkalimetal halides from the halogen reactions. These dashed curves serve to indicate what the transmission for the ozone case would be like if the product alkali-metal monoxide were entirely diamagnetic. RewlteforOzoneReictbtu The transmission curves of Figure 6 for the reactions of ozone with alkali-metal atoms lie progressively lower as Na K Rb. In the Na case, the transmission at wide angles is substantial, as high as -35%, whereas for K it is comparable to or barely above the residual transmission seen for nonreactive systems, and for Rb at angles above 30° the transmission is very low, definitely below the residual level (confirmed in several runs). Without further information, the interpretation of the transmission curves for the Na and K cases would remain ambiguous. The transmission in excess of the usual residual level could be attributed to reactively scattered alkalimetal monoxide which is (i) chiefly in the effectively diamagnetic 211state, (ii) chiefly in the paramagnetic 22;+ state but traveling with high kinetic energy as a consequence of the large reaction exoergicity, or (iii) a mixture with comparablecontributionsfrom

-

--

The Journal of Physical Chemistry, Vol. 97, No. 10, 1993 2117

Molecular Beam Chemistry I

-Y '5

I

I

0.6

I

Magnetic Deflection

fC

$ d

0.6

m ln

8en

0.4

.z $=

3

(I)

0.2

0.0

20

40 60 60 100 LAB ENERGY (kJlmole) Figure 7. Laboratory translational energy distributions estimated by 3 reaction. The vertical line rescaling the results of ref 8 for the Na 0 indicates, for an atom or molecule with a magnetic moment of 1 p ~the , lab energy threshold for transmission through the deflecting magnet. This threshold was estimated from the observed transmission of Na elastically scattered from N20, as outlined in Appendix B. 0

+

both these possibilities. For Rb, the extremely low transmission at wide angles shows unequivocally that (a) the nonreactively scattered atoms too fast to deflect (which would appear in this region for less reactive systems) are absent and (b) any reaction product at wide angles must be -100% paramagnetic and traveling slowly enough to be almost entirely deflected. Two factors allow us to resolve the ambiguities for the Na and K cases in favor of possibility ii. One factor is a correlation, well-established for reactions of alkali-metal atoms with electrophilic molecules, among the magnitude of the reaction cross section and the form of the angular distributionsof both unreacted atoms and product molecules.26 The large Arrhenuis preexponential factor for the Na + 0 3 reaction7corresponds to a reaction cross section of 150A2. This is very similar to the cross sections for reactions of alkali-metal atoms with diatomic halogen molecules? and in accord with the simple harpooning model, in which the cross section is chiefly determined by the difference between the ionization potential of the alkali-metal atom and the electron affinity of the reactant molecule.27The Na + 03reactive scattering study by the Berkeley group* indeed found the NaO angular distribution is very similar to that typical of alkali metal diatomic halogens. At present no experimental data are available for alkali metal ozone nonreactive scattering. However, in analogy with the halogen reactions, it seems safe to assume that in the ozone case the nonreactive scattering at wide angles will virtually disappear; it corresponds to close collisions which instead yield reaction.28 Accordingly, we expect that practically all the scattered signal beyond about &30° of the alkali-metal beam (cf. dashed curves of Figures 4 and 5) comes from reactively scattered alkali-metal monoxide. The other important factor required to assess the transmission profiles is the laboratory translational energy distribution of the MO molecules, P(ELAB).The Berkeley study8 of Na + 0, determined this distribution for the reactively scattered NaO, although the reactant relative kinetic energy (75 kJ/mol) was much higher than in our work (cf. Figure 2). Figure 7 shows P(ELAB)distributionswe have estimatedby rescaling the Berkeley results to correspond to our collision energy and assuming the fraction of the reaction energy released in relative kinetic energy of the productsremainsthe same for Na K Rb. Calculations employing these distributions to estimate the transmission levels attributable to molecules traveling too fast to be deflected are

-

+

+

--

outlined in Appendix B. The deflecting power of our magnet, in effect calibrated by analysis of nonreactively scattered atoms, is such that an atom or molecule with a magnetic moment of 1 p~ will be deflected if its translational kinetic energy is less than about ET = 43 kJ/mol, a nominal threshold for transmission. In Figure 6 we indicate (bars at right) nominal estimates of the transmission expected at wide angles. These estimatesassume that at wide angles the signal is due entirely to alkali-metal monoxide molecules in the paramagnetic 2Z+ electronic state with the lab translational energy distributions shown in Figure 7. For the Na reaction, the observed transmission at wide angles is indeed close to our estimate. At smaller angles, the observed transmission is much lower because a substantial part of the signal comes from paramagnetic, nonreactively scattered alkali-metal atoms. Since P(ELAB)lies lower for these atoms (cf. Figure 3) than for the NaO product, a much larger fraction of the atoms are deflected. Note that the transmission of NaO from the ozone reaction, attributed to the paramagnetic 2Z+state, is higher than that of NaO from the NO2 reaction, attributed to the diamagnetic 2 I I state (cf. Figure 4). This reflects the higher translational energy available in the ozone reaction by virtue of its strong exoergicity. For the K and Rb reactions, the observed transmission at wide angles in Figure 6 is much lower than our nominal estimate. This offers evidence that P(,ELAB)for these reactions in fact lies substantially lower than the distributions shown in Figure 7,i.e., that the fraction of the reaction energy released in relative kinetic energy of the products is smaller than in the Na reaction. This seems quite likely, since such a trend has been observed for reactions of alkali-metal atoms with halogen compounds.29 Branching Ratio. We conclude that a value of unity for the branching ratio designated byf2 preceding eq 5 is consistent with our magnetic deflection results for all three reactions, if the interpretation is constrained by invoking analogies with other alkali-metal atom reactions. For the Na case there remains some leeway, however. For instance, in Figure 6,some of the signal at wide angles might come from nonreactively scattered atoms. Also, it is possible that the P(EUB)distribution of Figure 7pertains to a mixture of NaO states, with the paramagnetic 2Z+product appreciably slower than thediamagnetic 211product. Our magnet would then efficiently deflect both the atoms and 2Z+molecules, so an appreciable portion of the observed transmission could be attributed to 2 l l molecules. If all of the transmission at wide angles were due to 2II molecules, the nominal branching ratio wou!d befi = 0.7,corresponding to a yield of roughly 30% 2II and 70% 2Z+. Since some of the 22+moleculeswould be traveling too fast to deflect, the actual f 2 would be appreciably larger even in this case. In this way we have inferred a rough lower bound, f 2 > 0.8, for the Na reaction. There is much less interpretative leeway for the K case and still less for the Rb deflection results; fi appears to be quite close to unity for those reactions. Our conclusions pertain to the alkali-metal monoxide product scattered at angles substantially away from the parent alkalimetal beam, since near it the high flux of nonreactively scattered atoms masks the product. For these stripping reactions, the alkalimetal monoxide angular distribution peab strongly forward along the alkali-metal beam. The branching ratiofi near the peak of the product angular distribution thus might differ from that for the wide-angle scattering amenable to magnetic deflection analysis. This could occur if reactive encounters at large impact parameters, which yield the forward scattering, favor a different electronic state than those at smaller impact parameters, which result in wide-angle scattering. A quantitative assessment is not feasible, since we lack means to measure the ratio of MO product to nonreactively scattered M atoms. If we again invoke the assumed resemblance to the halogen reactions, however, the dashed curves in Figures 4 and 5 serve to show the magnetic deflection profiles that would be expected if MO were formed in

-

2118 The Journal of Physical Chemistry, Vol. 97, No. 10, 1993

et

Shi et al.

:

Figure 8. Ion-pair model, M+O-, for alkali-metal monoxide 211and 2Z+ states, which correspond respcctivelyto ...u2r3and ...u1r4configurations of the valence shell p orbitals of the oxygen anion.

the diamagnetic ZII state. (Although Br2 is a heavier target than ozone, the kinematic difference would not much alter these transmission profiles.) This indicates that any appreciable difference in the branching ratio would be confined to smallangle scattering. Since the contribution to the total reaction cross section is weighted by sin 6, the estimate offi derived from the wide-angle scattering appears likely to be representative. As typical for strongly exoergic stripping reactions, the reactivelyscattered alkali-metal monoxide molecules are probably highly vibrationally excited. This affects the magnetic deflection analysis only indirectly, by altering the ratio of the spin-orbit coupling constant to the rotational constant. That ratio and the rotational angular momentum determine the extent to which the 211state can acquire paramagnetic character. The effect is minor, according to estimates given in Appendix A. The recent photoelectron spectroscopy study of the Na + 0 3 reaction22 observed bands assigned to NaO in both the X211and A22+states. From the relative intensities, the X/A population ratio was estimated to be between 1:2 and 1:4, corresponding to nominal values betweenfi = 0.67andf2 = 0.80 for the branching ratio. The spectra are not inconsistent with fi = 1, however, since part or all of the X211ground-state population may result from collisionaldeactivation. Evidence for substantial collisional deactivation was seen in changes of the relative X/A band intensities with total gas pressure. Collisional intervention was also implicated by the appearance of a band attributed to NaOz from either the secondary reaction of NaO with ozone22or the rapid termolecular combination of Na with molecular oxygen.30 The Berkeley study8 of Na + O3reactive scattering could not distinguish between NaO formed in the X2II or A22+ states. However, we note that the radiative lifetimeI4of the Az2+state considerablyexceedsthe flight timeof -0.1 msin that experiment. Our results therefore imply that the extensive fragmentation of NaO by electron bombardment in the detector stems from electronic as well as vibrational excitation.

Msedon That the M + O3reactions form MO predominantly or even solely in the *Z+state is startling. At least a comparable yield of theZIIstatewouldbeexpectad,inview ofitsenergeticproximity, its 2-fold weight in orbital degeneracy, and the large reaction exoergicity. For the NaO case, since 211 is the ground state, it would be the adiabatic preference. The predominant formation of *Z+also seems odd in terms of qualitative chemical bonding. Figure 8 depicts the simple cation-anion pair M + D , an appro-

Figure 9. Sketches of frontier molecular orbitals for ozone: 6a1, the highest occupied, and 2bl, the lowest unoccupied orbitals in the groundstate electronic configuration. Both are linear combinations of atomic valence p orbitals, antibonding between the central and each terminal atom, bonding between the two terminal atoms. On reflection in the plane of the molecule, the 6al orbital does not change sign and the 2bl orbital does change sign. The ground-state configuration for 0,is ...(6a1)~(2bl)I, and for Cl02-it is ...(6a1)~(2b1)~.

priate model since the bonding is quite ionic;is e.g., hyperfine splittings show the unpaired electron in NaO is 99.3% on the 0 atom.14 For the zIl state, the hole in the 0- valence shell is in a p r oxygen orbital transverse to the internuclear axis, so two electrons reside in the pu orbital aimed at the M+ cation. For the 22+state, the 0- hole is instead in the pu orbital; so only one electron is directed toward the cation. In this case, we might plausibly expect3’ that the electron-jump or harpooning mechanism,

M

-.

+ 0,

M++ o,-+ M+O- + 0,

(7) would form2II as the predominant product state rather than *2+. To rationalize the contrary experimental result, we examine other features that might foster electronic state specificity. We also discuss implications of Na0(2Z+) for mesospheric aeronomy, particularly the Chapman excitation scheme for the sodium airglow. The chemiluminescent reactions of alkaline-earth-metal atoms with C102offer a kindred case of electronic state specificitywith a contrasting result.32 For the MO product, there are a pair of excited states, A’Z+ and A’lII, with the same orbital configurations depicted in Figure 8. The emission spectra show unequivocally that the reactions produce much more of the A’III state than the AiZ+state (by factors of at least 10.50, and 100 for M = Ba, Sr, and Ca, respectively), even though these states are nearly isoenergetic. Since the electron affinities of ozone (2.1 eV)33 and chlorine dioxide (2.3 eV)34are both large and similar, the electron-jump model should be applicable to both. We consider these sibling reactions in turn, looking for aspects that might account for their opposite preferences in forming 2 and Il product states. Electronic State Specificity. For both reactions, the electron transfer in eq 7 can occur at distances 2-3 times larger than the MO bond lengths. The harpooning electron enters a molecular orbital, the 2bl orbital in Figure 9, that is antibonding between the central atom and the terminal 0 atoms. As is typical in alkali-metal reactions, this is the same orbital that leads to photodissociation. The harpooning mechanism thus amounts to dissociative electron attachment to the target molecule,enhanced by the electric field of the approaching alkali-metal cation. The unusual weakness of the ozone bond may permit the 0 3 ion to be largely dissociated to 0--.0~ by the time the M+cation arrives close enough to form the product M+O-. This suggests that we might regard the reaction as an ion-pair or geminate recombination in the presence of a third body, M+-O*-02. If

The Journal of Physical Chemistry, Vol. 97, No. 10, 1993 2119

Molecular Beam Chemistry weassume that with respect toelectronic interactionsthedeparting 02 acts merely as a benign spectator or chaperon, it is easy to see how the ion-pair interactioncould foster electronic state specificity. The requisite features, evident from qualitative analysis, are exemplified in the theoretical electronic structure calculations for MO molecules.ls Since the total spin is conserved, we need consider only doublet states. At large internuclear distances, the 22+and 211states stemming from the ion pair M+(1S)-.0-(2P) lie above the 2 2 - and 211 states arising from the atom pair M(2S).-O(3P). As the geminate combination proceeds, the 211 state descendent from the ion pair suffers a strongly avoided intersection with the 211 state from the atom pair, whereas the 2 2 + state does not interact with the 2 2 - state. I s Hence, at bonding distancestheion-pair combination will form the W state, whether or not it is the ground state. However, the avoided intersection causes the ion-pair combination to correlate with an excited 211 state (the C state), not energetically accessible in the reaction, rather than the lowest 211 state (X or A). The latter, although near the 2 2 + state (A or X) at theequilibrium distance and likewise ionic in character there, is forced by the avoided intersection to correlate with the atom pair at larger distances. This simplistic ion-pair combination model thus would produce MO predominantly or even solely in the 2Z+ state. Other aspects must be significant. According to the simplistic model, 2 / 3 of the M+--O- encounters would be fruitless, but that is inconsistent with the observed reactive scattering. The departure of 02, even if precipitous, need not be benign, and may have a major role in producing the 2 2 + state. As 0,dissociates, the emerging 0-may most reluctantly relinquish its p r bonding and therefore present a half-empty pa orbital to the approaching M+. Then all the M+-O- encounters would yield the 22+state. The analogy to photodissociation via population of the 2bI orbital also suggests electronic interactions could have a major role as 03-breaks up. Photodissociation of ozone in the strong Hartley continuum produces O2primarily in excited electronic states.35 If not quenched by the proximity of the cation,36such excitation might occur in the alkali-metal reactions. As seen in Figure 2, the alAgstate is more likely than blZg+,considering the disposal of energy in other modes. We note that the P ( E ) distribution*(cf. Figures 9 and 5 of ref 8) has an unusual shoulder above the primary peak and the spacing is suspiciously close to the excitation energy for 02 (a ’Ag). The C102 case differs from ozone in several ways. The harpooning electron again enters the 2bl orbital of Figure 9, thereby pairing with an electron already there in the parent molecule. Because C1 is more electronegativethan 0,the central atom now acquires more electron density than the terminal atoms. The parent bond strength is not particularly weak and electron attachment appears to give a relatively long-lived anion with a barrier inhibiting di~sociation.~~ The asymptote for the C10 0- channel is not the lowest; C10- + 0,C1+ 02-,and especially Cl- + O2all lie lower, in that order. Photodissociation likewise exhibits complexities, including a long lifetime before dissociat i ~ n , although ’~ C10 + 0 is the strongly dominant channel.3gThe reactions to form MO(X12+)+ C10(X211)are very exoergic but nonetheless go via a long-lived collision complex.40 The process of interest here, reaction to form MO in the A’III state in preference to the isoenergetic AIZ+ state, is a minor ~ h a n n e l ,and ~ ~no . ~dynamical informationabout it is yet available. It may not be amenable to the ion-pair combination model M+-*O--.ClO in view of the complicationsnoted above, although the strong field of the incoming M+ will hasten dissociation of the anion. In any case the utility of such a model for minor channels is doubtful. Rather than invoking symmetry constraints derived from the geminate combination model, we can consider a general stereodynamical a ~ p e c t . ~ IIfJ ~an S atom attacks a molecule along any symmetry element, electron transfer to form an S cation

+

cannot occur unless the parent molecule and its anion have the same symmetry. Electron transfer in a coplanar attack thus is allowed for N2O and NO2 (only Ar or AI species enter) but forbidden for O3(Al parent, BI anion, so A’- A’’) or for C102 (BI parent, AI anion, so A” Ar). As seen in Figure 9, for O3 and C102 the electron jump into the 2b1 orbital will occur most readily when the M atom attacks perpendicular to the plane of the molecule. For such broadside attack the electron affinity is maximal; hence, the radial distance at which the jump occurs is also maximal. This fosters reaction with the 2bl orbital of the anion aimed toward the incoming cation. If the population of this orbital goes into the pa orbital of 0- as the product M+Omolecule is formed, the pa would be singly occupied ( 2 2 + state) in the O3reaction and doubly occupied (A’lII state) in the C102 case. These heuristic considerations bring out questions for further study; as yet we lack a compelling theoretical explanation for the strong electronic state specificity seen in these reactions. Aerometric Implications. In the upper mesosphere Na O3 is the primary source20of NaO, and thus the aeronomy of the 22+ state now needs to be examined. Its major role seems likely to be reaction with mesospheric 0 atoms, even though the latter constitute only 0.1-1% of the total number density.41~~2 If NaO(22+)reacts as rapidly with O(3P) as the measured ratelg for Na0(211), the chemical lifetime of NaO(%+) with respect to this reaction in the 85-95-km altitude regime will be 10-100 ms. Owing to a very small transition dipole,I4radiative decay via 2Z+ 2n is negligibly slower. Collisional quenching of NaO(22+) by mesopheric species, chiefly N2 and 02, may also be slower than reaction with 0 atoms. Previous laboratory studies of NaO kinetics intended to elucidate atmospheric processeshave used the Na + N2O reaction as a quantitative and convenient s o ~ r c ethe ; ~Na~ + ~ O3 ~ ~reaction serves less well because of secondary reactions of NaO with 0zone.~~6 However, these flash photolysis or fast flow tubestudies were all performed at pressures so high that any NaO(ZZ+) produced by reaction of Na witheither N 2 0or Oswas collisionally quenched to the NaO(Tf) ground state before undergoing reaction. The relevance of such studies to upper atmospheric NaO reactions now appears questionable. An experimental attempt to study the formation of excited Na(2P) atoms from NaO(Q+) + 0 will have to render collisional quenching to NaO(211) slower than the reaction. This condition can best be met by a triple molecular beam experiment, in which an O(3P)atomic beam intersects a spray of N a O ( W ) generated from Na + O3 beams. Such an experiment appears difficult but feasible. Correlation Analysis. Previous theoretical discussions of processes involving NaO likewise need to be amended to take into account the 2Z+ state. In 1980, an exemplary discussion of the Chapman excitatation mechanism was given by Bates and Ohja,I8 based on symmetry correlations between reactant and product electronic states but considering only Na0(211). They concluded that the branching ratio to form Na(2P) could be as large as fin = l/3; that appeared consistent with the observed excitation, but subsequentexperimentsIgfoundfin = 0. Recently, we revised the correlation analysis23to include Na0(2Z+). With the aid of some additional postulates, we obtained f3n = 0 and fiz= 2 / + We comment further on the analysis here, since some aspects invite tests by electronicstructure calculations,and similar features appear in many metal oxidation reactions that involve multiple potential surfaces arising from open shell species with spin and orbital degeneracy. The correlation analysis of NaO + 0 Na + 0 2 involves three chief postulates. (1) Reactions of both NaO states proceed by electron transfer via NaO+ + 0-ion-pair configurations. (2) The reactions proceed only on doublet potential surfaces. Quartet surfaces, involving three parallel spins, are presumed to be too repulsive to permit reaction. (3) The electron transfer involves

-

+

-

-

2120 The Journal of Physical Chemistry, Vol. 97, No. 10, 1993

TABLE I: Branching Ratio Analysis for the NaO + 0 Reaction

variant all states all doublets all ionic all ionic doublets

hx

hn

Ill '13

'16

'13

'13 '14

0

'13

postulates used none only 2 1 and 3 1-3

one of the valence electrons least involved in bonding. In terms of the dominant molecular orbital configurations of Figure 8, this corresponds to

-

Na+0-(A2Z+)-.u1r4 and

Na+O(A311)-vr'r3

Na+O-(X2II)*w2r3 Na+O(X3Z-)-.u2r2 Electronicstructure calculations and photoelectron spectroscopy22 show that for NaO+ near the equilibriumbond distance, the X32and A3II states differ in energy by only 0.3-0.5 eV. Both these states might be expected to form almost equally well from NaO in either the 211or 2Z+state, contrary to postulate 3. If so, the correlation analysis would become much less restrictive. The potential surfaces for these reactions comprise four symmetry species, classified by total spin (doublet or quartet) and by reflection (A' or A") in the plane of the three atoms. Na0(211) + O(3P) gives rise to 12 surfaces, of which 6 correlate with ion-pair states (postulate l), but only 3 of those are doublets (postulate 2), all of which correlate with Na(%) + 02.If the three quartet surfaces were also reactive, as assumed by Bates and Ohja, one would also correlate with Na(2S) and the other two with Na(2P);thus, they obtainedhn = 2/6. From Na0(2Z+) + O(3P) there arise six surfaces, all correlating with ion-pair states but only three doublets; of these one correlates with Na(2S), and the other two correlate with Na(2P), giving f& = 2/3. Table I itemizes the branching ratios obtained with variant assumptions. Without all three postulates, we could not account for hn ==. 0, the experimental result of Plane and Husain.I9 The remarkable electronic state specificity displayed by both the M + Osreactions and the Chapman excitation process MO + 0illustrate how stronglyelectronicstructure effects can promote or impeded the formation of thermochemicallyallowed reaction products, even for very exothermic and facile reactions. Our results seem to reconcile the Chapman mechanism with current laboratory results and mesospheric data, pending further tests. Kinetic studies of NaO(ZI:+) are essential if the venerable Chapman mechanism is finally to be established quantitatively. This would enable aeronomers to more reliably monitor mesosphericozone concentrations by ground-based lidar measurements of sodium profiles and the airglow emissi0n.~4

Acknowledgment. We thank Gil Citro for his help in the early stages of these experiments and John Dyke, Bill Klemperer, and Steve Langhoff for useful discussions. We gratefully acknowledge support by the Atmospheric Sciences Division of the National Science Foundation Under Grant ATM-8204481 and the encouragement of Jarvis Moyers, Gerald Romick, and Brian Tinsley. Appendix A Effective Magnetic Moments Here we evaluate the electronic magnetic moments cc for 2 2 + and 211states,averaged over a thermal distribution of total angular momentum for thecase that Jisduechiefly to molecular rotation. We use units of the Bohr magneton and standard spectroscopic n ~ t a t i o n . ~For ~ ,an ~ ~angular momentum state )JM) the average has the general form

where the Boltzmann weighting factor WJ is normalized to the

Shi et al. partition function, so that

C(2J

+ l)WJ = 1

J

When many rotational states are populated, we may use the classical or high-temperature approximation for the partition function, Q = kT/B >> 1, and

w j = (l/Q> exp[-J(J + l)/Q1 (A3) This approximation is appropriatefor the MO molecules produced in the M 0 3 reaction. For the analogous reactions of alkalimetal atoms with halogens, the product rotational distributions47 correspond to rotational temperatures in the range 500-1 500 K. For such temperatures, the rotational partition function is of the order Q lo3 or larger for the MO molecules. The expectation value of the magnetic moment, (JMplJM), is governed by the angular momentum coupling.46 Again, the situation is relatively simple for the MO molecules. The 2 2 + state is a protypical instance of Hund's case b, with "spin-only" paramagnetism. The 211 state is fairly close to Hund's case a, even for high J, by virtue of a large spin-orbit interaction. This keeps the electronic spin coupled to its orbital motion and thus to the molecular axis, thereby fostering rotational quenching which renders the state effectively diamagnetic. 2E+State: Hund's Case b. For this case each rotational level occurs in closely spaced pairs with

+

(JMplJM) = M/J or - M / ( J + 1) (A4) aside from a factor of gs/2, where gs = 2.0023 is the electron spin gyromagnetic ratio. The thermal average in eq A1 thus factors as

Since the sum over M yields J ( J + l), the sum over J reduces to eq A2. Thus, we find simply ( p ) = gs/2, so the 2Z+ state is paramagnetic and has the same effective magnetic moment as a 2s atom. 211State: Hund's Case a. For this case the molecule acts as a symmetric top; the projection of J on the molecular axis is a good quantum number, given by Q = A + Z,the sum of the projections A and I: of the electronic orbital and spin angular momenta. Then (JMlplJM) = (A

+ g,Z)OM/J(J + 1)

(A6)

For the 2 1 1 ~ / 2component, A = f l , Z = f1/2, and Q = hence, A + gsI: = l e 3 , so this component is diamagnetic even without rotational averaging. For the component, A = f l , Z = *I/2, and Q = f3/2; hence, A + gsZ = f2, so the expectation value of eq A6 becomes 3M/J(J + 1). The thermal average in eq A1 reduces to

When Q is large, the summation can be replaced by integration and eq A3 then yields simply This is inversely proportional to the most probable J in the Boltzmann distribution, given by Jmp= '/~(2kT/B)l/~. As shown in Table 11, for the expected range of rotational temperatures eq A8 gives values of ( p ) for the MO(2113/2) molecules that are only a few percent of a Bohr magneton. The B value for NaO is from microwave spoctroscopy;14those for KO and RbO are from electronic structure calculations.2Js Although the rotational excitation produced in the M + 0 3 reaction could

Molecular Beam Chemistry

The Journal of Physical Chemistry, Vol. 97, No. 10, 1993 2121

TABLE II: Rotationally Averaged h)for MOPIIWZ) ( P ) , PE,for Trot,K

Appendix B Magnetic Deflection Calculations

~~

MO

B, cm-I

500

1000

1500

NaO KO RbO

0.424 0.251 0.210

0.093 0.071 0.065

0.066 0.051 0.046

0.054 0.042 0.038

TABLE 111: Intermediate Coupling Calculations for MO(*II) MO A, cm-I Y J sin2 w ~

NaO

-111

-262

-79

-186

KO

-19

-315

RbO

-79

-376

35 92 35 92 45 120 49 I32

0.016 0.090 0.032 0.143 0.020 0.102 0.015 0.090

be lower, this seems unlikely in view of the very large exoergicity and the resemblance to other reactions of alkali-metal atoms with strongly electrophilic molecules. Particularly for NaO, the rotational excitation may well be higher. This is suggested by analogy with the reactions of K and Cs with Br2, for which the product rotational temperatures were about 1500 and 850 K, re~pectively.~’ Magnetic deflection scales as the ratio of ( p ) to the lab translational energy. Thus, for MO molecules in the 2113/2 state the threshold parameter ET used in our discussion of Figures 6 and 7 (and in Appendix B) would be only a few percent as large as that for the 2Z+ state. This further enhances transmission of the 2 I I 3 1 2 molecules, making them appear even more nearly diamagnetic than they actually are. 2II State: IntermediateCoupling. When J becomes sufficiently high, the coupling in a 211state shifts from Hund’s case a toward case b. Then il is no longer a good quantum number and the 2111/zand2113/2componentsmix. Ifthecase blimit isapproached, ( p ) tends to eq A5 and a 211 state would exhibit ‘spin-only” paramagnetism like that of a 2Z+ state. For a given vibrationrotation level, the extent of mixing of the 211components induced by intermediate coupling45is governed by

where w is the ‘mixing angle” and

with Y = A/Bthe ratio of the spin-orbit coupling constant to the rotational constant. Case a holds well when ( Y - 2)2 greatly exceeds the J-dependent term in eq AlO, so w is small; case b is approached in the opposite situation, when w 45O. Table I11 gives specimen calculations for MO(211)which show that case a is a good approximation. The spin-orbit interaction for NaO in the lowest four vibrational levels has recently been determinedfrommicrowavespectra,I4whichgiveA=-111,-104, -99, and -85 cm-I for u = 0, 1, 2, and 3, respectively. These values lie between the coupling constants for the 0A = -1 18 cm-I, and for the 0 atom,49A = -79 cm-I. Since much of the MO reaction product probably is vibrationally excited, we include calculations using the 0 atom coupling constant, a likely lower bound. For illustration, we consider two J values. One is the most probable value (35 for NaO) for a Boltzmann distribution at 1500 K. The other value (92for NaO), a likely upper bound, corresponds to putting 25% of the reaction exoergicity into rotation. In the latter case, the M0(211) molecules acquire considerable case b character, lo%,but those with lower J will be much closer to case a. For mixing of this modest extent, the magnetic moment ( p ) = sin2w , not large enough to appreciably affect the deflection analysis.

-

-

Our experiments employed the same deflecting magnet used previously24and very similar molecular beam geometry. Thus, we refer to that work for most aspects of the procedures involved in calibration and estimation of the efficiency of magnetic deflection. The analysis outlined here is a shortcut that is adequate for our purposes. The deflection of a paramagnetic atom or molecule with a given magnetic moment and specified lab translational energy depends solely on properties of the magnet and geometrical parameters that remain fixed during an experiment. A straightforward calculation of the net observable transmission requires convoluting the flux profile defined by the collimating slits (C in Figure 1) with P(ELAB), the translational energy distribution. (A further convolution is necessary if there is also a distribution of magnetic moments.) Since for the reaction products P(ELAB) is not known, and can only be roughly estimated, we adopt a commensurate approximation which avoids the convolution procedure. Our approximationsimply assumes that paramagnetic species are 100% deflected if traveling slower than a threshold lab translational energy, denoted by ET, and 100% transmitted if faster. This we refer to as the step-function or threshold criterion; it holds well when the spread in deflection due to imperfect collimation is small compared to that due to the P(EL*B) distribution. The same value O f ET pertains for any alkali-metal atom and to any *Z+ alkali-metal monoxide molecule, since all have a magnetic moment of 1 /IB. The magnitude of ET was determined empirically, by fitting the observed transmission of elastically scattered alkali-metal atoms. For this we used the data for M + NzO, since under our conditions N2O is practically unreactive and its mass and hence the scattering kinematics are nearly identical to those of OS.Our procedure involved estimating the P(ELAB) distribution for elastic scattering as a function of the scattering angle. This was done using just the one kinematic diagram displayed in Figure 3, constructed for the most probable parent beamvelocitiesassuming Maxwell-Boltzmann distributions at the oven temperatures. Then P(ELAB) as a function of the lab scattering anglewas approximated by shifting the most probable velocity of the alkali-metal beam according to the dotted elastic scattering circle in Figure 3. The step-function criterion for deflection, with ET as a parameter, was then imposed on these shifted distributions to calculate the transmission for elastic scattering as a function of the lab angle. The solid curves in Figures 4 and 5 show the fits obtained by taking ET = 43 kJ/mol for all three systems, M = Na, K,Rb. This value of ET fits well the observed variation with M of the transmission at the lab angle tlc corresponding to the most probable centroid vector (denoted by C in Figure 3); there the transmission declines from 8% to 6% to 2% as Na K Rb. The apparent increase in the elastic transmission for K and Rb at wider angles is not meaningful. In that region theintensity of elasticscattering becomes quite small, so the experimental error in the transmission measurement (ratio of flux with magnet on and off) becomes large. The variation with the lab angle of the elastic transmission computed using our threshold criterion closely resembles the observed curves reported p r e v i ~ u s l yand , ~ ~ we find these can be fit well with ET values of about the same magnitude. Similar computations were carried out for comparison with the observed transmission of MO molecules from the M + O3 reactions. We began with the distribution of the product relative translational energy for the Na + 0 3 reaction, as determined in the Berkeley study.8 This we rescaled to correspond to our (lower) collision energy, simply by shrinking the abscissa scale in proportion to the total available energy. Thereby we assume the fraction of the reaction energy released in relative kinetic energy of the products remains the same for Na K Rb. From the rescaled relative kinetic energy distribution and the Jacobian for transformation from the center of mass (CM) to the laboratory

--

--

2122 The Journal of Physical Chemistry, Vol. 97, No. 10, 1993

system, we derived the P(ELAB)distribution for M O reactive scattering. For simplicity, this was evaluated at the lab angle Bc, wheretheMOlabvelocityisjust thescalar sumofitsCMvelocity and the centroid velocity. Figure 7 shows the P(ELAB) distributions thus obtained for NaO, KO, and RbO. Again employing our threshold criterion, we computed the transmission as the fraction of the area of the P(ELAB) distribution above ET = 43 kJ/mol. This assumes that all of the reactive scattering is paramagnetic, Le., MO(ZZ+). The values obtained for the transmission were 35%, 27% and 12% for NaO, KO, and RbO, respectively; these are indicated in Figure6. The decreasing trend in transmission is a kinematic effect; for reactions releasing the same relative kinetic energy, the lab translational energy of the MO product decreases as its mass increases. The kinematic trend is evident also in the velocity diagram of Figure 3. There, as Na K Rb, the arc that specifies the MO threshold lab velocity for deflection moves outward relative to the circles that indicate the fraction of available energy entering product relative translation.

--

References and Notes ( I ) BasedonOK heatsofformationof 145.348 kJ/molfor03and246.74 kJ/mol for atomic 0 in JANAF Thermochemical Tables, 3rd ed.: Chase, M. W., Jr.; Davies, C. A.; Downey, J. R., Jr.; Frurip, D. J.; McDonald, R. A,; Syverud, A. N. J . Phys. Chem. Ref. Dara 1985, 14, Suppl. No. I . (2) Langhoff, S. R.; Bauschlicher, C. W., Jr.; Partridge, H. J . Chem. Phys. 1986, 84, 4474. (3) Kolb. C. E.; Elgin, J. B. Nature (London) 1976, 263, 488. (4) Husain, D.; Marshall, P.; Plane, J. M.J. Chem.Soc.,Chem. Commun. 1985, 1216. 15) Aper. J. W.. 111: Talcott. C. L.; Howard. C. J. J . Chem. Phvs. 1986. 85, 5584. " (6) Silver, J . A.; Kolb, C. E. J . Phys. Chem. 1986, 90, 3263. (7) Worsnop, D. R.; Zahniser, M. S.; Kolb, C. E. J . Phys. Chem. 1991, 95, 3961. The Arrhenius form for k , which we cite is a corrected version of that reported in this paper. (8) Covinsky, M. H.; Suits, A. M.; Davis, H. F.; Lee, Y. T. J . Chem. Phys. 1992. 97, 2515. (9) Kwei, G. H.; Herschbach, D. R. J . Chem. Phys. 1969,51, 1742 and references cited therein. (10) Herm, R. R.; Herschbach, D. R. J . Chem. Phys. 1970, 52, 1317. ( I I ) Lindsay, D. M.; Herschbach, D. R.; Kwiram, A. L. J . Chem. Phys. 1974, 60, 315. (12) So, S. P.; Richards, W. G. Chem. Phys. L e r r . 1975, 32, 227. ( I 3) Allison, J. N.; Cave, R. J.; Goddard, W. A,, Ill. J . Phys. Chem. 1984, 88, 1262. (14) Yamada, C.; Fujitake, M.; Hirota, E. J. Chem. Phys. 1989,90,3033. (15) Langhoff, S. R.; Partridge, H.; Bauschlicher, C. W., Jr. Chem. Phys. 1991, 153, I . Bauschlicher, C. W., Jr.; Partridge, H.; Dyall, K. G. Chem. Phys. Lert. 1992, 199, 225. (16) Chapman, S. Asrrophys. J . 1939, 90, 309.

Shi et al. (17) Chapman, S. In Aurora and Airglow; Armstrong, E. G., Dalgarno, A,, Eds.; Pergamon, Oxford, 1955; p 204. (18) Bates, D. R.:Ojha, P. C. Nature (London) 1980, 286, 790. (19) Plane, J . M. C.; Husain, D. J . Chem. SOC.,Faraday Trans, 2 1986, 82, 2047. (20) Swider, W. J. Geophys. Res. 1986,91,6742; P1aner.SpaceSci. 1992, 40, 247. (21) Plane, J. M. C. Inr. Reu. Phys. Chem. 1991, I O , 55. (22) Dyke, J. M.; Shaw, A. M.; Wright, T. G. In Gas-Phase Meral Reactions; Fontijn, A., Ed.; Elsevier Science Publishers, B.V.: Amsterdam, 1992; p 467. (23) Herschbach, D. R.; Kolb, C. E.; Worsnop, D. R.; Shi, X. Nature 1992, 356,414. (24) Gordon, R. J.; Herm, R. R.; Herschbach, D. R. J . Chem. Phys. 1964, 41, 2218; 1968, 49, 2684. (25) Handbook of Chemistry and Physics, 71st ed.; Lide, D. R., Ed.; CRC Press, Boca Raton, FL, 1990-91. (26) Wilson, K. R.; Herschbach, D; R. J . Chem. Phys. 1968.49, 2676. (27) Gialason, E. A. In Alkali Vapors; Davidovits, P., McFaddan, D. L., Eds.; Academic Press: New York, 1979; p 415. (28) Anderson, R. W.; Herschbach, D. R. J . Chem. Phys. 1975,62,2666. (29) Riley, S. J.; Siska, P. E.; Herschbach, D. R.Faraday Discuss. Chem. Soc. 1979, 67, 27. (30) Husain, D.; Plane, J . M. C. J . Chem. Soc., Faraday Trans. 2 1982, 78, 163. (31) Kolb, C. E.;Gersh, M. E.; Herschbach, D. R.Combust. Flame 1975, 25, 31. (32) Engelke, F.; Sander, R. K.; Zare, R. N. J . Chem. Phys. 1976, 65, 1 146. (33) N0vick.S. E.; Engelking, P. C.; Jones, P. L.; Futrell, J. H.; Lineberger, W. C. J. Chem. Phys. 1978, 70, 2652. (34) Babcock, L. M.; Pentecost, T.; Koppenol, W. H. J. Phys. Chem. 1989, 93, 8126. (35) For a comprehensive review, see: Steinfeld, J. I.; Adler-Golden, S. M.; Gallaher, J. W. J . Phys. Chem. ReJ Dara 1987, 16, 911. (36) Havemann, U.; Zfilicke, L.; Nikitin, E. E.;Zembekov, A. A. Chem. Phys. Leu. 1974, 25, 487. (37) Wecker, D.; Christodoulides, A. A.; Schindler, R. N. fnr. J. Mass. Specrrom. Ion Phys. 1981, 38, 391. (38) Richard, E. C.; Vaida, V. J . Chem. Phys. 1991, 94, 163. (39) Davis, H. F.; Lee, Y. T.J . Phys. Chem. 1992, 96, 5681. (40) Davis, H. F.; Suits, A. G.; Lee, Y. T.In Gas-Phase Metal Reactions; Fontijn, A., Ed.; Elsevier Science Publishers, B.V.: Amsterdam, 1992; p 319. (41) Offerman, D.; Friedrich, V.;Ross,P.; von Zahn, U. Plant. SpaceSci. 1981, 29, 747. (42) S h a m W. E. Planer. Soace Sei. 1991. 39. 617. (43) Age; J. W., 111; Howa;d, C. J. Geophys. Res. Lerr. 1986, 13, 1395; J . Chem. Phys. 1987,87, 921. (44) Takahashi, H.; Clemesha, B. R.; Sahai, Y.; Batista, P. P.; Simonich, D. M. J . Geophvs. Res. 1992, 97, 5987. (45) Zare; R. N. Angular Momentum; Wiley-Interscience: New York, 1988; pp 300-304. (46) Townes, C. H.; Schawlow, A. L. Microwave Specrroscopy; McGraw-Hill: New York, 1955; pp 188-190, 284-286. (47) Maltz, C.; Herschbach, D. R. Discuss. Faraday Soc. 1967,44, 176. (48) Neumark, D. M.; Lykke, K. R.; Anderson, T.; Lineberger, W. C. Phys. Rev. A 1985, 32, 1890. (49) Saykally, R. J.; Evenson, K. M. J . Chem. Phys. 1979, 71, 1564.