Vibrational-mode-specific Energy Consumption Translational and Vibrational State Dependence of the Ba + N20 (vl, v2, u,) -+ BaO* + N2 Reaction BY DAVID J. WREN AND MICHAEL MENZINGER Lash Miller Chemical Laboratories, University of Toronto, Toronto, Ontario M5S 1A1, Canada Received 2 1 st December, 1978 The excitation functions eCL(E, T,) for forming chemiluminescent (CL) products in the (Ba + N20) reaction is found to depend sensitively on N20 vibrational temperature T,. In a second experiment thermal rate constants for CL production kcL, and for Ba beam attenuation kT, were measured as functions of N20 temperature, and activation energies were obtained. Analysis shows that u2- bending acts as promoting mode, and participation by uI (N-0 stretch) is highly likely. Promotion by v2 is consistent with the initial formation of an ion pair Ba+N20-.Rearrangement of this inter- mediate to BaO*(A' 'n) products, believed to be the CL emitter, is adiabatically allowed. Specificity of energy consumption is traditionally discussed in the context of vib- rot-el-trans reactant excitation in direct A + BC reactions.' A further aspect enters the picture with polyatomic molecules: The 3N - 6(5) vibrational degrees of freedom will generally show mode-specificity. Although little is known at present about these matters, simple symmetry considerations alone, i.e., the degree to which a given normal vibration projects onto the reaction coordinate, provide a starting point for predicting the efficacy of that mode. The present chemiluminescent (CL) atom-triatom reaction Ba + N20: --+ BaO* + N2 (1) will be shown to differ in an interesting way from such a naive expectation.This sheds a new light on its reaction dynamics. The Ba + N20 system has been studied extensively in recent years, with particular emphasis on problems of energy disposal and the nature and effects of the so-called " reservoir states ".2 In this paper we report energy consumption measurements by two complementary methods : (1) A crossed supersonic/thermal beam experiment alllows us to measure the CL excitation function eCL(j?, T,) over a range of vibrational temperatures T,. Super- sonic beams of a constant nominal energy3 are generated by changing the He/N20 seeding ratio as well as the nozzle temperature To. Since the vibrational distri- bution remains essentially unrelaxed at To, this allows one to vary T, N To independ- ently from J?.A pronounced vibrational enhancement of ecL(E7 T,) was found, in agreement with an early report on this The lowest collision energy achieved in this experiment was 9 kJ mol-'. (2) In order to cover the low energy region, thermal rate constants kcL(TN20) and kT(TN20) were measured as a function of TNz0, and activation energies were derived (kcL refers to total CL production and k, to attenuation of the Ba beam). The goal of the analysis was (a) to determine the vibrational mode(s) responsible for the enhancement and (b) to reconstruct (effective) state-specific excitation functions98 VIBRATIONAL-MODE-SPECIFIC ENERGY CONSUMPTION cTi(E) that are consistent with both measurements and extend over the whole energy range.This requirement turns out to be very stringent since it allows us to eliminate the u1 (N-0 stretch) mode as the only promoting mode (N-N stretch u3 is easily disqualified) while definitely requiring the v 2 bending mode to be active, possibly in conjunction with vl. This is explained, as b e f ~ r e , ~ by the initial formation of an ion- pair (Ba+N,O-) in a hard collision, followed by its rearrangement to observed products. This ion pair intermediate also resolves some difficulties in previous interpretation^,^ since it correlates adiabatically with several BaO* states, amongst others the A' Ill state believed6 to be the CL emitter. EXPERIMENTAL The molecular beam apparatus in which two types of measurement were performed has been described elsewhere.7 A.ENERGY CONSUMPTION: CL CROSS -SECTIONS rFCL(E, T,) as independent functions of (nominal c.m.) collision energy E and of N20 vibrational temperature T, were obtained by crossing a collimated effusive Ba beam with a chopped and collimated, (He-seeded) supersonic N20 beam. Dimensions and operating parameters are given in table 1. E and T.. were varied TABLE 1 ,-CROSSED-BEAM GEOMETRY AND OPERATING PARAMETERS N20/He beam: nozzle diameter nozzle temperature nozzle pressure skimmer diameter nozzle-skimmer nozzle-collimator nozzle-scattg. centre beam divergence Ba beam: oven temperature oven orifice diam. oven-scattg. centre beam divergence dN = 0.1 mm Po = 5.33 x lo4 Pa (400 Torr) 0.36 mm 12 mm 45 mm 95 mm 2.1" To = 280 - 869 K 973 K 3.1 mm 64 mm 7.1" by the N,O/He-seeding ratio (mole fraction) XNtO and by the nozzle temperature TO(=Tv, see below).The intersection volume was viewed by a bare E.M.I. 9558 QB photomultiplier coupled to a lock-in amplifier. Low resolution (10 nm spectral slitwidth) beam-beam spectra, recorded by using a multiple reflection White-Welsh cell9 and a + m monochromator, were, within the experimental noise, independent of E and T,. This dispenses with E, Tv-dependent correction factors in further analysis. The observed CL signal &b is related to the CL cross-section by: Here nBa, nNZO are the reactant number densities at the scattering centre and UR is the average relative velocity. The beam geometries were chosen to assure a constant collision volume V .The number density nBa was determined by monitoring the Ba flux on a quartz crystal micro- balance located 25 mm above the scattering centre. N20 densities were measured concur- rently with the light signals by a quadrupole mass spectrometer located in a differentially pumped chamber. The ionizer was 494 mm downstream of the nozzle. ComplementaryD . J . W R E N A N D M . M E N Z I N G E R 99 flux measurements using a closed ionization gauge operated in the phase sensitive mode’” agreed with the mass spectrometric results. The nominal collision energy I? is given by I? = &/2 = p(Uia + fikao) where CBa is the average velocity of the Maxwellian Ba beam and & is the measured streaming velocity of the supersonic beam. The results l i c ~ (fig.1) represent relative values since all measurements were uncalibrated. The N20 velocity distributions were measured in a separate experiment by time-of-flight as described else~here.’~~ B. THERMAL RATE CONSTANTS kCL(TNe0), kT(TNzO) for CL production and Ba beam attenu- ation were obtained in a thermal beam-gas experiment by measuring the pressure and temperature dependence of the CL intensity. An effusive Ba beam (x 1000 K, x 9 x lo9 atoms cm-3) was collimated and chopped at 50 Hz before entering a resistively heatable A1 scattering chamber (SC) through a 1.6 mm diameter orifice. The temperature of the SC(T,,, -- 298-591 K) was taken as the arithmetic mean (f5 % variance) of the readings from 3 thermocouples buried in the chamber walls. Pure N20 (Matheson >99.99 %) was admitted from a reservoir to the SC through a calibrated leak.The absolute SC pressure was computed by gas flow continuity from the flow rate into the chamber (= backing pres- sure, measured on a capacitance manometer, times conductance of leak) and the conductance of the scatterbox orifices towards the high vacuum chamber. The N20 gas density deter- mined in this fashion covered the nNxO = (3.6 x 1010)-(1.9 x 1014) C M - ~ range [correspond- ing to pNfO = 10-6-(5 x Torr at 298 K]. The Ba flux was monitored by a quartz crystal microbalance” located on the far end of the reaction chamber. A bare photomulti- plier (E.M.I. 9558 QB, cooled to 190 K) viewed a 6.2 mm long section of the Ba beam, 22.2 mm downstream of the SC entrance hole. This makes the scattering path length 1 = 22.2 i- 3.1 mm.The CL signal follows the relation: 12,13 Sbg(nN,O TNaO) = kCL( TN,0)nBanN20 exp [-lnN,OoT( TNIO)I (3) where V is the volume of the observation region (assumed constant) and oT is the effective Ba beam attenuation (=total scattering) cross-section. The latter represents an upper limit to the total reactive cross-section oR < oT. A corresponding limit to the reactive rate constant is given by kT(TNz0) = UoT(TNaO), where z7 = ( 8 R T e f f / 7 ~ ~ ) ” ~ , the reduced mass is p and Teff is the effective translational temperature characteristic of a thermal beam-gas experiment : l4 Teff = (MBaTNaO + MN,OTBa)/(MBa + MNaO). (4) Relative CL rate constants kCL(Terf) were obtained as a function of temperature as the limit- ing low pressure slope of &g(nNIO) determined by linear least square fits. oT(Teff) was obtained from linear least square fits to plots of h[&g(t?NzO, Tcff)/f?N,@Ba V] for data at higher nN20, where attentuation is appreciable. C.CHARACTERIZATION OF THE SUPERSONIC N20 BEAMS with respect to translational and internal energy distributions is crucial to our data analysis. The velocity distributions measured by time-of-flight and analysed as described elsewhere7 were used to (a) calibrate the collision energy scale and (b) to deconvolute the data. The N20 internal state distributions were inferred from the following considerations : As the local translational temperature decreases in the course of the adiabatic expansion, internal degrees of freedom will also tend to relax.The extent of this relaxation is characterized by the ratio Z / Z , of the average number 2 of collisions which one molecule suffers during the expansion (typically 2 x 10’- lo3) ‘’*16 to the number Z1 of (gas kinetic) collisions required to relax the internal mode i. Electronic degrees of freedom are unimportant since the lowest excited state lies 28 000 cm-’ above the groundstate and is negligibly p0pu1ated.l~ Molecules with small rotational spac- ings are known to relax rotationally with near gas-kinetic as experiments with N2 and CsF beams20p3 show. Accordingly we assume that N,O is rotationally relaxed and is100 VIBRATIONAL-MODE-SPECIFIC ENERGY CONSUMPTION characterized by a rotational temperature TR nearly equal to the local translational tempera- ture Tt w TR - AT.This assumption is also required by energy balance considerations in order to account for the measured beam energy. Vibrational distributions, on the other hand, are assumed to remain frozen at the nozzle temperature To N T,. Ample experimental 21,22 and theoretical evidence23 supports this assumption for the relatively stiff N20 modes (1288, 588, 2237 cm-l). The linear relation (Lambert-Salter plot),24 between log Z,,, and vmin, the frequency of the lowest energy mode that limits the rate of the overall relaxation (i.e., the v 2 = 588 cm-' bending mode), yields an estimate Z,,, z lo4 (at 300 K) in agreement with measured relaxation Another well established corollary of the vibrational cooling is the formation of clusters. Our source conditions do not favour dimerization 30331 and comparison with experiments performed under source conditions comparable to ours32 lead us to expect a cluster content of <1 % for our beams.We assume that this small contamination has no noticeable effect on the CL rate. RESULTS Our primary data, the CL excitation functions dCL(l?, To) == 6cL(E, T,), measured at different nozzle (=vibrational) temperatures are shown in fig. 1. The most strik- ing result is the strong enhancement of cross-sections with To. The solid curves E/kJ mol-' FIG. 1 .-Chemiluminescence cross-sections b,,(E, To) as functions of nominal collision energy I? for a series of nozzle temperatures To: 0 , 2 8 1 ; A, 389; 0 , 4 7 0 ; 0 , 5 4 8 ; V, 599; a, 716; A , 793 and y , 869 K. represent least square fits of the data points by two-parameter curvesb,, = CE-" except for the lowest temperature To = 281 K where below 19 kJ mol-I the flattening curve was drawn by hand. One is tempted to extrapolate this portion to a threshold below the energetically accessible region.The reproducibility of the To = T, = const. curves is &lo % from run to run due to systematic errors (gas mixtures XNz0, beam densities nNz0; To), but the experimental scatter of individual data points on these curves is only &6%.D. J . WREN A N D M. M E N Z I N G E R 101 BEAM-GAS EXPERIMENTS The relative rate constant for CL production kcL, and beam attenuation kT, as functions of Teff, are given as Arrhenius plots in fig. 2. The kT plot appears linear, and a linear least squares fit yields E: = 12.1 & 1 kJ mol-l.The k,, plot, however, is distinctly non-linear. The activation energy EaCL decreases with T,,, from EaCL (475 K) = 10.0 A linear fit gives EzL = 8.4 & 1.5 kJ mo1-l. 1.7 kJ mol-1 to EaCL (675 K) = 5.9 & 2.0 kJ mol-’. 1 . 2 - cn c .- ?I 0.8 n 0 L \ -L, 0.4 1.4 1.6 1.8 2.0 lo3 K / Teff FIG. 2.-Arrhenius plots for CL production ( OkcL) and Ba beam attenuation (Ok,). Solid lines are linear least square fits. The dashed line drawn freehand follows the curvature of the kcL data. An estimate of the T‘,,-dependence of the (relative) quantum yield @(Teff) = kCL/kT oc exp (+3.5/RTe,,) is obtained from these numbers by approximating the total reactive rate constant by k,. Our total attenuation cross-section at TNzo = 300 K is uT = 27 5 6 8L2, in agree- ment with earlier measurements12 and in contrast to a more recent value.13 The small value of the total reaction cross-section oR < uT confirms the earlier that one is dealing with “ hard ”, repulsive wall collisions.The experimental data are now analysed in the light of the following two ques- tions : (1) Which degree of freedom (trans, rot, vib, electron, excitation; clustering) is primarily responsible for the To effect? A translational effect is readily excluded by deconvoluting the measured 6,L33 and by observing that the resulting cross-sections oCL differ only insignificantly from the primary data. This also justifies the use of the primary data GCL in the subsequent analysis, and eliminates the need of using the de- convoluted ucL.The lowest electronically excited state of N20 (3Cf, To = 28 000 cm-’) l7 lies too high to contribute significantly. As shown above, rotation is relaxed to the translational (streaming) temperatures T’ = T R E 20-210 K [for pure N20 (To = 281 K) and 98% He-seeded N20 (To = 840 K), respectively]. Several other studies have revealed relatively weak dependences of reactivity on r o t a t i ~ n . ~ ” - ~ ~ Rotational enhancements of the reported magnitudes prove insufficient to account for our observations. N20 rotation can thus be eliminated as the dominant cause of the To effect. The cluster content has been shown above to be < z 1 %, eliminating (N20) clusters as a possible cause. This completes the proof, by successive elimina- tion, that N20 vibration is the source of CL enhancement at elevated To = T,.See text for activation energies.102 VIBRATIONAL-MODE-SPECIFIC ENERGY CONSUMPTION (2) Which of the three vibrational modes (ul, u,, u,) = (1288, 588, 2237 cm-1)41 is primarily responsible for the effect? This is now examined by decomposing the observed oCL into specific CL cross-sections bi of reactant state i: ocL(E, T v ) = 2 xi(Tv)bi(E)- ( 5 ) The weighting factors are the equilibrium populations xi(Tv) = gi exp (-Ei/krv)/C gi exp (-&i/kTv), (6) 1 where the degeneracies for g i = 1 for ul, u3 and gi = u, + 1 for 0,. The solution of the N linear equations (N = 8 in our case, see fig. 1) provides in principle N detailed cross-sections, provided the data were of high precision. We have restricted ourselves to N = 2 and 3 state analyses, since N 3 3 already yields unphysical 6, [i.e., a(,??) < O for some El.Excitation of a single mode at a time, rather than combination vibrxtions, is assumed to promote the reaction: model 1 (u, = 0, 1 . . .). The u, mode is assumed " active " in the states 2 (i, j , k), i 3 1 while 2 ( O , j , k ) forms the less reactive " ground " state. The u, (bending) mode was considered threefold: model 2a(u, = 0, 1 . . .) assumes 2 (i, 0, k ) the " ground" and 2 (i, j , k ) , j 1 the " active " state, model 26 (u2 = 0 I , 2 . . .) 2 (i, j , k), The following models were explored. i,k i , k i,k i,k i,k TABLE 2.-FITTING PARAMETERS [EQN (9)-( lo)] OF 6i(E) model C1" Eob n mc ~2~ p 02' C3a q 0 3 ' u1 = 0, l/u 2.28 2.5 0.82 0.030 8.64 1.27 u1 = 0, l/t 2.28 1.9 0.82 0.030 8.64 1.27 9.5 u2 = 01, 2/u 2.31 3.1 0.81 0.033 3.41 1.27 u2 = 01, 2/t 2.31 0 0.81 0.033 3.41 1.27 4.5 u 2 = 0, 1, 2/t 4.32 1.9 0.50 0.019 3.63 2.65 10.3 220 1.15 17.8 (4.22) (1.9) (0.050) (0.019) (5.74) (2.65) (3.2) (220) (1.15) (10.3) Units are C,/A' kJ'-" mol"-', C,/Az kJ-P molp and C3/Az kJ-4 mol-4.Units are kJ mol-'. Units are mol kJ-'. j = 0, 1 " ground state " and 2 (i, j , k ) ; j 2 2 " active " and model 2c (21, = 0, 1, 2 . . .), a three state model with 2 (i, j , k ) ; j = 0 and j = 1 and j 2 2; finally model 3 (v, = 0, 1 . . .) in which v3 was considered by taking the two 2 (i, j , k ) ; k = 0 and k > 1 states. For the analysis, the populations Xi* of the effective states i' were obtained by summing over the true molecular states i contributing to i', Xi* = 2 X i i , .The N linear eqn (5) were then solved successively at constant ,!? by a least squares optimiza- tion routine. The quality of the fits by the 5 models described above are illustrated in fig. 3. Synthetic " experimental " cross-sections ecalc(E, To) obtained from eqn (5) are plotted as a func- tion of To at l? = const. for comparison with the measured eCL(,??, To). It is evident i , k i,k i, i 1 The resulting effective state cross-sections ai(E) are summarized in table 2.D. J . WREN A N D M. MENZINGER 103 T I K FIG. 3.-Comparison of experimental acL (open circles) at ,!? = 48 kJ mol-' with CL cross-sections calculated from best fit effective state cross-sections a&??) for different models [eqn (8), (90) and (10a); parameters are given in table 21.(a) v1 active: (ul = 0, 1 . . . ; solid line), (ul = 01, 2 . . . ; dashed curve) (b) uz active: both the two and the three state models (u2 = 01,2 . . .) and (u2 = 0, 1,2 . . .) give good fits as shown by the solid line. (u2 = 0 , l . . . ; dashed line): (c) v3 active: (u3 = 0, 1 . . . ; solid curve). The (ul = 0, 1 . . .), (u2 = 01,2 . . .) and (u2 = 0, 1, 2 . . .) models yield acceptable fits. that models 1 (v, = 0, 1 . . .), 2b (0, = 01, 2 . . .) and2c (u, = 0, 1 , 2 . . .) alone provide acceptable fits to the data, eliminating model 3 (u3 = 0, 1 . . .), i.e., the u3 mode and model 2a (u, = 0, 1 . . .), from consideration. The same holds at other collision energies, I?. So far there is little to choose between models 1, 2b and 2c from the quality of the fits (fig.3) alone. To make further progress in deciding between these possibilities we now examine which model is capable of yielding thermal activation energies that agree with the measured EZL. RECONSTRUCTION OF di(E) AT LOW I? FROM EaCL The thermal rate constants (fig. 2) and the excitation functions (fig. 1) carry rate information from two mutually exclusive but overlapping energy ranges. We use the E,CL(Teff) information to reconstruct consistent cross-sections in the experiment- ally inaccessible low energy range. The activation energy Ea3 f RT; aln k/ aT3 appropriate to a three temperature beam-gas experiment, characterized by T,, T2 the (internal and translational) tem- peratures of gases 1 (internal states i) and 2 (internal states j ) and T, the (effective) translational temperature [eqn ( 4 ) ] , is given by : Ea3V'3) = 2 Cfij [(Elf) - $ RT3I i j + J13 2 Cfij [Ei - (&i)TII + J23 Z: I f i j [ ~ i - (&i)T21 (7) i i i j Here Jnl are the Jacobians (aT; '/8Tl-') and f i j ( T l , T,) = (XiXikii/k) are the relative contributions of states i, j to the overall rate, where the XiX, are the (Boltzmann)104 VIBRATIONAL-MODE-SPECIFIC ENERGY CONSUMPTION fractions of reactants in the molecular states i and j , ki, is the detailed rate constant of states Ij.and k = 2 2.hjkij is the total rate constant. (~5;~) is the average transla- tional energy of the i + j reaction.42 The effective state i' cross sections 6,. (I?) (fig. 4) were extrapolated below 12 kJ mol-I in an attempt to bring agreement between calculated and observed E t L .This agreement was iteratively improved by (1) imposing the physical constraint that cross-sections cannot diverge [reflected by the adjustable cutoff parameters D,, D, in TABLE 3.-cOMPARISON OF MEASURED AND CALCULATED ACTIVATION ENERGIES (FIVE MODELS FOR PROMOTING MODE) experiment calculated: Eacalc/kJ mol-' for models: TN,o/K Teff = Tz/K EaCL/kJ mol-l (ul = 0, Ilu) ( u , = 0, lit) (un = 01, 21u) (u2 = 01, 21t) (08 = 0, 1, 211) 300 470 9.8 f 0.8 18.9 7.3 24.6 8.7 9.9 (11.1) 600 697 6.4 & 2.1 20.4 19.3 16.8 15.8 9.1 (10.7) 1000 1000 - 13.1 16.7 8.0 10.0 7.6 (8.2) eqn (9b) and (lob)] and (2) by iteratively advancing from model 1 (v, = 0, 1 . . .) to 2b (u, = 01, 2 . . .) to model 2c (0, = 0, 1, 2 .. .). The stages of the calculation, whose results are summarized in table 3, are: (1) Excitation of Ba, i.e., the third term in eqn (7) was neglected. (2) The molecular excitation energies c1 were replaced by the internal reactive energies averaged over those molecular states i that contribute to the " effective " states i' in the finite models: ( ~ f ) ~ ' = 2 cii*Xiit/2 X i i f where, e.g., i = 0, 1 and 2, 3 . . . for model 2a. (3) The cross-sections a,.(,!?) for models 1, 2a, b, c were least square fitted by functions (the parameters D2, 0, are introduced later) : 1 1 a,(E) = CIE-'(E - Eo>" exp [-m(E - EO)] E 2 Eo (8) = o E < Eo 62(E) = C2E-' E > 0 2 ( 9 4 = a,@,> E < 0 2 (9b) a3(E) = C3E-' E > 0 3 (104 = @,(DJ E<D3 (lob) The fitting parameters are given in table 2.(4) Using the analytical expressions for ki and ((ET) - 3 RT,) given by LeRoy4, and extensions thereof to deal with the forms of eqn (9) and (lo), E,(T3) EE EZL(Teff) was calculated at several temperatures for several a,@) models (table 3). Models 1 (u, = 0, 1 . . . lu) and 2b (u2 = 01, 2 . . . lu) employ un-truncated (" u ") 6,@) functions (D2 = 0.0) that non-physically go to infinity as E+ 0. This over- emphasizes the contribution of the upper state to the overall rate and yields corre- spondingly high activation energies. In addition (v, = 0, 1 . . . lu) introduces a EzL temperature dependence contrary to that observed (fig. 2). The physically more reasonable truncated (" t ") models l(u, = 0, 1 . . . It) and 2b(v2 = O , l , 2 .. . It) assume constant 6, below the adjustable cutoff energy D2. However, Ea values are still too high since the energy ( E ; ) ~ ' of the upper effective state i' is too high. The results recorded in table 3 are those closest to the experimental Ea from among a series of el and b2 that employed (D2, Eo) combinations other than those given in tableD . J . WREN AND M . MENZINGER 105 f / k J mol" FIG. 4.-Effective state cross-sections 8,(g) based on three state model 2c (u2 = 0, 1,2 . . .). Solid lines: derived direktly from primary data fig. 1. Dashed curves : (decreased Eo in el and truncated d2 and &) give optimal simultaneous fit of dCL and E,CL (table 3, last column; parameters given in table 2 last line). Dot-dashed curves: a new form of e2 avoids the non-physical intersection with cfl (as in previous model).Bracketed parameters in table 2 were used. Bracketed E,Ca" in table 3, last column were obtained. (a) f i 3 , (b) and (c) e2, ( d ) el. 3. Therefore, to decrease EaCalC to the measured values 8-10 kJ mol-1 while obtaining the observed T-dependence, it is necessary to introduce a lower-lying, internally excited state, the only candidate being v2 = 1. The three-state model 2c(u2 = 0, 1,2(t) alone yields a gratifying fit to the experimental E,CL-values. This is taken as proof that v, alone as promoting mode is inconsistent with the experiments and v2 is required as promoting mode, either alone or in combination with ul. The qualitative content of this analysis is clear and significant despite the fact that its quantitative details are less satisfactory. We have no explanation for the fact that the unbiased 3 state analysis of ecL yields a e2 (solid curves in fig.4) which drops below 8, at high energies while approaching e3 at low energies. It may be an artefact that reflects the limited precision of the raw data and the inflexibility of the analytical expressions @)-(lo). Yet this model, after incorporating D2, D3 and Eo as adjust- able parameters (E,, has to be made to float in order to reproduce E,CL; yielding the dashed curves in fig. 4), is remarkably successful in reproducing both experimental data. An ad hoc cross-section dZ for the intermediate state that is physically more plausible (dash-dotted curve in fig. 4, bracketed values in tables 2 and 3) yields slightly worse data fits.New beam-beam experiments will be required, with better energy resolu- tion, a wider energy range that covers in particular the low energy regime and106 VIBRATIONAL-MODE-SPECIFIC ENERGY CONSUMPTION preferably state selection, to determine the detailed state cross-sections with higher precision than that achieved in the present work. DISCUSSION MODE SPECIFIC DYNAMICS The foregoing analysis shows that: (1) the gCL raw data (fig. 1) are consistent (fig. 3) with both u, and/or u, as the " promoting " modes while definitely excluding u3. (2) The values and the temperature dependence of the activation energy EaCL, however, can only be reproduced by a much more specific model (v, = 0, 1,21t) requiring the bent molecule u2 = 1 to be among the promoting states.This establishes u2 as active mode without excluding, however, a possible contribution from u,. This conclusion becomes physically plausible as follows : A vibrational analysis of N,044 shows that u1 and v3 represent essentially N-0 stretch and N-N stretch modes, respectively, while v2 designates the bending mode, as usual. Elementary considerations predict u, to be active, and u3 to be inactive in promoting molecular dissociation N,O+ N2 + 0 as well as reaction. The causes for the involvement of u2 are less obvious. Previously4 u2 has been suggested by us as promoting mode. This is based on the increase of the N 2 0 electron affinity with bending angle (fig. 5 ) , arising from the fact that in this 22 electron system an extra electron will enter the lowest unoccupied 374 1Oa) orbital, whose energy drops sharply with bending angle of the originally linear N,0.45 A striking demonstration of this fact was given by C h a n t r ~ ~ ~ who observed a z lo3 fold increase of the dissociative attachment rate of thermal electrons (e + N,O+ N, + 0-) upon raising the vibrational temperature from 350 to 1000 K.120 150 180 +O/deg FIG. 5.-Potential energies of N,O and N20- as functions of N-N-0 bond angle. (a) NzO- 'A", The CL rate can be enhanced by N 2 0 bending ( i e . , by the electron affinity) if a close-range electron transfer, reminiscent of harpooning (1 1) initiates the reaction, followed by rearrangement of the intermediate ion pair. The valence orbital structure of the BaO(XIX +) groundstate resembles the doubly ionic configuration Ba2+ (6so)O2-(2p6), or 0202~4, where all orbitals written are centred (6) N2O 'A', (c) N20- 'A'.Ba('S) + N,O('X+) -3 Ba+(,S) + N20-(2A') +- (Ba+O-)* + N2('C;)D . J . WREN AND M. MENZINGER 107 primarily on the oxygen atom. The low lying excited states which may act as reser- voirs or as emitters all resemble the singly ionic configuration Ba+(6s1)0-(2p5) where one electron has been transferred to an orbital centred on Ba (underlined): BaO*(a311, A”n) arise from 0~0~71~0, and BaO*(3Z+, A1n+) from 0207140. This is confirmed by orbital population The reaction must therefore-be accom- panied by charge separation. Our v,-promoting model merely suggests that this event is the initial and rate determining step. N-0 stretch versus N-N-0 bend? There is good reason for v1 = 1 and v, = 2 to be about equally reactive, as the two-state analysis suggests.The (100) and (02OO) states (the superscript “ 0 ” refers to the state with 1 = 0 vibrational angular momentum) have both the same C+ symmetry and similar energy, and are known to be moderately strongly mixed by Fermi ~esonance.~~ Thus, even in isolated mole- cules, the assignments v, = N-0 stretch and 221, = bend break down. In addition collisions with Ba are expected to randomize the phases of the bending motion and thereby increase the coupling. The A(02,0), 1 = 2 state may also be coupled to (100) in this fashion. In effect, the (100) and (020) states become dynamically indistin- guishable and the combination of EA enhancement and N-0 stretch is expected to be particularly effective.Since the (0, 1,0) state is not mixed with v, it is very significant that this state is required by the foregoing EaCL analysis. Within the credi- bility limits of the rather indirect analysis, this shows that the bending mode is indeed one promoting mode as suggested earlier. If in a hypothetical molecule an “ inactive ” mode (in zeroth order) is coupled to an “ active ” mode by Fermi resonance, then the former would also become dynamically active. In this sense one might consider the activity of v, secondary to that of the u2 bending mode. A direct test of the present conclusions by the use of state selected is desirable as well as feasible. The adiabatic correlations between reactants and p r o d u c t ~ ’ ~ ~ ~ ~ appear in a new light through the inclusion of the intermediate ion pair.The neutral reactants corre- late directly only with BaO(X’C+), and ad hoc assumptions were made5 to invoke the possible adiabatic formation of excited BaO* products. In the present picture, the ion pair Ba+(’S) + N20-[211(2A’ in C,)] with its open shell electron configuration correlates formally (spin disregarded) with several energetically accessible excited product states: with BaO(A’ Ill and a”) in Cz,, and with [XIC+ and 3C+ (unobserved)] in C, symmetry. The formation of triplet products (a”, 3C+), requires a spin-flip in the ion pair, a process that would be favoured by a long lived c ~ m p l e x . ~ ~ * ~ ’ A long lived complex, however, appears to be in discord5’ with the highly non-statistical nature of the excitation functions, to be discussed presently.The correlation with A’ ‘II is particularly gratifying since this state has recently been identified as a CL emitter.6 The question of the dynamical content of ai(E) is answered straightforwardly by separating the excitation functions into a dynamical B and a statistical p(E’) factor: 53*54 di(E) = &@)/I@’) where Bi is termed “ average state-to-state cross-section ”, E’ is the (average) product energy exclusive of electronic excitation. The rot-vib-translational product state density is given in the rigid-rotor-harmonic-oscillator approximation 55 as log p(f?’> = (s + r/2 + n/2 - 1) log I?’, where s = number of oscillators, r = Edi (di is the dimensionality of the rotors) and n = number of translational degrees of freedom.The state-to-state cross-section Bi is plotted for the (u, = 0, 1,2ln) model (dash-dot bi in fig. 4). in fig. 6. The pronounced translational energy dependence of the dynamical factors demonstrates the highly non-statistical nature of the title reaction. The in- ternal state dependence of ai confirms again the mode-specificity discussed above.108 VIBRATIONAL-MODE-SPECIFIC ENERGY CONSUMPTION 10 vr C 3 Y .- J i L d $ 1 \ b' 10 30 50 E / k J rnol-' FIG. 6.-State-to-state cross-sections ai(E) derived from effective state cross-sections bi(E) for (u2 = 0, 1, 2 . . .) model. The dash-pointed curve of fig. 3 (bracketed values in table 2) was used. (a) 33, (b) Z1 and (c) Zo. 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