Furaduy Discuss. Chem. SOC., 1987, 84, 127-143 Spin-Orbit Effects in Chemical Reactions Investigation of Ground-state Products from Reactions of Ba(3D) Mark L. Campbell? and Paul J. Dagdigian* Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 2121 8, U. S. A. The dependence of the cross-sections for production of ground-state barium halide products on incident spin-orbit state has been determined by means of optical-pumping state selection for the reaction of metastable Ba(6sSd 3 D ) with HCI, CH3Cl, HBr and CH3Br. In addition, cross-sections for the metastable D level were related to those of the 3DJ multiplet by optical pumping on an intercombination line. For alkyl halide (RX) reactants, the spin-orbit dependence of the reactivity for the ground-state channel was substantial with an ordering J = 1 > J = 2 > J = 3.This is an opposite order- ing to that previously observed for the chemiluminescence channels in analogous reactions. The hydrogen halide reactions exhibited a varying spin-orbit dependence with vibrational level. For the most highly populated vibrational levels v, the spin-orbit dependence was comparable in sign and magnitude to that for RX reactants, while a significantly diminished variation of reactivity with incident J was observed for lower u. The variation of spin-orbit effect with product vibrational level is believed to be due to the dependence of the reaction dynamics on incident impact parameter. It has been demonstrated for a variety of atomic reactants that the chemical reactivity of different spin-orbit levels associated with an atomic term of non-zero spin and orbital angular momentum can vary significantly.’ Significant differences in reaction rates have been observed for atomic multiplets with large spin-orbit splittings, such as Hg(3P0), Sn(3P), Pb(3P) and the metastable 3P0 inert-gas atoms, as might be expected, but also for terms with small splittings, such as F(’P0) and the metastable triplet states of the alkaline-earth atoms. In most studies, the total rate of collisional removal was measured for the different spin-orbit levels; however, in some experiments it was possible to determine the spin-orbit dependence for specific product channels.In our laboratory, we have carried out a series of studies of spin-orbit effects in reactions of the alkaline-earth atoms, Ca(3P0),2-4 Sr(’PO),’ and Ba(3D).6 An optical- pumping state selection technique was employed to perturb the near-statistical spin-orbit populations of beams of these metastable terms emerging from a discharge atomic beam source.’ Chemiluminescence channels of a number of reactions of these atomic species with diatomic halogens, alkyl bromides and iodides, as well as with N20 and NO2, were investigated.With the exception of Ca(3P0) + SF, and Ba(’D) + N20, NO2, for which no spin-orbit dependence was observed, the chemiluminescence cross-sections were found to vary significantly with incident atomic spin-orbit level. In all cases, the level of highest energy [ J = 2 for Ca(’Po) and Sr(3P0) and J = 3 for Ba(’D)] possessed the largest cross-section. The cross-sections from the lowest-energy spin-orbit level [ J = 0 for 3P0, J = 1 for ’ D ] were typically 5 to 10 times smaller than for the highest-energy level.For several reactions [Ca(’P*) + C12 and Sr(3P0) + HBr, CH,Br2] it was possible by laser fluorescence detection to investigate the spin-orbit dependence of the reaction t Present address: Department of Chemistry, U.S. Naval Academy, Annapolis, MD 21402, U S A . 127128 Ground-state Products from Reactions of Ba( 3D) channel leading to ground-state prod~cts.~~* In marked contrast with the chemilumines- cence channels, the lowest-energy spin-orbit level ( J = 0) was found to possess the largest cross-sections. These experimental results have been interpreted with the help of a pseudo-quenching model calculation for Ca(3P') + C1, by Alexander.' In this quantum-mechanical treatment, reactive collisions were simulated in an atom-atom collision by quenching to a lower asymptote via an ionic-covalent curve crossing.While the calculated cross-sections displayed a strong sensitivity to the strength of the ionic- covalent coupling, these model calculations could qualitatively explain the experimental results. The spin-orbit effect arises from differences in the evolution of the asymptotic spin-orbit level onto the various electrostatic potential-energy surfaces. Despite the small Ca( 3P0) spin-orbit splitting, an adiabatic correlation argument for the spin-orbit dependence seems to be valid, wherein wavefunctions arising from the lower-energy incident spin-orbit levels selectively undergo charge transfer to an ionic surface.The opposite ordering of reactivity for the chemiluminescence channel vs. the ground-state product channel can further be explained as arising from a selective removal of flux at the outermost ionic-covalent curve crossing. In the present paper we report on the spin-orbit dependence in the ground-state reaction channel of the Ba(6s5d 3D) + HX, CH3X(X = C1, Br) reactions. For these reactions we were able to determine relative spin-orbit dependent reaction cross-sections for a range of BaX product vibrational levels v. It has also been possible to determine reaction cross-sections for the second metastable Ba level, 6s5d '0, relative to those for 3D. Our experimental results show that the spin-orbit dependence for the '0 manifold varies with v.These data allow us to gain information on the dependence of the spin-orbit effect upon impact parameter. Experimental These experiments were carried out in a beam-static gas scattering arrangement, as described in detail in previous publication^.^*^" A near-eff usive beam of metastable electronically excited (6s5d 3DJ and ID2) Ba atoms was produced in a discharge beam source'' and passed through a slit into a reaction chamber, to which gaseous reagents were introduced at pressures of up to 1 mTorr (as measured with a capacitance manometer). Laser-induced fluorescence signals due to barium halide reaction products were detected in a zone 1.6+0.1 cm beyond the collimating slit. A home-made grazing- incidence dye laser,' ' of bandwidth 0.15 cm-' (double grating arrangement 1 2 ) , which was pumped at 10 Hz by an excimer laser (Lambda Physik EMG53MSC), was employed for excitation.The fluorescence was collected with f/ 1.5 optics and imaged unfiltered onto a Hamamatsu R928 or EM1 9816 photomultiplier tube, whose output was fed into a boxcar integrator. Excitation spectra were acquired under computer control (DEC LSI-11/23), and the spectra were stored on magnetic diskettes for later analysis. Optical-pumping depletion with a single-mode C.W. dye laser (CR599-21 with rhodamine 6G dye) was employed for state-selection of the Ba" beam. The laser beam intersected the atomic beam at right-angles ca. 2 cm in front of the beam source; typical laser power was 90 mW in a 4 mm diameter beam.The C.W. laser wavelength was adjusted to the centre of a given atomic transition with the aid of a fluorescence detector ca. 50 cm downstream of the main fluorescence zone, as described in detail previously.6 A small fraction of the laser beam was directed to the auxiliary detector and the pump laser wavelength was optimized by maximizing the atomic fluorescence signal intensity. The ' D, level and individual DJ spin-orbit states were depleted by tuning the laser to the 5d6p 'P1 +-6s5d 'D2 line at 582.6nm and lines of the 5d6p3P"-6s5d ' D multiplet at 590.8 to 61 1.1 nm, respectively. Cross-sections for the ' Dz level were related to those for '0J by pumping on the 5d6p 'Fg +-6s5d 'D3 intercombination line at 580.6 nm. [See the Ba energy-level diagram given in ref.(6).] Because of the numberM. L. Campbell and P. J. Dagdigian 129 Table 1. Energies (in eV) for the Ba* + RX -+ BaX reactions studied HCl 0.05 f 0.09 0.03 0.08 0.16 f 0.09 1.32 f 0.09 HBr -0.05 f 0.10 0.03 0.14 0.12 f 0.10 1.28 f 0.10 CH3Cl 0.91 f 0.09 0.04 0.10 1.05 f 0.09 2.21 f 0.09 CH,Br 0.71 f 0.10 0.05 0.16 0.91 fO.10 2.07f0.10 a Dg (BaX) - Dg(RX). The latter were calculated from data in ref. (15). 'Initial energy of the RX reactant, calculated from the enthalpy at 298 K. 'Average initial relative translational energy, computed by convoluting the beam and target gas velocity distributions [see ref. (16)]; the former was derived from time-of-flight measurements [ref. (17)]. dEav,('S) and E,vl(3D) are the total energy available to the products for the 'S and 30 reactions, respectively: E,,, = ADo+ Ein,(RX)+ E:,,,,+ Ein,(Ba*).Ef,,,, has been taken to be the average reported in column 4. Eint(Ba*) = 0, 1.160, and 1.413 eV for the IS, 3D and 'D states, respectively [ref. (IS)]. of naturally occurring Ba isotopes, some of which have hyperfine sp1iting,l3 it was not possible to remove all the atoms in a particular level. The C.W. laser was tuned to deplete the most abundant mass 138 isotope (72% natural abundance14), and account was taken of incomplete depletion in the analysis of the data. The extraction of reaction cross-sections for individual atomic reagent states from the change of the product signal intensity upon optical-pumping depletion requires knowledge of the relative atomic populations for the various optical pumping conditions.These populations for Ba D2 and Dj were previously derived from laser-induced fluorescence measurements.6 The population of the ID2 state was related to those of 3DJ by utilizing the IF! + 3D3 intercombination line, since the upper state of this transition decays mainly to 'D2 rather than to the 'DJ states. The relative ID2 and 'DJ populations are given in table I of ref. (6); the lines employed in the present study are numbers 8-14 inclusive in that table. With no optical pumping, the ID2 population is 16% of the total metastable atoms present. Results The reactions of Ba(3D, ID) with HX and CH3X reactants, with X = C1 and Br, were chosen for study here, in part because these reactions yield little or no chemilumines- cence, which would interfere with laser fluorescence detection of ground-state products.Both hydrogen and methyl halide reactants have been investigated in order to see whether their slightly different reaction dynamics affect the dependence of reactivity on incident spin-orbit state. The energetics of the reactions studied are displayed in table 1. We have employed values obtained from a mass-spectrometric thermochemical study" for the barium halide dissociation energies: D:( BaCl) = 4.48 f 0.09 eV and D:( BaBr) = 3.7 1 f 0.10 eV. The latter value is essentially identical to that determined from a chemiluminescence study.16 It can be seen from table 1 that the Ba('S) reactions with the hydrogen halides are approximately thermoneutral, while the methyl halide reactions and all those involving metastable Ba( '0, D ) are substantially exothermic.Laser Fluorescence Excitation Spectra Fig. 1 compares BaBr laser fluorescence spectra of the C 'I13,,-X 'Z+ Av = 0 and - 1 sequences for the HBr reaction with ground-state Ba( 'S) reactant (source discharge130 Ground-state Products from Reactions of Ba( 3D) c2n3,,- x2c+ AV-0 AV=-1 10 0 R21 --%-r++ 10 0 R2+Q21 4 10 0 r I 1 I I I 1 I 1 I I I 1 I 520 524 528 51 6 laser wavelength/nm Fig. 1. Laser fluorescence spectrum of the BaBr C ’II312-X *Z+ Av = 0 and -1 sequences obtained for the ( a ) Ba(’S) + HBr and ( b ) Ba” = HBr reactions. The RZ1 and R2 + QZl are separately denoted. Lines due to excitation of atomic Ba* from the discharge source are indicated. off) and with metastable Ba(’D, 30) atoms present (source discharge on).The former is essentially identical (but with somewhat better spectral resolution) to spectra previously reported both from thermal beam-static gas and crossed beam configurations.20*21 The R2+Q2, and RZ, band heads are separately discernible in the spectra, as previously observed by Munakata et aL2’ in excitation spectra of BaBr product from the Ba + CH,Br reaction. For the Ba(’S)+HBr reaction, BaBr vibrational levels up to v = 19 are detectable in the excitation spectrum. The product vibrational distribution for this reaction has been derived Assuming the thermochemistry given pre- viously is correct, the high-v tail of the vibrational distribution must arise from collisions in the high translational energy tail.With the source discharge on, the BaBr fluorescence excitation spectrum becomes considerably more complex [see fig. 1( b ) ] , and BaBr vibrational bands of considerably higher Y” are discernible (0’’ a 30), consistent with the higher Ba( ’0, ’ 0) + HBr reaction exothermicity (om,, = 53). As has been noted previously by Schultz and Siegelz’ in aM. L. Campbell and P. J. Dagdigian I 131 11. il 1111 h V"=25 I I I I I I I 516 520 524 528 laser wavelength/nm Fig. 2. Laser fluorescence excitation spectrum for the Ba* + HBr reaction. The contribution due to the residual Ba('S) in the Ba* beam has been subtracted from the spectrum in fig. l ( b ) as described in the text. spectroscopic study of BaBr product from the homologous reaction series Ba( ' S ) + CH,Br,-,, the high-u" bands of a given Au sequence overlap the next sequence Av + 1.In our spectrum we observe a filling in of the fluorescence signal between the Av = 0 and Au = -1 sequences. One puzzling aspect of our Ba* + HBr spectrum is the presence of additional unassignable, but reproducible, features, particularly among the low-v" bands of both the Au = 0 and -1 sequences. It is tempting to ascribe these extra features to high-v" bands of another sequence. For instance, the v"= 50 band of the Au = -1 sequence falls at approximately the same wavelength as v" = 19 of the Au = 0 sequence." However, we have not attempted to make further assignments by extensive studies of other Ba + RBr reactions or by spectral simulations. Since the metastable conversion efficiency of our source is large, but not 100'/0,'~ the spectrum taken with the source discharge on includes some contribution from the Ba('S) + HBr reaction.To estimate this contribution, we monitored the 'S density by laser fluorescence excitation of the Ba 'Po + ' S resonance transition at 553.56 nm. We found that the fluorescence intensity on this line is reduced to 15% of its original value when the source discharge is turned on. This estimated conversion efficiency is similar to that measured in a previously reported characterization of our Ba* source." Accord- ingly, we have subtracted 15% of the discharge-off spectra from those taken with the source discharge on. The resulting corrected spectrum for Ba*+HBr is displayed in fig. 2. Because of the uncertainties in our BaBr spectra noted earlier, we have not attempted to extract product internal-energy distributions.The band heads of the Av = -1 sequence in fig. 2 are most prominent around u"= 28; however, this appears to be due to a coalescence of two separate series of band heads. In spite of the difficulties in analysing these spectra in detail, we may nevertheless surmise that a broad range of BaBr vibrational levels are populated by the Ba(3D, ' D ) + HBr reaction up to and beyond v = 30. Fig. 3 presents BaBr laser fluorescence spectra for the CH,Br reaction both without and with the source discharge on. The spectrum for the Ba('S) reaction is essentially identical to that previously reported by Munakata et ~ 1 . ~ ~ in a crossed-beam study at a132 Ground-state Products from Reactions of Ba( 3D) c2n,,2L X2E+ AV=O AV=-1 R21 20 10 0 20 10 0 - 20 10 0 R2+Q2, ---A+++ 20 10 0 I I I I I I I 516 520 524 528 laser wavelength/ nm Fig.3. Laser fluorescence spectrum of the BaBr C 2r13,2-X 'E+ Av = 0 and -1 sequences obtained for the Ba('S)+CH,Br ( a ) and Ba*+CH3Br ( b ) reactions. R2, and R2+Qz, band heads are separately denoted. Lines due to excitation of atomic Ba* from the discharge source are indicated. ( b ) The contribution due to residual Ba('S) in the Ba" beam has been subtracted, as described in the text. comparable average collision energy. In accord with the larger reaction exothermicity, the BaBr product contains somewhat higher vibrational excitation than for the Ba( ' S ) + HBr reaction. However, in contrast to the latter, the highest vibrational level observed ( u = 25) has considerably lower internal energy than the total available energy Eavl( ' S ) for the CH3Br reaction.The excitation spectrum for the CH3Br reaction, shown in fig. 3( b ) , is considerably more complex and indicates substantial product vibrational excita- tion, with a broad vibrational-state distribution. Again, as with the corresponding HBr reaction, we have not attempted to extract a quantitative product-state distribution from the fluorescence excitation spectrum. Considerable BaCl product vibrational excitation is also evident for the Ba* + HC1 reaction. Fig. 4 shows laser fluorescence spectra for the Ba( IS) and Ba" + HC1 reactions.Av=o 0 n M. L. Campbell and P. J. Dagdigian c 2n ,,2- x2z+ AV=-1 n 1 I I I I I I 133 I I I I I 524 528 532 laser wavelength/nm Fig.4. Laser fluorescence spectrum of the BaCl C 211,,2-X 'Z'+ Av = 0 and -1 sequences obtained for the Ba('S)+HCl ( a ) and Ba*+HCl ( b ) reactions. Lines due to excitation of atomic Ba* from the discharge source are indicated. ( b ) The contribution due to residual Ba('S) in the Ba* beam has been subtracted, as described in the text. The former reaction is known to yield relatively little BaCl vibrational mainly because of the small amount of energy available to the products (see table 1). Only a few bands of low v are visible in the spectrum in fig. 4 ( a ) . In contrast, there is considerable fluorescence intensity between the sequences in fig. 4 ( 6 ) for the Ba* reaction, indicative of considerable product vibrational excitation.It also appears that the vibrational state distribution is very broad for this reaction, as was observed for the Ba*+HBr reaction, although we have again not attempted to extract a quantitative product-state distribution from the spectra.134 Ground-state Products from Reactions of Ba( 3D) 50 40 I I I I 1 I I I 524 528 532 laser wavelength/nm Fig. 5. Laser fluorescence spectrum of the BaCl C 2111,2-X 2Xc+ Av = -1 sequence obtained for the Ba( IS) + CC14 ( a ) and Ba* + CH3Cl ( b ) reactions. Lines due to excitation of atomic Ba* from the discharge source are indicated. Fig. 5 shows a BaCl excitation spectrum over the same wavelength range for the Ba" + CH3Cl reaction. In this case, the corresponding ground state Ba( 'S) reaction does not yield any detectable BaCl fluorescence signal, in agreement with a previous study.24 Hence, the spectrum in fig.5(b) contains no contribution from Ba('S)+CH,Cl. For comparison, a laser fluorescence spectrum for the Ba( 'S) + CC14 reaction is presented in fig. 5(a). This spectrum is essentially identical (but with higher spectral resolution) to that previously reported by Schmidt et aZ.*' in an extensive study of this reaction. Their derived BaCl product vibrational-state distribution was very narrow, with a most probable o of 43 and significant population only for levels rtl5 units about this peak.M. L. Campbell and P. J. Dagdigian AwO - 5 0 Av=+l C2rI,,,- X 2 F I I I I Ba c 135 I I 1 1 51 2 51 8 laser wavelength/nm Fig.6. Laser fluorescence spectrum of the BaCl C 'n3,*-X *C+ Av = 0 and C 2111,2-X 'X+ Av = + 1 sequences obtained for the Ba('S) + HCl ( a ) and Ba* + CH3CI ( b ) reactions. The R, and Q, + RI2 band heads for low v are overlapped in the latter sequence. Lines due to excitation of atomic Ba" from the discharge source are indicated. Comparison of our CC14 spectrum in fig. 5 ( a ) with those for Ba" + HCI and CHICl in fig. 4( 6 ) and 5( b ) , respectively, suggest that the BaCl vibrational-state distribution for both of these reactions are very broad and extend out beyond v = 45. Finally, in fig. 6( 6 ) we present a BaCl fluorescence excitation spectrum of the Ba" + CH3CI reaction for the C 2113/2-X 'C+ Av = 0 and C 211,/2-X 'Z+ Av = + 1 sequences. This spectrum is compared to that for the Ba('S)+HCl reaction, which is given in fig.6 ( a ) ; the latter has been presented in the literature previously." Bands of the C zII,,2-X 'Z+ Av = + 1 sequence for low v severely overlapped each other, as discussed previously by Siege1136 Ground-state Products from Reactions of Ba( ,D) and Schultz;" however, the high-u bands occur to the blue. We thus see further evidence for high BaCl vibrational excitation in the Ba*+CH,Cl reaction by the presence of significant fluorescence intensity in fig. 6(b) to the blue of the low-u R, heads. Dependence on Reactant Ba 3D Spin-Orbit State The dependence of the reaction cross-sections for formation of various product BaX vibrational states from specific Ba D spin-orbit levels was determined by recording the change of the fluorescence signal at appropriate probe laser wavelengths as the incident Ba3DJ, 'D2 state distribution was altered by C.W.dye laser optical pumping. Two different derivations of the extraction of spin-orbit-dependent cross-sections from these data have been given in previous publications.27336 In this study we employed the same analysis as that used to determine the spin-orbit dependence for chemiluminescence channels in a number of Ba* reactions.6 We give an abbreviated version of the relevant equations here. With the C.W. optical pumping dye laser off, the laser fluorescence signal for detection of a given BaX product state can be written as where n.6' and nyff are the relative number densities of the Ba ' D and ,DJ states, respectively, at the collision zone. We have normalized these atomic populations so that their sum equals unity. The proportionality constant c includes such factors as the target gas and total Ba" number density, the probe laser power and detection sensitivity.The quantities aJ and aD represent the cross-sections for production of the detected BaX states from a specific reactant Ba 'DJ spin-orbit state and the ID2 state, respectively. Eqn (1) assumes that any possible contribution to the detected product from reaction with residual Ba(*S) in the beam has been subtracted from the observed signal. When the C.W. dye laser is tuned to a particular Ba* optical-pumping transition (denoted as line i), the product signal changes by a factor Ri. The observed signal in this case is given by Siax = RiSiFx or where nJ,i and nD,i are the appropriate relative Ba" number densities when line i is pumped.After dividing eqn (1) and (3) by cu3 and carrying out some algebra, we obtain the following final equations: ( Ri n 7" - n , ,i) ( a , / a,) + ( Ri n zff - n 2,i) ( a,/ a,) -I- ( Ri n "6' - n D,i) ( aD/ a3) = n3 ,i - Ri n ". ( 4) Eqn (4) is a set of equations whose number equals the number of optical pumping transitions, with the unknowns being the cross-section ratios ( a,/ a3), ( a'/ a3) and ( uD/ u 3 ) . In our earlier derivation' we referenced the spin-orbit-dependent cross-sections to the average over the incident, unpumped, spin-orbit state distribution. The present normalization to the cross-section for a specific reactant state (in this case the J = 3 spin-orbit level) is preferable since the reference cross-section is then not dependent upon experimental parameters, i.e.the spin-orbit state distribution. Since the number of Ba* lines optically pumped is greater than the number of unknowns, the solution of eqn (4) requires a linear regression procedure. However, theM. L. Campbell and P. J. Dagdigian 137 Table 2. Observed changes Ri in BaBr product fluorescence intensities upon Ba* optical pumping Ba" + HBr Ba" + CH,Br Pump transition 0" = 20 v" = 25 v" = 28 vtt = 30 vn = 25 v" = 30 3P:t3D, 0.97*0.02 0.93f0.02 0.91f0.02 0.86f0.02 0.93*0.02 0.93*0.02 'P: t ,D, 0.94 f 0.02 0.92 * 0.02 0.89 f 0.02 0.82 f 0.03 0.91 f 0.02 0.90 f 0.02 ,Po c 3 D 2 1.02f0.03 1.06f0.03 1.12f0.03 1.16k0.03 1.08f0.02 1.08f0.02 314 c3 D2 0.93 * 0.02 0.93 * 0.02 0.94 f 0.02 0.90 f 0.02 0.93 f 0.02 0.91 f 0.02 'P: t ,D3 1.08 * 0.02 1.05 f 0.02 1.08 f 0.02 1.11 f 0.02 1.07 f 0.03 1.09 f 0.03 'P: c ID2 0.89 f 0.02 0.91 f 0.02 0.91 f 0.02 0.95 f 0.02 0.92 f 0.02 0.94 f 0.02 F; c D3 0.95 f 0.02 0.93 f 0.02 0.94 f 0.02 0.88 f 0.02 0.89 * 0.02 0.89 f 0.02 Table 3.Observed changes Ri in BaCl product fluorescence intensities upon Ba" optical pumping 'P: c 3 D , 0.90st0.02 0.85f0.02 0.80f0.02 0.93f0.03 0.92f0.02 0.94f0.02 ' P ; t ,D, 0.86 f 0.02 0.81 f 0.02 0.74f 0.02 0.92 f 0.03 0.88 * 0.02 0.90 f 0.03 'P: t ,D2 1.10 f 0.03 1.18 f 0.03 1.26 f 0.03 1.10 f 0.03 1.08 * 0.03 1.07 f 0.03 ' P ; t ,D2 0.90* 0.02 0.87 f 0.02 0.88 f 0.02 0.91 f 0.03 0.90 f 0.02 0.90 f 0.03 3 P : c 3 D 3 1.08f0.02 1.15f0.03 1.15f0.03 1.13f0.03 l.llf0.02 1.11 f0.03 P: e D2 0.97 f 0.02 0.97 st 0.02 0.98 f 0.02 0.94 f 0.03 0.92 f 0.02 0.92 * 0.03 F , t D3 0.87 f 0.02 0.87 f 0.02 0.86 f 0.02 0.90 f 0.03 0.91 f 0.02 0.86 f 0.03 1 0 a Unassigned feature in the C 2111,2-X 'X+ Av = +1 sequence. present problem is more complicated than the usual least-squares fit,26 since there are uncertainties in both the 'dependent variable' ( y = n3,i - Rin;") and in the 'independent variables' x, = RinXff - n,,i ( a ! = 1,2, D ) .This type of fitting problem has been considered a number of times in the As discussed in detail previously,6 we have employed a simple iterative procedure given by Irvin and Quickenden3' wherein each pump transition is given a weighting of ( u ; + C , a t a ; ) - ' , where a, is the cross-section ratio (u,/u3) to be fitted.Initially, the a, in the weighting function are set to zero and successive iterations of eqn (4) use the a, values determined in the previous iteration until convergence is achieved (typically 2 or 3 iterations). The dependence of the reaction cross-section on the incident Ba(3D) spin-orbit state was investigated for a number of product BaX vibrational levels in the HBr, CH3Br, HCl and CH3Cl reactions. In most cases, the reagent gas pressure was maintained at <0.5 mTorr" in order to avoid collisional equilibration of the spin-orbit levels by intramultiplet mixing. In several of the reactions spin-orbit effects were also measured at higher pressures (up to 1.5 mTorr); no systematic change in the intensity ratios Ri were observed with pressure.Tables 2 and 3 present the observed ratios Ri [as defined by eqn (2)] of product fluorescence signals with the C.W. dye laser on and off for the various Ba" pumping transitions. The particular spectral features used to detect the different BaX vibrational levels are denoted by arrows in fig. 2-6. For the BaBr product from the Ba" + HBr and CH3Br reactions, bands in the C 211s,,z-X 2Ct Au = -1 sequence were employed for *1 Torr = 101 325/760 Pa.138 Ground-state Products from Reactions of Ba( 3D) Table 4. Observed changes R, in BaX product fluorescence intensities for low vibrational levels upon Ba" optical pumping Ba" + HBr transition VII = 5 utt= 10 V f t = 10 Ba* + HCI Pump 3 0 3 0 P , t 3 D , 1.00*0.04 0.97f0.04 1.06f0.07 P 2 t 3 D , 1.02*0.04 0.97f0.04 1.06*0.07 ' P : e 3D2 1.03 f 0.04 1.01 f 0.04 0.99 f 0.07 3 P ; e 3 D 2 1.00*0.04 1.01 f0.04 1.02k0.07 ' P ; c D3 1 .OO f 0.04 0.99 f 0.04 1.04 f 0.07 ' P : c ID2 1.06f0.04 1.08 k0.04 1.18 f 0.08 ' F ; e 3 D 3 1.14f0.05 1.02Zt0.04 1.18f0.08 " Contribution to the fluorescence signal from the Ba('S)+ HCI reaction subtracted out, as described in the text.Table 5. Relative reaction cross-sections" for formation of specific BaX product vibrational levels as a function of the reagent Ba atomic state reaction BaX state O ( ~ D ~ ) / ~ ( ~ D ~ ) ~ r ( ~ D ~ ) l o ( ' D ~ ) ~ ( ' D ) / u ( ~ D ~ ) Ba+ HBr utl = 20 u" = 25 utt = 28 u" = 30 Ba+ CH3Br u" = 25 u" = 30 Ba + HCl uJr = 30 utt = 35 u" = 40 u" = 40 VII = 45 Avi/* = + 1 Ba + CH3Cl 1.52 f 0.21 1.70 f 0.22 2.08 f 0.26 2.81 f0.35 1.83 f 0.23 1.99 f 0.26 2.26 f 0.28 3.92 f 0.44 4.13 f 0.56 2.13 f0.29 2.16 f 0.28 1.98 f 0.26 1.33k0.14 1.26 f 0.13 1.32f0.15 1.56 f 0.18 1.32 f0.14 1.45f0.15 1.48 f0.16 1.83 f 0.23 1.86 i 0.26 1.55 f 0.17 1.53 f0.17 1.50 f 0.16 0.84 f 0.14 0.73 f 0.13 0.77 f 0.14 0.46 f 0.14 0.60 f 0.13 0.55 f0.13 0.42 f 0.12 0.35 f 0.1 5 0.24 f 0.17 0.61 f0.14 0.64 f 0.13 0.48 f 0.13 Estimated uncertainties are la detection of vibrational levels v" ranging from 20 to 30.The BaCl C 2111,2-X 'X+ Av = -1 sequence was used for detection of levels v" from 30 to 45 in the Ba" + HC1 and CH3Cl reactions. For the latter, an unassigned feature in the BaCl C 211-X 'X+ Au = +1 sequence was also studied. It can be seen in tables 2 and 3 that the product fluorescence signals change significantly upon alteration of the Ba( 'DJ ) spin-orbit populations.The effect of optical pumping was also investigated for several low BaX vibrational levels in the Ba" + HBr and HC1 reactions. In these cases, it was necessary to correct for the Ba('S) contribution to the reaction product signals. These data, which were corrected in the same way that the Ba( IS) contribution was subtracted from the excitation spectra, are given in table 4. We find for these levels that changing the Ba(3DJ) spin-orbit population by optical pumping has a small effect on the product densities. The data in tables 2 and 3 were used with eqn (4) to derive spin-orbit-dependent cross-sections for formation of the various BaX product vibrational levels.The atomic Ba state populations nyff, nJ,j etc. were measured by laser fluorescence detection pre- viously in our study of spin-orbit effects in the chemiluminescence channels of otherM. L. Campbell and P. J. Dagdigian 139 Ba" reactions. These relative populations, which are listed in table 1 of ref. ( 6 ) , were employed in the present analysis. The derived spin-orbit-dependent cross-section ratios are presented in table 5 . It can be seen from table 5 that, at least for formation of the higher BaX vibrational levels, there is a significant dependence of reactivity on incident Ba('D,) spin-orbit level, with an ordering J = 1 > J = 2 > J = 3 and as much as a factor of 4 difference in the J = 1 vs. J = 3 cross-sections. The reaction cross-sections for the ' D2 level are also smaller than for any of the 'DJ levels.It should also be noted that the spin-orbit dependence varies with product vibrational level. This is evident for the Ba" + HBr and HCl reactions over the range of u" = 20 to 40. We have not derived relative spin-orbit- dependent cross-sections from the data in table 4 for the low vibrational levels because of the essentially negligible change of the fluorescence upon optical pumping for these levels. It is nevertheless clear that the spin-orbit dependence is at best very small and much less than for the higher product levels. For the CH'Br and CH3Cl reactions, the variation of the spin-orbit effect us. product vibrational level is within the estimated experimental uncertainties in the relative cross-sections. Discussion The present results on the relative cross-sections for formation of ground-state BaX product from the various atomic reactant spin-orbit levels for the Ba('D) + HX, CH3X (X=Cl, Br) reaction contrast sharply with our previous observations' on the chemiluminescence channels of a number of other Ba('D) reactions.For formation of ground-state product, the lowest-energy J = 1 spin-orbit level possesses the largest cross-sections, with successively smaller values for J = 2 and J = 3; however, an exactly opposite ordering of reactivity was found for the chemiluminescence channels.' Exactly analogous spin-orbit effects were also observed for Ca(3P0) and Sr('PPO) and have been interpreted with the aid of a pseudo-quenching model calculation of Alexander.' Because of the congested nature of these alkaline-earth monohalide chemilumines- cence spectra and our relatively low spectral resolution, we were able to study spin-orbit effects for production of diff erent excited product electronic states, but without resolution of individual vibrational levels.Our previous work on the ground-state product channel of several Ca(3P0) and Sr('Po) reactions was confined to a few wavelengths of the fluorescence excitation laser, without identification of the specific vibrational level detected. In the present experiment, we have been able to determine the spin-orbit effect for production of a wide range of BaX product vibrational levels. We have found for the Ba(' D) + HX reactions that the spin-orbit dependence varies from essentially no detectable difference on reactivity of the different spin-orbit levels for formation of low product vibrational levels to a factor of 3 to 4 variation in 3D, us.'D3 cross-sections for the highest vibrational levels studied ( u = 30 and 40 for the HCl and HBr reactions, respectively). The analogous reactions of ground-state Ba( ' S ) with hydrogen halides have been extensively studied previously, both experimentally*0~~*~3' and the~retically.'~ These reactions exemplify a kinematically constrained class involving a reactive encounter of a heavy atom (H) with a heavy-light molecule (H'L) to produce a heavy-heavy diatomic product (HH') and a light atom ( L).37338 One consequence of the conservation of angular momentum I is that the reagent orbital angular momentum is channelled into rotational angular momentum j ' of the diatomic product.Noda et ~ 1 . ' ~ have taken advantage of this constraint on the Ba+HI reaction to gain information on the impact parameter dependence of reactivity from measurement of the BaI product rotational state distribu- tion. While the opacity function could not be definitively determined because of the140 Ground-state Products from Reactions of Ba( 3D) width of the initial relative velocity distribution, they were able nonetheless to conclude that the specific opacity for BaI( = 8) was strongly peaked around a limited range of impact parameters. Siege1 and S~hultz’~ have carried out classical trajectory calculations on several model potential-energy surfaces for the Ba+HCl and HBr reactions.They do indeed find a very strong correlation between I and j ’ , as expected from kinematic considerations. Moreover, they also observe a correlation of the product vibrational energy with incident impact parameter. For LEPS surfaces, but not for hyperbolic map function (HMF) surfaces, the product recoil energy was found to be independent of product vibrational energy, and hence a constant for a given reaction. Noda and Zare3’ have invoked the assumption of constant product recoil energy (CPR) to develop a simple model for the kinematically constrained H + H’L reactions. This so-called CPR model predicts a bell-shaped product vibrational state distribution, wherein the specific opacity functions for low and high vibrational levels are sharply peaked at large and smail impact parameters, respectively.They show that this model can be used to interpret the product vibrational state distributions for the Ba+HF35 and HI34 reactions, as well as the less-constrained Ba + CH3Br22 and CF314’ reactions. In view of a similar kinematic constraint on the excited state Ba(3D) + HCl and HBr reactions, we may thus associate small and large incident impact parameters with the formation of products of high and low vibrational excitation, respectively. From our experimental results, we hence conclude that differences in the reactivity of the 3D, incident spin-orbit levels are present only for small and not large impact parameter collisons. This would suggest that in large impact parameter collisions the identity of the incident spin-prbit state is lost‘ before the reaction occurs, i.e.before the ionic- covalent crossing point is reached, whereas such mixing in the entrance channel does not occur in near head-on encounters of small impact parameter. In other words, large incident orbital angular momentum appears to induce non-adiabatic transitions in the entrance channel. We can put this explanation on a quantitative basis with the help of the pseudo- quenching model of Alexander.’ Spin-orbit effects in chemical reactions, as well as the simpler non-reactive intramultiplet mixing process, is most conveniently described in a Hund’s case ( e ) basis,41 wherein the good quantum numbers include 1, L, S, J and J (nuclear orbital, electronic orbital, electronic spin, total electronic and total overall angular momenta, respectively). While the Hamiltonian is diagonal in J and the elf symmetry: it may be further diagonalized for each value of the interparticle separation R to yield fully adiabatic potential curves.In the potential models employed by Alexander’ for Ca(3P0) + C12, adiabatic curves correlating with the J = 0 and 1 asymptotic P spin-orbit levels, but not for J = 2, undergo an ionic-to-covalent transition [see fig. 1 and 2 of ref. ( 9 ) ] . Thus, reaction from J = 2 requires, within this model, a non-adiabatic transition. As discussed before in connection with a semiclassical treatment of collisional intramultiplet m i x i r ~ g , ~ ~ . ~ ~ the strength of such non-adiabatic transitions are related to matrix elements of operators d/dR and d2/dR2, which are components of the kinetic- energy operator, between the non-adiabatic wavefunctions.The former first-derivative operator is usually the dominant term.43 If we express the adiabatic eigenvectors in terms of the case ( e ) functions, i.e. 3 0 InJM) = c An,Jl(R)IJ1JM) ( 5 ) J. 1 then the relevant non-adiabatic matrix elements can be expressed asM. L. Campbell and 0.1 I I I I I I 1 14 16 18 P. J. Dagdigian 141 14 16 18 Rlbohr Fig. 7. Dependence on interparticle separation of the non-adiabatic coupling matrix element G;,,, ( R ) for transitions between levels adiabatically correlating asymptotically to reagent atomic spin-orbit levels in the pseudoquenching model of Alexander, described in ref. (9) (potential 11).Results for two values of the total angular momentum J [ ( a ) 5 , ( b ) 2501 are given for the f-labelled symmetry levels. This matrix can be obtained by numerical differentiation of the matrix of eigenvectors. [The label M in eqn ( 5 ) denotes the space-fixed projection of 5.3 We present in fig. 7 values of G,,,”(R) for two values of J for the f-labelled parity levels between eigenvectors which correlate asymptotically to the Ca( 3P0) spin-orbit levels. These were calculated for one of the potential models considered by Alexander’ (his model 11). With this model, the ionic-covalent crossing occurs near 13 bohr. It should be noted there are 3 f-labelled case ( e ) eigenvectors for J = 2[ I = J, J * 21, while there is only one each for J=O and l[Z=J]. It can be seen that for J = 5, which is representative of a small impact parameter collision, G,,,J(R) is quite small for most pairs ( n ’ , n ) levels and is appreciable outside the region where charge transfer occurs only between two pairs of levels.By contrast, Gnf,”( R ) attains appreciable size between most covalent adiabatic potential curves for larger J, although the absolute magnitude of the largest non-adiabatic matrix element is somewhat reduced. Such a dependence of the non-adiabatic coupling on the total angular momentum, and hence impact parameter, has already been documented for the J = 0 to 1 intramultiplet transition in Ca(’P”) non-reactive collisions; in this case, mixing can occur only though the coupling of electronic and nuclear angular rn~rnenta.~’ The non-adiabatic matrix elements in fig.7 attain magnitudes comparable to those previously calculated for the Ca(3P0)-He system, in which significant collisional intramultiplet mixing This pseudo-quenching model thus strongly suggests the importance of the nuclear orbital angular momentum, and hence impact parameter, in determining the magnitude of the spin-orbit effect on reactivity. Of course, Alexander’s model’ is inadequate to describe Ba(.lD) + HX reactions accurately both because of the model’s atom-atom character and differences baetween the CaCl, model potentials employed therein and the correct BaHX potentials. With regard to the latter, even in a quasidiatomic approxi- mation, three covalent potential curves (Z, lI and A) will arise for an atom in a D state [e.g.Ba(’D)], as opposed to two for a P-state atom [e.g. Ca(’PO)]. Nevertheless, our142 Ground-state Products from Reactions of Ra( 3D) qualitative conclusions about the role of impact parameter should still be valid for real systems since the number of covalent potential-energy surfaces will almost always be less than the number of ionic surfaces. [See table V of ref. (6) for an enumeration of potential-energy surfaces for Ba reactions.] It would be very interesting to test these ideas quantitatively by further model calculations using realistic potentials. From an experimental point of view, the dependence of the spin-orbit effect upon chemical reactivity as a function of product vibrational state is expected to be manifest in other reactions and or in other product channels, such as chemiluminescence.We are indebted to Millard Alexander for conversations about the theoretical interpreta- tion of our results. Support for this work was provided by the National Science Foundation. References 1 P. J. Dagdigian and M. L. Campbell, Chem. Rev., 1987, 87, 1. 2 H-J. Yuh and P. J. Dagdigian, J. Chem. Phys., 1983, 79, 2086; 1984, 81, 2375. 2 N. Furio, M. L. Campbell and P. J. Dagdigian, J. Chem. Phys., 1986, 84, 4332. 4 M. L. Campbell, N. F. Furio and P. J. Dagdigian, Laser Chem., 1986, 6, 391. 5 M. L. Campbell and P. J. Dagdigian, J. Am. Chem. SOC., 1986, 108, 4701. 6 M. L. Campbell and P. J. Dagdigian, J. Chem. Phys., 1986, 85, 4453. 7 H.-J. Yuh and P. J. Dagdigian, Phys. Rev. A , 1983, 28, 63. 8 P. J. 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