摘要:

Reactive Scattering of Alkali Dimers Alkali Atom-Dimer Exchange Reactions BY J. C. WHITEHEAD AND R. GRICE Dept. of Theoretical Chemistry, Cambridge University, Cambridge, CB2, 1 EW Receievd 28th December, 1972 Reactive scattering measurements for the alkali atom-dimer exchange reactions M’ + M2-+MM’+ M are reported, where M’ = Na, K and M2 = Csz, Rbz, K2. The total reaction cross sections are large >” 100 AZ, indicating that a major fraction of collisions, captured by the long range van der Waals attraction, lead to reaction. Very little (-10 %) of the available energy is disposed into product translation, consequently the MM’ dimer products are highly vibrationally excited (-75 % of the MM’ bond energy). Only an indication of the centre-of-mass differential reaction cross sections can be deduced from the data.Calculations of the reaction potential energy surfaces show a broad shallow basin ar: small internuclear distances, and suggest that the reaction dynamics must be direct or at most involve a short-lived complex. A number of molecular beam studies of the reactions of alkali dimers have been undertaken in the last few years. Reactive scattering measurements of alkali dimers with hydrogen atoms have been interpreted in terms of an oriented spectator model. Chemiluminescence from alkali dimers with halogen atoms and molecules has been observed. Reactive scattering measurements of both alkali halide 3* and alkali atom 5 * products from four centre alkali dimer reactions with halogen molecules have been reported and the reaction dynamics examined.The reactive scattering of alkali halide products from alkali dimers with polyhalides ’ and alkyl halides * have also recently been observed. However, all these reactions are charac- terised by the formation of alkali halide or hydride products with their ionic electronic structures. Thus the reactions involve considerable charge transfer by an electron jump mechanism and substantial reaction exoergicities. The exchange reactions of alkali dimers with alkali atoms offer an opportunity to study reaction dynamics where there is much less change in electronic structure and low reaction exoergicity. M’ + M2 + MM’ + M. Indeed, the potential energy surface for three alkali atoms should present a relatively simple three-electron problem for ab initio calculations, formally similar to H + H,.The diatomics in molecules calculation of Companion l o for Li3 shows the trimer to be stable by -9 kcal mol-I with respect to Li + Liz. Similar calculations by the authors l 1 for all the Na, Li systems also show these trimers to be stable. The pseudopotential calculations of Byers Brown l 2 predict Na,, K3 to be slightly unstable. However, experimental observations of alkali trimers in molecular beams from alkali nozzle expansions definitely show that they are stable. The alkali atom dimer exchange reactions may be important in determining energy transfer and condensa- tion in alkali nozzle beam expansion^.'^. l 5 3 20J . C. WHITEHEAD AND R. GRICE 321 EXPERIMENTAL METHOD The alkali dimer machine l5 has been described previously. Briefly an alkali nozzle beam source gives a mixed beam of atoms and dimers. An inhomogeneous magnetic field deflects the alkali atoms and the undeflected alkali dimers pass into the scattering chamber.The residual alkali atom impurity in the dimer beam has previously l5 been estimated < 10 mol percent ; this is probably a generous upper limit. For the present experiments l6 the apparatus has been augmented by a quadrupole mass spectrometer with a surface ionization ion source employing a Pt/W filament at -1500K. The alkali atom cross beam is generated in a double chamber oven equipped with crinkle foil slits. The oven head is run at least 100 K hotter than the lower chamber, in order to reduce l8 the alkali dimer impurity to fess than -0.2 % of the alkali atom cross beam.Most experiments were run at two values of the head temperature ; the data were always identical to within experi- mental error. The apparatus is shown schematically in fig. 1. The detector scans in the - L.N2 - H20 5iG+ FIG. 1.-Schematic diagram of the apparatus. The quadrupole mass filter and its ion optics stand vertically above ionization filament : A, alkali dimer oven ; B, alkali atom oven; D, surface ionization ion source ; F, beam flag ; M, magnet ; S, collimating slits ; T, tantalum radiation shield ; LN2, liquid nitrogen cooled cold shield ; H20 water cooled cold shield. plane of the reactant beams over the angular range 0 = - 30' to 120", where the laboratory scattering angle 0 is defined with the broad alkali atom beam at 0 = 0".During a typical experiment the scattering chamber pressure is - 5 x lo-' Tom. The quadrupole mass spectrometer resolves ions of different alkalis with cross talk 2 compared with unity for K, Rb, Cs ; so that the total cross talk for Na is "< 5 x However, since the Pt/W filament will ionise both M atoms and M2 dimers to M+ ions, the detector does not distinguish reactive from elastic scattering directly. As described in the next section, this distinction is achieved by kinematic discrimination. In addition, the ionisation efficiency l 9 for Na on Pt/W is - 5 x RESULTS AND KINEMATIC ANALYSIS The laboratory angular distributions of M+ signal from Na+M2, M = Cs, Rb, K and K+M2, M = Rb, are shown in fig. 2 and the appropriate Newton diagrams in fig.3. As the Newton diagrams indicate, the elastic scattering of M2 55-L322 REACTIVE SCATTERING OF ALKALI DIMERS dimers is constrained close to the dimer beam in these systems, since the M2 mass is much greater than that of the cross beam alkali atom. The laboratory angular limits of M2 elastic scattering are indicated by arrows in fig. 2. It is immediately apparent that there is considerable intensity measured beyond these limits. As the V 0 M2 1 . I I I I I I 1 I I"1 30' 6 0' 90' 120' laboratory scattering angle, Q FIG. 2.-Laboratory angular distribution of M+ signal for Na+ M2, M = Cs, Rb, K and K+ M2, M = Rb. Arrows denote the kinematically- aliowed limits of Mz elastic scattering. Successive curves are shifted down by one decade. H2 + Na + Cs, "Na "K FIG.3.-Newton diagrams for the most probable velocities of the parent beams for Na+M2, M = Cs, Rb, K and K+M2, M = Rb. Inner circle denotes the spectrum of recoil velocity vectors accessible to elastically scattered M2 ; outer circle, spectrum accessible to reactively scattered MM'+M at the recoil velocity noted. Newton diagrams indicate, this intensity may be attributed to reactively scattered MNa and M products which are much less constrained in laboratory coordinates due to the even disposition of mass between the product molecules. In the Na + M2 systems the M+ signal could be measured in both angular directions about 0 = go", down to the limiting sensitivity of the quadrupole detector. In the Rb, + K system, where the quadrupole mass discrimination is not assisted by inefficient surface ionisa- tion of Na, cross talk at the Rbf peak from the intense K cross beam limits theJ .C. WHITEHEAD AND R. GRICE 323 measurement to @> 55". As a check on the mass spectrometer detector, angular distribution measurements for Na+K2 were also made using a simple detector of a Pt/W filament and ion collector, relying on the inefficient Na surface ionisation to distinguish Kf. Over their range of validity, these measurements confirm the mass spectrometer measurements and also provide K2 beam attenuation measurements ; thus permitting the calculation of relative intensities. The mass spectrometer measurements of fig. 2 are normalised to these relative intensities. L I I I I I I I I I I 3 0 6 0 90 I20 laboratory scattering angle, 0 FIG.4.--Laboratory angular distribution of Csf signal from Na+ Csz (open circles), with matching distributions calculated from stochastic analysis (solid line). We have attempted to determine the centre-of-mass differential reaction cross section I,, (O,u), by the stochastic method of Entemann,20 which, when transformed to laboratory coordinates will reproduce the reactive scattering lying beyond the limits of M2 elastic scattering (arrows in fig. 2). Since, in these systems, the masses of both reaction products (MM' and M) are rather similar, conservation of linear momentum in the centre-of-mass system requires that they recoil with approximately equal and opposite velocities. Thus, the Zcm(O,u) must be approximately symmetric about 0 = go", for Mf signal, independent of the lifetime 21* 22 of the reaction complex.The approximation is best for Na+Cs2 and poorest for Na+K2. The differential reaction cross section is assumed to be separable in the form L n ( & 4 = T(wJ(u) (2)324 REACTIVE SCATTERING OF ALKALI DIMERS where 8 is the centre-of-mass scattering angle and u the product velocity. In all cases the velocity function was taken to be a Gaussian flux distribution with the peak velocity u* an adjustable parameter. Three symmetric forms of angular function were investigated : (i) isotropic (ii) " complex " distribution 21 with equal forward (8 = 0") and backward (8 = 180") peaking U(u) = ( u / u ~ ~ ) ~ exp 3[ 1 - (u/u*)~] (3) T(8) = 1.0 for all 8 (4) I (5) T(8) = sin 8*/sin 8 for 8* < 8 < 180" - 8* where 8" is an adjustable parameter, (iii) sideways (0 = 90") peaked distribution where the peak half width at half height H* is an adjustable parameter. The fits to the laboratory scattering data are shown in fig.4-7 and the corresponding T(8) functions in fig. 8. Fig. 4-7 show that the data do not predict a unique distribution, since the most characteristic structure in each case lies in the region where reactive = 1.0 for 8<8* and 8> 180°-8* T(8) = exp {-In 2[(8 - 9 0 ° ) / ~ * ] 2 ) (6) 60' 9 0' 120' laboratory scattering angle, 0 FIG. 5. -Laboratory angular distribution of Rb+ signal from Na+ Rbz (open circles), with matching distributions calculated from stochastic analysis (solid line).J . C. WHITEHEAD AND R. GRICB 325 FIG. laboratory scattering angle, 0 distributions calculated from stochastic analysis (solid line).6.-Laboratory angular distribution of K+ signal from Na + K2 (open circles), with matching G. laboratory scattering angle, 0 distributions calculated from stochastic analysis (solid line). 7.-Laboratory angular distribution of Rb+ signal from K + Rb2 (open circles), with matching326 REACTIVE SCATTERING OF A L K A L I DIMERS 1.0 0.5 scattering is obscured by the intense M2 elastic scattering. However, the data do serve to indicate the range of possibilities. While the Na+Cs, data appear com- patible with a very broadly peaked '' complex " or even isotropic distribution, the preference moves to a more sharply peaked " complex " distribution for Na + K2, with Na + Rb2 somewhere between the two. - -- However, the peak us of the product velocity distribution is well defined by the data and almost independent of the choice of T(f3).The values of u* are given in table 1, as are the initial relative velocities, u. The product translational energies E' are compared, in table 1, with the reactant translational energies, E, and found to TABLE 1 .-TRANSLATIONAL VELOCITIES (m s-l) AND ENERGIES (kcal mol-l) system 1) U* E E' EVlb A DO Na+ Cs2 910 200 2.1 1.2 4 3 .O Na+Rb2 1090 250 2.9 1.1 4 2.3 Na+ K2 1350 400 3.9 1.2 5 2.5 K+ Rb2 930 200 3.3 0.7 3 0.4 be consistently lower (E'<E). This low product translational energy is still more striking when compared with the total energy available to products (E+ ADo + EMz N 10 kcal mol-'), where the reaction exoergicities ADo are given 23 in table 1, and the initial 1 4 9 l 5 M2 vibrational excitation (EMS 21 4+4 kcal mol-l).Total reaction cross sections Qt are calculated for each of the T(f3) functions, by normalisation with the small angle (0 = 10') M2 elastic scattering, using the TABLE 2.-TOTAL REACTION CROSS SECTIONS Qr (A2) sideways " compIex " " complex " " complex " system H* = 50' isotropic B* = SO" B* = 30" 8* = 10" average Qcap Na+Cs2 155 120 115 105 - 125 180 Na+ Rbz - 145 145 135 1 60 145 155 Na+ K2 - - - 75 55 65 140 K+ R b - 125 115 80 - 105 175J . C. WHITEHEAD AND R . GRICE 327 method l6, 2 o of Entemann. In this calculation, the polarisability of the alkali dimer M2 is taken 24 to be twice the polarisability 2 5 of the alkali atom M. The results recorded in table 2 show only fairly weak dependence on T(8) and the average Qr calculated in each case probably represents a good “ order of magni- tude ” estimate.As a check on our approximation of a symmetric Icm(O,u), we have performed l6 stochastic analysis fits to the Na+K2 data, taking account of the different KNa and K masses. This analysis confirmed the fits of fig. 6 but could give no indication of the lifetime of the reaction complex. The region where discrimination might be possible is, again, that where reactive scattering is obscured by intense M, elastic scattering. DISCUSSION REACTION PATH We may consider two paths for these reactions ; the exchange reaction M’+M,-+MM’+M (path 1) (7) M’+M,+M+M+M’ (path 2) (8) and collisional dissociation which is simply the limiting case of MM’ vibrational excitation in path 1.The surface ionisation detector would not distinguish between the products of these two reaction paths. The exchange reactions are exoergic for Na + M, and nominally thermoneutral for K+Rbz with AD,, values listed in table 1. Taking the initial vibrational excitation of Cs,, Rb2 (654 kcal rn01-l)‘~ and K2 (4&4 kcal mol-l),I5 we calculate the MM’ product vibrational excitation Evib, listed in table 1. Since the bond energies 23 of KNa (14.3 kcal mol-l), RbNa (13.1 kcal mol-l), CsNa (1 3 kcal rnol-l),* RbK (1 1 kcal mol-l)* all exceed the estimated vibrational excita- tion, Evib, we may conclude that path 2 is energetically inaccessible and that the exchange reaction (path 1) is the major reaction path with the product MM’ molecule highly vibrationally excited.However, we cannot eliminate path 2 entirely, since the vibrational excitation of the M, reactant dimers is not known accurately and in any case there may be l4 a broad distribution of vibrational excitation. Thus path 2 may make some contribution in all the reactions studied. REACTION DYNAMICS AND ELECTRONIC STRUCTURE The magnitudes of the total reaction cross sections given in table 2, Qrr 100 A’, are large, indicating that reaction must occur for impact parameters as great as b - 6 A. but the van der Waals interaction contributes -0.5-2.0 kcal mol-l, due to the very large alkali atom polarisa- bilitie~,’~ (a-20-50A3). The capture cross section Qcap for a potential of the form V(r) = - C/r6 may readily be calculated 26 as since all collisions at impact parameters less than the orbiting impact parameter barb, at initial energy E, spiral into small internuclear distance.The van der Waals coefficient C is calculated using the Slater-Kirkwood formula 27 and polarisabilities used in the previous section. The capture cross sections Qcap, listed in table 2, are found to be of similar magnitude to the total reaction cross sections Q,, though * Where MM’ bond energies were not available from ref. (23) they were estimated by the relation DMM‘ = (DM~DMPJ+. At these separations, chemical bonding is small Qcap = nbzrb = ( ~ ~ w C / E ) + (9)328 REACTIVE SCATTERING OF ALKALI DIMERS consistently rather greater. This indicates that a major fraction of the collisions drawn into small internuclear distance by the long range van der Waals attraction undergoes an exchange reaction.However, the uncertainties in the experimental cross sections preclude any more precise estimate of the fraction undergoing reaction. The other features of the reaction dynamics also have implications for the form of the potential energy surface : (i) the differential cross section for Nat-K,, which appears to exhibit forward and backward peaking, becomes broader, perhaps even isotropic, for Na+Csz ; (ii) the product kinetic energies are very low in all cases ; (iii) the experiments give no information about lifetime of the reactive collision. RNa-Na(A) FIG. 9.-Potential energy surfaces for Li + Na2-+LiNa+ Na in the linear configuration, calculated by the London equation, surface (a) neglects overlap, surface (6) includes overlap.The zero of energy refers to separated atoms.J . C. WHITEHEAD AND R. GRICB 329 Diatomics in molecules calculations by Companion lo predict Lig to be stable by -9 kcal mol-l with respect to Li+Li2. Calculations by the authors l1 for all the Li, Na trimers also show them to be stable with respect to atom plus diatomic. In the case of mixed trimer (e.g., LiNa2) the most stable geometry places the lightest alkali atom in the centre position, e.g., NaLiNa is more stable than LiNaNa. The potential energy surfaces for the Li, Na reactions M'+M,+MM'+M, all show a broad shallow basin at small internuclear distances, which is only weakly dependent on the shape of the M2M' complex, but is most stable in the linear or near-linear configuration. Potential surfaces calculated for Li + Na, in the linear configuration are shown in fig.9. The basin blends smoothly into the long range van der Waals attractive region without any activation energy in either the entrance or exit valley. Now the reactions studied in this paper involve heavier alkali atoms for which no calculations are available. However, our Na + M2 systems are perhaps most closely similar to Li + Na2 (similar exeorgicity), so that we would anticipate a depth - 6 kcal mol-1 for the basin with respect to reactants, and that M Na M will be -2 kcal mol-' more stable than Na M M. Indeed, the stability of trimers of heavy alkali atoms has been demonstrated experimentally. We may gain a crude indication of the lifetime z of an M2M' complex in this basin, by applying the RRK equation 28 for a nonlinear triatomic complex with total energy E, dissociation energy to products E ~ , and vibrational frequency v For the Na + M2 reactions, where the exoergicity ADo - 2.5-3.0 kcal mol-1 offsets about half the basin depth, this gives an extremely short lifetime z-2/v.For the K + Rb, reaction, with nominally zero exoergicity, the reactant translational energy and the initial Rb, vibrational excitation, still result in a short lifetime z - 4/17. Thus, these considerations indicate, despite their approximate form, that the reaction dynamics will be direct, or, at most, involve a short-lived 22 complex. The observed symmetry of the differential cross section about 8 = 90°, arises from conservation of linear momentum for MNa and M with approximately equal masses and our detection of only the M+ signal.Perhaps the closest analogy to the present reactions, amongst other reactions studied in molecular beams, are the alkali atom-alkali halide exchange 21 reactions M + M'X+MX + M'. For these reactions the potential surface has a long-range dipole-induced dipole attraction and a well 29 of depth - 13.5 kcal mol-l at small internuclear distance. However, these reactions were studied with much lower reactant translational and vibrational energies relative to the potential well, than in our present reactions. They show long-lived complex dynamics with sharp forward and backward peaks in the differential cross section. Moreover, in the Li+KF, KBr reactions 30 where the reaction exoergicity partially offsets the potential well, the reaction dynamics go over to a short-lived complex, peaking more strongly forward than backward.Most of the enormous initial orbital angular momentum L> 350- 500 ti appears as orbital angular momentum of the products, L' = L, which results *l in the sharp peaking of these reactions. The initial orbital angular momen- tum is also large, L>250 A, in our M'+M, reactions and in view of the similarity of the potential surfaces, it seems likely that this will also appear as product orbital angular momentum L-L'. This accounts for the apparent sharp peaking in the Na+K, and K+Rb, reactions, where the masses of the three alkali atoms involved are not greatly discrepant.In the Na + Cs, reaction, however, there is much greater Cs, Na mass discrepancy, which may inhibit the transfer of initial orbital angular momentum to orbital motion of the heavy CsNa, Cs products, resulting in CsNa z = V-1[&/(&-&())]% (10)330 REACTIVE SCATTERING OF ALKALI DIMERS rotational excitation and broadening of the angular distribution. Such a “ light atom effect ” is seen in extreme form in the oriented spectator dynamics of alkali dimer-hydrogen atom reactions. In all the M’ + M2 reactions studied in this paper, the very small fraction (-10 %) of the available energy disposed into product translation E’ would be compatible with a direct mechanism. However, perhaps surprisingly, it would also be compatible with a long-lived complex (provided Lrrr L‘) due 31 to the large increase in reduced mass in going from reactants to products.For any reaction resulting in collisional dissociation, the product translational energy would also be very low due to the low excess energy available. Clearly, before a more discriminating analysis of the M’+M2 reaction dynamics can be attempted, better resolved differential cross sections must be obtained ; velocity analysis measurements may offer some hope in this direction. Finally, the exchange reactions would appear to provide an efficient vibrational energy transfer mechanism from M2 to MM’, in view of the large reaction cross section. In their analysis of condensation in an alkali nozzle beam expansion, Gordon et all4 found that only -0.07 kcal mol-l is transferred on average from vibration to translation in a single M+M, collision.This is in accord with our results for the exchange reactions where vibrational excitation of M2 is transferred to MM’ and enhanced by the reaction exoergicity. Support of this work by the Science Research Council is gratefully acknowledged. Y. T. Lee, R. J. Gordon and D. R. Herschbach, J. Chem. Phys., 1971,54,2410. W. S . Struve, T. Kitagawa and D. R. Herschbach, J. Chem. Phys., 1971,54,2759. G. M. Kendall, P. B. Foreman and R. Grice, Electronic and Atomic Collisions, ed. L. M. Branscomb et al. (North Holland, Amsterdam, 1971), p. 23. P. B. Foreman, G. M. Kendall and R. Grice, Mol. Phys., 1972,23,127. J. C. Whitehead, D. R. Hardin and R. Grice, Chem. Phys. Letters, 1972, 13, 319.J. C. Whitehead, D. R. Hardin and R. Grice, Mol. Phys., 1973,25, 515. P. B. Foreman, G. M. Kendall and R. Grice, Mol. Phys., 1973,25,529. P. B. Foreman, G. M. Kendall and R. Grice, Mol. Phys., 1973, 25, 551. D. R. Herschbach, Adu. Chem. Phys., 1966,10,319. l o A. L.Companion, D. J. Steible and A. J. Starshak, J. Chem. Phys., 1968,49, 3637. l1 J. C. Whitehead and R. Grice, to be published. l3 P. J. Foster, R. E. Leckenby and E. J. Robbins, J. Phys. B, 1969,2,478. l4 R. J. Gordon, Y. T. Lee and D. R. Herschbach, J. Chem. Phys., 1971,54,2393. l5 P. B. Foreman, G. M. Kendall and R. Grice, Mol. Phys., 1972,23, 117. l6 J. C. Whitehead, Ph. D. Thesis, (Cambridge University, 1972). B. T. Pickup and W. Byers Brown, Mol. Phys., 1972, 23,1189. Centronic Q806, Twentieth Century Electronics, King Henry’s Drive, New Addington, Croydon CR9 OBG, England. A. N. Nesmeyanov, Vapour Pressures of the Chemical Elements (Elsevier, Amsterdam, 1963). l9 J. H. Birley, E. A. Entemann, R. R. Herm and K. R. Wilson, J. Chem. Phys., 1969,51,5461. 2o E. A. Entemann, Ph.D. Thesis (Harvard University, 1963, 21 W. B. Miller, S. A. Safron and D. R. Herschbach, Disc. Faraday Soc., 1967,44, 108. 22 G. A. Fisk, J. D. McDonald and D. R. Herschbach, Disc. Faraday SOC., 1967,44,228. 23 Alkali dimer bond energies Do were taken from A. G. Gaydon, Dissociation Energies, (Chapman 24 P. J. Dagdigian, J. Graff and L. Wharton, J. Chem. Phys., 1971,55,4980. 25 B. Bederson and E. J. Robinson, Ado. Chem. Phys., 1966,10,1. 26 L. D. Landau and E. M. Lifshitz, Mechanics, (Pergamon Press, Oxford, 2nd edn., 1969), p. 51. 27 A. Dalgarno and W. D. Davidson, Adu. At. Mol. Phys., 1966,2,1. 29 A. C. Roach and M. S. Child, Mol. Phys., 1968,14,1. 30 G. H. Kwei, A. B. Lees and J. A. Silver, J. Chem. Phys., 1971,55,456. 31 S. A. Safron, N. D. Weinstein, D. R. Herschbach and J. C. Tully, Chem. Phys. Letters, 1972, and Hall, London, 3rd edn., 1968). S. A. Safron, Ph.D. Thesis, (Harvard University, 1968). 12,564.

ISSN:0301-7249    

DOI:10.1039/DC9735500320

出版商:RSC    

年代:1973

数据来源: RSC

摘要:

Facile Four-Centre Exchange Reactions BY D. L. KING AND D. R. HERSCHBACH Department of Chemistry, Harvard University, Cambridge, Massachusetts Received 16th April, 1973 Molecular beam experiments show that diatomic molecule exchange reactions involving an ionic bond proceed readily at thermal collision energies. Previous work found two such reaction families, alkali halide+ alkali halide and dialkalif halogen. This study adds a third, alkali halide+ halogen. For CsI+ C12-tCsC1+ ICl the product angular and velocity distributions indicate that a statistical collision complex is formed which persists for many vibrational periods and at least a few rotational periods. This complex presumably corresponds to the alkali trihalide salt, Cs+(ClICI)-. For the CsBr + ICI reaction only formation of CsCl+ IBr has been observed, even at collision energies well above the endoergic threshold for formation of CsT+BrCl.The energy disposal is not statistical and the product angular distribution is quite asymmetric about 90", indicating that a large fraction ( S + to +) of the collision complexes break up in less than one rotational period. The preferred directions of emission are 0" for CsCl and 180" for IBr, where 0" and 180" designate the incident beam directions (c.m. system) for ICI and CsBr, respectively. These properties can be plausibly interpreted in terms of the electronic structure of the trihalide group. Four centre reactions have long intrigued students of chemical dynamics because stringent collisional and electronic requisites for reaction might be expected in the concerted making and breaking of pairs of bonds.' Much recent work has pur- sued this theme, particularly in trajectory calculations 2-5 and electronic structure studies.6* The "textbook examples " are exchange reactions of diatomic molecules, including H2 + D2-+2HD (R1) H2+12-+2HI Br, + I2 --+ 21Br and a few others.The four bonds involved in these examples are all covalent bonds. However, qualitative arguments based on nodal properties of the electronic orbitals predict that such reactions will be " thermally forbidden " by a high activation energy.6 For sigma-bonded molecules this activation energy is expected to be comparable to the dissociation energy of a reactant bond. Many shock tube experiments have been interpreted by postulating that (Rl) proceeds via vibrational excitation, and the activation energy thus obtained is only -40 kcal mol-l.This mechanism has now received strong support in elegant work using vibrationally excited H2 and D2 prepared in a stimulated Raman laser.* These results are in severe conflict both with trajectory studies,2 which found the vibrational enhancement not drastic enough, and with extensive ab initio calculations of the H4 potential ~urface.~ Numerous transition-state geometries have been examined (with claimed accuracy - 10 kcal mol-l) and no reaction path found for ( R l ) with a barrier less than - 110 kcal rnol,-l which exceeds the H2 dissociation energy. For the notorious (R2) case, the activation energy likewise exceeds the I2 dissocia- tion energy ; careful photochemical experiments have shown the H, + I2 reaction to 33 1 (Rl)-(R3) and similar reactions have indeed suffered from recent scrutiny.332 FACILE FOUR-CENTRE EXCHANGE REACTIONS be negligible in competition with a termolecular I + Hz +I rea~tion.~ For the related reaction HI+DI, a molecular beam study found an undetectably small HD yield (cross section 20.05 A2) at collision energies far above the empirical activation energy.l0 This is certainly an allowed reaction, (at least as the reverse of I + HD +I), but apparently vibrational rather than translational activation is required.Trajectory studies of the various bi- and termolecular H212 processes have been carried out in great detail and the dominant reaction path is found to depend markedly on features of the potential surface which theory cannot yet e~tablish.~.Reaction (R3) and others involving interhalogens such as C12 + HBr have been widely cited as examples with apparently quite low activation energy, 2 15 kcaln~ol-~, both in gas phase and solution. The reaction previously attributed to (R3) now appears to be Brz+21,, however, and further work has also strongly implicated catalysis by surfaces or moisture in the ClZ + HBr case? l Recent crossed-beam studies of C12+Br2 find no bimolecular reaction occurs for collision energies up to - 30 kcal mol-I. In this context, exchange reactions of diatomic molecules which are found to go with zero or nearly zero activation energy offer a refreshing contrast. The examples, all provided by molecular beam experiments, include CsCl+ KT+CsI + KC1 K2 + Cl,+K + KCl + C1 +K*++Cl+Cl + KCI + KC1* csI+c1,-,cscl+Icl CsBr + ICl-,CsCl+IBr and similar reactions which involve one or more ionic bonds. In this paper we briefly review previously reported results for (R4) and (RS) and present a study of (R6) and (R7), with emphasis on qualitative electronic aspects of these facile reactions.SALT 4- SALT REACTION This might be termed a “ no-electron” reaction, since alkali halides are well approximated as closed-shell ion-pairs. The general case thus may be written as X- A+X-+ B+Y-+A+ B++A+Y-+B+X-. Y- The reaction is practically thermoneutral but the potential surface contains a deep basin corresponding to the intermediate salt dimer, as indicated in fig. 1. Thermo- chemical and structural studies have determined the dimer dissociation energy and shown the most stable configuration to be a cyclic, planar rhomboid.The strong long-range dipole-dipole interaction of the salt molecules guarantees a large cross section for forming the dimer complex, and the deep potential basin endows it with an appreciable lifetime before decomposing to yield the exchange products or to reform the reactants. indeed found a very large cross section for complex formation at thermal collision energy, roughly S200 A2. The mean lifetime of the complex is at least comparable to a rotational period, or 5 10-l’ s. The distributions in angle and velocity of the scattered salts are consistent The crossed-beam study of (R4) by Miller and SafronD . L . KING AND D .R . HERSCHBACH 333 with a simple statistical complex model, akin to the RRKM theory of unimolecular decay. Unexpectedly, the property most directly obtained from RRKM theory proved exceptional : the ratio of nonreactive to reactive decay of the complex was found to be some 2 or 3 times larger than statistical. Ionic model cal- culations predict less stable, linear chain isomers A+X-B+Y- or X-A+Y-B+ exist in addition to the rhomboid dimer. For (LiF)2 there is experimental evidence for both cyclic and linear forms. For (R4), the dissociation energy (to either CsCl+KI or CsI+ KCl) is estimated to be -36 kcal mol-1 for the cyclic dimers and - 19 kcal mol-1 for the linear isomers. The cyclic dimer is expected to dissociate statistically but the linear chain isomers may often dissociate nonreactively rather than rearrange to the cyclic form.This is especially likely in collisions with large impact parameters, where the large centrifugal momentum keeps the chain " ends " apart. The experimental results for (R4) provoked an extensive trajectory study of the salt +salt reaction by Brumer and Karp1~s.l~ This has confirmed the role of geo- metrical isomerism and elucidated many other aspects of the reaction. This discrepancy was attributed to geometrical isomerism.' DIALKALI +HALOGEN REACTION The reactant bonds are covalent in this case but an electron-jump mechanism is expected since the ionization potential of a diatomic alkali molecule is even lower than 20 c -40 -60 -80 CYCLIC DIMER u+cr CI- K' FIG. 1 .-Energy diagram for the KCl+ KCl and K2 + C12 reactions.Zero-point vibrational levels are shown for the reactants, possible products and intermediates. Asterisks denote electronic excitation ; photon energy for K* and KCl* emissions is also indicated. Energy of K,Cl and K,Cl* species obtained from pseudopotential calculations (ref. (17)) ; vertical doubleended arrow indicates uncertainty. Bell-shaped curves indicate initial distribution of reactant energy under experimental conditions. The lower part of the diagram is qualitatively similar for the CsCl + KI reaction.334 FACILE FOUR-CENTRE EXCHANGE REACTIONS that of an alkali atom. that the dominant reaction path should be Analogy to the alkali atom " stripping " processes suggests AB+XY+AB++XY--+(AB)+X-+Y+A+B+X-+Y. The electron-jump becomes possible at large distances, about 7-8A for (R5). The resulting dialkali ion is expected to dissociate more slowly than the halogen molecule ion since a vertical transition forms AB+ near its equilibrium internuclear distance, whereas the added electron in XY- enters a strongly antibonding sigma orbital.A transient (AB)+X- complex hence probably takes part ; such complexes govern reactions of alkali atoms with alkali halides.lS The released alkali and halogen atoms A and Y seldom have an opportunity to undergo electron transfer, A + Y -+A+ + Y-, because the curve-crossing radius for this transition is very large, e.g., about 22 A for K + CI, and the coupling matrix element is therefore extremely small. This mechanism l6 offers a drastic example of " electronic specificity ", since formation of A+B+X-+Y is much less exoergic than A+Y-+B+X-.As seen in fig. 1, the exoergicities are 32 and 133 kcal mol-', respectively, in the K, +C1, case. Angular distribution studies by Grice and his co-workers l6 and by Struve l7 have shown that A + B+X- + Y is indeed the predominant product channel for reactions of K2 with several halogens. For both A and B+X- the distributions peak strongly forwards and for Y backwards (with respect to the initial K2 direction). As expected, the large magnitude of the reaction cross sections, a,r 150 A2, and the shape of the product distributions are very similar to those for alkali atom stripping reactions. Chemiluminescence from both the alkali atom and the alkali halide has now been established for (R5) and other cases in crossed-beam experiments.17 The observed cross section is -0.3-3 A2 for K* emission and smaller for the KCl* emission. As seen in fig.1, the K* process is endoergic by -6 kcal mol-l. It can only occur by means of the reactant translational and internal energy and only when the accompany- ing salt molecule is formed in its lowest vibrational levels. The electron-jump mechanism is expected to put most of the reaction exoergicity into vibrational excit- ation of the B+X- molecules. A+(B+X-)t+A+X-+B* allows vibrational-to-electronic energy transfer to occur readily.' * The KCl* chemiluminescence is described elsewhere in this Discussion. However, the reactive exchange process SALT +HALOGEN REACTION Here ionic and covalent bonds must coexist and interact throughout the reaction.The absence of activation energy for (R6) and (R7) thus seems surprising. The reaction presumably involves formation of an alkali trihalide salt and charge migration within the trihalide group, A f X- + YZ-, A+( XYZ)-+ A+(ZY X)- -) A+Z- + XY. Fig. 2 shows very rough estimates of the A+(XYZ)- dissociation energies. These salts are apparently unknown in the gas phase but have been much studied in the solid phase and solution. In agreement with molecular orbital theory, the trihalide anions are linear or nearly linear and have the least electronegative atom (I, in this case) in the middle.20 This suggests that a comparison of (R6) and (R7) may show differences attributable to the preferred geometry and charge distribution in the trihalide group.D.L. KING AND D. R . HERSCHBACH ALKALI HALIDE i- HALOGEN REACTIONS 335 -501 I FIG. 2.-Energy diagrams for (a) CsI+CI2 and (b) CsBr+ICl reactions. Initial most probable relative translational energy E and vibration-rotation energy Ejnt of reactants are shown and corres- ponding final values E and Eint for products as derived from experiment. Dashed lines indicate very rough estimates of dissociation energies for possible alkali trihalide intermediates. EXPERIMENTAL The apparatus, beam geometry, and experimental procedures have been described 22 The reactant beams intersect at an angle of 90" and the scattering is measured in the beam plane. The detector comprises an electron bombardment ionizer, quadrupole massfilter, scintillation ion counter, and gated scalars synchronized with the beam modulation.About 0.1 % of the incoming molecules are ionized and counted. Velocity analysis is performed by installing a slotted disc chopper driven by a hysteresis motor and circuitry required to interface with a small computer, which is used to record the time-of-flight spectrum for scattering at various angles. The halogen beam was obtained from a supersonic nozzle, 0.11 mm in diameter and usually operated at 100-200 Torr and 300-350 K. Some experiments used the " seeding " technique with He as diluent to obtain higher collision energies. The salt beam was ob- tained by thermal effusion from a single-chamber stainless-steel oven 22 operated at - 2 Torr and - 1050 K. In auxiliary experiments a double-chamber salt oven was used to permit the source temperature and pressure to be varied independently. This enabled a test for possible perturbations due to the small fraction of dimers in the salt beam (a few percent).As in the other work,13* The angular width (full width at half maximum intensity) was 3" for the halogen beam and 5" for the salt beam. For the experiments reported here, the peak velocities C(ms-') in the parent beam distributions were : " no such effects were observed.336 FACILE FOUR-CENTRE EXCHANGE REACTIONS a 2 IC1 ICI CSl CsBr 470 4200 117O(II) 410 450 For the halogen beams the observed 0 is slightly below (7kT/m)3, which corresponds to complete rotational relaxation during the nozzle expansion. The full width at half maximum intensity was -30 % for the halogen beams and -50 % for the salt beams.The initial relative translational energies corresponding to these values of 9 are E = 2.5 kcal mol-1 for CsI+Ci2 and E = 3.9 and 16.2 kcal mol-l respectively in experiments I and I1 (see fig. 2) for CsBr+ ICI. In the reactive scattering measurements, halogen mass peaks were used since both the reactant and product salts fragment drastically (>95 %!) at the electron bombardment energy used (140 eV, chosen to avoid space charge effects at lower voltages). The angular distribution data were taken at 5" intervals over the laboratory range - 15" to + 120" (where 0" pertains to the halogen beam, 90" to the salt beam). Velocity distributions were measured at 9 angles in the laboratory range 20" to 110" for CsI+ C1, but have not yet been obtained for CsBr+ICl.In measurements of the product angular distributions, typical signals near the peak were -70-100 c s-l and counting times of 100 s gave signal-to-noise ratios of -30-40. In measurements of the product velocity distributions the resolution was -20 %. Typical signals (full velocity spectrum) were -20 c 9-l near the peak of the angular distri- bution and - 5 c s-l at wide angles, Counting times of 1-4 h were used at each scattering angle. RESULTS STATISTICAL COMPLEX CASE Fig. 3 shows a contour map of the CsI+C12 reactive scattering derived by trans- forming the laboratory (LAB) data to the centre-of-mass (c.m.) system. A standard approximation procedure was used which neglects the spread in parent beam velo- cities.2f Calculations using more elaborate procedures give similar maps, with smoother contours.However, the wobbIes serve as honest reminders of imperfect data. The approximate symmetry about 90" is evidence that the reaction involves a collision complex which persists for at least a few rotational periods. Further fCI from CsI + CI, 90" rao" .OO -- 1 CSI (32' *loo m/m" FIG. 3.-Polar contour map of angle-velocity flux distribution in the centre-of-mass system, for IC1 from CsI+Cl, reaction. Direction of incident C12 is designated as 0", direction of CsI as 180". Tic marks along radial lines indicate velocity intervals of 100 m s-'.337 evidence for this and some tentative information about the nature of the coupling and geometry of the transition-state for break-up of the complex can also be inferred from the map.Fig. 4 gives the distribution of final relative translational energy of the products, ICl+ CsC1, derived from the map in the usual way.21 The abscissa scale is normalized to the total available energy, P. L. KING AND D. R. HERSCHBACH Etot = E‘ -t Eint = E E,,, + ADO (1) as defined in fig. 2, with ADo the reaction exoergicity. The abscissa thus specifies both the fraction of energy in product translation, f = E’/Etot, and that in internal excitation, 1 -f = E{nt/Etot. CSI t ci2 - CSCl + ICI DISTRIBUTION OF PRODUCF TRANSLATIONAL 0.5 product translational energy, f = E‘/EtOt FIG. 4.-Distribution of product relative translational energy in the CsI + C1, reaction, in terms of fraction f = E/&,t of the total available energy (reaction exoergicity plus most probable reactant energy).Full curve represents “ best fit ” to experimental data. Points are derived from contour map of fig. 3 for three c.m. angles corresponding to kinematically most favourable region of the laboratory data : 9 = 90°( A), 1 loo( O), and 130°( x ). Dotted curve calculated from statistical model (eqn (2)) with M = 5 and n = 44. Dashed curve shows (1 -f)” with n = 43 and is normalized at f = 0.3 to data. According to an approximate statistical m0de1,~ the energy distribution is given by The factor f takes account of the centrifugal energy associated with separation of the products. The exponent rn = 3 if the transition-state is located at the exit centrifugal barrier and lies sufficiently far out to be governed by the r-6 attraction, whereas m-, 1 for a very steep exit potential.The factor (1 - f )” represents the energy level density of “active” vibrations and rotations, as in the RRKM theory of unimolecular decompositi~n.~~ This is a classical approximation, appropriate for our reactions because the zero-point energies are small and similar for reactants, complex, and products. The exponent n = s++r-2, where s and r denote, respectively, the number of vibrational modes and active rotations at the transition-state. The number of modes assigned to s and r depends on whether a “ tight ” or “ loose ” transition-state is assumed.24 For the tight case, a linear four-atom complex has s = 7, r = 0, and n = 5 ; a nonlinear one has s = 6, r = I, and n = 43.In the338 FACILE FOUR-CENTRE EXCHANGE REACTIONS loose case, the bending modes go over to free rotation of the product molecules, thus s = 3, r = 4, and n = 3. The fB parameter denotes the ratio of the maximum possible exit centrifugal barrier to the total available energy. In the simplest approximation, this is given by where p and p' are the reduced masses of the reactants and products.23 This formula assumes that centrifugal angular momentum is dominant in the reaction (indicated by the rather strong peaking in fig. 3) and the forces governing the entrance and exit channels are the same (rough but plausible in this case). According to eqn (2) the peak of the distribution occurs at whichever is smaller. Here, we findf, = 0.059 for rn = 3 andf, = 0.072 for m = 1.As seen in fig. 4, the model P(f) comes fairly close to the data, (with any rn between 3 and 1 and n between 3 and 5 ) and thus provides further evidence for the statistical character of the reaction. Results as good or better have been found for several other reactions.25 However, the low value off, estimated for CsI+Cl, indicates it should approach the simplest case, P(f) - (1 -f)", which would obtain if centrifugal motion were absent. This is a welcome situation, since the treatment of the centrifugal contribution is the crudest aspect of the model. In a more realistic model, the abrupt switch atf = fB given by eqn (2) would be rounded out and the relative normalization of the " centrifugal " (f<f,) and " statistical " (f >fB) portions of P(f) might change substantially.These considerations suggest the plot of fig. 5, which examines the f B = 'm(EIEto,) (3) 3= rn/(rn+n) or fB (4) f product internal energy, 1 -f FIG. 5.-Distribution of product internal energy, 1-A on log-log plot. Points from fig. 4 for 0 = 90"(A), 110"(0), and 130"(0). Lines show (1 -f)" for n = 3 and n = 4+, corresponding to a " loose " and " tight " statistical complex respectively.D. L . KING AND D. R. HERSCHBACH 339 " statistical '' region separately. For f> 2fB, the data appear to prefer the '' tight " model (n = 43 or 5). This result must be considered very tentative, but it illustrates again the possibility of deriving information about the effective number of modes contributing to energy exchange in the transition-state.26 Fig.6 shows the angular distribution obtained from the contour map. The peak- ing at 0" and 180" is the expected pattern for a complex which forms and dissociates with orbital angular momenta considerably larger than the rotational momenta of the reactant or product molecule^.^^ The strength of the peaking, and its concave upwards shape, thus contains information about angular momentum disposal in the reaction. 3.1 \ \ \ ICI from \ \ \ CSI + C12 - CSCl + ICI J CI2 DIRECTION CSI- 01 RECTION I I I l l I l l I I I I I [ , # c.m. scattering angle, 8 > 120° 150° t80" 30" SO" 90" FIG. 6.-Distribution of c.m. scattering angle for ICl from CsI+C12. Full curve represents " best fit " to data. Points obtained from contour map of fig. 3 for c.m. ICl velocities of 200(A) and 325( 0) m s-' ; also shown are points for 300( x ) m s-' obtained from a similar map generated by a least-square polynomial fit to the data.Dashed curve (MA = 0) is calculated from statistical complex model assuming a linear transition state (MA = 0). Dotted curve (ML = 150 ti) is calculated assum- ing a very nonlinear transition state corresponding to the " maximum reasonable estimate " of the moment of inertia about the axis of separation of the products. A transition-state treatment again provides a simple algorithm for calculating the shape of the di~tributi0n.l~ Three parameters are required : L,, the maximum orbital angular momentum with which the complex can be formed (at the given collision energy) ; Mo, the root-mean-square projection of the total angular moment- um on the initial relative velocity vector ; and MA, the corresponding projection on the final relative velocity vector.If the ratios Lm/Mo and MA/Mo are specified, the angular distribution can be read from reduced plots prepared by Miller.13* 2 5 For lack of a better procedure, we evaluate L, assuming an r6 entrance interaction with force constant C = 1.3 x erg cm6 obtained by customary approximations. This gives L, 21 320h, probably an overestimate. The corresponding cross section for complex formation is 6, = 95A2. The Mo parameter has a negligible contri- bution from C12 and thus is readily calculated from the CsI temperature and moment of inertia.13 This gives Mo 21 100 h. According to the model, for a " tight "340 FACILE FOUR-CENTRE EXCHANGE REACTIONS complex, M(, is related to the moment of interia of the transition-state about the axis of separation of the products.This axis lies close to a line through the heavy Cs and I atoms, so Mb essentially measures the root-mean-square distance of the pair of C1 atoms from that line. Fig. 6 shows results for two limiting cases. For M(, = 0 the 6.0 5.0 transition-state is linear and gives the strongest For M(, N 150 h, the transition state is close to c1 Cl I I or cs- - - - - -1 1 1 1 1 J I I I ~ ~ I 1 1 1 1 1 1 1 - I I I t - \ I - \ I I 1 \ M:, = 0 -+- possible peaking (for given Lm/Mo). a " boat " or " chair " form, c1 I cs- - - - - -I I Cl which gives the maximum moment of inertia about the separation axis and the weakest possible peaking.The experimental angular distribution indeed falls between these limits. The theoretical shape agrees closely with experiment for - 80 h. If the value of L, were decreased a correspondingly smaller value of Mb would be required ; a 50 % decrease in L, would require Md = 0. These model calculations thus suggest the transition state is not drastically nonlinear. NONSTATISTICAL CASE Fig. 7 shows the angular distribution for the CsBr +ICl reaction (Experiment I of fig. 2). The LAB distribution for this case exhibits a prominent bimodal structure. This provides favourable kinematics and enables the main features of both the c.m. angle and energy distribution to be reliably determined despite the lack of velocity analysis data.I5 The reaction is clearly quite nonstatistical.The c.m. angular dis- t 1 0 ' " ' " ' - ~ ' " - 1 1 ~ ~ 0" 30" 6@ 90" 120° 150°' 180° c.m. scattering angle, 8 FIG. 7.-Distribution of c.m. scattering angle for IBr from CsBr+ICl. Full curve derived from experimental data, dashed (A46 = 0) and dotted (MI: = 125 ti> curves calculated from statistical model assuming linear and very nonlinear transition states respectively.D. L. KING AND D. R. HERSCHBACH 341 tribution shows strong asymmetry, with IBr emerging predominately backwards with respect to the incident ICl and CsCl emerging backwards with respect to the incident CsBr. This asymmetry indicates a large fraction of the collision complexes (5 3 to 3) break up in less than one rotational period. For comparison, fig. 7 includes distribu- tions calculated from the statistical complex model (with C = 1.7 x erg cm6, L, N_ 500 A, Mo = 85 A), for the linear (Mh = 0) and chair (Mh = 125 ti) cases.The c.m. product translational energy derived from the kinematic analysis is distinctly higher than statistical ; it corresponds to about 40 % of the available energy. In a seeded beam experiment at collision energies above the endoergic threshold for formation of CsI+BrCl (Experiment 11, fig. 2), no BrCl was observed. DISCUSSION For the salt +salt reaction, easy four-centre exchange is not surprising since no electron rearrangement is involved. For the dialkali +halogen reaction, despite a formal resemblance to H2 +I2, easy reaction is perhaps even less surprising ; the electron-jump in effect makes this a biradical process, (K-)K+.. . Cl-(CI*). For the salt + halogen reaction, a likely mechanism seems less apparent. However, the lack of activation energy despite shuffling ionic and covalent bonds, the qualitative differ- ence between CsI + C1, and CsBr + ICl, and the failure to yield CsI + BrCl can all be plausibly interpreted in terms of the electronic structure of the trihalide anions. Fig. 8 shows the geometry and charge distributions in (ClIC1)- and (Cl1Br)-, as derived from molecular orbital calculations. 2o -0.58 + 0.16 -0.58 CI-I- 2 . ~ a 2 . 5 7 ~ ‘I I- 2.328 -0.69 + 0.15 -0.46 Br I- Br CI-I- 2.70a 2.62a 2.47a FIG. &-Bond lengths and charge distributions in trihalide anions and bond lengths in parent diatomic molecules. Formation of the alkali trihalide would provide a potential basin which facilitates reaction in all cases.However, by virtue of its low exoergicity, the CsBr+ICl exchange might seem more likely to go via a long lived complex than the CsI+Cl, reaction. The fact that this does not occur could be explained by the preference for having I as the central atom of the trihalide anion. If this preference is strong enough, the processes I- + c1, -+ICl+ Cl- and Br- + ICl-IBr + Cl- are very different, involving insertion as contrasted with “ end-on ” attack of the incident atomic ion, respectively. Fig. 9 indicates the situation this suggests. The Cs+I-+C1, process is pictured as proceeding by insertion, charge migration, and a “ revolving door ” rearrangement to give a roughly linear Cs+C1- . . . ICI transition- state. For Cs+Br- + ICI, in reactive configurations the Cs+ ion and I atom are likely to collide during the “ end-on ” interaction of Br- with ICl.The charge distribution suggests this may often be a repulsive collision, so that Cs+ would pick up the emerging CI- and depart quickly in the direction opposite to the incident salt. The failure342 FACILE FOUR-CENTRE EXCHANGE REACTIONS to produce CsfI- + BrCl is likewise consistent with the location of charge on the end atoms in the trihalides and the marked instability of (BrC1I)- relative to the (BrIC1)- anion.2o c r -0.69 - (0.69 + 6 1 & -0.46 + - (0.46- 6) FIG. 9.-Schematic reaction mechanisms illustrating formation of trihalide anions and charge migration. Support of this work by the National Science Foundation is gratefully acknow- ledged.For recent discussions, see : (a) S. W. Benson and G. R. Haugen, J. Amer. Chem. SOC., 1965, 87,4036 ; (b) S. H. Bauer and E. Ossa, J. Chem. Phys., 1966,45,434 ; (c) R. M. Noyes, J. Chem. Phys., 1968,48,323 ; ( d ) L. D. Spicer and B. S. Rabinovitch, Ann. Rev. Phys. Chem., 1970,21, 376; (e) T. F. George and J. Ross, J. Chem. Phys., 1971, 55, 3851. Also see ref. (2)-(11) and many papers cited therein. K. Morokuma, L. Pedersen and M. Karplus, J. Amer. Chem. SOC., 1967, 89, 5064. M. Mok and J. C. Polanyi, J. Chem. Phys., 1970, 53,4588. R. N. Porter, D. L. Thompson, L. B. Sims and L. M. Raff, J. Amer. Chem. Soc., 1970,92,3208 and J. Chem. Phys., 1973, to be published. R. L. Jaffe, J. M. Henry and J. B. Anderson, J. Chem. Phys., 1973, to be published. (a) R.Hoffmann, J. Chem. Phys., 1968, 49, 3739 ; (b) L. C. Cusachs, M. Krieger and C. W. McCurdy, J. Chem. Phys., 1968, 49, 3740; In?. J. Quantum Chem., 1969, 35, 67; (c) R. N. Porter and L. M. Raff, J. Chem. Phys., 1969, 50, 5216; 1969, 51, 1623; (d) B. M. Gimarc, J. Chem. Phys., 1970,53, 1623 ; (e) W. A. Goddard, J, Amer. Chem. Soc., 1972,94,793. ' (a) M. Rubinstein and I. Shavitt, J. Chem. Phys., 1969, 51, 2014 ; (b) C. F. Bender and H. F. Schaefer, J. Chem. Phys., 1972,57,217 ; (c) D. M. Silver and R. M. Stevens, J. Chem. Phys., 1973, to be published. Much other work is cited in those papers. S. H. Bauer, D. M. Ledermann, E. L. Resler and E. R. Fisher, Znt. J. Chem. Kinetics, 1973,5,93. J . H. Sullivan, J. Chem. Phys., 1967, 46, 73. lo S.B. Jaf€e and J. B. Anderson, J. Chem. Phys., 1969,51, 1057. l1 P. Schweitzer and R. M. Noyes, J. Amer. Chem. Soc., 1971, 93, 3561. l2 D. A. Dixon, D. L. King and D. R. Herschbach, this Discussion. l3 W. B. Miller, S. A. Safron and D. R. Herschbach, J. Chem. Phys., 1972, 56, 3581. l4 P. Brumer and M. Karplus, this Discussion. (a) W. B. Miller, S. A. Safron and D. R. Herschbach, Disc. Faraduy Soc., 1967,44, 108 ; (6) G. H. Kwei, A. B. Lees and J. A. Silver, J. Chem. Phys., 1971, 55,456; 1972,58,1710.D . L . KING AND D . R . HERSCHBACH 343 l 6 (a) P. B. Foreman, G. M. Kendall and R. Grice, Mol. Phys., 1972,23,127 ; (b) J. C. Whitehead, D. R. Hardin and R. Grice, Chern. Phys. Letters, 1972, 13, 319. (a) W. S. Struve, Ph.D. Thesis (Harvard University, 1972). (b) W. S. Struve, T. Kitagawa and D. R. Herschbach, J. Chem. Phys., 1971, 54, 2759. M. C. Moulton and D. R. Herschbach, J. Chern. Phys., 1966,44, 3010. l 9 W. S. Struve, J. R. Krenos, D. L. McFadden and D. R. Herschbach, this Discussion. 'O For reviews, see : (a) E. H. Wiebenga, E. E. Havinga, and K. H. Boswijk, in Ado. Inorg. Chem. Radiochem., H. J. Emeleus and A. G. Sharpe, eds. (Academic Press, New York, 1961), Vol. 3, p. 133 ; (b) A. I. Popov, MTP International Review of Science: Inorganic Chemistry, V . Gut- man, ed. (Butterworths, London, 1972), Series 1, Vol. 3, p. 53; (c) the data of fig. 8 are from E. H. Wiebenga and D. Kracht, Inorg. Chem., 1969, 8, 738. 21 J. D. McDonald, P. R. LeBreton, Y. T. Lee and D. R. Herschbach, J. Chem. Phys., 1972, 56, 769. 22 H. J. Loesch and D. R. Herschbach, J. Chem. Phys., 1972, 57,2038. 2 3 S. A. Safron, N. D. Weinstein, D. R. Herschbach and J. C. Tully, Chem. Phys. Letters, 1972,12, 24 See, for example, 0. K. Rice, Statistical Mechanics, Thermodynamics, and Kinetics (Freeman, 2 5 S. J. Riley and D. R. Herschbach, J. Chern. Phys., 1973, 58, 27 and other work cited therein. 26 (a) A. Lee, R. L. LeRoy, Z. Herman, R. Wolfgang and J. C. Tully, Chem. Phys. Letters, 1972, 12, 569 ; (b) J. M. Parson, K. Shobatake, Y. T. Lee and S. A. Rice, this Discussion. 564. San Francisco, 1967), pp. 495-573.

ISSN:0301-7249    

DOI:10.1039/DC9735500331

出版商:RSC    

年代:1973

数据来源: RSC

摘要:

Substitution Reactions of Fluorine Atoms with Unsaturated Hydrocarbons Crossed Molecular Beam Studies of Unimolecular Decomposition BY JOHN M. PARSON," KOSUKE SHOBATAKE,t YUAN T. LEE AND STUART A. RICE The James Franck Institute and Department of Chemistry, The University of Chicago, Chicago, Illinois 60637 Received 29th December, 1972 This paper briefly reviews an extensive set of studies of the reactions of fluorine atoms with olefins, dienes, aromatic and heterocyclic molecules by the method of crossed molecular beams. From measurements of the angular distribution of products and the recoil energy spectrum of products it is inferred that the statistical theories of reaction are inadequate. AIthough RRKM theory seems capable of predicting the ratios of cross sections for pairs of products, the same theory is incapable of accounting for the internal energy distribution of the products.The failure of the hypothesis that internal energy exchange is more rapid than chemical reaction is discussed and a proposal advanced to explain the origin of the failure. For more than a decade the validity of the theory of unimolecular decomposition has been investigated by the method of chemical activation.' Of particular importance in these studies have been bimolecular addition and insertion reactiom2 Now, the study of bimolecular addition reactions of atoms and molecules by the method of crossed molecular beams has several advantages over the conventional chemical activation method for testing the energy randomization hypothesis of the statistical theories of unimolecular decomposition.First, by controlling the velocities of the colliding atoms and molecules, the total energy of the activated complex can be defined to better than 1 kcal mol-l. Second, in a crossed beams experiment one observes the consequences of single collisions. There is no intermolecular energy transfer after the collision complex is formed, so that the experimentally observed product angular and velocity distributions and the relative reaction rates for competing decomposition channels can only reflect the efficiency of intramolecular energy transfer prior to decomposition of the activated complex. Recently, the addition of halogen atoms to olefin molecules has been extensively investigated by molecular beam methods. The reactions of C1 with several bromin- ated olefins have been studied by Herschbach and coworker^.^ At Chicago we have carried out a series of studies of reactions of fluorine atoms with some thirty different olefins, halogenated olefins, cyclic olefins, conjugated olefins and aromatic hetero- cyclic hydrocarbon^.^ In contrast to reactions involving chlorine atoms which, at thermal energy, can only lead to replacement of a heavier halogen in a substituted olefin, the reactions of fluorine atoms with olefin molecules can lead to multichannel decomposition.This situation comes about because the C-F bond is stronger than any other single bond with a carbon atom. Thus, it is to be expected that fluoro- olefin complexes have sufficient activation energy to break C-C, C-H or C-halogen * present address : Chemistry Department, Ohio State University, Columbus, Ohio.t present address : Chemistry Department, California Institute of Technology, Pasadena, California. 3443 . M . PARSON, K . SHOBATAKE, Y . T . LEE AND S . A. RICE 345 F+C,H, --I------ - -- - -t- -4 - * 50 UCAL I Fro. 1 .-Schematic energy diagram for the reaction of a fluorine atom with a butene molecule pro- ducing C4H7F+H or C3H5F+CH3. bonds. A schematic energy diagram for two competing reaction channels for F + 2- butene is illustrated in fig. 1. By varying the nature of the olefin molecule systematic- ally, the relation between competing reactions and the location of the initial activation, i.e., the position of the double bond, can be discerned. FJG. 2.-Top view of beam arrangement.346 UNIMOLECULAR DECOMPOSITION In this paper, we summarize information obtained mainly from the measurement of the translational energy distributions of product molecules, and the reIative rates of competing decompositions, in F + olefin reactions.Some of the consequences of the experimental findings for the theory of unimolecular reactions are also discussed. EXPERIMENTAL A schematic diagram of our experimental apparatus is shown in fig. 2. F atoms were produced by thermal dissociation at 750°C, formed into a beam, and velocity selected to 20 % full width at half maximum by a slotted disc selector. Olefin molecules were formed into a supersonic beam by flow from a free jet source using source pressures in the range 400-700 Torr behind a 0.1 mm diameter nozzle.The velocity distribution of the olefin molecules has a typical range of 15 - 20 % full width at half maximum. The peak velocities were always found to be slightly larger than (8 kT/m)*, indicating that some of the vibrational degrees of freedom, in addition to all the rotational degrees of freedom, relaxed during the isentropic expansion. The beams were collimated to 1.2' and 2.5" for F and the olefins respectively. The angular distributions of products were measured with a rotatable mass spectrometer detector. This detector, and other details of the experimental arrangement, have been described el~ewhere.~* 4u The velocity distributions of product molecules were measured by a time-of-flight method with a resolution of approximately 15 %.Collection and processing of time-of-flight data were executed by a minicomputer. A detailed description of this aspect of the experiments will be given eI~ewhere.~b ANALYSIS AND DISCUSSION OF EXPERIMENTAL RESULTS The F+C,H, reaction will be taken as an example to illustrate our method of data reduction. Fig. 3 and fig. 4 display the angular distributions of products and four laboratory frame product velocity distributions at various angles together with lab scattering angle FIG. 3.-0, Experimental laboratory angular distribution of C2H3F produced in the reaction F+ C2H4 ; -, best fit laboratory angular distribution based on centre-of-mass product distribution shown in fig. 5 ; - . - . -, laboratory angular distribution calculated from 12-oscillator phase-space theory model assuming an isotropic angular distribution in the centre-of-mass system of coordinates ; - - - - -, laboratory angular distribution calculated from 5-oscillator phase-space theory model assum- ing an isotropic angular distribution in the centre-of-mass system of coordinates. some calculated curves to be described later.In this reaction, since the life time of the complex is much longer than a rotational period (as can be seen from the forward- backward symmetry in the angular distribution) it is reasonabIe to assume that theJ . M . PARSON, K . SHOBATAKE, T . Y . L E E AND S . A . RICE 347 product energy distribution in the centre of mass frame is independciit of' centre-of- mass angle, although the product angular distribution might not be isotropic.The RRK form was taken for the product energy distribution :4a P ( E ' ) - (E' - VJf'" - )( Etotat - E')" - . (1) For this reaction, we used the velocity distribution at laboratory angle 0, = 50.5' to determine s and V, because this laboratory angle is close to the c.m. velocity direction; hence the product molecules are emitted at practically the same centre-of-mass angle. 0 5 10 15 lab velocity lo4 cm s-' FIG. 4.--3, Experimental laboratory velocity distribution of C2H3F produced in the reaction F+ C2H4 at four laboratory angles, as indicated ; - , best fit laboratory velocity distributions based on centre-of-mass product distribution shown in fig. 5 ; - - - - -, laboratory velocity distribution cal- culated from RRKM theory assuming an isotropic angular distribution in the centre-of-mass system of coordinates. The results are, then, independent of the yet to be obtained centre-of-mass angular distribution.Setting n = 3 we find for the parameters of eqn (1) : s = 2.5 and V, = 1.2 kcal mol-l, with uncertainties of roughly (+ 1.0, -0.5) for s and k0.5 kcal mol-l for V,. With this P(E'), the predicted integrated signal at each laboratory angle was compared with the angular distribution using a least squares fitting procedure to determine the best Legendre polynomial representation of the c.m. angular distri- bution. Only the first two even polynomial coefficients were allowed to be non-zero because the data were not precise enough to allow evaluation of additional para- meters. The calculated laboratory velocity distributions at other angles using this c.m.angular distribution are found to agree well with the experimental data (fig. 4). Fig. 5 displays a contour map of the final best-fit c.m. flux density. The P(E') obtained from velocity distribution measurements is actually not drastically different from the best fit results obtained by assuming an isotropic centre-of-mass angularT F+C,H,-C,H,F+H 9 0" T c. rn. VeIoci! y (m-') c, *, I F I I I- I k--y 203 m- FIG. 5.4ontour map of CzHJF flux density distribution in the centre-of-mass system of coordinates produced in the reaction F+C2H4. These contours are obtained by fitting the laboratory angular and velocity distributions. 0-7 t F+C,H,-CC2H3 F + H 1 0.5 2 !! $ 0.3 "'t I I\ 'I ' \ I \ I \ I \ I \ I \ 1 ', E', kcal mol-' FIG.6.-Product translational energy distributions for the reaction F+ C2H4+C2H3F+ H. -, best fit energy distribution obtained from experimental results ; - . - . -, best fit energy distribution obtained by onfy fitting laboratory angular distribution assuming an isotropic angular distribution in the centre-of-mass system of coordinates ; -..-..-, energy distribution calculated from 12-oscillator phase-space theory model ; . . . . ., energy distribution calculated from 5 oscillator model ; - - - - -, energy distribution calculated from RRKM theory. Potential barriers for the product channel are adjusted, each of the last three calculations to best match the width of laboratory angular distribution.J . M. PARSON, K . SHOBATAKE, Y. T. LEE AND S . A .RICE 349 distribution, as is seen in fig. 6. Moreover, it comes remarkably close to the pre- dictions obtained from a simple phase-space theory calculation of the recoil energy distribution when only 5 vibrational modes instead of all 12 of C2H3F are assumed to be active during the decomposition of the complex. The existence of a non-statistical internal energy distribution, deduced from the implication that only some of the vibrational degrees of freedom are activated, is also implied by the observations of McDonald of chemiluminescence in this reaction. He found a significant difference between the spectral distributions of emission from C2H3F produced by F + C2H4 and the thermal radiation of C2H3F molecules. The observed slightly favoured sideways scattering in the angular distribution of products is also interesting.Miller, Safron and Herschbach have described a mechanism for sideways peaking in which an oblate complex dissociates along its symmetry axis. The model is not applicable to C,H4F since it is prolate and H does not depart along the symmetry axis. However, the constraints imposed by the nature of the potential energy surface and the conservation of angular momentum make the decomposition very similar to that of an oblate complex. If a fluorine atom must approach a C2H4 molecule (approximately) perpendicular to the plane of the molecule in order to form the C2H4F complex, and if Lp J (as expected here), then the three heavy atoms in C2H4F will rotate in a plane roughly perpendicu- lar to L. If the transition state for the hydrogen atom emission has a geometry with the CH bond considerably extended, then the rest of the molecule will be relaxed to almost a planar geometry.Consequently, the hydrogen atom must leave the complex perpendicular to the plane determined by the C-C-F arrangement, and v’ will be approximately parallel (or antiparallel) to L and thus perpendicular to v. Most of the initial orbital angular momentum will then remain as product molecular angular momentum of C2H3F. Note that this polarization of product emission will not occur if the departing atoms are considerably heavier than hydrogen atoms, since the angular momentum related to the C-C-F rotational motion can then no longer dominate the total angular momentum, with the consequence that a more isotropic angular distribution is generated.A similar slightly sideways peaked angular distribution was observed in the reaction F+C6D6-+C6D5F+D.4b- On the other hand, the product angular distribution was found to be almost isotropic in the reaction F+C4HS-+ C3H5F + CH3.4b The mechanism is portrayed in fig. 7. T FIG. 7.-Mechanism of F+C2H4+C2H3F+ H reaction illustrating the relation between the angular momentum and the preferred orientation of the product separation. The non-statistical product translational energy distribution deduced for the reaction F+C2H4-+C2H3F+H is actually found to be a common feature for all of the H and CH3 emission reactions we have studied. Fig. 8 shows a comparison of experimentally determined best-fit recoil energy distributions with those calculated by phase-space theory and RRKM theory lo for reactions of F+C4Hs+C3H5F+350 UNIMOLECULAR DECOMPOSITION 0.5- CH3.A 4-atom model, which neglects all hydrogen atoms in C3H5F gives better agreement with experiment than does the calculation which includes all 9 atoms. For reactions in which multichannel decomposition is possible, the mass spectro- metric identification of product molecules is sometimes complicated by their frag- mentation in the ionization process. In a crossed molecular beam experiment the I - I I I 5 I I1 - 0.4t I\ I I I I -1 F+I -BUTENE 0. I 0.0 5 10 15 20 25 E'lkcal mol-' FIG. 8.-Product translational energy distribution in the reaction F+ C4Hs+C3H5F+CH3. -, best fit energy distributions obtained from experimental angular and velocity distributions ; - .- . -, energy distributions calculated from phase-space theory 4-atom model neglecting all H atoms in CJHSF ; . . . . ., energy distributions calculated from phase-space theory including all atoms in C3H5F ; - - - - -, energy distributions calculated from RRKM theory. The same potential barriers in the product channel were used for each of the last three calculations as determined from the best fit distributions. difficulties arising from fragmentation are usually not serious since the kinematic relations for different channels are often very different, with the consequence that the products from different channels usually appear in different angular and velocity ranges. Fig. 9 shows the time-of-flight spectra of products measured at mass 59 (C3H4F+) in F+butene reactions. C3H4F+ could come from both C4H7F and C3H,F after electron beam ionization, but the two peaks corresponding to C4H7F and C3H,F are clearly separated in velocity space.Fig. 10 shows the angular distribution of products from the reaction F+m-xylene at mass 123 and mass 109. At mass 109, both H emission and CH, emission were observed, but the part contri- buted by H emission can be subtracted from the angular distribution of mass 123, and the angular distribution of CH3 thereby obtained.J . M . PARSON, K . SHOBATAKE, Y . T . LEE A N D S . A . RICE 351 Average product translational energies, reactive cross sections for CH3 and H emission, and their ratio in many reactions in which both CH3 and H emission were observed, are listed in table 1.The higher average translational energies character- istic of CH3 emission reactions can be rationally attributed to a higher energy barrier for CH, emission, under the assumption that the excess potential energy over that required for dissociation is converted into product translational energy. The potential barrier for CH3 emission from the complex was estimated to be 4.4, 4.9 and 5.5 kcal mob1 for 1 -butene, 2-butene and isobutene, respectively. The potential barrier for C-Cl rupture was found to be negligibly small. laboratory velocity /ms-' FIG. 9.-0, Experimental laboratory velocity distribution measured by monitoring m/e = 59 in the reaction of F+ 1-butene, F-tcis 2-butene and Ffisobutene; - , best fit C3H5F velocity distri- bution; - - - - -, best-fit C4H7F velocity distribution.In all cases listed in table 1, the cross sections for CH, emission are much larger than those for H emission. This is just what one expects from the statistical theory of unimolecular decomposition, since CH3 emission channels are more exoergic than H emission channels. It is interesting to note that in spite of the fact that not all the vibrational degrees of freedom are equally active in the reaction complex, the extent of energy mixing is suficient that the RRKM theory estimate of o(CH,)/a(H) is in352 UNIMOLECULAR DECOMPOSITION reasonable agreement with experiment. The agreement, of course, follows from the insensitivity of a(CH3)/a(H) to the extent of energy mixing provided that a sufficient number of vibrational modes is activated.0 .d 3 1.0 2 1 5"3 I I -5 0 0" 30" 60" 90" lab scattering angle, 0 FIG. lO.-(a) Newton diagram for F + m-xylene. (b) Experimental laboratory angular distribution measured by monitoring m/e = 123 ; (C6H3(CH&F product). (c) Experimental laboratory angular distribution measured by monitoring rnle = 109 (superposition of C6H3(CH&F and CsH4CH3F products). TABLE 1 .-AVERAGE PRODUCT TRANSLATIONAL ENERGIES, REACTIVE CROSS SECTIONS AND THE RATIOS BETWEEN CH3 EMISSION AND H EMISSION CHANNELS reactant products < E ' ) /kcal mol-1 u,/Az QCH~ /OH cis 2-butene trans 2-butene isobutene 1 - bu tene 1 -3-pentadiene C5I c41 (H3C)ZC=CH(CHs) G I c41 tetramethylethylene C d toluene C7I M-x ylene CSI C d c 61 4.6 10.1 4.6 10.1 4.6 10.9 4.6 9.3 4.9 7.1 5.3 9.3 5.4 8.3 6.8 9.3 7.8 11.0 0.30 22 6.6 0.23 40 9.1 0.24 30 7.3 0.026 115 3 .O 1.1 3.8 4.1 0.19 15 2.9 0.48 32 15.4 7.1 2.7 19.4 2.7 9.7 26J .M . PARSON, K, SHOBATAKE, Y . T. LEE AND S. A . RICE 353 SOME COMMENTS ON THE THEORY OF CHEMICAL REACTIONS The hypothesis that randomization of the internal energy of a molecule is fast relative to chemical reaction is deeply imbedded in all theories of reaction rate." The experiments we reportY4 and those of others,12 suggest that this hypothesis is not universally valid. How, then, must our interpretation of the rate of chemical reac- tions be changed? It is to be expected, in general, that excitation of an isolated molecule generates a non-stationary state with non-random energy distribution. The fact that a sample of many molecules excited by thermal collisions may have an ensemble average random distribution of internal energy does not detract from the force of this statement.Now, if the density of product states is large, the rate constant for the reaction i-*fis of the form where (i, k'r'u') and df, k"r"u") refer to the electronic and translation-rotation-vibration states of reactant and product, P(i, k'r'u') is the distribution of prepared states, and H i n t defines the coupling between the prepared nonstationary reactant state and the product state. The function of the rapid energy randomization hypothesis is to permit eqn (2) to be rewritten in a representation in which the excitation of any particular degree of freedom is only a function of its thermodynamic weight.In this limit, P(i, k'r'v') is a microcanonical distribution for an isolated molecule, or a canonical distribution for an ensemble of molecules excited by thermal collisions. The counter extreme to the hypothesis that internal redistribution of energy is rapid is, of course, that it is slow. In that case P(i, k'r'v') depends on the excitation source. The evaluation of the rest of eqn (2) is the same in both limiting cases. In the intermediate case, when the rates of energy redistribution and complex decomposition are comparable, eqn (2) cannot be used. In the following we consider some of the consequences of the hypothesis that internal energy redistribution is slow. The cleanest case for theoretical study is that corresponding to photogeneration of a single nonstationary vibronic state of the reactant.Although few data are available for polyatomic molecules, we may call upon studies of radiationless tran- s i t i o n ~ , ' ~ ' ~ ~ Lee's investigations of the photochemistry of cyclobutanone,16 and the interpretations of the photodecompositions of HCCCl and S0218 for guidance. The theory of radiationless processes in the statistical limit shows that the rate of decay of a prepared state is dominated by the influence of geometry changes and frequency changes between the reactant and product. For the case of a large molecule there is usually an acceptable partitioning of the normal modes into two sets, one consisting of those that undergo only small displacements and frequently changes, and another consisting of those for which these changes are large.Although all changes in molecular geometry and vibrational frequencies influence the absolute rate of reaction, it is the subgroup that suffers large changes that determines the relative dependence of reaction rate on energy of the initial nonstationary state. Indecd, those modes with largest frequencies and which undergo the largest frequency changes and displacements are most likely to be excited in the product. This theoretical prediction has been confirmed both for the radiationless transition 1B2u+3Blu in benzene l9 and in the reaction F+C2H,. In the latter case molecular orbital calculations imply that the complex C2H4F is nonplanar, with the F bonded to one carbon and the hydrogens bent down and away from the F atom.20 Since C2H3F is 55--M354 UNIMOLECULAR DECOMPOSITION planar, the out-of-plane bending modes of the product should be vibrationally excited, as observed by McDonald. The same effect, as well as the propensity for energy transfer to high frequency modes, has been inferred to be important in the photodecomposition of HCCCI, where it is necessary to explain the slow decomposi- tion via CC1 bond breakage. If we restrict attention, now, to bimolecular reactions that proceed through a long lived reaction complex, we must consider two general classes of molecular excitation.When reaction occurs by virtue of thermal collisions, it seems very likely that the ensemble of reaction complexes that is formed in a macroscopic sample has an (ensemble averaged) canonical distribution of internal energy.Note that this statement does not imply that in any given complex there is rapid redistribution of the internal energy. In fact, we believe that the extensive studies of thermal unimolecular reactions that verify RRKM theory really show that the ensemble of reaction com- plexes has a random (but not randomized) distribution of internal energy, and that these studies do not directly test the energy randomization hypothesis. There is not, for us, any conflict between these data and those we report, which are based on chemical excitation in molecular beams with defined velocities. In general, we expect chemical excitation by reaction of two species with defined velocities to generate a non-uniform initial energy distribution in the reaction complex.Although this method will ordinarily not excite single modes of the reaction complex, it is likely to confine the excitation to a subset of the set of all vibrational modes. Therefore, arguments analogous to those described for the case of photochemical excitation can be used to develop a theoretical description of the reaction complex. If vibrational relaxation is slow relative to chemical reaction, it also might be slow relative to the rate at which product molecules recoil. Then we must expect there to be exchange between vibrational and translational energy, and rotational and trans- lational energy, with some modes playing a larger role than others in the energy exchange. Provided that only one electronic surface is involved in the energy exchange, the most important factor in the vibration-translation energy transfer process is the overlap between the Fourier spectrum of the force between receding products and the vibrational frequency spectra of the products.Classical calcula- tions 21 suggest that when one of the products is H or CH3 the exchange between vibrational and translational energy is inefficient; it seems to be somewhat more efficient when both products have comparably large masses. This difference can be understood in terms of the dynamical conditions on separability of bond motions.22 The exchange of rotational and translational energy depends on particular details of the structure of the reaction complex, e.g., the displacement between the (asymp- totic) product trajectory and the centre of mass of the complex, the moments of inertia of the complex, and other factors.Actual calculations of the various forms of energy exchange are tedious, and the currently available descriptions of vibration- translation and rotation-translation energy exchange in polyatomic reaction com- plexes are inadequate. A complete analysis of the role of vibration-rotation- translation energy exchange in the rate process must also describe the evolution of the reaction coordinate from the fully bonded to unbonded limits, including the associated geometry changes. Only the very first steps in the solution of this problem have been taken.22* 23 All of the preceding has been argued under acceptance of the notion that vibra- tional relaxation is slow compared with chemical reaction.For the case of photo- chemical decomposition of HCCCl this implies a vibrational coupling smaller than cm-l, and our results for the reactions of F and various olefins and aromatics, and the energy dependence of the fluorescence of benzene and other molecules, giveJ . M . PARSON, K. SHOBATAKE, Y . T . LEE A N D S . A . RICE 355 comparable bounds. This interaction strength is surprisingly small. While it might be marginally acceptable to base our argument on small anharmonicities when we deal with initial states that correspond to small vibrational excitation on an upper elec- tronic surface, the argument appears improbable when it refers to high vibrational excitation of the ground electronic manifold. Yet the experimental data clearly imply that vibrational relaxation is slower than photon emission, or reaction complex decomposition, in the cases cited.We propose that vibrational relaxation is indeed small, but not for the classical reason that the anharmonicities of vibrations are small. Instead, we suggest that the environment of a normal mode (or a bond oscillator) fluctuates rapidly and with large amplitude when there is considerable internal energy and that, because of these fluctuations, the vibrations are localized as are electronic states in a dense disordered system. Indeed, in the special case that the anharmonicities are quartic, and the magnitudes of the quartic coefficients random an exact isomorphism can be established between the vibrational and electronic situa- t i o n ~ .~ ~ We note that the existence of localized states has been demonstrated in the electronic case.25 It remains to be established whether or not more general vibra- tional force fields lead to the same conclusion, but it seems likely to be so since the localization effect depends on the existence of fluctuations in environment and not the source of the fluctuations. S.A.R. wishes to thank the Directorate of Chemical Sciences, AFOSR, and YTL the U.S. Atomic Energy Commission for financial support. We have also benefited from the use of facilities at the University of Chicago supported under the Materials Research Laboratory Program of the National Science Foundation. (a) B. S. Rabinovitch and D. W. Setser, Adv. Photoclzem., 1964,3,1 ; (b) H. W. Chang and D. W. Setser, J.Amer. Chem. Soc., 1969, 91, 7648. (a) C. W. Larson and B. S. Rabinovitch, J. Chem. Phys., 1970,52,5181 ; (6) E. A. Hardwidge, C. W. Larson and B. S. Rabinovitch, J. Amer. Chem. SOC., 1970, 92, 3278 ; (c) J. Knox and K. C. Waugh, Trans. Furaduy SOC., 1969, 65, 1585. D. R. Herschbach, private communication, this Discussion. (a) J. M. Parson and Y. T. Lee, J, Chem. Phys., 1972,56,4658 ; (6) J. M. Parson, K. Shobatake, Y. T. Lee and S. A. Rice, J. Chem. Phys., 1973,59,1402 ; (c) K. Shobatake, Y. T. Lee and S. A. Rice, J. Chem. Phys., 1973, 59, 1416, 1427, 1435. Y. T. Lee, J. D. McDonald, P. R. Lebreton and D. R. Herschbach, Rev. Sci. Znstv., 1969, 40, 1402. P. E. Siska, Ph. D. Thesis (Harvard University, Cambridge, Mass., 1969). ’ J. D. McDonald, private communication, this Discussion. * W. B. Miller, S. A. Safron and D. R. Herschbach, Disc. Furaday Soc., 1967, 44, 108, 291. J. C. Light, Disc. Furaday SOC., 1967, 44, 14. lo R. A. Marcus, J. Chem. Phys., 1952, 20, 359. l 1 See, for example, P. J. Robinson and K. A. Holbrook, Unimolecular Reactions (John Wiley, New York, 1972). l 2 (a) J. D. Rynbrandt and B. S. Rabinovitch, J. Chem. Phys., 1971, 54, 2275 ; (b) Z. Herman, A. Lee and R. Wolfgang, J. Chem. Phys., 1969,51,452 ; (c) R. L. LeRoy, J. Chem. Phys., 1970, 53, 846. l3 For recent reviews see: J. Jortner, S. A. Rice and R. M. Hochstrasser, Ado. Photochem., 1969, 7 , 149 ; K. F. Freed, Topics Curr. Chem., 1972, 31, 105. l4 (a) K. G. Spears and S. A. Rice, J. Chem. Phys., 1971, 55, 5561 ; (b) B. K. Selinger and W. Ware, J. Chem. Phys., 1970,53, 3160. I s A. Abramson, K. G. Spears and S. A. Rice, J. Chem. Phys., 1972,56, 2291. l6 J. C. Hemminger and E. K. C. Lee, J. Chem. Phys., 1972,56, 5284. (a) K. Evans and S. A. Rice, Chem. Phys. Letters, 1972, 14, 8 ; (6) K. Evans, R. Scheps, S. A. Rice and D. Heller, J.C.S. Furaduy ZZ, 1973, 69, 856. M. H. Hui and S. A. Rice, Chem. Phys. Letters, 1973, 20, 41 1 ; 1972, 17, 474.356 UNIMOLECULAR DECOMPOSITION l9 D. Heller, K. F. Freed and W. Gelbart, J. Chem. Phys., 1972,56,2309. zo K. Shobatake, S. A. Rice and Y. T. Lee, unpublished. 22 K. G. Kay and S. A. Rice, J, Chem. Phys., 1973,58, 4852. 23 R. A. Marcus, J. Chem. Phys., 1966,45,4493. 24 This special case was called to our attention by Prof. K. F. Freed. 25 See K. F. Freed, Phys. Rev. B, 1972, 5,4802. K. Shobatake, S. A. Rice and Y. T. Lee, J. Chem. Phys., 1973,59,2482.

ISSN:0301-7249    

DOI:10.1039/DC9735500344

出版商:RSC    

年代:1973

数据来源: RSC

摘要:

Reactive Scattering of Methyl Radicals CH3 + ICI, IBr, I2 BY C. F. CARTER, M. R. LEVY AND R. GRICE Theoretical Chemistry Department, Cambridge University, Cambridge CB2 1EW Received 28th December, 1972 Angular distribution measurements of methyl iodide reactive scattering from crossed beams of methyl radicals and halogen molecules, ICI, IBr, I2 are reported. The methyl radical beam is generated by pyrolysis of azomethane flowing through a heated tantalum tube at -1600 K ; the halogen molecule beam issues from a nozzle beam source at -380 K. Reactively scattered methyl iodide is detected by an electron bombardment mass spectrometer. The differential cross sections peak sideways in centre-of-mass coordinates, showing a marked similarity to the corresponding deuterium atom-halogen molecule reactions.Qualitative molecular orbital theory offers a compre- hensive rationalisation of methyl radical, deuterium atom and halogen atom reaction dynamics with halogen molecules. Recently, two preliminary reports ' 9 of reactive scattering measurements of methyl radical reactions with halogen molecules have been published. These are the first molecular beam studies of free radical reactions to be undertaken. Thus, it is of particular interest to compare the reaction dynamics with those of halogen atoms 3-7 and deuterium atoms 8-10 with halogen molecules, which have been previously studied in molecular beams. The halogen atom reactions proceed by a short-lived complex mechanism 3* due to short range attraction. However, the deuterium atom reactions show O strong repulsion between the reaction products.Qualitative molecular orbital arguments 11* l2 have been used in rationalising I3 separately the potential surfaces of the halogen and deuterium atom reactions. The observation of methyl radical reactions may offer the opportunity to develop a comprehensive theory of the reaction dynamics of atoms and free radicals with halogen molecules. The reactions of methyl radicals with halogen molecules are important in the photohalogenation l4 of methane, and in the photolysis and pyrolysis I6 of methyl iodide. They are fast reactions with low activation energies ( E a r 2.5 kcal mol-I). Indeed, iodine molecules are frequently used as radical scavengers in gas kinetics; the methyl radical plus iodine molecule reaction has essentially zero activation energy.In this paper we report reactive scattering measurements of methyl iodide product from methyl radical reactions with halogen molecules, CH3+IY-,CH3T+Y where Y = Cl, Br, I. APPARATUS AND EXPERIMENTAL CONDITIONS The non-alkali reactive scattering apparatus is shown in fig. 1 and 2. The basic design follows that of Lee et a1.l' with modification to the beam sources and detector pumping. The main scattering chamber, fig. 1, consists of a stainless steel box (interior dimensions 91.5 x 91.5 x 58.5 cm, wall thickness 5 cm top, 3.8 cm sides and bottom), lined with a liquid 357358 REACTIVE SCATTERING OF METHYL RADICALS FIG. 1.-Diagram of the apparatus ; upper panel, plan view ; lower panel, side view : A, stainless steel scattering chamber ; B, stainless steel source chambers ; C, liquid nitrogen cooled cold shield : D, detector UHV chamber ; E, source bulkheads ; F, aluminium alloy flanges ; G, liquid nitrogen cold trap ; H, oil diffusion pumps ; N, free radical source ; 0, Tec Rings ; P, nozzle source ; Q, skimmer ; V, beam chopper.C.F . C A R T E R , M . R . LEVY A N D R . G R I C E 3 59 nitrogen cooled cold shield (0.6 cm nickel plated copper). It is pumped by two unbaflled, 2800 1. s-l, oil diffusion pumps (Edwards E09) l 8 which may be isolated from the chamber by butterfly valves (Edwards QSB9). The rotatable lid of the chamber is supported by a 50.8 cm i.d. ball bearing race and sealed by two Teflon " Tec Rings ". The detector assembly, fig. 2, built onto the lid, consists of three UHV chambers differentially pumped by radial electric field pumps with a high (400 1. s-l) pumping speed for active gases, but lower (101.s-l) for inert gases. The pumping of the innermost chamber, containing the electron bombard- ment ion source," may be augmented by a liquid helium cryotrap in addition to the liquid vertical section E FIG. 2.-Diagram of the detector : A, high voltage feed through ; B, bearing race ; C, cathode ; D, plastic scintillator ; E, ion source ; H, liquid He cryotrap ; I, ion lenses ; L, scattering chamber lid ; N, liquid nitrogen cold trap ; P, photo multiplier ; Q, quadrupole rods ; R, light baffle ; S, slide valve ; T, radial electric field pumps ; X, buffer chamber ; Y, inner chamber ; Z, ion source chamber. nitrogen trap ; this was not employed in the present work however.Ions drawn from the ion source are mass analysed by a quadrupole mass spectrometer (Q50) 2o and detected by a Daly 21 scintillation detector. Pulses from the photomultiplier (60973) 22 are amplified (NE4634 Fast Amplifier),23 discriminated (NE4635 Fast Discriminator) from background noise pulses and counted by a fast dual scaler (100 MHz, 908) 24 which is gated in synchron- ism with the beam chopper. The gating circuitry, constructed in our laboratory from ?TL integrated circuit logic modules, gives equal gating times for each scalar to better than one part in lo5. The " on " scalar counts signal plus background and the " off" scalar counts background. The detector system may be isolated from the scattering chamber by a slide valve sealed with a Viton 0 ring.An angular range of 140" of laboratory scattering angle (0 = - 25", 11 5") is accessible to the detector. As indicated in fig. 1, both beam sources are doubly differentially pumped by unballied oil diffusion pumps, 2800 1. s-' for the source chambers (Edwards E09), 680 1. s-l for the buffer chambers (Edwards EM), which may be isolated by butterfly valves (Edwards QSB9 and and QSB4). The liquid nitrogen cooled cold shield also serves as a partition between the360 REACTIVE SCATTERING OF METHYL RADICALS chambers, thus providing cryotrapping to both chambers when appropriate. The methly radical source, based on the design of Kalos and G r ~ s e r , ~ ~ generates radicals by pyrolysis of a suitable precursor gas flowing through a tantalum tube (0.1 cmx 0.6 cm cross section) heated to - 1600 K, by a resistance heater element. In this way the precursor molecules are dissociated and the resulting radicals issue directly into the molecular beam before their concentration is too greatly reduced by the very rapid radical recombination reactions.Azoniethane is employed as a precursor gas at a pressure - 1-2 TOK rather than the dimethyl mercury used by Kalos and Grosser. The yield of methyl radicals is even so rather low, probably -10 %. ?he methyl radical beam is chopped by a slotted rotating drum driven by a hysteresis synchronous motor (Globe SC) at 60 Hz in the buffer chamber. The halogen molecule beam is generated from a nozzle beam source (0.03 cm diameter) at a pressure - 20 TOIT and -380 K.The halogen gas is supplied by a glass gas line for ICI and by a stainless steel oven in the source chamber for IBr, I1. During a typical experiment, the pressure in the methyl source chamber is - Torr, and the scattering chamber Torr, the halogen source chamber - Torr. Beam widths of 3.5" were employed for both beams. RESULTS AND KINEMATIC ANALYSIS In these experiments, the CHJI reactive scattering is - 10 counts s-' and the background - lo2 counts s-l. Counting times of 100 s were employed with repeated measurements at each scattering angle. The accuracy of data at the peak of the distributions is better than & 10 %. The laboratory scattering angle 0 is measured from the methyl radical beam at 0 = O", toward the halogen beam at 0 = 90".The laboratory angular distributions of reactively scattered CHJ from CH3 + IC1, IBr, I2 are shown in fig. 3-5, together with Newton diagrams constructed for the most FIG. 3.-hboratory angular distribution (number density) of reactively scattered CHJ from CH, + ICLC. F. CARTER, M. R . LEVY AND R . GRICE 361 probable velocities of the reactant beams; the CH3 beam is taken as a Maxwell- Boltzman distribution, and the halogen nozzle beam velocity based on time of flight measurements lo of an I2 nozzle beam. The angular distribution data points are relative number densities given directly by the difference of the " on " and " off" scalars. The angular distribution for CH3 + ICl shows a broad distribution peaking laboratory scattering angle, 0 I Id rr;' I FIG.4.-Laboratory angular distribution (number density) of reactively scattered CHJI from CH3 + IBr. Different symbols denote data from separate runs. TABLE 1 .-TRANSLATIONAL ENERGIES AND REACTION EXOERGICITIES (kca1 mol-l) A Do CH3Y + I A Do system E E' m3I-I-y CH3 + ICl 3.1 5 4 31 CH3 + IBr 3.1 9 12 25 CH3 + Iz 3.1 10 18 18 at 0 fi 70-SO", similar to the angle of the centre of mass vector, 0 = 68". The distribution narrows and shifts backward to 0 fi 80-90" for CH3 +IBr, and still further backward to 0 fz 100-110" for CH3+12. Preliminary measurements for CH3 +Br, indicate that the CH,Br distribution peaks at wide angles 0 21 100" in agreement with the data of McFadden-et aZ.l As the Newton diagrams indicate, these distributions correspond to sideways peaking in centre-of-mass coordinates.362 REACTIVE SCATTERING OF METHYL RADICALS laboratory scattering angle, 0 I 3 -I 10 ms I FIG.5.-Laboratory angular distribution (number density) of reactively scattered CH31 from CH3 + Iz. Different symbols denote data from separate runs. C b + ICl-+ClijI + Cl c.m. scattering angle, 8 FIG. 6.Differential cross section of reactively scattered CH31 from CH3 + ICI, centre-of-mass system, calculated by F.V. approximation.C . F . CARTER, M . R . LEVY AND R . GRICE 363 The laboratory angular distributions have been transformed to the centre of mass coordinate system using the FV approximation.26 Product translational energies E’, listed in table 1, appropriate lo to the corresponding deuterium atom-halogen molecule reactions, have been employed in the absence of any experimental informa- tion about the actual product velocity distributions.A qualitative justification for this estimate is considered below. The spheres about the tips of the centre of mass I C~+I&+CH-;I+Br I c.m. scattering angle, 8 system, calculated by F.V. approximation. FIG. ’I.-DiRerential cross section of reactiveIy scattered from CH3 + IBr, centre-of-mass CH, + 12+ CYI + I 0 c.m. scattering angle, 6 system, calculated by F.V. approximation. FIG. 8.- Differential cross section of reactively scattered CH31 from CH3 +Iz, centre-of-mass velocity vectors c in the Newton diagrams of fig. 3-5, indicate the spectrum of velocity vectors accessible to CHJ product with translational energy equal to the reactant translational energy, E’ = E, (inner circle), or with all the available energy disposed into product translation, E’ = E + AD,, (outer circle).The reaction exoergicities ADo are given 27 in table 1. As these Newton diagrams suggest, the form of centre-of- mass differential cross section compatible with the data is rather insensitive to the364 REACTIVE SCATTERING OF METHYL RADICALS assumed product translational energy within these limits. The differential cross sections are shown in fig. 6-8 as a function of centre-of-mass scattering angle 8, where the direction of incident CH3 defines 8 = 0". The CH3+IC1 differential cross section, fig. 6, shows a broad peak about 8 N 90". However, the CH3 +IBr differ- ential cross section, fig. 7, has narrowed and shifted backward slightly to 8 N 110".The CH3+12 differential cross section, fig. 8, has shifted still further backward to 8 N 130". These differential cross sections compare ' with CH3+Br2 peaking at 8 21 120-140", and perhaps CH3 + Cl, rebounding directly backward, 8 5 150". The results bear a striking resemblance to the centre-of-mass angular distributions for the deuterium atom-halogen molecule reactions,' O which change from sideways to backward peaking along the sequence D+12, Br,, CI, and show a backward shift in the sideways peaking along the sequence D + ICl, IBr, I,. Even the values of the peak positions for the corresponding methyl radical and deuterium atom reactions appear to be closely similar ; with the methyl radical reactions consistently being shifted slightly backward - 10-20" compared with the deuterium atom reactions.The total reaction cross section Q, may be crudely estimated by dividing the pre- exponential factor in the rate constant by the mean collision velocity. This gives Qr - 1 A2 for 14=* 15c CH3 + Cl,, I2 the only reactions for which data are available. A similar magnitude, Qr- 5 A' was obtained lo for the deuterium atom reactions. DISCUSSION The reactions of methyl radicals with halogen molecules (CH3 +XU) involve only covalent interactions. The magnitude of the total reaction cross section, Qrw 1 A2, indicates that reaction occurs only in collisions at small impact parameters (say b<2A), when the methyl radical approaches close to the halogen molecule. Thus, these reactions are analogous both to the reactions of halogen atoms with halogen molecules 3-7 (Z+XY) which exhibit short range attraction and the reac- tions of deuterium atoms with halogen molecules (D +XY) which exhibit lo repulsion in the exit valley of the potential surface.In fact, our experimental results indicate strongly that the CH3 +XY dynamics are very similar to those of D +XY rather than Z+XY. It is instructive to examine how this dichotomy arises by exploring the electronic structure of the three-body reaction complex. FIG. 9.-Schematic diagram of molecular orbitals in the linear configuration for the triatomic reaction complexes H+XY, CH3+XY and Y+XY, where X, Y denote halogen atoms. Shaded and un- shaded areas denote phases of the atomic orbitals.C. F. CARTER, M. R . LEVY AND R .GRICE 365 In a series of classic papers, Walsh has discussed the molecular orbital theory of triatomic molecules l 1 BAB and hydrides l2 HAB. The valence molecular orbitals for HXY and YXY in the linear configuration are indicated schematically in fig. 9. The appropriate Walsh diagrams 11* l2 for the variation on bending of these orbital energies, as a function of interbond angle a, are shown in fig. 10. In HXY there are 15 valence electrons and in YXY (or ZXY) 21 valence electrons which result in electron configurations for the linear case of a' 9 a a' a a a a's d YXY angle a angle a angle a FIG. 10.-Walsh diagrams for molecular orbitals of triatomic reaction complexes H+XY, CH3 + XY and Y +XY, where X, Y denote halogen atoms. Diagrams are appropriate when the electronegativ- ity of X is less than that of Y.The discussion in the text deals primarily with this situation. The corresponding molecular orbital description of CH3XY may be constructed by referring first to the electronic structure of the diatomic molecules. The molecular orbital configurations 28 of the hydrogen halides HX ( 0 ) ~ ( 7 c ) ~ and halogen molecules X,(~,)~(n,)~(n,)~ have been determined by photoelectron spectros~opy.~~ The niolecular orbital configuration of the methyl halides CH3X(ne)4(aa,)2(n,)4 is analogous 30 to that of the heteronuclear halogen molecules YX. The nx orbitals are nonbonding and correspond to the lone pair px, p y electrons of the halogen atom. The Gal orbital is the C-X bonding orbital consisting of the halogen atornp, orbital and the carbon sp, hybrid orbital.The ne orbital is predominantly localised on the CH, group and is the principal CH, bonding orbital. In contrast to the analogous nu orbital in X2, the ne orbital has a high ionisation potential as indicated by photo- electron spectroscopy 31 and lies below the aa, orbital for CH3X, X = C1, Br, I. Thus, the molecular orbital configuration for CH,XY is quite analogous to YXY (or ZXY) as indicated for the linear case in fig. 9. However, the lowest x bonding orbital,366 REACTIVE SCATTERING OF METHYL RADICALS h e is localised mainly on the CH3 group and is the CH3 bonding orbital ; it probably lies below the 2a bonding orbital. The higher n: orbitals are localised mainly on the X, Y atoms, the lower 2n being XY bonding and the higher 3n* being XY antibonding.The 3a* orbital is CX bonding and XY antibonding ; the highest orbital, 4a* is both CX and XY antibonding. In CH3XY there are 21 valence electrons, which results in the electron configuration for the linear case of The corresponding Walsh diagram for CH3XY is shown in fig. 10. Now consider collinear approach of the atom or methyl radical to the halogen molecule. In the H + XY and CH3 + XY cases the highest occupied orbital is 3 8 as indicated in eqn (2) and (3). In both cases, the 30" orbital is HX or CH3X bonding and XY antibonding. The XY antibonding effect corresponds to the a* antibonding orbital of the halogen molecule XY which is occupied in the XY photodissociation. None of the other orbitals occupied in the HXY or CH3XY complex will greatly alter the XY bonding from that of the isolated XY molecule.Consequently, there should be a strong XY repulsion in the exit valley of the potential surface for both H +XY and CH3 +XY. This repulsive energy release will appear predominantly as translational energy 32 of the reaction products. However, collinear approach of Y +XY or Z+XY presents a very different situation. The highest occupied orbital (see eqn (2) for YXY) is o:, which is antibonding for both XY bonds, as indicated in fig. 9. The a: electron only partially offsets the bonding (o~)'(o,)~ electrons. The (nU)"(.3"(n~)" electrons give no net bonding or antibonding effect. Hence the YXY complex should be bound and will exhibit an attractive basin in the potential surface at short range.Reactive scattering measurements of Z + XY exchange reactions show the influence of an attractive basin which is deepest for X = I, shallower for X = Br and replaced by a repulsive barrier for X = C1. Hence, the stability of the YXY complex is enhanced by charge transfer interaction when the electronegativity of X is less than that of Y. Thus the major dichotomy in the form of potential surfaces, as indicated by the experimental data for methyl radicals, deuterium and halogen atoms with halogen molecules, is readily explained by a qualitative molecular orbital theory. Monte Carlo calculations 33 for the reaction of a light atom with a heavy diatomic molecule with repulsive energy release in the diatomic bond, reveal that the direction of recoil of the heavy atoms is largely unaffected by the light attacking atom.The differential cross section for reactive scattering then mirrors the dependence of the reactivity of the diatomic upon its orientation with respect to the incoming atom. The situation will be particularly clear cut lo for the H+XY reaction due to the very light hydrogen atom. However, calculations 34 with a heavier attacking atom using the DIPR model 33 suggest that the differential cross section for CH3 +XY may still show a strong correlation with the preferred orientation for reaction. The geometry of the HXY and CH3XY complexes may be determined from the Walsh diagrams of fig. 10. For HXY the two electrons in the 2n*-a'sx orbital and for CH3XY the two electrons in the 3n*-a'sx orbital will foster bending, Moreover, we have argued that in the linear configuration (see fig.9) the 2n*, 3n:* orbitals are largely localised on the XY molecule. In the bent configuration the a'sx orbitals become increasingly localised on the X atom. Thus we would expect the variation of these orbital energies with angle a to be very similar for HXY, CH3XY. For HXY the electron in the 30-a'* orbital and for CH3XY the electron in the 3a*-a'* orbital will tend to straighten the triatomic complex. In the linear configuration (see fig. 9) the 30* orbitals in both HXY and CH3XY are HX or CH3X bonding and XY antibonding. CH3XY(saJ2(osy)2( 1 1 n:e)4(2~)2(2n)4(3n:*)4(30*). (3)C . F . CARTER, M. R . LEVY A N D R . GRICE 367 In the bent configuration, this orbital becomes l2 largely localised as ap, orbital on X overlapping out of phase with both thep, orbitals of Y and the sp hybrid orbital of CH,.Again the variation of this orbital with bending should be qualitatively similar for HXY, CH3XY. Thus, at least at a heuristic level, the Walsh diagrams indicate a qualitative similarity in the interbond angle a and hence in the differential cross section for the H + XY and CH, + XY reactions with a given halogen molecule XY. The tendency to a bent configuration is enhanced 35 by a decrease in the electro- negativity of the X atom which increases thep character of its hybrid orbitals. Thus the reactive scattering data shows for both HXY and CH3XY that the bending of the triatomic complex increases along the sequence X = CI, Br, I. The electronegativity of Y also influences the bending of the complex in a similar fashion lo for HIY and CH31Y where Y = C1, Br, I but the effect is less pronounced.This is in line with the molecular orbital theory since the orbitals which influence the bending become localised mainly on the X atom in the bent configuration. Moreover, repulsive energy release should decrease with increased bending along the sequence X = C1, Br, I due to the reduced X-Y antibonding character of the 30*-a’* orbital. Finally, the H+XY and CH3+XY reactions may share yet another feature. Matrix isolation studies have observed 36 the stable linear radicals X-H-X, X = C1, Br. This structure must provide a substantial well in the H + X, potential energy surface. However, molecular orbital 37 and valence bond lo* l 3 considerations indicate that this well is isolated by a potential barrier and plays no part in the reaction dynamics.Calculations 38 on the Walden inversion reaction predict a substantial well for the (X-CH,-Y)- ion. should leave a stable X-CH,-Y radical. Again this well in the potential surface for CH3+XY should be isolated by a potential barrier. The low repulsive energy release lo for D+ICI offers the best opportunity for involvement of the I-D-CI configuration. However, the experimental data lo shows no evidence for D migration between I and C1. The CH3 +ICl reaction with a much lower reaction exoergicity (table 1) than D + IC1 offers an even more favourable case for the involvement of the I-CH3-CI configuration. However, our observation of CH31 reactive scattering intensity for CH3 + ICl comparable to CH3 + IBr, Iz argues against major CH3 migration between I and C1.Removal of a single antibonding electron Support of this work by the Science Research Council is gratefully acknowledged. D. L. McFadden, E. A. McCullough, F. Kalos, W. R. Gentry and J. Ross, J. Chem. Phys., 1972,57, 1351. C. F. Carter, M. R. Levy and R. Grice, Chem. Phys. Letters, 1972, 17, 414. Y . T. Lee, J. D. McDonald, P. R. LeBreton and D. R. Herschbach, J. Chem. Phys., 1968,49, 2447. Y . T. Lee, P. R. LeBreton, J. D. McDonald and D. R. Herschbach, J. Chem. Phys., 1969,51, 455. D. Beck, F. Engelke and H. J. Loesch, Ber. Bunsenges. Phys. Chem., 1968,72, 1105. N. C. Blais and J. B. Cross, J. Chem. Phys., 1970, 52, 3580. ’ J. B.Cross and N. C. Blais, J. Chem. Phys., 1971, 55, 3970. J. Grosser and H. Haberland, Chem. Phys. Letters, 1970, 7, 442. H. Haberland and J. Grosser, Electronic and Atomic Collisions, ed. L. M. Branscomb et al. (North Holland, Amsterdam, 1971), p. 27. lo J. D. McDonald, P. R. LeBreton, Y . T. Lee and D. R. Herschbach, J. Chem. Phys., 1972,56, 769. l 1 A. D. Walsh, J . Chem. Soc., 1953, 2266. l 2 A. D. Walsh, J . Chem. SOC., 1953, 2288. l 3 D. R. Herschbach, Potential Energy Surfaces in Chemistry, ed. W. A. Lester (IBM, San Jose, 1971), p. 44.368 REACTIVE SCATTERING OF METHYL RADICALS l4 (a) G. B. Kistiakowsky and E. R. Van Artsdalen, J. Chem. Phys., 1944,12,469 ; (b) M. Ritchie and W. I. H. Winning, J. Chem. SOC., 1950,3583 ; (c) R. Eckling, P. Goldfinger, G.Huybrechts, G. Martens, L. Meyers and S . Smoes, Chem. Ber., 1960,93, 3014. Is (a) H. C. Anderson and G. B. Kistiakowsky, J. Chem. Phys., 1943,11,6 ; (b) R. R. Williams and R. A. Ogg, J. Chem. Phys., 1947,15,696; (c) R. D. Schultz and H. A. Taylor, J. Chem. Phys., 1950,18,194; ( d ) E. O’Neal and S. W . Benson, J. Chem. Phys., 1962,36,2196. l6 (a) S. W. Benson and E. O’Neal, J. Chem. Phys., 1961,34, 514; (b) J. H. Sullivan, J. Phys. Chem., 1961,65,722 ; (c) M. C. Flowers and S. W. Benson, J. Chem. Phys., 1963,38,882. Y. T. Lee, J. D. McDonald, P. R. LeBreton and D. R. Herschbach, Rev. Sci. Instr., 1969,40, 1402. l8 Edwards High Vacuum Ltd., Crawley, Sussex, England. l9 G. 0. Brink, Rev. Sci., Instr., 1966, 37, 857. 2o V. G. Micromass Ltd., Nat Lane, Winsford, Cheshire, England. 21 N. R. Daly, Rev. Sci. Instr., 1960, 31, 264. 22 E.M.I. Electron Tube Division, Hayes, Middlesex, England. 23 Nuclear Enterprises, Sighthill, Edinburgh, Scotland. 24 Borer, Solothurn, Switzerland. 25 F. Kalos and A. E. Grosser, Rev. Sci. Imtr., 1969,40, 804. 26 E. A. Entemann, Ph.D. Thesis (Hmard University, 1967). 27 Halogen molecule bond energies were taken from A. G. Gaydon, Dissociation Energies, (Chapman and Hall, London, 3rd edn, 1968) ; methyl halide bond energies from G. Herzberg, Electronic Spectra of Polyatomic Molecules (Van Nostrand, Princeton, 1966). 28 R. S. Mulliken, Phys. Reu., 1942,61,277; J. Chem. Phys., 1940, 8,382; 1940,8,234. *’ D. C. Frost, C. A. McDowell and D. A. Vroom, J. Chem. Phys., 1967, 46,4255. 30 R. S. Mulliken, Phys. Rev., 1935, 47,413. 31 A. W. Potts, H. J. Lempka, D. G. Streets and W . C. Price, Phil. Trans. A, 1970,268,59. 32 P. J. Kuntz, E. M. Nemeth, J. C. Polanyi, S. D. Rosner and C. E. Young, J. Chem. Phys., 1966, 3 3 P. J. Kuntz, M. H. Mok and J. C. Polanyi, J. Chem. Phys., 1969,50,4623. 34 P. J. Kuntz, Mol. Phys., 1972, 23, 1035. 35 A similar effect in the geometry of radicals, CH3 planar and CF3 pyramidal, is discussed by L. Pauling, J. Chem. Phys., 1969,51,2767. 36 P. N. Noble and G. C. Pimentel, J. Chem. Phys., 1968,49,3165 ; V. Bondybey, G. C. Pimentel and P. N. Noble, J. Chem. Phys., 1971,55, 540. 37 C. Maltz, Chem. Phys. Letters, 1971, 9, 251. 38 A. M. Woolley and M. S . Child, Mol. Phys., 1970, 19, 625. 44,1168.

ISSN:0301-7249    

DOI:10.1039/DC9735500357

出版商:RSC    

年代:1973

数据来源: RSC

摘要:

GENERAL DISCUSSION Dr. D. W. Davies and Mr. G. del Conde (University of Birmingham) said: It is disappointing that the experimental results given so far have all been interpreted in terms of semi-empirical potential surfaces. We have recently obtained some ab initio results for Li3 which are relevant to Whitehead and Grice's work on the scattering of alkali atoms by alkali diatomic molecules. They have presented a semi-empirical potential surface for LiNa, which indicates at least 5 kcal/mol stability with respect to LifNa, or Na+LiNa, and they have quoted a diatomics in molecules calculation as showing that Li, is about 9 kcal/moi more stable than Li + Li,. Other semi-empirical calculations have given the results that Na, and K3 are unstable with respect to Na+Na, and K+K2 respectively.There seems to be some doubt about the symmetries of the lowest states. We find "C,' for the equal bond length (Dmh) linear Li3, and 'B2 for the corresponding bent (1 35") Li3 (C,,). For a 45" angle we obtain ' A as the lowest state. This is in accordance with simple molecular orbital arguments. Companion et al., however, in their valency bond calculation obtained ,A1 for the most stable obtuse angled (137") isosceles triangle and 2B2 for the acute angled (34") triangle. Our results are given in table 1. They were obtained using contracted Gaussian orbitals to simulate a double zeta plus polarization Slater basis set with the ATMOL 2 programme on the Rutherford Laboratory IBM 370/195 computer. Each run required about 5 min computing time. TABLE OPEN SHELL RESTRICTED HARTREE FOCK RESULTS FOR THE ENERGY OF Lig RELATIVE TO 3Li (AW) distances/a.u.energies. -A Wlkcal mol- 1 Lil . . . Liz Liz-Li~ linear ( 1 80") bent (135') 6.0 9.0 2.51 2.41 8.0 2.79 2.66 7.5 2.94 2.83 6.5 3 .oo 3.08 6.0 (2Ez) 2.06 ('&) 2.46 5.05 - 9.0 8.0 7.5 6.5 6.0 Lit . . . Lij = Li, . . . Liz Liz-Li, 6.5 4.98 6.0 4.59 5.0 3.82 4.06 4.06 4.36 4.27 4.54 4.42 4.62 4.51 4.42 4.5 I 3.85 4.22 bent (45") 2A1 6.16 6.19 -22.3 ('B2) * 1 a.u. = 627.5 kcal/mol Basis set 1s 1s' 2s 2s' 2p 2p' 3GTO/STO. J. C. Whitehead and R. Grice, Paper in this Discussion. A. L. Companion, D. J. Steible and A. J. Starshak, J. Chem. Phys., 1968, 49, 3637 B. T. Pickup and W. Byers Brown, MoI. Phys., 1972, 23, 1189. 369370 GENERAL DISCUSSION For an unperturbed Li, molecule (bond length 5.05 a.u.) there is a small attraction for Li with a minimum energy at about 7 a.u.for both the linear (180O) and the 135" approach. The minimum is about 5 kcal/mol and the difference between the two approaches about 0.1 kcal/mol. For Liz stretched to 6 a.u. the energy of Li3 is higher than that of unperturbed Liz + Li ; but similar behaviour is found with minima at about 7 a.u. For perpendicular approach by the Li atom (45" isosceles triangle) to an unper- turbed Liz (4.98 a.u.) the energy is about 13 kcal/mol lower than for the linear ap- proach, and it is lower still for a 4.59 a.u. Liz distance. For a smaller isosceles triangle of sides 5.0, 5.0, 3.8 the energy rises sharply. These results give some support to Whitehead and Grice's conclusion that the potential surface is very flat for systems of this type ; but the low energy of the acute angled isosceles triangles, also suggested by Companion et al. ,2 requires further investigation.The reliability of single configuration molecular orbital calculations of this type, particularly for open shell systems, is an interesting question. In these calculations the energy of Li3 is a rigorous upper bound to the true energy. The energy relative to 3Li is not bounded : but experience has shown that such calculations for closed shell systems usually give a minimum with the correct ge~metry.~ They are not reliable at distances far removed from the minimum. The results reported here are first steps towards an ab initio potential surface for Li3. The energy for Liz suggests that a considerable scaling up would be desirable, and it may be that linear Li3 is about 3 kcal/mol lower in energy than Li + Li2.r I I I 1.0- K2+ 1 2 6606 8 4 8 - n A 0 v) * - - .- El G .- 8 s I 0 - (d v) - l3 8 - .CI -1.0 - 8 4 6 4 @ @ - 1 I 1 Dr. S. M. Lin and Dr. R. Grice (Cambridge University) said: We should like to report the observation of chemi-ionisation in reactive scattering potassium dimer K2 beam with a range of halogen containing of a supersonic molecules. The J. C. Whitehead and R. Grice, Paper in this Discussion. A. L. Companion. D. J. Steible and A. J. Starshak, J. Chem. Phys., 1968, 49, 3637. H. F. Schaefer, The Electronic Structure of Atoms and Molecules (Addison Wesley, 1972), pp. 325-33 1.GENERAL DISCUSSION 371 initial translational energy (E N 10 kcal/mol-l) is not greatly above the thermal energy range.The molecular beam apparatus previously used for reactive scattering measure- ments with an alkali dimer beam has been augmented with a Faraday cup ion detector placed below the scattering zone and a repeller plate above. The dependence of the ion signals measured for the K2+Iz reaction on flagging the I, beam as a function of repeller voltage is shown in fig. 1. Equal positive and negative ion signals are observed on changing the polarity of the repeller plate. There is a very rapid change close to zero volts indicating that the ions have low translational energies in laboratory coordinates. This is in accord with the low energies of the incident beams. The ion current is normalised by monitoring the dimer beam attenuation and the intensity of scattering with a surface ionisation detector. The ratio of total cross section for chemi-ionisation Qi to the total reaction cross section Qr may thus be determined.The results for K, + 12, HgC12, Hg12 are given in table 1. When the total reaction cross section Qr has been separately determined in a reactive scattering experiment, the total cross section for chemi-ionisation may be calculated as given in table 1. However Qi will in general be less accurate than the ratio Qi/Qr since total reaction cross sections Qr are not very accurately determined in crossed beams experiments. TABLE TO TOTAL CROSS SECTIONS FOR CHEMI-IONISATION Qi AND REACTION er (UNITS A”) reaction QilQr Q i Qr K2+L 1 .3 ~ - 2.0 N 150 K2 + HgC12 4 . o ~ 10-4 0.08 190 K2 + HgI2 2 . 6 ~ 10-4 0.04 140 The largest chemi-ionisation cross section Qi is exhibited by K2 +I2 where two ionisation paths (1) are energetically accessible. K2 + X,-+K+ + KX + X- (1) -+K2X+ + X-. The K, + HgX, reactions show chemi-ionisation cross sections lower by a factor N 30-50. In these reactions only one ionisation path (2) is energetically accessible. K2 + HgX,-,K,X+ + Hg +X- (2) The alternative path (3) is endoergic even with the initial translational energy E = 10 kcal mol-l. K2 + HgX2 + K+ + KX + Hg + X-. (3) Finally, no chemi-ionisation was observed for the reactions of more complicated polyhdide molecules K2+CH13, CBr,. This places an upper bound on these chemi-ionisation cross sections Qi 2 0.001 A’.Chemi-ionisation has previously been observed for reactions with high initial translational energies or with electronically excited specie^.^ However, the only P. B. Foreman, G. M. Kendall and R. Grice, Mol. Phys., 1972, 23, 117. D. R. Hardin, K. B. Woodall and R. Grice, Mol. Phys., 1973, in press. G. A. L. Delvigne and J. Los, Physica, 1972, 59,61 ; A. M. C. Moutinho, A. P. M. Baede and J. Los, Physica, 1971,51,432 ; K. Lacmann and D. R. Herschbach, Chern. Phys. Letters, 1970, 6, 106; R. K. B. Helbing and E. W. Rothe, J. Chem. Phys., 1969,51, 1607. H. Hotop, F. W. Lampe and A. Niehaus, J. Chem. Phys., 1969,51, 593 ; S. Y. Young, A. B. Marcus and E. E. Muschlitz, J. Chem. Phys., 1972,56, 566.372 GENERAL DISCUSSION previous observation of chemi-ionisation arising from '' chemical energy " of reaction appears to be the associative ionisation of uranium atoms with oxygen molecules.Prof. J. D. McDonald (University of Illinois) said : The angular distributions of methyl iodide measured by Grice et al. from reactions of methyl with halogen mole- cules, as well as earlier measurements of the angular distributions of hydrogen halides from reactions of D atoms with halogens can be explained qualitatively by a very simple model. This model should easily represent the angular distribution of pro- ducts from any reaction which satisfies two conditions. First, the attacking particle must be much lighter (about 5 times or more) than both the transferred particle and the left-over residue of the molecule. Second, the potential energy surface (the reaction being reduced to a three-body problem) must be strongly repulsive.\ 0 Due to the strong repulsion between the separating particles (in the D + I2 reaction, the DI and the I) the two fragments separate from each other along the direction toward which their line of centre points when the light particle reaches them. Thus, the scattering angle 8 is approximately equal to the angle q5 between the direction of approach of the attacking particle and a line pointing from the transferred particle to the leaving one (see fig. 1). The substrate molecule BC can be considered to be a cylindrically symmetric ovoid, divided into zones such that, if the particle A hits the molecwle in one zone (vertical shading in figure) AB may be formed, if A hits in a second zone (horizontal shading) AC may be formed, otherwise the reaction cannot occur (white part in figure).This model has been compared with classical trajectory calculations for the case D + I2 ; the I2 molecule can be considered a prolate ovoid with major-to-minor axis ratio of 1.4 : 1. LEPS-type surfaces are approximately of this form. The D +IC1 and CHz +IC1 reactions, with sideways peaked angular distributions require either a nonreaction end zone (illustrated in the figure) or a major-minor axis ratio of 4 : 1 ifthe whole molecule can react. Present experiments are incapable of differentiating these two cases. Prof. J. C. Polanyi and Mr, J, E. Schreiber (University of Toronto) said: It has been proposed 2* that the shift from backward to sideways scattering of the molecu- lar product in the series of reactions D+C12, Br2, Iz, may be indicative of reaction through progressively more-bent configurations. For the reaction D + C12, according to this hypothesis, the potential-energy surface would be such as to favour collinear approach of D to C12.For D+Iz it would favour something closer to lateral W. L. Fite and P. Irving, J. Chem. Phys., 1972, 56,4227. D. R. Herschbach, Conference on Potential-Energy Surjaces in Chemistry, ed. W. A. Lester Jr. (IBM Research Laboratory, San Jose, California ; Publication RA18, 1971), p. 44. J. D. McDonald, P. R. LeBreton, Y . T. Lee and D. R. Herschbach, J. Chem. Phys., 1972,56, 769.GENERAL DISCUSSION 373 approach. In the present Discussion Carter, Levy and Grice have reported a similar systematic shift in product angular distribution for the series CH3 + C12, Br,, 12, and have suggested that the explanation may parallel that for the D +X, series.In both series, D +X2 and CH3 +X,, the essential element in the argument is that the rapid approach of the light attacking-species, A, precludes any large amount of rotation of the molecule under attack, BC, during the reactive encounter. Following the approach of A there will be substantial repulsive energy release between B and C leading to recoil along the B-C axis ; the direction of this axis relative to the line of approach of A therefore determines the location of the peak in the product angular distribution. This sort of strong correlation between direction of approach and product scattering angle has in fact been observed in a model (called the DIPR model 3, which assumes that the repulsion between the products operates along the initial B-C coordinate ; the most favourable case for the application of this model was thought to be that in which the masses of B and C were large compared with A.The question remains whether this is indeed a tenable description of the H+X2 and CH3 +X2 reactions, and, further, whether it is a unique description. has just reported some 3D trajectory calculations for the system D + X2. He concludes (a) that a potential-energy hypersurface that favours nearly lateral approach can readily explain the results obtained for D + 12, but (6) that this explanation cannot at the present time be regarded as entirely ~ n i q u e . ~ In the course of an independent trajectory study (prompted by the Harvard group’s striking experi- mental data, and a continuing interest in the dynamics of these reactions stemming from infra-red chemiluminescence experiments) we have come to conclusions in accord with McDonald’s finding (a).In addition (c) we have examined Carter, Levy and Grice’s proposal that the dynamics of CH3 + I2 be regarded as comparable to H + 12, and have found the analogy to be a valid one. Our lateral-approach hypersurface was made up of two parts; an underlying non-directional LEPS surface (barrier height 23, = 0 for all angles of approach) with a repulsive function superimposed. The repulsion produced a barrier of E, M 10 kcal mol-’ for collinear approach by D from either end of Iz, leaving a narrow lateral channel with negligible energy-barrier.The angle between this lateral channel and the B-C axis could be adjusted. With the angle (having the centre-of-mass of I2 at its apex) set at approx. 40°, the collision energy fixed at T = 10 kcal mol-’, and reagent vibrational plus rotational states Monte Carlo selected from 300 K thermal distri- butions, 1430 trajectories were run in 3D. Of these, 209 reacted to give the differ- ential cross-section shown in fig. l(a). The scattering angle for the molecular product is 180-Oat, hence fig. l(a) shows a differential cross-section for the molecular product peaked a little backward of sideways-in accord with the experimental result. With the mass of the attacking atom increased to 15 a.m.u., in order to simulate CH3, the differential cross-section (fig.l(6)) resembled that for H+12, but with the mean value shifted significantly (though moderately) in a direction corresponding to more-backward scattering of the molecular product. The applicability of the H + I2 surface to the CH3 +I2 problem may, therefore, go even further than Carter, Levy C. F. Carter, M. R. Levy and R. Grice, Paper in this Discussion. K. G. Anlauf, P. J. Kuntz, D. H. Maylotte, P. D. Pacey and J. C. Polanyi, Disc. Faradczy SOC., 1967,44,183. P. J. Kuntz, M. H. Mok and J. C. Polanyi, J. Chem. Phys., 1969, 50,4623. J. D. McDonald, Previous comment in this Discussion. This latter conclusion is in accord with recent work by Anderson and Kung who observed sideways-peaked scattering from a virtually isotropic LEPS potential-energy surface ; J.B. Anderson and R. T. V. Kung, J. Chem. Phys., 1973,58,2477. The initial direction of approach of A defines the forward direction. McDonald374 GENERAL DISCUSSION and Grice suggested, since the H+I, (lateral-approach) surface is able to account not only for the sideways-peaked scattering but also for the moderate shift toward more- backward scattering for CH3 + I, ; i.e., this shift could be a purely kinematic (mass) effect. (The computed backward shift is not as large as that seen experimentally, but this may be connected with the fact that the trajectories were for a higher collision energy, T, than would correspond to the experimental conditions for CH3 +I2 ; enhanced T would shift the mean angle forward).In reality, of course, this kinematic shift may not be the dominant one, since we have neglected all effects due to the chemistry and structure of CH3. 40 - r( I .c) v) N $ - n 8 9 4 20- - W eat Idel2 datldeg FIG. 1 .-Computed differential cross-section versus centre-of-mass scattering angle for the atomic product of the reactions H + 12+HI + I and CH3 + 12+CH31 + I. The inset <elsin O> gives the mean angle for the differential cross-section of the atomic product. Subtract all angles from 180" to obtain the scattering information regarding the molecular product (quoted in the experimental work). Dr. J. C. Whitehead and Dr. R. Grice (Cambridge University) said: Recent laser- induced fluorescence studies of Na,, K2 produced in supersonic nozzle beams show no evidence for dimer vibrational excitation.Taking this to indicate zero vibrational TABLE 1 .-LOWER BOUNDS TO MM' PRODUCT VIBRATIONAL EXCITATION (UNITS kcaI/moI) Na+ Cs2 4 Na+ Rbz 4 Na+& 5 K+ Rbz 3 system Evib excitation of our Cs,, Rb, beams, which is below the estimate from velocity analysis and our K2 beam, which coincides with the lower limit from velocity analysis we obtain lower bounds to the MM' product vibrational excitation Evib as indicated in table 1. These should be compared with the values Evib given in our paper,4 which in the light of ref. (1) are probably overestimates. The lower bounds to Evib corres- M. P. Sinha, A. Schultz and R. N. Zare, J. Chem. Phys., 1973, 58,549. R. J. Gordon, Y. T. Lee and D. R. Herschbach, J.Chem. Phys., 1971, 54,2393. P. B. Foreman, G. M. Kendall and R. Grice, Mol. Phys., 1972,23,117. J. C. Whitehead and R. Grice, this Discussion.GENERAL DISCUSSION 375 pond to vibrational excitation of MM‘ product to -30 % of the bond energy and to -20 % of the total available energy being disposed into product translation. The estimated lifetimes of the M2M’ complexes, based on the RRK formula, would be increased to -3/v for Na+ M2 and to - 1O/v for K+Rb2. Thus our conclusion that the reaction dynamics are direct or at most involve a short-lived complex would be unaltered for Na+M2 but a life-time comparable to the rotational period might be indicated for K + Rb2. Mr. D. A. Dixon, Mr. D. L. King and Prof. D. R. Herschbach (Harvard University) said : The reaction C12 + Br2+2BrC1 is one of several interhalogen systems for which rate studies have offered evidence (tentative because of possible catalysis by moisture or surfaces) for a four-centre mechanism with a relatively low activation energy, 15-20 kcal/mol.’ According to a molecular orbital correlation diagram given by Hoffmann,2 a much larger activation barrier is expected, comparable to the promotion energy of two electrons from bonding to antibonding orbitals and thus above the I I I I I x4-x x i x Y-fY Y I Y x2+y2 - ---+-- 2 - -+f+--e-xY +XY I 1 2 1 2 w- r A A A A r-0- * * * a 2+ or A S r*+ IT* r*- fl* n*+ fl* v“-* .i.l”+ n* 7f-ff sy+ n ::%! S A s s -- * - w n-rf +‘iy 6- d SA w (r- Q r+ (r s s ..U S S (T+r (b) FIG. 1 .-Correlation diagrams for four-centre halogen molecule exchange reaction proceeding through a square planar transition-state. Symmetry planes are denoted 1 and 2 ; S and A indicate whether an orbital remains unchanged or changes sign on reflection in one of these planes.Case (a) considers only p u and pa* orbitals, (b) includes in-plane components of pn- and pn-* orbitals. The out-of-plane pr and pn* orbitak are omitted as they correlate separately. For simplicity, the diagrams assume maximum transition-state symmetry but the nodal properties which govern the qualitative correlations are similar for other planar, nonlinear geometries. P. Schweitzer and R. M. Noyes, J. Amer. Chem. SOC., 1971, 93, 3561 and work cited therein. R. Hoffmann, J. Chem. Phys., 1968, 49, 3739.376 GENERAL DISCUSSION dissociation energy of the weaker reactant bond.For C1, + Br2 this is r45 kcal/mol. Fig. I(a) shows Hoffmann’s diagram, which considers only the sigma molecular orbitals derived from the valence p orbitals of the halogen atoms. Fig. l(b) is a correlation diagram which includes the pi orbitals and shows that linear combinations of the reactant p a , pn, pn*, and pa* orbitals correlate with product px*, pa*, pa, and pn orbitals, respectively. Diagram (b) likewise predicts the reaction is “ forbidden ” for reactants in the ground electronic state. This results from the upper avoided crossing between the p n and pa* orbitals ; the lower crossing is unimportant since it involves filled orbitals. However, in diagram (a) the product p a orbitals are unfilled whereas in (b) the product pn orbitals are unfilled.A substantially lower activation energy than predicted by (a) is thus indicated by (b) ; for CI,+Br, this energy is perhaps as low as -20-30 kcal/mol. A lowering of the activation energy by vibronic interactions has also been suggested. These considerations encourage further experimectal pursuit of the halogen molecule exchange reaction. In a crossed-beam study of C12 + Br2, we have found no evidence of reaction at collision energies up to about 30 kcal/mol. The experiments employed a “ double nozzle-beam ” arrangement. The nozzle orifice diameter was 0.075 mm for C1, and 0.17 mm for Br,. The Cl, beam was “ seeded ” with helium to obtain high collision energies. In most runs a 5 % C12, 95 % He mixture was used, with total pressure within the nozzle about 1OOOTorr and the nozzle temperature varied up to about 750 K.The Br, nozzle was operated at pressures up to about 900 K. At the highest temperatures, the reactant beams contained less than 0.1 % halogen atoms, whereas the proportion of vibrationally excited molecules was -35 % for C1, and -60 % for Br, (assuming negligible relaxation during the nozzle expansion, in accord with experimental results for other systems). The reactant beams were crossed at go”, with the C12 beam modulated at 70 Hz. The scattering was observed over a 150” range in the plane of the parent beams by monitoring the BrCI+ mass peak. The counting time at each angle was usually 100 s. For the extreme conditions used here, the BrClf background was unusually large, typically -250 counts/s. However, the nominal BrCl+ scattering signals, defined as the difference of readings taken with the Br, beam flag open and closed, were only 0 to 6 -F 3 counts/s. These nominal signals showed only random scatter in replicate runs, with no features attributable to the exchange reaction.From experience with other systems, we estimate the reaction cross section to be less than 0.01 A2. Prof. J. D. McDonald (University of Minois) said : We have performed infra-red chemiluminescence experiments which measure the distribution of energy among the vibrational modes of the products of unimolecular reactions. These experiments are made possible by a new apparatus consisting of a large reaction chamber, 30 cm x 30 cm x 130 cm, a DigiLab FTS-14 infra-red Fourier transform spectrometer, and a mercury doped germanium detector.The entire apparatus (including optics) is cooled to 85 K or lower. The wavelength range is 2-14 pm. The product vinyl fluoride from the reaction F+CH,CHX where X is C1 or Br was found to have a distribution of energy among its vibrational modes which closely approximates (within - 15 %) the distribution calculated assuming a random final state distribution. There was no significant emission from the C-H stretching modes of the vinyl fluoride; the calculated value is too small to be observed. The experiments were performed at pressures sufficiently low ( N Tom) that vibrational relaxationshould be negligible compared to product removal on the 77 K walls of the apparatus. T. F. George and J.Ross, J, Chem. Phys., 1971,55,3851.GENERAL DISCUSSION 377 Fluorine atoms were produced either by microwave discharge in CF, (F atoms at 300 K) or thermal dissociation of F2 (F atoms at 1100 K). The resultant product distributions were the same at the two temperatures. We have also observed a uni- molecular intermediate, cyclooctanone, containing > 100 kcal/mol of energy above its ground state, formed by addition of O(3P) atoms to cyclooctene, which lives long enough (> The ratio of infra-red intensi- ties of the C-0 stretch and the sum of all C-H stretches agrees with calculations assuming a random state distribution. s) to travel into ow observation zone. Mr. J. T. Cheung, Prof. J. D. McDonald and Prof. D. R. Herschbach (Harvard University) said : We have studied several reactions of chlorine atoms with olefins and find examples of both statistical and nonstatistical behaviour.The intermediate chloroalkyl radicals formed in these reactions are vibrationally excited by -29 kcal mol-l, the sum of the initial collision energy, the loss in bond strength in converting from C=C to C-C (- 57 kcal mol-I) and the gain in forming the new C-Cl bond (- 80 kcal mol-l). For unsubstituted olefins, the excited radical can decay only be re-emission of the C1 atom, whereas for bromo-olefins it can also release the Br atom with substantial exoergicity, about 13 kcal mol-'. Fig. 1 shows product translational energy distributions (derived from velocity analysis data) for three such reactions which appear to be statistical : Cl+ CH,=CHBr+CH,=CHCl+Br (4 Cl+ CH3CH-CHBr+CH,CH-CHCl +Br (b) C1+ CH,-CBrCH,+CH,-CClCH, + Br (4 C1+ CH2=CHCH2Br-+ClCH,CH=CH, + Br. (4 These reactions all have large cross sections, -20-35 A.The product angular distribution (c.m. system) shows at least approximately symmetrical forward-back- ward peaking for reactions (a), (b), and (c) whereas the forward peak is more pro- nounced for reaction (4, by a factor of -3. The translational energy distributions for (a), (b), (c) are seen to agree well with those predicted by the simple statistical model discussed in the Introductory Lecture and in the Four-Centre Paper. This model is designated by the rather awkward label " RRKM +AM ", since it involves compounding the radial energy distribution in the Rice-Ramsberger-KasseI-Marcus transition-state with the centrifugal angular momentum of the departing product molecules.' The curves shown in fig.1 were calculated assuming an r6 attraction in the centrifugal barrier region (rn = 3), with no exit potential barrier. A " tight " transition-state was used, but the results differ only slightly for a " loose " one. The distributions obtained using the usual approxi- mate quantum energy level density and assuming all degrees of freedom to be " act- ive " (dotted curves) are nearly the same as distributions calculated using the classical level density and neglecting the hydrogen atoms (dashed curves). Thus, even for a model based on energy randomization in the transition-state, the quantum weighting makes the light H atoms " statistically inactive ".Reaction (a) hence is practically equivalent to the classical four-atom case (n = 4 9 , and reactions (b) and (c) to the classical five-atom case (n = 73). S. A. Safron, N. D. Weinstein, D. R. Herschbach and J. C. Tully, Chem. Phys. Letters, 1972.12, 564. G. 2. Whitten and B. S. Rabinovitch, J. Chem. Phys., 1963, 38, 2466. and one which is markedly nonstatistical :378 GENERAL DISCUSSION The translational energy distribution for reaction ( d ) is displaced upwards relative to that predicted by the statistical model. This can be attributed to the short lifetime of the collision complex, its revealed by the asymmetry of the angular distribution. The translational energy release corresponds to that expected for a classical complex with only three heavy atoms (n = 4) rather than five.I I ' I I I I I I 1 - "\J Br+ CI - Tc'+ Br 0 5 10 15 0 5 10 15 translational energy E'/(kcal/mol) FIG. 1 .-Distributions of product relative translational energy in reactions of chlorine atoms with olefins : (a) vinyl bromide, (b) 1-bromopropene, (c) 2-bromopropene and (d) ally1 bromide. Full curves from experimental data; other curves from the " RRKM+AM" statistical model for a " tight " complex : dotted curves calculated using quantum level density and including all atoms ; dashed curves calculated using classical level density but neglecting H atoms. For (d) curves are also shown for the classical model assuming only four (+) or three (A) rather than five heavy atoms (carbon or halogen) participate in intramolecular energy exchange.According to the statistical model, the anisotropy of the product angular distri- bution is governed primarily by the moment of inertia of the transition-state complex about its dissociation axis. For these reactions, the anisotropy essentially provides a measure of the root-mean-square distance of the C atoms from a line between the C1 and Br atoms. The observed anisotropy for (a), (b), (c) indicates that in the transition- state both the C1 and Br atoms are attached to the same carbon atom. This implies that the product chloro-olefin has the Cl atom attached to the C atom to which Br was originally bonded (in contrast to the usual rule which has C1 added to the less substituted C atom). For (b) and (c) this inference was verified experimentally.We found that isomeric chloro-olefin molecules can be distinguished by comparing the variations in intensity of several fragment ion mass peaks as the electron bombardment voltage is varied. This technique showed that (b), the 1-bromo-propene reaction, W- B. Miller. S. A. Safron and D. R. Herschbach. Disc. Faraahv Sm.- 1967- 44. 108 : .T. C'hprn-GENERAL DISCUSSION 379 forms elclusively 1-chloropropene whereas (c), the 2-bromopropene reaction, forms exclusively 2-chloropropene. The " RRKM+AM " model is much simpler to use than phase space theory and displays explicitly the functional dependence of the product distributions. Par- ticularly for large molecules, the results obtained are practically the same. Fig. 2 illustrates this for the F + isobutene reaction studied by Parson, Shobatake, Lee, and Rice.Two sets of curves are shown, one corresponding to the classical 5-atom case, the other to the 4-atom case. I I I I I E'lkcal mol-' FIG. 2.Distribution.s of product relative translational energy for the F + isobutene reaction as calculated for various models. A 6 kcal mol-' exit potential barrier is assumed. The phase space results are from fig. 8 of the paper by Parson, Shobatake, Lee, and Rice. 0, phase space all atoms ; x , RRKM +AM, loose complex with quantum counting ; 0, RRKM + AM, tight complex with quantum counting; - . -, phase space 4 atoms ; A, RRKM+AM, 4 atom tight complex classical. Prof. R. A. Marcus (University of IZZinois) said: I should like to comment on the interpretation of these beautiful experimental results of Lee and his collaborators.The spiked-curves in fig. 6 and 8 (and in other papers) and termed RRKM are mis- labelled. RRKM only describes the distribution of states in the activated complex region, not in the products region. To test RRKM one really needs instead measurements, direct or indirect, of lifetimes of energetic molecules. However, if one introduces some added assump- tions, one can use RRKM to make predictions of the type in fig. 6 and 8. When these added assumptions are wrong, as they surely are in the curve of Lee et al., since the latter ignores exit channel effects on the translational state distribution, the resulting theoretical curve will be wrong. These interactions change considerably the shape of the theoretical plot in fig.6 and 8. an example of an " added ap- proximation" which does not ignore exit channel interactions. Only when the In this connection I have discussed elsewhere R. A. Marcus, J. Chem. Phys., 1966,45, 2630.380 GENERAL DISCUSSION activated complex is truly “ loose ” are such interactions negligible. When, instead, the step from activated products to products’ is energetically downhill, i.e., when the reverse step has an activation energy, the activated complex is typically at least “ semi-rigid ”, and so exit channel interactions occur. (More precisely, the relation in ref. (I) was given for the reverse reaction, but one can use microscopic reversibility.) I should like to endorse thoroughly the remarks of Herschbach in this connection. When all is said and done, namely when the errors in fig.6 and 8 are corrected, one suspects that indeed only a subset of the vibrational modes may be active, perhaps for reasons indicated in my response to one of Rice’s questions. However, one has to distinguish between what has been proven experimentally and what is more con- j ect ural. Dr. J. M. Parson, Dr. K. Shobatake, Prof. Y. T. Lee and Prof. S . A. Rice (University of Chicago) said : In the past, calculations of rate constants for unimolecular reactions based on RRKM theory have almost universally adopted one dimensional reaction coordinates. While it is obvious that it is necessary to conserve angular momentum in the reaction process, it is only recently that attention has been paid to this point in the theoretical analyses.The sharply pointed distributions in fig. 6 and 8 of our paper result from calculations based on RRKM theory with the additional assump- tions that the reaction coordinate is one dimensional a d the barrier height has the value which gives a best-fit to our angular distribution data. We are quite aware that the unrealistic spike in the theoretical recurrent energy distribution is a result of the assumed one dimensional reaction coordinate and is not, per se, a failure of the energy randomization hypothesis. Our conclusions relevant to the adequacy of the energy randomization hypothesis are actually dependent on comparisons between experiment and calculations based upon the more realistic statistical phase space theory. We agree, as pointed out by Herschbach, that if conservation of angular momentum is added to the canonical RRKM theory the predictions will be very close to those of the phase space theory.In that sense, it is perhaps more appropriate to refer to the curve we have labelled phase space theory as RRKM theory. Of course, the matter of labelling is not the heart of the problem. We are aware, and we agree with those who also comment, that the recoil energy distribution of product molecules does not directly test RRKM theory, but rather that additional assumptions must be tacked on to that theory if a recoil energy distribution is to be predicted. Clearly, if the additional assumptions were unrealistic the pre- dicted distributions will be of questionable value. In the reaction of F+C2H4 to form C2H3F, there is a barrier in the exit channel which was detehned from the translational energy distribution of product molecules to be about 1 kcal/mol. The important question is how this 1 kcal/mol of potential energy will be distributed amongst the various degrees of freedom of the product molecules and how, during the process of product separation, the translational and internal degrees of freedom are coupled.These questions can not be answered in general but for a system like F + C2H4 there is an extreme asymmetry in the product masses so that the potential energy associated with the barrier should go almost entirely into translational motion. Our conclusion that the reaction complex has a non-statistical energy distribution is based on the assumption that when a light particle leaves the complex the exit channel interaction will not greatly modify what can be deduced about the distribution of states in the activated complex.Clearly, this assumption will not be valid for the case that a heavy particle leaves the reaction complex, or that a complicated particle R. A. Marcus, J. Chem. Phys., 1966,45,2630.GENERAL DISCUSSION 38 1 with internal degrees of freedom leaves the reaction complex. On the other hand for the particular case of H atom emission, the combination of small exit channel barrier and small mass lead us to believe that the deduction of the distribution of energy in the reaction complex can be quite realistic. Prof. R. A. Marcus (University of Illinois) said: The comments of Parson et al. indicate a misunderstanding of activated complex theory's and RRKM's aims and methods; perhaps it would be helpful to recall the latter.The aim of ACT and RRKM theory is to calculate a rate constant k, or a specific dissociation rate constant kEJ. Because of the quasi-equilibrium assumption, one needs to solve for such a purpose only the dynamics over an infinitesimal interval (st, sS + ds) of the reaction coordinate s ; the resulting dynamical problem is of course trivial. When in addition to calculating rates one wishes to obtain detailed information on final state distribution of reaction products, which ACT and RRKM do not try to do, one needs to solve the dynamics over a large s-interval, from sx to s = CQ. Only in the case of the loose activated complex can they be solved readily ; the result has been given in an excellent paper by Herschbach and coworkers.' When the activated complex is loose, RRKM and phase space theory become similar. To adapt RRKM one could use the statistical-dynamical treatment, which I mentioned earlier, for connecting states at Is1 = 00 with those at s = s#, or employ some other method.The problem is not solely one of disposal of some translational energy via some one- dimensional vibrational-translational mechanism. One has a coupled translational- vibrational-rotational or orbital problem which can be handled by a statistical- dynamical or other approach. When it is not loose, phase space theory no longer applies. Mr. C. F. Carter, Mr. M. R. Levy, Dr. K. B. Woodall and Dr. R. Grice (Cambridge University) said : We are seeking to extend the theory of the reactions 2-4 of atoms and radicals with halogen molecules by studying fluorine atom and oxygen atom reactions.The F atom and 0 atom beams were produced, in the molecular beam apparatus described previ~usly,~ by a microwave discharge source operating at N 0.5 Torr with CF4 and O2 gases respectively. As examples, angular distribution measurements of reactive scattering are shown for F + I2 in fig. 1, and 0 + I2 in fig. 2. The molecular orbital theory for F+XY, while formally similar to that of the halogen atom reaction Y +XY, as indicated in fig. 9 of ref. (4), may still involve considerable asymmetry due to the very electronegative F atom. Particularly for F+12 with 21 valence electrons in the configuration the 3a* orbital may be significantly F-I bonding and 1-1 antibonding, as in the H, CH, +XY Thus, a greater degree of repulsive energy release might be anticipated for F + I2 compared with the C1+ I2 stripping reaction ' 1 6and the Br + I2 reaction 6 * FII(la)2(2a)2( ln)4(2n)4(3n*)4(3a*) (1) which involves a short-lived complex.S. A. Safron, N. D, Weinstein and D. R. Herschbach, Chem. Phys. Letters, 1972, 12, 564. D. R. Herschbach, Conf. on Potential Energy Surfaces in Chemistry, W. A. Lester, ed., Santa Cruz, 1970, 44. J. D. McDonald, P. R. LeBreton, Y. T. Lee and D. R. Herschbach, J. Chem. Phys., 1972, 56, 769. C. F. Carter, M. R. Levy and R. Grice, this Discussion. Y. T. Lee, P. R. LeBreton, J. D. McDonald and D. R. Herschbach, J. Chem. Phys., 1969,51, 455 ; J. B. Cross and N.C. Blais, J. Chem. Phys., 1971,55,3970. H. J. Loesch and D. Beck, Ber. Bunse.ilges. phys. Chem., 1971, 75, 736. 2447. ' Y. T. Lee, J. D. McDonald, P. R. LeBreton and D. R. Herschbach, J. Chem. Phys., 1968, 49,382 GENERAL DISCUSSION 0 \@ A 90' 1; 0" laboratory scattering angle 0 EL30.4 t I lo3 ni s-' FIG. 1 .-Laboratory angular distribution (number density) of reactivity scattered F1 from F-t 12. n B I . ._ x 0.0 0' 30' 60' 90- 120' laboratory scattering angle 0 t 1 lo3 ni s-' FIG. 2.-Laboratory angular distribution (number density) of reactivity scattered 0 1 from 0 + 12.GENERAL DISCUSSION 383 Preliminary kinematic analysis of the angular distribution data of fig. 1 indicates intensity of reactive scattering over a broad range from sideways to backward scattering.Although velocity analysis measurements are in progress to characterise the differential cross section more precisely, the angular distribution data are in clear contrast with the sharp forward peaking of C1+12.2* The molecular orbital theory for O+XY offers a 20 electron system formally comparable with F+XY, though the electronegativity of 0 is less than that of F, comparable with C1. Moreover, the triplet ground state oxygen atom O(3P) with a singlet halogen molecule XY('C) correlates with the lowest triplet potential surface. For O+I, this has the configuration OII( I o)*(20)~( 17~)~(27~)~(37~*)~(3o*) (2) which places an electron in the 30* orbital and suggests a surface involving sufficient repulsive energy release at least to give direct dynamics, as in Cl+I,.However, a singlet potential surface, with the configuration OII( 10)~(20)~( 1 7~)~(271)~(3n*)~ (3) lies lower in energy than the triplet surface. Since the 3 8 orbital is unoccupied this should be a highly attractive surface with a potential well at small internuclear dist- ance ; indeed, OCI,, OBr, are chemically stable molecules in this electronic state. of the 0 + 1 2 angular distribution of fig. 2, shows it to be consistent with a product translational energy distribution peaking at low energy, E'wO.1 kcal mol-', with a long tail extending to higher energy and appropriate to a long-lived comple~.~ The data for 0 + I, are consistent with an angular distribution symmetric about 0 = 90°, but velocity analysis measurements are in progress to confirm this.for O+Br, are also con- sistent with a long-lived cornple~.~ Hence, the O+Br, data agree with the more sophisticated velocity analysis measurements of Herschbach.6 Thus it appears that the O+Br,, I, reactions may undergo a transition from the initial triplet surface to the lower singlet surface. However, our measurements for O+ICl, where 0 1 is the predominant reaction product, preclude a transition to the singlet surface in this case, since OCl would then have been the preferred reaction product (see the comment by Dixon, Parrish and Herschbach). Kinematic analysis Our angular distribution measurements Dr. Y. C. Wong and Prof. Y. T. Lee (University of Chicago) said: We are quite interested in the report of Grice et al. on the F+12 reaction, since we also carried out experiments on this reaction some time ago.Our experiment was performed under somewhat different conditions ; F atoms were produced by thermal dissociation of F2 in a nickel oven rather than by microwave discharge, resulting in a slightly higher collision energy in our experiment. In contrast to a thermally distributed F beam used by Grice et a!., in our experiment the velocity of faster fluorine atoms was selected by a slotted disc velocity selector with full width A full account of this work will be submitted to Mol Phys. Measurements have also, been made on F+Ir by Y . T. Lee (private communication). Y. T. Lee, J. D. McDonald, P. R. LeBreton and D. R. Herschbach, J. Chent. Phys., 1969, 51, 465; J. B. Cross and N. C. Blais, J. Chern. Phys., 1671, 55, 3970.H. J. Loesch and D. Beck, Ber. Bimsenges. phys. Chem. 1971, 75, 736. F. A. Cotton and G . Wilkinson, Adiwnced hiorganic Chemistry (Wiley Interscience, N.Y. 1962). S. A. Safron, N. D. Weinstein, D. R. Herschbach and J. C. Tully, Chem. Phys. Letters, 1972, 12, 563. D. R. Herschbach, this Discussion, Introductory Lecture.384 I I I I I I I F + I i - IF t I ' I I I - - GENERAL DISCUSSION laboratory scattering angle, 0 FIG. 1.-Laboratory angular distribution of IF from F+12. E I E total E'/kcal mol-' FIG. 2.-Centre-of-mass angular and energy distributions which give best fit to the data shown in fig. 1.GENERAL DISCUSSION 385 half maximum of 20 %. Consequently, our experimental conditions are much better defined. The laboratory angular distribution of IF is shown in fig.1 and the best fit centre of mass energy and angular distributions for the data shown in fig. 1 are presented in fig. 2. These results are in contradiction with what has been concluded in the preliminary kinematic analysis of Grice et al. The angular distribution of IF in our experiment is nearly isotropic, with a mild forward peak somewhat more pronounced than the backward peak ; this result contrasts with the distribution of a broad range from sideways to backward as Grice et al. stated. The energy distribution of product molecules indicates that most of the exoergicity should be in vibrational motion of IF, unless a significant amount of I*(2P+) is formed in this reaction. The average translational energy is only about 15 % of the total energy available.This conclusion also does not substantiate Grice et al.'s anticipation from a simple molecular orbital consideration that a greater degree of repulsive energy release should be observed for F + I2 compared with the C1+ I2 and Br + I2 reactions. One should be extremely cautious in the interpretation of angular distributions from a " primitive experiment " in which both beams have thermal velocity distri- butions, since both cross sections and angular distributions might depend on relative velocities of reactants, rather strongly in many reactions. Thus the conclusions derived could be quite erroneous except for some favourable cases. The only experiments which will give unambiguous results are those experiments in which both beams are velocity selected and the product velocities are also analyzed.Mr. C. F. Carter, Mr. M. R. Levy, Dr. K. B. Woodall and Dr. R. Grice (Cambridge University) said : We are very interested in the report of Wong and Lee on the F+I, reaction. The centre of mass angular and velocity distributions fitted to their laboratory angular distribution data, at initial translational energy E = 1.93 kcal mol-l, have been compared with our laboratory angular distribution data at lower initial translation energy, E-0.7 kcal mol-l. Agreement could not be obtained by including any " reasonable " dependence of the total reaction cross section on the initial velocity of F atoms. Indeed, matching to our data with the centre of mass angular distribution of Wong and Lee necessitates a product translational energy distribution displaced to significantly lower energy (peaking at E'N 1 kcal mol-') for scattering in the forward hemisphere.Thus the F+12 reactive scattering appears to depend appreciably on initial translational energy in this energy range. Simple molecular orbital theory does not give an unequivocal prediction of the energy disposal. The repulsive energy release fostered by the 3a* orbital will be offset by increased charge transfer interaction in F + 12, which enhances attractive energy release. The kinematic analysis of our data indicated that the product translational energy distribution peaks below E' = 5 kcal mol-I (or < 15 %) in accord with the conclusions of Wong and Lee. Mr. D. A. Dixon, Dr. D. D. Parrish, and Prof. D. R. Herschbach (Harvard Univer- sity) said: We have also been interested in the possibility of transitions between triplet and singlet potential surfaces in reactions involving oxygen atoms.This question was posed by results for the reaction Ba('S,)+ 02(3C;) + BaO('Z)+O(3P,). The reaction is exoergic by -20 kcal mol-' but proceeds via a long-lived complex even at collision energies of - 18 kcal mol-I.' If the long-lifetime is attributed to an H. J. Loesch and D. R. Herschbach, J. Chern. Phys., 1973 (to be published). 55-N386 GENERAL DISCUSSION attractive basin in the potential surface, as usual, the dissociation energy of the BaO, complex inferred from unimolecular decay theory is quite large, 5 150 kcal mol-' with respect to the reactants. There is infra-red spectroscopic evidence for an ionically bound Ba+O; molecule.' The bond strength is unknown, but empirical correlations suggest values in the range 100-150 kcal mol-I.The spectra indicate a strongly bent molecule, with C,,, symmetry. The usual molecular orbital description thus predicts a singlet ground state, since the number of electrons is even and a bent triatomic molecule has nondegenerate orbitals. However, the reactants approach and the products depart on a triplet potential surface. This suggests that the reaction may involve switching from the initial triplet surface into the singlet basin and then back to the final triplet surface. The long complex lifetime might depend largely on those switches rather than the depth of the basin. On the other hand, a triplet ground state for Ba+O; cannot be ruled out.The electron-jump gives a triplet configuration, Ba(t4) + O,(tt)+Ba+(t)O;(lff). The elementary molecular orbital procedure is not reliable when comparing singlet and triplet states.2 For example, CH, is a strongly bent molecule but has a triplet ground state which corresponds to an excited molecular orbital c~nfiguration.~ For BaO, the question may be resolved by an e.s.r. matrix isolation e~periment.~ A similar situation obtains for the reaction O(3Pg)+BrZ(1Z:) -+ Br0(211)+Br(2P,). As discussed in the Introductory Lecture, this again proceeds via a long-lived complex. The reactants approach on a triplet surface, whereas the products can depart on either a singlet or triplet surface. A stable OBr, molecule is known, with C2,, symmetry and probably a singlet ground state.However, two arguments indicate that the surface corresponding to this symmetric OBr, is unlikely to govern the reaction. As in the reactions of hydrogen atoms or halogen atoms with halogen molecules, orbital correlations predict that insertion of the 0 atom into the Br, bond will be inhibited by a substantial energy barrier.5 The " electronegativity ordering rule ", derived from the Walsh scheme and supported by much empirical evidenc~,~ also predicts that O+Br, goes via end-on attack rather than by insertion. According to this rule, the preferred geometry of an XYZ complex has the least electronegative atom in the middle. These considerations suggest that the reaction proceeds predominantly via an 0-Br-Br complex.The analogous 0-C1-Cl molecule has been found. In a matrix isolation study,6 and the isoelectronic (F-Cl-Cl)+ ion is also known.7 An 0-Br-Br complex, even if considerably nonlinear, might well have a triplet ground state. In constructing his diagrams, Walsh emphasized that the a*'-3a* orbital (see fig. 10 of the paper by Carter, Levy, and Grice) might cross the a"-3n* and a's-37F orbitals and lie below them at large bond angles. If so, even the elementary molec- ular orbital analysis predicts a triplet ground state at cc = 180" and in a better approxi- mztion this might well remain the ground state at a- 150". The orbital configuration S. Abramowitz and N. Acquista, J. Res. Nat. Bur. Staid, 1970, 75A, 23. L. C. Allen, in Sigma A4olecular Orbital Theory, 0.Sinanoglu and K. B. Wiberg, eds. (Yale Univcisity Press, New Haven, 1970), p. 227. C. F. Bender, H. F. Schaefer, D. R. Franceschetti and L. C. Allen, J. Amer. Chern. Soc., 1972, 94, 6888. D. M. Lindsay, work in progress, Harvard University. J. D. McDonald, P. R. LeBreton, Y. T. Lee and D. R. Herschbach, J. Chem. Phys., 1972, 56, 769 and papers cited therein. M. M. Rochkind and G. C. Pimentel, J . Cheni. Phys., 1967, 46, 4481. ' R. J. Gillespie and M. J. Morton, Znorg. Chem., 1970, 9, 811.GENERAL DISCUSSION 387 of this triplet state is . . . (30*)~(3n*)~ or . . . (3c~*)~(a’s)(a’’) whereas the singlet discussed by Carter, et al. is . . . (371”)~ or . . . ( a ’ ~ ) ~ ( a ” ) ~ . We have carried out a CNDO-UHF calculation for triplet linear 0-Cl-Cl and indeed find the 30” orbital energy to be about 24 kcal mol-’ below the 3n* orbital.Accordingly, it is at least plausible that O+Br2 goes via a triplet 0-Rr-Br surface. The electronegativity rule suggests some interesting chemical variations. The O+IX reactions, with X = C1 or Br, would be expected to yield primarily IO+X rather than XO + I, although the latter path is much more exoergic. We find IC1 and IBr indeed give I 0 with a large cross section but no detectable C10 or BrO. The 0 + F2 reaction would be expected to prefer the symmetric OF2 geometry rather than 0-F-F, since oxygen is less electronegative than fluorine. Thus, despite the fact that O+F2 is much more exoergic than the other O+halogen reactions, it seems likely to require a relatively large activation energy.Experiments to test this are planned. We have also studied the 0+Cl2 and 0 + 1 2 reactions, although not yet with velocity analysis. For 0 + C1, the angular distribution is compatible with the collision complex mechanism if an activation energy of 3 kcal mol-’ is included, in accord with a flow-tube study., For O+I, the angular distribution is accurately predicted by the same statistical complex model used for the 0 + Br, case. Dr. G. Hunter (York University) (communicated): In the study of molecular dynamics there is an apparent dichotomy between rigorous theory on the one hand, and semi-empirical interpretation of experimental measurements on the other. The interaction potentials inferred from the latter approach tend to be much simpler than those involved in precise theoretical calculations.The work of Bunker and Goring- Simpson on alkali-methyl iodide reactions is a good example of this dichotomous situation. Their results, together with those of other theoretical calculations reported here, support the view that the three methyl hydrogen atoms make no effective contri- bution to the dynamics of the reaction. This conclusion supports the semi-empirical approach. I would like to present a new quantum mechanical idea which resolves this appar- ent dichotomy. To be explicit, let us consider alkali-methyl iodide collisions. First of all for simplicity consider elastic collisions. Denote the reaction co-ordinate (alkali atom-methyl iodide distance) by R, and the remaining co-ordinates (all electronic plus rotational and vibrational within the CHJ molecule) by r.We assume that the scattering angle 8 has been separated out. Then the idea is that the total wave function for a particular angular momentum state Y l ( R , r ) may rigorously be expressed as a product of an unbound (scattering) radial wave functionfi(R), and another function $(r, R) such that V(R) = (4IHl4)r is the potential function for the scattering process. H is the total internal hamiltonian (with the 8 dependence replaced by 1(1+ 1)/2pR2 iiiclzrding the kinetic energy operator associated with R. The subscript r on the expectation value (41H14)r denotes integration over the coordinates Y. In statistical terms +(r, R) is interpreted as a conditional probability amplitude. It is essentially defined variationally by the expectation value ( 41Hl+)r.In the case of an atom-atom collision (A-B), I’ would simply be the set of electronic co-ordinates, so that 4(r, R) is the electronic wave function, and V(R) is the adiabatic Born-Oppenheimer potential for the corresponding electronic state of the diatomic Subsequently, we have learned of flow tube studies in which O+F2 gave no detectable reaction under conditions where O+Br2 gave a very large yield. See M. Kaufman and C. E. Kolb Chem. Znstr., 1971, 3, 175. M. A. A. Clyne and J. A. Coxon, Trans. Faruday SOC., 1966, 62, 2175.388 GENERAL DISCUSSION molecule A-B. +(r, R) and Y(R) would actually differ slightly from the usually defined electronic wave function and adiabatic potential in so far as (+IHl+)r is the expectation value of the total internal hamiltonian rather than just the electronic hamiltonian. In the alkali-methyl iodide case V(R) is obtained by additionally integrating over the rotational and vibrational coordinates of CH31.Thus in this case V(R) involves an appropriately weighted average over all of the possible orientations and phases of the CH31 internal motion. For an experiment involving oriented molecules, such as that reported by Brooks, the orienting external field would have to be included in the hamiltonian H in order to calculate the appropriate radial potential V(R). For a particular exit channel there will be a corresponding internal state +‘(I-, R) and a potential V’(R) = (+‘IHl+’)r. The whole scattering process (into one exit channel) is thus describable in terms of two radial potentials V(R) and V’(R). The incoming and outgoing channels are connected by the uniqueness of the total wave function : that is f(R)+(r, R) =f’(R)+’(r, R) for values of the coordinates where V(R)= V‘(R). In the absence of electronic excitation this matching procedure would be virtually independent of the electronic coordinates in r. The further extension to reactive collisions is simply that the reaction (radial) coordinate in the exit channel is R’ (different from R), so that the internal coordinates of the resulting fragments (r’) are not all the same as those in the incoming channel. The radial potential for the exit channel is in this case V‘(R’) = (+’IHl$’)rp. As for inelastic collisions there is a matching condition f ( R ) 4 ( r , R) = f’(R’)+’(r’, R’) in the reaction zone. If the reaction produces three rather than two fragments, then R’ represents the relative coordinates (two distances and an angle) of the separating fragments, so that V’(R’) is a surface rather than a radial potential. The importance of this theoretical idea is that it shows that all two-body collision processes (the bodies being atoms or molecules) are describable in terms of one or tow radial potentials V(R) and V’(R’) : it really isn’t necessary to consider the dynamics of all of the atomic nuclei on a multi-dimensional potential energy surface. This will considerably simplify classical trajectory calculations as well as quantum mech- anical methods. Ab initio calculation of the radial potentials V(R), V’(R’) is of course a formidable problem : some kind of super Hartree-Fock procedure is indi- cated. On the other hand, determination of these potentials semi-empirically from experimental data is now seen to be a theoretically sound procedure. The description of collisions in terms of potential profiles (presented by Prof. Polanyi in his Concluding Remarks) is also placed on a sound theoretical basis by this theory : the profiles are to be interpreted as the potentials V(R), V’(R’) defined above, rather than as sections through the multi-dimensional potential energy surface. Thus this theory unites the semi-empirical approach (notably propounded by Herschbach during this meeting) with the rigorous approach of the pure theoretician. The formal aspects of this theory will be presented for publication in the near future. The extension to inelastic scattering is fairly straightforward.

ISSN:0301-7249    

DOI:10.1039/DC9735500369

出版商:RSC    

年代:1973

数据来源: RSC

摘要:

MOLECULAR BEAM SCATTERING * BY J. C. POLANYI Department of Chemistry, University of Toronto, Toronto M5S 1Al Receit-ed 13th June, 1973 Surprisingly, this has been the first general discussion that our Division has held on the topic of molecular beam scattering. In fact, of course, the past days have not been restricted to a discussion of that technique. Molecular beams, when they are not an end to one's means, are a means to an end. Rather than make the molecular beam method our topic, we have centred our discussion on the phenomena that this remarkable technique has made accessible. As a consequence, this meeting has been the intellectual heir to the General Discussion on the " Molecular Dynamics of Chemical Reactions of Gases " held five years ago in Toronto. That Discussion, in its turn, was the successor to the General Discussion on the " Inelastic Collisions of Atoms and Simple Molecules " that took place five years prior to that, in Cambridge.[I have traced our indebted- ness to still earlier Discussions previously and shall have occasion to refer to it again]. The present Discussion has encompassed the topics of these two earlier ones-and more. If one could have said it in a single breath, it would have been entitled a General Discussion on the Elastic, Inelastic and Reactive Scattering of Atoms and Molecules in Gases. Following tradition we began with a session devoted to theory. This has come to take the place of an opening prayer ; a prayer for understanding. We then passed on, rather briskly, from the sublime to the experimental. The experiments were ordered into a hierarchy of ascending complexity. First, elastic scattering in which only translation suffered change, then inelastic scattering in which one form of motion was transposed into another, and finally reactive scattering in which there was transfer not only of motion but also of mass.ELASTIC, INELASTIC AND REACTIVE SCATTERING Let me start by summarizing, very briefly indeed, how things seem to stand in each of the sub-areas into which our discussion has been divided : elastic, inelastic and reactive scattering (see tables 1, 2 and 3, respectively). The fundamental objective in each area is the same, namely to improve our understanding of the interatomic forces. In the case of elastic scattering the inter- atomic potential U(r) (whose slope gives the force) has a form which is now fairly well understood. The constants which govern the potential in its various formulations include E and r,; respectively the depth and location of the long-range attractive potential-well arising from the London dispersion forces.It is encouraging that, at least for pairs of atoms, the magnitudes of these physical quantities are quite weakly " model-dependent ".2s 39 It is only in the realm of elastic scattering that we are able to make this sort of claim. * Summarizing Remarks. 389390 MOLECULAR BEAM SCATTERING Elastic scattering is the most highly-developed of the three fields in which beam scattering studies are made. This is, of course, because the large cross-sections for elastic scattering make the detection of scattered particles easier than for most inelastic or reactive processes. To say that it is easier, is not to say that it is easy.For example it has only recently become possible to obtain sophisticated elastic scattering data for labile collision partners (atomic hydrogen and electronically-excited atomic TABLE 1 .-ELASTIC SCA~ERING Considilrable data. Wide range of collision energies ; 10-2-10 53 eV. Form of U(r) (rot. av’d) known. r, and E only weakly dependent on form of U(r). Know rm to 0.01-0.1 A. Know E to 0.01-0.1 eV. Need studies of anisotropy of A+ BC. Need studies for labile partners. TABLE z.-INELASTIC SCATTERING Few scattering studies ; field opming up. Current approx. data include : T-R, T t , V, T-+Dissocn., Collision-energies 0.1-100 eV.Anisotropy of U(r, 0) important. Aligned studies needed. Configuration-space somewhat more limited than for reaction, hence theoretical problems sometimes less severe. T+R-,V, V-+E,T-+E. TABLE 3.-REACTIVE SCATTERING Numerous studies. Much scope for extension and sophistication. Considerable final-state selection (energies and angles). Increasing initial-state selection (energies and angles). Collision-energies (neutrals) 0.1-10 eV. Less-sophisticated experiments restricted to 02 1 A’. Moresophisticated experiments restricted to 02 10 A’. Qualitative features of hypersurfaces emerging : barrier-locations, regions of max. energy-rise or -fall, potential-wells, surface-crossings. Quantitative features derived, but with questionable uniqueness.mercury 4, ; there is scope for more development of elastic scattering studies in this direction (Otto Stern would have been surprised ; his disciples were doing magnetic moment studies on beams of atomic H and 0 in the late 1920’s. Things get harder once it becomes necessary to scatter one beam off another, in order to define collision energies and scattering angles). A development that is (so far as I know) still awaited, though it is within the reach of present day technology, is elastic scattering in which one of the collision partners is an oriented molecule, for example a dipolar molecule partially aligned in an electric field (cf. ref. ( 5 ) and (6)). The case of molecular hydrogen which we have heardSUMMARIZING REMARKS 39 1 discussed at this meeting is, as the authors note, likely to be exceptional in presenting a very isotropic interaction potential for elastic scattering.' The phenomena encompassed by elastic scattering occur at energies up to and beyond the threshold energy at which inelastic scattering sets in.The study of in- elastic collisions by means of molecular beams is in one sense a well-established tech- nique. It has what in this field is a venerable history, extending back 8 years.' An impressive list of energy-transfer phenomena have been observed (in table 1, T, R, V and E symbolize translational, rotational, vibrational and electronic energies). Nonetheless it seems fair to say that we know rather little in detail about any of these phenomena. Few people have, until now, chosen to work in a field in which even the simpler problems tend to raise experimental difficulties on the level of a rather sophisti- cated reactive-scattering experiment.Inelastic scattering experiments require energy-selection of the collision partners (i.e., some knowledge of T, R, V or E ) as well as energy-selection of the scattered " products ", since the objective is to measure 6T, 6R, 6 V or 6E. To be of real value 6T, 6R, 6 V or 6E should be measured over a range of T, R, Vor E. These difficult experimental problems are now beginning to find solutions. New developments reported in the course of this Discussion include reports of limited but encouraging successes with the measurement of rotational excitation in ion-molecule collisions,* vibrational deactivation in triple-beam experiment^,^^ and also rotational and vibrational excitation in energetic neutral-neutral collisions (the first two results were based on time-of-flight analysis, the last on infra-red emission).The inversion of inelastic scattering data to obtain the form of the potential in the relevant region of configuration-space is a problem that is only beginning to be tack- led.' The degree of success will no doubt be high so long as the data is fragmentary or approximate, i.e., the demands being made on the potential-function are modest. What we want, however, are unique solutions. These we may hope to get when the detail in the experimental data becomes somewhat richer than it is today, or the theoretical input from ab initio calculation becomes a good deal greater.(From the latter standpoint, the case of Li-!- + H2 discussed at this meeting looks particularly promi sing). 8 * 41 The anisotropy of U(r) is unquestionably going to be of importance in inelastic scattering. It will determine the torque that produces rotational excitation. It will also figure in descriptions of vibrational excitation, for the same reasons that it is of importance in determining the cross-section for reactive encounters. (A collision that excites internal motion in a molecule is an abortive reactive encounter. In the exceptional case that the collision partners are incapable of forming a new bond, the abortive reaction can only be coilisional dissociation, A + BC-A + B + C. The importance of angle-of-approach in collisional dissociation has been remarked on at this meeting lo).Clearly it would be most valuable to have inelastic scattering data for aligned collision partners. We can expect such experiments before long. Reactive scattering has become an extremely active field in recent years, justifying the optimistic predictions of its devotees. Though the Millenium is not yet upon us, it is in sight. To a limited extent, and for a limited range of reactions, final-state selection of angles (including polarization of the molecular angular momentum with respect to the velocity of the attacking atom ' I ) and energies (translation, vibration and rotation) has been achieved. The laser-induced fluorescence method described at this meeting l2 is a recent and powerful addition to the tools available for measuring product energy-distribution.It has been used for vibrational distribution measure- ments, and should ultimately also be of value in measuring rotational distributions. Following the previous Discussion in this series,' I had the pleasure of announcing the392 MOLECULAR BEAM SCATTERING betrothal of beam scattering to spectroscopy. I can now read the second banns of marriage. If final-state selection is possible then so also, in principle, is initial-state selection. The difficulty is that at this extreme of exclusivity the flux of products is likely to be too small for measurement. For this reason it is exceptional for initial-state and final- state selection to be combined in reactive scattering experiments. We have heard, nonetheless, how initial-state orientation 5* has been selected, and (for the first time) how this information can be incorporated into a classical trajectory study,5* 6* l3 ie., into the search for an acceptable potential-function.We have also heard of attempts to determine the effect on reaction cross-section and product energy distribution of variation in reagent translation 5 * l4 vibration l4 and r0tati0n.l~ As an example of the extreme difficulty of obtaining good data at this high level of detail, it may be noted that for the well-studied reaction K + CH31, which has a reactive cross-section - 35 A2, the differential cross-section and product translational energy-distribution have so far been obtained over a range of reagent collision-energies from 0.077 to 0.16 eV (a range of slightly less than 2 kcal m~l-~).' The total cross-section, by contrast, has been studied over 10 x the energy range ; 0.1-1.0 eV (with most intriguing results).POTENTIAL FUNCTION The potential-energy function for chemical reaction is a hypersurface. Inversion of the experimental data regarding reaction dynamics to obtain the potential-energy hypersurface is a hazardous procedure. However, it seems fair to say that over the past decade there has, for example in the case of the K + CH31 reaction just referred to, " been a steady growth in the reliability of the potential-energy hypersurface that can be extracted from the experimental data. . . ,'.I3 This has been achieved in the main through a series of attempts to isolate the principal features of the hypersurfaces that govern the dynamics, thus greatly reducing the effective number of variables.A most helpful conceptional aid in grappling with the potential-energy surfaces governing chemical reactions was described by M. G. Evans and M. Polanyi at the General Discussion of the Faraday Society on " Reaction Kinetics ", in 1937. (Both Michael Polanyi, and Sir Eric Rideal, whose far-sighted interest in what were then called " Molecular Rays " led to the first textbook on this are in the audience today). The O.E.P. approach (the 0 was R.A. Ogg, who initiated the method in earlier work with M. Polanyi) represents the collinear potential-energy surface by means of a sequence of 2D cuts (for reaction A+BC these would be U(rAB) and u(rBC)). On the collinear potential-energy surface these cuts would be perpendicular to one another.In the O.E.P. representation they are connected in sequence to form a single plot of U(r), for which the abscissa Y changes sequentially from rAB to rBc, then back to rAB, and finally back to rBc. The corresponding route across the collinear energy-surface is shown at the lower left of fig. 1. Reagents A + BC exist at large rAB (symbolized A-B in the figure) ; products are at large rBC. The O.E.P. route across the surface follows the curve of the minimum- energy path only in a rough qualitative way. Its merit is that it decomposes the potential-energy changes along the minimum-energy path into two-body interaction terms. Inspections of the potential-energy " profile " for the reactive case (bottom of fig. 1, central column) shows that the initial potential rise is ascribed to reagent repulsion R, and the residue of the potential-rise en route to the barrier crest is attri- buted to energy expended in stretching the bond under attack, S.In the descent from the barrier-crest the tension in the new bond is first relaxed with energy release S', and subsequently the products separate releasing the repulsive energy R'. The barrier-SUMMARIZING REMARKS 393 crest is characterized by R + S = R' + S'- Q (where Q is the energy released by the reaction). Ogg, Evans and Polanyi used this approach as a means to the crude calculation of barrier-heights or (more commonly) changes in barrier-height. Our present concerns in the field of reaction dynamics go beyond barrier-height to such questions as barrier- location, and the location of the downward-slope representing the release of the P-E SURFACE P-E PROFILES T V I m A-B Ez s" s, A - B j I A-B+ I 1 1 +A-B B-C+ 7 w I a [I N E LAST IC] cm 4 1 I \ I I 1 I I I ' ; I I 1 I .. . t-A-B$ B-C--+ B-c+ &-B IREACTIVE] ,+ L- B-C+ +A-B T w I a 1 W I CL I , . I +A-B B-C- I 1 I +A-B B-C+ FIG. 1 .-Column 1 compares, on a collinear potential-energy surface, the regions of configuration- space explored by elastic, inelastic (T+ V ) and reactive scattering. Column 2 does the same using O.E.P. energy-profiles. Column 3, second row, exemplifies the essential features for inelastic scattering of the type T-tE. Column 3, bottom row [taken from M. H. Mok and J. C. Polanyi, J. Chem. Phys., 1969, 51, 14511 suggests a simplified representation appropriate to a " typical " reaction (exothermic from left to right, endothermic from right to left).reaction energy. We can use the O.E.P. pictures to advantage in these new contexts. Where O.E.P. attempted to reduce their energy-profiles to still simpler representations we can usefully do the same-though in the light of our present understanding of the " typical " energy-surface we should, I think, choose a different reduced-representation from theirs. I shall have occasion to refer to these points in a little more detail, later.394 MOLECULAR BEAM SCATTERING Fig. 1 makes a comparison between the regions of configuration-space which ,we explore in elastic scattering experiments, inelastic scattering and reactive scattering.The comparison is made both in terms of the collinear potential-energy surface for reaction A+BC-+AB+C (column l), and in terms of the corresponding O.E.P. potential-energy profiles (column 2). The diagrams assume that elastic or inelastic scattering, as the case may be, have been studied both in scattering experiments A + BC and also in experiments on AB + C. The figure is intended to underscore the point already made by the organising committee for this Discussion when they drew up the programme, namely that elastic, inelastic and reactive scattering studies are related-not only in experimental approach, but also at a fundamental level. We can look forward to the time when we have studies of reactive, inelastic and elastic scattering for the same system, in sufficient detail that it becomes possible to splice together the portions of the interaction-potential revealed by the individual phenomena.The reactions of alkali metal atoms with alkali dimers, that we have heard discussed, l 6 could be a candidate for such a three-pronged attack. The reaction may be governed by a potential in which the London dispersion-force attraction passes smoothly into the long-range portion of a shallow potential-well that owes its existence to “ chemical ” forces (i.e., to the delocalisation of charge). With one exception, the potential-energy surfaces and profiles in fig. 1 assume that the process can be understood in terms of nuclear motions in the field of a single electronic state. This is a tempting simplification (though we cannot yet be certain how often it is warranted) since the problem of inversion of the scattering data is already so difficult.The undoubted exception (fig. 1, column 3, row 2) is inelastic scattering in which translational motion of the nuclei is converted to electronic excitation; T-+E. If the quantisation of vibronic states were included, this figure would exhibit a large array of curve crossings. Overlap between adjacent crossing regions (due to the operation of the uncertainty principle) could then complicate the interpretation. Fortunately a single-curve-crossing provides an adequate represent- ation for short interaction times. Multiple crossing of a different sort, due to the involvement of three electronic states, is shown at the right of the T+E schematic drawing (fig.1) : R’-R’*++R’**. This sort of process was postulated over 30 years by K. J. Laidler as an explanation for the quenching of atomic sodium (“P-,~S) in collisions with molecular hydrogen. The intermediate state, R’*, in his work, was an ionic state arising out of the transfer of an electron from the alkali metal, M, to the collision partner, BC. The concept has been developed by Nikitin and co-workers, and shows promise of providing a frame- work within which the new details of T+E transfer in M+AB collisions, presented at this meeting,18 can be understood. The remainder of these remarks will be devoted in large part to comments on the topic of reactive scattering in relation to the present Discussion. The phenomenon of reactive scattering, as fig. 1 indicates, embodies the subject matter of inelastic and elastic scattering. Most often the concepts that are familiar to us in the inelastic and elastic scattering regimes are obscured by the dynamical processes peculiar to reaction. However, this is not always the case.In view of the scope of the present Discussion it is particularly interesting to look for cases in which the simpler phenomena are evident within the more complex one. The O.E.P. representation of the energy-changes in chemical reaction as being R-+S-+S’+R’ (central picture, bottom row of fig. 1) is less familiar than is reduction of this sequence to the rudimentary picture of S-+ R’, i.e., a rise in potential due to the stretching of the bond under attack followed by a fall due to repulsion (not shown in 4 *SUMMARIZING REMARKS 395 fig.1 ; for an example see ref. (1)). An alternative reduction, which seems likely to have more general applicability, is indicated in the lower right-hand comer of fig. 1 : R+S’+R’. In the exothermic direction, reagent repulsion is held to be principally responsible for raising the potential-energy to the barrier-crest value. Thereafter, a portion of the product energy, S’, is released as the new bond relaxes to its normal equilibrium separation, and the remainder, R’, is released as the products separate. The quantities S’ and R’ can be approximately identified with the “ attractive ” and the “ repulsive ” components of the energy release ; sQI and 91. 9 @ Jzr ,-4 7 0 Jd *=4 = 4 O/O = 0 O/O = 96 rABlA FIG. 2.-Three exothermic LEPS potential-energy surfaces (reagents at lower right, proLxts at upper left) for collinear rcaction A + BC-tAB + C.The surfaces are arranged vertically in ascending order of “ attractiveness ”. At the left percent attractive energy-release is given according to the “ per- pendicular ” energy-drop measured on the surface. At the right is recorded the percentage attractive, mixed and repulsive energy-release for the L+ HH mass-combination, obtained by the “ trajectory ” method (a single collinear trajectory). Contour energies are in kcal mol-I ; all three reactions have the same exothermicity. (The symbol t denotes a mass of 1 a.m.u., H E 80 a.m.u.). The barrier crest, designated by X, shifts to “ earlier ” locations along ~ A B as the surfaces become more attractive, according to the general expectation for a chemically-related (“ homologous ”) series of reactions.[Surfaces taken from P. J. Kuntz, E. M. Nemeth, J. C. Polanyi, S. D. Rosner and C. E. Young, J. Chem. Pliys., 1966, 44, 11681. Separation of exothermic energy-release into attractive and repulsive components was suggested by the speculations of M. G. Evans and M. Polanyi regarding the dynamics of the sodium-flame reactions M + X2 and X + M1, presented at the General Discussion of the Faraday Society on Luminescence, in 1938. By the time of the 1967 Discussion on the Dynamics of Chemical Reactions, classical trajectory studies (which began to appear in 1962) had revealed some of the strengths and weaknesses of this method of categorization. There is no doubt that the “ attractive ”-“ repulsive ” antithesis is fundamental and revealing.It even seems worthwhile to employ a quantitative index of “ percent attraction ” and “ percent repulsion ”, %d1 and %91, based on a perpendicular measurement on the collinear energy-surface.396 MOLECULAR BEAM SCATTERING Provided a typical trajectory for the system in question does follow a more-or-less perpendicular path across the energy-surface, %dl will correlate with %(I?$), the mean percentage of the total energy-release that appears as product vibration. Fig. 2 shows three collinear potential-energy surfaces, increasing in %dl from surface @ to @ to @. Fig. 3 shows the correlation between %dl and %(I?$) for these three surfaces, and also for a variety of other surfaces.(The computations which yielded the data of fig. 3 were not restricted to collinear reaction; they were performed in 2D. The values of %(E+) would differ by an insignificant amount for 3D). In every case recorded in fig. 3 the mass-combination was L + HH (i.e., atom A was light, and atoms B and C were heavy) and the energy-surface was of the LEPS variety (London, Eyring, Polanyi, Sat0 surfaces, favouring collinear approach). For L + HH the characteristic path across the potential-energy surface is sufficiently rectilinear to result in a strong correlation between %dI and %(Ek) (the droop in the the curve at high %dl, will be discussed later). I R /’ 20 I I I i 20 40 60 80 100 dl, % FIG. 3.-Mean vibrational excitation in the products of L+HH reaction on 8 potential-energy hyper- surfaces, plotted against the (perpendicular) attractive energy-release.(Fall-off in <E+) at high d~ is due to indirect reaction). [P. J. Kuntz, E. M. Nemeth, J. C. Polanyi, S. D. Rosner and C. E. Young, J. Chern. Phys., 1966,44, 11681. Several L + HH reactions have figured in our discussion at this meeting ; H + C12+ HCl+ C1,I4 CH3 +I,+CH31 + 1,’’ F+ 12+F1 +I,43* 44 and Na+ Cs,-+NaCs + Cs.16 The fact that the second of these reactions can be approximated as L + HH (analogous to H + 12+HI +I) has been noted.20 In going from H + C12 to H +I2 or CH3 +I2, there is good reason to suppose that the preferred angle of approach alters from collinear for H+Cl, to bent for H+12 20* 21 and for CH3+12.19* 2o If this is the case then the definition of %dI, and its utility as a measure of %(&) (or more likely, %(E++El;), where EL is product rotational excitation) needs to be investigated for surfaces involving varied direction of approach. This has not yet been done.The case of the L + HH reaction Na + Cs, also involves special features. In the first place,SUMMARIZING REMARKS 397 the exothermicity is minimal, and secondly the dynamics may be dominated by the location of a potential-well.16 It should be noted that the correlation between %.dl and %(E$) illustrated for L+HH in fig. 2 applies in a qualitatively similar fashion to reactions of other mass- combination, provided that the mass-combination does not alter significantly as %.dl is changed. This has figured in the discussion that we have heard of the family of reactions Ba + HX(H + HL), to which more-detailed reference will be made shortly.A correlation that has come to the fore since the Discussion of 1967 is one that can be seen by inspection of the selection of collinear energy-surfaces shown in fig. 2. In chemically-related series of reactions a lower energy-barrier correlates strongly with an “ earlier ” energy-barrier, which in turn correlates with increased percentage attractive energy-release (the series of surfaces (iJ-)@-)@ shows all three effects). If one makes the plausible assumption that there is (even over a restricted region of rAB) parallelism between the energy-profiles for a related series of reactions, then these correlations can be made graphic. In fig. 4 this has been done for an energy-profile that can be regarded as a smoothed version of the R-+S’-)R’ pattern shown at the lower-right of fig.1. If the parallelism between the profiles for reactions 0 and Q, fig. 4, extends into the exit valley of the energy-surface (i.e., along r,,, to the right of the vertical “ equal bond-extension ” line) then there will in addition be the well-known O.E.P. correlation between increased reaction-energy and diminished barrier-height ; - AE = a- AQ.’ However, this is a weaker correlation, hence it is shown as a likely but not necessary condition in fig. 4. Fig. 4(b) makes the point that cross-section and percent attractive 8 ( b ) ONSET a EARLIER 0 7 GREATER&(%) FIG. +Schematic energy-profiles along the path of minimum energy for chemically-related pairs of reactions.Exothermic reaction proceeds from left to right. Along the first half of the abscissa r- is decreasing (reagents approach), along the second half ~ B C is increasing (products separate). The vertical line marks the point along the reaction coordinate at which new and old bonds are equally extended ; ~ A B - T ~ B = r g c - r i C . In (a) the hypothetical reaction (21 has a lower energy barrier, hence an “ earlier ’’ energy barrier and greater percentage attractive energy release d, than reaction CD. In (b) the pair of reactions have negligible energy barriers, but CD has an earlier onset of attrac- tion and hence greater %.d. [M. H. Mok and J. C. Polanyi, J. Gem. Phys., 1969, 51, 1451).398 MOLECULAR BEAM SCATTERING energy-release can correlate even in the absence of any activation barrier, if the variation in cross-section is simply due to increased range of interaction ; earlier onset of interaction (0 in the fig.4(b)) takes the place of an earlier barrier. This could be a better representation in comparing members of the homologous series M +XR (M = alkali metal atom, X is a halogen atom and R is an alkyl group; m a homologous series either M is varied, or X, or R). These simple amsiderations are of no value in comparing widely differing chemical reactians, such as M+Xz compared with M+XR. Both have large cross-sections but whereas the former has a large %dl) the latter has a relatively small %dl.'* l3 In such cases, as well as in the matter of preferred intermediate configurations, empiricism must be linked to an appreciation of the changing nature of the chemical binding.The application of simple molecular orbital theory constitutes a significant step along that road ; (see ref. (19), (37) and earlier references cited there). The correlation exemplified in fig. 4(a) has been applied in this Discussion to the family of reactions Ba+HX (X = F, C1, Br, I).', As X is varied there is an order- of-magnitude change in total reactive cross-section, 0,. Increased cross-section could be due to decreased barrier-height. This in turn would (in general) imply " earlier " barriers and increased %&I. It is, in fact, found that the %(E;) increases with increasing 0,. * The fact that (E;) is practically invariant with change in the isotopic mass of the central atom conforms to previous experimental and theoretical evidence concerning CI+HI-+ClH+I compared with Cl+DI-+ClD+I, H+Cl,+HCl+Cl compared with D + C12 + DCl + C1, and F + H, + FH + H compared with F + D2+ FD + D.The total reactive cross-section may change somewhat as a consequence of isotopic substitution, but this modest kinematic effect has insignificant consequences for (E;). MASS-COMBINATION Large kinematic effects due to substantial changes in mass-combination are important. A change from the mass-combination L + HH l4 to H + LH(F + HC1 14) or H+HL(Ba+HX 12) results in markedly different reaction dynamics on a given energy-surface. In the latter cases, product vibrational excitation will be greater, and the angular scattering of the molecular product will be more-forward than for L +HH (see below).This is because the repulsive part of the energy-release tends to occur while the heavy attacking atom is still some distance from the atom under attack. This is called " mixed energy release ", corresponding to trajectories that cut the corner of the potential-energy surface. The extreme mass-combinations that appear to favour mixed energy-release are mA rz rn, $ m,, and mA z mB % m, ; i.e., the attacking atom much heavier than either B or C in the molecule under attack. In terms of the skewed and scaled potential-energy surface, the former condition (H + LH 14) corresponds to a strongly skewed surface, and the latter (H+HL 12) to one that has been scaled so that the exit valley is wide compared with the entry valley.The case in which A is heavier than both B and C also favours mixed energy release. In the examples under discussion 12* l4 the repulsion in HL-H or HHoL (the dot indicates the site of the repulsion) tends to force the central atom against the heavy attacking atom, to produce internal excitation in the newly formed bond. The fact that %(E;) is in the surprisingly low range of approximately 10-40 % for the family of reactions Ba+ HX is, therefore, indicative of a highly repulsive potential-energy surface and/or an exceptionally narrow reaction-channel which forces the trajectories into a perpendicular reaction-path (diminishing the " corner-cutting " referred to above). In the reactive system, the separation of C1H.X gives some insight into V-TS U M M A R I Z I N G R E M A R K S 399 mixing for non-reactive scattering HCl +X, under conditions that are intriguing since they correspond to a partially-aligned inelastic scattering event (the products of Cl+HX are most likely to separate as ClHOX, whereas the products of H+ClX l4 separate as HCLX).As always, however, the results from reactive scattering cannot be transposed uncritically to inelastic scattering ; the different initial states for the two phenomena imply that the system is exploring different intermediate configurations. As studies of the individual phenomena reveal more detail, these differences will be- come of central importance. L+ H+ SbRFACE I 8 4 I 3 4 LL LH HL HH BACK FOR&. DECD. REPN. INCD. ATTN. FIG. 5.-Twenty-one computed product angular distributions (obtained from batches of 3D traject- ories) for AB formed in reactions A+ BC-tAB + C on the three LEPS potentialenergy hypersurfaces whose collinear sections are shown in fig. 2.The collision energy was 1 kcal mol-I above the barrier height, corresponding to approximately room-temperature reaction. In each distribution backward scattering is at the left of the graph, forward scattering at the right. For the matrix at the left of the figure, the attacking atom A was light (L I 1 a.m.u.). For the matrix at the right, A was heavy (H = 80 a.m.u.). Only seven mass-combinations are shown ; the eighth, H+ HH, would be identical to the first, L+ LL. [J. C. Polanyi and J. L. Schreiber, in Physical Chemistry-An Advanced Treatise. eds. H. Eyring, W. Jost and D.Henderson (Academic Press, New York, 1973), chap. 9, to be pub- lis hed] . The utility of the simple separation of energy-release into attractive and repulsive contributions extends beyond the correlation with product energy-distribulion docu- mented in fig. 3 to the correlation with product angular distribution shown in fig. 5. The three potential-energy hypersurfaces used to obtain these data were the same as the three shown in collinear section in fig. 2, and designated by arrows in fig. 3. They become increasingly attractive from @-+@+@. It is evident that there is a shift to more-forward scattering of the molecular product as the surfaces become more attractive (less repulsive). As before, the qualitative effect is the same for any particular mass-combination, though on a given surface there is evidence of important kinematic effects as a consequence of changing mass-combination. Mass-combinations that favour mixed energy-release tend to give more-forward scattering.This is because the repulsion that otherwise would propel the new molecule AB back along the direction from which the attacking atom A came, becomes, instead, internal motion of AB. In view of the highly-repulsive surface implied by the low ( E ; ) for Ba+HX, the400 MOLECULAR B E A M SCATTERING scattering in this case is likely to be backward-peaked, despite the fact that the mass- combination is somewhat favourable for forward scattering. The mass-combination for K + ICH, 5 * and for K + ICF3,6 namely L + HL in the three-particle approxima- tion, favours backward-scattering.In these cases the breadth of the backward- peaked distribution provides a useful indicator of the extent to which the energy-release is repulsive. Fig. 5 , on which these comments are based, refers to potential-energy surfaces that favour reaction as a result of roughly collinear approach from the reacting end of the molecule under attack (i.e., the B end of BC). The aligned experiments on K+IR, with R = CH, or CF3 and K approaching from the I end of IR, do show back- ward-peaked scattering. For K+ICH,, approach from the R end to yield KI is disfavoured; this is likely to be the normal case. For K+ICF, rear-approach (from the CF3 end) to form KI represents a reaction path of comparable probability to frontal-approach. (Could this be due to initial formation of K++CFJI-as if the thermoneutral reaction to form KF were about to take place-followed by negative- charge migration to the slowly-moving I ?).Whatever the reason for the facility of reaction from the CF3 end of CFJ, the outcome is of considerable interest. The KI formed by this route is scattered forward. This is simply explained if one supposes that, perhaps due to the aligning field, the CF,-I axis does not rotate to a major extent during the time required for reaction. The initial direction of motion of the attacking atom, K, defines the forward direction. The recoil of I away from CF, (that produced the backward scattering in the reaction from the I end) is, as before, SIDE SCATT. ( FORW. ) BACK SCATT. SCATT. L 4 FIG. 6.-Correlation between direction of approach of atomic species A and angular scattering of the molecular product, AB.The labelling indicates the expected direction of scattering of AB with respect to the direction of approach of A. (Approach of A from the C end of BC to give product AB will be disfavoured in many systems, consequently it is indicated parenthetically). The correlation will be most evident for the masscombination L+ HH-+LH+ H, on a repulsive surface. directed along the CF3-I axis. However, with K approaching from the rear (CF,) end of CF,-I, the recoil velocity of I is directed (approximately) along the continua- tion of the direction of approach of K. For normal " frontal " approach of A to the B end of BC, the reIease of the B-C repulsion gives rise to a momentum in B directed backwards, and sufficiently large to carry B backward. If the encounter is successful in producing AB, then AB must follow B into the backward hemisphere.By contrast the (less common) approach of A from the rear (C) end of BC to form the same product, AB, will, by a strictly parallel argument, give rise to forward scattering. Fig. 6 was drawn for the mass-combination L+HH, since for this mass-combina- tion the molecule under attack has been shown (in trajectory calculations) in general to rotate by only a small amount during the time of a reactive collision. This suggested Forward scattering of KI results. Fig. 6 illustrates this.SUMMARIZING REMARKS 401 to D. R. Herschbach and his associates that, for this particular mass-combination, one can infer the preferred direction of approach of A to BC directly from the observed angular scattering of AB.If this is so, then the (reasonably well-established) poten- tial-energy surface for H + C12+ HCI + C1 that favours collinear approach should be replaced in the case of H+12-,HI+I 20* 21 or CH3+12-+CHsI+I 2o by a surface that favours more-nearly sideways approach (since the latter reactions, as noted above, scatter the product approximately sideways '). Though this interpretation is very likely to be correct, it is worth noting that even in this case, which by virtue of the " light-atom anomaly " is so favourable for the inversion of reactive scattering data to the interaction potential, ((E;) is unusually sensitive to %dJ, the postulate of a non-linear direction-of-approach does not yet offer a unique interpretation of the experimentally-observed sideways-peaked scatter- ing.21 Nonetheless a " unique '' potential (i.e., one having qualitative features that appear uniquely able to explain the observed scattering) should be within reach, in view of the detailed information that we have, or are currently obtaining for the 4 3 5 9 2 I 0' I I ' 0 I 1' ' x emol/deg FIG.7.-Correlation between increased impact parameter b and increased forward-scattering of product AB, in a system having the mass combination H+LH+HL+H. The points refer to trajectories computed in 3D for the reaction C1+ HI+ClH+ I, with reagents Monte-Carlo selected from a 303 K distribution. Reactive encounters with a collision energy T< 1.24 kcal mol-I are symbolized by x 's, T> 1.24 kcal mol-' by 0's.(Stratified sampling increased the number of points below the lower broken line by 5 x , and decreased the number above the upper broken line by 0.5 x ). The curve indicates the dependence of Omol on b for hard-sphere elastic scattering, with a distance of closest approach equal to the sum of the normal equilibrium separations, r&-i+rh, = 2.9 A. [C. A. Parr, J. C. Polanyi and W. H. Wong, J. Chem. Phys., 1973,58, 5).402 MOLECULAR BEAM SCATTERING H + X2 and CH3 + X2 families of reaction. The reaction M + ICH3 is an example of a case where an extensive search for an acceptable potential-energy surface produced a solution which did not appear to admit of further wide variation in the parameters.For certain mass-combinations the kinematics are such that the particles ride, so to speak, rough-shod over the energy surface, only registering a crude impression of its features. The case of H+LH(X+HY where X and Y are halogen^'^) provides an extreme example. Fig. 7 shows the computed product angular scattering as a function of the reagent impact parameter for such a case. Even though the collision energy is only - 1-2 kcal mol-', the momentum of the heavy attacking atom, A, relative to the heavy atom in the molecule under attack, C , dominates the outcome to such an extent that the motion of the central atom (responding to the potential field embodied in the energy-surface) has little effect on the outcome. The product angular distribution is adequately described simply by the elastic scattering of A off C (solid line in fig.7). SIMPLE MODELS Of course, the cases in which one can usefully describe the reactive scattering event in terms of elastic or inelastic (non-reactive) scattering, will be few. A much more PRODUCT- FORCE MODELS A + BC+A--BXC+AB+C (a) I M P @ & J (d DIPR @ M FIG. 8.-Five types of simple " product-force models ". In all five models the outcome of reaction is calculated from the relaxation of A--B*C in its retreat from the activated state. In each case a force (pictured here as repulsive) is assumed to be located between the separating particles, B-C. Var- ious assumptions are made regarding the new bond A--B. Model (a) is the Impulsive model, (6) is the Constant Force model, (c) the Simple Harmonic Force model, (d) the DIPR model (Direct Interaction with Product Repulsion), and (e) the FOTO model (Forced Oscillation in a Tightening Oscillat~r).~~ [Cf.J. C. Polanyi and J. L. Schreiber, in Physical Chemistry-An Advanced Treatise, eds. H. Eyring, W. Jost and D. Henderson (Academic Press, New York, 1973), Chap. 9, to be published].S U M M A R I Z I N G REMARKS 403 important meeting ground between these categories of phenomena will be found in the detailed treatments of reactive scattering (classical, semi-classical or quantum mech- anical 22* 38) that concurrently yield data on elastic, inelastic and reactive events. A still more intimate meeting ground is to be found in the realm of simple models. These tend to be models for elastic or inelastic scattering which have been slightly elaborated so that the mechanics to which they give rise can reasonably be regarded as embodying the central features of at least some types of reactive encounters. The five simple models indicated pictorially in fig.8 are all of this type. Despite their crudity, simple models are important since their " moving parts " are open to in- spection-in contrast to the oftentimes mysterious workings of potential energy hypersurfaces. INCD. COLLN ENERGY AND/OR 0.3 c. 1 3. I - INCD. INTERNAL ENERGY FIG. 9.-Solid lines show three-dimensional DIPR model predictions for product angular distribu- tions (top row) and energy distributions (bottom row ; Eiot is product rotational excitation, Efnt is product vibrational plus rotational excitation).The total product repulsion used in the DIPR model calculations was decreased in four stages, from left to right in the figure. The model therefore simulates the effect of decreased %B?, implying increased %d. In the DIPR formulation this is mathematically equivalent to the effect of increased collision energy (hence the arrow at the top of the figure). The qualitative consequences of these changes are summarized at the foot of the figure. The dots (open or closed) record the corresponding distributions from 3D trajectories on comparable potential-energy hypersurfaces. [Based on P. J. Kuntz, M. H. Mok and J. C. Polanyi, J. Cheni. Phys., 1969, SO, 46231. The models indicated in fig. 8 are all based on the notion that the products are retreating from the barrier-crest ; i.e., the salient features of the energy-profile (cf.fig. 1, lower right-hand corner) are S' and R'. The models are more sophisticated than the O.E.P. representation in fig. 1, however, since they allow for the coizcicrrent release of S' (extension in the new bond, A--B) with R' (repulsion in B C ) . Model (a), the impulsive model, is the most rudimentary. It assumes an instantaneous release of force in B C , and derives the outcome from momentum conservation. Model (6) provides for a constant B C force of finite duration, forcing a simple harmonic oscillator (S.H.O.) that can be initially under tension. Model (c) resembles404 MOLECULAR BEAM SCATTERING (b), but with a linearly decaying (i.e., S.H.) force in BC. Model (d), the DIPR model (an acronym for Direct Interaction with Product Repulsion), assumes that a generalised force produces a known total impulse between atoms B and C.(In the case illustrated, this is an exponentially decaying force). The product translational energy, T', is obtained from the recoil of C, rotational excitation, R', from conserva- tion of angular momentum, and Y' from conservation of energy. The simple DIPR model is able to explain some fundamental correlations, des- cribed above. Foremost among these are the correlations between increased attract- ive energy-release (decreased product repulsion, in the model) and increased product forward scattering, with concurrent increase in the internal excitation, Y' + R'. The predictions of the DIPR model, in both these regards, are recorded in fig.9. It is instructive that so crude a model as the DIPR model is able to simulate these correlations. They are not, it would seem, particularly subtle effects. If we want to explain the effect of mass-combination on the outcome of chemical reaction, or to account for still more subtle phenomena such as the effect of a redistribution of the reagent energy between Tand V, the DIPR model will be inadequate. Models (b) and (c) (the Constant Force, and the S.H. Force models) come closer to reality since they couple A to the repulsive interaction of B and C, from the outset. They are deficient, however, in ignoring the remarkable fact that in the second half of a chemical reaction the B *C repulsion is forcing oscillation into an oscillator that is increasing its char- acteristic frequency and decreasing its equilibrium separation all the while.i.e. it is a bond in the process of being formed. Model (e), the FOTO tries to make good this omission by describing the reactive event as Forced Oscillation in a Tighten- ing Oscillator. The model (at present restricted to the collinear case) accounts quite well for the effect of changes in mass-combination on reaction dynamics, in a manner which lends itself to interpretation in terms of changing attractive, mixed and repulsive energy-release. REAGENT ENERGY Up to this point, these comments have dealt with the characteristics of product energy and angular distributions, their dependence on the nature of the interaction and their dependence on the masses of the reacting species. However, this Discussion has been distinguished by reports of direct (though sometimes crude and limited) measure- ments of the effect on reaction dynamics of changes in reagent energy.These have appeared under various headings. We have heard of the unexpectedly sharp maxi- mum in the total cross-section for the reaction K+ICH,-,KI+CH, at 0.18 eV (4.1 kcal mol-') collision en erg^.^ This feature poses a challenge to the0~y.l~' 35* 36 There has been discussion (both theoretical and experimental) of the intriguing question of the relative effectiveness of reagent translation and vibration, T and V, in promoting exothermic reacti~n,'~ and their relative effectiveness in promoting endo- thermic r e a ~ t i o n . ~ ~ ' ~ ~ Theory and (approximate but direct) experimental evidence seem to agree that reagent translation is likely to be more effective than vibration in promoting exothermic reaction.I4 Theory 2 5 and experiment 2 5 * 26 agree that the converse applies in the case of endothermic reaction ; reagent vibration tends to be more effective than translation.The simplified O.E.P. energy-profile shown in the lower-right-hand corner of fig. 1 (which has already served us well) can be used to render these latter findings plausible. It postulates that A-B repulsion, R, is the major requirement for barrier- crossing in the exothermic direction. It is to be expected that relative motion of A with respect to B (reagent translation) will most readily lead to A.B. In the reverse, endothermic, direction there is, in addition to a requirement for repulsion R' in B*C, aSUMMARIZING REMARKS 405 W I n very significant energy-rise labelled S’.This corresponds to stretching of the bond being broken in the endothermic reaction, A--B. The potential-rise S’ can be achieved most readily if that portion of the reagent energy for endothermic reaction is placed directly into AB, i.e., if a substantial part of the reagent energy is present as vibration in the bond under attack. (This rationale implies that the characteristic energy- profile for endothermic reaction resembles that in the exothermic direction, at least qualitatively. This is a good approximation for endothermic reagent energies not greatly in excess of the endothermic barrier height 25). TA I 1’ W I a. L I I 0--0--0 B-C- t - A - 8 FIG.10.-These energy profiles record only the diference between the energy changes for thermal reaction and energy changes appropriate to the case of enhanced reagent translational energy (AT, in excess of the minimum energy required to cross the barrier, Ec) or enhanced reagent vibrational energy (A V> Ec). The activated state is indicated by i. For ATit is compressed, for A Vit is most often extended (the dynamics depend on the initial phase of vibration). In either case += is at a potential energy substantially in excess of Ec. There has also been discussion for exothermic reactions of the effect of reagent- energy enhancement, AT or AY in excess of the barrier-height, on the product energy di~tributi0n.l~ Experiment and theory are in general accord that AT-+AT’+ AR’ (enhanced product translation and rotation), and A V+A Y’ (enhanced product vibrational excitation). This “ adiabaticity ” with respect to additional energy in406 MOLECULAR BEAM SCATTERING excess of the barrier-height has been traced to the fact that AT gives rise to a more compressed intermediate configuration than would otherwise be obtained, whereas AY gives rise (most often) to a more-extended intermediate configuration.The enhanced product translation in the former case and enhanced product vibration in the latter case can, accordingly, be understood as being due to a measure of " induced repulsive energy-release " arising from AT, and " induced attractive energy-release " arising from AV. Fig. 10 makes use of the O.E.P. type of representatiOn to clarify this.All that is recorded in the figure is the dipereme in energycprofile in the presence of the enhanced reagent energy, as compared with that in the absence of this additional energy. For AT this difference takes the form of enhanced R and R' ; for A V it takes the form of enhanced S and S'. (Fig. 10 of ref. (14) shows the corresponding changes as they would appear on a collinear energy-surface). A well-known effect of enhanced reagent translational energy is to increase the percentage of forward scattering of the molecular product. On a previous occasion I suggested that one might usefully define a " stripping threshold energy ", T,, which could be the collision-energy above which >90 % of the molecular product is scat- tered into the forward hemisphere.In part, as we have seen, the value of T, will depend on the reactant mass-combination; in part it will depend on the extent of interaction between atom B and C.' If we can make an allowance for the former effect, then we can use T, to obtain a measure of the interaction between B and C. In the common case that B and C repel, we would be obtaining a measure of the repulsive energy release, 9. Of course there are other clues to the magnitude of 9 than T,. The suggestion that T' be used as the index of 9 was based on the notion that it would eventually be experimentally feasible to vary T for many reactions, and then to codify these reactions uniformly in terms of their T,. The time when we can do this experimentally has not yet arrived.We can, however, exemplify the value of such a procedure from a theoretical standpoint, out of the present Discussion. In an ambitious 6-atom trajectory study of Rb+ICH, l 3 the collision energy was increased from 0.025 to 4 eV. The result was that the scattering of the RbI product shifted from backward to sideways to forward. The stripping threshold energy has a value T,>5 eV. This is surely connected with the fact that the bCH3 repulsion is substantial. For the DIPR model the effect of increased T is to decrease the time during which the B-C force operates, i.e., to decrease the repulsive impulse. As a result, increased col- lision energy is mathematically equivalent to decreased repulsion, as indicated in the arrow over fig. 9. (The model also predicts the gross changes in product energy distribution as the spectator-stripping limit is approached.It fails, however, to take any account of such subtle effects as " induced repulsive energy-release ', since there is no mechanism for momentum of A to become enhanced B-C repulsion). If some simple form is chosen for the repulsive force as a function of time, F(t), then the value of T, can be used to obtain the parameters governing F(t), and hence the repulsive impulse at any other collision energy. This would be a still more useful exercise in terms of models such as (b), (c) and (e) of fig. 8, which make some allowance for the role played by the relative masses of A, B and C, as distinct from the form of the potential-energy function. Simple models can make the relationship between T, and 9 explicit." I N D I RE C T " R E A C T I 0 N The account given here of various types of interaction, and their consequences for reaction dynamics, has up to this point been incomplete in one important regard ; no mention has been made of the possibility that reaction products instead of separatingSUMMARIZING REMARKS 407 cleanly might suffer secondary, tertiary, and further, encounters. I have spoken of reaction, throughout, as if it were a “ direct ” process. This is evident in the five models pictured in fig. 8. The trajectory calculations on potential-energy hyper- surfaces do, however, allow for the possibility of direct or indirect encounters.’ Looking back at the evidence for a positive correlation between attractive energy release and product vibrational excitation obtained from the trajectory calculations (recorded in fig.3) it is clear that at high %d1 the mean vibrational excitation %(E+) falls. Inspection of the trajectories shows that this is due to the effect of indirect reaction. There is too little product-repulsion to separate the products before oscillation in the new bond can give rise to secondary encounters. Incipient vibration in the new bond is, therefore, dissipated, in the course of secondary en- counters, into product translation and rotation ; (&) starts to diminish toward its statistical value. This Discussion has seen a considerable flowering of interest and information regarding the difficult domain of indirect (complex) enc~unters.~~ The results are generally characterized by an outcome that corresponds to the statistical expectation in some regards, and to deterministic behaviour in others.The extensive studies of unimolecular decomposition in crossed molecular beams exemplify this nicely.’’ The ratios of cross-sections for alternative pairs of products (e.g., +C4H8+ C4H8F,*tt-+C3HSF + CH3- or +C4H7F + He) is statistical, whereas the translational- energy distribution in the products is not. The simplest interpretation is that the choice of reaction path is determined in a statistical region of strong mixing (e.g., in C4H8F*++), but that the product energy-distribution is determined by specific forces operative in the exit channels. These simple explanations (along with those advanced throughout the present paper) should be treated with reserve, in view of the fact that there are often contrary, no less convincing, explanations to account for precisely the opposite type of behav- iour. Thus, in the course of a wide-ranging study of four-centre exchange reactions 2 8 it has been shown that the reaction CsCl+KI+CsI+KCI proceeds through a long- lived collision complex (many vibrations, - 1 rotation).The angular and velocity distributions of the scattered molecules are consistent with a simple statistical model, resembling the RRKM (Rice, Ramsperger, Kassel, Marcus) theory for unimolecular decay. In this case, however, the property most directly obtained from KRKM theory, the ratio of nonreactive to reactive decay, was found to be 2-3 times larger than the statistical prediction.There may, of course, be no conflict at all between this example and the previous one. There is reason to suppose that the 4-atom intermediates MXM’X’ have preferred atomic arrangements. 28 Trajectory computa- tions (exceptionally difficult to perform for these long-lived species) confirm that with the involvement of two forms of intermediate dimer, the non-statistical yield of products is e~plicable.~~ The (largely attractive) forces operating between the products may turn out to be consistent with statistical angular and energy distri- butions ; this remains to be established. NEW THEORETICAL APPROACHES Theoretical discussion at this meeting began with a consideration of the funda- mental practical question ; the choice of optimal theoretical approaches from among the considerable range of scattering treatments available.22 Discussion then focused on the semi-classical method, which has great attractions in the treatment of phen- omena for which the purely classical method is definitely unsati~factory.~~~ 47 Such408 MOLECULAR BEAM SCATTERING phenomena are in the minority, but this may not always be the case.For example, with increasing energy-resolution it will become possible to explore partial and total reactive cross-sections in their threshold-energy regions. The form of these functions in the threshold region can be markedly affected by quantum restrictions on the products, and by tunneling processes (whose probabilities are too low to be of import- ance well above threshold). The semi-classical m e t h ~ d , ~ * ~ ~ * 48 which uses data from exact classical trajectory calculations to evaluate the quantities required for a quantum mechanical description, has been shown in a number of cases to describe quantum effects accurately.Since its point of departure is a classical trajectory calculation, there is no restriction on the potential-energy hypersurface that can be treated by this means. In the present Discussion we have heard how this method can be applied selectively to only those degrees of freedom that are strongly quantised, treating the remainder classically,30 and we have also seen how the method can be applied to the type of reactive encounters that span the gap between " direct " and statistical reaction. Looking into the future at the close of our previous Discussion I said that I would be surprised if ab initio calculations of potential-energy surfaces did not figure sig- nificantly at our next meeting.I can now report that ab initio surfaces have not figured significantly, and that I am surprised. The brightest hope that they offered us in the course of this Discussion was in connection with the inelastic scattering experiments on Li++H2.8 For this case information is coming available on the extent to which the ab initio surface is able to account for the experimental finding^.^' The difficulty of making ab initio calculations to a chemical accuracy over a sufficient range of configurations to be of value for prediction, hardly needs to be restated. Though it has not been to the fore in the present Discussion, very sub- stantial progress has in fact been made in the field of ab initio computation in recent years.The importance of this line of endeavour perhaps does need to be stressed. It will provide an extremely valuable standard against which our future empirical and semi-empirical efforts can be measured. The information-theoretic approach to reaction dynamics represents an intriguing new departure.24 The outcome of a dynamical process is considered in relation to the statistical outcome. The more the former deviates from the latter the greater the " surprisal ". If, for example, a reaction deposits a fraction f$ of its energy into vibration, with a probability P(f;), and if the corresponding statistical expectation for a closed system (a microcanonical ensemble) were Po(f+), then the surprisal would be defined as Z(f;) = -log[P(f;)/P*(f;)].The surprisal is therefore a local measure (for a given V, in the example cited) of the deviation of the observed probability from the statistical expectation. In some cases, the surprisal is found to vary linearly with the energy-mode to which it refers. In these cases an extreme " compaction " of data is achievable ; a matrix of - 100 detailed rate constants k(u', J') (rates into specified quantum states of vibration and rotation obtained from an infra-red chemi- luminescence study of a single reaction) can be represented in terms of two numbers ; 1". and &, respectively the slopes dI(f$)/df+ and dZ(fd)/df{. At present no reason is known why the surprisal should vary linearly with energy (corresponding to a monotonous logarithmic change in P/P0).339 34 However, there are already enough cases in which the variation of the surprisal with energy is simpler than the variation of the reaction outcome with energy (the raw experimental data), to make this new vantage point a noteworthy one.It would seem to be particularly interesting to apply the approach to reactions which involve indirect (complex) encounters. For these reactions, the statistical quantity Po is the natural datum against which to measure the observed outcome, P.SUMMARIZING REMARKS 409 A great deal has now been begun in the field of molecular dynamics. A little has been concluded. On the days that we incline to modesty we may say of our work, as Francis Bacon did of his, that it " seemeth .. . not much better than that noise or sound which musicians make while they are tuning their instruments; which is nothing pleasant to hear, but yet is a cause why the music is sweeter afterwards . . .". In truth that is quite a brave assessment, since it implies a faith that some considerable orchestration will follow. In the light of the discussion we have heard at this meeting (dissonant at times, but we are dealing with modern music) this appears to be a very reasonable expectation. ' J. C. Polanyi, Disc. Furuday SOC., 1967, 44, 293. D. D. Fitts and M. L. Law, this Discussion, p. 179. R. W. Bickes, B. Lantzsch, J. P. Toennies and K. Walaschewski, this Discussion, p. 167. T. A. Davidson, M. A. D. Fluendy and K. P. Lawley, this Discussion, p. 158. R. B. Bernstein and A. M. Rulis, this Discussion, p. 126. P. R. Brooks, this Discussion, p. 299. A. Kuppermann, R. J. Gordon and M. J. Coggiola, this Discussion, p. 145. H. E. van den Bergh, M. Faubel and J. P. Toennies, this Discussion, p. 203. A. M. G. Ding and J. C. Polanyi, this Discussion, p. 225. lo Y. T. Lee, this Discussion, based on work of F. P. Tully, H. Haberland and Y. T. Lee. l 1 D. S. Y. Hsu and D. R. Herschbach, this Discussion, p. 116. l 2 H. W. Cruse, P. J. Dagdigian and R. N. Zare, this Discussion, p. 277. l 3 D. L. Bunker and E. A. Goring-Simpson, this Discussion, p. 93. l4 A. M. G. Ding, L. J. Kirsch, D. S. Perry, J. C. Polanyi and J. L. Schreiber, this Discussion, p. 252. ' R. G. J. Fraser, Molecular Rays, ed. E. K. Rideal (Cambridge University Press, London, 193 1). l6 J. C. Whitehead and R. Grice, this Discussion, p. 320. M. S. Child, this Discussion, p. 30. E. Gersing, H. Pauly, E. Schadlich and M. Vonderschen, this Discussion, p. 211. l 9 C. F. Carter, M. R. Levy and R. Grice, this Discussion, p. 357. 2o J. C. Polanyi and J. L. Schreiber, this Discussion, p. 372. '' J. D. McDonald, this Discussion, p. 372. 22 R. G. Gordon, this Discussion, p. 22. 23 M. D. Pattengill and J. C. Polanyi, this Discussion, p. 63. 24 R. D. Levine and R. B. Bernstein, this Discussion, p. 100. 2 5 D. S. Perry, J. C. Polanyi and C. Woodrow Wilson Jr., this Discussion, p. 127. 26 D. J. Douglas, J. C. Polanyi and J. J. Sloan, this Discussion, p. 310. 27 J. M. Parson, K. Shobatake, Y. T. Lee and S. A. Rice, this Discussion, p. 344. 28 D. L. King and D. R. Herschbach, this Discussion, p. 331. 29 P. Brumer and M. Karplus, this Discussion, p. 80. 30 W. H. Miller and A. W. Raczkowski, this Discussion, p. 45. 31 R. A. Marcus, this Discussion, p. 34. 32 J. N. L. Connor, this Discussion, p. 51. 33 J. C. Polanyi, J. L. Schreiber and J. J. Sloan, this Discussion, p. 124. 34 R. D. Levine, this Discussion, p. 125. 35 R. B. Bernstein, R. A. LaBudde, P. J. Kuntz and R. D. Levine, this Discussion, p. 120. 36 R. M. Harris and D. R. Herschbach, this Discussion, p. 121. 37 D. A. Dixon, D. L. King and D. R. Herschbach, this Discussion, p. 375. 38 G. G. Balint-Kurti and B. R. Johnson, this Discussion, p. 59. 39 U. Buck, H. 0. Hoppe, F. Huisken and H. Pauly, this Discussion, p. 185. 40 M. S. Chou, F. F. Crim and G. A. Fisk, work described by D. L. King, H. J. Loesch and D. R. Herschbach, this Discussion, p. 222. 41 G. M. Kendall and J. P. Toennies, this Discussion, p. 227. 42 A. Ben-Shaul, this Discussion, p. 307. 43 C. F. Carter, M. R. Levy, K. B. Woodall and R. Grice, this Discussion, p. 381, 385. 44 Y. C. Wong and Y. T. Lee, this Discussion, p. 383. 45 Comments in this Discussion, p. 113-1 16, p. 377-381. 46 W. H. Miller, this Discussion, p, 119. 47 G. D. Barg, H. Fremery and J. P. Toennies, this Discussion, p. 59. 48 Comments in this Discussion, p. 68-79, p. 119-120.

ISSN:0301-7249    

DOI:10.1039/DC9735500389

出版商:RSC    

年代:1973

数据来源: RSC

摘要:

AUTHOR INDEX * Aquilanti, V., 187, 231. Baht-Kurti, G. G., 59. Barg, G. D., 59. Ben-Shaul, A., 123, 307. van den Bergh, H. E., 203. Bermtein, R. B., 100, 120, Bickes Jr., R. W., 167. Bosanac, S., 65, 73. Bottner, R., 221. Brooks, P. R., 299, 3 18. Brurner, P., 80, 114, 116. Buck, U., 185. Bunker, D. L., 93, 121. Carter, C. F., 357, 381, 385. Cheung, J. T., 377, Child, M. S., 30. Coggiola, M. J., 145. del Conde, G., 369. Connor, J. N. L., 51, 76, 120. Cruse, H. W., 277. Dagdigian, P. J., 277, 31 1. Davidson, T. A., 158. Davies, D. W., 369. Davis, R. W., 189. Ding, A. M. C., 225, 252. Dixon, D. A., 375, 385. Douglas, D. J., 310. Faubel, M., 203. Fitts, D. D., 179. Fluendy, M. A. D., 158. Freed, K. F., 68. Freniercy, H., 59. Gengenbach, R., 186. George, T. F., 64, 76. Cersing, E., 211.Gilbert, R. G., 64. Gordon, R. G., 22. Gordon, R. J., 145. Goring-Sirnmon, E. A.. 93. I , 93. Crice,R., l-13, 320, 357, 370, 374, 381, 385. Ham, D. O., 313. Harris, R. M., 121. Herschbach, D. R., 1 13, 1 16, 121, 222, 229, 233, Hoppc, H. O., 185. Hsu, D. S. Y., 116. Huisken, F., 185. Hunter, G., 387. Johnson, B. R., 59. Karplus, RI., 80. Kendall, G. M., 227. King, D. L., 222,331, 375. Kirsch, L. J., 252. ' Krenos. J . R., 229, 314. Kuntz, P. J., 120. Kupperrnann, A., 145. La Budde, R. A., 120, 221. 314, 318, 331, 375, 377, 385. Lacman, K., 318. Lantzch, B., 167. Larsen, R. A., 229. Lawley, K. P., 158, 189. Lee, Y. T., 344,380, 383. Levine, R. D., 73, 100, 120, 125, 221, Levy, M. R., 357,381, 385. Liao Law, M., 179. Lin, S. M., 113, 370. Lin, Y.-W., 76.Liuti, G., 187. Loesch, H. J., 222, 229. McDonald, J. D., 372, 376, 377. McFadden, D. L., 314. McNamee, P. E., 318. Marcelin, G., 318. 37, 310. Marcus, R. A., 9, 34, 64, 71, 75, 115, 312, 317, Menzinger, M., 126, 312. Miller, W. H., 45, 71, 11 9. Moutinho, A. M. C., 317. Morokurna, K., 76. Murrell, J. N., 73. Ogilvie, J. F., 189. Parr, C. A., 308. Parrish, D. D., 385. Parson, J. M., 344,380. PattengiII, M. D., 63. Pauly, H., 185, 191, 211. Perry, D. S., 127, 252. Polanyi, J. C., 63, 124, 127, 225, 252, 308, 310, Raczkowski, A. W., 45. Rice, S. A., 114, 344, 380. Ross, U., 221. Rulis, A. M., 293. Schadlich, E., 211. Schreiber, J. L., 72, 124, 252, 372. Shobatake, K., 344, 380. Simons, J. P., 67. Sloan, J. J., 124, 310. Struve, W. S., 314. Tardy, D. C., 308. Toennies, J. P., 59, 129, 167, 186, 203, 221, 227. Vonderschen, M., 211. Vecchio-Cattivi, F., 187. Volpi, G. G., 187. Walaschewski, K., 167. Welt, W., 186. Whitehead, J. C., 320, 373. Wilson Jr., C. W., 127. Wolf, G., 186. Woodall, K. B., 381, 385. Wong, W. H., 308, 383. Wren, D. J., 126, 312. Zare, K. N., 277. 379, 38 1. 372, 389. * Thc references in heavy type indicate papers submitted for discussion. 41 0

ISSN:0301-7249    

DOI:10.1039/DC9735500410

出版商:RSC    

年代:1973

数据来源: RSC