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. 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