GENERAL DISCUSSION Prof. H. I. SchiH (McGiZZ University) said Prof. Norrish has referred to the (1) reaction 0 + N02+NO + 0 2 in which he and his co-workers have detected oxygen excited to the eighth vibrational level. Such excited molecules have more than the 24 kcal/mole required to decom-pose 0 3 . An attempt was made in our laboratory to study the reaction using the mass-spectrometer technique described in our paper. No such decom-position was detected. This is in agreement with the conclusions of McGrath and Norrish that reaction (2) has a very small rate constant. They find however that the reaction O:(v>,17)+ 03-d02+ O('0) (3) does have a large rate constant. I would like to ask Prof. Norrish why he thinks k3 should be so much greater than k2. Also the reaction q 3 P ) + 03-+ 0; + o2 (4) is sufficiently exothermic to produce 0; in vibrational levels above v = 17 and so might initiate chains.However we found that in the reaction between O(3P) and 0 3 one O3 molecule was consumed per 0-atom. This is again in agreement with the conclusion of McGrath and Norrish. Does Prof. Norrish have any comments on the reason why the higher vibrational levels are not populated in this reaction? (Paper by Basco and Norrish.) Prof. R. G. W. Norrish (Cambridge University) said I wish to refer to the ap-parent anomaly exposed by the paper of Dr. Callear and that which Dr. Basco has just read. It relates to the difference of rates of decay of vibrationally excited NO in the two processes. I have pointed out that in my opinion in the population of the vibrational levels of the X2II state of NO by fluorescence or collisional de-activation from the A2Z+ level it is unrealistic to conclude that only the first level is initially populated.All vibrational levels from t = 0 to v = n must be populated initially but resonant relaxation of the kind NOu=,+NOu=,,-2~ = 2NOu,,,-, (1) must occur so rapidly that the whole process completed by the final stage must be over before spectroscopic observation by means of kinetic spectroscopy can be achieved. This leaves only NO,1 which must be finally deactivated by collisional degradation. Now in the reaction NOCl+ hv = NO* + C1 (2) the NO is produced with up to 11 quanta of vibration in the X2ll state and although its disappearance is rapid it is readily observable spectroscopically.The photo -lysis in this work is almost exclusively produced by light lying between 2600 and 2000& and since D(NOC1) is 38 kcal there is ample energy to populate the level NOu=2+NOu= = NOu=, 27 274 GENERAL DISCUSSION u = 11 which requires 55 kcal. I think the apparent anomaly can be resolved if we assume that all the excited NO is produced in the higher levels say from u = 12 to v = 10. Truly resonant relaxation of the type described above will then stop at v = 11 and lower levels will have to be produced by the much slower process of collisional deactivation with NOCl or other species. Such collisional deactiva-tion will still depend on resonance but of a much lower probability than that repre-sented by eqn. (1) because the vibrational frequencies are not nearly so closely adjusted.There is thus time for all the lower levels to be populated and seen spectroscopically. Molecules such as N2 with no resonance correspondence are quite inefficient and have no observable effect. Added NO,=o is of low efficiency because of the lower probability of the reaction NO,=m+NO"= = NO,=,,-1)+NO,= (3) owing to the lower degree of resonance between widely separated values of v. This is an extreme statement of the case. During the progress of the flash, lower levels of v will become populated and the " gap " will be replaced by an irregular population of levels probably involving a minimum which will have the effect of putting " the brake on " the collapse of the system to v = 1. Since the NO* with the exception of X2IIN0,=1 does not outlive the period of the flash any photograph shows an instantaneous cross-section in time of the distribution of excited molecules " on the way down " there being a continuous feed in from upper levels during the period of the photoflash.Alternatively it may be suggested that any other mechanism which could give rise to an irregularly populated spectrum of v levels-such as the primary reaction itself-would have the effect of slowing down the process of vibrational relaxation in comparison to a mechanism which gives rise to a " smooth " spectrum of u levels, as may be postulated for NO* produced in the experiments cited by Dr. Callear. Finally it may be said that the addition of NO to the NOCl system strongly reverses the photolysis resulting in an overall NOCl continuum which makes any accurate photometric estimation impossible.Such qualitative effects as are observed are not in my opinion of sufficient magnitude to affect the above argument one way or the other. Dr. F. D. Findlay and Prof. J. C. Polanyi (University of Toronto) (communicated): We find that when HCl,=o is introduced into a vessel where H is reacting with CIz to form vibrationally-excited HCl there is a general diminution in emission intensity from all vibrationally-excited levels. (The experiment is performed under condi-tions of temperature and pressure ca. 1-5 mm 7OO0C where a chain reaction is taking place and where it has been demonstrated that H or C1 will promote the reaction hence replacement of H by C1 through H + HCl+H2 + Cl will not diminish the intensity).Successively higher vibrational states in general exhibit increasing amounts of deactivation. However the diminution in intensity is found to be anomalously large for u = 2 (60 % decrease as compared with 31 % for u = 3, 43 % for v = 4 53 % for v = 5 71 % for u = 6 90 % for v = 7) and exceptionally small (4 % decrease) for u = 1. It is difficult to explain this otherwise than by postulating a rapid energy transfer, HC1,=2 + HCl,=o+2HC1,=1 This would be a resonant transfer of the type that Prof. Norrish and others have discussed (energy discrepancy 105 cm-1 0.30 kcal/mole). Dr. J. W. Linnett (University of Oxford) (communicated) Basco and Norrish find that NO molecules produced from chlorine atoms and ClNO are not vibration-ally excited while those produced by photodissociation of ClNO may possess up t GENERAL DISCUSSION 275 eleven vibrational quanta.The first is to be expected because the equilibrium NO bond length in nitric oxide (1.15 A) is in effect the same as that in nitrosyl chloride (1-14A). The second could be readily understood if the NO bond length in the excited state from which dissociation occurs were different from that in nitric oxide in its ground state. It is perhaps worth drawing attention to the conclusion of Johnston and Berth that for the excited state of FNO examined by them the NO bond length is greater than that in the ground state. They suggested that the bond order decreased from 2 to 1+ on excitation; I have proposed that the reduction is from 2$ to 2.If a similar change in NO bond length occurs when ClNO absorbs the radiation producing dissociation then some vibrational excitation in the NO produced is probably to be expected. Prof. R. G. W. Norrish (Cambridge Unioersity) said I think the results obtained with NOCl and NOBr may be ultimately explained if the NO* in these cases is pro-duced initially only in high vibrational states (see discussion following paper by Basco and Norrish). Mr. M. A. A. Clyne and Dr. B. A. Thrush (University of Cambridge) said We have investigated the mechanism of one of the reactions of the type A+BCD = AB* + CD (which results in the formation of vibrationally excited molecules) by studying the isotopic distribution in the products of the stoichiometric reaction of 1 8 0 oxygen atoms with N1602 in a fast flow system.The results can be summarized by the equation 1 8 0 + N1602=$(180160 + N160) + &(I602 + NlsO). This provides clear evidence that the reaction proceeds via an intermediate in which all the 0 atoms are equivalent i.e. having D3h or C3v symmetry. The vibra-tional excitation of the 0 2 molecule formed but not of the NO molecule formed is then explained by the large change in 0-0 distance and small change in N-0 distance in going from the reaction intermediate to the products. No evidence could be found that this reaction yielded electronically excited 0 2 molecules in the 1cg' state. Prof. R. G. W. Norrish (Cambridge University) said I should like to refer to the reaction of chlorine atoms with Ozone1 which provide a remarkable example of specificity of three-body collision.The photosensitized decomposition of ozone by chlorine is a chain reaction involving the propagating steps Cl+03 = C10+02 ClO+O3 = C10+202. This has more recently been confirmed by kinetic spectroscopy and in addition the C10 has been shown to be vibrationally excited.2 The chains are terminated by the reactions C1O+C10 = c12+02 The latter reaction takes place predominantly when the concentrations of chlorine and oxygen are relatively high and gives rise to the short-lived red vapour C1206. The point I wish to make is that M as third body is represented only by C12 or 0 2 nitrogen and carbon dioxide being quite ineffective. This apparent specificity was explained by supposing short-lived complexes (sticky collision) to be formed between chlorine atoms and the third body represented by C13 and Cl.00.C13 Cl+03+M = C103+M'. 1 Norrish and Neville J. Chem. Soc. 1934 1864. 2 McGrath and Norrish Proc. Roy. Soc. A 1960,254 147 276 GENERAL DISCUSSION has been postulated by Rollefson both on theoretical grounds and in connection with the photosynthesis of phosgene where it is found to act similarly in a specific manner. Dr. N. Basco (University of Shefield) (contributed) From the quantum yield for the decomposition of ozone by visible light and from the fact that oxygen mole-cules possessing up to 75 kcal/mole of vibrational energy are observed in the flash photolysis of ozone it appears that the efficiency of vibrationally excited oxygen molecules in decomposing ozone is somewhat limited unless they possess much more energy than is necessary on purely energetic grounds.Since however the average energy of the nitrogen molecules is -21 kcal mole and 75 % of them can decompose ozone the maximum vibrational energy required for decomposition by NZ cannot be much more than 30 kcal/mole i.e. 5 quanta and it may well be that 4 quanta are sufficient. This difference between 0; and N; might be explained by the relative inefficiency of relaxation of NZ by ozone compared with that of 0; by ozone so that in the former case nearly all molecules with sufficient energy eventu-ally decompose ozone. The difference in relaxation is probable by virtue of the closeness of the vibration frequencies in ozone to those of oxygen whereas those of nitrogen are considerably greater.Likewise NO* with up to 55 kcal of vibrational energy can be observed in the presence of nitrosyl chloride and the quantum yield for decomposition of NOCl is two down to at least 2537A. Here again due to the closeness of the vibration frequencies of NO and NOCl relaxation may be more efficient than chemical reaction. The value for the proportion of the nitrogen molecules produced in an excited state may be compared with one of about 30 % estimated by Prof. Norrish and myself for hydroxyl radicals produced in a series of reactions O’D+HR and con-trasted with the very low (or zero) value obtaining in the reaction H+NOa. Clearly no generalization is yet possible on experimental grounds. (The paper by Morgan, Phillips and Schiff.) Prof.A. R. Ubbelohde (Imperial Coll. London) said In connection with the paper by Basco and Norrish our information about the transmission of repulsive forces along a chain of bonded atoms is still scanty. General considerations of the dependence of repulsions on the interpenetration of Thomas-Fermi clouds of non-bonded electrons suggest that in a sequence even strongly repulsive encounters between A and B will normally transmit only weak repulsion between C and D. This in turn determines the maximum potential energy of vibration available in the molecule CD if it splits off after the collision. Only feeble vibrational excitation could be expected. Mr. P. E. Charters Dr. B. N. mare and Prof. J. C. Polanyi (University of Toronto) (communicated) Cashion and Polanyi 1 in a study of the reaction observed infra-red emission from HCl which was ten times as great as that from NO.This could have been due to the fact that vibrational excitation arose prin-H+NOCl-+HCl+NO (1) cipally by a process A + BCD-+AB+ + CD 1 Cashion and Polanyi J. Chern. Physics 1961 35 600 GENERAL DISCUSSION 211 as Prof. Ubbelohde is supposing in his remarks or it could have been due to rapid collisional deactivation of NO. We have now repeated these experiments at two orders of magnitude lower total pressure and find that the NO emission intensity is below the limit of detectability by a thermocouple detector and consequently must be less than 4 % of the total HCl photon intensity. This confirms process (2) and is in agreement with the findings of Basco and Norrish.Prof. D. R. Herschbach (University of California) said Vibrationally excited product molecules have now been detected in about 30 exothermic atomic exchange reactions. However as yet there are only a few studies which indicate what frac-tion of the products are excited. From a theoretical viewpoint this information is essential. Without it we cannot tell whether the excited products represent the main course of the reaction or merely an interesting but practically negligible side effect. The reactions for which there is such information have all been mentioned at this Discussion. For the alkali reactions M2+X+MX+ M (14 and M+ RI-+MI+ R (1b) there is evidence that most of the products are highly excited whereas for some H atom reactions, H+ BC+HB +C (24 and H+BCD-+HB+CD (2b) with BC = C12 BCD = 0 3 ClNO N02 it is now established that the products are formed predominantly in low vibrational states.Perhaps the most fundamental motivation for the study of product excitation is that it may contribute to the experimental characterization of the potential sur-faces for reactions. The pronounced difference between the reactions (1) and (2) is thus encouraging and presumably it can be interpreted along lines indicated in early qualitative discussions of potential surfaces.1 2 The angular distribution of products provides another and in principle a quite direct approach to the study of these surfaces. However the theory of scattering from a multidimensional potential surface has until now remained swaddled in formal theorems.Recently an extensive programme of calculations on reactive scattering has been undertaken by Bunker and Blais,3 who use Monte Carlo methods to integrate the classical equations of motion. They have begun with a study of reaction (lb), based on a surface constructed so that most of the fall in potential energy is associ-ated with attraction between the reactants and not repulsion between the products. This feature was suggested as a necessary condition for vibrational excitation by Evans and Polanyi in their analysis 2 of reaction (la) and has been discussed more recently by Smith.4 In the calculations of Bunker and Blais the three interacting particles (CH3 is treated as a single atom) are not restricted to be collinear.For the sake of economy in computing time however it proved necessary to restrict the trajectories to a plane. Each collision is initiated with a randomly chosen impact parameter and angular orientation of the CH3I molecule. The thermal distributions of relative velocity and rotation and vibration of CH31 are also included. 1 Eyring Gershinowitz and Sun J. Chem. Physics 1935 3 786. Glasstone Laidler and 2 Evans and Polanyi Trans. Faraday Soc. 1939 35 178. 3 private communication from Dr. Bunker (Los Alamos Scientific Laboratory New Mexico, 4Smith J. Chem. Physics 1959 31 1352. Eyring Theory of Rate Processes (McGraw-Hill New York 1941). March 1962) who has kindly permitted me to describe this work here 278 GENERAL DISCUSSION The results obtained indicate that the assumed potential can account for all of the qualitative features inferred from the molecular beam experiments.The predicted distribution of product excitation is broad but shows a pronounced peak which puts most of the energy of reaction into vibrational excitation of the MI molecule. The angular distribution in the plane da/dX falls off more or less linearly from a maximum near x = 0" to a value about one-tenth the maximum at x = 180". Thus the intensity per unit solid angle (derived by averaging do/dx over azimuthal angles) is predicted to be strongly peaked along the direction of the initial relative velocity vector and quite asymmetric about = go" as observed. (It is noted, however that restricting the trajectories to a plane automatically imposes the glory effect regardless of how the angular momentum is partitioned between orbital and rotational motion.) In virtually all the successful collisions the trajectories " turn the corner '' smoothly and the complex proceeds to decompose within a vibrational period.This is not found to be the case when the calculation is limited to head-on collisions (i.e. b = 0 only); a large fraction of the collisions then lead to com-plicated " snarled " trajectories and da/dx has a maximum in the vicinity of = 90". Bunker and Blais are now extending these calculations to different potential surfaces and to other reactions. Dr. H. 0. Pritchard (University of Manchester) said I find the results presented by Charters and Polanyi puzzling. The fact that HC1+ is more likely to be formed in a lower vibrational state than in a higher one means that when we consider the reverse reaction HCl + Cl+H + C12 the more vibrationally excited is the HC1 the slower it will react.Since the reaction co-ordinate can only be described by an extension of the H . . . C1 distance it seems odd that the concentration of energy in the H-Cl vibration actually slows the reaction down. I would like to ask Dr. Herschbach whether it is feasible to settle this problem using a molecular-beam experiment ? We could consider a reaction like HBr + K, and we would need to have a velocity selector in each beam. Then for a fixed value of the relative translational energy one could study the rate of reaction as a function of the internal energy (rotational +vibrational) of HBr by varying the source temperature between say 200 and 1200"K and one could then repeat the process for various values of the relative translational energy.I realize this experiment is difficult but it seems to me that it should be possible from a detailed analysis of the results to decide what relative contribution is made to the activation energy by translational and internal energy and maybe even to find the relative contributions of the vibrational and rotational energy individually. Prof. D. R. Herschbach (University of California) (contributed) Unfortunately the direct experiment suggested by Dr. Pritchard would be extremely difficult. If velocity selectors (with resolution 1 of 10 %) were placed in both beams the yield of product would be reduced by a factor of about 10-5 or 10-6; at the peak of the angular distribution only 103 to lo4 product molecules sec-1 cm-2 would arrive at the detector (a monolayer in 104 years).Signals this weak have been detected in beam experiments,2 but elaborate instrumentation is required. There is the further handicap that even at 1200°K practically all of the HBr would still be in the ground vibrational state. It is possible to select a particular vibrational and rotational state of a beam by means of an electric resonance Stark-effect spectrometer.3 In favourable cases several of the lowest states can be resolved and the fraction of the original intensity 1 Hostettler and Bernstein Rev. Sci. Ins&. 1960 31 872. 2 Ramsey MoZecuZur Beams (Clarendon Press Oxford 1956) p.387. 3 Moran and Trischka J. Chem. Physics 1961 34 923 GENERAL DISCUSSION 279 transmitted in a selected beam is as much as 10-4. Again the apparatus required is complicated however. In a shock tube experiment Schott and Kinseyl have obtained results which indicate that the rate of the reaction H+02-+0+OH is enhanced when the 0 2 is vibrationally excited. Prof. J. C. Polanyi (University of Toronto) said I agree with Dr. Pritchard that it would be odd if concentration of energy in the H-Cl vibration were found to slow down the reaction HCl+Cl+H+C12. However though odd it could still be the case. Consider for a moment the exothermic reaction H+C12-+HCl+C1 that Mr. Charters and I have been studying. It is of course possible to draw a potential energy surface for this reaction across which a point mass (or more properly the average of a statistical assembly of sliding point masses) will prefer to travel by a path which passes smoothly out of the exit valley; that is to say a path involving little vibrational excitation of the products.If we try to send sliding masses in the reverse direction across this same surface we shall not necessarily increase their chances of crossing the barrier if we force them to oscillate to and fro as they move up the entry (previously the exit) valley. I remarked that we would not necessarily increase the chances of crossing the barrier in the reverse direction if we forced the point mass to oscillate. However, I left open the possibility that we might increase the chances of crossing the barrier in the reverse direction by introducing vibrational excitation into the bond under attack.This would not be contrary to the principle of microscopic reversibility, so long as the sliding masses after crossing the barrier in the endothermic direction, emerged in a non-thermal distribution. This point should perhaps be underlined. What precisely is involved in applying “ detailed balancing ” to the system H+ C12-+HCl+Cl? The observation is that when room temperature H is mixed with room temperature C12 (93 % in II = 0), the rate of reaction is greater into lower vibrational levels of the product HC1. It follows that the rate of the reverse reaction HCl+ Cl-H + C12(v = 0) decreases as HC1 is raised to higher vibrational states. It does not follow that the rate of reaction HClfCl to form C12 in any vibrational state decreases as HC1 is vibrationally excited.Dr. Pritchard’s expectation (which I shared2) that the rate of exothermic reaction would be greater into higher vibrationally excited states of the product molecule is probably exemplified in the series of reactions X + Na2jNaX + Na and Na+XM-+NaX+ M (X is Cl Br or I ; M is Cd or Hg).39 4 There are however two rather obvious differences between this family of re-actions and the H+Cl2 reaction. The first of these is that in the H+Cl2 reaction, the attacking atom is very light and the vibrational energy spacing in the product is very wide. As a consequence it is possible that the sliding point mass representa-tion (which is classical) may fail for the H + C12 case but succeed for the more common X+Na2 type of case.If this is so then even without marked dissimilarities be-tween the potential energy surfaces dissimilar behaviour would be expected. The second difference is that the rotational energy spacing is close for the product NaX wide for HCl. Since the total available angular momentum is not too different in the two cases it will be argued that it is less probable that energy will appear as rotation in NaX than in HCl. 1 Schott and Kinsey J. Chem. Physics 1958 29 1177. 2 Polanyi J. Chem. Physics 1959 31 1338. 3 Polanyi Atomic Reactions (Williams and Norgate London 1932). 4 Evans and Polanyi Trans. Faraday Soc. 1939 35 178 280 GENERAL DISCUSSION Fig. 1 and 2 exemplify this. They summarize the results of a calculation in which it is assumed in order to get some actual figures that 80 % of the heat of reaction goes into internal energy (rotation + vibration symbolized W‘) the remaining 20 % being dissipated as recoil energy.(Dr. Herschbach this Discussion reports 10 % as the recoil energy in a number of exchange reactions K+IR). The percentage of the internal energy W’ that will go into vibration is the balance of the percentage that is likely to go into rotation. This latter percentage we shall obtain from the requirement, J‘ < [J + L], where J’ is the rotational angular momentum of the product molecule J and L are the rotational and the orbital angular momenta of the reagents (this symbolism conforms with that of Dr. Herschbach’s paper). Higher values of J than the upper ~ %W b s Vibration FIG.l.-H+C12 (0 is C12). FIG. 2.-Cl+Na2 (+ is Na2). limit set by eqn. (1)* appear less probable much higher values much less probable, since they require for conservation of angular momentum a precise cancellation of J’ with L’ that is cancellation of the rotational angular momentum of the pro-duct molecule with the orbital angular momentum of the products as a whole. This chosen upper bound for J (eqn. (1)) is seen to be somewhat arbitrary. It is interesting nonetheless to compare the consequences of this choice in the two families of reactions under consideration. J is a constant for a given reagent molecule at a given temperature. L varies with the line of approach of the attacking atom. The rings in fig. 1 and 2 indicate various possible approaches characterized in each case by the impact parameter (b,A) which gives the distance of closest approach at the moment of grazing collision.L = pvb where p is the reduced mass and v is the relative velocity. For atomic hydrogen v was taken as 4.5 x 105 cm/sec (kinetic energy 2.5 kcal/mole ; equivalent to the activation energy for the reaction H+C12). For atomic chorine II was taken as 5 x 104 cm/sec (kinetic energy 1 kcallmole; normal thermal energy of 0.5 kcal would probably suffice to bring about the reaction Cl+ Na2 but by somewhat exaggerating the velocity of C1 we are erring on the side that will tend to minimize the striking difference between fig. 1 and 2). From the figures it is seen that as the distance of closest approach is increased to about 2A, the maximum available angular momentum increases by a factor of 1.7 for H+Clz, * In my remarks at the Discussion I neglected these ; I am most grateful to Dr.Herschbach for pointing this out to me GENERAL DISCUSSION 28 1 2.2 for Cl+Na2. This is equivalent to roughly a threefold ((1.7)2) increase in the energy that can go into rotation of the product from H + C12 and a five-fold increase for Cl+NaZ. For HCl product where an appreciable amount of energy can always go into rotation a three-fold increase in that amount of energy is very significant in decreasing the percentage that is bound to go into vibration. For NaX where only a trifling amount of energy can go into rotation a five-fold increase in that energy has no significance. Fig 3 is a schematic potential energy diagram in the reaction co-ordinates of two processes A+BC-+AB+C one of which is depicted as leading to a high vibra-tional level in a “normal” potential energy curve and one as leading to a low vibrational level of a potential energy curve which includes a high energy of rotation.FIG. 3.-Schematic potential energy diagram in the reaction co-ordinates of exothermic processes A+-BC+AB+C; one with low rotational energy of product AB (solid line) and one with high rotational energy of AB (broken line). Both reactions have activation energy E and heat of reaction Q. To sum up except when the product molecule has a very low moment of inertia, a large percentage of the internal energy will be present as vibration in the pro-duct. In the rare event that the product does have a low moment of inertia the distribution among vibrational states of product is likely to be sensitive to the dis-tribution of impact parameters in a statistical sample of “ successful ” collisions (collisions leading to reaction).Prof. D. R. Herschbach (University of California) (contributed) From the con-servation laws alone it is not possible to establish a maximum fraction of W’ that can appear as rotational excitation. The products are allowed to have any values of L’ and J’ consistent with energy conservation as long as the vector sum L’+ J’, equals the total angular momentum supplied by the reactants L+ J. In a reaction A+BC+AB+C the rotational energy of AB is proportional to J’2 = I L+ J 12+L’2-2 I L+ J I L’ cos $, where $ is the angle between L‘ and L+ J.When $ > 4 2 for example the L 282 GENERAL DISCUSSION and J vectors can both have much larger magnitude than L+J. Thus the con-servation laws allow all of the energy released in the reaction to go into rotation of AB; what fraction actually does cannot be predicted without assuming some-thing about the forces involved in reactive collisions. These forces are expected to become effective only in sufficiently close collisions. This permits a rough estimate of the maximum initial impact parameter b and the total angular momentum that can contribute significantly to reaction [as indicated already under eqn. (17) of our paper]. The range of the final impact parameter b’ is likewise expected to be limited by the short range of the forces.Here we define b’ as the distance of closest approach of a pair of product molecules when their asymptotic straight-line trajectories are extrapolated backwards. The maximum values of b and bf in a reactive collision probably cannot be much greater than bond lengths in the reactant and product molecules. The restriction which this assumption imposes on the orbital angular momentum of the products L’ = p’db’ has been discussed elsewhere.1 2 It also implies an upper limit on the rotational momentum J’ given by This limit is determined with L’ oriented oppositely to L+J. Another rough bound probably more representative of the average rotational excitation may be obtained by assuming L is distributed isotropically with respect to L+ J ; an average over all orientations then yields If L‘ is assumed to be negligibly small (1) and (2) are equivalent and we obtain the bound considered by Polanyi, Eqn.(3) may also be derived from the less stringent assumption that L’ < 2 I L + J I cos $ for the dominant contributions to reaction ; this requires $ < n/2 and L’ < 2 I L+ J I however. These various bounds are compared in table 1. For the J’ z I L + Jmax I +L&ax. (1) (J”) t I L + J&ax I +G2ax- (2) J’z I L+ J Imax- (3) reaction Na2+ C1 H+ C12 K+ CH31 Rb+CH31 CS + CH31 TABLE 1 bound to rotational assumed I excitation (kcal/mole) bmax (A) (1) (2) (3) 2.5 43 30 2 any 36 36 36 4-0 10 5 3 4.0 5 3 2 4.0 3 2 2 examples treated by Polanyi we used the same parameters and assumed that the probability of reaction is negligible unless b72.5 A.For the M+ RI reactions we used values of the final relative velocity v’ derived from the observed angular dis-tributions and took b74-0A. The results given in the table refer to the rotational excitation of MI and do not include any excitation of CH3. Since the small moment of inertia of the CH3 radical enables it to carry away large amounts of rotational energy with relatively low angular momentum (e.g. 10 kcal/mole for J3 = 20 h/2n in contrast to KI which has only 1.7 kcal/mole for J4 = 100 h/Zx), the observation that in reactions involving larger R groups the internal excitation does not decrease (but rather increases somewhat) suggests that CH3 must have little rotational momentum probably no more than 10 h/27r GENERAL DISCUSSION 283 Table 1 and other calculations 1 9 2 lead to the rule stated by Polanyi with two amendments which recognize the role of L’.First even for a product with a large moment of inertia we can set a low limit on the rotational excitation only when we have evidence that GaX is not too large. The reason the M + RI reactions conform to the rule is that the v’ estimated from experiment is rather small and thus &ax is less than I L+ J Imax. For the Naz + C1 example this is no longer the case because the value of v’ used is much larger. Also the moment of inertia of NaCl is con-siderably smaller than that of the MI molecules. Second for H atom reactions as well as others we must expect the actual distribution of rotational excitation (in contrast to the upper bound) to be sensitive to the distribution of both b and b’.In the H+C12 example we note that up to 36 kcal/mole (100 % of W’) may go into rotational excitation regardless of the value of b’. However in H atom reactions there is usually a large increase in reduced mass on formation of the pro-ducts (p<p’). Angular momentum therefore can be readily taken up in orbital motion even for rather small values of v’ and b’. Thus the upper bound to the rotational excitation will always be high when a product has a very small moment of inertia but the actual excitation produced in the main course of the reaction may be far below the bound (as in the CH3 example) and will be strongly affected by the forces that govern the break-up of the collision complex.There is a case exemplified by the reactions M + HX- MX + H, in which a high level of rotational excitation in a product is required by the postulated bounds on the impact parameters. On the reactant side L%J whereas on the product side we expect L’QJ and consequently L x J’. That is here we expect pvb+p‘u’b’ since the reduced mass of the products (approximately just the mass of H) is far smaller than that of the reactants (26 times smaller for K+HBr 66 for Cs+HI). Because the reaction is only slightly exothermic u’ cannot become large enough to offset more than a fraction of the mass ratio. The velocity depend-ence of the scattering of K+HBr beams does indeed indicate that KBr is formed with high rotational momentum.2 An interesting consequence of L N J’ is that the angular momentum of MX is predicted to be strongly polarized with J’ nearly perpendicular to the direction of the initial relative velocity vector.In a beam experiment this polarization should have a pronounced effect on the deflection pattern obtained when the MX molecules are made to pass through an inhomo-geneous electric field.1 Such an experiment is being attempted at Berkeley. In principle it should give information about the distribution of L in those collisions which lead to reaction. Dr. A. B. Callear (University of Cambridge) said The relaxation of vibration-ally excited nitrogen by nitrous oxide is probably due to the vibrational exchange process, since nitrous oxide has a vibrational frequency at 2222 cm-1. The energy discrep-ancy is thus about 130 cm-1.According to fig. 9 of my paper such an exchange should require about 1000 collisions. The majority of polyatomic molecules show a single relaxation time 3 corresponding to the vibration-translation relaxation of molecules in their lowest vibrational level which for N20 is 588 cm-1. This would N ~ ( v = l)+N2O(u = 0) = N ~ ( v = O)+N2O(u = l), 1 Herschbach The Vortex 1961 22 348. 2 Beck Greene and Ross J. Chern. Physics (to be published) and private communication. 3 Lambert and Salter Proc. Roy. Soc. A 1959 253 277 284 GENERAL DISCUSSION require 10,000 collisions for relaxation. Thus if N20 does exhibit a single relaxation time (it is doubtful if ultrasonic measurements have been made at temperatures where the highest vibrational frequency makes a significant contribution to the specific heat) the rate of vibrational relaxation in N2+N20 mixtures will be about 106 times faster than in pure N2 when relaxation requires about 1010 collisions at room temperature.Even if the largest energy interval the difference between the two highest frequencies of the N20 molecules (937 cm-I) determines the rate of relaxation the rate of relaxation would still be faster than in pure N2 by several powers of 10. Dr. F. Kaufman (Ballistic Research Lab. Maryland) said I would like to clarify a point in our paper. In all experiments from which kinetic information on the decay of OH was obtained the concentration of NO2 added to the gas stream containing H-atoms was less than that of the H-atoms present. Under these con-ditions OH formed equals NO2 destroyed.When excess NO2 is used however, this equivalence no longer holds because the three reactions H + NO2 -+ OH + N02, 20H+H?O + 0, and OH + 0 - 0 2 + H, produce the over-all stoichiometry 2H + 3N024H20 + 0 2 + 3N0, i.e. 3N02 are destroyed by 2H. This scheme is in accord with Prof. Schiff’s findings and with Dr. Thrush’s recent results but in conflict with Clyne and Thrush’s earlier paper.1 Regarding the effect of M in three-body recombination processes one must not generally expect M effects as large as those in iodine atom recombination. Mr. Kelso and I are now carefully studying the rate of 0 + NO + M+N02 + M for a wide range of M. Though the role of electronically-excited states of NO2 in this reaction has not yet been clarified our early results indicate that a factor of three in the rate constant encompasses the effect of varying M = He Ar 0 2 C02, N20 or SF6.Finally indiscriminate statements should no longer be made about the large fraction of the energy liberated in atom-molecule reactions which goes into vibrational excitation of the newly-formed bond. There is no doubt that many such reactions produce some preferential vibrational excitation in the new bond but it is often implied that most product molecules initially come away with high vibrational energy i.e. that much or most of the total energy of reaction goes into that particular internal degree of freedom. This is not supported by any of the examples studied within the last eight years. On the contrary all quantitative studies have shown that the fraction of product molecules which have very high vibrational excitation is either small or negligible.Prof. G. Porter (University of Shefield) said Mr. G. Black and I 2 have made a preliminary study of the decay of OH radicals produced by the vacuum u.-v. flash photolysis of water vapour and have obtained results which at first sight, appear to conflict with those of Del Greco and Kaufman. We found that the decay 1 Clyne and Thrush Trans. Furaduy Soc. 1961,57,2176. 2 Black and Porter Proc. Roy. SUC. A 1962,266 185 GENERAL DISCUSSIOP\t 28 5 was second order in OH and first order in inert gas pressure and interpreted this in terms of the reactions ki H+OH+ M+H20+M, OH+OH+M+H202+M. k2 The observed termolecular rate constant is then equal to kl+2k2 and since it seems improbable that kl is less than k2 the termolecular recombination process (2) must predominate over the bimolecular reaction k3 OH+OH+H20+0 proposed by Del Greco and Kaufman.These results can however be reconciled in the following way. If the recom-bination rate constant kl has a value in the range 10-30 to 10-31 cm 6 molecule-1 sec-1 and the value of k3 is 2.5 x 10-12 cm3 molecule-1 sec-1 as given in the paper the mechanism should change from 2nd to 3rd order in the pressure range 10-2 to 10-1 atm. Our work was all carried out at higher pressures than 10-1 atm and that of Del Greco and Kaufman at lower pressures than 10-2 atm. The order of magnitude of k2 is reasonable for the recombination of simple radicals of this type.Prof. H. I. SchB (McGiZZ University) said We have recently studied the reaction of H-atoms with NO2 and with 0 3 in a fast-flow system using a mass spectrometer. reactant added mm 10-2 FIG. 1. Fig. 1 shows the amount of 0 3 and NO2 destroyed for the same initial H-atom concentration as a function of the initial reagent concentration. The reaction time was 25 msec. It is apparent that the reactions which consume NO2 are faster than those which consume 03. The plateau values correspond to 1.5&-0.1 NO2 mole-cules reacted per H-atom originally present and 3.1 +O-2 0 3 molecules reacted per H-atom 286 GENERAL DISCUSSION In the reaction with N02 the amount of NO formed was equal to the amount of NO2 consumed. This stoichiometry is consistent with the mechanism H+N02+NO + OH OH+OH-+H20+ 0 0 + OH+Oz + H 0 + N02+NO + 0 2 (3) (4) and the value of kl was found to be 4.8 x 10-11 cm3 molecule-1 sec-1 at room temperature.The same stoichiometry is obtained whether k3> k4 or vice versa. However, Clyne and Thrush 1 have measured the HNO emission accompanying the reaction and concluded that one H-atom is consumed per NO2 molecule. They claim that NO2 can be used as a titrant for H-atoms. However if k3 is as large as Del Greco and Kaufman suggest then the stoichiometry obtained by Clyne and Thrush would not apply. Would Dr. Kaufman care to comment on this point? The corresponding mechanisms for the 0 3 reaction would be H + 03+OH + 0 2 OH+OH+HzO+O 0 + OH+02+ H 0+03+202. (6) Again a maximum of 1-5 0 3 molecules would be destroyed per H-atom initially present as compared with the observed value of 3-1+2.Kaufman has suggested that the reaction may be faster than originally believed. If this reaction were included the 0 3 decomposition could be increased to 2 per H-atom. However addition of H2 actually decreased the amount of 0 3 consumption. OH + H2+H20 + H (7) There may however be a chain reaction resulting from the reaction OH 4- 0 3 - + H02 4- 0 2 (8) followed by HOz + O3-+OH 4- 202 (9 ) and H02+H-+OH+OH. (10) Alternately the OH formed in reaction (3) could be vibrationally excited and de-compose 0 3 by the reaction Inclusion of this reaction could lead to a total of 3-5 moles of 0 3 decomposed per mole of H-atoms. To test these alternatives N20 was added to the system.This should de-activate OH* but have no effect on the chain. The amount of 0 3 decomposed de-creased when N20 was added indicating that reaction (1 1) does play an important role in this system. (Paper by Del Greco and Kaufman.) Mr. M. A A. Clyne and Dr. B. A. Thrush (University of Cambridge) said We are in full agreement with Del Greco and Kaufman regarding the mechanism of the H+NOz reaction and the absence of vibrationally excited OH in this reaction. In experiments on the infra-red emission from this reaction carried out at Ottawa OH' +03+OH+02+O. (1 1) 1 Clyne and Thrush Trans. Faraday Soc. 1961 57,2176 GENERAL DISCUSSION 287 last summer in collaboration with Dr. D. A. Ramsay one of us (B. A. T.) was unable to detect emission by OH but observed strong emission by H20 formed in the subsequent reactions.Our results,l however can only be explained by the gener-ation of hydrogen atoms in the reaction of OH with H2, This is consistent with the results of Del Greco and Kaufman who show that k5 = 7 5 2 x 10-15 cm3 molecule-1 sec-1 at 310"K and suggest an activation energy E5 < 6-5 kcal/mole. The earlier value 2 reported for E5 of 10 kcal/mole is similar to that (9.2+0-6 kcal/mole) for the reaction 3 0 + H2+ OH + €3, and the experimental technique used in the early work suggests that the measured activation energy was actually that of reaction (6) since reaction (2) rapidly converts OH to 0. OH+H2+H20+H. (5) (4) Providing sufficient time is allowed for the rapid subsequent reactions, OH+OH+HzO+O (2) and 0 + OH+H + 0 2 (4) to proceed to completion H atoms in the absence of excess molecular hydrogen can be titrated with NO2 using the disappearance of HNO emission to indicate the end point.The overall stoichiometry is [NO21 = +[HI which agrees with a calori-metric ratio of 0-53 to within the known errors of such measurements.1 We have measured the concentrations of oxygen atoms produced in the H+NOz reaction. These concentrations are governed by reactions (2) and (4) and are given by the relationship 1/[0] = 3k4t when k2t[OH]>l. Under these conditions plots of 1/[0] against time were excellent straight lines yielding kq = 5+2 x 10-11 cm3 molecule-1 sec-1 at 293°K. This is about four times greater than the value reported by Del Greco and Kaufman but the difference may arise from the different methods used to study this reaction i.e.the difference between homogeneously generated 0 atoms and oxygen atoms from a separate flow system. Dr. B. G. Gowenlock (University of Birmingham) contributed The value of D(H-NO) = 48.6 kcal mole-1 reported by Clyne and Thrush enables us to estimate the value of D(CH3-NO). This value has importance in relation to the mechanisms proposed for the inhibition of chain reactions by nitric oxide. Inspection of the table shows that that D(H-X) > D(CH3-X) by about 15-25 kcal mole-1. X CH3 NH2 F C1 Br I OH OCH3 COCH3 C6H5 D(H-X) 102 104 137 102 87 71 118 100 91 102 D(CH3-X) 84 80 110 80 67 54 88 77 73 89 Thus we estimate D(CH3-NO) as 30 + 5 kcal mole-1.This value suggests that the equilibrium may participate in nitric-oxide-inhibited reactions. A previous estimate 4 of D(CH3-NO) = 57 +4 kcal mole-1 was based on the approximate equivalence of B(X-NO) and D(X-NO2). Thus an anomalous position is presented for bond dissociation energy patterns either D(CH3-NO) CH3 + NOSCH3NO 1 Clyne and Thrush Trans. Faraday SOC. 1961,57 2176. 2 Avramenko and Kolesnikova Zhur. Fiz. Khim. 1950 24 207. 3 Clyne and Thrush Nature 1961,189 135. 4 Gowenlock Trotman and Batt Chem. SOC. Spec. Publ. 1957 10,75 288 GENERAL DISCUSSION is much less than D(CH3-N02) or D(CH3-NO)*D(CH3-N02) and thus D(CH3-NO) > D(H-NO). It is a consequence of Clyne and Thrush's value for D(H-NO) that one of these anomalies exists. Mr. M. A. A.Clyne and Dr. B. A. Thrush (University of Cambridge) (contributed) : The values of D(R-NO) may be close to those for D(R-02) since the value of D(H-NO) = 48-6 kcal/mole given in our paper is very close to the accepted value of D(H-02) = 47 k 3 kcal/mole. An additional similarity between HNO and HO2 is that our value for the rate constant for the reaction H+02+Ar = H02+Ar, 1.2f0-3 x 1016 cm6 mole-2 sec-1 at 293"K is remarkably close to the value of 0-8k 0.1 x 1016 for H + NO + Ar at 293°K given in our paper. Our value of D(H-NO) also yields some information about D(N-H) which is thought to be close to 85 kcal.1 Taking D(N-H) = 85-x kcal/mole we obtain D(HN=O) = 114 + x kcal/mole for the related isoelectronic species D(O=O) = 1 18 kcal/mole and D(HN=NH) = 1 10 + 2x f 5 kcal/mole.2 This suggests that D(N-H) lies between 80 and 85 kcal/mole.Dr. B. A. Thrush (University of Cambridge) said Investigations of chemilumin-escent combination reactions such as those reported by Dr. Sugden and by our-selves stress the importance of considering all the stable electronic states of a molecule XY which can be formed in a three-body combination process X+Y + M since com-bination via electronically excited states is comparable in rate to combination directly into the ground state. In cases such as HNO where there is rapid crossing between the radiating state and the excited state formed in the initial combination the vibra-tional intensity distribution in the electronic emission spectrum provides a measure of the steady-state energy distribution of the excited molecules formed in a com-bination reaction.This distribution falls off at an energy which is several times kT below the dissociation limit. These highest levels are presumably depopulated by collisional redissociation a process which would be favoured by the associated increase in entropy and which would account for the observed negative temperature coefficient of these combination reactions. Dr. E. E. Nikitin (Acad. of Sci. Moscow) said The ratio EIkTis a poor criterion for the validity of the perturbation approach to the non-equilibrium rate constant. Generally speaking deviations from the equilibrium distribution at the bottom of the potential well decrease with increasing E/kT ratio but in many cases the rate constant is dependent on the population of the upper energy levels.A good ap-proximation to k can be expected for cases where transitions from the bottom of the well proceed as rapidly as from the top. This is the case for approximately equal masses (m-M). Thus for m-M the energy dependence of k is expected to be the same as that obtained for the simple dissociation model in which perturbation of the equilibrium distribution is neglected and dissociation occurs in every collision for which the total energy (internal energy plus the kinetic energy along the line of collision) exceeds E. For this model the expression for k k- cAv(E/?)* exp (- EP) - Ac(E/M)* exp (-PE) is identical with (12) except for the numerical factor. On the other hand when m+M and the amount of energy transferred is small, it is better to use the ladder model for dissociation in which k-cAu(AE)P exp (-PE), 1 Gaydon Dissociation Energies (Chapman and Hall London 1953).2 Foner and Hudson J. Chem. Physics 1958,28,719 GENERAL DISCUSSION 289 and AE is an energy step near the dissociation limit. Introducing AE-yE for a collision of atom M with energy N E with atom rn with energy - kT and u - (kT/rn)f, one obtains k - Ac(y/flM)*bE exp -flE). This is consistent with (21) but not with (12). Thus the Fokker-Planck equation seems to give the right answer for 7-0 and the perturbation approach fails completely. Dr. E. E. Nikitin (Acad. of Sci. Moscow) said In connection with Bak's paper, it is interesting to consider the applicability of hard-sphere model to the calcxlation of the vibrational relaxation times and the dissociation rate constant of diatomic molecules in a heat bath.The most important parameter in any collision theory is < = wz where w = a(&) is the vibrational frequency near the energy level E of diatomic molecule and z is the collision time. For a Morse potential we can put (E is dissociation energy M reduced mass of the molecule l / a range of action of exchange forces m reduced mass of colliding pair). We obtain therefore, For the hard-sphere model to be applicable the condition c+ 1 must be fulfilled. It is evident from the above that for vibrational relaxation when the energy region concerned is small (&E) condition 5 4 1 is unlikely to be fulfilled. For most cases B- 1 and the adiabatic theory of Landau and Teller is a good approximation.The hard sphere model can be applied to the non-equilibrium dissociations if condi-tion <B- 1 is fulfilled in the energy range kT near the dissociation limit E. Intro-ducing E-C-kT we obtain for this case <-(m/M)*. So under condition m<M, the hard-sphere model is a reasonable one and eqn. (21) of Bak's payer gives the non-equilibrium rate constant. Prof. Thor A. Bak (University of Copenhagen) said I agree with Dr. Nikitin that for small masses eqn. (21) is better than eqn. (12). I believe however that the simple Fokker-Planck approach is only valid for an extremely small mass ratio. As far as I know the range of validity of the expansion of the integral operator is not known and it is therefore a little dubious to use it for finite mass ratios but a correction of this kind to the simple Fokker-Planck results appears to be necessary.I should like to add that we have shown recently 1 that the rate constants derived from the Fokker-Planck equation using the Morse potential and the cut-off harmonic potential only differ by a factor of about 2. In the Fokker-Planck limit anharmoni-cities therefore seem to be of minor importance. Prof. G. Porter (Shefield University) w d Ole o f the consequences of the kinetic scheme given in my paper is that departures from third-order kinetics are predicted at low temperatures or when the heat of formation of the complex is very high. R+M+RM will be shifted so far to the right that most radicals exist as complexes. My col-leagues Dr. Townsend and Prof.Szabo have realized this situation in the system of iodine atoms with nitric oxide as a chaperon. At low pres5urcs of NO the re-Under these conditions the equilibrium 1 Bak and Andersen Mat. Fys. Medd. Dan. Vis. SrAk 1961 33 no. 7. 290 GENERAL DISCUSSION action is third order with the very high rate constant of 3-0 x 1013 1.2 mole-2 sec-1 at 60°C but at high NO concentrations the rate falls off until eventually the recom-bination rate decreases nearly linearly with NO pressure. This system is an interesting extreme case of the complex mechanism of atom recombination and indeed we have been able to observe the absorption spectrum of the NO1 intermediate and to follow the kinetics of the reaction via the 12 and the NO1 concentrations separately.Dr. E. A. Ogryzlo (University of Br. Columbia) said Prof. Porter presents three mechanisms by which " third-order recombination reactions " can occur in the presence of a chaperon M. However eqn. (2) which is derived from this scheme allows only two of these mechanisms to contribute to the process for any given combination of R and M. One of the assumptioiis in the paper which leads to this conclusion is that [RM*]/([RM*] + [RM]) = exp (- AE/RT). (3) Even if one assumes a negligible entropy difference between RM + RM* (is. identical statistical weight factors for the two states) the relation must be P M * I exp( - AE/RT) [RM] + [RM*] = 1 + exp( - AE/RT)' (4) and therefore [RM]/[RM*] = exp (AEIRT) (5) from which K7 = exp (AEIRT). (6) The substitution of eqn.(6) into eqn. (1) yields k = k,K + k,K + kllK exp (AEIRT) = k,' + k,"+ krlll, where ki k:' and kfll are the third-order rate constants for mechanisms 1 2 and 3 respectively. It should be noted that when AE = 0 and there exist no bound states of RM*, [RM] = 0 and hence the third mechanism ceases to exist. It is also important to remember that eqn. (7) is based on an insignificant entropy difference between RM and RM*. This is not likely to be the case for very weakly bound complexes, where the entropy change may well dominate the relative concentrations of these two species. Thus for example when AE is small and M is polyatomic a small equilibrium concentration of RM could result in mechanism (2) dominating the recombination process. Prof. G. Porter (Shefield University) said The modifications suggested by Dr.Ogryzlo are incorrect as can be seen by examination of the limiting condition AE-0 [RM]-+O. His eqn. (4) and ( 5 ) become inequalities as this limit is ap-proached and the last two terms of his eqn. (7) become identical so that the contribu-tion of mechanism 2 is counted twice. The second term of eqn. (2) in my paper incorporates both mechanisms 2 and 3 and is applicable to all values of A,?? down to zero. The validity of the equation [RM*]/([RM*] + [RM]) = exp (- AE/RT) is readily appreciated if the meaning of the two concentration terms is considered carefully. [RM*] is the concentration of complexes of R and M with energy 3 AE and [RM] is the concentration of complexes with energy -c AE. Both sides of the equation are therefore equal to the fraction of complzxes having energy > AE in two square terms.The equation does of course ass;ime negligible entropy differ-ence between RM and RM" GENERAL DISCUSSION 291 Prof. T. L. Cottrell (University of Edinburgh) said If Prof. Porter’s radical-molecule complex theory is correct then there should surely be a detectable equilib-rium concentration of I3 molecules in iodine vapour. The vapour density data of Perlman and Rollefson 1 which lead to an accurate value of the heat of dissociation of iodine do not suggest that any I3 is present. I should like to ask Prof. Porter whether he has calculated the I 3 concentration he would expect under their experi-mental conditions and therefore whether there is a real discrepancy here? Prof.G. Porter (Shefield University) said The equilibrium constant of forma-tion of I3 from I and I2 is estimated from the recombination results to be about 4 x 10-3 exp (5000/RT) 1. mole-1. Under the experimental conditions of Perlman and Rollefson (723-1274°K and 0-1-1 atm) this leads to a concentration of I3 some-what less than the 0.3 mole % given by these authors as the lower limit of 13 which could have been detected. Dr. J. Keck (AVCO Res. Lab. Mass.) said I should like to point out that the variational theory 2 developed by the author also fits the observed recombination rates presented by Porter. In the temperature range from 300 to 500°K where the experiments were performed the variational expression for the recombination rate constant given by eqn.(45) of ref. (1) is k = kB(0) = 2.0 x 10802 (exp (~/RT)-0.6)1.~ molew2 sec-l (1) where CT is the range in 8 and E is the depth in kcal of the Lennard-Jones potential used to represent the interaction between an iodine atom and the chaperon. Note that the numerical factors in eqn. (1) are uniquely determined by the interaction potentials between the particles. The factor exp (EIRT) which gives the main tern-perature dependence of both the variational theory and the radical-molecule complex theory has its origin in the assumption common to both theories that IM is in equilibrium with I+M. A rough criterion for the validity of the assumption is that [R]/[M] < exp ( -E/RT). The apparent negative activation energy implied by eqn. (1) is E = ~/[1-0.6 exp (-E/RT’].If we use the experimental values of to determine E as Porter has done and choose a mean value of 0 = 3.7 A determined from parameters given in Hirschfelder Curtiss and Bird,3 we obtain the results plotted in fig. 1. It is clear that the variational theory fits the observations just as well as the radical-molecule complex theory. However the former theory gives binding energies somewhat smaller than the latter. In the cases involving inert-gas chaperons this leads to binding energies which are closer to those expected for the Van der Waals force and therefore seem more acceptable. In fact considering the possibility 4- 5 of an additional small negative temperature coefficient in the pre-exponential factor of eqn. (1) due to lack of equilibrium in the vibrational degrees of freedom it is possible that there is no additional force in these cases at all.In cases which do not involve inert-gas chaperons there remains a clear indication of additional forces. This possibility was recognized by the author in his earlier work,2 and it is for this reason that absolute calculations of rate constants were limited to inert-gas chaperons. 1 J. Chem. Physics 1941 9 362. 2 Keck J. Chem. Physics 1960,32 1035. 3 Hirschfelder Curtiss and Bird Molecular Theory of Gases and Liquids (John Wiley and Sons, 4 Widom J. Chem. Physics 1960 34 2050. 5 Pritchard J. Physic. Chem. 1961 65 504. Inc. New York 1954) 292 GENERAL DISCUSSION The reason for the difference in the binding energy predicted by the two theories is that the pre-exponential factor in the radical-molecule complex theory is pro-portional to the temperature while that in Athe variational theory is nearly tem-perature independent.This in turn is associated partly with the fact that the vari-ational theory leads to cross-sections which decrease with increasing temperature and partly with the fact that in the variational theory we have averaged over the forces which act on the particles while in the radical-molecule complex theory, the average is over the relative velocity of approach of the particles. VAR I AT ION AL 0 1 I I I I 2 3 4 5 E (kcal mole-1) FIG. 1 .-Comparison of experimentally observed recombination rate constants k for iodine in the presence of various chaperon molecules with curve predicted by the variational theory.The parameter E is the depth of the Lennard-Jones potential used to fit the observed temperature coefficient. Although the agreement between theory and experiment exhibited in fig. 1 is very satisfactory in an overall sense the assumption of a collision diameter in-dependent of the chaperon molecule is certainly unrealistic. We have therefore, analyzed the data to obtain the collision diameters as well as the binding energies with the objective of making more apparent possible correlations between these parameters and the character of the chaperon. The results are shown in fig. 2. The circles indicate the experimental values and the bars are theoretical values com-puted from data given in Hirschfelder Curtiss and Bird on the assumption that iodine is equivaknt to xenon.In obtaining the experimental values we have multiplied eqn. (1) by a correction factor [PI 2/(p3 + p12)]0-9 suggested by the Monte Carlo trajectory calculations reported in the paper submitted to the Discussions by the author. While strictly speaking this correction was calculated only for the inert-gas chaperons it probably has some validity even for complex chaperons and in any case it is not very large. The most obvious trend in results is the tendency for simple molecules to have collision diameters somewhat smaller than the theoretical values. This does not seem unreasonable since the existence of an additional attraction between the iodin GENERAL DISCUSSION 293 and chaperon would certainly tend to move the minimum in the potential curve to smaller values of internuclear separation.For complex chaperons the comparison can only be made for benzene in which case the experimental collision diameter is larger than the theoretical. Whether this is significant is not clear but one possible explanation would be that the possibility of transferring energy to vibrational degrees of freedom in complex molecules makes them more efficient chaperons. This effect is not included in the present calculations. 0 EXP. I HCB I I I I l l 1 1 1 I I I 1 0 0 lo o o 0 0 0 0 0 I I I I 0 0 0 0 0 I l l 0 I I I l l I I I 1 -2 05 I 2 5 E (kcal) FIG. 2.-Lennard-Jones parameters for the interaction of iodine with various chaperon molecules M. The circles are the experimental values deduced from observations presented by Porter; the bars are the theoretical values obtained from data in Hirschfelder Curtiss and Bird on the as-sumption that iodine is equivalent to xenon.Although it is probably somewhat premature to take these observations too seriously the author feels that use of refined theories in conjunction with reaction rate data is a potentially powerful method of obtaining information about the intermolecular forces which operate in chemical reactions. I am sure this feeling is shared by Prof. Porter and one purpose of these comments was to emphasize this point. In concluding I would like to point out some of the advantages of the variational theory over competing theories. First it relates the reaction rate directly to the interaction potential without the usual uncertainty involving the choice of an effective cross-section which arises in most three-dimensional collision theories.Secondly it includes all the classical reaction paths leading to recombination. Thirdly it can be systematically improved using objective mathematical procedures. Finally it can be applied in principle to any chemical reaction and is thus a promising basis for a unified theory of chemical reaction rates. Dr. F. T. Smith (Stanford Res. Inst. Calif.) said In using information on classical trajectories from large-scale computers we must not forget that our prob-lems are really quantal. The classical approximation is good for large quantum numbers (shall we say for vibrations FZ >lo?) but this means large quantum numbers in all degrees of freedom.As an example take the exchange reaction A+BC-+AB+C assuming an activ-ation barrier. First the average This coiidition is not often fulfilled. There are two restrictions to a classical treatment 294 GENERAL DISCUSSION de Broglie wavelength of thermal motion say 1 = h(pkT)-? must be small compared to characteristic lengths (radii of curvature for instance) of the features of the potential surface A Q ao (1). This condition is most obviously violated in reactions involving the lightest atoms especially H and when it is violated quantal interference effects are to be expected. The second condition for a classical treatment can be formulated easily if you consider the region of the saddle-point where the col is long and smooth enough to have ao9A.In this region the co-ordinates are approximately separable and those normal to the reaction co-ordinate include rotations and vibrations of the activated complex. For a completely classical approximation to be valid all these motions must be in states of high quantum number. Thus for even the highest vibration frequency in the transition state we have the condition hvzax <AT (2). Such a condition is seldom satisfied in chemical kinetics. This condition is not new-it was recognized by Eyring and others long ago in their use of the quantal partition function for vibrations and the zero-point vibrational energy in the transition state. As long as the condition (2) is not satisfied deductions from classical trajectory calculations arr. always questionable.In 3-body reactions treatments such as Keck's are somewhat better justified as one is more likely to be in the region of high quantum numbers. Nonetheless, quantum effects may become important-for example in the passage near the top of a rotational barrier where the de Broglie wavelength becomes large. Prof. K. J. Laidler (University of Ottawa) said The two basic mechanisms for atom and free-radical combination may be formulated in a manner slightly different from that of Prof. Porter as follows. The energy-transfer mechanism using Prof. Porter's notation is 1 2R329, R +M+R2+M. 2 5 The species RZ is one in which (following the ideas of and Ramsperger for the reverse unimolecular reactions) Hinshelwood Kassel Rice there is free flow of energy between s of the normal modes.The equilibrium constant for reaction (1) can then be written as fa bs-l j- (s-l)!' K = -where the f are the conventional partition functions (products of translational, rotational and vibrational factors) and b is equal to Eo/RT where Eo is the energy in excess of the zero-point energy No exponential term appears in this equation since there is no transfer of energy. As suggested by Prof. Porter k5 may be set equal to the collision number 2, so that the third-order rate constant for the combination process becomes For the combination of atoms s = 1 and k is found to be of the order of 109 to 1010 1.2 mole-1 sec-1 in agreement with the experimental values for the combination of iodine atoms in the presence of He Ar and H2. The higher rates obtained with 12, C6H6 etc.as third bodies cannot however be explained in terms of this mechanism. 1 Gill and Laidler Proc. Roy. SOC. A 1959 250 121 GENERAL DISCUSSION 295 For radical combinations s is greater than unity (-9 for CH3+CH31) and the As Prof. Porter pointed out such reactions calculated k values are much higher. probably always occur by this energy-transfer mechanism. Porter’s radical-molecule complex mechanism may be written as follows : 3 4 7 R+M+RM*, RM* +M+RM + M + AE, 8 1 1 RM + R+-t+R2 + M, and the combination rate constant is k = klK3K7. (3) If reaction (3) produces an energized species in which there is flow between s’ normal modes Since in reaction (7) there is the disappearance of the species having flow within s’ modes (s‘- l)! AE K = ~ bS’-l exp -RT‘ The combination rate constant is then f R M AE f R f M RT k = 2 - exp -( 5 ) (lo9 to lo1’) exp (AEIRT).(7) For atoms the rate constant corresponding to this mechanism therefore exceeds that for the energy-transfer mechanism by the factor exp (AEIRT). For all except the inert gases this factor may be sufficiently large to ensure that the reaction occurs largely by the complex mechanism. For the inert gases on the other hand since there is a repulsive interaction between the atom and the inert gas molecule it would appear more correct to re-gard AE as negative. The complex mechanism is thus unimportant and the energy-transfer mechanism predominates. This point of view differs slightly from that taken by Prof.Porter. It is important to realize that for atom combinations it does not seem possible to explain high rates in terms of a large number of degrees of freedom. The s appearing in eqn. (2) is unity for atoms and the term bs-l/(s- l)! is unity. The s’ appearing in eqn. (4) relates to the complex RM and therefore can be large if M is a complex molecule but s’ has disappeared in the final rate expression (6). Prof. A. R. Ubbelohde (Imperial College London) said What does Prof. Laidler mean by the “ free flow ” of vibrational energy in different degrees of freedom of a polyatomic molecule? In experiments that point to the intervention of complex collisions in a process such as A*+B-+A*+B V 1 v 2 where v1 and v2 refer to different vibrating modes and not merely harmonics th 296 GENERAL DISCUSSION internal transfer only occurs through collision with B.But the availability of internal energy for disruption of a particular bond in pseudo-unimolecular de-composition needs fresh discussion. Does this internal energy fluctuate from one part to another of the molecule that is about to decompose spontaneously? Dr. J. W. Linnett (University of Oxford) said I would like to say a few words regarding the so-called passage of energy between normal modes and consider what this means. First it must be stressed that a molecule in a given energy level remains in that level until it loses or gains energy on a collision or by the emission or ab-sorption of radiation. However the potential-energy functions of real molecules do not consist solely of quadratic terms and the vibrations are not simple harmonic.Nevertheless it is possible in principle to deduce the simple harmonic wave functions appropriate to the quadratic part of the potential energy function. It is then usual to treat the cubic quartic etc. terms as perturbations and to represent the true wave function of any given level as a linear combination of the wave functions of the simple harmonic system. One might say therefore that for each level there is a certain probability associated with each normal mode whose wave function is present in the linear combination. According to these considerations, it appears that difficulties of comprehension sometimes arise because the states of the real molecule which is an anharmonic oscillator are described in terms of the wave function of the non-existent harmonic oscillato- i.e.in terms of its normal modes. Dr. F. T. Smith (Stanford Res. Inst. Calif.) said It should be emphasized that Keck’s and Porter’s theories are fundamentally different even though it may be possible to obtain a similar pattern of prediction from them. Keck’s theory involves not more than three independent particles in the reaction 2R + M+R2 + M, but Porter’s requires at least 4 particles in all three (or more) to maintain equilibrium in the reaction R+ 2M + RM + M (2) R+ RM+R2 + M. (3) (1) and one more for the final step In principle as the pressure of M is reduced the equilibrium in (2) will fail and its kinetics will ultimately become important. Porter’s overall reaction will then go over to fourth-order kinetics 2R + 2M+R2 + 2M.At some point the third-order process (1) should take over and I would expect a smooth transition from Porter’s mechanism to one like Keck’s. It might be possible to detect this experimentally. There is little doubt that Porter’s mechanism is correct for large and complicated M’s but it is not so clear with regard to atoms and some very small molecules. Porter formally divides process (1) into two parts the formation of a transient pair RR* or RM* and its subsequent collision with the third partner. The dis-tinction is more than merely formal when RR* or RM* has a lifetime much longer than the time they would have spent near each other if there had been no interaction between them (incidentally this point of view leads to a useful general definition of a collision lifetime that is independent of any specific assumptions about the range of the collision.1) The simplest examples are the long-lived orbiting collisions that can occur with attractive intermolecular potentials ; their importance has been stressed by Oldenberg and Bunker.It is often useful and meaningful to distinguish 1 Smith Physic. Res. 1960 118 349 GENERAL DISCUSSION 297 these cases from the pure 3-body collision where all three partners come into inter-action almost simultaneously. In this connection it would be helpful if Keck’s trajectories could be analyzed to see how many of the reaction paths involve long-lived orbiting pairs. This would contribute to our conceptual understanding of the mechanism.Dr. J. W. Linnett (University of Oxford) said Dixon-Lewis Williams and Sutton in the final paragraph of their paper remark that for the recombination of hydrogen atoms hydrogen nitrogen and water are approximately equally effective as third bodies. On the other hand for iodine atoms Porter records a wide range of third-body coefficients. One wonders therefore whether the behaviour of iodine atoms may be different from that of atoms of low atomic number. If this were the case the reason might be that iodine atoms are able to form a transitory com-plex IM of the type suggested by Porter because the outer electron shell can expand beyond the octet so’that a co-ordinate link from M can be formed. On the other hand this might not be possible for atoms of the first short period or for hydrogen.Selley Gould and I have studied the effect of carbon tetrafluoride and sulphur hexafluoride as third bodies for Hf02 D+02 and 0 + 0 2 association reactions and while these relatively large molecules are quite effective as third bodies they are only of the order of ten times as effective as molecular oxygen in the above processes. Perhaps also the study of the recombination of the other halogen atoms might be instructive in deciding whether complexes like IM are important. Dr. G. Martens (University of Brussels) said With reference to the communica-tion of Prof. Porter and the comment of Dr. Linnett I believe a good test of the radical-molecule complex theory could be the study of the bromine and chlorine atom recombinations.Data are now available for bromine due to Britton and Davidson Palmer and Hornig Givens and Willard etc. Much less is known about chlorine atoms. We are able to measure the three-body recombination of chlorine atoms with chlorine molecules as a third body in the photochlorination of carbon monoxide. At about 500°K the rate equation can be written in the form, l l v 2 = A(k,-.+ Kk,-,[Cl,]/[CO]), where A is a factor involving the reactant concentrations and the propagation rate constants; kr-a and are respectively the rate of radical-atom and atom-atom recombination ; K is the equilibrium constant of the CO-Cl dissociation determined by Burns and Dainton. The plot of 1/19 against [Cl2]/[CO] is a straight line whose slope divided by the intercept permits one to calculate keu.A value of approxim-ately 2 x 1010 1.2 mole-2 sec-1 was found. This may be compared with recent results of Hiracka and Hardwick at 1600°K (J. Chem. Physics 1962 36 1715). I believe this permits one to discard some unlikely high values given in the literature. Dr. P. F. Knewstubb (University of Cambridge) said With reference to fig. 4 of Dr. Fite’s paper I should like to suggest that the ion current denoted H20f would perhaps be more correctly assigned to NHt. A similar conclusion has been reached in the study of ions in flames where the inert diluent of the flame is nitrogen. Evidence bearing even more directly on the question arises from some recent studies I have made of ions extracted from glow discharges? where nitrogen was one of the systems studied.The ions were analyzed by a mass spectrometer which was of sufficiently high resolution to separate the peak observed at 18 a.m.u. into a doublet. The upper component was assigned to NH; and the lower to H2Of. Their ratio varied considerably with the conditions but the relevant point is that the NHZ was generalIy the larger 298 GENERAL DISCUSSION Dr. G. F. 0. Langstroth and Dr. J. B. Hasted (University College London) said: For the reactions, 0++0,-+0,++0 (1) Of+N2+NO++N (2) we have measured the respective rate constants ko and kNz at 300°K. The method is essentially that developed by Dickinson and Sayers (1960). A time-resolving mass-spectrometer was used to observe the decay of O+ ions in the afterglows of d.c. discharges pulsed with ten 2 psec pulses per second in oxygen and in oxygen+nitrogen mixture assuming that the above reactions together with diffusion are the only important loss processes for O+ ions after waiting times greater than 200 psec.Mixture pressures were from 10-3 to 3 x 10-2 mm Hg and helium was added to a pressure of approximately 1 mm Hg to inhibit the loss of ions by diffusion. The mass spectrometer is of the miniature radio-frequency type with a resolution m / A r n ~ 3 0 . Ions enter the mass spectrometer through a 0.3 mm diam. circular aperture in a platinum disc of 6 mm diam. In the circumstances appropriate to the experiment we believe that the output current for a given ion species is proportional to the density of that species in the afterglow. In eqn. (1) the Of ion density obeys the relation an,* - - D,V2no+ - ko2pO2no+ dr where no+ denotes the number density of O+ ions D the ambipolar diffusion co-efficient for o+ ions in helium ko the rate constant for the reaction and p ~ the partial pressure of 0 2 expressed in molecules per cm3.The time-dependent part of the solution is given by no+ = + exp (- t]re), 7,' (D,/A2)+ kozpoz, and QI~O+ is a constant. The quantity A is the characteristic diffusion length found by imposing the boundary condition no+ = 0 at the container walls and is a constant for a given geometry. Semi-logarithmic plots of Of ion currents against time in the afterglow show linear regions over nearly a decade in current and 300 p e c in time. Similar plots given by Dickinson and Sayers 1 show linearity over a factor of about three only in current and even over this range some of their plots show considerable curvature.From the slope of a straight line fitted to a plot of 24 experimental values of rgl against PO by the method of least squares we obtain koz = (1.810.2) x crn3/sec. A straight line fitted to a plot of r;l against the partial pressure of an 02+N2 mixture may be shown to have a slope given by (ko,+ a k ~ ~ ) / ( a + 1) where a repre-sents the ratio of nitrogen partial pressure to oxygen partial pressure and is accurately known. This relation allows us to plot (ko,+ a k ~ ) against a. The four points so far obtained representing 600 decays lie very close to a straight line indicating a high degree of internal consistency for the measurements.From its slope we obtain the value, k, = (4-7 0.5) x 10- l2 cm3]sec. 1 Dickinson and Sayers Proc. Physic. SOC. 1960,76 137 GENERAL DISCUSSION 299 Dr. A. J. B. Robertson (King’s College London) (communicated) The occurrence of heterogeneous reactions on the tungsten filament which is present in the usual type of mass-spectrometer ion-source may be troublesome when ion-molecule reactions are investigated as Talrose Markin and Larin have found. Perhaps the difficulty could be eliminated by using an ion source in which the electron beam is produced from a cold cathode by field emission of electrons. Experiments have been carried out here by M. Warrington on the use of thin wires as electron sources of this kind. Much of the early work on field emission was carried out with thin wires stretched along the axis of a coaxial cylinder and electron currents were ob-served as a function of the applied voltage. Several workers observed anomalously large emissions when new wires were used which had not been subjected in vacuum to a drastic heat treatment. We have tried to follow up these observations and have found that several kinds of wires are effective electron sources for example, 10 ,u diam. platinum wires prepared from Wollaston wire 4-10 ,u diam. electro-polished or normal tungsten wires and drawn tungsten wires which have not been cleaned at all and are still coated with graphite and oxides. These last wires are in fact the best emitters in respect of stability of emission and size of emission for a given field and a wire of 25 ,u diam. can be used. A current of mA can be obtained very easily from such wires by placing them mid-way between two parallel plates and applying a voltage of 5-10 kV. An electron beam can be readily extracted using a slit cut in one of the plates. We have not yet investigated the teduction of the energy of the electron beam with retarding potentials. We do not know whether the uniformity in space of an electron beam produced in this way would be good enough for use in mass spectrometers. Emission prob-ably occurs at numerous sharp points on the wire and if there are enough of these the separate emissions might merge to give an electron beam uniform enough for practical use. An ion source using this field emission principle could be operated down to very low temperatures