H . S . W. MASSEY 33 CHARGE NEUTRALIZATION BY REACTION BETWEEN POSITIVE AND NEGATIVE IONS BY JOHN L. MAGEE Department of Chemistry, University of Notre Dame, Notre Dame, Indiana, U S A . Received, 5th February, 1952 The mechanism of reaction between positive and negative ions is examined for application to polyatomic ions of interest in radiation chemistry. It is found that polyatomic ions are expected to have larger neutralization cross-sections and a greater diversity of products than corresponding atomic cases. Metathetical processes of the type are not expected to occur. A+ + B- -> C 4- D Estimates of the cross-sections for neutralization of Of by 0- and by 0 2 - are made. 1 . INTRODUCTION.-charge neutralization by reaction between positive and It has negative ions occurs in any irradiated system which forms negative ions.2CHARGE NEUTRALIZATION 34 been recognized that the reaction may be of considerable importance in radiation chemistry293 although little attention seems to have been given it in this con- nection.The mechanism of the reaction of atomic ions has been discussed.4.5 However, reactions in which at least one of the ions is diatomic or polyatomic are of most interest for our present purpose. Ion neutralizations which leave both reactants in their lowest states are usually very exothermic. On the basis of energetics alone, ion neutralization could go by many paths, leading to a variety of products, including various excited states of atoms, radicals and molecules. Products can form via dissociation, rearrange- ment or chemical reaction of the initial ion pair.The actual products in any given case are determined by competition between various processes and depend upon the potential energy surface of the individual system. We have not solved the pertinent reaction-rate problem, but have merely attempted to sketch its general features. In view of recurrent evidence for specific “ hot atom ” and “ hot radical ” effects,6 it is of particular interest to know the kinetic energy with which the pro- ducts are formed as well as their electronic and vibrational states. 2. GENERAL FEATURES OF MECHANISM.-The initial state of the system A+ + B- will usually correspond to a very highly excited electronic state of the system7 A + B. After charge transfer, the system will almost invariably be in a lower electronic state.Hence, the process will usually be “ non-adiabatic ”.8*9 The various configurations of the system at which the state A+ + B- has potential energy equal to that of other states correspond to conditions for possible transition from the ionic state to the various neutral states. For large separations of A and B the wave function for the system corresponds closely to a product of wave functions for the two isolated components and a relative motion term. If A and B are both neutral, they will not interact very strongly until the separation RAB is very small, of the order of kinetic theory molecular diameters. The charged state A+ + B- is very different in this respect, since it has a long range coulombic interaction. The potential energy for these states contains the coulombic energy term - e2/RAB for values of RAB appreciably larger than kinetic theory diameters.Thus the state A+ + B- has the property that its potential energy may cross that of many neutral states during a collision; at any intersection a transfer can be made to the neutral state. The problem of the transition probability for a system with two crossing potential curves has been examined.lo.11312 The system of most interest here is more complicated than the simple case usually treated for two reasons. (1) Ions in general will be poly- atomic and thus the system will have many degrees of freedom in addition to RAB. (2) During a given collision there will usually be many crossing points so that the various transitions cannot be treated as independent events.We con- sider the influence of each of these factors. Transition is improbable to states which have distant crossing points (RAB large) because the interaction between initial and final states is too weak. The system cannot transfer to a state which has a crossing point too close. There is strong interaction and so transition occurs both on approach and separation, with no resultant reaction. The situation is illustrated by the schematic potential curves of fig. 1. In fig. 1, at the distant crossing point a, interaction with the terminal neutral state A’ + B’ is negligible. At c the interaction is so strong that there is no possibility for transfer to the terminal state A”’ + B”‘. At the crossing point b the interaction is of such a magnitude that a transition is probable.Since any crossing point is passed twice in a given collision (if at all) the total reaction prob- ability must be 2p(l - p ) where p is the probability for making the transition and 1 - p is the probability for failure of reverse transition on separation. The maximum value of 2 p ( l - p ) is one half and gives the maximum value of the probability for neutralization in a collision in which only one intersection is passed. There is a most favoured set of final states for any neutralization.J O H N L . MAGEE 35 In 5 5 it is shown that for several intersections the neutralization probability can approach unity under favourable conditions. For polyatomic ions such a simple one-dimensional curve cannot represent the behaviour except under special conditions.It may represent the system with fair accuracy for large separations. It must, however, break down badly for small separations. For example, in systems which approach as closely as c very definite possibility for a chemical process exists. A+ + B- --f C + D C + X + Y etc. The importance of such chemical contribution depends, of course, upon its ability to compete with all the neutralization processes possibly occurring at large separa- tions. The summed cross-section of the latter can be quite great. The number of crossing points for a given system, their positions and inter- actions determine the cross-section for neutralization and the product distribution. FIG. 1 .-Schematic potential curve for A+ + B- and representative neutral states of A 4- B.There may be no crossing point at all: e.g. for Cs+ + F- the ionic state is the lowest state for all separations. In another case, Brf + Br-, there are only two possible final states ; one has a crossing at about 50ao and is of the type a of fig. 1 and the other is almost certainly of type c. Such cases are probably of no interest in radiation chemistry. Polyatomic ions are generally expected to have a greater density of crossing points. These will tend to have smaller individual transition probabilities than corresponding atomic cases, but this condition actually tends to make the net neutralization cross-section larger. The explanation is that a large transition probability made up of a sum of small transition probabilities is favourable because the back-reaction becomes extremely improbable.crossing points of the various excited states Aj + Bk with A+ + B- are easily calculated. At any such point, R j k , the potential energy of the state for singly charged ions is approximately Many cases will have practically a continuum of final states. 3. DETERMINATION OF CROSSING PoINTS.-The approximate positions Of distant e L Rjk’ E(A+, B-1 - - while the neutral state has the approximate potential energy E(Aj, Bk).36 CHARGE NEUTRALIZATION The E terms are the values of the energy of the entities in the parenthesis for infinite separation. (3.1) If the system changes from one state to the other, it means that simultaneously the two transitions The existence of a crossing point means that E(A'-, B-) - E(Aj, Bk) =- e2iRjk.R- + Bk -1 c ; AE = &(B), (3.2) A ' 4- c + A ; AE.7 G(A), (3.3) take place very much as in the isolated entities. Ek(B) and E'(A) denote the corresponding energy changes. We can also write E,(A) -t Ek(B) e2/Rjk. (3.4) The positions of the available states can be known from spectroscopic data for A and B which include the ionization potential of A, along with the electron affinity of B. All values of Ej(A) and &(B) which yield positive values for Rjk give possible final states. Thus, for cases where either A or B or both are poly- atomic, each possible electronic state will have a series of crossing points corre- sponding to the various possible vibrational and rotational states of the products. The value of EI,(B) depends on the electron affinity of B defined for the par- ticular vibration state involved and the vibrational state of the product.It is actually possible to have Ek(B) negative. Those transitions occur most which involve least extensive electron rearrangement. The most important end state may frequently be the ground electronic state of B in various possible vibrational states. Since A+ is in an ionized state, there is a Rydberg series of states into which the electron can be captured. The smallest possible value of Ej(A) is, therefore, very close to zero. However, the relation (3.4) restricts the accessibility of these states. Only those states are accessible which have an ionization potential greater than the electron affinity of B (otherwise the value of Rjk turns out to be negative and without physical significance).This restriction usually decreases the density of crossing points from the near continuum resulting from the Rydberg series to somcthing smaller. If the ion B has a large electron affinity, all highly excited states of A may be unavailable. We have noted that the negative ion B- may have vibrational excitation so that its " electron affinity " is actually negative. The 0 2 ion furnishes an example. According to the Block-Rradbury theory13 of electron capture, in 0 2 the end state is a vibrational state of 0 2 - which is 0-12 to 0.18 eV higher in energy than the original 0 2 molecule. The relative importance of negative ions in such states must be small since they will lose their extra electron rather quickly unless collisional deactivation is effected.The reaction 0' + o--Z oj f ok (3.5) has been considered in some detail.49 5 Since the products are atoms, the number of available final states can be known with certainty. These states are listed in table 1 along with values of ,!$(A) + &(B) (in electron volts) and Rjk. The electron affinity is uncertain to & 0.2 eV; the resulting uncertainty in Rjk is in- dicated. The first five states certainly have interactions with the coulombic state of type c (fig. 1) and cannot possibly contribute to the neutralization. The end states listed as 6, 7 and 8 have crossing points of type b and determine the neutralization cross-section while 9, 10 and 11 are certainly of type a. The reaction Of + 0 2 - - oj 3- ( 0 2 ) k (3.6) can have a variety of initial states since 0 2 - can be in several different vibrational states.14 Let us consider 0 2 - in its lowest vibrational state which is - 1 eV lower in energy than the lowest state of 0 2 (plus, of course, a free electron of zero energy).JOHN L.MAGEE 37 In table 2 we have listed only crossing points to final states which involve the first 11 vibrational levels of the lowest electronic state of 0 2 and which occur in the TABLE 1 .-CROSSING POINTS FOR REACTION Of + 0- product designation 1. 3 p 2- 3p 2. 3P + 1D 3. 1D ~ ID 4- 3 P i 1s 5. ID 7 1s 6. I S - I S 7. 3P 1- (3S)5S 9. 3P + (3p)5P 10. 3 P + (3p)3U 11. 11) -t (3S)SS 8. 3P -+ (3~)3S range of R;k .ti E(ev) Rjk(ao) 11.35 1’ 0.2 - - I - 9.39 7.43 7-1 8 5.22 - - - 1 - - 3.0 I 9-0 8.5-9.7 2.25 12.0 11‘1-13.2 1.87 14.5 13.1-162 0.65 42.0 32-109 0.40 68.0 45-1 36 0.29 94.0 56-300 TABLE SOME CROSSING POINTS FOR THE REACTION Of f 0 2 - - ~ ( 0 2 ) is the vibrational quantuni number of 0 2 (3S)3S 2 10.1 (3S)3S 9 18-9 (3S)5S 4 10.1 (3PI3P 1 19.3 (3S)3S 5 10.8 (3S)3S 10 21.3 (3S)3S 3 11.0 (3P)jP 3 21.6 (333s 4 11.7 (3PI3P 2 22.5 (3S)5S 6 11.7 (3P)jP 4 24.5 state of 0 V ( O 2 ) Rjli state of 0 d 0 9 ) R;k (3S35S 7 12.6 (3PI3P 3 26.9 (3S)3S 5 12.7 (3PYP 5 29.2 (3S)5S 8 13.7 (3P>3p 4 31.6 (3P)jP 0 14.6 (3PYP 6 35.2 (3S)SS 9 15.0 (4S)3S 0 40.0 (3S)3S 6 13-9 (4S)5S 0 35.3 (3S)3S 10 15.0 (3PI3P 5 40.0 (3S)3S 7 15.2 (3PYP 7 46-8 (3S)3S S 16-8 (3Pj3P 0 16.9 (3P>3P 2 18.6 (3PYP 1 16.4 (4S)5S 1 47.7 range 1Oao < R;k < 50ao.There are 33 of these.15 An uncertainty in the electron affinity of 0 2 enters this calculation but this has not been indicated; the affinity is taken as 1 eV.Several other known electronic states 16917 of 0 2 furnish final states in the same region, as we see from fig. 2. One of these, the 3&- state which has a dissociation limit at 7 eV above the ground state furnishes a continuum of final states for R 2 2 0 4 ; a second state, the 3Zu+ which has a dissociation limit at 5 eV furnishes a continuum for R Z 8 ~ . There is a considerable increase in the complexity of a system over the atomic case when only one ion is diatomic. The most important change is the great increase in the number of accessible final states. It is probably a safe conclusion that for polyatomic systems the density of states is always high.However, cases must be examined individually. For Of + 0 2 - we have the possibility of a direct transition to a dissociated state of 0 2 , which is one mechanism for the formation of atoms in such a reaction. The transition to a stable excited state followed later by an internal conversion process may actually be more probable, but this question must be examined. For the system 0 2 f + 0 2 - it is certain that the densities of crossing states is higher than for O+ + 02-, but the highly excited electronic states of 0 2 are not known well enough to justify a calculation.38 CHARGE NEUTRALIZATION 4. TRANSITION moBABILITY.18-We are concerned with a system A+ + B- which suffers a collision such that its classical hyperbolic orbit crosses N neutral states of the system, where Nmay be a very large number.First we would like to know the total probability that the system emerges from the collision in an uncharged state. The orbit crosses each state twice (except for the special case of a single contact at the turning point for radial motion, which we shall ignore). Let us call the apriuri probability that a transition is made at the nth intersection, FIG. 2.-Some potential curves for the system 02-. FIG. 3.--Position of 2N intersections of a system which has ,V neutral states. Pn ; 1 - Pn will be the a pviori probability that a transition is not made. We must count the total number of ways in which success can be obtained in passing the 2N intersections. Fig. 3 shows a classical orbit which has approximately zero total energy. Intersection of the circles of radii R, with this orbit give the 2N crossing points of the N neutral states.Let us assume that the neutralization probability is known for a system which differs from the one in consideration only in having the first state removed. We call this neutralization probability P ~ - 1 ( 2 , 3 . . ., N). We shall always mean by PN-k the total probability of neutralization for the completeJOHN L. MAGEE 39 shell of states k + 1, k -1- 2, . . ., N, which involve the innermost 2(N - k ) crossing points. The probability we want can be derived from PN-1 by the simple consideration which follows. At the first crossing the probability for making the transition is po ; in systems in which transition occurs at R1 no further intersection is passed until return to RI on separation.Here there is the probability p1(1 - p1) for emerging neutral Systems which do not make the first transition have the probability (1 - p l ) P ~ - . for becoming neutralized in the 2 ( N - 1) inner intersections. The fraction (1 - pl)(l - P N J ) will emerge ionic as they approach the R1 intersection on separation. Here pl(1 - p1)(1 - P N J ) will finally lose their charges. The value of PN (i.e. the net probability of neutral emergence) is obtained by adding up the three classes of such emergence. P N = pl(1 - P1) + (1 - P1)pN-1 PI(1 - PI)(] - PN-l), (4.1) It is a very simple matter to develop from this recurrence relation the general ex- pression for PN since it is known that This can be written in a more compact form : (4.4) (4.5) where the symbol 17 denotes a continued product.If we take all the pn the same, we can sum the series in (4.5) and write (1 - p2N) = 2p(1 - (1 - (1 - p)2”). (4.6) A N pN = A p2j-2 = 1 - (1 - p)2 j = 1 As For large N and small p we have the limit p~ w 1 - e-2Np. (4.7) the product 2Np gets large, PN approaches unity. For N moderately large and p > i, eqn. (4.6) approaches As p + 1, we see that practically all neutralization occurs at the first transition point. The second term on the right represents the small contribution to the total prob- ability of the remaining neutral states. Thus a large number of states of the type c (fig. 1) still have a negligible neutralization probability. Returning to eqn. (4.1) we see that success indicated by the first and third terms on the right leads to the first neutral state and the second term gives the total of transitions into the other N - 1 states.If we collect these terms, we can write The product distribution is, of course, also of great interest. PiV = Al(1 ipN-1) $. p1PN-I. (4.9)40 CHARGE NEUTRALIZATION The second term on the right of this equality is subject to the same analysis, and by the process of iteration we obtain N pN = PK, (4.10) K= 1 where (4.1 1) and ,on represents the fraction of transitions to the nth neutral state. (4.5) we have From eqn. In $ 5 cross-section estimates have been made. as yet been studied for a specific case. collisions of ions with positive energy (&vm2) can be written The product distribution has not 5.Low PRESSURE CROSS-SECTION.-The cross-section for charge transfer in u(uW) == 2n P(b)bdb, JOm (5.1) where b is the distance between the asymptote of the classical hyperbolic orbit of the pair and a parallel line through the origin of co-ordinates. P(b) is the prob- ability for successful transition on this particular orbit as obtained by the methods of the previous section. It is more convenient to express this integral in terms of bo, the radius of closest approach. The expression for the angular momentum (5.2) L = p a b = pobo relates b and bo. Since TO is also a function of bo, we must use and the cross-section can be written as (5.4) In order to determine the appropriate value of uc0 to use in (5.4) for a thermal distribution, an average must be made.The thermal reaction rate is given in terms of a bimolecular rate constant k' which has been averaged over thermal velocity distribution. Since the value of P(b0) does not depend upon vcO and make the average, is so much larger than rW, we make the assumption that (5.7) Division of (5.7) by the average thermal velocity (SkT/p~)g gives the thermaI cross-section (5.8) 03 a(th) = 27i J 0 P(bo)hodbo+~~m(hli)dho.JOHN L . MAGEE 41 This cross-section can be approximated by the second term, which is much larger than the first, and the cross-sections of table 3 were obtained with the approxima- tion. Use of the formulas of the previous section for calculation of P(b0) requires an explicit expression for p,. Since the problem presents quantum-mechanical difficulties beyond the scope of this paper, we shall take the expression of Zener,lo P,, == 1 - exp i_ 1 (5.10) where Ha’ is the matrix element of the perturbation Hamiltonian between the ionic state and the nth neutral state, v, is the velocity along the trajectory at the nth crossing point and S, is the absolute value of d(Eo - E,)/dx at the crossing point.Eo, En are the potential energies of the charged and neutral states respectively. As examples we shall estimate the cross sections for the reactions Of + 0- + 0’ + 0” (5.1 1) o+ + 0 2 - -+ 0‘ -t 0 2 ” (5.12) We need only the matrix elements H,’ in order to (5.13) The basis for this formula and probable values of the parameters a, and q, are discussed in $8. It is shown that tc, depends upon the asymptotic form of the one-electron wave function and for the cases (5.11) and (5.12) varies between about 0.3 and 0.6.The factor qn is the overlap integral for all parts of the wave function other than that of the jumping electron. In the diatomic case, therefore, qn contains a vibrational overlap. The integral in (5.9) was computed numerically. Results are reported in table 3. which were discussed in $ 3. make the calculation, and we take for all of them H,’ = 4 x 10-3 xn (~~R,)3e-~“~nq~. TABLE 3.-cROSS-SECTION SUMMARY ; VALUES ARE GIVEN IN 1Ov13 CM2 j: P(bo)dbo, in ao, is indicated for each case in parenthesis Y. reaction 42 042 0.50 1.00 o++ 0- 10.0 - 4.2 (4.5) - 1.0 6.0 (6.5) 8.5 (9.2) 0.44 (0.48) 0.1 - 2.5 (2.7) - O+ 1- 0 2 - 1.0 32.0 (35.0) - - 0-1 27-0 (29.0) 11.0 (12.0) - 0.01 7.4 (8.0) - - For the case of O+ + 0-, calculation was made as if only states 6, 7 and 8 (table 1) existed.If q n ~ 1 we have a thermal cross-section of almost 10-12 cm.2. Variation of the parameter qh was made to determine the sensitivity of the calculation to the absolute value of the matrix element. This variation is of considerable interest in view of the uncertainty in the wave functions used in the calculation of H”’. The most favourable value of q, occurs because of the changing of the intersections in the direction of type c (fig. 1) for large 4, to type a for small qn. There is a rather high sensitivity of CJ to increase of cc, since the range of the interaction is reduced thereby. In the calculation for Of + 02- only the levels listed in table 2 were considered. The most probable value of ar is somewhere between 0.25 and 0.50.The factor q, is, of course, smaller for this case because of the vibrational overlap integral. The most probable value of is about 0.5. B42 CHARGE NEUTRALIZATION It is expected that qn2 should lie between 0.01 and 0.1. We have taken the same value of qn for all final states, although each one should have its own value. For a transition between two electronic states from a givcn initial vibrational state, = 1. Fig. 2 suggests17 that about 10 vibrational states are accessible, and so some of the qn2 must be greater than 0.1 and some of them less. There is, of course, in this case also some uncertainty in the magnitude of the matrix element which can also be put into q 2 and so we have taken from 1 to 0.01.The calculated cross-sections for Of + 0 2 - are larger than for Of -1 0-. It is to be expected that a system which has a large number of accessible final states should have larger cross-sections since they are not as greatly influenced by such variable factors as the actual positions of crossings, magnitudes of inleraction, etc. It should also be noted that many final states for Of + 0 2 - have been ignored in this treatment. 6. EFFECT OF pmssum.-The theory of Thomson 19 describes satisfactorily the pressure dependence of ion recombination below an atmosphere total pressure. In Thomson’s theory all ion pairs which suffer a collision such that their relative energy drops below zero will react without separating again.However, we must note that the latter condition is met for values of b w 1000ao. Very few orbits so described have values of bo such that charge transfer can be expected to take place during the first transit, for 5 5 shows that bo must be about 30ao or less for approximately unit transfer probability. On the capture collision most ions will be trapped into orbits which have such extremely small charge-transfer probability that they will have to change into more favourable orbits before discharging. The mechanism for changing orbits is, of course, collision with neutral molecules which take up small amounts of energy and increase the binding of the ions. The qualitative effect of this pressure-dependent mechanism on the reaction products is clear. Orbits which have such a small transition probability per cycle that they would contribute a negligible amount to the zero-pressure cross-section make the dominant contribution at high pressure.There are two reasons for this change: the statistical favouring of these orbits will keep them relatively more highly populated; the velocity in the negative energy (is., bound) orbits is lower than for the free case, and (see eqn. (5.10)) the probability for transition at any crossing-point is increased. In the pressure dependent region, the states of higher product excitation will be favoured. At the same time, the kinetic energy of the products will be smaller, both because the products have more electronic excitation and the transfer has been made from bound orbits. -The considerations above have strongly suggested that the charge transfer which effects the neutralization in molecular ion recombination take splace at a rather large distance.In this initial act, therefore, the reaction partners remain intact, i.e. keep their constituent atoms and configurations. Thus a simple metathetical reaction of the type 7. ROLE OF POSITIVE-NEGATIVE ION NEUTRALIZATION IN RADIATTON CHEMISTRY. A+ + B- +- C + D is not to be expected. Dissociation may, of course, follow immediately, but the probability for chemical rearrangements which involve both A+ and B- would seem small. Another conclusion is that rather highly excited states are favoured as end states. This means that large amounts of kinetic energy will generally not be given to the products-one electron volt would probably be an unusually large amount for the pressure dependent mechanism.Along with the high energy states one expects molecular rearrangements and dissociations (predissocjation). Radi- cals should be very common reaction products, as has been assumed. If comparison is made between the neutralization of a given molecular positive ion by an electron and by reaction with a negative ion there would seemJOHN L . MAGEE 43 to be two differences. (i) The available excited states of the ion have lower energy for the ion reaction, because the electron is already bound to the extent of the electron affinity and furthermore the coulombic potential energy is effectively degraded in the pressure-dependent mechanism. (ii) The negative ion can share the excitation energy and furnish dissociation products to the subsequent reactions.Since it is known that negative ions form in irradiated systems, particularly those containing oxygen, it is clear that this neutralization step must be included in the reaction mechanism. The neutralization products will greatly influence the subsequent reactions, and they must be determined for each case separately. 8. APPENDIX: EVALUATION OF MATRIX ELEmms.-We shall use a one electron ap- proximation for the matrix element Hjk’. Since interatomic separations are so large at the crossing points of most interest it is clearly the asymptotic form of the wave function which determines the matrix element. The one-electron wave function obeys the wave equation (8.1) where T + V(u) is the Hamiltonian operator and I is the ionization potential.V(r), the potential energy of one electron, in the field of the nucleus plus the other electrons. goes to zero exponentially with the distance for negative ions. The asymptotic form of he radial part of the wave function for 0- is, therefore, (T + W>>$ = - 44 where CI is related to the ionization potential as cc = 4T.I. (8.3) The value of the wave function is undetermined by this procedure, but the exponential The wave function for 0- used in the calculation of dependence should be accurate. he matrix element is (8.2) normalized to unity. The oxygen atom has a potential V(r) which is coulombic at large distances, and so the radial wave function behaves asymptotically as In this case we have taken the nodeless wave function, normalized for this state.uo(r) N une - OCr. (8.5) As pointed out for the 0- case above, the absolute value is not well determined but the Y dependence should be reliable. The 0 case is different, however, in that as the excita- tion increases, the wave function approaches the hydrogen wave functiops, especially for large angular momenta. For such cases the wave function can be known almost exactly. In the initial state the electron is on the negative ion B and we take for the perturbation operator (8.7) Integration with wave functions (8.4) and (8.6) with n = 3 gives H‘(R) = - 4 x 10-3 cce --DIR[(aR)3 - 5 ( d ) - 15 - - (8.8) ccR 30 1 * The same value of CI has been used in both wave functions. The lead term of (8.5) was used (5.13).The ionization potential of 0- is 2.2 eV, which gives 0-4 for a. The final states of most interest correspond to 3s excitations (see table 1, states 8 and 9) with ionization potentials approximately 4 eV, or cx 0-55. It would seem, therefore, that M = 0.5 is the most reasonable value to take for this case.44 GENERAL DISCUSSION The Sam': integral was used in the case of O+- + 0 2 - for the electronic interaction. In this case the ionization potential is approximately one eV and so a a 0.25. The sam': final states of oxygen are important (table 2). The value of cc should be somewhat lowzr, bztwzen 0.25 and 0.50. The matrix element in the diatomic case also has a vibrational overlap integral q. The schematic potential curves 17 of fig. 2 suggest that in the 0 2 - --f 0 2 + e transition there are possibly 10 final states accessible. Thus, since Eq,2 = 1, an average value of q n 2 of 0.1 would seem reasonable. 1 This work is a contribution from the Radiation Project of the University of Notre, Dame, supported in part by the Atomic Energy Commission under contract AT(11-1)-38. 2 Magee and Burton, J . Amer. Chem. Soc., 1951, 73, 523. 3 Burton, J. Physic. Chem., 1947, 51, 611. 4 Bates and Massey, Phil. Trans. A , 1943, 239, 269. 5 Massey, Negative Zons, (Cambridge, 2nd edn., 1950), p. 93. 6 Hamill, Williams, Schwarz and Voiland, forthcoming publication ; Prigogine, J . Physic. Chem., 1951, 55, 765 ; Hamill and Schuler, J. Amer. Chem. Soc. 1951, 73, 3466 ; Schultz and Taylor, J . Chem. Physics, 1950, 18, 198. 7 Here and throughout the paper A and B designate arbitrary entities : molecules, radicals or atoms. 8 Glasstone, Laidler and Eyring, Theory of Rate Processes (McGraw-Hill, New York, 1941). 9 Laidler and Schuler, Chem. Rev., 195 1, 48, 153. 10 Zener, Proc. Roy. Soc. A , 1932, 137, 696. 11 Landau, 2. Physik. Sowjet, 1932, 2,46. 12 Stueckelberg, Helv. physic. Acta, 1932, 5, 370. 13 Bloch and Bradbury, Physic Rev., 1935, 48, 689. 14 There is some uncertainty as to the positions of the low electronic states of 0 2 - . In this paper we tacitly assume that 0 2 - has the potential curves given by Massey in fig. 6(a), ref. (5), p. 31. 15 Energies of the states of atomic oxygen were taken from Bacher and Goudschmidt, Atomic Energy States (McGraw-Hill, New York), 1932. 16 Herzberg, Spectra of Diatomic Molecules (Van Nostrand, New York, 2nd edn.), p. 446. 17The relative position of the curves for 0 2 - and 0 2 is not known very accurately. Fig. 2 must be considered as schematic. 18 This section was prepared in collaboration with Mr. W. C. Hourt. 19Thomson, Phil. Mag., 1924, 47, 337.