Multiple Chemiluminescent Channels in the Reaction Mn + SF6

J. Phys. Chem. 1996, 100, 2809-2818

2809

Multiple Chemiluminescent Channels in the Reaction Mn + SF6 f MnF + SF5 Dale L. Herbertson† and Martin R. Levy* Department of Chemical and Life Sciences, UniVersity of Northumbria at Newcastle, Ellison Place, Newcastle upon Tyne NE1 8ST, U.K. ReceiVed: September 21, 1995X

Five different MnF* emitting statessA7Π, e5Σ+, d5Π, c5Σ+, and b5Πshave been observed from collisions between SF6 molecules and a pulsed, laser-ablated beam of Mn atoms. The various excitation functions, measured up to nominal collision energy ET0 ) 2000 kJ mol-1, have been modeled by the multiple line-ofcenters approach. The analysis indicates that MnF*(A7Σ+) is predominantly formed on a single potential surface, with probable progenitor Mn*(z8PJ); the e5Σ+, d5Π, and c5Σ+ states are formed via three common potential surfaces, with likely reagent state Mn*(a6DJ), while the a6DJ state is also likely to be the progenitor of MnF*(b5Π). Partial depletion of the b5Π state at high energy seems to be accompanied by enhanced yield of the other emitters. All reactions seem to be characterized by a shift forward in transition state location with increasing collision energy. The results suggest an electron jump barrier at short internuclear distances, forced outward at higher collision energies due to lack of time for the SF6 to distort to the equilibrium geometry of SF6-.

TABLE 1: MnF States and Transitions24-28

Introduction A number of studies have addressed the reaction dynamics of metal atoms with SF6. Angular scattering measurements on K, Rb, Cs, + SF61 and electric resonance2,3 and electric deflection4,5 measurements on the Cs reaction indicate a longlived complex, with statistical energy partitioning. Product rotational polarization in Cs + SF66,7 has been found to be small, suggesting a loose transition state where the products can rotate freely. On the other hand, angular scattering measurements on Li + SF68,9 find a short-lived complex, and here electric resonance data10 indicate that dynamics, rather than statistics, still dominate the energy partitioning. “Diffusion cloud” experiments at ∼380 K, using infrared laser excitation of SF6(V),11,12 find that only one S-F stretching vibrational mode is important for K + SF6, i.e., SF6 behaves like a diatomic; however, ∼10 modes appear to be involved for the Na reaction, which has a higher activation energy. Reactions of nonalkali metals have received less attention. In group 2, angular scattering measurements13 find that the Ba reaction proceeds via a long-lived complex, while in Ca*(3P,1D), Sr*(3P) + SF6, chemiluminescence has been observed from several metal fluoride electronic states,14,15 and the excitation function of the Ca*(1D) f CaF*(A2Π) reaction has been determined.16,17 On the other hand, in group 14, the Sn(3P) reaction yields chemiluminescence exclusively from SnF2*(3B1).18 Of the d-block metals, only Sc, Y, La + SF6 appear so far to have been investigated,19,20 to the extent that chemiluminescence has been detected. For Sc and Y, the spectrum is dominated by a “selective feature” whose production is second order in the halogen, implying a secondary process. The source of this effect is still open to interpretation, but it may well involve ScF, YF(ν′).21 In this paper we report translational excitation functions for the reactions

Mn + SF6 f MnF*(b5Π,c5Σ+,d5Π,e5Σ+,A7Π) + SF5 This represents one of a series of investigations in this laboratory † Present address: Heaton Manor School, Jesmond Park West, Newcastle upon Tyne NE7 7DP, U.K. * To whom correspondence should be addressed. X Abstract published in AdVance ACS Abstracts, January 15, 1996.

0022-3654/96/20100-2809$12.00/0

state 7Σ+

leading configurationa 1

1

Te, kJ mol-1

X a5Σ+ b5Πi c5Σ+ d5Πi

...[1δ24π2

9σ ]10σ ...[1δ24π29σ1]10σ1 ...[1δ24π39σ1] ...[1δ24π29σ2] ...[1δ24π29σ1]5π1

0 ∼7 ∼153b ∼180b 242

e5Σ+ A7Π

...[1δ24π29σ1]11σ1 ...[1δ24π29σ1]5π1

∼273b,c 341

transition, λ00/nm

b5Πi f a5Σ+, 819 c5Σ+ f a5Σ+, 690 d5Πi f a5Σ+, 504 d5Π f X7Σ+, 495 e5Σ+ f a5Σ+, ∼450c A7Π f X7Σ+, 351

a From Launila et al.;28 the filled 8σ, 3π (halogen p) and lower orbitals have been omitted. The orbitals in square brackets are predominantly metal 3d, while the 10σ, 11σ, and 5π orbitals are considered to be respectively 4s/4p hybrid, 4pσ, and 4pπ, although in all cases the contributions will vary with configuration. In view of the high excitation energy of the Mn+*(...3d54p, z5PJ) level, ∼519 kJ mol-1,45 we have proposed22,23 that the d5Π and e5Σ+ leading configurations may instead be ...[1δ29σ24π1]10σ1 and ...[1δ24π2]10σ2. The a5Σ+ and c5Σ+ states are considered by Launila et al. to arise from different combinations of the two leading configurations shown; the ...10σ1 contribution to the a5Σ+ state is estimated to be ∼57%.25 b Incorporating a5Σ+ estimate. c This work and comparison with MnCl;22-24 exact value of λ00 not known.

on the chemiluminescent reactions of Mn atoms with halogens and halides, of which Mn + SnCl422 and SiCl423 have already been communicated. The MnF electronic spectroscopy has recently been significantly clarified, as Table 1 illustrates.24-28 Like the SnCl4 case, the fully ground-state reaction

Mn(a6S) + SF6 f MnF(X7Σ+) + SF5 is exothermic, though uncertainty exists over the precise magnitude of the SF5-F bond energy. Kiang, Estler, and Zare14,15 found a value of 391 ( 15 kJ mol-1, based on the highest vibrational levels populated in each SrF* state in the Sr*(3P) + SF6 chemiluminescent reaction. However, Herron and Tsang29 have disputed this, claiming instead the value 420 ( 10 kJ mol-1, as more compatible with a wide range of kinetic data. Taken with D0(MnF) ) 424 ( 14 kJ mol-1,30 these two numbers lead to exoergicities of 33 ( 21 and 4 ( 17 kJ mol-1, respectively. Whatever the true value, reagent electronic (Table 231) or translational excitation will clearly be required for chemiluminescence to be observed. Indeed, even with excited © 1996 American Chemical Society

2810 J. Phys. Chem., Vol. 100, No. 8, 1996

Herbertson and Levy

TABLE 2: Mn State Excitations31 (with Spin-Orbit Splitting) state

Ei/kJ mol-1

a6S

0 207 ( 4 222 ( 2 281 ( 2

a6DJ z8PJ a4DJ

Mn atoms, nominally exothermic channels may still need significant translational energy to overcome any barriers, if Mn + SF6 follows the same pattern as the SnCl4 and SiCl4 reactions.22,23 Procedure The apparatus and technique have already been fully described in previous communications.22,32,33 The Mn atomic beam is generated by pulsed laser ablation of a solid metal target and separated into different velocities by means of a long flight path. SF6 (BDH, 99.9%) is taken directly from the lecture bottle and admitted to the scattering chamber to maintain a nominal pressure, as indicated by a Penning gauge, of typically 0.08 Pa. At a fixed flight distance x, the Mn beam is monitored by its long-lived Mn(z8PJfa6S) metastable emission, and any chemiluminescence is also detected. In this beam-gas configuration, the nominal collision energy ETo ) 1/2µV2 ) 1/2µ(x/t)2, where µ is the reduced mass, V the beam velocity and t the flight time, while the relative cross section, σ(ET0), is obtained by dividing the chemiluminescence signal by the beam signal at each delay time and correcting for the different detection efficiencies and for metastable radiative decay. As noted previously,23,32 this procedure assumes a relatively short radiative lifetime for the chemiluminescent species; here, where we present excitation functions up to ET0 ) 2000 kJ mol-1, data at the highest energies might be depressed for lifetimes g1.6 µs. As argued previously,23 the lifetimes should be much shorter. Indeed, the predominantly common energy dependence found here for three of the band systems suggests that must be so, since it would be very improbable for all three to have identical radiative lifetimes g1.6 µs. Since only a tiny quantity of metal is vaporized on each laser shot, both luminescent signals are small and erratic, prohibiting the employment of a monochromator to measure a resolved emission spectrum. As with Mn + SnCl4,22 therefore, excitation functions for the different MnF* states were obtained by isolating the emission band systems by means of suitable filter and photomultiplier combinations: 330-380 nm (“ultraviolet”), 417-490 nm (“blue”), 470-510 nm (“green”), 590-690 nm (“red”), and >780 nm (“infrared”). In contrast to the SiCl4 reaction,23 only a very small signal was found in the region 470-490 nm, so the blue and green ranges can, as with Mn + SnCl4, be considered as 417-470 and 490-510 nm, respectively. The different filter regions then correspond, in order of increasing wavelength, to the following MnF band systems: (1) A7Π f X7Σ+;28,34 (2) a blue system, anticipated by comparison with MnCl22-24 and labeled e5Σ+ f a5Σ+ by analogy with the MnH ∼450 nm system;35 (3) d5Π f a5Σ+ (∼495 nm)26 and d5Π f X7Σ+ (∼505 nm);27 (4) c5Σ+ f a5Σ+;25 and (5) the IR system, labeled b5Π f a5Σ+,25 again by analogy with MnH.35 Results and Analysis Time-resolved luminescence has been detected in all five wavelength regions studied. The various translational excitation functions are displayed in Figures 1-5 and represent the result of respectively ∼15 300, ∼9200, ∼10 200, ∼8200, and ∼8200 laser shots. Taking into account photocathode sensitivity and window and filter transmission efficiencies, the peak cross

Figure 1. Excitation function, σ(ET0), for production of “ultraviolet” MnF chemiluminescence. Point-to-point resolution corresponds to 0.2 µs time delay. The curve shown corresponds to the best fit, by the multiple line-of-centers approach (MLC), to the derived yield function Y(ET0) in Figure 7. The apparent spike at low collision energies is spurious, reflecting the small beam and luminescence signals at very long delay times; the comparable negative-going data at such times are not shown.

Figure 2. Excitation function, σ(ET0), for production of “blue” MnF chemiluminescence. The solid line corresponds to the best MLC fit to the combined blue-red yield function data in Figure 8; the same curve is shown in Figure 4.

Figure 3. Excitation function, σ(ET0), for production of “green” MnF chemiluminescence. The curve shown consists of the fit in Figures 2 and 4, plus an additional feature, revealed by subtracting that fit (see Figures 9-11).

sections for the UV, blue, green, red, and IR emissions are Very approximately in the ratio 12:2:1:27:24, although the actual intensities of the UV and IR signals are the smallest. All signals are characterized by a threshold e100 kJ mol-1 and a falloff at high energies. The fall is sharpest for the blue, green, and red

Reaction Mn + SF6 f MnF + SF5

J. Phys. Chem., Vol. 100, No. 8, 1996 2811

Figure 4. Excitation function, σ(ET0), for production of “red” MnF chemiluminescence. The solid line corresponds to the best MLC fit to the combined blue-red yield function data in Figure 8. The same curve is shown in Figure 2.

-σ1 e σ0. The yield plot, eq 2, therefore always shows positive slope. In such circumstances, depletion has been attributed to either (a) competition with some other channel or (b) “recrossing”,37 in which trajectories are reflected, from the repulsive wall of the potential surface, back along the entrance channel. Whatever the cause, we can write36 σ0 ) πP0R02 and σ1 ) -πP0PdRd2, where R0 and Rd are the internuclear distances at which reaction and depletion, respectively, take place, P0 is the probability of reaction at R0, and Pd is the probability of subsequent depletion as the system penetrates to Rd. Since Pd e 1.0, Rd/R0 g |σ1/σ0|1/2. The bilinear behavior observed in those reactions shows that their opacity functions for reaction and depletion, P0(b,ET) and Pd(b,ET), are well approximated by step functions. On the other hand, in Mn*(a6DJ) + SnCl4 f MnCl*5 (c Σ+,d5Π,e5Σ+),22 Mn*(a6DJ) + SiCl4 f MnCl*(c5Σ+),23 and in a number of other reactions,36 e.g. Ba + N2O(ν2)1),38,39 “complex” depletion has been observed, in which the negative σk term (or a sum of such terms) exceeds the sum of the preceding positive terms and is followed by further positive terms so that eventually ∑σk ∼ 0. In such circumstances the yield plot shows a negative slope for a range of energies, before a leveling off or secondary rise. This behavior has been attributed to a forward shift in transition state location, R0 f Rs, at line-of-centers energy Es, but with the same reaction probability. As illustrated in panels a-d of Figure 6,22,36 such a shift will only manifest itself when the maximum impact parameter for reaction at Rs, with threshold Es, exceeds that for reaction at R0, with threshold E0, i.e. when

σs(ET - Es) g σ0(ET - E0)

(3)

In, for example, a three-term expansion of eq 1,

σ(ET) ) σ0(1 - E0/ET) + σ1(1 - E1/ET) + σ2(1 - E2/ET) Figure 5. Excitation function, σ(ET0), for production of “infrared” MnF chemiluminescence. The solid line corresponds to the best MLC fit to the infrared yield function data in Figure 12.

data; in fact, these excitation functions appear very similar, except for a relatively stronger high-energy “tail” in the green case. Overlay of the blue and red data indicates that they are virtually indistinguishable. The data have been analyzed in terms of the multiple lineof-centers (MLC) model discussed previously:22,23,36

σ(ET) ∼ ∑σk(1 - Ek/ET)

(1)

Here k ) 0, 1, 2, ...; generally at least one σk value (k > 0) is negative, and each process only contributes from its threshold Ek. If the model holds, then the yield function

Y(ET) ) ETσ(ET) ∼ ∑σk(ET - Ek)

(2)

should in principle be composed of several linear sections with different slopes. However, in practice, in our beam-gas configuration, we measure only the nominal collision energy ET0, which is an average over all contributing SF6 velocities. The resulting nominal yield function, Y(ET0) ) ET0σ(ET0), retains the multilinear form, but with curvature in the region of each threshold. Fortunately that curvature, and therefore the whole yield function, can be exactly calculated if the σk and Ek parameters are given.22,23,33 Hitherto, two broad categories of excitation/yield function with positive thresholds have been identified, characterized by the magnitude of the rate of depletion from the initial rise. In “simple” depletion, as in M + HX (M ) metal, X ) halogen)36 and in Mn*(a6DJ) + SiCl4 f MnCl*(b5Π,e5Σ+),23 eq 1 consists typically of only two terms, the second being negative, with

(4) where -σ1 ∼ σ0 + σ2, the third term arises directly from eq 3. We therefore write σs ) σ0 + σ2, with σ0 ) πP0R02 and σs ) πP0Rs2, from which we derive Rs/R0 ) (σs/σ0)1/2 and (from eq 4) Es ) (σ0E0 + σ2E2)/σs. Of course, for this interpretation to be valid, the unseen shift in reaction transition state must occur before the onset of depletion, i.e. Es < E1. Should the shift be accompanied by a change in reaction probability, then a corresponding rise or fall process would be clearly observed, with threshold Es; generally, this has not been the case. As panel e of Figure 6 illustrates, a forward shift requires the transition state on the lowest energy path to lie in the exit valley of the potential surface, but with restricted access thereto; as collision energy increases, a point (Es) is reached where the curvature of the surfaces in the constriction region forces trajectories to surmount an earlier barrier. With increasing energy, the exit valley is completely closed off, and depletion occurs at Rd, which can even exceed Rs. The present data show that all the Mn + SF6 chemiluminescent excitation functions exhibit “complex” rather than “simple” depletion. 1. UV Region (330-380 nm). The yield plot corresponding to the data of Figure 1 is displayed in Figure 7: the sharp negative falloff, and subsequent secondary rise before the final more moderate falloff, are clear. The solid line indicates the fit obtained by nonlinear least-squares regression,40 assuming four contributing processes in eq 2. For this, χ2 ) 1.75, and the correlation coefficient r ) 0.986. A smaller number of processes than four gives unsatisfactory fits, and a higher number is not justified by the quality of the data. The backcalculated excitation function fit is shown by the solid line in Figure 1, while Table 3 shows the best fit parameters, the

2812 J. Phys. Chem., Vol. 100, No. 8, 1996

Herbertson and Levy

Figure 8. Yield function, Y(ET0), calculated from the combined blue and red excitation functions of Figures 2 and 4. The solid line again shows the MLC least-squares best fit.

Figure 6. Complex excitation function falloff model.22,36 (a) At low collision energy, reaction only occurs at R0. (b) As ET increases, the transition state for reaction shifts forward to Rs at low impact parameters, but the overall cross section is not affected. (c) At higher energies, depletion starts at Rd. (d) At higher energies still, σ starts to rise again, as reaction at Rs can now occur at impact parameters >R0. (e) Schematic of potential surface features consistent with the above behavior: the bold line represents the minimum-energy path; 1, 2, and 3 are trajectories with progressively higher collision energy, and X is the saddle point.

Figure 7. Yield function, Y(ET0), calculated from the ultraviolet excitation function data of Figure 1. The solid line shows the leastsquares best fit generated on the basis of the MLC model.

normalization in σk corresponding to the excitation function data. Although inevitably there is a degree of correlation between the derived values of the parameters, the off-diagonal elements of the correlation matrix are all satisfactorily small. If only one process contributes to the observations, then the parameters lead to σs ) σ0 + σ2 ) 2.21 ( 0.16, Es ) 268 ( 21 kJ mol-1 and Rs/R0 ) 1.36 ( 0.05. Assuming that Pd ) 1.0 for depletion from ∼714 kJ mol-1, we find a value 0.86 ( 0.09 from the earlier threshold of ∼371 kJ mol-1 and Rd/R0 ) 1.40 ( 0.07. The final negative falloff in Figure 6 indicates that Rd > Rs. However, in view of our deductions below for the blue and red regions, we cannot exclude the possibility that two independent processes contribute to the UV data, the threshold at ∼484 kJ mol-1 being an unresolved double and σ3 representing the falloff in the higher energy process. In that case, the two processes cannot be unambiguously resolved, but by subtracting |σ3| from σ2, we estimate that the lower threshold process might have Rs/R0 ∼ 1.26, Es ∼ 233 kJ mol-1, and Rd/ R0 ∼ 1.30. 2. Blue and Red Regions (417-470 and 590-690 nm). As remarked above, the blue and red excitation functions in Figures 2 and 4 are virtually indistinguishable. The yield functions calculated from these data are likewise strikingly similar, each displaying some seVen linear sections. There are some small differences, but at this stage experimental uncertainty seems to be the most likely cause. To test this conclusion, we have sought to establish whether one MLC model form could satisfactorily fit both data sets, and to this end, we have combined both sets to generate the common blue/red yield function shown in Figure 8. The nonlinear least-squares fit to this composite, also displayed, required seven parameter pairs, with χ2 ) 0.278 and r ) 0.997. The resulting back-calculated excitation function is compared with the original data in Figures 2 and 4. Within experimental error, a common functionality is seen to be responsible for both luminescences. As before, Table 3 shows the best fit param-

TABLE 3: Parameters of the Analysis (σk/arbitrary units; Ek/kJ mol-1) k emission (MnF state) UV (A7Π)

σk Ek blue (e5Σ+)/green (d5Π)/red (c5Σ+) σk Ek green (d5Π) σk Ek IR (b5Π) σk Ek

0

1

2

3

1.187 ( 0.015 85.5 ( 1.5 0.63 ( 0.07 47 ( 2 0.075 ( 0.002 173 ( 14 1.213 ( 0.006 114 ( 1

-2.02 ( 0.16 371 ( 5 0.71 ( 0.07 87 ( 3

1.02 ( 0.16 484 ( 14 -0.80 ( 0.04 223 ( 3

-0.32 ( 0.06 714 ( 26 -1.09 ( 0.04 327 ( 3

-0.78 ( 0.02 -0.71 ( 0.02 0.109 ( 0.013 565 ( 6 897 ( 9 1522 ( 59

4

5

6

0.56 ( 0.02 -0.23 ( 0.02 0.22 ( 0.01 533 ( 6 758 ( 16 1069 ( 13

Reaction Mn + SF6 f MnF + SF5

J. Phys. Chem., Vol. 100, No. 8, 1996 2813

TABLE 4: Possible Deconvolutions of Derived Blue/Red Parameters (σk/arbitrary units; Ek/kJ mol-1) k 0

1

I a b c

σk Ek σk Ek σk Ek

0.56 47

σk Ek σk Ek σk Ek

0.63 47

-0.88 230 0.78 90

b c

3

-1.01 327

4

-0.80 223 0.71 87

-1.09 327

5

6

0.32 533 0.23 533

II a

2

-0.23 758

0.23 1069

0.17 533 0.39 533

0.38 758 -0.61 758

0.22 1069

eters, the normalization in σk corresponding to the excitation function data; the off-diagonal elements of the correlation matrix are again all satisfactorily small. The sharp negative slopes in Figure 8 again demonstrate that we must be dealing with “complex” depletion. The parameters appear at first to suggest a single excitation function, since their overall sum is zero and since they do not readily fall into subsets with the same property and which satisfy the requirement that Es falls below the depletion threshold. However, there are simply too many processes for a single excitation function to be reasonable. The three negative σk values in fact indicate that there are probably three overlapping excitation/yield functions, which must presumably have some similar thresholds which we are unable to resolve, within the quality of the data. In this context the order of signs of the σk values, two positive followed by two negatives, and their relative magnitudes, suggest the separation

Ya(ET) ) σ0(ET - E0) + σ2(ET - E2) + ... Yb(ET) ) σ1(ET - E1) + σ3(ET - E3) + ...

(5)

Substitution for the positive and negative terms, as if this were simple depletion, leads to respective Rd/R0 values of 1.13 ( 0.14 and 1.24 ( 0.13, but since this is clearly complex depletion, we anticipate a following positive σk for each, with Es 1) is the number of vibration-rotational modes involved at the critical transition state. The fact that all the yield functions show a clear linear initial rise, i.e. n ) 1, indicates that the transition state involves very little coupling between reagent translation and the SF6 internal degrees of freedom. We can therefore set the contribution from Ev,r(SF6) at essentially zero. With these considerations, eq 7 and the MnF state energies in Table 1 lead to the minimum values of Ei(Mn*) displayed in Table 5 for each of the (deconvoluted) product channels. For the common e5Σ+/d5Π/c5Σ+ functionalities, the e5Σ+ excitation energy has necessarily been employed in the calculation, while Ei(Mn*) g 0 has been inserted for the deconvoluted ∼533 and ∼484 kJ mol-1 processes since large negative values are meaningless. It is clear from Tables 2 and 5 that ground state atoms could be responsible for these two high-threshold

processes (possibly a common processsif indeed both exist), for the b5Π channel, and perhaps for the d5Π channel with threshold 173 ( 14 kJ mol-1, but all other processes require excited atoms. The strongest Mn* candidate, by comparison with previous experiments,22,23,41 is the a6DJ state. However, for the A7Π process with threshold ∼85.5 kJ mol-1, it is not immediately evident that reaction by Mn*(a6DJ) is feasible. Its excitation, ∼207 kJ mol-1, does fall within the uncertainty of the Ei limit in Table 5, but that ambiguity derives in part from the SF5-F bond energy determination by Kiang, Estler, and Zare. Given Herron and Tsang’s higher estimation of D0, the true value is unlikely to be on the low side, and consequently Ei(Mn*) may well be out of reach of the a6DJ state. The most likely reagent species in this case is therefore z8PJ. A number of other factors argue in favor of this second excited state as the major precursor of MnF*(A7Π). In the first place, the A state is a relatively uncommon product in these reactions, being absent from Mn + SnCl4,22 SiCl4,23 and CF4.41 Second, we have two separate product channelssA7Π and e5Σ+/ d5Π/c5Σ+swith almost the same initial threshold but different functionality, suggesting different reagent states. Third, given that A7Π is at least the sixth excited state of MnF, its formation from Mn*(a6DJ) atoms might tend to be disfavored. By contrast, production of MnF*(A7Π) from Mn*(z8PJ) is a strong possibility since formation of the intervening quintet states from this species is spin-forbidden. For similar spin conservation reasons, we tend to discount the third metastable level, a4DJ, as a source for MnF*(A7Π). The crude comparability, given at the end of the Results section, of the A7Π and c5Σ+ σ0 values, much larger than those for the intervening d5Π and e5Σ+ states, also tends to confirm the attribution to different reagent states. Although the anticipated z8PJ:a6DJ ratio in our atomic beam is ,1,32 the a6DJ reactivity will be distributed among a large number of product channels, including the X7Σ+ and a5Σ+ states not observed here, whereas the z8PJ reactivity should be concentrated into the MnF X7Σ+ and A7Π states. While two of the z8PJ substates will be depleted by emission during the time period corresponding to the measurements, the most excited level, J ) 9/2, is truly metastable,31 so its population will be sustained. The absence of any noticeable curvature to the UV yield function suggests that the J ) 9/2 level makes the dominant contribution, although such curvature could be disguised if, as argued above, a separate high-threshold process is also present. For the common e5Σ+/d5Π/c5Σ+ excitation functions, clearly three states could contribute, Viz. a4DJ, a6DJ, and a6S for the ∼47, ∼87, and ∼533 kJ mol-1 thresholds, respectively. Such a possibility is, however, difficult to reconcile with the constant, nonstatistical branching ratio into these three MnF states, since different potential surfaces (e.g. sextet and quartet) would be involved. The different thresholds and transition state shifts do indicate that the interactions must differ, but if the same reagent state is involved, then the same branching ratio might still result, as the energetics would be the same and the transition state geometry perhaps not too different. Since a6DJ atoms are unlikely to be completely excluded, they must be preferred over a4DJ atoms. Of course, our conclusion that the e5Σ+ and c5Σ+ excitation functions are virtually identical may have disguised true but small differences. Indeed, the additional contribution to the d5Π data, with E0 ∼ 173 kJ mol-1, may reflect an increased branching into that product on one potential surface. In fact, bearing in mind the imprecision in the separation (cf. Figure 10), it is not impossible that the true threshold of the additional process is coincident with Es for process a (Table 5). A change

2816 J. Phys. Chem., Vol. 100, No. 8, 1996 in branching concomitant with a transition state shift has already been proposed for Mn + SiCl4,23 to explain the high-energy partial depletion of MnCl*(c5Σ+) and enhancement of MnCl*(d5Π) observed in that reaction. Because of the closeness of Es and Ed for process a here, only a single loss feature would be observed for the c5Σ+ and e5Σ+ channels and a single net production feature for the d5Π channel. The attribution of MnF*(e5Σ+,d5Π,c5Σ+) production to Mn*(a6DJ) argues strongly that this species is also the reagent for MnF*(b5Π). Only in Mn + F2, Cl2,42 both of which are much more exoergic than Mn + SF6, has b5Π production from reaction of ground state atoms definitely been observed, and in both those cases a6DJ atoms contribute also. Therefore, given that only one reagent state is responsible here, it must be Mn*(a6DJ), despite the Ei value in Table 5. This result tallies with the deduction above of a connection between b5Π depletion and enhanced e5Σ+/d5Π/c5Σ+ production from ∼533 to 565 kJ mol-1 since, as discussed, the almost constant branching ratio also implies a single reagent state for the latter. 3. Potential Surfaces. In the first paper in this series,22 the observation of unique excitation functions for MnCl*(e5Σ+,d5Π,c5Σ+) production from Mn*(a6DJ) + SnCl4 suggested that the reaction takes place on individual potential surfaces in which entrance channel effects dominate. For Mn + SiCl4,23 the situation is a little more complex: while the MnCl* e5Σ+, d5Π, c5Σ+, and b5Π states seem to be predominantly formed on four distinct surfaces, it also appears that high-energy c5Σ+ depletion leads to enhanced d5Π production and that both those states could originate from a common reactive process at low collision energy. The Mn + SF6 reaction takes this complexity a stage further: (i) the A7Π state is now formed, predominantly (it seems) from Mn*(z8PJ); (ii) the c5Σ+, d5Π, and e5Σ+ states now arise from several common processes; and (iii) high-energy MnF*(b5Π) depletion appears to result in enhanced production of the c, d, and e states and perhaps of the A state as well. Like Mn + SnCl4, SiCl4, however, all the Mn*(a6DJ) reactions here show significant excess barriers, as the Ei minima in Table 5 fall well below the true values in Table 2: e.g., for the ∼87 kJ mol-1 e5Σ+/d5Π/c5Σ+ process, the barrier must be ∼54 ( 21 kJ mol-1 above the e5Σ+ asymptote. Indeed, in both Mn + SiCl4 and Mn + SF6, the lowest emitting product state, b5Π, has the highest initial threshold, although by contrast, formation of MnF*(A7Π) from Mn*(z8PJ) + SF6 requires very little excess energy over the endothermicity. The transition state shifts observed here (excluding b5Π) are also comparable to or even greater than those observed for SnCl4 and SiCl4; indeed, the shifts for the A7Π channel are among the largest found so far.22,23,36 In Mn + SiCl4, the collision energy dependence of chemiluminescence was discussed in terms of a hierarchy of “inner” ionic-covalent curve crossings.52 It was shown, on the basis of Magee’s well-known formula,53 that the critical crossings between Mn*(...3d64s1, a6DJ) + SiCl4 and Mn+*(...3d6,a5DJ) + SiCl4-(X2A1) occur at very short internuclear distances, which can only be reached by C3V type approach of Mn toward the Si. However, for the reaction to proceed, the Mn has to move off the C3 axis, toward a Cl atom, reducing the symmetry to Cs. In both point groups, intermolecular electron repulsion will split the energies of the ...3d6 spatial configuration (symmetric ...3d5, + 1 left over), resulting in a series of avoided crossings (see Figure 12 of ref 23). It was deduced that the two lower ionic curves, E(A′,A′′), give rise to MnCl*(c5Σ+,d5Π) respectively; the E(A′′) component, at least, of the next pair goes over to MnCl*(b5Π); and the upper, A(A′) surface leads to MnCl*(e5Σ+). The significant transition state shift shown by the c5Σ+ channel alone was correlated with the high-energy and short

Herbertson and Levy TABLE 6: Calculated Electron Jump Crossing Radii (Å) for Mn + SF6 f Mn+ + SF6- 31,44-45,48 a7S

Mn+ state SF6- state

X ˜ 2A

Mn state a6S a6DJ z8PJ a4DJ a

a5S

1g

A ˜ 2T/E

X ˜ 2A

2.26 3.40 3.53 (4.15)

2.08 3.01 3.11 (3.58)

a5DJ

1g

A ˜ 2T/E

X ˜ 2A

1g

A ˜ 2T/E

1.90 2.66 (2.74)a 3.09

1.77 2.41 (2.48) 2.76

1.76 2.39 (2.46) 2.73

1.65 2.19 (2.24) 2.47

Spin-forbidden processes in parentheses.

internuclear distance of the crossing between the lowest E(A′) ionic and covalent surfaces. In Mn + SF6 likewise, avoided crossings between ionic and covalent potential surfaces are likely to dominate the interaction, sincesas indicated by Table 1smost of the MnF excited states can be characterized as Mn+*F-. However, a complication arises in estimating the crossing radii because a range of values of the SF6 adiabatic electron affinity have been reported.54-57 Most of the earlier measurements,54,55 which were largely based on endothermic charge transfer or ion-pair formation under single-collision conditions, support a value 0.5-0.6 eV. On the other hand, more recent kinetic measurements56,57 on a number of SF6- reactions have concurred on the value 1.05 ( 0.10 eV, while a similar value, 0.90-1.00 eV, has been found58 from an SCF calculation of the potential energy curves of SF6 and SF6- as a function of the symmetric stretch coordinate. For this lowest energy state of SF6-, it is calculated that the extra electron enters the symmetric 6a1g(σ*) orbital,58,59 increasing the S-F bond length from 1.567 to 1.710 Å, but there is a barrier to electron acceptance since the SF6-SF6- crossing occurs at ∼1.61 Å, ∼0.23 eV above the SF6 energy minimum. Streit56 has suggested that the discrepancy between the earlier and later values of the electron affinity derives from the formation of an excited state, SF6-*, about 0.5 eV above the ground state. He postulates that this excited state is uniformly produced in the earlier, threshold determination, measurements because of their common “short” interaction time. In line with Stockdale et al.,54 he argues that attachment, and presumably charge exchange, to SF6 would be greatly facilitated if the electron entered an orbital of lower than a1g symmetry, i.e. 6t1u (4pS) or 4eg (3dS).59 That would lead to a Jahn-Teller distortion in SF6- which traps the electron by enhancing the coupling of electronic and nuclear motion; thus, in short-duration collisions, formation of excited SF6-* would have a greater cross section than that of the ground state and could reasonably be expected to be the process observed in the threshold determination measurements. Accepting these arguments, we denote the ground and first ˜ 2A1g and A ˜ 2T/E and ascribe excited states of SF6- simply as X respective electron affinities of 1.05 ( 0.10 eV and 0.5 ( 0.1 eV. For Mn(a6S) f Mn+(a7S,a5S,a5DJ,z7PJ), the ionization potentials are respectively 7.43, 8.62, 9.23, and 12.22 eV.31,45 From these data, along with the Mn atomic state energies in Table 2, we derive the crossing radii listed in Table 6. Of course, such radii should only be regarded as tentative: this is a crude model, ignoring intermolecular repulsion and higher elements of the multipole expansion of the interaction, i.e. the fact that SF6- is not a point charge; the SF6- A state excitation has not been definitively measured; there are likely to be other excited states of SF6- at relatively low energy; and the close ˜ 2T/E and a5DJ-X ˜ 2A1g radii suggests coincidence in the a5S-A that there may be a degree of mixing and splitting between these ionic curves. Nonetheless, the radii should at least give us a qualitative departure point for our understanding of the processes involved.

Reaction Mn + SF6 f MnF + SF5

Figure 13. (a) Zero-impact parameter Mn-SF6 geometry facilitating approach to inner ionic-covalent curve crossings; dimensions are in angstroms, and two of the six F atoms are completely obscured. The Mn-S distance corresponds to contact between the Mn atom and three F atoms at the van der Waals radii of the latter. (b) Schematic of wide impact parameter collision geometry, showing possible distortion of the SF6 to allow the Mn-S distance to reach 2.4 Å. Here only a single F atom is completely obscured.

In the Mn-SF6 system, four approach geometries involving any symmetry element are possible: C4V, C3V, C2V, and Cs. Since, however, the S-F equilibrium bond length is 1.567 Å60 and the Mn atomic radius and F van der Waals radius are 1.18 and 1.35 Å, respectively,61 most of the inner crossing radii are unlikely to be reached in the C4V configuration. The best chance of penetrating to short internuclear distances again occurs for C3V geometry, as illustrated in Figure 13a, although as Figure 13b shows, nonzero impact parameter collisions require initial Cs approach if the shortest internuclear distances are to be reached. Even in C3V, the Mn-SF6 potential should start to become repulsive at Mn-S length ∼3.1 Å. That repulsion should increase relatively slowly with falling internuclear distance, as the three-fluorine “umbrella” just needs to open by a modest amount, and the Mn and F will interpenetrate (i.e. the SF6 behaves as a “soft” sphere, cf. Figure 13b); but clearly ground state Mn atoms are very unlikely to reach the inner crossings in Table 6, except at very high energiessa result consistent with our conclusion that chemiluminescence here derives entirely from excited atoms. As noted above, of course, the simple Magee formula cannot be rigorously applied, especially in this sort of close C3V/Cs geometry. Nonetheless, the calculated radii for the excited atomic states imply that the inner crossings could be reached, albeit with some barriers. Again, as with Mn + SiCl4, a hierarchy of crossings involving Mn*(a6DJ) and Mn+*(a5DJ) will arise, whose location and energy will depend on the degree of splitting of the different odd d-electron orientations. The common e5Σ+/d5Π/c5Σ+ energy dependence nonetheless remains to be explained. The different values of Es, Ed, and Rs/R0 for the deconvoluted ∼47 and ∼87 kJ mol-1 processes (Table 5) suggest that each process derives from a distinct avoided crossing with a different ionic potential. As suggested earlier, the geometry of each of the crossings must be very similar for the same branching ratio to occur, but the fact that multiple states arise indicates that some factor is mixing the potentials. One possible mechanism for this is SF5 vibrational motion in the exit channel. Alternatively, in view of the presence of additional ionic surfaces ˜ 2T/E), which in turn will be split by corresponding to SF6-*(A Jahn-Teller distortion, many of the ionic “curves” could in fact consist of several closely interacting potentials. The two thresholds observed would then represent unresolved averages over several “bunched” curve crossings.

J. Phys. Chem., Vol. 100, No. 8, 1996 2817 To reach these inner crossings, trajectories would still be expected to turn the corner of the potential surface: as already noted, the adiabatic electron affinity of 1.05 eV for SF6 f SF6-(2A1g) involves the S-F bond stretching from 1.567 to 1.710 Å, and a similar change is anticipated for the 2T/E state. As collision energy increases, i.e. as the Mn comes in more rapidly, there may not be time for this stretching to occur, so that, as argued previously,23,36 the system will be forced to surmount an earlier barrier, as sketched in Figure 6. In the present case, the 53.5° skewing angle62 of the surface, resulting from the mass combination, makes the turning region particularly sharp. Intuitively, we would expect higher thresholds to correspond with higher shifts, but in principle a more repulsive ionic potential could give rise to a smaller shift from a higher threshold (cf. Table 5 and Figure 12 of ref 23). Whatever the surfaces leading to MnF*(c5Σ+,d5Π,e5Σ+), the high b5Π threshold, and its low transition state shift, are anomalous. As indicated above, the comparable situation in Mn + SiCl4 was rationalized in terms of b5Π production from a higher ionic curve than those leading to c5Σ+, d5Π, and e5Σ+, the relevant crossing occurring at higher energy but longer internuclear distance. This inverted excitation order was attributed to nuances of the product state electron configurations (cf. Table 1), such that the b5Π state experiences higher repulsion from the SiCl3 moiety. Clearly a similar situation could be happening here with the SF5. The difference, however, is that b5Π depletion at high collision energy appears to result in enhanced formation of c5Σ+, d5Π, e5Σ+, and perhaps A7Π. The lack of significant specificity suggests that this too is an entrance channel effect, involving a further degree of mixing of the surfaces involved. The absence of MnCl*(A7Π) in Mn + SnCl4, SiCl4, and the production here of the MnF* analog from Mn*(z8PJ), can be attributed directly to the presence of the low-lying SF6-* state, since it affords an excited octet surface not available in the other systems. In this channel, however, the transition state shift is higher than those for Mn*(a6DJ), despite the higher calculated crossing radius in Table 6. The very small excess barrier (cf. Table 5) provides the key: the endothermicity of the process, rather than the position of the ionic-covalent curve crossing, defines the initial transition state, which must therefore lie in the exit valley. With increasing collision energy, however, the ionic-covalent curve crossing will still shift forward, so that it, rather than the endothermicity, now defines the transition state. Conclusions The reaction between SF6 and a laser-ablated beam of Mn atoms yields chemiluminescence from five different MnF* states in the collision energy range ET ) 0-2000 kJ mol-1. Analysis of the excitation functions, by the multiple line-of-centers approach, indicates that: (1) MnF*(A7Π) is predominantly formed on a single potential surface, with threshold ∼85.5 kJ mol-1 and probable progenitor Mn*(z8PJ); a minor additional contribution (possibly due to Mn*(a6DJ), see below) may also occur above ∼484 kJ mol-1. (2) The e5Σ+, d5Π, and c5Σ+ states are formed via three common potential surfaces, with thresholds ∼47, ∼87, and ∼533 kJ mol-1, and likely reagent state Mn*(a6DJ). (3) The a6DJ state is also likely to be the progenitor of MnF*(b5Π), threshold ∼114 kJ mol-1. (4) Partial depletion of the b5Π state from ∼565 kJ mol-1 may well be the origin of the enhanced yield observed for the c, d, e, and A states (cf. (1) and (2) above) at about the same energy. (5) All reactions are characterized by a shift forward in transition state location with increasing collision energy, the shift being greatest for A7Π and least for b5Π.

2818 J. Phys. Chem., Vol. 100, No. 8, 1996 As in Mn + SnCl4, SiCl4, production of the emitting states has been attributed predominantly to “inner” ionic-covalent curve crossings at short internuclear distance. The preferred geometry, C3V/Cs, splits the covalent and ionic potentials corresponding to Mn*(a6DJ) and Mn+*(a5DJ), respectively, allowing a number of crossings to occur at different approach distances and energies. However, here the common thresholds for MnF*(c5Σ+,d5Π,e5Σ+) production suggest a much more complex interaction than previously. The two thresholds at ∼47 and ∼87 kJ mol-1 imply avoided crossings with distinct ionic curves (or close groups of curves), but some factor must be mixing the curves as they evolve toward the product states. That factor could be SF5 vibrational motion, but alternatively, Jahn˜ 2T/E) could Teller distorted curves corresponding to SF6-*(A be interacting with the other ionic curves to produce bunched curve crossings which are only detected as averages. The initial b5Π threshold is anomalously high. As for Mn + SiCl4, it has been suggested that this arises from a greater degree of repulsion at the transition state, due to nuances of the electron configuration. The depletion of b5Π in favor (apparently) of the other emitting states has been ascribed to a further degree of surface mixing in the entrance channel. The production of MnF*(A7Π) is attributed to the presence of the excited SF6-* potential, since it offers an excited octet ionic surface not available in Mn + SnCl4, SiCl4. In this case, however, the threshold seems likely to be determined by the endothermicity of the process, with the relevant ionic-covalent curve crossing occurring well below that. In all cases the initial transition state seems to lie toward the exit valley; i.e., the SF6 has to stretch a little to reach the geometry of SF6-. The transition state shifts have been attributed to insufficient time, at high collision energy, for the stretching to occur, i.e. for the system to turn the very sharp corner of the potential surface. Acknowledgment. We thank the U.K. Science and Engineering Research Council (now the Engineering and Physical Sciences Research Council) for the equipment grant which led to this research, unknown referees for helpful comments, and Prof. J. L. Gole for communication and discussion of results prior to publication. References and Notes (1) Riley, S. J.; Herschbach, D. R. J. Chem. Phys. 1973, 58, 27. (2) Bennewitz, H. G.; Haerten, R.; Mu¨ller, G. Chem. Phys. Lett. 1971, 12, 335. (3) Freund, S. M.; Fisk, G. A.; Herschbach, D. R.; Klemperer, W. J. Chem. Phys. 1971, 54, 2510. (4) Maltz, C. Ph.D. Thesis, Harvard, 1969. (5) Maltz, C.; Herm, R. R.; Herschbach, D. R. Citation in ref 1. (6) Hsu, D. S. Y.; Herschbach, D. R. Faraday Discuss. Chem. Soc. 1973, 55, 116. (7) Hsu, D. S. Y. Ph.D. Thesis, Harvard, 1974. (8) Parrish, D. D.; Herm, R. R. J. Chem. Phys. 1971, 54, 2518. (9) Behrens, Jr., R.; Herm, R. R.; Sholeen, C. M. J. Chem. Phys. 1976, 65, 4791. (10) Mariella, R. P.; Herschbach, D. R.; Klemperer, W. J. Chem. Phys. 1973, 58, 3785. (11) Eyal, M.; Grabiner, F. R.; Agam, U.; Gamss, L. A. J. Chem. Phys. 1981, 75, 4396. (12) Eyal, M.; Grabiner, F. R.; Agam, U.; Gamss, L. A. J. Phys. Chem. 1983, 87, 3400. (13) Herm, R. R.; Lin, S. M.; Mims, C. A. J. Chem. Phys. 1973, 77, 2931. (14) Kiang, T.; Estler, R. C.; Zare, R. N. J. Chem. Phys. 1979, 70, 5925. (15) Kiang, T.; Zare, R. N. J. Am. Chem. Soc. 1980, 102, 4024. (16) Verdasco, E.; Saez Rabanos, V.; Gonza´lez Urena, A. Laser Chem. 1989, 10, 521.

Herbertson and Levy (17) Verdasco, E.; Menendez, M.; Garay, M.; Gonza´lez Urenˆa, A.; Benoist D’Azy, O.; Poblete, F. J.; Taieb, G. Laser Chem. 1992, 12, 123. (18) Rosano, W. J.; Parson, J. M. J. Chem. Phys. 1986, 84, 6250. (19) Gole, J. L.; Preuss, D. R.; Chalek, C. L. J. Chem. Phys. 1977, 66, 548; 1977, 67, 850. (20) Gole, J. L.; Chalek, C. L. Proc. Electrochem. Soc. 1978, 78-1, 278 (Proceedings of the Symposium on High Temperature Metal Halide Chemistry, 1977). (21) Brayman, H. C.; Fischell, D. R.; Cool, T. A. J. Chem. Phys. 1980, 73, 4246. (22) Herbertson, D. L.; Newnham, D. A.; Levy, M. R. Can. J. Chem. 1994, 72, 850. (23) Newnham, D. A.; Levy, M. R. J. Phys. Chem. 1996, 100, xxxx. (24) Mesnage, P. Ann. Phys. 1939, 12, 5. (25) Launila, O.; Simard, B. J. Mol. Spectrosc. 1992, 154, 93. (26) Launila, O.; Simard, B. J. Mol. Spectrosc. 1992, 154, 407. (27) Devore, T. C.; Gole, J. L. Manuscript in preparation. (28) Launila, O.; Simard, B.; James, A. M. J. Mol. Spectrosc. 1993, 159, 161. (29) Herron, J. T.; Tsang, W. Abstracts, XII International Symposium on Gas Kinetics, Paper H25, Reading, 1992. (30) Kent, R. A.; Ehlert, T. C.; Margrave, J. L. J. Am. Chem. Soc.; 1964, 86, 5090. (31) Sugar, J.; Corliss, C. J. Phys. Chem. Ref. Data 1985, 14 (Suppl. 2), 388 ff. (32) Levy, M. R. J. Phys. Chem. 1989, 93, 5195. (33) Levy, M. R. J. Phys. Chem. 1991, 95, 8491. (34) Rao, S. V. K.; Reddy, S. P.; Rao, P. T. Proc. Phys. Soc. 1962, 79, 741. (35) Balfour, W. J.; Lindgren, B.; Launila, O.; O’Connor, S.; Cusack, E. J. J. Mol. Spectrosc. 1992, 154, 177. (36) Levy, M. R. Res. Chem. Kinet. 1993, 1, 163. (37) LaBudde, R. A.; Kuntz, P. J.; Bernstein, R. B.; Levine, R. D. J. Chem. Phys. 1973, 59, 6286. (38) Jalink, H.; Janssen, M. H. M.; Geijberts, M.; Stolte, S.; Parker, D. H.; Wang, J. Z. W. In SelectiVity in Chemical Reactions; Whitehead, J. C., Ed.; Reidel: Dordrecht, 1988. (39) Parker, D. H.; Jalink, H.; Stolte, S. Faraday Discuss. Chem. Soc. 1988, 81, 184. (40) Fig.P for Windows, Version 2.2; Fig.P. Software Corporation, Durham, NC. (41) Herbertson, D. L.; Levy, M. R. J. Phys. Chem., to be submitted. (42) Hughes, T. J.; Spence, M. A.; Levy, M. R. Manuscript in preparation. (43) Bagral, B. K.; Murphy, S. J.; Levy, M. R. Manuscript in preparation. (44) Catala´n, M. A.; Meggers, W. F.; Garcia-Riquelme, O. J. Res. Natl. Bur. Stand. 1964, 68A, 9. (45) Younger, S. M.; Fuhr, J. R.; Martin, G. A.; Wiese, W. L. J. Phys. Chem. Ref. Data 1978, 7, 495. (46) Levy, M. R. J. Phys. Chem. 1991, 95, 8500. (47) DeKock, C. W.; Gruen, D. M. J. Chem. Phys. 1968, 49, 4521. (48) Jacox, M. E.; Milligan, D. E. J. Chem. Phys. 1969, 51, 4143. (49) Hayes, W. Proc. Phys. Soc. 1955, 68A, 1097 and references therein. (50) Pearse, R. W. B.; Gaydon, A. G. The Identification of Molecular Spectra, 4th ed.; Chapman Hall: London, 1976. (51) Gonza´lez Uren˜a, A. Mol. Phys. 1984, 52, 1145. (52) Menzinger, M. In Gas Phase Chemiluminescence and ChemiIonization; Fontijn, A., Ed.; Elsevier: Amsterdam, 1985; p 25. (53) Magee, J. L. J. Chem. Phys. 1940, 8, 687. (54) Stockdale, J. A. D.; Compton, R. N.; Schweinler, H. C. J. Chem. Phys. 1970, 53, 1502. (55) Lias, S. G.; Bartmess, J. E.; Liebman, J. F.; Holmes, J. L.; Levin, R. D.; Mallard, W. G. J. Phys. Chem. Ref. Data 1988, 17 (Suppl. 1), 1. (56) Streit, G. E. J. Chem. Phys. 1980, 77, 826. (57) Grimsrud, E. P.; Chowdhury, S.; Kebarle, P. J. Chem. Phys. 1985, 83, 1059. (58) Hay, P. J. J. Chem. Phys. 1982, 76, 502. (59) Hay, P. J. J. Am. Chem. Soc. 1977, 99, 1013. (60) CRC Handbook of Physics and Chemistry, 74th ed.; CRC Press: London, 1993-4. (61) James, A. M.; Lord, M. P. Macmillan’s Chemical and Physical Data; Macmillan: London, 1992. (62) Polanyi, J. C.; Schreiber, J. L. In Physical Chemistry: An AdVanced Treatise; Jost, W., Ed.; Academic Press: New York, 1970; Vol. VIA, p 383.

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