J. Phys. Chem. 1983, 87, 3474-3479
3474
Energy-Entropy Trade-offs in the Unimolecular Decompositions of SF6C. Lifshitz Depadment of Physical Chemistry, The Hebrew Unlverslty of Jerusalem, Jerusalem 9 1904, Israel (Received: August 18, 1982)
The data on autodetachment from SF6- and predissociation to SF5-+ F are reviewed. It is concluded that they can be reconciled with a moderately high activation energy and a low activation entropy for the autodetachment process, SF6- SF6 + e, Eo = 0.8 eV and ASt = -14 eu, provided the activation energy for e + SFs SF5-+ F is 0.43 eV.
-
-
The gas-phase anion SF6-has been the subject of numerous studies. Three important recent contributions have studied the electron photodetachment of the sulfur hexafluoride anion,l the negative ion chemistry and electron affinity of SF,2 and the kinetics and thermochemistry of electron attachment to SF6.3 No observable photodetachment from SF6- was detected in the first study and a loose SF6-structure which is distorted significantly from that of the neutral has been suggested.l The second study, which employed the flowing afterglow technique, has recommended the value of EA(SF6) = 1.0 f 0.2 eV for the electron affmity of SF,. Of major importance in that study has been the observation that NHT exchanges charge with SF6and therefore EA(SF6)I 0.74 eV. In the third study, Heneghan and Benson carried out RRKM calculations for the lifetime of S F c toward autodetachment
SF6- ---* SF6
+e
(1)
and have come to the conclusion3that the electron affinity of SF, must be in the neighborhood of 32 kcal/mol(=1.4 eV). The electron affinity was deduced from the observed bimolecularity of the electron capture process down to 0.1 torr Ar bath gas4and from estimated entropies of SF6and SF6-.3Contrary to the conclusions of Drzaic and Brauman,' Heneghan and Benson3 concluded that the structures of SF6and SF6- were similar. The preexponential A factor for the thermal electron ejection reaction from SFC was deduced to be close to ekT/h at 300 K, i.e., comparable to those for tight transition states: with near zero activation entropy. Two important aspects of the unimolecular chemistry of the sulfur hexafluoride anion are related to the competing dissociative reaction channel SF6-
-+
SF5-
+F
(2)
and will be discussed in this paper. (a) Metastable transitions have been observed for reaction 2 in magnetic sector instrument^.^-^ The observation of metastable ions requires the survival against autodetachment of SF,-, having enough energy to dissociate via reaction 2, at least for the time spent in the ion source and up to the field free region where reaction 2 takes place. This fact has been recognized previously by K10ts.~ (b) Any model suggested for the reactant SF6- ion of reaction 1has to fit experimental data (1) Drzaic, P. S.;Brauman, J. I. J. Am. Chem. SOC.1982, 104, 13. (2)Streit, G. E.J. Chem. Phys. 1982,77,826. (3) Heneghan, S.P.; Benson, S. W. Int. J. Chem. Kinet. 1983,15,109. (4)Fehsenfeld, F. C. J. Chem. Phys. 1970,53,2000. (5)Lifshitz,C.;MacKenzie Peers, A.; Grajower, R.; Weisa, M. J. Chem. Phys. 1970,53,4605. (6)Lifshitz, C.; Weiss, M. Chem. Phys. Lett. 1972,15,266. (7)Ahearn, A. J.; Hannay, N. B. J. Chem. Phys. 1953,21,119. (8)Hickam, W. M.; Fox, R. E. J . Chem. Phys. 1956,25, 642. (9)Klota, C. E. Chem. Phys. Lett. 1976,38,61. 0022-3654/83/2087-3474$0 1.50/0
for reaction 2 as well. The threshold energy assumed for reaction 1and the degree of tightness or looseness of SF6-, determined by the choice of vibrational frequencies, affect those of reaction 2. An analysis of literature data on SF6-,as well as of additional experimental data to be presented here, will be shown to require a relatively high threshold energy for reaction 1, namely, Eo, = EA(SF6)= 0.8, in agreement with the recent experimental data of Streit,2as well as a very loose SF6-reactant in agreement with Drzaic and Brauman1 so that ASl+ = -14 eu for reaction 1 at 300 K. Experimental Section The CH4 single-focusing magnetic sector mass spectrometer and RPD ion source, employed in the study of unimolecular metastable ions of reaction 2, has been described previ~usly.~ In a mass spectrometer of this type, ions dissociating in the ion source are detected as fragments; ions which do not dissociate or which dissociate following passage through the magnetic field are detected as parent ions, while ions which dissociate between the acceleration region and the magnetic field, in the field-free region, are collected at nonintegral mass positions-they are the so-called "metastable" ions. The minimum time taken for ions of m/z 146 to reach the field free region of the instrument is 2 ps. Figure 1 shows the fractional abundance of ions detected as parent, normal fragment, and metastable ions in the CH4 as a function of k-the rate constant for unimolecular decomposition of a parent ion of mass 146. These abundances have been calculated as previously described by Chupka.lo The experimental abundances of metastable ions, in relation to those of normal parent and fragment ions of reaction 2, were obtained as previously5 by employing correction factors for the peak areas and multiplier gain. Ion source pressures were 10" torr while the pressure in the field free region was Ilo4 torr. Operating conditions for the RPD source were as follows: 1.5-ps electron pulse length, an ion drawout pulse length of 0.5 ps, and a repetition rate of 5 X lo4 Hz. The delay time between the end of the ionizing pulse and the beginning of the drawout pulse was minimal, 0.1 ps. The decay characteristics of autodetaching anions have been studied by varying the delay time of the ion-drawout pulse, from nominally zero up to about 9 ps, with respect to a short (0.2 ps) ionizing electron pulse. Ions are lost from the source during the delay time by drifting in addition to autodetachment. The drifting was corrected for by employing calibrations using stable fragment ions which do not autodetach (for example, I- or SF,-). Using this technique for the nitrobenzene anion, we obtained an autodetachment lifetime, T = 32 ps, in agreement with pre-
-
(10)Chupka, W. A. J. Chem. Phys. 1959,30, 191.
0 1983 American Chemical Society
The Journal of Physical Chemistty, Vol. 87, No. 18, 1983
Unimolecular Decompositions of SFc
normal products
SF,-PRDUCTS
0 03.0 5
1
4.0 2
3475
! 5.0 ?
d
6.0
log k Flgure 1. The fractional abundance of ions detected as parent (SF,-), normal fragment, and metastable ions ( m *) as a functlon of the rate coefficient for dissociation of SF,-. These abundances were calculated for the characteristlc residence times in the CH4 mass spectrometer. The unlabeled curve is for the sum (parent fragment metastable). The difference between the sum and a fractional abundance of 1.0 is due to ions which are not detected.
+
+
vious results" (see Figure 2). Negative ions are formed by electron capture not only during the electron pulse but for up to -3 ps following the pulse. This has been shown to be due to reflected low-energy electrons staying within the source. In this respect, the present experiment is more akin to the ion cyclotron resonance (ICR) e~perimenta'~-'~ rather than to the time-of-flight (TOF) one,16where the electrons make a single pass through the ionization chamber. Indeed, electrons staying within the ion source, following autodetachment, may be recaptured by SFG. Collision-induced dissociation of SFc was studied on a double mass spectrometer previously employed for studies of negative ion-molecule and collision-induced react i o n ~ . ' ~ * This ' ~ is a beam-collision chamber apparatus which provides mass analysis of the product ions. The collection stage is fixed at Oo (LAB) scattering angle. A mass and energy resolved beam is produced in the first stage mass spectrometer. This beam is decelerated in a retarding lens and impacted upon the target gas in the field-free collision chamber. The energy spread of the projectile ion beam entering the collision cell is 0.3 eV (lab) full-width at half-maximum. The Doppler broadening has a full-width at half-maximum, Wl12= ( l l . l y k T E ~ M ) 'in /~ the center-of-mass system where y, It, T , and ECM are as previously defined:18 y = m / M + m, where m is mass of the incident ion and M is the mass of the neutral target; k is Boltzmann's constant; T is the collision chamber temperature; and ECM= [ M / ( M+ m])Ehb,where ECM and Ebb are the nominal center-of-mass and laboratory energies, respectively. The O-(N02,0)N02-reaction with cr = 63 A2 at 0.3-eV laboratory energy was taken as the reference reaction in determining reaction cross sections.
QET Calculations The RRKM formalism was employed and rate coefficients were calculated as a function of internal energy of (11) Christophorou, L. G. Adu. Electron. Electron Phys. 1978,46,55. (12) Henis, J. M. S.; Mabie, C. A. J. Chem. Phys. 1970, 53, 2999. (13) Odom, R. W.; Smith, D. L.; Futrell, J. H. Chem. Phys. Lett. 1974, 24, 227. (14) Odom, R. W.; Smith, D. L.; Futrell, J. H. J.Phys. B 1975,8, 1349. (15) Compton, R. N.; Christophorou, L. G.; Hurst, G. S.;Reinhardt, P.W. J. Chem. Phvs. 1966. 45. 4634. (16) (a) Lifshitz: C.; Tiernan, T. 0.; Hughes, B. M. J. Chem. Phys. 1973,59, 3182. (b) Ibid. 1980, 72, 789. (17) Lifshitz, C.; Wu, R. L. C.; Tiernan, T. 0.;Terwilliger, D. T. J. Chem. Phys. 1978,68, 247. (18) Tiernan, T. 0.;Hughes, B. M.; Lifshitz, C. J. Chem. Phys. 1971, 55, 5692.
"ah --. 7 I21 -.I 3 1
- ,141
- ,151 -- .I7 0
,
1
I
2
3
4
6
5
6
7
l
8
9
Delay Time, microseconds Flgure 2. Semilog plots of normalized experimental ion currents for nitrobenzene and sulfur hexafluoride anlons as a function of delay time between ion formation and ion ejection for analysis. Results are presented for an electron energy corresponding to the maxima of the electron capture peaks.
the SF,- ion, according to eq 3, for reactions 1 and 2 , respectively. E-Eo
(3) Here E is the internal energy of the molecule ion, Eo is the threshold energy of the reaction, p(E) is the density of states at energy E of the SF6-ion, CoE-EoP(Ev')is the sum of the number of vibrational states available for reaction in the transition state configuration, cr is the reaction path degeneracy factor, and h Planck's constant. Model frequencies adopted for the reactant anion and activated complexes of reactions 1 and 2 were employed to compute activation entropies for the two reactions as suggested by Rosenstock et al.'9920and by Heneghan and B e n ~ o n .The ~ general approach has been to a s ~ u m e ~ ~ ~ ~ * ' a tight transition state (low activation entropy, low preexponential A factor for the thermal reaction) for reaction 1and a loose transition state (high activation entropy, high A factor) for reaction 2. Two models were adopted for reactions 1and 2 (Table I). In model A the vibrational frequencies of the reactant sulfur hexafluoride anion were taken according to ref 3. In model B, the vibrational frequencies of SF, were taken to be those of a SF6--F complex, following Drzaic and (19) Rosenstock, H. M.; Stockbauer, R.; Parr, A. C. J . Chem. Phys. 1979, 71, 3708. (20) Rosenstock, H. M.; Stockbauer, R.; Parr, A. C. J. Chem. Phys. 1980, 73, 773. (21) Klots, C. E. J . Chem. Phys. 1967, 46, 1197.
3478
Lifshitz
The Journal of Physicel Chemistry, Vol. 87,No. 18, 1983
TABLE I : QET Models ~
reactant ion configuration cm-' (degeneracy) [ji,
transition-state configuration u ' cm-' (degeneracy) A S f 3 0 0 K , eu A,(300 K), s-' transition state configuration v i r cm-' (degeneracy) Bi, cm-' (degeneracy) AS*300KI eu A,(300 K), s-'
model A
model B
700 ( l ) ,625 (2), 925 (3), 594 ( 3 ) , 500 (3), 325 ( 3 )
241 (2), 435 (2), 590 ( 2 ) , 342, 269, 4 3 5 , 4 6 9 , 522, 796, 100 ( 3 )
Reaction 1 700 ( l ) 625 , (2), 925 (2), 594 (3),
773.5 (l), 641.7 (2), 947.5 (2), 615.5 (3), 523 ( 3 ) , 347 ( 3 ) - 14 1.45 X 10"
500 (3), 325 ( 3 ) -0.13 1.59 x 1 0 1 ~ Reaction 2 700 (l), 625 (2), 925 (2), 594 (3), 500 (3), 325 ( l ) 1, 2 ( 2 )
241 (2), 435 (2), 590 (2), 342, 269, 4 3 5 , 4 6 9 , 522, 796 0.3416 ( 2 ) 4.28 1.38 x 1014
12.6 10l6
Brauman.l These frequencies were constructed from those of SF5- which are known22with three extra 100-cm-l frequencies. As previ~usly,~ one antisymmetric stretch 925 cm-' was chosen as the reaction coordinate of reaction 1 in model A. In model B of reaction 1, the frequencies of the activated complex were taken equal to those of SF6 minus one antisymmetric stretch. Two SF bending modes were weakened in the critical configuration of reaction 2 in both models A and B, such that A , = 10l6s-l for model A, in agreement with previous estimates3 and A , = 1.4 X 1014s-l for model B. Densities of states were calculated by the Whitten-Rabinovitch f ~ r m u l a t i o nas~ ~were sums of states at high energies. Exact enumeration of states was employed at low energies. Results and Discussion Autodetachment Lifetimes. The autodetachment process was first observed by Edelson et al.u Time-of-flight experiments reported on short autodetachment lifetimes for SFc of 25,15 and 69 ps,25respectively. ICR experiments reported12-14on long lifetimes ranging from 100 l.~sto 10 ms. calculation^^,^^ have indicated that the autodetachment lifetime depends on the internal energy of the anion, which in turn depends on the electron energy distribution and on the internal energy of the neutral molecule prior to electron a t t a ~ h m e n t . ' l * ' ~ *It~ ~was pointed that it was incorrect to characterize the autodetachment process with a single lifetime or rate constant and that, in fact, the observed lifetimes of SF6-are dependent upon the experimental observation time. The sulfur hexafluoride anion was not observed to autodetach under our experimental conditions (see Figure 2) in spite of our relatively short observation time. Radiative stabilization suggested on a time scale of millisec o n d cannot ~ ~ ~ be operative in the present experiments. Two effects are operative: (a) Most of the secondary electrons captured by the SF6 are of low energies, leading to a reduced internal energy in the anion, as in the ICR experiment. (b) Because of the high electron capture rate ~oefficient,~ k , = 2.2 X lo7 cm3/(molecule s), a notable fraction (-20%) of the autodetached electrons can be recaptured by SF6at torr. Odom et al.14 have devised (22) Christie, K. 0.;Curtis, E. C.; Scheck, C. J.; Pilipovich, D. Inorg. Chem. 1972,11, 1679. (23) Robinson, P. J.; Holbrwk, K. A. 'Unimolecular Reactions";Wiley-Interscience: London, 1972; p 134. (24) Edelson, D.; Griffiths, J. E.; McAfee, Jr., K. B. J . Chem. Phys. 1962, 37, 917. (25) Harland, P. W.; Thynne, J. C. J. J.Phys. Chem. 1971, 75, 3517. (26) Stock, M. G.; Strachan, P. C. H.; Parker, R. H.; Donovan, R. J.; Knox, J. H. In 'Dynamic Mass Spectrometry"; Price, D., Ed.; Heyden: London, 1974; Vol. 4. (27) Foster, M. S.; Beauchamp, J . L. Chem. Phys. Lett. 1975,31, 482.
/
5
-
0
I -I
/
IO!-
= I 5 913eu. ~10~~Sec-'
A,
c
w
Y
g i
/oEo
=0.54eV
4
0
1
2
I
3
I
1
1
I
1
4
5
6
7
8
log k ( E t
J
=O)
Flgure 3. Sensitlvity analysis for reaction 1. The value of log k , at an excess energy above threshold of E+ = 0.43 eV (which corresponds to the onset of reaction 2), is plotted as a function of log k at E+ = 0,the threshold for reaction 1. The two modeis A and B (see Table I) correspond to different activation entropies. The energy threshold Eo, of reaction 1, is treated as a parameter and is varied along the curves A and 6,for models A and B, respectively, between 1.36 and 0.54 eV.
an elegant method to overcome the problem of electron recapture by using an rf electron ejection pulse of variable duration. Free electrons resulting from the autodetachment of SF, were thus immediately removed from the cell. Multiexponential decays of SFc were observed14as is expected from theo+21 with the longest lifetimes (- 10 ms) most probably corresponding to the autodetachment energy threshold. Metastable ions at m* = 110.5 have been observed by us for reaction 2. If SF6 captures electrons within the accelerating field, just in front of the field free region, and the resulting SF6-dissociates in the field free region, the product SF5-cannot be collected at m* = 110.5. Only SF6ions, which have been fully accelerated, before entering the field free region, contribute to the metastable peak at the nonintegral mass of 110.5. This means that ions having enough energy to dissociate via reaction 2 survive for 2 ps. The energy threshold for reaction 2 is known4 t o be 0.43 eV above that of reaction 1. We have calculated the rate coefficient for reaction 1 at its threshold, assuming the parameters of model A and a threshold energy of 1.4 eV, corresponding to the electron affinity of SF6according to Heneghan and B e n ~ o nthis ; ~ gives kl = 1.17 X lo4 s-l. At 2.5 kcal/mol above threshold, kl = 1.47 X lo5 s-l, in good agreement with Heneghan and B e n ~ o n .At ~ 0.43 eV above threshold, k , = 2.9 X lo7 s-l and for t = 2 X lo4 s the fractional abundance of parent ions left for dissociation With this model in the field free region is only 6.5 X there should be no observable metastable ion for reaction
-
me Journal of Physlcal Chemistry, VOI. 87, NO. is,
Unimolecular Decompositions of SF6-
09
08
10
II I n t e r n a l E n e r g y , eV
12
1983 3477
13
14
Figure 5. Calculated breakdown curves for the reactant, normal products, and metastable products of reactions 1 and 2; fractional abundances are plotted as a function of Internal energy: model B and EA(SF,) = 0.8 eV.
Eo= 1.23 e V Model B
0.5 0.8
0.9
1.0
1.1
1.2
1.3
1.4
E (eV) Flgure 4. Autodetachment and dissoclatlon rate coefficlents ( k , and k,, respectively) of SF,- as a furction of intemal energy E, of the anion, according to model 6, for an assumed electron affinity EA(SF6) = 0.8
eV. 2. We have calculated the rate coefficient for reaction 1 using models A and B and various threshold energies Eo (Le., various values of the electron affinity, EA(SF6)). At each Eo,klwas calculatedat threshold (E+ = 0) and at 0.43 eV above threshold, E+ = E - E o = 0.43 eV. The results are shown in Figure 3. Model A, which is due to Heneghan and Benson, is clearly inadequate for the whole range of plausible electron affinity value^^-^ of SF6, because it predicts no observable metastable ion for reaction 2. Model B is also inadequate for EA(SF6) = 0.54 eV, the value used by Drzaic and Brauman in their calculations,' since it predicts kl(E+=0.43 eV) = 1.04 X lo' s-l and a fractional abundance of 9.3 X 10-lo following t = 2 X lo4 s. However, model B gives for EA(SF6) = 1.0 f 0.2 eV, which is the electron affinity of SF6within the error limits given by Streit,2 kl(E+=0.43 eV) = (1.46;;,i4) X los. If EA(SF6) = 1.2 eV (and the threshold energy is Eo = 1.2 eV for reaction l),then the fractional abundance of parent ions left to dissociate in the field free region is 0.94, while for Eo = 0.8 eV it is 0.204 and at any rate an observable metastable ion is expected for reaction 2. The analysis carried out here (Figure 3) is reminiscent of the sensitivity analysis carried out by Rosenstock and c ~ - w o r k e r sfor ~ ~positive * ~ ~ ions where neither Eo nor ASt are known and a unique pair is obtained from the experimental data. There are two additional problems in the case of SF6-: (a) The vibrational frequencies of the reactant SF, are not known and two quite different seta have been employed previ~usly'.~ and in models A and B. In the case of positive ion dissociations, ASt was varied by varying the vibrational frequencies of the activated comp l e ~ On . ~the~ other ~ ~ hand, both models A and B assume very similar activated complex frequencies (essentially
c
u
LL
1.20
1.25
1.30
E (ev) Flgure 6. Recalculated breakdown curves. The curves of Figure 5 were renormallzed to Include the ionic products only. Fractional abundances are plotted as a function of internal energy E. The area beneath the metastable curve (shaded) is indicated for EA(SF ) = 0.8 eV. The experimental area found was (3.1 f 1.0) X 10-!fr eV.
those of neutral SF6minus one stretch). (b) k(Et=O) and k(E+=0.43eV) me not known uniquely, only a range of SF, ion lifetimes is known. Represented in Figure 4 are the calculated rate-energy dependences for reactions 1 and 2 according to model B, for EA(SF6)= 0.8 eV. The calculated range of autodetachment lifetimes is from -1 ps to -2 ms, i.e., varies over three orders of magnitude in agreement with experimental observation^.^"^^*^ For EA(SF6)= 1.2 eV, model B gives a range of lifetimes from 31 ps to 30 ms. Unimolecular Dissociation. Breakdown curves for parent, normal fragment, and metastable ions of reaction 2 have been previously determined by ~ 9 . ~These 9 ~ give the fractional abundance of the ions as a function of electron energy. The area below the metastable breakdown curve was found to be 3.1 X in units of fr.eV (where fr = fractional abundance). It has been previously attempted5 to reproduce this area by model calculations which did not take autodetachment into account. Figure 5 presents calculated breakdown curves for EA(SF6) = 0.8 eV. In these calculations, the unobserved SF6 product of reaction 1 has been hcluded-SF, formed in the ion source and in the field free region (SF6 and SF6 (m*),respectively). The rate energy dependence of Figure 4 was employed to construct Figure 5. It is clear that with this model most of the reaction of SF6- in the field free region is due to autodetachment. The curves for SF,-, SF5-, and the metastable of reaction 2 were renormalized for com-
3470
Lifshitz
The Journal of Physical Chemistry, Vol. 87, No. 18, 1983
parison with experiment and are shown in Figure 6; the fr eV for EA(SF6) = 0.8 eV. metastable area is 5 X The calculated areas, for EA(SF6) = 1.0 eV and EA(SF6) fr eV, refr eV and 1.9 X = 0.7 eV, are 2.6 X spectively. If one assumes that the experimental and fr eV, the calculated areas are correct to within f l X calculated value for EA = 0.8 eV is seen to be in good agreement with experiment. Model B, with an electron affinity EA = 0.8 eV, is seen to agree with the experimental data. It is not a unique solution, however. If the reactant ion configuration is changed, so that A S for reaction 1is -17 eu instead of -14 eu, agreement with ion lifetimes and with the metastable ion intensity is obtained for EA = 0.6 eV. Conversely, if the configuration of the reactant ion is made less loose (by taking three 200-cm-l frequencies instead of 100-cm-' ones) so that ASt for reaction 1 is -10 eu, agreement with ion lifetimes and with the metastable ion intensity is obtained for EA = 1.0 eV. Unimolecular metastable ion dissociations have been previously reported."s In work with quadrupole mass analyzers the observation of m* at nonintegral masses is impossible. However, two peaks were obtained in the SF, signal as a function of electron energy.28s29 The narrow peak at near zero energy was ascribed to metastable SF6ions having lifetimes in the microsecond range2s and showing a strong temperature d e p e n d e n ~ e while , ~ ~ the intensity of the broad peak at -0.38-0.5 eV was almost temperature independent. The occurrence of the highenergy peak has prompted several authors to suggest the existence of an excited electronic state (or states) Even without below the SFf + F dissociation limit.2~4~B~29 invoking such a state, a range of ion lifetimes is predicted for reaction 2 (Figure 4) and the rate coefficient for reaction 2 should depend on the observation time just as for reaction 1. In flowing afterglow experiments: in the pressure range of 0.1-1.5 torr, only very fast dissociations with 7 I3 X s can take place between successive collisions. These do not contradict our observation, under very low pressure conditions of
