On the Competition Between Electron Autodetachment and Dissociation of Molecular Anions

We treat the competition between autodetachment of electrons and unimolecular dissociation of excited molecular anions as a rigid-/loose-activated complex multichannel reaction system. To start, the temperature and pressure dependences under thermal excitation conditions are represented in terms of falloff curves of separated single-channel processes within the framework of unimolecular reaction kinetics. Channel couplings, caused by collisional energy transfer and “rotational channel switching” due to angular momentum effects, are introduced afterward. The importance of angular momentum considerations is stressed in addition to the usual energy treatment. Non-thermal excitation conditions, such as typical for chemical activation and complex-forming bimolecular reactions, are considered as well. The dynamics of excited SF6− anions serves as the principal example. Other anions such as CF3− and POCl3− are also discussed.


Introduction
V ibrationally excited molecular anions may undergo a variety of processes such as dissociation to anionic and neutral fragments, autodetachment of electrons, radiative stabilization, and collisional deactivation (or activation). The competition between these channels is governed by the energy E and the rotational state of the anion (the latter symbolically characterized by an angular momentum quantum number J). While the influence of the energy is always taken into account, angular momentum effects are often neglected. As the overall reaction represents a multichannel system, channel coupling effects also have to be accounted for. The present article intends to illustrate the competition between the various channels using thermally excited SF 6 − anions as the main example. Other anions are considered as well. Finally, non-thermal excitation conditions are discussed with respect to angular momentum effects.
At sufficiently high energies, vibrationally excited anions At even higher energies, the additional dissociation may be included. Reaction (1) corresponds to a simple bond fission with a loose activated complex (AC) which is located at the centrifugal maximum of an ion-induced dipole potential (plus some valence contributions, see, e.g., [1,2]). In contrast to Reaction (1), Reaction (2) effectively involves a rigid AC, located at the crossing of the SF 5 − -F and SF 5 -F potential curves [3][4][5][6]. Figure 1 illustrates this crossing for the non-rotating and rotating SF 6 − /SF 6 system in comparison to the potential of the dissociating anion SF 6 − . The crossing in the SF 6 − -system probably involves a small energy barrier, but even without that barrier, the crossing occurs at a more compact nuclear configuration of SF 6 − than that relevant for Reaction (1). Considering the nuclear motion only, the system then is of rigid-AC/loose-AC character (one has to note, however, that nuclear and electronic motions in this description are separated which is an essential element of the Bkinetic modeling approach^as justified later on).
One of the consequences of the rigid-AC/loose-AC character is markedly different J dependences of the channel threshold energies E 0,i (the subscript i = 1 corresponds to the dissociation channel (1) while i = 2 corresponds to the detachment channel (2)). This may even lead to Brotational channel switching^ [8,9] of channels (1) and (2). While E 0,1 (J = 0) is larger than E 0,2 (J = 0), at some value of J (denoted by J sw ), the ordering of the E 0,i may change from E 0,1 (J) > E 0,2 (J) for J < J sw to E 0,1 (J) < E 0,2 (J) for J > J sw . As this is also of relevance for non-thermal conditions, this effect will be further explored below.
The branching fraction of the reaction may be derived from a master equation simulation of the multilevel system symbolized by Reactions (1) − ]). First, these falloff curves may be calculated for Bseparated channels^(e.g., with the channels (1), (4), and (5) for k dis and with the channels (2), (4), and (5) for k det ). Afterward, proper modeling requires channel coupling effects to be taken into account [10]. It is emphasized that the SF 6 − system is not unique in this regard; other anion fragmentation processes will behave in an analogous way.
Falloff Curves for Separated Electron Detachment and Dissociation Processes of SF 6 − Falloff curves for non-dissociative electron attachment to SF 6 (in the presence and absence of radiative stabilization (3)) have been elaborated within the Bkinetic modeling approach^of [11]. The rate coefficients k at were determined for equal electron and bath gas temperatures T between 200 and 1400 K and for bath gas concentration [N 2 ] between 10 10 and 10 20 cm −3 . Like other falloff curves, these can be represented in the form [12] with rate coefficients k, limiting high-pressure rate coefficients k ∞ , limiting low-pressure rate coefficients k 0 (being proportional to [N 2 ] and of the same dimension as k ∞ ), x = k 0/ k ∞ , and Bbroadening factors^F(x) approximated by where F cent = F(x = 1) and N = 0.75- 1.27 log F cent (where log = 10 log). Taking advantage of the modeling of k at,0 , k at,∞ , and F at,cent for electron attachment of [11] and inserting these values for k 0 , k ∞ , and F cent into Eq. (8), k at is obtained. It then can be converted into thermal rate coefficients for detachment k det , employing the corresponding equilibrium constant The following parameters were calculated for the falloff curves of k at (without radiative stabilization (3)): k at,0 ≈ [N 2 ] 2.5 × 10 −18 exp(− T/80 K) [1 + 3.5 × 10 −22 (T/K) 7 ] cm 6 s −1 , k at,∞ ≈ 2.2 × 10 −7 (T/500 K) -0.35 cm 3 s −1 , and F at,cent ≈ exp(− T/520 K) [11,13].
Since the publication of [11,13], the electron affinity EA of SF 6 has been disputed [4,7,[14][15][16][17]. As K det and k det both include a factor exp(− EA/k B T), the value of EA is of primary importance for these two quantities. In addition to EA, also the vibrational partition function Q vib (SF 6 − ) had to be modified [7], because marked anharmonicities of the vibrations of SF 6 − were discovered in [4]. These refinements influence not only K det , k det , and k at but also the falloff curves for dissociating SF 6 − . This is illustrated in the following. Falloff curves for k dis , i.e., for the dissociation of SF 6 − to SF 5 − + F, are also represented in the form of Eq. (8). In this case, it appears appropriate to start with the limiting highpressure rate coefficients k rec,∞ ≈ 2.15 × 10 −10 cm 3 s −1 for combination of an ion with a neutral species in a charge-induced dipole potential (see [13]; k rec,∞ here is assumed to be independent of the temperature). With the corresponding equilibrium constant, this leads to k dis,∞ . On the other hand, the limiting low-pressure rate coefficient k dis,0 can directly be calculated from the unimolecular rate theory as elaborated in [12]. Analogous to K det and k det , both K dis and k dis include a factor exp[−EA/k B T].
In addition, however, they include the factor exp[−ΔE 0 /k B T] where ΔE 0 corresponds to the energy difference between SF 6 + e − and SF 5 − + F at 0 K (being 0.41 eV [7]). Furthermore, K dis and k dis include the strongly anharmonic vibrational partition function Q vib (SF 6 − ). Analogous to the dispute about the EA of SF 6 , the energy difference ΔE 0 has multiple values in the literature (see, e.g., [3,7,13,14,[18][19][20][21][22][23]). (The dissociation channel (6) of SF 6 − *requires higher energies than SF 5 − formation [22] and, therefore, is not further considered here.) In view of the difficulties with EA, ΔE 0 , and Q vib (SF 6 − ), it appears important to analyze to what extent the modeled rate constants become independent of these difficulties, because some of the uncertainties compensate each other.
The largest uncertainties encountered in the modeling of k dis,0 can be estimated within the formulation of the unimolecular rate theory described in [12]. k dis,0 contains a factor ρ vib,h (EA + ΔE 0 ) F anh /Q vib for SF 6 − , where ρ vib,h (EA + ΔE 0 ) denotes the harmonic vibrational density of states and F anh is an anharmonicity factor. The anharmonicity contributions in Q vib and the factor F anh in part compensate each other. However, the anharmonicity in Q vib has been essential in the third-law evaluation by [7] of the experimental ratio k det /k at = K det , leading to the electron affinity EA = 1.03(± 0.05) eV. It should be mentioned that this value was supported by the most detailed quantum chemical calculations of [15]. In the modeling of k dis,0 , besides EA + ΔE 0 and the ratio ρ vib,h (EA + ΔE 0 ) F anh /Q vib , the average energy <ΔE coll > transferred per collision between SF 6 − * and M remains an uncertain parameter. Keeping in mind these uncertainties and leaving a fine-tuning of k dis,0 to the comparison with the experiments, we model k dis,0 with the harmonic frequencies of SF 6 − from [24] (such as given in [13]), EA = 1.03 eV from [7], a total collisional energy transfer frequency approximated by the Langevin collision frequency Z = 6.37 × 10 −10 cm 3 s −1 (for collisions between SF 6 −* and N 2 [14]) and <ΔE coll >/hc ≈ −200 cm −1 [25,26]. This leads to While k dis,0 (T) relies on modeling, k det,0 directly follows from the experimental k at,0 [7] and the revised K det from [7], one obtains Around 650 K, where measurements of the branching fraction R(SF 5 − ) are available [13,14,27,28], obviously k det,0 is much larger than k dis,0 , i.e., k det,0 > k dis,0 . This is in contrast to k dis,∞ and k det,∞ where the former is given by while the latter amounts to such that k dis,∞ > k det,∞ . The comparison of the pre-exponential factors of Eqs. (14) and (15) classifies detachment as an effectively rigid-AC process and supports the view of the Bkinetic modeling approach^given in the BIntroduction.^On the other hand, dissociation is clearly a loose-AC bond fission reaction. The observation of k dis,0 < k det,0 and k dis,∞ > k det,∞ (near 650 K) indicates that there must be a crossing of the two falloff curves at some [N 2 ] (denoted by [N 2 ] x or by the corresponding bath gas pressure p x ). In order to locate p x , we also need F cent which, for simplicity, we use in the form F dis,cent ≈ F at,cent as calculated in [11]. Figure 2 illustrates pairs of falloff curves for 600, 650, and 700 K. The curves cross near [N 2 ] x ≈ 1.5 × 10 15 cm −3 (corresponding to p x ≈ 0.1 Torr). At this pressure, dissociation is close to its low-pressure limit while detachment is closer to its high-pressure limit. Figure 3 shows the corresponding branching fraction R(SF 5 − ) for T = 650 K, being constructed with R(SF 5 − ) = k dis /(k dis + k det ) from Figure 2 (it should be mentioned that Figure 3 is consistent with Figures 8 and 9 of [14]). As the exponential factor exp[− ΔE 0 /k B T] dominates R(SF 5 − ), while other not so well-known contributions have only weaker temperature dependences, the evaluation of the temperature dependence of R(SF 5 − ) provides safe access to ΔE 0 . This formed the basis for the fit of ΔE 0 ≈ 0.41 eV in [7,29]. However, channel coupling effects were neglected so far. Therefore, one has to make sure that rotational channel switching and the related multichannel coupling effects do not matter too much. In the following section, we explore to what extent the rigid-AC/loose-AC multichannel character of the system requires multichannel coupling corrections.

−
The foregoing section provided falloff curves for separated electron detachment and dissociation of thermally excited SF 6 − . It illustrated that electron detachment in the language of Bkinetic modeling^effectively proceeds as a rigid-AC process whereas dissociation is a loose-AC process. In this situation, rotational channel switching, such as described in the BIntroduction,^modifies the branching fractions which-so far-were calculated assuming separated, single-channel, falloff curves.
The rigid AC of the electron detachment process is located at the nuclear configuration where the potential curves of SF 5 -F and (SF 5 -F) − cross (see Figure 1). This crossing happens at an S-F distance r x ≈ 1.58 Å which corresponds to a structure with an effective rotational constant B e (r e /r x ) 2 ≈ B e (B e is the rotational constant, being 0.0907 cm −1 for SF 6 and 0.0750 cm −1 for SF 6 − , while r e ≈ 1.56 Å for SF 6 and 1.76 Å for SF 6 − ). The threshold energy E det,0 (J) for rotating SF 6 − then roughly increases as (a barrier of about 5.2 meV in [5] was fitted with the help of the low-temperature experiments of [6]; however, this value is only of little relevance for the estimate of J sw ). The threshold energies E 0,dis (J) correspond to the centrifugal barriers in the (SF 5 − -F) potential and can be estimated for an ion-induced dipole potential as shown in [1]. As the second term of Eq. (17) and the extra energy due to the centrifugal maxima in the dissociation process in excess of the energy EA + ΔE 0 are both small compared to ΔE 0 , they are neglected here. The switching value J sw then follows from the relationship With ΔE 0 ≈ 0.41 eV, this leads to For J > J sw , E 0,det (J) becomes larger than E 0,dis (J), i.e., rotational channel switching occurs and rotationally hot SF 6 − has a smaller threshold energy for dissociation than for electron detachment.
Rotational channel switching is the dominant cause for channel coupling in rigid-AC/loose-AC, two-channel, reaction systems [10]. Branching fractions R 1 for the energetically less favorable channel (at J = 0; R 1 corresponds to the energetically less favorable channel) are defined by R 1 = k 1 /(k 1 + k 2 ). At a given temperature, R 1 varies with the bath gas concentration [M]. It increases from a limiting low-pressure value of R 1,0 to a limiting high-pressure value of R 1,∞ . This increase can be represented in approximate form by  Figure 3) while channel coupling effects remain negligible. The results of the previous section (as illustrated by Figure 3), therefore, were not Bcontaminated^by rotational channel switching and channel coupling effects.

Non-thermal Activation Conditions
It has to be emphasized that the described analysis of channel coupling effects in terms of Eq. (20) applies to thermal energy and angular momentum distributions only. In many experiments, however, the anions are produced with non-thermal distributions. For example, dissociative electron attachment (DEA) experiments start with non-thermal distributions of the states of the anions. These relax toward thermal distributions only in the presence of collisions. DEA then behaves as a Bchemical activation system.^The corresponding relaxation of the branching fractions R(SF 5 − ) toward their equilibrium values has been followed experimentally in [14]. For the time during the relaxation, master equation simulations have to describe the competition between the reaction steps (1)-(3) and the collision processes (4) and (5). The yields of the corresponding chemical or photochemical activation systems as a function of the primary excitation energy and the bath gas pressure have been modeled in [27]. The results can directly be applied to DEA. Meanwhile, the uncertainty in the value of <ΔE coll > for collisional energy transfer and, in particular, of the change of the angular momentum distribution during the collisional relaxation limits the accuracy of the simulation. Further work is required to analyze the consequences of rotational channel switching under non-thermal activation conditions which are certainly different from those of the thermal excitation analyzed here. Finally, the analogy of the chemical activation situation to the pressure and temperature dependence of complex-forming bimolecular reactions should be stressed, such that the approximate expressions for yields from the corresponding treatment may become helpful [28].
Apart from rotational channel switching in rigid-AC/loose-AC multichannel systems, also Bvibrational channel switching,^particularly under non-thermal excitation conditions, is of importance [9]. The specific rate constants k dis (E,J) for fixed J at some energy E sw then cross the corresponding k det (E,J). This was illustrated, e.g., for DEA of SF 6 − at J = 0 in Figure 5 of [13]. Under thermal excitation conditions, this effect is responsible for the markedly different preexponential factors of k dis,∞ (T) and k det,∞ (T) in Eqs. (14) and (15). Under non-thermal excitation conditions and in the absence of collisions, the differences of the k(E,J) will cause quite different time dependences of the decaying anions. Energy and angular momentum as well as channel switching effects then will all have to be taken into account. Oversimplification of the multichannel character of the process and its energy and angular momentum dependence may have been the reason for different interpretations of experiments (possibly also for the different values derived for EA of SF 6 in [4,7,[14][15][16][17]).

Systems with Loose-AC/Rigid-AC and Rigid-AC/Rigid-AC Channels
Analogous to the SF 6 − example, one should inspect rotational channel switching effects in other DEA systems. First, we consider the CF 3 − example where compete. With an electron affinity of EA = 1.82 (± 0.05) eV for CF 3 [30] and an energy difference ΔE 0 = 0.22 (± 0.02) eV [31], this system according to Eq. (18) has a smaller J sw than SF 6 − . The crossing between the (CF 2 -F) and (CF 2 -F) − potential curves here takes place at r x ≈ r e [32], such that J sw ≈ 70 (with B e ≈ 0.360 cm 1 ). This confirms again a loose-AC/rigid-AC character of the system. Experimental studies of the DEA to CF 3 [32,33] so far have only been concerned with the chemical activation regime of the process, and rotational channel switching effects were not yet considered. If the process would have been followed over the relaxation period from chemical activation to thermal distributions, the branching fraction would have been characterized by Eq. (20) with R 1,0 ≈ exp(− 2570 K/T). Obviously, this would have been relevant for temperatures which were beyond those considered so far. However, as emphasized above, channel switching effects are important as well during the relaxation stage typically achieved in DEA experiments.
Multichannel coupling effects caused by rotational channel switching are ubiquitous, e.g., in DEA to other fluorocarbon radicals [34], in DEA to CF 3 Br [33], or in DEA to POCl 3 [35][36][37]. The latter system could be affected by rotational channel switching in particular, as small values of ΔE 0 are observed (ΔE 0 ≈ 0 for the production of POCl 2 − + Cl and ΔE 0 = 0.11 eV for the production of POCl 2 + Cl − ). The preliminary modeling with a chemical activation scheme here was successful under the assumption of a loose AC for the POCl 2 + Cl − channel while a more rigid AC was found for the POCl 2 − + Cl channel. The presence of several competing channels with different individual J sw further complicates the analysis. In this case, branching fractions under thermal and non-thermal conditions may take advantage of the multichannel codes elaborated in [10].
One observation from the analysis of the experiments on the POCl 3 system in [37] deserves further attention. Assuming a loose-AC character for all dissociation channels, Brigidity factors^f rigid in that analysis were fitted. These factors account for an anisotropy of the potential beyond the isotropy of the dominant ion-induced dipole potential between the dissociation fragments. This fitting in [37] led to markedly smaller values of f rigid for the nearly thermoneutral POCl 2 − + Cl channel than for the endothermic POCl 2 + Cl − channel. This observation may suggest that the former channel involves some intermediate energy barrier. This might signal rigid-AC channel behavior of this dissociation channel. Multichannel coupling effects under thermal conditions for rigid-AC/rigid-AC then would be characterized by Eq. (20) with where γ denotes the average energy transferred per up collision (related to the total <ΔE coll > by <ΔE coll >/hc = γ − α where γ ≈ αk B T/(α + k B T; α and γ traditionally are given in cm −1 ) and α is the average energy transferred per down collision). In this case, instead of rotational channel switching, collisional processes would be responsible for multichannel coupling effects.

Conclusions
The present article characterizes the competition between electron autodetachment and fragmentation of vibrationally excited molecular anions in the language of chemical kinetics. The main conclusion consists in the statement that autodetachment of electrons effectively corresponds to a rigid-activated complex process, while fragmentations mostly have loose activated complexes (although sometimes the latter also may be governed by rigid-activated complexes). A rigid-AC/loose-AC character of the reaction gives rise to rotational channel switching where energetically less favorable reaction channels dominate over energetically more favorable channels when the ion rotates rapidly. In the presence of collisions, also multichannel coupling effects have to be taken into account. The branching fractions under thermal excitation conditions can be represented approximately by Eqs. (18), (20), and (21). The importance of energy and angular momentum effects under non-thermal, chemical-activation type, excitation conditions is stressed as well.