Octafluorooxalane, C4F8O, has recently attracted attention as a possible replacement of SF6 in high voltage insulation, and its reactivity with respect to free-electron attachment was investigated by mass spectrometry. The most intense signal peaks at 0.9 eV and corresponds to the parent anion, C4F8O; fragments stemming from complex breakup reactions are detected starting above ∼1.6 eV. Since parent anions in free-electron attachment are normally associated with threshold attachment or an embedding environment allowing excess energy deposition, this observation is highly unusual. Based on density functional calculations, it was nevertheless interpreted as attachment followed by intermolecular-vibrational-relaxation. Here, electron-attachment to octafluorooxalane is studied computationally. First, the electron affinity (EA) is characterized using density functionals and ab initio methods. Moreover, the negative vertical EA is estimated by extrapolating electron binding energies computed in the vicinity of C4F8O to the geometry of neutral octafluorooxalane. Then, alternative explanations for the 0.9 eV peak are considered. Specifically, a ring-opening reaction that yields a distonic isomer of C4F8O is identified. Our analysis reveals that the chain isomer possesses many conformers, all of which are considerably more stable than the ring isomer, and that the time scale for the unimolecular ring opening reaction is significantly faster than 1 μs. Thus, at the experimental energy, the ring isomer of C4F8O is predicted to convert practically completely into the chain isomer, and we argue that the long lifetime and the peak position are effectively determined by the properties of the ring-opening transition state.

Recently, the formation of the long-lived transient anion C4F8O as well as dissociative attachment products following free-electron capture by C4F8O, octafluorotetrahydrofurane, or octafluorooxolane (OFO) was observed using single electron attachment as well as electron swarm techniques1,2 (see Fig. 1 for the structural formula of OFO). In the single electron experiments, anion yields were measured in the dependence of the incident electron energies using mass spectrometry implying anion lifetimes in excess of 10−5 s.1,2 Remarkably, the parent anion of OFO, C4F8O, represents the most intense anion signal whose maximum occurs at 0.9 eV and that shows a width of ∼0.6 eV. This behavior is highly unusual because parent anions are typically formed in one of two ways: either at threshold by intramolecular vibrational relaxation (IVR) of the excess energy—SF6 is a prototypical example—or, alternatively, at higher energies provided the initially formed short-lived anion is interacting with some type of environment, it can release its excess energy to, say, a cluster, a surface, a condensed phase, or even a collision (see Ref. 1 for exceptions). Neither applies to OFO: 0.9 eV is much higher than typical threshold peaks and the authors demonstrate that the experiment is performed under conditions producing isolated molecules.1,2

FIG. 1.

Structural formula of octafluorooxolane including the carbon numbering scheme.

FIG. 1.

Structural formula of octafluorooxolane including the carbon numbering scheme.

Close modal

To explain the extraordinary above-threshold observation of a parent anion, the authors of Ref. 1 then perform a limited density functional study of the neutral OFO [Becke exchange and Lee-Yang-Parr correlation (B3LYP)3 with the 6-31+G(2df) basis set4]. Neutral OFO and C4F8O are found to differ essentially by a single C–F bond, which is considerably elongated in the anion. Comparing the energies at these two geometries, the anion is found to be more stable than neutral OFO by about 0.4 eV (0.5 eV if harmonic zero-point corrections were taken into account). Moreover, the authors compute adiabatic potential energy curves in the stretched bond, and the substantial bond length difference together with the high electron affinity (EA) indeed suggests that electron reejection is only possible in a small region in nuclear coordinate space close to the geometry of the neutral (see Fig. 4 in Ref. 1). Thus, the long lifetime of C4F8O is explained in terms of the standard attachment-followed-by-IVR mechanism.1 

Yet, while the computations presented in Ref. 1 may explain the long lifetime of a C4F8O anion formed above threshold, they cannot explain the position of the 0.9 eV peak. There is, of course, no doubt that the long-lived anion is formed at 0.9 eV; however, resonances of saturated fluorocarbon molecules lie at considerably higher energies, for example, the lowest resonance of C2F6 occurs at 5 eV,5 and while one may expect OFO to have resonances at energies lower than 5 eV, a resonance position as low as 0.9 eV seems unrealistic.

Here we computationally explore electron attachment to OFO including possible reactions induced by the attached electron. First, the existing computational findings are compared with electron affinities obtained using other density functionals and other basis sets as well as ab initio methods. Moreover, we estimate the vertical EA (VEA) using an extrapolation along a linear transit coordinate between the neutral and the anion minimal energy structures. In view of our findings, we then investigate electron-initiated reactions to explain the experimental observations. Implications of our results regarding the lifetime of C4F8O and regarding the use of C4F8O as a replacement for SF6 in high-voltage insulation6 are discussed.

Four density functionals as well as three different ab initio methods were used. The primary density functional method employed for most geometry optimizations and frequency calculations is Head-Gordan’s range-separated hybrid (ωB97X);7 however, for comparison, we also performed calculations with the three-parameter hybrid of Becke exchange and Lee-Yang-Parr correlation (B3LYP),3 the one-parameter hybrid of the Perdew-Burke-Ernzerhof functional (PBE0),8 and Truhlar’s 2006 hydbrid functional (M06-2X).9 For all density functional calculations, Dunning’s triple-ζ basis set was augmented with a minimal set of diffuse functions (may-cc-pVTZ)10,11 since density functional calculations as such and specifically for anions are less sensitive to high angular momentum diffuse functions than ab initio methods,11,12 and our test calculations show that the effects of a full augmentation on electron affinities for the present system are indeed small (differences of less than 15 meV). Geometry optimization was also performed with orbital-optimized Møller-Plesset perturbation theory (OO-MP2) which is, in particular, for radicals an improvement over straightforward MP2 and reduces spin-contamination substantially (see Ref. 13 and the references therein). Single-point energies were evaluated using the domain-based local pair natural orbital coupled-cluster with single, double, and non-iterative triple [L-CCSD(T)] substitutions method,14,15 and vertical electron binding energies (VEBEs) of the neutral were computed using the back-transformed domain-based local pair natural orbital equation-of-motion coupled-cluster with the single and double (L-EA-EOM-CCSD) substitution method.16 The L-CCSD(T) computations for the C4F8O anion are based on unrestricted Hartree-Fock wavefunctions, but even at the transition state investigated (see below), spin-contamination is very mild (ŝ2< 0.78), and the T1 diagnostic remains below 0.015 at all geometries. All ab initio calculations were performed using the fully augmented triple-ζ basis set (aug-cc-pVTZ), and in the L-CCSD(T) and L-EA-EOM-CCSD calculations, the 1s electrons were frozen in their core orbitals. The Orca package17 was used for all calculations.

Most L-CDSD(T) single-points were evaluated at OO-MP2 optimized structures; however, several calculations were also performed at density functional optimized structures. The influence of the particular geometry used was found to be mostly minor, for instance, electron affinities differed by less than 15 meV. The only exception is M06-2X structures because for OFO and its anions, the M06-2X functional tends to predict somewhat shorter bond lengths than either of the other functionals or OO-MP2. If we evaluate the quality of a geometry by its single-point L-CCSD(T) energy in the sense that L-CCSD(T) is presumably our most reliable method and that a lower L-CCSD(T) single-point energy indicates that the given structure is closer to the L-CCSD(T) minimum, we are led to the conclusion that ωB97X, PBE0, and OO-MP2 geometries have practically the same quality (energy differences of a few meV), while the corresponding M06-2X structures are less satisfactory (200 meV higher in energy).

Molecular EAs are defined as the energy difference of the neutral (N electrons) at the geometry of the neutral and the anion ((N + 1) electrons) at the geometry of the anion, EA = EN(neutral) − EN+1(anion); that is, a positive EA indicates that the anion is more stable than the neutral. Three comments on this general definition are in order. First, when computing EAs, zero-point corrections may or may not be included. We will always explicitly state whether an EA value has been corrected. Second, note that the general definition refers to the global minimum of the anion. While this definition is useful for small molecules, it becomes increasingly impractical for larger systems with many isomers. The global minimum may simply be unknown or inaccessible under practical conditions. Thus, we use a more specific definition of EA that implies the minimal energy structure of the anion reached by a local optimization started from the geometry of the neutral. In other words, our EA definition takes only electron attachment and relaxation of the molecular framework into account. Last, while the definition can be directly used to compute EAs for all density functional methods, OO-MP2 and L-CCSD(T), L-EA-EOM-CCSD yields only VEBEs and the EA must be computed from the VEBE at the anion geometry and the distortion energy of the neutral from its equilibrium to the anion geometry: EA = (EN(anion) − EN(neutral)) − VEBE(anion), where positive VEBEs indicate the vertically bound anions. In order to minimize the error in the L-EA-EOM-CCSD EA, the best distortion energy available should be used, and here it is computed employing L-CCSD(T) energies.

As a starting point, we reinvestigated the minimal energy structures of OFO and its anion using various density functionals as well as two ab initio methods. All methods agree with the principal findings in Ref. 1. Neutral OCO displays a puckered ring structure with C2 symmetry, and all its C–F bond lengths fall into a narrow range between 1.33 and 1.34 Å. The only exception is bond lengths predicted by the M06-2X functional which tend to be somewhat shorter (0.02 Å). The C4F8O minimal energy structure most directly related to OFO is also a ring structure, and the two rings align well with each other with the exception of one of the two C(2)–F bonds, which shows a considerably increased bond length in the anion (see Fig. 1 for the carbon numbering scheme). We compute the EA of OFO as the energy difference between these two structures (see Sec. II).

Both essential properties, the EA of OFO and the length of its long C–F bond, have been computed with different methods, and the results are collected in Table I. Regarding the C–F bond length, an astonishingly large scatter without apparent trends is observed: Values range from 1.86 Å for M06-2X to 1.98 Å for B3LYP (Table I). This is not totally unexpected: since the bond in question is a weak three-electron bond, the stretching frequency associated with it (282 cm−1 with the ωB97X functional) is less than half of the next higher stretching frequency in the anion, and therefore, similar to Ref. 1, we predict a very shallow energy minimum with respect to this particular bond length.

TABLE I.

Method comparison focusing on the two key properties of OFO and its cyclic anion: the EA and the bond length of the long C–F bond of C4F8O. The L-EA-EOM-CCSD and L-CCSD(T) EA values were computed using OO-MP2 geometries. Zero-point corrections have not been included.

EA (meV)R(C–F) (Å)
B3LYP 343 1.98 
PBE0 66 1.93 
M06-2X −8 1.86 
ωB97X 88 1.97 
OO-MP2 −8 1.88 
L-EA-EOM-CCSD −126 … 
L-CCSD(T) −194 … 
EA (meV)R(C–F) (Å)
B3LYP 343 1.98 
PBE0 66 1.93 
M06-2X −8 1.86 
ωB97X 88 1.97 
OO-MP2 −8 1.88 
L-EA-EOM-CCSD −126 … 
L-CCSD(T) −194 … 

In contrast to the long C–F bond length, the EA of OFO varies more systematically (Table I). With roughly 350 meV, B3LYP predicts by far the strongest binding. All other density functional methods and OO-MP2 predict the neutral and the anion to be essentially isoenergetic: EAs range from about −10 meV for M06-2X and OO-MP2 to about 90 meV for ωB97X. [Negative EAs imply that the anion lies energetically above the neutral; however, the anion is still vertically stable; that is, it processes a large positive VEBE.] Including higher-order correlation effects tips the scales even more in the direction of the neutral: L-EA-EOM-CCSD predicts an EA of −126 meV and our presumably most reliable result for the EA obtained with L-CCSD(T) is −194 meV. Yet, higher-order correlation effects are known to converge slowly with respect to complete basis set extrapolation, and basis sets larger than aug-cc-PVTZ may be expected to yield somewhat less negative EAs. In any event, B3LYP seems to be a particularly unsatisfactory choice for computing EAs and VEBEs of OFO, and regardless of convergence issues, the computed EA is sensitive to higher-order electron correlation effects.

As a second key property beyond the EA, we have estimated the VEA, that is, the energy of the anion formed by electron attachment at the structure of the neutral. Neutral OFO is expected to form a short-lived resonance state, or temporary anion, with a negative VEA because it lacks substructures with high local electron affinity such as nitro groups or quinones. Moreover, OFO lacks a π system as well as third row atoms with potentially low-lying σ* orbitals, and thus, the lowest resonance can only be a fairly high lying σ* state (the lowest resonance of C2F6 occurs at 5 eV5), which can be expected to show a short lifetime or large width. Unfortunately, the characterization of short-lived σ* resonances still represents a considerable challenge, in particular, if wavefunctions including higher-order electron-correlation effects are needed. Here, we only estimate the negative VEA using the so-called R-extrapolation method.18 In the R-extrapolation method, positive VEBE values computed in a region of nuclear coordinate space where the anion is vertically stable are extrapolated into a domain where the anion is a resonance. This method should not be confused with other extrapolation methods that employ artificial potentials to obtain positive VEBEs, but do not change the geometrical structure.18–20 A coordinate suitable for the present purpose is the linear transit coordinate, s, which is 0 at the geometry of the neutral and 1 at the geometry of the anion and interpolates linearly between these two structures. This coordinate is unbiased regarding either potential energy surface; it is proportional to the C–F bond length extension, and since the neutral and the anion structure align well with each other apart from the C(2)–F bond being stretched, s should provide a reasonable path from the neutral to the anion structure. The results from the R-extrapolation method are shown in Fig. 2. Computing VEBEs with the ωB97X functional and, directly, with the L-EA-EOM-CCSD method for values of s between 0.6 and 1 and extrapolating these VEBEs to s = 0 yield a VEA of −2.75 eV for ωB97X and −2.84 eV for L-EA-EOM-CCSD. Thus, our results suggest a fairly low-lying σ* resonance.

FIG. 2.

R-extrapolation of positive VEBEs in the vicinity of the minimal energy structure of C4F8O along the linear transit coordinate s. The coordinate s is defined to be 0 at the geometry of the neutral and 1 at the geometry of the anion and interpolates linearly between these two structures. Note that a linear transit—by definition—cannot represent a minimal energy pathway on either surface. However, since the two ring structures align well except for one C–F bond, a linear transit is expected to be an excellent compromise. ωB97X structures were used, and the VEBE was computed with both the ωB97X functional and L-EA-EOM-CCSD.

FIG. 2.

R-extrapolation of positive VEBEs in the vicinity of the minimal energy structure of C4F8O along the linear transit coordinate s. The coordinate s is defined to be 0 at the geometry of the neutral and 1 at the geometry of the anion and interpolates linearly between these two structures. Note that a linear transit—by definition—cannot represent a minimal energy pathway on either surface. However, since the two ring structures align well except for one C–F bond, a linear transit is expected to be an excellent compromise. ωB97X structures were used, and the VEBE was computed with both the ωB97X functional and L-EA-EOM-CCSD.

Close modal

We are now in the position to take a fresh look at the long-lived C4F8O ion formed at an electron energy of about 0.9 eV. Electron capture followed by IVR might still explain the experimental observations,1 however, in a slightly different manner than suggested in Ref. 1: The peak maximum of 0.9 eV suggests initial capture in the low-energy wing of the undoubtedly broad σ* resonance. Anions captured at higher energies would show shorter lifetimes—either with respect to electron reejection or with respect to some dissociative channel, while anion formation at lower electron energies would become increasingly improbable due to the width of the σ* resonance. If this interpretation was correct, one might expect changes of the high-energy side of the peak if not the peak position itself in the variation-of-time-window experiments reported in Ref. 1. While these experiments were inconclusive as far as lifetime measurements are concerned, no changes of the peak positions and shapes were reported either, suggesting that either the change in experimental time window is too small to notice any differences or that the observed C4F8O species is not the valence anion of the ring.

Here, we consider two alternatives to an explanation involving straightforward storage of the excess energy in the vibrational degrees of freedom. First we investigated the existence of non-valence states of the OFO anion, which might have explained the long lifetime by non-diabatic trapping of the initially formed σ* resonance on an adiabatic surface slightly below the potential energy surface of the neutral. That is, whenever the valence anion would have approached the geometry of the neutral, its electronic state would have non-diabatically changed into a non-valence state, representing, in a sense, a reverse-doorway electron capture mechanism.21–23 Yet, despite its eight fluorine atoms, it turns out that OFO does not possess any non-valence bound anion states; apparently a higher polarizability associated with heavier halogens or a delocalized π system, or, alternatively, a higher dipole moment would be needed.

The second alternative investigated was a dissociative attachment-like process, in the sense that the excess electron would initiate dissociation of a bond, but not dissociation of the molecule. Clearly, only the bonds in the ring can be broken without dissociating C4F8O as such, and the products of these ring-opening attachment reactions will be distonic radical anions, that is, anions with a separate charge and radical site at either ends of their chain. Considering only distonic isomers, three different bonds can be broken since, say, opening the left or right C–O bond will yield the same radical anion even though the two bonds are not symmetry equivalent in the reactant (Fig. 3). Whereas the electron-induced bond-cleavage of the two C–C bonds (b) and (c) in Fig. 3 would require significantly more energy than 0.9 eV, the C–O bond (a) can—in principle—be broken because the reaction product is not only more stable than neutral OFO, but also significantly more stable than the neutral C4F8O ring.

FIG. 3.

Reaction energies for the electron-induced ring-openings: C4F8O + e → C4F8O (distonic chain isomer). Note that while this energy differs from the bond dissociation energy of the C4F8O ring isomer by the EA of OFO, it can be directly compared to the peak observed at 0.9 eV. The energies in the figure have been computed using the ωB97X functional and are reported in eV; the values in parentheses have been corrected for zero-point effects.

FIG. 3.

Reaction energies for the electron-induced ring-openings: C4F8O + e → C4F8O (distonic chain isomer). Note that while this energy differs from the bond dissociation energy of the C4F8O ring isomer by the EA of OFO, it can be directly compared to the peak observed at 0.9 eV. The energies in the figure have been computed using the ωB97X functional and are reported in eV; the values in parentheses have been corrected for zero-point effects.

Close modal

Of course, knowing that the OFO anion can in principle undergo ring-opening is insufficient. We need to know whether this process can be efficient at an energy of about 0.9 eV above neutral OFO; in other words, we need to know the energy of the transition state of the bond breaking reaction. This structure has been identified using three different density functionals, PBE0, M06-2X, and ωB97X. All are in qualitative agreement; however, while PBE0 and ωB97X agree very closely, M06-2X predicts not only somewhat shorter bond lengths but also a significantly lower activation energy. As one may expect, the two bonds most strongly involved in the reaction coordinate are the C–O bond, which is ruptured, and the C–F bond, which is initially very long, but shows a normal length in the distonic product. These bonds are shown in Fig. 4, and their values at the transition state are given in Table II. The transition state is still a well-defined five-membered ring; however, the C–O bond length has increased by roughly 0.4 Å while the long C–F bond of the C4F8O reactant has shortened by roughly 0.2 Å.

FIG. 4.

Transition state for the electron-induced ring-open reaction of the OFO anion. Two internal coordinates essentially define the reaction coordinate: the C–O bond to be broken (R1) and the long C–F bond of the C4F8O ring isomer (R2) shortening to a normal C–F distance. Values for R1 and R2 at the transition state are given in Table II.

FIG. 4.

Transition state for the electron-induced ring-open reaction of the OFO anion. Two internal coordinates essentially define the reaction coordinate: the C–O bond to be broken (R1) and the long C–F bond of the C4F8O ring isomer (R2) shortening to a normal C–F distance. Values for R1 and R2 at the transition state are given in Table II.

Close modal
TABLE II.

Activation energy, Ea, zero-point correction (ZPC) to Ea, and geometrical parameters R1 and R2 of the transition state for the electron-induced ring-open reaction of the OFO anion defined in Fig. 4. R1 and R2 represent the bond lengths most heavily involved in the ring-opening reaction coordinate, namely, the C–O bond to be ruptured and the long C–F bond of the C4F8O ring isomer (R2) shortening to a normal C–F distance. Most of the table contains results obtained using the specified density functionals, while the last row of the table contains activation energies derived from L-CCSD(T) calculations at the respective density functional geometries. All energies are given in eV, and all bond lengths are given in Å.

PBE0M06-2XωB97X
Ea 0.714 0.404 0.791 
ZPC −0.044 −0.079 −0.044 
Ea + ZPC 0.670 0.325 0.747 
R1 1.758 1.746 1.779 
R2 1.761 1.722 1.768 
 L-CCSD(T)// 
 PBE0 M06-2X ωB97X 
Ea 0.732 0.561 0.736 
PBE0M06-2XωB97X
Ea 0.714 0.404 0.791 
ZPC −0.044 −0.079 −0.044 
Ea + ZPC 0.670 0.325 0.747 
R1 1.758 1.746 1.779 
R2 1.761 1.722 1.768 
 L-CCSD(T)// 
 PBE0 M06-2X ωB97X 
Ea 0.732 0.561 0.736 

The activation energy for the ring-opening reaction of the C4F8O anion is roughly 0.7 eV: 0.73 eV at the L-CCSD(T) level using ωB97X or PBE0 geometries; 0.71 eV with PBE0; and 0.79 eV with ωB97X. Only the M06-2X Ea and the L-CCSD(T) Ea value obtained at the M06-2X geometry are somewhat lower (see Table II). Zero-point corrections to these values are small (40–80 meV) and—as one would expect—stabilizing with respect to the transition state in the sense of lowering the activation barrier. Thus, our best value for the activation energy is 0.73 eV = 70 kJ/mol = 17 kcal/mol, an activation energy associated with rapid reactions at room temperature in solution. Now, the experiment is probably better represented by microcanonical conditions, and the relevant question rather pertains to the available energy above the barrier, in particular, since tunneling corrections can be expected to be negligible because the reaction coordinate involves heavy fragments only. While this energy can be computed directly from the zero-point corrected energy difference between neutral OFO and the transition state for the electron-induced ring-opening reaction, the real process consists of electron trapping and bond-breaking steps, and it will turn out to be more instructive to split the energy into three contributions: the energy of the incoming electron, E, the electron affinity, EA, and the activation energy, Ea,

C4F8O+e(E)C4F8O(E+EA)[C4F8O](E+EAEa).

Considering initially E = 0, we can compute the barrier height, Eb = EaEA, for bond rupture as viewed from the vibrational ground state of neutral OFO. Using density functional structures, energies, and zero-point corrections, Eb is found to be about 0.2 eV lower than Ea. By contrast, if density functional structures and zero-point corrections are combined with L-CCSD(T) single-point energies, Eb and Ea are found to be essentially identical (differences of less than 20 meV). The different behavior at the density functional and L-CCSD(T) level is easily understood: Owing to the weaker bonds in the anion, zero-point corrections always stabilize both anion structures (ring and transition states) with respect to the neutral. Moreover, of the two anion structures, the transition state is somewhat more stabilized, again, due to its looser structure. Since uncorrected density functional EAs tend to be close to zero (at least for the functionals used here: Tables II and I), the difference of Ea and Eb is essentially a zero-point effect. By contrast, when using L-CCSD(T) energies, the stabilizing effect due to the zero-point correction is almost exactly canceled by the negative EA (Table I) so that Eb and Ea are close.

For an electron energy of E = 0.9 eV, the initially formed ring isomer of the C4F8O anion therefore lies at least 0.15 eV above the ring-opening transition state, and this energy is a conservative estimate since CCSD(T) electron affinities typically converge from above regarding basis set convergence and since anharmonic effects are expected to be stronger in the anionic transition state structure than in the neutral. Using Rice–Ramsperger–Kassel–Marcus (RRKM) theory24 to estimate the unimolecular rate of the ring-opening process, the conservative values for Ea and Eb yield at 0.9 eV a rate of k(E = 0.9 eV, Eb = 0.75 eV) = 3 × 106 s−1 or a half-life of 0.3 μs. This is very much a lower limit for the rate or an upper limit for the half-life. Just assuming that a complete basis set extrapolation will yield a lower EA by, say, 0.1 eV, yields a rate of k(E = 0.9 eV, Eb = 0.65 eV) = 3 × 108 s−1 and an associated half-life of 0.004 μs. Moreover, anharmonicities will also contribute to increasing k. Thus, we predict that at an electron energy of 0.9 eV, one of the C–O bonds of C4F8O can be broken to yield a distonic chain isomer of C4F8O and that the reaction will be fast on the mass spectrometric time scale.

The structural formula of the ring-opening product, i.e., the distonic C4F8O chain anion, is shown in Fig. 5. The three C–C bonds of this C4F8O isomer represent internal rotors, and the distonic anion will therefore have 27 conformers some of which will be related by symmetry. We studied only five of these conformers concentrating on the rotations with respect to the C(1)–C(2) bond and the central C(2)–C(3) bond (see Fig. 5 for carbon numbers). These conformers are found to vary slightly in energy, but most importantly, they are all more stable than the ring isomer of C4F8O by ∼0.4 to 0.6 eV regardless of the computational approach (Fig. 6). Specifically, the anti-anti conformer, that is, the conformer schematically shown in Fig. 5, is predicted to be least stable, while gauche-gauche conformers are predicted to be the most stable within the investigated group (Fig. 6). Be that as it may, the distonic anion, once formed, possesses enough internal energy to overcome internal barriers, and a rapid exchange of conformers is guaranteed. Owing to the three internal rotors and the different conformers showing different energies, it is quite challenging to predict a specific rate constant for the reverse reaction. However, since the distonic chain isomer will show a much larger density of states than the ring isomer and the activation energy for the reverse reaction will be considerably higher than Ea for the ring-opening reaction, we are confident to predict a rate dramatically smaller than k(E) for the reverse reaction. The distonic radical anion, once formed, should thus effectively be trapped by entropy.

FIG. 5.

Structural formula of the distonic chain isomer of C4F8O including the carbon numbering scheme.

FIG. 5.

Structural formula of the distonic chain isomer of C4F8O including the carbon numbering scheme.

Close modal
FIG. 6.

Overview of the energy changes associated with the electron-induced ring-opening reaction of OFO. From left to right, the different species are neutral OFO, the ring isomer of the anion, the transition state for opening of the ring, and five conformers of the distonic chain isomer of C4F8O [specifically anti-anti, anti-gauche, gauche-gauche, gauche-gauche’, and gauche-anti with respect to bonds C(1)–C(2) and C(2)–C(3)]. All energies are relative to neutral OFO so that the electron energy E can be directly read off the ordinate and so that all bars for the neutral are plotted on top of each other. For all anionic species, the L-CCSD(T) energy is always the highest, the ωB97X energy is always the lowest, and the OO-MP2 energy–if given–provides a middle ground.

FIG. 6.

Overview of the energy changes associated with the electron-induced ring-opening reaction of OFO. From left to right, the different species are neutral OFO, the ring isomer of the anion, the transition state for opening of the ring, and five conformers of the distonic chain isomer of C4F8O [specifically anti-anti, anti-gauche, gauche-gauche, gauche-gauche’, and gauche-anti with respect to bonds C(1)–C(2) and C(2)–C(3)]. All energies are relative to neutral OFO so that the electron energy E can be directly read off the ordinate and so that all bars for the neutral are plotted on top of each other. For all anionic species, the L-CCSD(T) energy is always the highest, the ωB97X energy is always the lowest, and the OO-MP2 energy–if given–provides a middle ground.

Close modal

Recently, electron capture by octafluorooxalane has been reported to produce the parent anion C4F8O as the product with highest intensity.1,2 The associated peak is located at 0.9 eV above threshold and possesses a width of about 0.6 eV (FWHM). As the authors of Refs. 1 and 2 point out, this observation is truly remarkable, as parent anion formation in free-electron attachment is normally limited to the threshold region.

Here electron capture by OFO has been studied theoretically. First, the EA of OFO was investigated using four different density functionals and three ab initio methods. It turned out that the B3LYP functional chosen for a limited computational study in Ref. 1 is satisfactory regarding geometrical structures, but less than satisfactory regarding the EA of OFO. All in all, the EA is predicted to be close to zero and higher-order correlation effects are found to have a strong impact on the EA. Our best value, derived from zero-point corrected L-CCSD(T) energies, is −63 meV. In other words, the C4F8O anion is predicted to be slightly less stable than OFO; however, in view of the incomplete triple-ζ basis set, correlation effects lacking in CCSD(T), and anharmonic effects, a better estimate of this value is probably practically zero if not slightly positive. Be that as it may, regardless whether the EA is −63 meV or slightly positive, OFO and its parent anion can be considered to be essentially isoenergetic.

Moreover, the energy of the short-lived temporary anion formed by vertical electron attachment to OFO, that is, the negative VEA of OFO, was estimated by extrapolating positive VEBEs computed in the vicinity of the minimal energy structure of C4F8O to the geometry of the neutral (R-extrapolation). Independent of the electronic structure method used to obtain VEBE input data for the extrapolation, the VEA is predicted to be about −2.8 eV. This energy is expected to be associated with a broad short-lived σ* resonance and compares favorably with resonances known from other perfluorinated compounds, which in turn implies that the C4F8O species observed experimentally is formed by electron capture in the low-energy wing of this resonance.

Now, while an electron capture plus IVR explanation of the 0.9 eV peak is still conceivable—at lower energies, electron capture could become increasingly inefficient owing to the width of the resonance, while at higher energies, the lifetime of C4F8O could be limited owing to electron reejection or dissociative processes—we also investigated alternative explanations for the observation of a long lived C4F8O species in the 0.9 eV range. We identified, in particular, an electron-induced reaction that is dissociative in the sense that a bond is ruptured, but instead of dissociating the anion as such, the oxolane ring is opened yielding a distonic chain isomer of C4F8O. The main findings from the analysis of this ring-opening reaction are the following: the distonic product has many conformers which are more stable than the C4F8O ring by 0.2–0.4 eV. The activation energy for the reaction is about 0.73 eV, and a very conservative estimate of the microcanonical rate constant at an energy of 0.9 eV above the neutral yields a bond rupture time scale ten times faster than the experimental time scale. However, as discussed above, one may expect the ring-opening reaction to be at least two orders of magnitude faster than this estimate, and anharmonic corrections will further increase the unimolecular rate. Thus, we predict the electron-induced ring-opening reaction of OFO to proceed quickly on the mass spectrometric time scale, and since recrossing the barrier is by far less likely than crossing, we predict that practically all ions detected are C4F8O distonic isomers.

The fast electron-induced ring-opening reaction changes the interpretation of the 0.9 eV peak fundamentally. All C4F8O ring isomers formed by electron capture in the 0.9 eV region as well as those formed at higher energies will either lose their excess electrons due to autodetachment or react quickly to form the distonic isomer. At lower energies than 0.9 eV, the transformation to the distonic isomer will become increasingly unlikely; however, the channel is still expected to stay open for several tenths of an eV, in particular, since our conservative estimate of the rate constant neglected any anharmonic corrections to the EA, to the activation energy, and to the rate itself. At energies lower than 0.9 eV, either electron-capture by the neutral ring may become inefficient or the ring-opening reaction will become too slow to compete with electron reejection. At energies higher than 0.9 eV, the distonic C4F8O isomer will contain so much internal energy that further truly dissociative pathways start to open up, which is in agreement with the onsets of various experimentally observed fragments. In fact, various of the detected fragments can be explained in a far more straightforward way if the distonic isomer is assumed as an intermediate, for example, CF2O can be produced by a single bond cleavage from the distonic chain. In conclusion, the position of the remarkable C4F8O peak would be explained as a sweet spot for the efficient formation of the distonic radical anion with low enough energy to avoid further bond rupture reactions.

The predicted excess electron-induced ring opening is part of a large class of electron-induced, electron-transfer induced, or electron-catalyzed bond-cleavage reactions. Dissociative attachment represents one well-known example, in this particular context; however, we would like to draw additional attention to the following ring-opening reactions: Elimination of N2 from a five-membered aromatic ring triggered by excitation-induced electron-transfer,25 a synthetic method for the ring-expansion of strained three and four-membered rings triggered by photoinduced electron-transfer,26 and the opening of three-membered N-containing rings (aziridines) by electron attachment in solution (electron transfer from a metal to the molecule).27 In contrast to typical dissociative attachment processes, these three ring-opening reactions are driven by the stability of the products (N2 is formed, very strained rings are opened). The electron-induced ring-opening of OFO studied here is thus a hybrid. It has, on the one hand, the character of a typical dissociative attachment reaction, yet, since a bond in a ring is opened, it represents at the same time an isomerization rather than fragmentation reaction. It is tempting to speculate that analogous electron-induced ring-opening reactions may explain at least some of the parent anions observed far above threshold (see Ref. 1 for a list of seven unexplained cases). Six of these unexplained molecules have one or more rings; however, all of these rings are in contrast to the saturated OFO aromatic in character, and therefore the analogy is less than perfect, and the electron-induced ring-opening explanation has to remain speculation at this point.

Last, let us discuss how the electron-induced ring-opening reaction may affect the use of OFO in high-voltage insulation. Even though our computed rate constants do not apply to a solution environment, the activation energy itself does, and it is sufficiently low to predict fast ring-opening at room temperature provided the ring isomer of C4F8O is formed. Also, electron capture in solution cannot be directly compared with processes in the gas phase, but solvation effects will probably stabilize the resonance state and electron capture might be eased by solvated electron states. In any event, once an excess electron becomes trapped on the OFO ring at room temperature, the ring will open to produce the distonic C4F8O isomer. Now, while SF6 is chemically inert, the distonic radical ion can be expected to be quite reactive and to undergo all types of radical reactions. Thus, the question is not so much whether OFO would decay in an electron-rich environment, but rather how quickly it would do so. These radical reactions may offer an alternative to account for the difference between the electron attachment behavior to OFO under single molecule collision in beam experiments and under high pressure conditions in swarm experiments Ref. 2, however, without further characterization of the reaction products this has to remain speculation. An experiment investigating trying to characterize long-lived C4F8O seems straightforward in principle: Create some electrons in an OFO solution, either by ionizing radiation or by adding a metal such as sodium or magnesium, and observe changes in some spectrometric signature. For instance, the ring isomer is predicted to have its most intense IR bands in the center of its stretching region between 1000 and 1200 cm−1, while for the distonic conformers, the most intense stretch occurs in the vicinity of 1600 cm−1 and one of the low-energy stretches around 850 cm−1 also shows considerable intensity.

Support by the National Science Foundation under No. CHE-1565495 is gratefully acknowledged.

1.
J.
Kočišek
,
R.
Janečková
, and
J.
Fedor
,
J. Chem. Phys.
148
,
074303-1
(
2018
).
2.
A.
Chachereau
,
J.
Fedor
,
R.
Janečková
,
Kočišek
,
M.
Rabie
, and
C. M.
Franck
,
J. Phys. D: Appl. Phys.
49
,
375201
(
2016
).
3.
A. D.
Becke
,
J. Chem. Phys.
98
,
5648
(
1993
).
4.
L. A.
Curtiss
,
P. C.
Redfern
,
K.
Raghavachari
,
V.
Rassolov
, and
J. A.
Pople
,
J. Chem. Phys.
110
,
4703
(
1999
).
5.
C.
Szmytkowski
,
P.
Mozejko
,
G.
Kasperski
, and
E.
Ptasińska-Denga
,
J. Phys. B: At., Mol. Opt. Phys.
33
,
15
(
2000
).
6.
M.
Rabie
and
C. M.
Franck
,
IEEE Trans. Dielectr. Electr. Insul.
22
,
269
(
2015
).
7.
J.-D.
Chai
and
M.
Head-Gordon
,
J. Chem. Phys.
128
,
084106
(
2008
).
8.
C.
Adamo
and
V.
Barone
,
J. Chem. Phys.
110
,
6158
(
1999
).
9.
Y.
Zhao
and
D. G.
Truhlar
,
Theor. Chem. Acc.
120
,
215
(
2008
).
10.
T. H.
Dunning
, Jr.
,
J. Chem. Phys.
90
,
1007
(
1989
).
11.
E.
Papajak
,
J.
Zheng
,
X.
Xu
,
H. R.
Leverentz
, and
D. G.
Truhlar
,
J. Chem. Theory Comput.
7
,
3027
(
2011
).
12.
J. M.
Herbert
, in
Reviews in Computational Chemistry
, edited by
A. L.
Parrill
and
K. B.
Lipkowitz
(
John Wiley & Sons
,
Hoboken, NJ, USA
,
2015
), Vol. 28, pp.
391
517
.
13.
F.
Neese
,
T.
Schwabe
,
S.
Kossmann
,
B.
Schirmer
, and
S.
Grimme
,
J. Chem. Theory Comput.
5
,
3060
(
2009
).
14.
C.
Riplinger
and
F.
Neese
,
J. Chem. Phys.
138
,
034106
(
2013
).
15.
C.
Riplinger
,
B.
Sandhoefer
,
A.
Hansen
, and
F.
Neese
,
J. Chem. Phys.
139
,
134101
(
2013
).
16.
A. K.
Dutta
,
F.
Neesea
, and
R.
Izsák
,
J. Chem. Phys.
145
,
034102
(
2016
).
17.
Orca, Version 4.0.1.2, A package of programs by Frank Neese, Technical director Frank Wennmohs, with contributions from
D.
Aravena
,
M.
Atanasov
,
U.
Becker
,
D.
Bykov
,
V. G.
Chilkuri
,
D.
Datta
,
A. K.
Dutta
,
D.
Ganyushin
,
Y.
Guo
,
A.
Hansen
,
H.
Lee
,
R.
Izsák
,
C.
Kollmar
,
S.
Kossmann
,
M.
Krupička
,
D.
Lenk
,
D. G.
Liakos
,
D.
Manganas
,
D. A.
Pantazis
,
T.
Petrenko
,
P.
Pinski
,
C.
Reimann
,
M.
Retegan
,
C.
Riplinger
,
T.
Risthaus
,
M.
Roemelt
,
M.
Saitow
,
B.
Sandhöfer
,
I.
Schapiro
,
K.
Sivalingam
,
G.
Stoychev
, and
B.
Wezisla
, https://orcaforum.cec.mpg.de/.
18.
S.
Feuerbacher
,
T.
Sommerfeld
, and
L. S.
Cederbaum
,
J. Chem. Phys.
121
,
6628
(
2004
).
19.
J.
Horáček
,
P.
Mach
, and
J.
Urban
,
Phys. Rev. A
82
,
032713
(
2010
).
20.
T.
Sommerfeld
and
M.
Ehara
,
J. Chem. Phys.
142
,
034105
(
2015
).
21.
T.
Sommerfeld
,
Phys. Chem. Chem. Phys.
4
,
2511
(
2002
).
22.
T.
Sommerfeld
,
J. Phys.: Conf. Ser.
4
,
245
(
2005
).
23.
J. N.
Bull
and
J. R. R.
Verlet
,
Sci. Adv.
3
,
e1603106
(
2017
).
24.
P.
Pobinson
and
K. A.
Holbrook
,
Unimolecular Reactions
(
Wiley Interscience
,
New York
,
1972
).
25.
A.
Banerjee
,
D. H. G.
Ganguly
, and
A.
Paul
,
Phys. Chem. Chem. Phys.
18
,
25308
(
2016
).
26.
E. W.
Bischof
and
J.
Mattay
,
J. Photochem. Photobiol., A
63
,
249
(
1992
).
27.
K. A.
Tehrani
,
V. T.
Nguyen
,
M.
Karikomi
,
M.
Rottiers
, and
N.
De Kimpe
,
Tetrahedron
58
,
7145
(
2002
).