Ionisation of PF3: absolute partial electron ionisation cross sections and the formation and reactivity of dication states

Absolute partial electron ionisation cross sections, and precursor-specific partial electron ionisation cross sections, for the formation of cations from phosphorus trifluoride (PF3) are reported over the electron energy range 50-200 eV. The absolute values are determined by the measurement of cross sections relative to the formation of PF3 using 2D ion-ion coincidence time-of-flight mass spectrometry and subsequent scaling using binary encounter-Bethe calculations of the total ionisation cross section. This new dataset significantly augments the partial ionisation cross sections for electron ionization PF3 found in literature, addressing previous discrepancies in the branching ratios of product ions, and provides the first values for the precursor-specific cross sections. Comparisons to calculated cross sections from the literature are encouraging, although there are discrepancies for individual ions. The coincidence experiments indicate that double and triple ionisation generate approximately 20 % of the cationic ionisation products at 200 eV electron energy. One dissociative dication state, dissociating to PF2 + F+, is clearly identified as the lowest triplet state of PF3 and five different dications (PF3, PF2, PF2+, P2+ and F2+) are detected in the mass spectra. The dication energetics revealed by the experiments are supported by a computational investigation of the dication’s electronic structure. The cross sections reported will allow more accurate modelling of the role of the ionization of PF3 in energetic environments. A first investigation of the bimolecular reactivity of metastable states of PF3 is also reported. In collisions with Ar, O2 and CO dissociative single electron transfer dominates the product ion yield, whereas collision-induced dissociation of the dication is important following collisions with Ne. Consideration of the energetics of these processes indicates the reactant dication beam contains ions in both the ground singlet state and the first excited triplet state. The deduction regarding the longevity of the triplet state is supported by metastable signals in the coincidence spectra. Weak signals corresponding to the formation of ArF+ are detected following PF3 collisions with Ar, and experimental and computational considerations indicate this new chemical bond is formed via a collision complex. Page 1 of 23 Physical Chemistry Chemical Physics P hy si ca lC he m is tr y C he m ic al P hy si cs A cc ep te d M an us cr ip t O pe n A cc es s A rt ic le . P ub lis he d on 2 6 A pr il 20 21 . D ow nl oa de d on 4 /2 7/ 20 21 2 :3 8: 45 P M . T hi s ar tic le is li ce ns ed u nd er a C re at iv e C om m on s A ttr ib ut io n 3. 0 U np or te d L ic en ce . View Article Online DOI: 10.1039/D1CP01328A


Introduction
Phosphorus trifluoride (PF 3 ) is a molecule commonly used both in research laboratories and in industry, with particular applications in metal-ligand chemistry. 1,2 In addition, phosphorus and fluorine containing compounds are often used in plasma-assisted surface modification 3 and PF + and PF 2 + have both been investigated for their contributions to the chemistry in interstellar clouds. 4 Thus, the electron ionisation, and subsequent fragmentation, of PF 3 are of interest to both materials chemists and astrochemists. Previous studies have revealed significant ion yields involving chemical bond formation following collisions between fluorinated dications and neutral molecules, [5][6][7][8][9] and so the potential formation of long-lived dications following electron ionisation of PF 3 , as investigated in this study, could therefore allow access to new bond-forming ion chemistry.
The ionisation and subsequent chemistry of PF 3 in electron-rich environments can only be wellmodelled if these is an understanding of the ionic electronic states populated and reliable cross sections are available to characterize their formation and behaviour. Indeed, electron ionisation of molecules, and the production of cations, have long been recognised as a primary route for the formation of plasmas, 10 dose deposition in radiotherapy, 11 and the formation of species in planetary atmospheres 12 and the interstellar medium. 13 Generating usable and reliable partial ionisation cross sections to characterize the consequences of electron ionisation of PF 3 , and qualitative data exploring the properties of the dications formed following multiple ionisation of this molecule, are the aims of this study.
The yield of cations following a given electron-molecule collision is quantified by the total ionisation cross section, which is a function of the incident electron energy. Partial ionisation cross sections (PICS) involve a decomposition of the total ionisation cross section into cross sections for forming individual product ions. PICS allow, for example, modelling of the abundance of different ions in electron rich environments. Precursor-specific partial cross sections (PS-PICS) quantify the proclivity for forming an individual ion via a given level of ionisation (single, double, triple ...) as a function of electron energy. Data on relative, and in some cases absolute, PS-PICS have been extracted from experiment for several molecules. [14][15][16][17] However, in the electron collision energy range of concern in this paper (50 eV -200 eV) there have been a limited number of computational approaches to generating PICS or PS-PICS for complex molecules, and certainly no established algorithms available to the non-specialist. [18][19][20][21][22] In this paper we recognise that relative PICS and PS-PICS are relatively routine to measure experimentally with the appropriate apparatus, whilst total ionisation cross sections can be calculated robustly and routinely. Hence, we present a route to generating absolute PICS and PS-PICS, important data for modellers, by developing a methodology for placing the experimental relative cross sections on an absolute scale using a computational determination of the total ionisation cross section. We apply this approach in a study of the electron ionisation of PF 3 .
Previous studies of electron scattering from PF 3 have included the calculation of the total elastic and total inelastic (ionisation and excitation) cross sections (0.15 to 5000 eV), 23 measurement and calculation of elastic differential cross sections between 2.0 -200 eV, 24 measurement and calculation of integral and differential vibrational cross sections, 25 measurement of ion appearance energies and relative ion intensities at 70 eV, 26,27 measurement of experimental absolute total scattering cross sections (0.5 to 370 eV) 28 and calculations of partial differential ionisation cross sections at 100 eV and 200 eV. 29 Photoionisation of PF 3 has also been investigated. 30 Of particular relevance to the cross sections determined in the current study are the theoretical studies of Vinodkumar et al. 23 and Kumar. 29 Vinodkumar et al., 23 over the energy range 15 -5000 eV, used the spherical complex optical potential (SCOP) method to calculate various elastic and inelastic cross sections, including the total ionisation cross section of PF 3 . Kumar 29 used the Jain-Khare semi-empirical approach to calculate partial ionisation cross sections for the production of cations for ionisation of PF 3 at electron energies from threshold to 1000 eV. This paper reports values of the PICS and PS-PICS for PF 3 following electron ionisation (50 -200 eV). Coincidence mass spectrometry measurements provide relative PICS as well as relative PS-PICS. 17 The binary encounter Bethe [BEB] method is then used to calculate the absolute total ionisation cross section of PF 3 , to which the experimental relative cross sections are then robustly normalized. For molecules where an experimental determination of the absolute total ionisation cross section is available, a normalization of relative experimental PICS with the absolute total ionisation cross section to yield absolute PICS (the nomenclature commonly used for these scaled experimental data, and adopted here) has been performed in the past. 31,32 However, the procedure illustrated in this paper, exploiting the modern computational facility to determine robust total ionisations cross sections routinely, allows the extension of this scaling procedure to larger and more reactive/unstable species, these species are often those of interest in many energised environments. In addition, this work extends this procedure to generate absolute values for the PS-PICS and well as the PICS.

Experimental details
Relative PICS and PS-PICS are determined from coincidence mass spectrometry experiments. The coincidence time-of-flight mass spectrometer (TOF-MS) used in these experiments has been described in detail before, 15,33 and is of the Wiley-McLaren design. 34 Ions are formed in the, initially field-free, source region of the TOF-MS, at the intersection of a pulsed electron beam and an effusive gas jet. The gas jet and the electron beam are oriented in a mutually perpendicular arrangement and both are perpendicular to the principal axis of the TOF-MS. The electron pulses are 30 ns long and have a frequency of 50 kHz. The energy calibration and spread of the electron beam is determined via calibration to the Ar double ionisation threshold, giving an observed kinetic energy spread of ~0.5 eV. An effusive flow of PF 3 is introduced into the experiment via a hypodermic needle, giving a typical pressure of 10 -6 Torr in the vacuum chamber as recorded via an ion gauge. Following the passage of the electron pulse across the source region, a pulser applies a voltage to the repeller plate of the TOF-MS accelerating cations into the second (acceleration) field of the MS and then on into the drift tube. Ions with a kinetic energy up to 11.5 eV perpendicular to the TOF axis will hit, and are detected by, a microchannel plate stack at the end of the drift tube. As most dicationic kinetic energy releases are less than 9 eV in total, 35 the vast majority of monocation pairs formed by dicationic fragmentations are collected. The arrival times of ions at the detector are recorded by a time to digital converter (TDC), started by the application of the voltage to the repeller plate. The TDC is capable of recording multiple "stop" signals for an individual electron pulse. These arrival times are classified as one of: (i) single ion detections, (ii) pairs or (iii) triples of ions. As has been discussed before in the literature, 36 extraction of relative PS-PICS from these coincidence data requires the ion detection efficiency of the apparatus. The detection efficiency is determined via recording reference spectra of CF 4 for which PS-PICS are available. 16,37 The relative PICS we determine from our dataset do not depend on the ion detection efficiency. 38 At least three sets of experiments, generating three determinations of the relative PICS and PS-PICS, are carried out at each incident electron energy with the results then averaged. Each experiment lasts 6-8 hours and involves approximately 10 9 data acquisition cycles. Bimolecular reactions of the parent dication PF 3 2+ with target gases Ar, Ne, CO, and O 2 have been investigated in a separate crossed-beam apparatus. These experiments identify collision products, and provide information on relative reaction cross sections, at selected collision energies. The operation of this experiment has been described in detail in the literature. 39,40 In brief, ions are generated from PF 3 in a purpose built low-pressure ion source. Here, electron collisions (200 eV) with the precursor molecule generate the full range of ionised species (parent ions and fragments). The pressure in the source is closely controlled and maintained at a low enough pressure to minimize dication losses due to collisions with neutral species. Ions from the source are accelerated into a velocity filter (crossed electric and magnetic fields) where the dication projectile is selected by its m/z value. The purity of the resulting beam is >99 % with minimal contamination from other ions which are weakly transmitted by the mass filter. The selected projectile ion (PF 3 2+ in this study) is then electrostatically decelerated to the desired laboratory collision energy (4 V [8 eV] in the lab frame). The selected and decelerated ion beam is crossed perpendicularly with an effusive gas jet of the target gas in the collision region of the experiment. The pressure in the collision region is also carefully controlled to maintain single collision conditions, with pressures below 5 x 10 -6 Torr as measured by an ion gauge remote from the collision region. The charged collision products are periodically accelerated from the collision region, perpendicular to the direction of the dication beam, into a TOF-MS by applying an appropriate voltage across the collision region. At the end of the TOF-MS the ions extracted are detected by a multichannel plate detector.
To ensure spectra are able to distinguish between the products of the desired collisions and those with any background gas in the vacuum chamber, or any products from the metastable decay of the projectile dication, spectra are recorded both with and without the collision gas present. 41 This procedure involves subtracting the appropriately normalized contribution from a series (at least two) of "gas-off" spectra from the relative ion intensities from interspersed (again at least two) "gas on" spectra to give values for the corrected relative product ion intensities at a given collision energy. At least three such determinations are performed at each collision energy for each collision gas. The standard deviations of the individual relative ion intensities across each determination are used in further error processing.
The determination of accurate relative product ion intensities from the above spectra is complicated by the variation in the velocity of the different product ions in the direction of the dication beam, transverse to the TOF axis. 42 As noted above, the dication beam is directed perpendicular to the principal axis of the TOF and as such the velocity of the detected ions in the direction of the dication beam translates into a velocity transverse to the axis of the TOF. The more translationally energetic the ion the smaller the volume of the collision region that is imaged onto the TOF-MS detector, resulting in differences in the detection efficiency of different ions as a function of their velocity. In an extension of the procedure used to correct for these discrimination effects, 42 a SimIon 43 simulation of the extraction region and TOF system allows an assessment of this geometric discrimination as a function of ion velocity. This simulation assumes dication and product beam diameters of 4 mm, as determined from previous simulations of the beam path. Testing shows increasing or decreasing this diameter by 1 mm changes the final cross section by up to 8 % across the collision energy range used here, and this has been included in our estimate of the uncertainties of the relative intensities. The lengths of cylindrical volumes of the dication and product beams extracted onto the MCP, and hence the relative detection efficiencies, are determined, as described in detail in the literature, from the geometries of the TOF, the kinetic energies of the different ions. 42 Estimates of the typical kinetic energy release in the various classes of dication reactions are used to determine the product ion velocitieis. 42 As shown by Burnside and Price 42 , using the above procedure for product ions derived from the dication, the ratio of the recorded intensities of the different products can be reliably transformed to yield relative reaction cross sections, which clearly quantify the branching between the different reaction pathways. The ions derived from the neutral collision partner have a very different laboratory frame velocity distribution, and spatial distribution, to those derived from the dication, 42 and as such the relative intensities of these products cannot be easily compared with the products derived from the dication.
The PF 3 used in this study was synthesised in-house. 44 In brief, PCl 3 was added dropwise onto ZnF 2 suspended in acetonitrile under controlled vacuum conditions. The presence of the acetonitrile allowed good control of the temperature of the reaction mixture. The gaseous PF 3 product resulting from this procedure was then trapped at liquid nitrogen temperatures and subsequently purified. See Supplementary Information for further details of the synthesis of PF 3 . The product was purified several times by trap-to-trap distillation. Traces of Cl containing contaminants are seen in the ionisation mass spectrum. However, such contaminants do not affect the partial cross sections we extract due both to the fact the associated mass peaks do not interfere with those of PF 3 and the fact that the impurities are at a very low level. Additionally, very weak signals are also present due to traces of the acetonitrile solvent. These contaminants from the synthesis, and any air/water present as background gas in the apparatus, contribute significantly less than 1% of the ion counts in any of the ion peaks of interest in any mass spectrum.

Data processing: coincidence TOF-MS
The data processing and analysis of the coincidence mass spectra are laid out in full here. A 'singles' mass spectrum is generated as a histogram of the flight times of ion arrivals in the TOF-MS where only a single ion is detected following a repeller plate pulse. The mass scale of this mass spectrum, and the associated coincidence spectra, is calibrated by recording a mass spectrum of a reference gas (e.g. Ar) under the same experimental conditions. A baseline correction is applied to the summed counts associated with each mass spectral peak, to remove the small background present due to detector noise and stray ions. This procedure yields the ion intensities in the singles spectrum. Further corrections are made, where necessary, if there is a potential contribution from an ion from the background gas to a mass peak of interest. For example, in the case of PF 3 2+ , with a mass of 44, any contribution from CO 2 + is evaluated using the intensities of unmasked signals from CO 2 and the associated partial ionisation cross sections. 14 Due to the low levels of impurities in our gas sample, as described above, such corrections are small.
'Pairs' and 'triples' are events where two or three ions are detected in coincidence, respectively, following one pulse of the repeller plate. The flight times associated with each of these individual events are stored and subsequently processed offline. To begin this processing, all the detected ion pairs are plotted in a 2D histogram (a 'pairs' spectrum) using the TOF of the lightest ion (t A ) and the TOF of the heavier ion (t B ) as the two ordinates. The number of counts (intensities) in each of the peaks in the pairs spectrum, peaks which correspond to different dissociation reactions of PF 3 2+/3+ , are evaluated to yield the number of counts for a given ion in the pairs spectrum P 2 [X + ]. It is important to note that the pairs spectrum, although dominated by dissociative double ionisation events, also involves a contribution from higher levels of ionisation. For example, pairs are detected from triple ionisation where one species is a dication and the other a monocation (P 3 [X + ]). Some monocation pairs also result from triple ionisation where the third ion is not detected as the experimental ion detection efficiency is less than unity. Such events contribute to the values of P 2 . Indeed, the non-unit ion detection efficiency of the apparatus allows ions from dissociative multiple ionisation to contribute to the singles spectrum. These contributions are included explicitly in the data reduction described in the next section.
To process the triples, the time of flight range corresponding to the mass of one ion (ion A) which could potentially contribute to the spectrum (t A ) is selected (e.g. P + ) and then a 2D histogram is generated of all ions (t B and t C ) that are detected in coincidence with an ion in the time window for ion A. This process is then repeated for all potential combinations of possible of triples. Evaluation of the intensities of the peaks in these triples spectra yields T[X + ]. Very small ion signals are visible in the triples spectrum which can be attributed to quadruple (or higher) ionisation. However, since these signals are very weak the contribution of quadruple and higher ionisation is neglected in the subsequent analysis.
Both the pairs and triples spectra contain a contribution from false coincidences. The number of false coincidences is kept low by operating at low ion count rates. As has been described before in the literature, we use an ion-autocorrelation function to evaluate the contribution of false counts (at most 1-2 %) in each peak in the triples or pairs spectra, and hence correct our values of P n [X + ] or T[X + ] for false coincidences. 33 Conversely, a source of missing counts in the coincidence histograms is the deadtime of the TOF-MS discrimination circuitry, which is unable to process a second ion arrival within 6 32 ns of a first ion. This dead-time results in reduced counts for pairs or triples involving ions with the same mass (e.g. F + + F + ). We can readily correct for these losses by extrapolation of a one-dimensional ion-ion coincidence (t B -t A ) spectrum for the reaction of interest to the t B -t A =0 limit, as detailed in earlier work. 45 In the data reported here, such a deadtime correction is applied to the F + + F + pair and the triples 3F + , 2F + + P + and 2F + + PF + .
Additional signal losses arise for ion pairs and triples where the transverse kinetic energy release of an ion is sufficient (~ 11.5 eV) for the ion to miss the detector. 46 Such losses are readily apparent in the shape of the peaks in the pairs or triples spectrum which become "hollowed" in the centre. These losses are corrected for quantitatively, on a peak by peak basis, by determining the counts required to give the expected flat-topped peak in a one-dimensional t B -t A spectrum. 45 However, we should note that losses of highly energetic ions from single ionization events (> 11.5 eV) which miss the detector cannot be quantified. However, such fragment ions are expected to be a very minor component of the yield from single ionisation, as evidenced by the excellent agreement of previous datasets from our apparatus with other experiments where complete collection of fragment ions is demonstrated. 15,47

Data reduction: coincidence TOF-MS
Relative PICS and relative precursor-specific PICS are extracted from the corrected ion intensities in the singles, pairs and triples spectra: The instrumental ion detection efficiency is necessary to extract the PS-PICS and is determined, as noted above, via calibration spectra 45 recorded with CF 4 , 16,37 prior to the PF 3 experiments. Using this methodology the value of f for the experiments involved in this study was found to be 0.25, a value in accord with previous determinations for our apparatus. 48 An example of the relationship between the detected ion intensities in the singles mass spectra I[X + ] and the detection efficiency is shown by Eqn. (1), where N n is the number of X + ions formed via ionising events involving the loss of n electrons from a PF 3 molecule. Similar equations can be constructed for pairs and triples P 2 [X + ], P 3 [X + ], T[X + ] as shown in the literature 14 . Using the equations constructed for the ion intensities in the various spectra (singles, pairs triples), the required relative cross sections can be determined. For example, relative PICS  r [X +/2+ , E] are the cross sections for forming the fragment ion X + , X 2+ from any level of ionisation relative to the cross section of formation for the parent monocation (PF 3 + ) as a function of electron energy E, as shown in Eqn. (2).
[ ] The values of and are determined for each of the ions detected with sufficient intensity in the PF 3 singles spectrum. The derivation of the above equations, and the other related equations for this analysis, have been described in detail in the literature. 33,48 It is possible to determine the kinetic energy release (KER) of each dicationic dissociation reaction detected in the pairs spectrum This determination is performed by generating a TOF difference spectrum for the dissociation of interest, a histogram of intensity against (t B -t A ) as discussed above. 33 Such a difference spectrum, for a given dication dissociation channel, has a characteristic square shape with a width determined by the KER of the associated dissociation. By optimizing the fit of a Monte Carlo simulation of the difference spectrum, incorporating an electrostatic model of the TOF-MS and various parameters characterizing the dissociation, to the experimental difference spectrum, the value of the KER can be estimated. 33 The KER and the energies of the dissociation products E frag , relative to the ground state of PF 3 , can then be summed to provide an estimate of the energy of the dicationic precursor state E p (X 2+ ) responsible for the dissociation (Eqn. (4)). In this procedure the dissociation products are assumed to be formed in their ground electronic states, and rovibrational excitation of the products is neglected. Thus, E p (X 2+ ) provides a lower limit on the energy of the dicationic precursor state.
This methodology for determining KERs has been shown to produce values that agree well with those in the literature. 15,36,45 The uncertainty associated with a KER determination is assessed by the range of values for which the simulation and real spectrum 'fit', with the modal value then reported; this uncertainty is usually of the order of ±0.5 eV.

BEB calculations
Total electron impact ionisation cross sections have been computed using the binary-encounter Bethe (BEB) method of Kim and Rudd 49 as implemented in the new Quantemol electron collisions (QEC) expert system 50,51 . QEC is a graphical user interface that wraps Molpro, 52 for generating molecular orbitals and properties, and UKRmol+ 53 to generate a variety of molecule-electron scattering cross sections. BEB is a semi-empirical method, simply requiring the occupation, binding and average kinetic energies of the electrons in the occupied orbitals of the target molecule. BEB has a track-record of generating reliable predictions for total ionisation cross sections. Thus, for example, a recent data compilation of electron collision cross sections for NF 3 and CH 4 by Song et al. 54,55 chose to recommend the BEB cross section in preference to several experimental determinations. As part of the present study all electron BEB calculations were performed using Hartree-Fock target wavefunctions and three different Gaussian basis sets for the PF 3 target; specifically, the 3-21G, 6-21G and cc-pVDZ basis sets. The calculation using the 6-21G basis set gave larger cross sections than the other two basis sets, this difference arising primarily from differences in the generated orbital kinetic energies. Additionally, the cc-pVDZ basis set uses higher order spherical harmonics, with up to d orbital functions for the P atom, allowing for more realistic molecular orbitals. Hence, here we adopt the value given by the largest basis set employed (cc-pVDZ ) with an uncertainty estimate obtained using the difference between this and the results of the 6-21G calculations. A further increase in the size of the basis set did not result, given the BEB methodology, in a significant increase in the accuracy of the calculated cross section with respect to the marked increase in computational cost.
In order to normalize the relative PICS and PS-PICS determined in our experiment, to the BEB function representing the total ionisation cross section B(E) as a function of the electron energy E, the following procedure was developed. We define: where is the partial ionisation cross section for generating the parent ion and is the partial ( ) ( ) ionisation cross section for generating fragment ion i. From our experimental data we can construct: where , as noted above, is the relative cross section for formation of ion i, a value derived from [ , ] the experimental data. Combining equations (5) and (6) results in: We know and from the experimental data (Eqn. 5) and the calculation respectively. Hence ( ) ( ) using Eqn. (7). we can determine . Then using the definitions in Eqn. (5) we have: ( ) Thus, the relative PICS from the experiment can be converted to absolute values using the [ , ] value of . Given that, as can be confirmed from the experimental data: ( ) scaling by can also be used to place the PS-PICS on an absolute scale. Here, as noted above, ( ) indicates the number of electrons lost by PF 3 in the ionising collision.

Electronic structure calculations
Electronic structure calculations using Gaussian16 (Rev. A03) 56 have been used to support the experimental findings. Relevant equilibrium geometries, and adiabatic and vertical ionisation energies, were determined for the neutral, cation and dicationic states of PF 3 . These quantities were calculated, for the lowest lying states of appropriate multiplicity, for each of the charge states. Stationary points were located using the MP2 algorithm with a cc-pVTZ basis set and verified as minima by frequency analysis. The energetics of these stationary points were then determined using single-point CCSD(T) calculations with the same basis set, and corrected for zero-point energies using the vibrational data from the MP2 geometry optimizations. This methodology has been successfully used in the past, by several groups, to determine dication geometries and energetics 57 . Along with the geometries of an isolated PF 3 2+ ion, the geometries of [Ar-PF 3 ] 2+ complexes were also investigated.

Results and Discussion
As outlined above, relative PICS and PS-PICS of PF 3 were determined using the mass spectral data generated by the coincidence TOF-MS. Similarly, mass spectra revealing the product ions generated following bimolecular collisions of PF 3 2+ and the neutral species Ar, Ne, O 2 , and CO were collected using the crossed beam apparatus.

Electron Ionisation of PF 3
TOF-MS coincidence spectra were recorded following electron ionisation of PF 3 at electron energies between 50 eV and 200 eV. From the coincidence data at an individual electron energy, singles spectra (e.g. Figure 1) and pairs spectra (e.g. Figure 2) are assembled. These spectra were analysed, as described above, to produce the relative PICS for each ion (Figure 3) and the relative PS-PICS ( Figure  4), where appropriate. Several coincidence spectra (typically of duration 7-hours) were recorded at each electron kinetic energy and the relative cross sections at a given electron energy averaged to give final values of  r [X +/2+ , E] and  n [X +/2+ , E] for each electron energy investigated. These relative values are then normalized to the BEB model, again as described above, to produce absolute values of the cross sections. As noted above, these absolute cross sections are of significantly more value for modellers than the relative values.
The ions present in the PF 3 singles TOF-MS are: PF 3 + , F + , PF + , P + , PF 2 + , PF 2+ , P 2+ , PF 2 2+ , PF 3 2+ , F 2 + , and F 2+ . To the best of our knowledge the literature reports no previous observations of F 2 + , and F 2+ following ionisation of PF 3 . The results of the BEB calculation of the total ionisation cross section are compared to previous calculations available in the literature in Figure 5 and the resulting absolute PICS are compared to available calculations in Figure 6 and Figure 7.  The pairs spectra (e.g. Figure 2) reveal the charge-separating dissociations generate the following pairs of dications: F + + F + , F + + P 2+ , PF 2+ + F + , P + + F 2+ , P + + F + , PF 2 2+ + F + , PF + + F + and PF 2 + + F + . These ions pairs result from double or triple ionisation of PF 3 in a single electron-molecule collision. In addition to the peaks in the pair spectrum, which correspond to rapid dissociation of the PF 3 2+/3+ multiply charged ions, there is a clear signature of a slower, metastable, dissociation ( Figure 2): a tail extending to low t B and high t A from the peak for the PF 2 + + F + pair. Such a tail reveals that some dissociations forming PF 2 + + F + occur on the timescale of tens of nanoseconds when the metastable PF 3 2+ ion has moved out of the source region of the TOF-MS. The ion triples PF + + F + + F + , F + + F + +F + and P + + F + + F + are also detected on the triples spectrum. Table 1 lists the partial ionisation cross sections (PICS) we determine, following the normalization of the relative cross sections extracted from the experiment to the calculated total ionisation cross section. As described above, the quoted uncertainties reflect the combination of the estimated uncertainties from the calculation and the relative experimental values. The PICS are shown graphically in Figure 3. It is worth noting that the most abundant ion produced via electron ionisation, in the energy range investigated is PF 2 + , rather than the parent ion, PF 3 + . Production of the P + ion is far more significant than that of the F + ion in the lower half of the energy range, where single ionisation dominates. F + production increases, relative to P + , with increasing collision energy, as there is a significant contribution to the F + yield by multiple ionisation above 85 eV (Figure 4). Production of P + by single ionisation can involve the production of three F atoms or F 2 + F. The cross section for the production of the PF 2+ dication is found to be of the same order of magnitude as the generation of PF + and F + . The cross sections for formation of PF 3 2+ and PF 2 2+ are also non-negligible. This efficient dication formation stimulated our further study of the bimolecular reactivity of PF 3 2+ , described below. PS-PICS were determined for each ion detected and are tabulated in the Supplementary Information (Table SI1). Selected PS-PICS are shown graphically in Figure 4 revealing, as noted above, that double ionisation is responsible both for the majority of the F + ions generated above 75 eV and for a sizable proportion of the P + and PF + production. The PS-PICS also reveal a significant proportion of the F + ions detected are formed by triple ionisation, above 150 eV, though the contribution to other ion yields via triple ionisation is small.  Precursor-specific partial ionisation cross sections (PS-PICS) for the formation of the detected charged products from electron ionisation of PF 3 . σ n indicates formation via initial n = 1 (single), n = 2 (double) and n = 3 (triple) ionisation of PF 3 . Arrows indicate the axis associated with a given dataset. Error bars represent one standard deviation of the experimental data, propagated with the uncertainty estimated for the BEB calculation. Prior to a comparison of our derived cross sections to those found in literature, we note the important contribution of multiple ionisation to the ion yields in this system. In many treatments of electron ionisation, single ionisation (one electron in, two electrons out) is considered the only channel and multiple ionisation is neglected. Our dataset allows the determination of the ion yield of the single, double, and triple ionisation channels. At low energies single ionisation is certainly dominant: we see that at 50 eV electron energy single ionisation accounts for 98 % of ions produced. As the electron energy increases the contribution of multiple ionisation to the ion yield increases as well. At 100 eV, single ionisation produces 87 % of ions, while double and triple ionisation contribute 12 % and < 1 % respectively. At 150 eV, single ionisation produces 81 % of ions, with 17 % and < 2 % due to double and triple ionisation respectively. At 200 eV, the maximum energy studied here, the maximum contribution of higher order ionisation also occurs, with 79 %, 18 % and < 3 % of ions produced being single, double or triple ionisation respectively. In these energy ranges, and potentially at higher ionization energy as well, the likelihood of an electron-PF 3 collision removing 2 or more electrons is up to 20 %. These figures should be noted in relevant models. As in previous work, where PS-PICS (relative or absolute) have been determined for a variety of small molecules, we see that considering just single ionisation in a description of the consequences of electron-molecule collisions is a poor description of the ion yield above the double ionisation energy. 16,33,58,59 There have been several previous investigations of the electron ionisation of PF 3 . However, no previous experimental determinations of the PICS following electron-PF 3 collisions are available in the literature. The appearance energies and relative intensities of ions following electron-PF 3 collisions were reported in 1975. 27 This early study did not detect the weak signals from F 2+ and F 2 + ions revealed in the current work, undoubtedly due to the greater sensitivity of modern instrumentation. The branching ratios between the monocationic products (F + , P + , PF + , PF 2 + and PF 3 + ) following electron ionisation at 70 eV were reported in an early mass spectrometric study by Torgerson and Westmore. 60 These ratios differ to those reported here, notably underestimating the relative yields of lower mass fragments and the highest intensity fragment, PF 2 + , by up to 50%, and overestimating the relative yields of dications by up to 600%. It appears likely in the earlier work that the apparatus may have discriminated against ions with high kinetic energy, leading to the under-reporting of the yields of atomic and low mass fragments. Such discrimination in early mass spectrometric investigations of dissociative ionisation has been noted before. 33,45,58,59 The appearance energies reported by Torgerson et al., 27 are for ionic products generated at or below 40 eV, and are not accessible in the current study.
A comparison of the results of the current study to previous theoretical determinations of the ionisation cross sections of PF 3 is possible. As noted above, Vinodkumar et al. 23 used the SCOP method to calculate elastic and inelastic electron scattering cross sections and from these data extracted the total ionisation cross section. 61 Vinodkumar et al. compare the cross section they extract to a total ionisation cross section calculated using the BEB method. Figure 5 clearly shows that there is good general agreement (within 10%) between the various calculated total ionisation cross sections, including that from the current work, particularly given the differences in methodology and basis sets. This uncertainty is well-represented by the uncertainty estimates on our BEB calculation, evaluated as described above.
Partial ionisation cross sections, directly comparable to the work here, have been calculated by Kumar using the Jain-Khare semi-empirical method (SEM). 29 Kumar considered the formation of PF 3 + , PF 2 + , PF + , PF 3 2+ , PF 2 2+ , P + , PF 2+ , F + , and P 2+ over electron energies from threshold to 1000 eV. No calculated values are available for the F 2 + and F 2+ ions. A comparison of Kumar's calculated PICS 29 with our absolute PICS are shown in Figure 6 and Figure 7.
For the higher intensity cations (Figure 6), the SEM method generates PICS in fair agreement with the experimental values but overestimates the yield of the PF 2 + cation and underestimates the PICS for PF 3 + and PF + . Figure 7 shows that the SEM calculations dramatically underestimate the PICS for P + , F + and P 2+ as well as reversing the relative intensities of F + and P 2+ with respect to P + . The calculation of the PICS by Kumar 29 uses the experimental differential optical oscillator strengths, extracted from (e,2e) spectra, reported by Au et al. 62 The optical oscillator strengths (from the (e,2e) data) for P 2+ formation are clearly less than that for P + , 62 supporting our experimental data in ratio order if not in intensity (Figure 7 right). In contrast, the current experimental findings indicating F + has lower yield than P + for all electron energies below 175 eV are not supported by the oscillator strengths. The reported oscillator strengths 62 and calculated 29 PICS report values for F + that surpass those for P + above 70 eV. Considering the good agreement of previous relative cross sections derived from our apparatus with experimental work from other groups, the ratio of F + to P + in our data is expected to be reliable. One cause for the disagreement could be that losses of the translationally energetic atomic fragment ions in the experimental spectra used for the extraction of the oscillator strengths could then have skewed the calculations. The fair agreement in the PICS for the heavier monocations, where ion losses due to translational energy effects are likely to be far less serious, support this conclusion.  into PF 2 + + F + , following ionisation at 75 eV electron impact energy. See text for details.
As noted above, the data we record in the pairs spectrum allows for the determination of the kinetic energy release of the charge-separating dissociation reactions following multiple ionisation; data of interest to ionospheric and plasma kinetic modelling 63 . The t B -t A data for the PF 2 + + F + pair, and the associated Monte Carlo simulation, used to determine the kinetic energy release for this channel are shown in Figure 8. The simulation reveals a KER of 3.4 ± 0.5 eV (at 75 eV ionising energy) for the formation of PF 2 + and F + . The pairs spectra indicate the threshold for PF 2 + + F + production is below 50 eV, the lowest electron energy accessed in this work. The "square" form of the t B -t A peak is readily modelled with a single KER indicating a single dissociation pathway dominates the formation of this ion pair.
As discussed above, E p (PF 3 2+ ), the energy of the dissociative dication precursor state forming the PF 2 + + F + , pair can be estimated from the KER. From heats of formation and ionisation energies 64 we determine the energy of the PF 2 + + F + asymptote, relative to the ground state of PF 3 , as E frag = 32.0 eV, assuming ionic formation in their vibrationless ground electronic states. Combining with the measured KER results in E p (PF 3 2+ ) = 35.4 ± 0.5 eV.

Computational investigation of PF 3 2+
To attempt to associate the precursor energy extracted above with a specific state of PF 3 2+ we have investigated the electronic structure of the dication computationally. The methodology employed has been discussed in Section 2.5. The geometries and energetics of the PF 3 0/+/2+ minima revealed by our calculations are listed in Table 2. The values for the PF 3 neutral can be used to assess the reliability and accuracy of our methodology. These values agree satisfactorily with higher level calculations and experimental data within a few tenths of a degree and a few hundredths of an Angstrom. 65,66,67 Early consideration of the ground-state geometry of PF 3 + involved some debate about the relative stability of D 3h and C 3v structures, before the pyramidal geometry was confirmed. 68 Theoretical work from 1973 66 indicated a C 3v structure with a bond length of 1.57 Å and a F-P-F angle of 109 o in reasonable agreement with our calculated values. More recent higher-level calculations generated a bond length of 1.50 Å and a F-P-F angle of 108.6 o . 69 The adiabatic ionisation energy (AIE) and vertical ionisation energy (VIE) of PF 3   The calculations reveal the ground state of PF 3 2+ , a closed shell singlet, is of a D 3h geometry. The lowest lying triplet dication state, calculated to lie 35.3 eV above the neutral, is in excellent agreement with the dication state energy determined from our experiments (35.4 ± 0.5 eV) hinting strongly that the triplet dication state is the source of the PF 2 + + F + pair, particularly given that the singlet ground state of PF 3 2+ lies markedly lower in energy ( Table 2). The other ion pairs we detect in our coincidence spectra, such as P + + F + and PF + + F + , exhibit complex coincidence peak shapes indicating multiple dissociation pathways and energy dependencies. Hence no attempt to extract the KER of these dissociation reactions was made.

Bimolecular collisions of PF 3 2+
Mass spectra following bimolecular collisions between PF 3 2+ and the neutral species Ar, Ne, CO and O 2 were recorded as described above. Figure 9 shows product ion peaks from a representative raw ("collision gas on") mass spectra for the PF 3 2+ /Ar collision system. Such spectra are processed as described above, and in the literature, 42 to reveal the product ions that result from bimolecular collisions (Table 3) by subtracting the, appropriately normalized, signals in mass spectra recorded with the collision gas off from those recorded with the collision gas on. 1.9 C + , O + , CO + F + , PF + , PF 2 + , PF 3 + As described above, the relative reactive cross sections, for the channels generating ions derived from the dication, can be derived by consideration of the detection efficiency of these products in our transverse experimental geometry as described by Burnside. 42 Such an analysis allows us to correctly compare the fluxes into these product channels for a given collision system. The results of this analysis are presented in Table 4 for interactions with Ar, O 2 and CO. The product ion signals for the Ne collision system are too weak to robustly support this additional processing and are discussed separately. Table 4 Relative reaction cross sections for producing various ionic reaction products from PF 3 2+ following collisions with Ar, O 2 and CO at the listed kinetic energies. The values are normalized to the cross section for forming PF 2 + (for each collision partner) and given in the form a(b) which represents (a ± b) where b gives the uncertainty. An asterisk indicates that the original ion intensity is sufficiently weak that the uncertainties introduced by the correction for the collection efficiency do not yield a robust value. See text for details.  Table 4 shows that formation of PF 2 + is the dominant product channel following collisions with Ar, O 2 and CO. PF 3 + is a minor product in all the collision systems. A PF + signal is observed following collisions with Ar, but there is a large uncertainty in the relative intensity of this signal due to the subtraction of comparable PF + signals in the "gas-off" spectra due to traces of this ion in the dication beam. Traces of F + are detected in all the collision systems. F 2 + formation is detected in the Ar collision systems, which are those having the highest collision energy.
The majority of product ions observed following collisions of PF 3 2+ with Ar, O 2 and CO ( Table 3, Table  4), result from single electron transfer. Although, the formation of PF 2 2+ following collisions with Ar and O 2 clearly originates from a collision-induced neutral loss (collision induced dissociation) channel. This collision induced channel is very weak in comparison with the electron transfer processes. For this reason the relative reaction cross sections for PF 2 2+ production were not included in Table 4. Similar collision-induced processes involving F atom loss from fluorinated dications have been previously observed for CF 3 2+ , SiF 3 2+ and SF 4 2+ . 8,71 Using the dicationic energetics reported in Table 2, we can determine (using literature values for the ionisation energies of the neutral targets 64 ) that single-electron transfer populating the ground state of the monocation from the ground state of the dication is exoergic for Ar (3.1 eV), CO (4.8 eV) and O 2 (6.8 eV) readily accounting for our observation of PF 3 + signals in these collision systems. Indeed, these exoergicities show that routes to the formation of PF 3 + will lie in the favoured (2-6 eV) exoergicity reaction window for efficient electron transfer for all three dication-neutral collision systems. 5 In addition to PF 3 + formation, it is clear from our data ( Table 4) that dissociative electron transfer (DET) is in fact the major product channel following these collisions: PF 2 + is the major product derived from the dication. In a DET process the nascent, and energised, PF 3 +* product of an initial electron transfer step subsequently dissociates into a daughter ion (e.g. PF 2 + +F). 5 Accessing the asymptotes for forming PF 3 + with sufficient internal excitation to allow dissociation to PF 2 + and PF + requires an extra 4.6 and 9.1 eV of internal energy to be deposited in the nascent PF 3 +* . This additional energetic burden makes these dissociative processes endothermic for collisions of the ground state of PF 3 2+ with Ar, and well-outside the reaction window for collisions with CO. It is important to note in the considerations of the energetics of these reactions that, in this collision energy regime, it has been shown that the long-range nature of the dicationic electron transfer process means that the translational energy of the collision system does not efficiently couple into the chemical energetics. 5 Thus, it is well established for this class of reactions, that processes with exoergicities outside the reaction window (2-6 eV exoergicity) are strongly disfavoured. 5  The formation of PF + , a minor channel, appears more significant in the more energetic collisions with Ar than with the molecules (CO,O 2 ) where the collision energy is lower. This observation strongly indicates that the formation of PF + is via a collision-induced fragmentation process, rather than electron transfer, perhaps fragmentation to PF + + F + +F. Figure 9 Representative section of a mass spectrum recorded following collisions of PF 3 2+ /Ar at T CM = 2.5 eV, highlighting single electron transfer and the significantly larger yield of PF 2 + than PF 3 + . See text for details. An inset (x20, 3 point smooth) shows signals attributed to ArF + Considering the PF 3 2+ /Ne collision system (Table 3), the product ion yields here are very low and no clear Ne + signals are detected. The absence of Ne + shows electron transfer is very weak in this collision system in accord with the endothermic energetics (exoergicity = -2.7 eV) where even the extra internal energy of the triplet dication only allows access to the very edge of the reaction window. Inefficient electron transfer from the triplet dication state is likely the source of the very weak PF 3 + signals, as our experimental geometry will make the detection of the small number of corresponding Ne + ions very inefficient. The traces of F + , PF 2 + and PF 2 2+ ions in this collision system almost certainly result from collision-induced charge separation or neutral loss. 8,71,76 As shown in Figure 9 we see weak signals corresponding to ArF + following collisions of PF 3 2+ with Ar. This weak ArF + signal exhibits a tail to longer flight times, the tail linking to the PF 2 + peak. Such tails have been observed before 77 in our experiments and associated with the metastable decay of dicationic collision complexes. Such a feature here is consistent with the decay of [Ar-PF 3 ] 2+ to ArF + + PF 2 + . Indeed, collision complexes have been identified as a key intermediate in the pathways to many bond-forming products generated in dication neutral collisions and ArF + has been observed before as a product following collisions of fluorinated dications with argon. 78 Supporting this mechanistic deduction is the fact our computational methodology identifies energetically accessible local minima corresponding to [Ar-PF 3 ] 2+ on both the triplet and singlet surfaces. The geometries and energetics of these collision complexes are given in the Supplementary Information. In other studies of dicationic bond-forming reactivity, where the operation of a mechanism involving dicationic complexation has been unambiguously demonstrated, 72 similar computational investigations have identified local minima corresponding to the corresponding collision complex.
In summary, where exoergic, dissociative single electron transfer from the neutral collision partner to PF 3 2+ dominates the ion yield in bimolecular collisions. The reactivity and energetics hint strongly that the first excited metastable triplet state of the dication is responsible for the bulk of the reactivity observed, with a minor contribution from the ground singlet state of the dication. When electron transfer is energetically disfavoured, weak collision-induced dissociation processes give some product ion flux. A small signal from a bond-forming process generating ArF + is observed from the PF 3 2+ /Ar collision system. Metastable features in the mass spectrum, and supporting calculations, implicate the involvement of a collision complex on the pathway to generating ArF + .

Conclusions
Absolute partial electron ionisation cross sections, and precursor-specific partial electron ionisation cross sections, for the formation of cations from phosphorus trifluoride (PF 3 ) are reported over the electron energy range 50 -200 eV. The absolute values are determined by the measurement of cross sections relative to the formation of PF 3 + using 2D ion-ion coincidence time-of-flight mass spectrometry and subsequent scaling using binary encounter-Bethe (BEB) calculations of the total ionisation cross section. This new dataset significantly augments the partial ionisation cross sections for electron ionization PF 3 found in literature, addressing previous discrepancies in the branching ratios of product ions, and provides the first values for the precursor-specific cross sections. Comparisons to calculated cross sections from the literature are encouraging, although there are discrepancies for individual ions. The coincidence experiments indicate that double and triple ionisation generate approximately 20 % of the cationic ionisation products at 200 eV electron energy. One metastable dication state, dissociating to PF 2 + + F + , is clearly identified as the lowest triplet state of PF 3 2+ and five different dications (PF 3 2+ , PF 2 2+ , PF 2+ , P 2+ and F 2+ ) are detected in the mass spectra. The cross sections reported will allow more accurate modelling of the role of the ionization of PF 3 in energetic environments. A first investigation of the bimolecular reactivity of metastable states of PF 3 2+ is also reported. In collisions with Ar, O 2 and CO dissociative single electron transfer dominates the product ion yield, whereas collision-induced dissociation of the dication is responsible for the small ion yields following collisions with Ne. Consideration of the energetics of these processes indicates the reactant dication beam contains ions in both the ground singlet state and the first excited triplet state. The deduction regarding the longevity of the triplet state is supported by metastable signals in the coincidence spectra. Weak signals corresponding to the formation of ArF + are detected following PF 3 2+ collisions with Ar, and experimental and computational considerations indicate this new chemical bond is formed via a collision complex.