2.1. The Ionization Potential
The most important parameter for electron-induced chemistry is very often the ionization potential, IE
, of a substance. Values for most chemical compounds can be found in the literature or in databases such as the NIST Chemistry Webbook [7
]. There exist a number of theoretical approximations that describe the energy dependence of the ionization cross-section, starting from IE
. The most commonly used one is the Binary Encounter-Bethe (BEB) model [8
], which takes a number of molecular parameters as input, all of which are quite easily accessible by quantum chemical calculations. Together, the IE
as onset and σBEB
as the energy dependence, give an accurate prediction of the ionization probability by electron impact. For energies that are not greater than IE
by more than a few eV, no significant fragmentation of the molecular compound is observed. This is referred to as ‘soft ionization’. If the formed cation undergoes a chemical reaction, IE
should give an accurate prediction of the energy dependence of product yields.
depicts the calculated formation cross-section of ethylamine from the net reaction
which is triggered by electron impact ionization of either ethylene (C2
) or ammonia (NH3
), as well as experimentally obtained data of the amount of ethylamine actually produced. Upon inspection of the data, two things are very clear: (1) There is considerable product formation at energies below the predicted threshold; and (2) product formation reaches saturation between 10 and 12 eV, even though there is a predicted increase at higher energies.
The second observation is explained more easily. The very simple kinetic model used here is based on the assumption of initial rates, i.e., that use of starting materials is negligible. It also neglects any product degradation by the electron beam. The first observation, the shift in energy, however, is not explained by such omissions in the modeling. The data used for the prediction was obtained in the gas phase, where produced cations do not feel any influence of other molecules. In the condensed phase, the energy of the cation is lowered by the polarization of the surrounding medium, which leads to a lowered ionization potential. This is an effect universally observed in experiments with ions in the condensed phase. The shift is usually around 2 eV [12
The gas phase data for ionization potentials, although widely available, is not directly applicable to condensed-phase chemistry, because of the energy shift that ensues when ions are stabilized by polarization of a matrix.
2.2. DEA Cross-Sections
When dealing with electrons with an energy below the ionization threshold of a substance (gas phase IE
minus approximately 2 eV), the most discussed process that leads to chemical reactions is DEA. The formed radical anions are highly reactive and the specificity with which bonds can be cleaved allows for very precise reaction control. This makes DEA a powerful tool in a chemist’s toolbox. Fortunately, there is some data available on EA and subsequent fragmentation channels, at least for small molecules like water [15
], ammonia [16
], carbon monoxide [17
], and carbon dioxide [18
] Here, the same caveats as in IE
data apply: The process forms an ionic species, which is stabilized by polarization and thus the energy at which these processes are observed is lowered with respect to the gas phase. The predictions of fragmentation patterns and especially about where the charge and the radical site end up, nevertheless are very valuable when trying to untangle a reaction mechanism.
Rawat et al. [19
] measured absolute DEA cross-sections in ammonia and found two energies at which DEA occurs. At the lower of the resonances, centered around 5.5 eV, cross-sections for the formation of NH2−
(and by extension H*) were determined to around 1.6 × 10−18
, while the formation of H−
* was observed with a cross-section of 2.3 × 10−18
. At the higher resonance, centered around 10.5 eV, the cross-sections were 1 × 10−19
and 5 × 10−19
. This data helped a lot in understanding the formation of formamide (H2
NCHO) from the electron irradiation of mixed CO:NH3
ices in a reaction like,
The energy dependence of formamide production shows a resonance with a maximum between 8 and 9 eV (Figure 2
). This resonant shape and product formation observed at energies as low as 6 eV pointed to DEA as the initial electron–molecule interaction process.
The reaction could proceed via either the NH2
* radical or the H*
radical attaching to carbon monoxide. The formed intermediate radicals *H2
NCO or *HCO could then go on to form formamide after reaction with another molecule of ammonia. However, neither of the two radicals could be observed experimentally, since both are very short-lived species thanks to their extremely high reactivity. In cases like this, the reaction mechanism can often be inferred by looking at the side-products of the reaction. If the reaction proceeds via the *H2
NCO radical, one side-product would be formed by addition of another amino-group (–NH2
) rather than an –H. This would form the molecule urea ((H2
CO). If the reaction proceeds via the *
HCO radical, the corresponding side-product would form by addition of –H rather than –NH2
, leading to formaldehyde (H2
CO) (see Figure 3
). The gas phase data by Rawat et al. [19
] predicts a ratio of 5:1 urea:formaldehyde. The experiment, however, shows absolutely no trace of urea at all, while formaldehyde is formed in about the same quantity as formamide. This is a very strong indication that the reaction proceeds via the channel that is less favorable in the gas phase. This could be due to a perturbation of the electron structure with respect to the gas phase, which is caused by close proximity to other molecules. In the case of water ice, it has been shown that DEA energies can shift with film thickness and temperature and thus film structure, and can even be higher than in the gas phase [21
]. These changes to electronic structure can very well have an influence on electron affinity of the fragments and thus on branching ratios for anion formation.
Data on DEA in the gas phase can thus predict which reaction channels are possibly open in condensed-phase chemistry. They need to be corrected in terms of energy due to stabilization of ions and absolute cross-sections seem to be no reliable indication of which channels are actually most active in condensed-phase chemistry, but they do give a prediction of what possible reaction products could look like.
2.3. Prediction of Possible Reaction Routes
In the last example of this paper, the reaction of ethylene and water to form ethanol,
shall be described. It is the analogous reaction to the formation of ethylamine from Section 2.1
, and above the ionization threshold, the reaction indeed proceeds in much the same way, with only the NH3
replaced by H2
O. Below the ionization threshold, however, there is also some formation of ethanol, especially at energies below 4 eV. Figure 4
depicts the experimental data as well as some σBEB
-based predictions for the formation via EI above the ionization threshold.
There is obviously some significant process at work at very low energies. Since this was not observed in the case of ethylene + ammonia, but is observed in ethylene + water, ostensibly DEA to water must be responsible. DEA cross-sections of water were reported by Curtis et al. [23
]. Their data, unfortunately, shows the lowest resonance centered around 6.5 eV, with absolutely nothing happening below 5 eV. While this needs to corrected for stabilization of the ion, a shift of around 4 eV cannot be explained in this way, ruling out DEA to water as the initiating step in the reaction. DEA cross-sections to C2
have also been reported, by Szymańska et al. [24
], but in much the same way as in water, no anion formation was observed below 6 eV. The only process that is known to occur is a non-dissociative electron attachment to water at around 1.5 eV. It produces the short-lived C2
* radical anion, which quickly decays by auto-detachment (loss of the electron). It is not readily apparent why this process should lead to product formation in the case of ethanol, but not in the case of ethylamine. This conundrum was resolved by looking at the chemistry of the C2
* radical anion. It is a strong base and will quickly abstract a proton from a nearby water molecule when embedded in a water ice matrix. The formed ethyl radical *C2
cannot decay back and is thus available for driving the reaction to ethanol. This is not possible with the much less acidic ammonia. This type of process can of course not be captured by gas phase experiments, where great care is taken to eliminate contaminants such as water, and where molecular beams are tuned so as to exclude interactions between molecules.