The TPEPICO has good resolution, however it has one major disadvantage. This disadvantage is that the threshold detector is contaminated with hot electrons that manage to make it close enough to the center due to the simplistic nature of a line of sight analyzer that differentiates hot from threshold electrons only by angular divergence.41 One attempt to correct for this error was to use velocity-focusing optics. This was set up so that the electrons were separated from the molecule and passed through two acceleration regions and then through deflection plates. The
electrons are thus electrostatically focused so that the zero kinetic energy electrons focus towards the center of the plate and the energetic “hot” electrons are focused on the rings around the center.42
Fig. 2.4.7: Setup of TPEPICO velocity focusing optics technique.42
This setup allows for subtraction of the hot electrons and therefore noise suppression creating a cleaner TOF spectrum.42 Building on this technique, the idea to use of imaging on the electrons was considered so that it would be possible to analyze the whole photoelectron spectrum from 0 to about 1 eV, which can be collected and then visualized to aid in the subtraction of the hot electrons. This technique was installed in an apparatus termed the “iPEPICO” (imaging photoelectron photoion coincidence) at the Paul Scherrer Institut’s VUV beam line in the Swiss Light Source facility in Villigen, Switzerland.41 The iPEPICO acts as a cross between the PEPICO and TPEPICO setups, to compromise between the disadvantages of both methods with dispersive electron kinetic energy analyzers. The analysis of the electron kinetic energy and the ion TOF analysis are taken simultaneously.41 The advantage of crossing these two together is that it allows for both the higher collection efficiency of the TPEPICO with the higher extraction fields of the PEPICO.41 Then,
high TOF spectra resolution due higher extraction fields along with a electron kinetic energy analysis with a resolution of better than 1 meV.41
2.4.4: The miniPEPICO Modeling Program
As seen in figure 2.4.1 in subsection 2.4.1, it is possible to model a theoretical breakdown diagram to try to match to experimental data using the miniPEPICO program, developed by Professor Bálint Sztáray and others.43 The program is capable of modeling the dissociative photoionization in the TPEPICO and iPEPICO experimental apparatuses by computing: the thermal energy distribution of the neutral molecule, the energy distribution of the molecular ion as a function of photon energy, and the resolution of the experiment. It is possible to model both parallel and consecutive dissociation paths and from this, is able to reproduce experimental breakdown curves and TOF distributions.43
The breakdown diagram is the fractional ion abundances as a function of the photon energy, which is modeled using the calculated ion energy distributions and the dissociation rates. For a fast, single dissociation all ions that have more energy than the dissociation limit will dissociate and lead to the fragment ion observed, so the ratio of the parent ion may be given as:43
𝐵𝐷(ℎ𝜈) = tL¶0yL𝑃d(𝐸, ℎ𝜈) 𝑑𝐸
8
(𝐸𝑞𝑛. 2.4.6𝑎) where Pi is the normalized internal energy distribution of the parent ion given as a function of the internal energy at a given photon energy. However, for a slow dissociation, not all ions with enough energy to dissociate may do so within the timescale of the experiment. This leads to what is known as a “kinetic shift”. This means another term must be added to equation 2.4.6a to account for the ions that are not able to dissociate within the maximum time an ion has to dissociate in to be recorded as a fragment ion (τmax):43
𝐵𝐷(ℎ𝜈) = t 𝑃d(𝐸, ℎ𝜈) 𝑑𝐸 L¶0yL 8 + t 𝑃d(𝐸, ℎ𝜈) ∗ exp(−𝑘(𝐸) ∗ 𝜏HŒ>) 𝑑𝐸 (𝐸𝑞𝑛. 2.4.6𝑏) §∞ L¶0yL
where k(E) is the internal energy-dependent rate constant. This allows the fragment ion fractional abundance to be:43
𝐵𝐷pºŒ»H•IŠ(ℎ𝜈) = t§∞ 𝑃d(𝐸, ℎ𝜈) ∗ (1 − exp(−𝑘(𝐸) ∗ 𝜏HŒ>)) 𝑑𝐸
L¶0yL
(𝐸𝑞𝑛. 2.4.6𝑐) When trying to model a parallel dissociation, the breakdown curve for some fragment ion ‘i’ is:43
𝐵𝐷d(ℎ𝜈) = t 𝑃d(𝐸, ℎ𝜈) ∗ 𝑘d(𝐸) ∑ 𝑘½ ½(𝐸)¾1 − 𝑒𝑥𝑝 —− r 𝑘½ ½(𝐸)𝜏HŒ>˜¿ 𝑑𝐸 §∞ L¶0yL (𝐸𝑞𝑛. 2.4.6𝑑) where NÀ(L)
∑ NÁ Á(L) are the branching ratios at a particular ion internal energy.
43
TOF distributions are used to determine the experimental dissociation rates.43 Figure 2.4.8 shows an example of a TOF model. In figure 2.4.8 the green dots represent experimental TOF distributions with the red line passing through being the computed TOF distribution. The fragment ion peak shape may be computed by the following formula:43
𝐹𝑟d(ℎ𝜈) = t 𝑃d(𝐸, ℎ𝜈) §∞
L¶0yL
∗ lexpl−𝑘(𝐸) ∗ 𝜏(𝑇𝑂𝐹d)m − expl−𝑘(𝐸) ∗ 𝜏(𝑇𝑂𝐹d§†)mm𝑑𝐸 (𝐸𝑞𝑛. 2.4.7) where Fri(hv) is the normalized height of the fragment ion peak in channel i at a given energy, P(Ei, hv) is the internal energy distribution of the parent ion, and τ(TOFi) is the τ value that corresponds to the time of flight of channel i.43
Fig.
2.4.8: An example of a TOF distribution in the miniPEPICO program.43
The dissociation rates may be modeled by using one or more of the three unimolecular rate theories implemented in the program: RRKM theory, VTST (variational transition state theory), and the simplified adiabatic channel model (SSACM). In all of the rate theories the usual transition state theory expression may be employed to obtain the dissociation rates:43
𝑘(𝐸) =𝜉𝑁‡(𝐸 − 𝐸8)
ℎ𝜌(𝐸) (𝐸𝑞𝑛. 2.4.8) where 𝑁‡(𝐸 − 𝐸
8) is the sum of the states of the transition state, 𝜌(𝐸) is the parent ion density of