the process takes place and also on calculating the cross sections and rate constants of these ultrafast processes [16–18]. In a way, we can visualize DEA process as an electron-molecule scattering phenomenon popularly studied using advanced quantum mechanical principles. As discussed earlier, implementing quantum approach to examine the characteristics of resonant electron attachment process in simple diatomic molecules is quite accomplished. However, as the complexity of the target molecules increases it may possess several TNI states and in such cases, it is very difficult to employ the quantum approach to deduce the features of resonant electron molecule scattering effectively. It is also to be noted here that if a given
"resonance" is associated with different decay channels, it is even more difficult to calculate the DEA cross sections using ab initio electronic structure methods and quantum dynamical calculations. A more detailed description of DEA process or theresonant electron molecule scatteringprocess in quantum viewpoint is given in the next section.
1.4 Electron molecule scattering theory: A quantum ap- proach
Electron-molecule scattering phenomenon is widely used to identify the metastable contin- uum states associated with physical and chemical processes like energy exchange between electronic and nuclear motions, electron transport, and so forth. In electron-molecule scat- tering theory, "resonance" is referred as an electron-impact scattering phenomenon which involves the formation of a TNI [20]. During resonance, the projectile becomes temporarily trapped in the vicinity of the target molecule and the energy at which resonance occurs is commonly referred to as the "resonance energy" [21]. Resonance take place when the incoming electron gets attached by a virtual molecular orbital. The captured electron may re-emit (autoionize) after a time, typically within 10−15 s to 10−12s which is substantially longer than the transit time for unhindered propagation across the molecule [20]. In short, we can consider this electron-scattering phenomenon as the formation of a short-lived negative ion, since the molecule acquires an extra electron during this process and the compound state
8 Introduction posses a finite lifetime. Theoretical considerations manifest the formation of the short lived negative ion as a "characteristic peak" or "resonance" in the scattering cross section. Thus, this phenomenon is also termed as "resonance electron scattering" [20, 21]. It should be noted here that the terms likeresonance, temporary negative ion, and compound stateused throughout in this dissertation is referring to the same physical entity.
1.4.1 Feshbach and Shape resonance
Molecular negative-ion resonances are traditionally divided into two categories,Shapeand Feshbach resonances [20, 21, 23]. Let us briefly consider, on account of the electronic configuration of a generic TNI, what these entities are. If aresonant stateis produced without causing any variation in the electronic configuration of the target molecule, then a "one"
particle resonance is formed. This can be treated simply as the addition of an electron into the virtual molecular orbital of the target involved during the collision. Whereas, in some cases the extra electron does perturb the electronic configuration of the target molecule during resonance formation popularly known as the so-called "two-particle" resonance, or "core-excited" resonance. In a two-particle resonance, the energy of TNI (M∗− in the Fig. 1.2) can be either above or below the energy of the corresponding electronically excited target molecule (M∗). If the energy of M∗− is greater than that of M∗, then the TNI corresponds to an open-channel resonance. The other category falls into the closed-channel core-excited resonance, also known aselectronic Feshbachresonance. Feshbach resonances are characterized by their inability to decay directly into the ground electronic state (M).
From Fig. 1.2, it is clear that such a transition requires long lifetime since it needs more time to rearrange the electronic configuration. Let us now consider both the one-particle resonance and open channel core-excited resonance. In either of the two cases, the incoming electron gets trapped in to the effective potential formed via the interaction between the incident particle and the target molecule. The shape of the potential allows the particle to remain inside the barrier. The TNIs formed this way are termed asshaperesonances. From the Fig.
1.3, it is clear that the projectile will experience an attractive potential in those spatial regions where the molecular mass is centered. This region is surrounded by a region of repulsive
1.4 Electron molecule scattering theory: A quantum approach 9
Fig. 1.2M, M∗are the neutral species at their ground and excited state respectively. M− and M∗− are displayed schematically to illustrate the formation of resonances such as Shape, Feshbach, and core-excited open channel resonances [20, 21, 23].
Fig. 1.3Potential energy curve representing the dynamical trapping of an incoming particle.
E0is the kinetic energy of the projectile. ’r’ is the internuclear distance. Since the shape of the potential is responsible for the formation of a resonance state, this type of resonance is known as Shape resonance [23].
10 Introduction potential. The particle initially trapped inside the barrier may tunnel through depending upon it’s kinetic energy. There comes a situation when a combined action of both the attractive and repulsive regions prevent the particle’s re-emission (also called autodetachment) at least for the time necessary for the TNI to be experimentally detected.
1.4.2 Overview of the resonance scattering process
In summary, the physics of the "resonant electron-molecule scattering" process [23] can be collectively classified into the sequence of the following stages:
(i)Capture:- The processes responsible for the formation of the negative ion state. It consists the mechanism by which the projectile gets trapped into the target molecule.
(ii)Dynamics:- The distortion take place within the target molecule after the attachment of the incident particle. This stage comprises events like excess energy transfer or redistribution within the host molecule, or some rearrangement within the compound system. All these processes take place within the lifetime of the resonance.
(iii)Detachment:- This stage attributes all those processes responsible for the decay of the metastable state formed in stage 1.