**3. Modification of electron capture and decay of transient anions in the condensed phase**

In principle, the formation and decay of TMAs of condensed molecules can be described using a modified gas‐phase picture. For molecular solids or sufficiently thick molecular films condensed onto a metallic substrate or a dielectric surface, the target molecules are unaffected by the substrate, and they exist in the physisorbed state [27]. This weak form of adsorption is characterized by a lack of a chemical bond between molecules, so that the electronic structure and vibrational frequencies of the condensed molecule are essentially unchanged from those in the gas phase [17, 27]. Conversely, electron–molecule scattering is modified in the condensed phase as well as the properties of TMAs [17, 20].

Low‐energy (0 – 30 eV) electrons have wavelengths comparable to the distance between molecules in condensed media. Hence, they interact within molecular solids via delocalized processes, predominantly including static and correlation interactions with neighboring molecules, excitation transfer, and coherent scattering [28–31]. Such conditions make it difficult to transfer electron scattering and attachment data from the gas phase to the condensed phase. Even though theoretical models have tried to approximate these processes, the resulting calculations differ substantially from the available experimental data [31–34]. For example, in the gas phase, the incoming electron wave function is a plane wave, whereas scattering events in the condensed phase are those of a diffracted electron wave function that depends on the ordering of the solid. It can be readily seen from Eq. (2) that this change in the partial wave content of the scattered electron wave modifies the capture cross section. Furthermore, *Γa* in Eq. (2) changes in the condensed phase, since new decay channels (e.g., phonon modes) appear and the TMA is formed at lower energy due to the polarization potential induced by the temporarily localized electron [17, 35] and possible lowering of the symmetry of the anion state [20]. The dash curve in **Figure 1** shows the lower energy of the potential‐energy curve of the condensed‐phase transient anion AB‾. The lower energy causes the curves AB and AB‾ to cross at a shorter internuclear distance *RC'* than that in the gas phase (*RC*). This leaves less time for autoionization of the TMA. In other words, the value of the integral in Eq. (3) becomes smaller, and *Ps* becomes larger. Moreover, lowering the potential curve of the TMA changes the number of decay channels. The intramolecular channels are decreased because of the lower TMA energy, but new intermolecular channels must be added to take into account decay into collective vibrations (phonon modes). Hence, the resonance lifetime may increase or decrease, and so the DEA cross section (i.e., the DEA intensity depends on the details of AB and AB‾potential‐energy curves and the number of decay channels). In addition, electron transfer from one molecule to another may occur, and hence provide additional decay pathways for TMAs [36]. For very large biomolecules, such as DNA, electron transfer between elemental subunits also impedes electron localization [35]. Hence, due to intramolecular electron transfer, the probability of TMAs forming on specific subunits can also be reduced.

2 a

b

(*R*)=ћ/ Г*a*(*R*), such that the survival probability of the TMA, after electron

*dt P exp <sup>R</sup>* (3)

ë û (2)

Ã

é ù ê ú

e

*AP E vC*

s

*s*

autodetachment, *τ<sup>a</sup>*

184 Radiation Effects in Materials

capture, is given by

biomolecular thin film).

**condensed phase**

phase as well as the properties of TMAs [17, 20].

<sup>Ã</sup> )=λ <sup>g</sup> <sup>χ</sup> (

where *λ<sup>e</sup>* is the de Broglie wavelength of the incident electron, *g* is a statistical factor, and χν is the normalized vibrational nuclear wave function. *Γa* and *Γ<sup>b</sup>* are the local energy widths of the AB‾ state in the F–C region and the extent of the AB‾ curve in the F–C region, respectively. The width of the transient anion state in the autodetaching region defines the lifetime *τa* toward

> 0 Ã( )

*R a*

where *R0* is the equilibrium bond length of the anion at energy *E* and *Rc* is the internuclear separation beyond which autodetachment is no longer possible. Hence, the DEA cross section depends exponentially on the lifetime of the TMA and the velocities of the fragments.

For further information on the mechanism of TMA formation and its effects on isolated electron–molecule systems, the reader is referred to previous works [15, 16, 22–26]. Information on resonance scattering from single layer and submonolayers of molecules physisorbed or chemisorbed on conductive surfaces can be found in the review by Palmer and Rous [20]. The following section provides information essentially on TMA formation in the condensed phase (i.e., in molecules in solids, condensed onto a dielectric surface or forming a molecular or

**3. Modification of electron capture and decay of transient anions in the**

In principle, the formation and decay of TMAs of condensed molecules can be described using a modified gas‐phase picture. For molecular solids or sufficiently thick molecular films condensed onto a metallic substrate or a dielectric surface, the target molecules are unaffected by the substrate, and they exist in the physisorbed state [27]. This weak form of adsorption is characterized by a lack of a chemical bond between molecules, so that the electronic structure and vibrational frequencies of the condensed molecule are essentially unchanged from those in the gas phase [17, 27]. Conversely, electron–molecule scattering is modified in the condensed

Low‐energy (0 – 30 eV) electrons have wavelengths comparable to the distance between molecules in condensed media. Hence, they interact within molecular solids via delocalized processes, predominantly including static and correlation interactions with neighboring molecules, excitation transfer, and coherent scattering [28–31]. Such conditions make it difficult

é ù = -ê ú ê ú ë û <sup>ò</sup> *Rc*

> The increase in DEA cross section resulting from the shift of the curve crossing point in **Figure 1** from *RC* to *RC'* can be illustrated experimentally by covering a metal surface with a multilayer film of a condensed rare gas and depositing a molecule on the film surface. As an example, **Figure 2** shows the result of such an experiment in which a 0.1 monolayer (ML) of CH3Cl was condensed onto a 20 ML thick Kr film [37]. The variation of a surface charging coefficient *As*, which is directly proportional to the absolute cross section (*μ*) for the reaction (1) recorded between incident electron energies 0 and 2.5 eV, is shown in the inset of **Figure 2**.

$$\text{e}^- + \text{CH}\_3\text{Cl} \rightarrow \text{CH}\_3\text{Cl}^- \rightarrow \text{CH}\_3 + \text{Cl}^- \tag{4}$$

Within this energy range there exists a single structure in the *AS* energy dependence, the maximum of which lies at approximately 0.5 eV for large Kr coverage. The peak denotes the energy of the TMA CH3Cl*‾*. As the Kr film thickness is reduced, the transitory CH3Cl‾ anion moves closer to the metal substrate, and the energy of the maximum in the inset lowers owing to the larger polarizability of the metal compared to Kr. The lower curve in **Figure 2** shows this shift in energy of CH3Cl*‾*with decreasing thickness. However, as the energy of transitory CH3Cl*‾* on the Kr film lowers, according to **Figure 1**, *RC'* becomes smaller and *PS* increases. Thus, as seen in the experimental curve with the full squares in **Figure 2**, the magnitude of the absolute cross section for Cl*‾*production at the peak values increases with decreasing thickness of the Kr film. When CH3Cl*‾* is formed too close to the metal substrate, the additional electron transfers to the metal, and *μ* sharply decreases.

**Figure 2.** CH3Cl*‾* formation and dissociation by electrons of 0–2.5 eV incident on submonolayer amounts of CH3Cl physisorbed on a multilayer film of Kr. (a) Variation of the charging coefficient of the film As due to CH3Cl*‾* dissocia‐ tion. (b) Variation with film thickness of: (■) the amplitude of the maximum in the charging cross section (*μ*); (‐·‐·) the amplitude of the maximum in *μ* calculated with the *R*‐matrix method [37]; (•) variation of the energy of maximum in *μ* and As; and (‐‐‐) a parametric fit of this maximum using the image charge model [38].

In the condensed phase, TMAs differ from their gas‐phase counterparts, in the following ways: (1) the electron energies required for their formation are usually lower by 0.5–1.5 eV, dependent on the local polarization of the solid and/or changes to the anion's symmetry; (2) due to their lower energies, they usually have fewer intramolecular decay channels, although, new intermolecular channels via electron emission into the dielectric may appear; (3) the lifetimes will be longer or shorter due to the changes in the number of decay channels, energy, and symmetry; (4) the initial electron capture probability, and the cross sections for decay into particular intermolecular and intramolecular excitations or for DEA may vary by orders of magnitude, as these are dependent on energy, intramolecular and intermolecular electron transfer, and symmetry. In summary, when a TMA is formed on a molecule located inside or at the surface of a molecular or biomolecular solid, its gas‐phase characteristics are usually considerably affected by the local environment.
