Temporary anion resonance

Finally, this chapter covers not just bound-state methods but also methods that can safely be applied to metastable anions (i.e., temporary anion resonances), which is a far less mainstream topic. For metastable anions, the emphasis of this chapter is on those methods that have been implemented in standard quantum chemistry codes and are therefore widely available to the chemistry community. 

Anions that are formally unbound but metastable can be chemically important. These temporary anion resonances are discussed in detail later... 

Assuming that the products R + R are lower in energy than the reactants (Rj - R2 plus an infinitely separated electron), then the intermediate species (Rj - R2) is a temporary anion resonance, since the bound-state configuration of moieties Rj, R2, and an extra electron is R -l-R, not the anion (Rj -R2) . Whether reaction [1] will occur in practice depends sensitively on the barrier(s) and nonadiabatic couplings involved in the second step (nonadiabatic transition to the dissociative a state), as well as the energy of the incident electron, which controls whether the temporary anion resonance can be accessed or not. 

This section defines and explains some basic chemical and quantum-mechanical concepts concerning anions. Bound anions (where M is lower in energy than M, at the minimum-energy geometry of the former) are considered first, and subsequently we discuss metastable anions, also known as temporary anion resonances. For easy reference, a list of acronyms is provided at the end of this chapter. 

The discussion earfier implicitly assumes that the anion M is bound, that is, lower in energy than the neutral molecule Mat the geometry of M . At the heart of dissociative electron detachment, however, are temporary anion resonances that are metastable only with respect to autodetachment. This is the case, for example, when the anion M is formed at the neutral molecule s geometry in the example depicted in Figure 1. Flere, the anion is higher in energy at the neutral molecule s most stable geometry. 

To motivate the discussion of temporary anion resonances, we first discuss the basic quantum mechanics of the resonance phenomenon, using a piecewise constant potential that facilitates analytic results. This is a standard graduate-level quantum mechanics exercise, but the results should be qualitatively informative to readers who have not seen them. 

Temporary anion resonances can be broadly classified according to two criteria. First, does the electron attach to the ground state of the molecule M, or is M excited in the process If M remains in its ground state, then the resonance is classified as a single-particle resonance, since excitation of M s electrons can be ignored in a quaHtative treatment. In contrast, a core-excited or target-excited resonance involves electronic excitation of M, for example. 

For temporary anion resonances, VAEs can be measured experimentally by means of electron transmission spectroscopy, " in which an atomic or molecular sample is bombarded by a beam of electrons having well-defined kinetic energy. A change in current, due to attenuation of the electron beam, can then be detected as the kinetic energy of the electrons is tuned through a resonant VAE. 

In this section, we discuss the ways in which weakly-bound anions place special demands on quantum chemistry calculations. It is presumed, in this discussion, that the anion M is a bound species (VDE > 0) at the molecular geometry in question, such that the application of bound-state quantum chemistry methodology is appropriate. Referring to the situation in Figure 1, bound-state methods are appropriate for the description of the anion AB only for R > R. For R < R, the neutral molecule is lower in energy, and application of bound-state methods to M is not appropriate. Electronic structure methods for temporary anion resonances are discussed later in this chapter. 

That said, and while KT EAs do still find some utility in stabilization calculations of temporary anion resonances (as discussed later in this chapter), for bound states of M there is little reason to rely on KT since Hartree-Fock calculations are nowadays computationally facile on large molecules, often in large basis sets. It is therefore easy to compute a ASCF value for the EA, which includes the effects of orbital relaxation, simply by computing separately the Hartree-Eock energies of M and M , assuming that the latter is bound. (If it is not, then neither the KT nor the ASCE value of the EA is reliable.) This raises an important point, namely, that one obtains a positive EA from KT only when lumo < for very weakly-bound anions there may be... 

As compared to the MOM approach discussed earlier, other methods for treating metastable states are somewhat more involved, and understanding them requires a few concepts that go beyond bound-state quantum mechanics. One idea that is needed is the notion of analytic continuation of the bound-state energy levels into the complex plane. A heuristic explanation of why this is necessary goes as follows.In some ways, a temporary anion resonance resembles a stationary state of the molecular potential, at least in the sense that the probability distribution is relatively localized around the molecule (see Figure 13). At the same time, however, the resonance has a finite lifetime and will ultimately tunnel out of the potential that is responsible for it. In view of these facts, it... 

The CCR idea has been around for a long time, as reviewed in Refs. 389 and 391, and many applications to temporary anion resonances have been reported. Nevertheless, this technique has remained somewhat specialized. Within the context of electronic structure theory, what is required for a CCR calculation is to combine the complex-scaled Hamiltonian in Eq. [63] with the usual wave function ansdtze, and this involves extending quantum chemistry codes to handle complex-valued wave functions and energies and non-Hermitian matrices. CCR implementations of the Hartree-Fock, configuration interaction, and multiconfigurational SCF (MCSCF) models have been reported but are not available in standard... 

Table 9 Resonance Energies and Widths (Both in eV) for the Lowest Temporary Anion Resonances of Uracil...

While CCSD(T), MP2, DFT, and so on are appropriate for bound anions, theoretical description of metastable anions requires specialized techniques. Many of these techniques are well-established but have seen far less use as compared to bound-state quantum chemistry. In this chapter, we have discussed a variety of techniques (the maximum overlap method, CCR, and stabilization methods) that are all based, at some level, on modifications to bound-state quantum chemistry that can be implemented as reasonably straightforward modifications of standard bound-state quantum chemistry codes. It is this author s hope that this review of such methods for temporary anion resonances will prompt renewed and increased interest in these techniques. 

The orbital <[>res is a resonant orbital, in which a hot electron is attached to form a temporary anion. We assume that desorption is triggered by single orbital resonance to ([>res through an extension to multi-resonant levels is straightforward. The term n) is the occupation of the electron in the ground state, and is required to keep the Pauli principle. The coefficient r eN is the reactive eN coupling factor and assumed to be... 

The relevance of the above kind of electronic shape resonance to chemistry Is twofold. First, In environments such as plasmas, electrochemical cells, and the ionosphere, where free electrons are prevalent, the formation of such temporary anions can provide avenues for the free electrons to "cool down by transferring kinetic energy to the Internal (vibrational and/or electronic) degrees of freedom of the fragment. (6-14) Second, metastable states may play Important roles in quenching excited electronic... 

Temporary anion states may be broadly classified either as shape resonances or core-excited resonances (4). The former are well described by a configuration in which the impacting electron attaches to an atom or molecule in one of the originally unoccupied orbitals. In the latter, electron capture is accompanied by electronic excitation, giving rise to a temporary anion with a two-particle-one-hole (2p-lh) configuration. One can further distinguish core-excited resonances into those In which the resonance lies energetically below its parent state and those in which it lies above. The former are referred to as Feshbach resonances and the latter as core-excited... 

In spite of these developments. It Is important to realize that ETS provides no Information on the decay channels of temporary anions. Further progress toward a detailed understanding of resonances In complex molecules will require careful studies of the vibrational levels and electronically excited states of the neutral molecule which are formed upon electron detachment. These measurements provide essential data related to the electronic configuration of the anion and the distortion It undergoes during its lifetime. 

Dissociative attachment can be divided into resonant and nonresonant cases. The resonant case is fairly amenable to theoretical treatment (Bardsley et ai, 1964 O Malley, 1966). In that case, the dissociation process can often be well modeled semiclassically in terms of the lifetime of the temporary anion and the survival probability for it to move fl om the geometry at which attachment occurs to the point beyond which the anion is more stable than the neutral. While a fully detailed theoretical treatment can be complex (O Malley, 1966), the minimal ingredients to form a useful estimate of the cross section are an anion potential energy surface and a resonance lifetime or width, each of which can be computed in a fairly straightforward manner. 

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