Resonance state region

Fig. 1. The Marcus parabolic free energy surfaces corresponding to the reactant electronic state of the system (DA) and to the product electronic state of the system (D A ) cross (become resonant) at the transition state. The curves which cross are computed with zero electronic tunneling interaction and are known as the diabatic curves, and include the Born-Oppenheimer potential energy of the molecular system plus the environmental polarization free energy as a function of the reaction coordinate. Due to the finite electronic coupling between the reactant and charge separated states, a fraction k l of the molecular systems passing through the transition state region will cross over onto the product surface this electronically controlled fraction k l thus enters directly as a factor into the electron transfer rate constant...

It was noted earlier that the charge density of a narrow resonance band lies within the atoms rather than in the interstitial regions of the crystal in contrast to the main conduction electron density. In this sense it is sometimes said to be localized. However, the charge density from each state in the band is divided among many atoms and it is only when all states up to the Fermi level have contributed that the correct average number of electrons per atom is produced. In a rare earth such as terbium the 8 4f electrons are essentially in atomic 4f states and the number of 4f electrons per atom is fixed without reference to the Fermi level. In this case the f-states are also said to be locaUzed but in a very different sense. Unfortunately the two senses are often confused in literature on the actinides and, in order not to do so here, we shall refer to resonant states and Mott-localized states specifically. 

This is the manner at which the wave packet in Section 2 evolves just outside the interaction region as portrayed in Figure 1.7 and Eq. (23), where rj(t) = e rt/2 A . There we got that the exponential increase of the amplitude goes exactly as the imaginary part of the complex momentum of the stationary state = Im[kres] = 0.0048[a.u.]. This shows that even outside the barriers, there is a region where the evolution is similar to that of the stationary resonance state. 

The decay of Nal can be described in an alternative way [K.B. Mpller, N.E. Henriksen, and A.H. Zewail, J. Chem. Phys. 113, 10477 (2000)]. In the bound region of the excited-state potential energy surface, one can define a discrete set of quasi-stationary states that are (weakly) coupled to the continuum states in the dissociation channel Na + I. These quasi-stationary states are also called resonance states and they have a finite lifetime due to the coupling to the continuum. Each quasi-stationary state has a time-dependent amplitude with a time evolution that can be expressed in terms of an effective (complex, non-Hermitian) Hamiltonian. 

The bottleneck of very short lifetimes of resonace states (10 14s) becomes less severe once one assumes that the primary role of resonance states is to provide doorways to bound valence anionic states, with lifetimes determined by kinetics of the following chemical reactions [36], The reactions might proceed on these regions of potential energy surfaces, at which valence anions are bound with respect to the neutral species. The rates of these chemical transformations, e.g., the SSB formation, do not have to compete with short lifetimes of resonance states. It is worth noting that even for a kinetic barrier of ca. 20 kcal/mol, the half lifetime amounts (at 298 K) to about 30 seconds. Hence, if the kinetic barrier for SSB formation were lower than 20-23 kcal/mol, all nucleotides that could form stable anions would have enough time to cleave the C-O bond on the timescale of the electrophoretic assay of DNA damage. 

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