Electron real intrinsic

The first attempt to describe the dynamics of dissociative electron transfer started with the derivation from existing thermochemical data of the standard potential for the dissociative electron transfer reaction, rx r.+x-,12 14 with application of the Butler-Volmer law for electrochemical reactions12 and of the Marcus quadratic equation for a series of homogeneous reactions.1314 Application of the Marcus-Hush model to dissociative electron transfers had little basis in electron transfer theory (the same is true for applications to proton transfer or SN2 reactions). Thus, there was no real justification for the application of the Marcus equation and the contribution of bond breaking to the intrinsic barrier was not established. 

The complex quantity, y6br = e (y(3)r) + i Im (x r), represents the nuclear response of the molecules. The induced polarization is resonantly enhanced when the Raman shift wp — ws matches the frequency Qr of a Raman-active molecular vibration (Fig. 6.1A). Therefore, y(3)r provides the intrinsic vibrational contrast mechanism in CRS-based microscopies. The nonresonant term y6bnr represents the electronic response of both the one-photon and the two-photon electronic transitions [30]. Typically, near-infrared laser pulses are used to prevent the effect of two-photon electronic resonances. With input laser pulse frequencies away from electronic resonances, y(3)nr is independent of frequency and is a real quantity. It is important to realize that the nonresonant contribution to the total nonlinear polarization is simply a source for an unspecific background signal, which provides no chemical contrast in some of the CRS microscopies. While CARS detection can be significantly effected by the nonresonant contribution y6bnr [30], SRS detection is inherently insensitive to it [27, 29]. As will be discussed in detail in Sects. 6.3 and 6.4, this has major consequences for the image contrast mechanism of CARS and SRS microscopy, respectively. 

A very different approach is the use of non-atom-centered basis functions such as plane waves. Due to their intrinsic periodic nature, they are mostly employed for electronic structure calculations of periodic solids [10]. A more recent development is the usage of real-space wavefunctions either by discretization on real-space grids or in a finite-element fashion [11], In a non-atom-centered basis, the basis set obviously does not depend on the atomic positions, which makes it ideally suited for ab initio molecular dynamics simulations, since the forces acting on the nuclei can be evaluated much more easily than in an atom-centered basis [10]. 

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