Spectroscopy external electronic perturbations

Before returning to the non-BO rate expression, it is important to note that, in this spectroscopy case, the perturbation (i.e., the photon s vector potential) appears explicitly only in the p.i f matrix element because this external field is purely an electronic operator. In contrast, in the non-BO case, the perturbation involves a product of momentum operators, one acting on the electronic wavefimction and the second acting on the vibration/rotation wavefunction because the non-BO perturbation involves an explicit exchange of momentum between the electrons and the nuclei. As a result, one has matrix elements of the form (P/ t)Xf > in the non-BO case where one finds lXf > in the spectroscopy case. A primary difference is that derivatives of the vibration/rotation functions appear in the former case (in (P/(J.)x ) where only X appears in the latter. 

The time-dependent theory of spectroscopy bridges this gap. This approach has received less attention than the traditional time-independent view of spectroscopy, but since 1980, it has been very successfully applied to the field of coordination chemistry.The intrinsic time dependence of external perturbations, for example oscillating laser fields used in electronic spectroscopy, is also expKdtly treated by modern computational methods such as time-dependent density functional theory, a promising approach to the efficient calculation of electronic spectra and exdted-state structures not based on adjustable parameters, as described in Chapter 2.40. In contrast, the time-dependent theory of spectroscopy outlined in the following often relies on parameters obtained by adjusting a calculated spectrum to the experimental data. It provides a unified approach for several spectroscopic techniques and leads to intuitive physical pictures often qualitatively related to classical dynamics. The concepts at its core, time-dependent wave functions (wave packets) and autocorrelation functions, can be measured with femtosecond (fs) techniques, which often illustrate concepts very similar to those presented in the following for the analysis of steady-state spectra. The time-dependent approach therefore unifies spectroscopic... 

In general, they can all be properly dealt with in the framework of perturbation (response) theory. According to the discussion in section 5.4, we may add external electromagnetic fields acting on individual electrons to the one-electron terms in the Hamiltonian of Eq. (8.66). Fields produced by other electrons, so that contributions to the one- and two-electron interaction operators in Eq. (8.66) arise, are not of this kind as they are considered to be internal and are properly accounted for in the Breit (section 8.1) or Breit-Pauli Hamiltonians (section 13.2). Although the extemal-field-free Breit-Pauli Hamiltonian comprises all internal interactions, such as spin-spin and spin-other-orbit terms, they may nevertheless also be considered as a perturbation in molecular property calculations. While our derivation of the Breit-Pauli Hamiltonian did not include additional external fields (such as the magnetic field applied in magnetic resonance spectroscopies), we now need to consider these fields as well. 

In this chapter, we review electronic structure in hydrogenlike atoms and develop the pertinent selection rules for spectroscopic transitions. The theory of spin-orbit coupling is introduced, and the electronic structure and spectroscopy of many-electron atoms is greated. These discussions enable us to explain details of the spectra in Fig. 2.2. Finally, we deal with atomic perturbations in static external magnetic fields, which lead to the normal and anomalous Zeeman effects. The latter furnishes a useful tool for the assignment of atomic spectral lines. 

Electroabsorption and electroreflectance have provided a sensitive and selective tool to study delocalized electron states in semiconductors (1). Singularities of the band structure, like band extrema respond particularly sensitive to electric fields and the corresponding optical transitions are clearly resolved even in case of low oscillator strength. In case of localized states, however, the external fields in the range of 10 kV/cm cannot compete with the much larger local fields and the field induced perturbation of optical transitions becomes unresolvable. This limitation qualifies electromodu-lated spectroscopy as a selective tool to study delocalized states in organic crystals. 

Electron spin resonance spectroscopy is formally similar to NMR if one considers an unpaired electron as taking the role of a spin -1/2 nucleus in an NMR experiment. However, because of the much greater size of the electron magneton (the Bohr magneton) versus the nuclear magneton, much weaker external fields are employed in order to observe transitions with radiofrequency radiation. As a result, coupling interactions between the electron and magnetic nuclei may require a treatment beyond that of first-order perturbation theory. 

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