Electronic absorption spectroscopy wave functions

Electronic absorption spectroscopy charge transfer transitions, 19 71 d-d transitions, 19 70, 71 flavocytochrome b, 36 269-271 intraligand transitions, 19 71-80 of organometallics, 19 69-80 Electronic coupling, between donor and acceptor wave functions, 41 278 Electronic nuclear double resonance spectroscopy, molybdenum center probes, 40 13... 

The cross section a is a fundamental property of the molecule and as such is related to the molecular wave functions for the two states between which a transition is induced. Hence it is desirable to separate the contributions to a that arise from purely kinematic quantities such as the impact energy of the electron beam from those that depend solely on the properties of the molecule. To this end, a dimensionless quantity, the oscillator strength, is introduced in optical absorption spectroscopy, defined by the relation22... 

Deviations from OGM were recognized early on spectroscopic properties of molecular crystals Davydov shifts and splittings of absorption bands in molecular crystals are clear deviations from OGM and were rationalized based on the excitonic model (EM) [10, 14, 15, 16, 17]. This same model proved extremely successful to describe the complex and technologically relevant spectroscopy of molecular aggregates, i.e. of clusters of molecules that spontaneously self-assemble in solution or in condensed phases [IS]. Much as it occurs in molecular crystals, due to intermolecular electrostatic interactions the local bound electron-hole pair created upon photoexcitation travels in the lattice and the corresponding wave function describes an extended delocalized object called an exciton. We explicitly remark that the Frenkel picture of the exciton, as a bound electron-hole pair, both residing on the same molecule, survives, or better is the basis for the excitonic picture. The delocalization of the exciton refers to the fact that the relevant wave function describes a Frenkel exciton (a bound e-h pair) that travels in the lattice, and this is of course possible even when electrons and/or holes are, separately, totally localized. In other terms, the EM describes localized charges, but delocalized excitations. 

George SD, Metz M, Szilagyi RK, Wang HX, Cramer SP, Lu Y, Tolman WB, Hedman B, Hodgson KO, Solomon EL 2001. A quantitative description of the ground state wave function of Cua hy x-ray absorption spectroscopy comparison to plastocyanin and relevance to electron transfer. J Am Chem Soc 123 5757-5767. 

Let us now introduce the standard Born-Oppenheimer separation by which molecular states are written as a product of an electronic wavefunction depending parametrically on the nuclear coordinates J/j (Q,q) and a purely vibrational wave-function X/v(Q)- This is also done in Chapter 8, but we repeat this treatment with the aim of highlighting its consequences on the system TDSE. Once more we remind the reader that, since the focus here is on condensed-phase spectroscopy, we do not consider the role of molecular rotations, whose contributions to the absorption spectra can be detected only in high-resolution experiments. It is worthwhile to note, however, that they could be included in the time-dependent approach studying the propagation of suitable rovibronic wavepackets. 

Tensor representations, synonymous for product representations and their decomposition into irreducible constituents, are useful concepts for the treatment of several problems in spectroscopy. Important examples are the classification of the electronic states in atoms and the derivation of selection rules for infrared absorption or the vibrational Raman or hyper-Raman effect in crystals. In the first case the goal is to reduce tensors which are defined as products of one-particle wave functions, while in the second case tensors for the dipole moment, the electric susceptibility or the susceptibilities of higher orders have to be reduced according to the irreducible representations of the relevant point groups. 

To see how we should be able to study the evolution of a collision let us consider first how intermolecular potentials between atoms bound together are studied. This is done, of course, via spectroscopy. One starts with the Born-Oppenheimer approximation for the total molecular wave function this enables one to describe the motion of the nuclei in a potential that depends on the separation between them. This result, the existence of a specific adiabatic potential, rests on there being no appreciable mixing between electronic states. One of its corollaries, the Franck-Condon Principle, enables one to interpret and invert (e.g. using the R.K.R. method) the vibrational spectra in terms of the interatomic potentials in different electronic states. To what extent can we extend such a technique to free-free spectra, in other words, to absorption in the middle of a transient molecule — a collision complex — and deduce information about the potentials between atoms as they collide ... 

In regions of the spectrum where a tunable laser is available it may be possible to use it to obtain an absorption spectrum in the same way as a tunable klystron or backward wave oscillator is used in microwave or millimetre wave spectroscopy (see Section 3.4.1). Absorbance (Equation 2.16) is measured as a function of frequency or wavenumber. This technique can be used with a diode laser to produce an infrared absorption spectrum. When electronic transitions are being studied, greater sensitivity is usually achieved by monitoring secondary processes which follow, and are directly related to, the absorption which has occurred. Such processes include fluorescence, dissociation, or predissociation, and, following the absorption of one or more additional photons, ionization. The spectrum resulting from monitoring these processes usually resembles the absorption spectrum very closely. 

Infra-red (IR) spectroscopy functions to probe vibrational transitions (2000-50 000 nm 5000-200 cm i.e. wave number - typical IR spectroscopy units) in the singlet ground electronic state of molecules. The absorption principles of IR spectroscopy are identical to those of UV-visible and CD spectroscopy. Hence the Beer-Lambert law (Equation (4.3)) applies. Moreover, absorption band intensities are determined by the transition dipole moment and there are extensive perturbation and coupling effects. Overall though, values of molar extinction coefficients for vibrational transitions, are up to 10 times lower in magnitude... 

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