Spectroscopic transitions, quantum mechanics

FRET is a nonradiative process that is, the transfer takes place without the emission or absorption of a photon. And yet, the transition dipoles, which are central to the mechanism by which the ground and excited states are coupled, are conspicuously present in the expression for the rate of transfer. For instance, the fluorescence quantum yield and fluorescence spectrum of the donor and the absorption spectrum of the acceptor are part of the overlap integral in the Forster rate expression, Eq. (1.2). These spectroscopic transitions are usually associated with the emission and absorption of a photon. These dipole matrix elements in the quantum mechanical expression for the rate of FRET are the same matrix elements as found for the interaction of a propagating EM field with the chromophores. However, the origin of the EM perturbation driving the energy transfer and the spectroscopic transitions are quite different. The source of this interaction term... 

A particularly useful probe of remote-substituent influences is provided by optical rotatory dispersion (ORD),106 the frequency-dependent optical activity of chiral molecules. The quantum-mechanical theory of optical activity, as developed by Rosenfeld,107 establishes that the rotatory strength R0k ol a o —> k spectroscopic transition is proportional to the scalar product of electric dipole (/lei) and magnetic dipole (m,rag) transition amplitudes,... 

Spectroscopic techniques look at the way photons of light are absorbed quantum mechanically. X-ray photons excite inner-shell electrons, ultra-violet and visible-light photons excite outer-shell (valence) electrons. Infrared photons are less energetic, and induce bond vibrations. Microwaves are less energetic still, and induce molecular rotation. Spectroscopic selection rules are analysed from within the context of optical transitions, including charge-transfer interactions The absorbed photon may be subsequently emitted through one of several different pathways, such as fluorescence or phosphorescence. Other photon emission processes, such as incandescence, are also discussed. 

Oxidation by direct H transfer from the a-carbon of alcohols to the pyrroloquinoline quinone (PQQ) cofactor of alcohol dehydrogenases was studied using ab initio quantum mechanical methods <2001JCC1732>. Energies and geometries were calculated at the 6-31G(d,p) level of theory, results were compared to available structural and spectroscopic data, and the role of calcium in the enzymatic reaction was explored. Transition state searches at the semi-empirical and STO-3G(d) level of theory provided evidence that direct transfer from the alcohol to C-5 of PQQ is energetically feasible. 

Molecules for which a temperature-dependent dielectric susceptibility is observed in gas phase are commonly called polar. Polar molecules have microwave spectra with transitions corresponding to AJ= 1 and are deflected by inhomogeneous electric fields. In the conventional approach, these phenomena are attributed to the presence of permanent dipole moments in such molecules. In contrast, the notion of permanent dipole moments (which are zero for spectroscopic states) plays no role at all in the fully quantum-mechanical treatment outlined above. The temperature-dependent component of x arises from the existence of low-lying spectroscopic states for which... 

This study led to the observation of a reversible Mott-Hubbard metal-insulator transition in the nanocrystal ensemble wherein the coulomb gap closes at a critical distance between the particles. Tunnelling spectroscopic measurements on Aims of 2.6 nm Ag nanocrystals capped with decanethiol reveal a coulomb blockade behavior attributable to isolated nanocrystals [203]. On the other hand, nanocrystals capped with hexane and pentane thiol exhibit characteristics of strong interparticle quantum mechanical exchange (see Figure 4.28). Similar behavior was observed... 

These include multipole moments, molecular polarizabilities, ionization potentials, electron affinities, charge distributions, scattering potentials, spectroscopic transitions, geometries and energies of transition states, and the relative populations of various conformations of molecules. Some of these properties are directly related to molecular reactivity (e.g., charge distribution, molecular polarizabilities, scattering potentials), and they can be implemented in QSAR studies. Quantum mechanical methods can therefore be used to obtain reactivity characteristics in order to relate molecular structure to the observed biological activity (183, 230). 

Limitations to the spectroscopic measurement of the temperatures from line intensities lie in possible deviations from ideal thermodynamic behavior in real radiation sources, but also in the poor accuracy of transition probabilities. They can be calculated from quantum mechanics, and have been determined and compiled by Corliss and Bozman at NIST [10] from measurements using a copper dc arc. These tables contain line energy levels, transition probabilities and the so-called oscillator strengths for ca. 25000 lines between 200 and 900 nm for 112 spectra of 70 elements. Between the oscillator strength f (being 0.01-0.1 for non-resonance and nearer to 1 for resonance lines) there is the relationship [11] ... 

The hardness of Mg(II) and Mn(II) ions (relative to Cu, Zn, Fe, Co, or Ni) prevents extensive donation of rr-electrons from ligands to metal within the metal complexes. Thus it is unlikely that the earlier proposed extensive delocalization of electrons could be the basis of catalysis in metal-dependent proteases. This conclusion has been verified by more recent spectroscopic and magnetic data, along with quantum mechanical calculations related to stereochemistry, reactivity, d-d transitions, and charge transfer complex formation . 

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