Electronic transitions, between quantized

Abstract Silver clusters, composed of only a few silver atoms, have remarkable optical properties based on electronic transitions between quantized energy levels. They have large absorption coefficients and fluorescence quantum yields, in common with conventional fluorescent markers. But importantly, silver clusters have an attractive set of features, including subnanometer size, nontoxicity and photostability, which makes them competitive as fluorescent markers compared with organic dye molecules and semiconductor quantum dots. In this chapter, we review the synthesis and properties of fluorescent silver clusters, and their application as bio-labels and molecular sensors. Silver clusters may have a bright future as luminescent probes for labeling and sensing applications. 

Unlike the processes of absorption and luminescence emission, scattering of light need not involve an electronic transition between quantized energy levels in atoms or molecules. Instead, a randomization in the... 

Atomic spectral moments can be expressed in terms of the averages of the products of the relevant operators. Let Oi,C>2, --,Ok be the operators of interactions in definite shells or the operators of electronic transitions between definite shells in the second quantization form. The average of... 

Colloidal metal nanopartides may have optical absorption spectra with an absorption peak that resembles that of colloidal semiconductor particles (cf. Figure 2.11 and Figure 2.13). However, this absorption does not derive from transitions between quantized energy states. Instead, in metal partides the collective modes of motion of the electron gas may be exdted, and these are referred to as surface plasmons [122,123]. The peak in the absorption spectrum is the resonance frequency for the generation of surface plasmons. The size-dependence of the plasmon frequency is... 

Radiative transition An electronic transition between energy bands that produces photons and possibly phonons (quantized lattice vibrations). A nonradiative transition is an electronic transition that produces only phonons. 

The Bohr model adds quantization to what is a classical mechanics description involving simple electrostatics. The Bohr model is certainly not a full quantum mechanical description of the atom. It assumes that the laws of classical mechanics do not apply during an electron transition between energy levels, but it does not state what laws should replace classical mechanics. 

The model of metal-ammonia solutions that has emerged is based on ionization of the metal atoms to produce metal ions and electrons that are both solvated. The solvated electron is believed to reside in a cavity in ammonia, and thus it may behave as a particle in a three-dimensional box with quantized energy levels. Transitions between the energy levels may give rise to absorption of light and thereby cause the solutions to be colored. The dissolution process can be represented as... 

In contrast to ESR spectroscopy, which can only be used to study species with unpaired electrons, NMR spectroscopy is applicable to the investigation of all polymer samples. Nuclei with non-zero total nuclear spin (e.g., 1H, l3C, 19F, 14N) will have a magnetic moment which will interact with an external magnetic field resulting in quantized energy levels. Transitions between these energy levels form the basis of NMR spectroscopy. 1H and 13C... 

Quantum dots are objects with sizes in all three directions equal to few nanometers. Such systems resemble molecules and the energy levels of electrons in them quantize. Energies of the transitions between these levels depend on quantum dots material and size, and those transitions are the base for the quantum dots laser radiation. 

Let us first consider the normal Zeeman effect, which applies to transitions between electronic states with zero total spin magnetic moment, so-called singlet states. Like the projection Ms of S in the Stern-Gerlach experiment, the projection Ml of the spatial angular momentum L is space quantized in the external magnetic field. We shall describe the quantization of the spatial angular momentum by means of quantum mechanical methods in detail later. Suffice it to say that each state with spatial angular momentum quantum number L splits into 2L + 1 components, i.e., a P state (L = 1) splits into three components with... 

Bound electronic states exhibit a discrete spectrum of rovibrational eigenstates below the dissociation energy. The interaction between discrete levels of two bound electronic states may lead to perturbations in their rovibrational spectra and to nonradiative transitions between the two potentials. In the case of an intersystem crossing, this process is often followed by a radiative depletion. Above the dissociation energy and for unbound states, the energy is not quantized, that is, the spectrum is continuous. The coupling of a bound state to the vibrational continuum of another electronic state leads to predissociation. 

We indicated in the Introduction that the reasons for writing this article are two-fold (i) to present a survey of the various conical intersections which govern potential transitions between electronic states and (ii) to establish the 3-state quantization of the NACM for molecular systems. 

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