Energy level structures

Nuclear spin relaxation is caused by fluctuating interactions involving nuclear spins. We write the corresponding Hamiltonians (which act as perturbations to the static or time-averaged Hamiltonian, detemiming the energy level structure) in tenns of a scalar contraction of spherical tensors ... 

The bonding in molecules containing more than two atoms can also be described in terms of molecular orbitals. We will not attempt to do this the energy level structure is considerably more complex than the one we considered. However, one point is worth mentioning. In polyatomic species, a pi molecular orbital can be spread over die entire molecule rather than being concentrated between two atoms. 

We will first consider possible assignments for the fluorescing states in laser-excited PuF6(g) based on available energy level structure and thermodynamic information. We will then consider some of the implications of the long-lived PuF6 fluorescence we have observed in terms of potential photochemical separation processes. 

Prediction of the energy level structure for Pu2+ (5f ) is of particular interest since no spectra for this valence state of Pu have been reported. On the basis of what is known of the spectra of Am2+ (26), Cf2" (27), and Es2+ (28), there appears to be evidence for a very small crystal-field splitting of the free-ion levels. Such evidence encourages use of a free-ion calculation in this particular case. The parameter values selected are indicated in Table V. Based on the systematics given by Brewer (19), the first f- d transition should occur near 11000 cm-, so the f- -f transitions at higher energies would be expected to be at least partially obscured. A... 

The electrostatic and spin-orbit parameters for Pu + which we have deduced are similar to those proposed by Conway some years ago (32). However, inclusion of the crystal-field interaction in the computation of the energy level structure, which was not done earlier, significantly modifies previous predictions. As an approximation, we have chosen to use the crystal-field parameters derived for CS2UCI6 (33), Table VII, which together with the free-ion parameters lead to the prediction of a distinct group of levels near 1100 cm-. Of course a weaker field would lead to crystal-field levels intermediate between 0 and 1000 cm-1. Similar model calculations have been indicated in Fig. 8 for Nplt+, Pu1 "1 and Amlt+ compared to the solution spectra of the ions. For Am t+ the reference is Am4" in 15 M NHhF solution (34). 

Predicted energy-level structure CsNpFg, and CsPuFg in the range... 

Figure 10. Predicted energy-level structure for NpF6, PuF6, and AmFg in the range 0-18000 cm-. ...

CsPuF6 was prepared and verified to be isostructural with corresponding compounds of uranium and neptunium. Its decomposition was studied in an inert gas atmosphere and in vacuum. Its spectrum has been measured in the region 400-2000 nm. The energy level structure of Pu5+ in the trigonally distorted octahedral CsPuF6 site was computed from a predictive model and compared with the observed spectrum. 

Figure 21. A low-energy portion of the energy level structure of a tunneling center is shown. Here e < 0, which means that the reference, liquid, state structure is higher in energy than the alternative configuration available to this local region. A transition to the latter configuration may be accompanied by a distortion of the domain wall, as reflected by the band of higher energy states, denoted as ripplon states.

Fig. I Schematic representation of the molecule packing structure (top) and energy level structure (bottom) of H- and J-aggregates as compared to those of the monomer molecule (M)...

As can be seen from the energy level structure diagram, the relative position of the HOMO and LUMO levels are not less important than the energy gap between them, since they control the possibility of charge injection. At this point, however, note, that a MO scheme is often used for illustration, but more properly the total energy states of the molecules and their radical cations and anions that may be subjected to electronic rearrangement have to be considered. Bearing this in mind, the measured values of redox potentials can be translated into the molecular orbital picture. 

Halonen, L. (1987), Rotational Energy Level Structure of Stretching Vibrational States in Some Small Symmetrical Molecules, /. Chem. Phys. 86, 588. 

Finally, it should be mentioned that Raman and infrared absorption spectra (i.e., absorption spectra among vibrational levels) are very often complementary methods with which to investigate the energy-level structure associated with vibrations. If a vibration (phonon) causes a change in the dipolar moment of the system, which occurs when the symmetry of the charge density distribution is changed, then the vibration... 

Molecular orbital theory is a semi-empirical method devoted to interpreting the energy-level structure of optical centers where the valence electron cannot be considered as belonging to a specific ion. In our ABe reference center, this would mean that the valence electrons are shared by A and B ions. The approach is based on the calculation of molecular orbitals (MO) of the ABe pseudo-molecule, V mo, from various trial combinations of the individual atomic orbitals, V a and of the A and B ions, respectively. The molecular orbitals V mo of the center ABe are conveniently written in the form... 

Yttrium aluminum borate, YAlj (603)4 (abbreviated to YAB), is a nonlinear crystal that is very attractive for laser applications when doped with rare earth ions (Jaque et al, 2003). Figure 7.9 shows the low-temperature emission spectrum of Sm + ions in this crystal. The use of the Dieke diagram (see Figure 6.1) allows to assign this spectrum to the " Gs/2 Hg/2 transitions. The polarization character of these emission bands, which can be clearly appreciated in Figure 7.9, is related to the D3 local symmetry of the Y + lattice ions, in which the Sm + ions are incorporated. The purpose of this example is to use group theory in order to determine the Stark energy-level structure responsible for this spectrum. 

Fe—S dimers, 38 441-452 four-iron clusters, 38 455-464 energy level structure, 38 455-456 oxidized and reduced configurations, 38 456-457... 

A better description of the energy level structure of the actinide atoms is obtained by adding to (3) terms of relativistic origin, which, in fact, represent the magnetic interaction of orbital and spin momenta of the electrons. (They are of particular importance for actinides since they depend on the fourth power of the atomic number Z) ... 

Although based on a simplified parametric description of the electronic structure of the molecule and of the leads, the framework discussed in this section has the advantage of leading directly to the computation of measurable quantities (the I-V curves). Thus, it is possible to relate the experimental observations to the quantum-mechanical properties of the systems under investigation, e.g., the electronic energy-level structure of the molecule and the relation of such levels to the energy of the leads. A timely improvement in this direction will come from the implementation of manageable methods, which combine a parameter-free atomistic description of the electronic... 

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