Energy-level splitting

Figure 4-3. Energy level splitting for a nucleus with / = 5 in applied field Hn. The energy separation is proportional to Ho-...

Studies of many coordination complexes reveal a common pattern in the energetic effects of the various ligands. This pattern is described by the spectrochemical series, in which ligands are listed in order of increasing energy level splitting ... 

Energy level splitting in a magnetic field is called the Zeeman effect, and the Hamiltonian of eqn (1.1) is sometimes referred to as the electron Zeeman Hamiltonian. Technically, the energy of a... 

Fig. 2. Energy level splitting of Cr3+ in octahedral environment and after tetragonal distortion.

Figure 3.2 An energy-level-splitting diagram (cf. Fig. 1.3) for interaction of orbitals A F

Figure 3.13 The energy-level-splitting diagram (cf. Figs. 1.3 and 3.2) for interaction of filled NBOs l a and l b (with energies ea(L) = < b(L) and interaction element F ab = (f2a F f2b>) to form MO levels e , Eq. (3.48).

The four-electron destabilization rationale The rotation barrier of ethane is sometimes explained in terms of the mnemonic energy-level-splitting diagram shown in Fig. 3.58. The figure purports to depict how two filled MOs of ethane ( and 4>+) evolve perturbatively from two... 

Figure 3.58 The mnemonic energy-level-splitting diagram for the four-electron destabilizing interaction of two occupied non-orthogonal orbitals.

NMR spectroscopy (a commercial unit shown in Fig. 1.49) uses the fact that some atomic nuclei have a magnetic moment, e. g. very distinct in a proton, the nucleus of hydrogen, but also inl3C, 3IP, 14N, and 33S. In an external magnetic field the energy levels split, as described in quantum mechanics. The size and extend of the split is given by Eq. (9)... 

Figure 12.2 Magnetic field dependence of the energy levels of ortho- and para-H2. Parahydrogen (p-H2) is a singlet that is unaffected by the magnetic field, whereas orthohydrogen (o-H2) is a triplet. Its energy levels split, showing the Zeeman effect.

Predicting the energy level splitting induced by a reduction in symmetry (due, for instance, to pressure effects). 

This means that the fifthly degenerate d energy level splits into two levels in an octahedral crystalline field one triply degenerate and the other doubly degenerate. 

For a better understanding of the energy level splitting of triplet and singlet levels Ti and Si, let us neglect the closed-shell electrons and consider just a two-electron system ... 

On a molecular level, absorption of terrestrial infrared radiation of the appropriate wavelength corresponding to the energy-level splittings in the molecule... 

The second moment ju2 can be written explicitly in terms of the atomic energy-level splitting AEsp and any interaction between the bond ij and its local atomic environment. It follows from eqs (7.86) and (7.98) that... 

Example Problem Determine the temperature at which kBT is equal to the energy level splitting for the metastable state of 123Te at 247.6 keV in an external magnetic field of 4.0 tesla (T). 

Transitions between the two spin states (+1/2 and -1/2) can be induced by oscillating electromagnetic radiation (v in the microwave region) applied perpendicularly to 77. The energy-level splitting is referred to as the Zeeman effect, illustrated in Figure 16.1. Normally in the EPR measurements, v is maintained at a fixed value and 77 is permitted to vary until the resonance is matched. 

Figure 16.1. (a) Simplified scheme of EPR phenomenon, showing the energy-level splitting (Zeeman effect) for the electron spin S = 1/2 (Ms = +1/2) as a function of applied magnetic field (H), (b) the EPR absorption line, and (c) first derivative of absorption line, indicating the g value and line width (AH), normally detected in the EPR spectra. 

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