Energy-level diagram, derived from molecular

Fig. 2 The molecular orbital energy level diagram derived from semiempirical orbital overlap methods. An alternative numbering system is shown for some orbitals to maintain consistency with later calculations. Adapted from [5]...

Fig. 6.4. Energy-level diagrams derived from MS-SCF-Xa calculations on tetrahedral ZnS/ , CdS/ , and HgS/ clusters and the linear HgS, cluster (after Tossell and Vaughan, 1981). Makeup of particular molecular orbitals in terms of atomic-orbital character is shown by the boxes in the diagram.

J KEY CONCEPT PROBLEM 14.13 Draw a molecular orbital (MO) energy-level diagram for 02-, including the MOs derived from the oxygen 2s and 2p orbitals. Show the electron population of the MOs, and verify that 02 is paramagnetic and has a bond order of 1.5. 

The following molecular orbital energy-level diagram shows the energies and electron occupancies of the MOs derived from the atomic 2p orbitals for an oxygen-containing binary compound of potassium. 

Fig. 8. Molecular orbital scheme for a Cp2M2(ju.-CO)2 system. (A) An energy level scheme derived by successive perturbations while (B) the diagrams represent the bridging orbitals. Taken with permission from Ref. 62, copyright Royal Society of Chemistry.

Molecular Orbitals of H2. The simplest example of a diatomic molecule is H2. For this molecule, the only atomic orbitals available are the Is orbitals of the hydrogens. These orbitals interact to yield bonding als and antibonding als molecular orbitals the molecular orbital energy level diagram is shown in Figure 2-3. (Subscripts are often used to designate the atomic orbitals from which the molecular orbitals are derived.)... 

The vibration-rotation spectrum can be understood on the basis of a partial energy level diagram for the lowest vibrational and rotational levels (Fig. 3.9). The upper and lower level quantum numbers are denoted by (v J ) and (v"J ), respectively. Transitions for which AJ— -h 1, AJ = — 1, and A J = 0 (the latter occurring only in states with nonzero orbital angular momentum along the molecular axis) are called R-, P-, and Q-branch transitions. The transition frequencies are derived from... 

The sequence of energy levels obtained from a simple molecular orbital analysis of an octahedral complex is presented in Fig. 1-12. The central portion of this diagram, with the t2g and e levels, closely resembles that derived from the crystal field model, although some differences are now apparent. The t2g level is now seen to be non-bonding, whilst the antibonding nature of the e levels (with respect to the metal-ligand interaction) is stressed. If the calculations can be performed to a sufficiently high level that the numerical results can be believed, they provide a complete description of the molecule. Such a description does not possess the benefit of the simplicity of the valence bond model. 

The major focus of the book is on mineral crystal structures that provide an ordered array of anions forming coordination polyhedra around the central cations. The thermodynamic data underlying many of the geochemical applications described in the first ten chapters are derived from energies of absorption bands in the optical spectra of minerals, which are most simply explained by crystal field theory. Use of experimentally determined energy level data rather than energy separations computed in molecular orbital diagrams is the emphasis of these early chapters. 

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