Term symbols, electronic structure

Most complexes showing spin-state transitions are in fact of low symmetry. In order to describe their electronic structure it is convenient to employ term symbols appropriate to cubic symmetry and this practice will be followed below. The most common transition-metal ions for which spin-state transitions have been observed are Fe " (3d ), Fe " (3d ) and Co (3d ), a minor role being played by Co " (3d ), Mn " (3d ), as well as Cr " and Mn " (3d ). The relevant ground states for an octahedral disposition of the ligands are LS Ui,(t ,) and HS r2,(t ,e ) for iron(II), LS and HS Ai,(t, e ) for... 

In tier (1) of the diagram (for the electronic structure of iron(III)), only the total energy of the five metal valence electrons in the potential of the nucleus is considered. Electron-electron repulsion in tier (2) yields the free-ion terms (Russel-Saunders terms) that are usually labeled by term ° symbols (The numbers given in brackets at the energy states indicate the spin- and orbital-multiplicities of these states.)... 

Notice that the fine structure term found here has the same form (and the tensor is given the same symbol) as that obtained from the electron dipolar interaction. Unlike the dipolar D-tensor, however, the spin-orbit coupling D-tensor in general does not have zero trace. Nonetheless, we introduce analogous parameters ... 

Section treats the spatial, angular momentum, and spin symmetries of the many-electron wavefunctions that are formed as antisymmetrized products of atomic or molecular orbitals. Proper coupling of angular momenta (orbital and spin) is covered here, and atomic and molecular term symbols are treated. The need to include Configuration Interaction to achieve qualitatively correct descriptions of certain species electronic structures is treated here. The role of the resultant Configuration Correlation Diagrams in the Woodward-Hoffmann theory of chemical reactivity is also developed. 

Many of the complexes which occur in spin equilibrium possess ligands with complicated structures. Trivial abbreviations are used, with structural formulas given in the table in which the complex first appears. Generally the complexes are of low symmetry, but in the description of their electronic structure idealized symmetries are assumed and the appropriate term symbols are used accordingly. 

We will see in due course that there are important correlation rules between atomic term symbols and molecular electronic states, rules that are important in understanding both the formation and dissociation of diatomic molecules. Elementary accounts of the theory of atomic structure are to be found in books by Softley [3] and Richards and Scott [4], Among the more comprehensive descriptions of the quantum mechanical aspects, that by Pauling and Wilson [5] remains as good as any whilst group theoretical aspects are described by Judd [6],... 

These angular momentum selection rules figure prominently in the fine structure of alkali atom spectra. The filled-shell core electrons have zero net orbital and spin angular momentum, so the term symbols 2 Si/2,... 

The question of which diatomic term symbols may be obtained by adiabatically bringing together atoms A and B, initially in electronic states with angular momentum quantum numbers (/a, Sa) and Sb), can be answered without recourse to electronic structure calculations. Since the electronic (orbital plus spin) degeneracies on the respective atoms are (2/a + 1)(2sa + 1) and (2/b + 1X2% + 1), a total of (2/a + 1)(2sa + 1)(2/b + 1)(2sb + 1) diatomic states must correlate with the separated-atom states. According to one of the... 

Furthermore, the change in L can come about only if the occupancy change corresponds to a change of 1 in the I quantum number of one and only one electron. That is, A/ = 1 while = 0. For example, a change from the occupancy Is 2s 2p to the occupancy Is 2s 2p is a change in one and only one of the electrons / values of 1. The term symbol for the first occupancy is P, and so transitions are allowed to term symbol states arising from the second occupancy, but only if they are or D. When we consider the fine structure of the spectra, which means the small energy differences due to spin-orbit interaction, a selection on / applies ... 

In the previous chapter, the structures of many molecules and ions were described by drawing structures showing how the electrons are distributed. However, there is another way in which the structures of molecules are described. That way uses different language and symbols to convey information about the structures in an efficient, unambiguous way. In this way, the structures of molecules and ions are described in terms of their symmetry. Symmetry has to do with the spatial arrangement of objects and the ways in which they are interrelated. For example, the letter T" has a plane that bisects it along the "post," giving two halves that are identical in relationship to that plane. However, the letter "R" does not have such a plane that divides it into two identical parts. This simple example illustrates a symmetry characteristic that is known as a plane of symmetry. There is much more that can be done with symmetry in terms of molecular structure so this chapter is devoted to this important topic. 

In Sections 9-3 and 9-4, we will show you two types of chemical bonds ionic and covalent. It is important to be able to represent compounds in terms of the atoms and valence electrons that make up the chemical species (compounds or polyatomic ions). One of the best ways is to use Lewis symbols and structures. 

Hybrid states of this sort are to be formed from structures with the same value of J and also with the same parity. The parity of a configuration is even in case that it involves an even number of electrons in orbitals with odd value of l (p,/, etc.) and odd in case that it involves an odd number of electrons in orbitals with odd l. In tables of spectral terms the parity is often indicated by use of a superscript ° on the symbols of states with odd parity. In the above example of neutral osmium the two configurations considered have even parity. 

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