After having presented briefly in Chapter 1 the general approach to the description of correlated electrons in solids using a simplified model – the nondegenerate Hubbard model (1.6) – from this chapter on we turn toward a more detailed treatment of the physics of transition metal compounds, which will take into account the specific features of d-electrons. The well-known saying is that “the devil is in the details.” Thus if we want to make our description realistic, we have to include all the main features of the d states, the most important interactions of d-electrons, etc. We begin by summarizing briefly in this chapter the basic notions of atomic physics, with specific applications to d-electrons in isolated transition metal ions. For more details, see the many books on atomic physics; specifically for application to transition metals, see Ballhausen (1962), Abragam and Bleaney (1970), Griffith (1971), Cox (1992), and Bersuker (2010).

Elements of atomic physics

Here we recall some basic facts from atomic physics, which will be important later on. We give here only a very sketchy presentation; one can find the details in many specialized books on atomic physics, for example the works cited above and Slater (1960, 1968).

The state of an electron in an atom is characterized by several quantum numbers.