The d- and f-block elements are often referred to as transition metals and rare earth metals respectively. The terms “d” and “f” refer to partially filled atomic electron sub-shells of the particular elements. Most of these elements are hard relatively un-reactive metals, at least when compared with alkali metals like sodium.
Chemical elements are composed of atoms. The structure of each atom is a nucleus surrounded by an electron cloud. In the nucleus are protons and neutrons bound together by the strong and weak forces. An element is characterized by the number of protons, the “atomic number.” Each proton possesses an atomic charge of “1” balanced by one electron, charge “-1”, in the electron cloud. An atom with six protons would usually (except it were an ion) have six electrons and, as fate would have it, be a carbon atom. We don't categorize elements by electron number because electrons enter and leave an atom with relative ease. Electrons in the electron cloud are not all bunched together but maximally distributed in spatial regions of mathematically high probability (the why having to do with quantum mechanics, Hamiltonians and the oh so approximate application of Schrödinger’s superlative equation, to the extent their electromagnetic attraction to positively charged protons in the nucleus will allow.
Consequently, these electrons organize themselves in a variety of clever and commendable ways. The first level of organization is “shells”. The first shell has two electrons (one spinning clockwise, one counter-clockwise) the second eight, the third 18, the fourth 32 and so on. These shells are further divided in sub-shells. (The initiated will recognize the 4 “quantum numbers”). The first shell has one sub-shell called “s” spherical in shape. Each later shell has an “s” sub-shell. The second shell additionally has a “p”-sub-shell with space for 6 electrons organized in 3 “orbitals” with two electrons each. These orbitals resemble 3 dumbbells nuclear centered and oriented at 90 degree angles to each other. Shell 3 (and greater), in addition to s and p, possesses a “d”-sub-shell with space for 10 electrons in 5 orbitals and levels and shell 4 (and greater) possesses in like manner sub-shell “f” with space for 14 electrons and 7 “orbitals”.
As heavier elements contain more and more protons (and neutrons but that is another story) as we move from hydrogen to helium to carbon to iron and so on, correspondingly, electrons begin to fill higher and higher shells, sub-shells and orbitals. An element’s characterizing “block” is the lowest sub-shell that is not completely filled. This determines the material and chemical properties of the element. “S” block elements tend to be silvery-white, low density, highly reactive metals. P block elements tend to be “non-metals:” gases like oxygen or chlorine or solids like phosphorus, carbon or sulphur. Some metals occupy the less filled end of the p-block like aluminum and lead. “D”-block elements tend to be darker, relatively un-reactive hard metals like iron, chromium and manganese (OK at the upper end of the d-block there are “soft” metals like gold, silver, copper and liquid mercury). Finally, f-block elements tend to be silvery, softer, moderately reactive metals including cerium, europium, dysprosium and lutetium. OK so hard, dark, relatively un-reactive uranium and thorium are also in this f- block. Exceptio probat regulam.
The ground state (un-excited) orbitals fill up as the number of electrons increases with increasing atomic number according to the following order –1s->2s->2p->3s->3p->4s-> 3d->4p->5s->4d->5p->6s->4f->5d->6p->7s->5f which covers all of the natural elements. Notably, the 3d, 4d and 5d orbitals fill up only after electrons have occupied the “s” orbital in their respective higher shells. The 4f and 5f orbitals are only occupied after the 6s and one of the 5d and the 7s and one of the 6d orbital positions have been occupied respectively.
This fact together with the increasingly specific directional geometry of the d- and f- orbitals are the basis of the chemistry of these elements. In the d-block, ionization occurs first by loss of the s electrons of the next shell up and then whatever number of electrons are on the d-orbital for the first half of the d-series. From then on the two electron ionization is preferred. The f-block atoms lose their “s” and single “d” electrons and typically do not possess other easily accessible ionic states. Ionization energy varies linearly for the f-ionizations (function of nuclear attraction). Ionization in the d-sub-shells departs from linearity initially to conform briefly again at the more stable “half filled shell”. The same departure is evident for the later half of the d-serieses.
Transition metal chemistry is dominated by displacement of energy levels for ground state orbitals by more electron-rich molecules (ligands) approaching the transition metal compounds. The splitting of previously equal intra-sub-shell energy levels is described by electromagnetic effects (crystal field theory) or molecular orbital calculations. The former is usually adequate but the latter better explains covalent metal carbon bonding and effects of π(double/triple bond related) ligand orbitals. Finally there is a brief description of spectroscopic rules and effects (forbidden transitions/ charge transfers/ excited states/ colors/ f-block luminescence) and magnetic effects (spin-orbit coupling/paramagnetism) generated by occupation of metal and metal-ligand orbitals by electrons with paired or, conversely, parallel spins.