text: In general, ligands are viewed as electron donors and the metals as electron acceptors, i.e., respectively, Lewis bases and Lewis acids. This description has been semi-quantified in many ways, e.g. ECW model. Bonding is often described using the formalisms of molecular orbital theory.
  Ligands and metal ions can be ordered in many ways; one ranking system focuses on ligand hardness (see also hard/soft acid/base theory). Metal ions preferentially bind certain ligands. In general, hard metal ions prefer weak field ligands, whereas soft metal ions prefer strong field ligands. According to the molecular orbital theory, the HOMO (Highest Occupied Molecular Orbital) of the ligand should have an energy that overlaps with the LUMO (Lowest Unoccupied Molecular Orbital) of the metal preferential. Metal ions bound to strong-field ligands follow the Aufbau principle, whereas complexes bound to weak-field ligands follow Hund's rule.
  Binding of the metal with the ligands results in a set of molecular orbitals, where the metal can be identified with a new HOMO and LUMO (the orbitals defining the properties and reactivity of the resulting complex) and a certain ordering of the 5 d-orbitals (which may be filled, or partially filled with electrons). In an octahedral environment, the 5 otherwise degenerate d-orbitals split in sets of 3 and 2 orbitals (for a more in-depth explanation, see crystal field theory):
  *3 orbitals of low energy: d, d and d and
  *2 orbitals of high energy: d−y</sub>.
  The energy difference between these 2 sets of d-orbitals is called the splitting parameter, Δ. The magnitude of Δ is determined by the field-strength of the ligand: strong field ligands, by definition, increase Δ more than weak field ligands. Ligands can now be sorted according to the magnitude of Δ (see the table below). This ordering of ligands is almost invariable for all metal ions and is called spectrochemical series.
  For complexes with a tetrahedral surrounding, the d-orbitals again split into two sets, but this time in reverse order:
  *2 orbitals of low energy: d−y</sub> and
  *3 orbitals of high energy: d, d and d.
  The energy difference between these 2 sets of d-orbitals is now called Δ. The magnitude of Δ is smaller than for Δ, because in a tetrahedral complex only 4 ligands influence the d-orbitals, whereas in an octahedral complex the d-orbitals are influenced by 6 ligands. When the coordination number is neither octahedral nor tetrahedral, the splitting becomes correspondingly more complex. For the purposes of ranking ligands, however, the properties of the octahedral complexes and the resulting Δ has been of primary interest.
  The arrangement of the d-orbitals on the central atom (as determined by the strength of the ligand), has a strong effect on virtually all the properties of the resulting complexes. E.g., the energy differences in the d-orbitals has a strong effect in the optical absorption spectra of metal complexes. It turns out that valence electrons occupying orbitals with significant 3 d-orbital character absorb in the 400–800 nm region of the spectrum (UV–visible range). The absorption of light (what we perceive as the color) by these electrons (that is, excitation of electrons from one orbital to another orbital under influence of light) can be correlated to the ground state of the metal complex, which reflects the bonding properties of the ligands. The relative change in (relative) energy of the d-orbitals as a function of the field-strength of the ligands is described in Tanabe–Sugano diagrams.
  In cases where the ligand has low energy LUMO, such orbitals also participate in the bonding. The metal–ligand bond can be further stabilised by a formal donation of electron density back to the ligand in a process known as back-bonding. In this case a filled, central-atom-based orbital donates density into the LUMO of the (coordinated) ligand. Carbon monoxide is the preeminent example a ligand that engages metals via back-donation. Complementarily, ligands with low-energy filled orbitals of pi-symmetry can serve as pi-donor.