There are a variety of known chemical bonding interactions including covalent, ionic, and metallic bonding among others. The theories associated with bonding are often developed around the covalent bonds and extended to ionic and metallic bonding. There are a variety of active theories or models associated with covalent bonding, the building block of molecules. These theories make various approximations rendering each them useful for describing different nuances of common molecular bonding.
Modern bonding theories such as VBT, LFT, and MO Theory assumes that bonds are formed by atoms sharing electrons in directional orbitals. This by all accounts represents reality accurately. A more simplified or primitive model such as VSEPR Theory presupposes no orbital directionality. CFT actually treats electrons of the two atoms as repulsive as the two atoms attract electrostatically. However, VSEPR Theory and CFT are widely considered the simplest and historic ways to introduce molecular structure and d-orbital splitting to students. As a result, material based on these theories is still included in most courses and most standardized tests.
Valence Bond Theory (VBT) an early bonding theory that has developed into Modern valence bond theory. VBT views bonds as weakly coupled orbitals with each atom sharing a valence electron in a manner governed by the octet or 18 electron rule. Lewis structures are a representation of VBT's most basic bonding while molecular geometry is derived from orbital hybridization. Orbital hybridization is often taught with VESPR Theory despite significant differences in the underlying theory.
Valence shell electron pair repulsion (VSEPR) Theory The simplest and most primitive of the theories currently taught. Describes molecular geometry through the repulsion of electron fields which include bonds and lone pairs. It does not require any application of orbital shape.
Crystal Field Theory (CFT) This approximation begins with the geometries of the d orbitals derived from quantum mechanics. Ligands with their electron density are assumed to destabilize the metal d orbitals they interact with raising their energy while the remain d-orbitals drop in energy to balance the overall change in energy.
Molecular Orbital (MO) Theory A current and often applied model of molecular bonding. MO Theory assumes that bonds are derived from a linear combination of atomic orbitals. In this linear combination each pair of atomic orbitals involved in bonding results in a bonding and anti-bonding orbital. The destabilized of orbitals of CFT are now seen as anti-bonding component of orbitals that have overall been stabilized through bonding interactions.
Modern computational chemistry applies components of bonding models to simulate various chemical phenomenon associated with bonding. Computational chemistry also extends beyond covalent bonding to investigate the interactions of groups of molecules and higher order structure. In these systems the chemical bond is often simplified and approximated to reduce computing time.