A chemical bond is not a single observable quantity but a useful emergent description of electron density, energy lowering, and topology of the electronic structure. Different theories emphasize different aspects: valence bond theory, molecular orbital theory, density-based analyses, and energy decomposition methods.

Single-determinant methods work well when one electronic configuration dominates. Multireference problems arise in bond breaking, diradicals, transition metal complexes, and excited states where several configurations contribute comparably. These cases require methods such as CASSCF, MRCI, or tailored coupled-cluster approaches.

Density functional theory maps the many-electron problem onto the electron density, dramatically reducing computational cost. Its accuracy depends on the exchange-correlation functional, and modern developments include range-separated hybrids, double hybrids, and machine-learned functionals.