To hybridize or not to hybridize? This is the dilemma

A general approach to hybridization, without imposing orthogonality of the hybrids of the central atom, is formulated. It is shown that the overlapping hybrids follow the rules of electronegativity of the central atom, and they increase with the increase of electronegativity (e.g. NH₄ ⁺ > CH₄ > BH₄ ⁻). For a given electronegativity, the hybrid-hybrid overlap decreases as the number of equivalent bonds increases (e.g., CH₄ < CH₃ ⁺, CH₂ ²⁺). Having the hybrid-hybrid overlap enables us to deduce the promotion energy invested by the various atoms to form the molecule; the larger the overlap the smaller the degree of hybridization, and the lesser is the promotion energy needed from the central atom to achieve maximum bonding. The approach is applied to the dicarbon molecule, C₂. It is shown that after taking into account the promotion energy (∼46 kcal mol⁻¹ per C), C₂ exhibits a quadruple bond.