Background, definitions, and assumptions

As far as we know, human beings and other biological organisms exist in the universe only on or near the surface of one rocky planet, where the physical conditions permit the existence of self-replicating long-chain molecules. These molecules are formed as individual atoms bound together via Coulomb forces. Binding takes place when the individual atoms are close enough together that the outer valence electrons of each atom can experience the potential well of the neighboring atom's nucleus as comparable to the potential well of its own atom's nucleus. In an ionic bond, for example, the atom with lower ionization potential “gives” its electron(s) to the neighboring atom that has higher electron affinity. In a covalent bond, the valence electrons of each atom simultaneously fill the valence bands of both atoms in the bond.

Nonetheless, whatever the exact nature of the molecular bond, in the bound molecular system, these valence electrons, in some sense, “belong” to both atoms simultaneously, with their exact positions with respect to the neighboring atomic nuclei known only to the accuracy allowed by the quantum-mechanical uncertainty principle. Thus, the binding energy of a typical di-atomic molecular bond is comparable to the binding energy of the valence electrons to the atom. The electron binding energy is typically a few electron volts (eV). One electron volt is the energy required to move one electron across a potential difference of one volt, equal to 1.6022 × 10−12 erg, a relatively small amount of energy. A typical covalent carbon–carbon molecular bond, for example, has a binding energy of ~4 eV. The covalent carbon–carbon molecular bond forms the basis of all known biological organisms on Earth.