and thus cannot describe the true wavefunction. However, by taking the sum and difference (linear combinations) of VB determinants, two approximate wavefunctions can be obtained: ΦHL is the wavefunction as described by Heiter and London originally, and describes the covalent bonding between orbitals a and b in which the spins are paired, as expected for a chemical bond. ΦT is a representation of the bond that where the electron spins are parallel, resulting in a triplet state. This is a highly repulsive interaction, so this description of the bonding will not play a major role in determining the wave function. Other ways of describing the wavefunction can also be constructed. Specifically, instead of considering a covalent interaction, the ionic interactions can be considered, resulting in the wavefunction This wavefunction describes the bonding in H2 as the ionic interaction between an H+ and an H-. Since none of these wavefunctions, ΦHL (covalent bonding) or ΦI (ionic bonding) perfectly approximates the wavefunction, a combination of these two can be used to describe the total wavefunction where λ and μ are coefficients that can vary from 0 to 1. In determining the lowest energy wavefunction, these coefficients can be varied until a minimum energy is reached. λ will be larger in bonds that have more covalency, while μ will be larger in bonds that are more ionic. In the specific case of H2, λ ≈ 0.75, and μ ≈ 0.25. The orbitals that were used as the basis (a and b) do not necessarily have to be localized on the atoms involved in bonding. Orbitals that are partially delocalized onto the other atom involved in bonding can also be used, as in the Coulson-Fischer theory. Even the molecular orbitals associated with a portion of a molecule can be used as a basis set, a processes referred to as using fragment orbitals. For more complicated molecules, ΦVBT could consider several possible structures that all contribute in various degrees (there would be several coefficients, not just λ and μ). An example of this is the Kekule and Dewar structures used in describing benzene. Note that all normalization constants were ignored in the discussion above for simplicity. Relationship to Molecular Orbital Theory History The application of VBT and MOT to computations that attempt to approximate the Schrödinger equation began near the middle of the 20th century, but MOT quickly became the preferred approach between the two.