Bonding and ant bonding orbitals
Just as an atomic orbital (AO) is the wavefunction for an electron in an atom so a molecular orbital (MO) is that for a molecule; an MO will extend over two or more atoms. Exact MOs will be calculated by solution of Schrödinger's equation for the one-electron ion but as in atoms the extension of the orbital approach to manyelectron systems involves approximations. For MOs a further approximation is made: rather than using the same but very complicated wavefunction for it is convenient to express each MO as a linear combination of AOs, the so-called LCAO approximation. This approximation have to be refined considerably for quantitative calculations on computers, but it is adequate for qualitative purposes and provides very efficient pictures of how chemical bonds form, and how they are related to the valence AOs of the atoms involved.
Fig. 1. Formation of a bonding and antibonding MO from the overlap of 1s AOs in H2