Molecular Orbitals for Homonuclear Diatomic MoleculesValence atomic orbitals on each atom in the diatomic molecule can linearly combine (linearcombination of atomic orbitals -LCAO) to form molecular orbitals for the molecule. Thenumber of molecular orbitals formed is equal to the number of atomic orbitals combined. In thesimplest case there are four atomic orbitals on each atom (an s orbital and three p orbitals) sothere are a total of 8 atomic orbitals and therefore 8 molecular orbitals can form. The atomicorbitals can be classified by their symmetry and for a diatomic molecule the critical symmetryreference is the line connecting the two atoms. The s orbital and the p orbital lying on the axisfor each atom are symmetric with respect to rotation about the molecular axis. They belong tothe same symmetry group. The four molecular orbitals that form from these atomic orbitalsatom also are symmetric with respect to rotation about the molecular axis and are called sigma(σ) bonds. There are two equivalent p orbitals on each atom that are mutually perpendicular tothe molecular axis and each other. These are named the px and py orbitals. The orbitals areanti-symmetric with respect to rotation of 180o about the molecular axis. The four molecularorbitals that form from these orbitals also are anti-symmetric with respect to rotation of 180oabout the molecular axis and are called pi (π) orbitals. A simplified way to consider themolecular orbitals that form from the atomic orbitals of the same symmetry is to examine anidentical orbital on each atom and to linearly combine them. One combination will concentrateelectron density between the nuclei holding them together and is called a bonding molecularorbital. The other combination will remove electron density from between the two nuclei and iscalled an anti-bonding molecular orbital. This process is illustrated for the sets of s and porbitals on each atom. The signs represent the sign of the wave function and do not implycharge.Because these atomic orbitals have the same symmetry, the separate treatment of the s andpz orbital sets is an approximation. The use of all four atomic orbitals to form four molecularorbitals manifests itself in the value of the energy of each orbital and that will be discussedwhen the energy level diagram is considered.The atomic orbitals of pi symmetry can be combined in the same fashion. The px set and thepy set yield equivalent sets of pi bonding molecular orbitals and pi anti-bonding molecularorbitals. The sets derived from the px orbitals are mutually perpendicular to the sets from thepy orbitals. The process is pictorially represented by the illustration for the px set of orbitals.The py set yields an equivalent set of molecular orbitals that are perpendicular to the molecularorbitals derived from the px set.A molecular orbital energy level diagram shows the relative energy of the atomic orbitals andthe molecular orbitals formed from them. An idealized diatomic molecule diagram is shown.Electrons are placed in these molecular orbitals starting with the lowest available empty orbital.Each energy level holds two electrons. The energies of the px and py bonding pi orbitals arethe same. These are called degenerate orbitals. The px and py anti-bonding pi orbitals alsoare degenerate. When electrons are placed in these orbitals they enter spins paired untilforced to pair (Hund's Rule). Note also that the energy level order has the bonding pi set lowerin energy than the sigma pz bonding orbital. This results from considering all four sigmasymmetry orbitals as a group. The sigma s orbitals, both bonding and anti-bonding, aresomewhat lower in energy as a result and the sigma p orbitals, both bonding and anti-bonding,are somewhat higher in energy as a result. The sigma p bonding orbital thus moves above thepi bonding orbitals in energy. Chemists are used to classifying bonds by order: single, doubleor triple. For diatomic molecules whose bonding is described by molecular orbitals a termcalled bond order is defined. In this definition fractional bond orders are possible.Just as the atomic orbital energy level diagram can be represented by the electronconfiguration of the atom, so too the molecular orbital energy level diagram can berepresented by the molecular orbital electron configuration of valence electrons.Just as in atomic electron configurations, the existence of degenerate orbitals and parallelelectron spins must be recognized. The configuration below for dioxygen (12 valenceelectrons) shows a bond order of 2 but there are two unpaired electrons (spins parallel in thepx and py anti-bonding pi orbitals).Heteronuclear diatomic molecules do not have the same symmetry as homonuclear systemsand the energy of the atomic orbitals is not the same; consequently, the molecular orbitals andtheir resultant energies are not equivalent. Regardless, as a first approximation, the results forthe homonuclear system can be used to interpret heteronuclear diatomic systems. s( ) s*    px( ) py( ) pz( ) px*    py*    pz*    s( )2 s*    2 px( )2 py( )2 pz( )2 px*    1 py*    1 pz*    Bond Order = No. of electrons in bonding orbitals -No. of electrons in anti-bonding