Molecular Orbitals for Homonuclear Diatomic Molecules Valence atomic orbitals on each atom in the diatomic molecule can linearly combine linear combination of atomic orbitals LCAO to form molecular orbitals for the molecule The number of molecular orbitals formed is equal to the number of atomic orbitals combined In the simplest case there are four atomic orbitals on each atom an s orbital and three p orbitals so there are a total of 8 atomic orbitals and therefore 8 molecular orbitals can form The atomic orbitals can be classified by their symmetry and for a diatomic molecule the critical symmetry reference is the line connecting the two atoms The s orbital and the p orbital lying on the axis for each atom are symmetric with respect to rotation about the molecular axis They belong to the same symmetry group The four molecular orbitals that form from these atomic orbitals atom also are symmetric with respect to rotation about the molecular axis and are called sigma bonds There are two equivalent p orbitals on each atom that are mutually perpendicular to the molecular axis and each other These are named the px and py orbitals The orbitals are anti symmetric with respect to rotation of 180o about the molecular axis The four molecular orbitals that form from these orbitals also are anti symmetric with respect to rotation of 180o about the molecular axis and are called pi orbitals A simplified way to consider the molecular orbitals that form from the atomic orbitals of the same symmetry is to examine an identical orbital on each atom and to linearly combine them One combination will concentrate electron density between the nuclei holding them together and is called a bonding molecular orbital The other combination will remove electron density from between the two nuclei and is called an anti bonding molecular orbital This process is illustrated for the sets of s and p orbitals on each atom The signs represent the sign of the wave function and do not imply charge Because these atomic orbitals have the same symmetry the separate treatment of the s and pz orbital sets is an approximation The use of all four atomic orbitals to form four molecular orbitals manifests itself in the value of the energy of each orbital and that will be discussed when the energy level diagram is considered The atomic orbitals of pi symmetry can be combined in the same fashion The px set and the py set yield equivalent sets of pi bonding molecular orbitals and pi anti bonding molecular orbitals The sets derived from the px orbitals are mutually perpendicular to the sets from the py 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 molecular orbitals derived from the px set A molecular orbital energy level diagram shows the relative energy of the atomic orbitals and the 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 are the same These are called degenerate orbitals The px and py anti bonding pi orbitals also are degenerate When electrons are placed in these orbitals they enter spins paired until forced to pair Hund s Rule Note also that the energy level order has the bonding pi set lower in energy than the sigma pz bonding orbital This results from considering all four sigma symmetry orbitals as a group The sigma s orbitals both bonding and anti bonding are somewhat 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 the pi bonding orbitals in energy Chemists are used to classifying bonds by order single double or triple For diatomic molecules whose bonding is described by molecular orbitals a term called bond order is defined In this definition fractional bond orders are possible Bond Order No of electrons in bonding orbitals No of electrons in anti bonding orbitals 2 Just as the atomic orbital energy level diagram can be represented by the electron configuration of the atom so too the molecular orbital energy level diagram can be represented by the molecular orbital electron configuration of valence electrons s s p p p x y px z py pz Just as in atomic electron configurations the existence of degenerate orbitals and parallel electron spins must be recognized The configuration below for dioxygen 12 valence electrons shows a bond order of 2 but there are two unpaired electrons spins parallel in the px and py anti bonding pi orbitals s 2 s 2 p p p 2 x 2 y z 2 1 px py 1 pz Heteronuclear diatomic molecules do not have the same symmetry as homonuclear systems and the energy of the atomic orbitals is not the same consequently the molecular orbitals and their resultant energies are not equivalent Regardless as a first approximation the results for the homonuclear system can be used to interpret heteronuclear diatomic systems