Molecular Orbital Theory Quantum mechanics describes the electrons in an atom using wave functions called atomic orbitals. Atomic orbital located on individual atoms definite energy contains up to 2 electrons with opposite spins visualized using a 3-D representation

Molecular Orbital Theory 3-D representation of some atomic orbitals: z y y y x x x z z s orbital p orbital d orbital

Molecular Orbital Theory Molecular Orbital Theory describes the electrons in a molecule using wave functions called molecular orbitals. an allowed state for an e- in a molecule Molecular orbitals are associated with the whole molecule not with an individual atom.

Molecular Orbital Theory Molecular Orbitals are analogous to atomic orbitals in many ways: Definite energy Can hold 2 e- with opposite spins Visualized using a 3-D representation

Molecular Orbital Theory When 2 atomic orbitals overlap, two new molecular orbitals are formed: Bonding molecular orbital Antibonding molecular orbital

Molecular Orbital Theory Bonding molecular orbital Constructive interference between two atomic orbitals leads to a build up of e- density between the nuclei lower energy than atomic orbital Bonding MO

Molecular Orbital Theory Antibonding molecular orbital Destructive interference leads exclusion of electrons for the region between the nuclei Highest electron density is located on opposite sides of the nuclei higher energy than atomic orbital Antibonding MO Bonding MO

Molecular Orbital Theory Bonding and antibonding molecular orbitals can be either s or p molecular orbitals: s molecular orbital: A molecular orbital in which electron density is centered around the internuclear axis s bonding MO s1s s2p s antibonding MO s*1s s*2p

Molecular Orbital Theory p molecular orbital: A molecular orbital in which electron density is concentrated on opposite sides of the internuclear axis p bonding MO: p2p p antibonding MO: p*2p

Molecular Orbital Theory The interaction of atomic orbitals to form bonding and antibonding molecular orbitals can be depicted using a molecular orbital diagram. Molecular orbital diagram: an energy level diagram that shows the energy level of molecular orbitals relative to the atomic orbitals from which they’re derived

Molecular Orbital Theory The MO diagram for H2 molecule: s*1s 1s 1s H atom s1s H atom bonding electrons H2 molecule

Molecular Orbital Theory The MO diagram for He2 molecule: antibonding electrons s*1s 1s 1s He atom s1s He atom bonding electrons He2 molecule

Molecular Orbital Theory The He2 molecule has 2 bonding electrons and 2 antibonding electrons. The energy decrease from the 2 electrons in the bonding MO is offset by the energy increase from the 2 electrons in the antibonding MO. He2 is not a stable molecule!

Molecular Orbital Theory In MO Theory, the stability of a covalent bond can be related to its bond order: Bond order = (# bonding e- - # antibonding e-) 2 Single bond: bond order = 1 Double bond: bond order = 2 Triple bond: bond order = 3 Fractional bond orders also exist!

Molecular Orbital Theory The bond order for H2 molecule: Bond Order = (2 - 0) = 1 2 The hydrogen atoms in an H2 molecule are held together by a single bond.

Molecular Orbital Theory The bond order for an He2 molecule: Bond order = (2 - 2) = 0 2 No bond exists between two He atoms.

Molecular Orbital Theory Drawing MO Diagrams: Start with a “skeleton” MO diagram showing the molecular orbitals This will be given to you. Use only the valence electrons of the atoms Follow the aufbau principle Each MO can hold a maximum of 2 electrons Follow Hund’s rule. Keep electrons unpaired until all MO’s having the same energy have 1 e-.

Molecular Orbital Theory You are responsible for determining the correct # of valence electrons for each atom and placing the electrons into the MO diagram. You must be able to calculate bond order. You must be able to predict whether molecule exists or not.

Molecular Orbital Theory Example: Complete the MO diagram for N2. Calculate the bond order. s*2p p*2p s2p p2p s*2s s2s

Molecular Orbital Theory Example: Complete the MO diagram for the O2 molecule. Determine the bond order. s*2p p*2p p2p s2p s*2s s2s

Molecular Orbital Theory The MO diagram for O2 predicts that there are two unpaired electrons. Molecules like O2 that contain one or more unpaired electron(s) are called paramagnetic attracted to a magnetic field

Molecular Orbital Theory The MO diagram for N2 predicts that all electrons are paired. A molecule like N2 that does not contain unpaired electrons is diamagnetic. Weakly repelled by a magnetic field

Molecular Orbital Theory Example: Is Ne2+ paramagnetic or diamagnetic? s*2p p*2p p2p s2p s*2s s2s