-- The VSEPR and valence-bond theories don’t Molecular Orbitals -- The VSEPR and valence-bond theories don’t explain the excited states of molecules, which come into play when molecules absorb and emit light. -- This is one thing that the molecular orbital (MO) theory attempts to explain. Molecules respond to the many wavelengths of light. The wavelengths that are absorbed and then re-emitted determine an object’s color, while the wavelengths that are NOT re-emitted raise the temperature of the object.

molecular orbitals: wave functions that describe the locations of electrons in molecules -- these are analogous to atomic orbitals in atoms (e.g., 2s, 2p, 3s, 3d, etc.), but MOs are possible locations of electrons in molecules (not atoms) -- MOs, like atomic orbitals, can hold a maximum of two e– with opposite spins -- but MOs are for entire molecules MO theory is more powerful than valence-bond theory; its main drawback is that it isn’t easy to visualize.

The overlap of two atomic orbitals produces two MOs. Hydrogen (H2) (antibonding MO) s*1s 1s 1s + s1s (bonding MO) H2 molecular orbitals H atomic orbitals -- The lower-energy bonding molecular orbital concentrates e– density between nuclei. -- For the higher-energy antibonding molecular orbital, the e– density is concentrated outside the nuclei. -- Both of these are s molecular orbitals.

Energy-level diagram (molecular orbital diagram) s*1s 1s 1s s1s H atom H atom H2 m’cule 1s H atomic orbitals + H2 molecular orbitals s1s (bonding MO) (antibonding MO) s*1s

Consider the energy-level diagram for the hypothetical He2 molecule… s*1s 1s 1s s1s He atom He atom He2 m’cule 2 bonding e–, 2 antibonding e– No energy benefit to bonding. He2 molecule won’t form.

bond order = ½ (# of bonding e– – # of antibonding e–) -- the higher the bond order, the greater the bond stability -- a bond order of... 0 = no bond 1 = single bond 2 = double bond 3 = triple bond -- MO theory allows for fractional bond orders as well. What is the bond order of H2+? 1 e– total 1 bonding e–, zero antibonding e– BO = ½ (1–0) = ½

Second-Row Diatomic Molecules Li 3 6.941 Be 4 9.012 B 5 10.811 C 6 12.011 N 7 14.007 O 8 15.999 F 9 18.998 Ne 10 20.180 1. # of MOs = # of combined atomic orbitals 2. Atomic orbitals combine most effectively with other atomic orbitals of similar energy. 3. As atomic orbital overlap increases, bonding MO is lowered in energy, and the antibonding MO is raised in energy. 4. Both the Pauli exclusion principle and Hund’s rule apply to MOs.

Use MO theory to predict whether Li2 and/or Be2 could possibly form. s1s s*1s 1s 2s s*2s s2s Li Li BO = ½ (4–2) = 1 Li2 “YEP.”

Bonding and antibonding e– cancel each 2s s*2s s2s Bonding and antibonding e– cancel each other out in core energy levels, so any bonding is due to e– in bonding orbitals of outermost shell. Be Be Be2 BO = ½ (4–4) = 0 “NOPE.”

Molecular Orbitals from 2p Atomic Orbitals The 2pz orbitals overlap in head-to-head fashion, so these bonds are... s bonds. -- the corresponding MOs are: s2p and s*2p z x y The other 2p orbitals (i.e., 2px and 2py) overlap in sideways fashion, so the bonds are... p bonds. -- the corresponding MOs are: p2p (two of these) and p*2p (two of these)

Rule 3 above suggests that, from low energy to high, the 2p MOs SHOULD follow the order: LOW ENERGY HIGH ENERGY s2p < p2p < p*2p < s*2p General energy-level diagrams for MOs of second-row homonuclear diatomic molecules...

s*2p s*2p “Mr. B” p*2p p*2p s2p p2p p2p s2p same for both s*2s s*2s For B2, C2, and N2... For O2, F2, and “Ne2”... s*2p s*2p “Mr. B” p*2p p*2p (or Mr. C) s2p p2p (or Mr. N) p2p s2p same for both s*2s s*2s s2s s2s (1s MOs are down here) Here, the interaction between the 2s of one atom and the 2p of the other is strong. The orbital energy distribution is altered. Here, the interaction is weak. The energy distribution is as expected.

paramagnetism of liquid oxygen paramagnetism: describes the attraction of molecules with unpaired e– to a magnetic field diamagnetism: describes substances with no unpaired e– (“di-” = two; diamagnetic = “dielectron”) ~ -- such substances are VERY weakly (almost unnoticeably) repelled by a magnetic field Use the energy diagrams above to tell if diatomic species are paramagnetic or diamagnetic. paramagnetism of liquid oxygen

Paramagnetic or diamagnetic? s2s s*2s p2p p*2p s2p s*2p s1s s*1s B2 C2 N2 O2 F2 O2+ O22– C22– (10) (12) (14) (16) (18) (15) P D