Molecular Orbital Theory Bonding Models: Lewis Structures and VSEPR Valence Bond (VB) or Localized Electron (LE) Theory Molecular Orbital (MO) Theory Bonding Models: Lewis Structures and VSEPR Valence Bond (VB) or Localized Electron (LE) Theory Molecular Orbital (MO) Theory Ease of use Accuracy

Molecular Orbital Theory   

Molecular Orbital Theory For homonuclear diatomic molecules (O 2,N 2, Cl 2,etc) the molecular orbitals (MOs) can be approximated as linear combinations of atomic orbitals. Ψ bonding orbital = Ψ MO = [Ψ 1 + Ψ 2 ] Ψ antibonding orbital = Ψ MO* = [Ψ 1 - Ψ 2 ] * Ψ = wave function of the electrons combining

Molecular Orbital Theory A molecular orbital is formed from interactions between two atomic orbitals that merge when two atoms attempt to share electrons, which then may or may not be occupied by the electron(s) from the atoms. These new molecular orbitals result from orbital overlap occurring during an attempt to bond. MO Theory doesn’t treat the electrons as belonging to specific bonds, but as being spread out over the whole new molecule that has been formed. MO theory treats electrons as if they are delocalized, or spread out over the entire molecule, now orbiting in a new orbital created by two electrons merging in their wave functions. Molecular orbitals form when: the symmetries of the atomic orbitals are compatible with each other, the region of overlap between the two atomic orbitals is significant, and the atomic orbitals are relatively close in energy to each other A molecular orbital is formed from interactions between two atomic orbitals that merge when two atoms attempt to share electrons, which then may or may not be occupied by the electron(s) from the atoms. These new molecular orbitals result from orbital overlap occurring during an attempt to bond. MO Theory doesn’t treat the electrons as belonging to specific bonds, but as being spread out over the whole new molecule that has been formed. MO theory treats electrons as if they are delocalized, or spread out over the entire molecule, now orbiting in a new orbital created by two electrons merging in their wave functions. Molecular orbitals form when: the symmetries of the atomic orbitals are compatible with each other, the region of overlap between the two atomic orbitals is significant, and the atomic orbitals are relatively close in energy to each other

Molecular Orbital Theory The number of molecular orbitals (MOs) that can be formed must equal the number of atomic orbitals of the combining atoms In MO theory we construct the orbital interaction diagram first and then put in the electrons according to the aufbau principle AB A-B A-B*

Molecular Orbital Theory Bond order = ½ [(number of bonding electrons) – (number of antibonding electrons)] While the bond order cannot be measured directly, we can make correlations between the bond order and bond distances, bond dissociation energies, and bond stability Bond order = ½ [(number of bonding electrons) – (number of antibonding electrons)] While the bond order cannot be measured directly, we can make correlations between the bond order and bond distances, bond dissociation energies, and bond stability SpeciesBond orderBond distance Bond dissociation enthalpy H2+H pm255 kJ/mol H2H pm458 kJ/mol

Molecular Orbital Theory – Homonuclear Diatomics We eventually want to use molecular orbital theory to explain the bonding in polyatomic molecules and ions such as: H 2 O, CO 2, NH 3, BF 3, CH 4, NO 3 -, and B 2 H 6. To do this we are going to have to look at the symmetry of different sized atomic orbitals that are overlapping. Before we consider these molecules, where a detailed look at symmetry is important, we will start with molecules in which symmetry is more straightforward – homonuclear diatomic molecules such as H 2, O 2, and F 2 – as the orbitals on each atom are identical We eventually want to use molecular orbital theory to explain the bonding in polyatomic molecules and ions such as: H 2 O, CO 2, NH 3, BF 3, CH 4, NO 3 -, and B 2 H 6. To do this we are going to have to look at the symmetry of different sized atomic orbitals that are overlapping. Before we consider these molecules, where a detailed look at symmetry is important, we will start with molecules in which symmetry is more straightforward – homonuclear diatomic molecules such as H 2, O 2, and F 2 – as the orbitals on each atom are identical

Molecular Orbital Theory – H 2

Molecular Orbital Theory – H 2 +

Molecular Orbital Theory – He 2 +

Molecular Orbital Theory – He 2

Molecular Orbital Theory – Li 2 Li 2  (1s) 2  * (1s) 2  (2s) 2 Bond order = ½ [(4) – (2)] = 1.0

Molecular Orbital Theory – Be 2 Be 2  (1s) 2  * (1s) 2  (2s) 2  * (2s) 2 Bond order = ½ [(4) – (4)] = 0.0 Be Be 2 Be This is evidence for an extremely unstable Be 2 species with a bond energy of only 10 kJ mol -1

Molecular Orbital Theory – valence 2s and 2p The p z orbitals, can interact with each other along the bond axis to form a  bonding molecular orbital,  g (2p z ), and a  antibonding molecular orbital,   *(2p z ). The p z orbitals, can interact with each other along the bond axis to form a  bonding molecular orbital,  g (2p z ), and a  antibonding molecular orbital,   *(2p z ).

Molecular Orbital Theory - p z orbitals for s bonding

Molecular Orbital Theory – valence 2s and 2p The p orbitals, p x and p y, which are perpendicular to the bond axis, can overlap in a sideways manner to form  bonds. The overlap in the  bonds is smaller than the direct overlap in the  bonds. The bonding MO is  u, while the antibonding MO is  g *. The p orbitals, p x and p y, which are perpendicular to the bond axis, can overlap in a sideways manner to form  bonds. The overlap in the  bonds is smaller than the direct overlap in the  bonds. The bonding MO is  u, while the antibonding MO is  g *.

Molecular Orbital Theory – p x orbitals for  bonding

Molecular Orbital Theory – X 2 diatomics, such as F 2, O 2

Molecular Orbital Theory – O 2 Why is O 2 paramagnetic, even though its electron configuration from localized electron bonding theory shows otherwise?

Molecular Orbital Theory - F 2

Molecular Orbital Theory - energy exceptions - Notice that the  2p and the  2p orbitals are flipped - why is this?

Molecular Orbital Theory - energy exceptions

DiatomicBond distance (pm) Bond dissocation energy (kJ/mol) Bond order Magnetic properties Li diamagnetic Be 2 (245)(10)0 B2B paramagnetic C2C diamagnetic N2N diamagnetic O2O paramagnetic F2F diamagnetic

Molecular Orbital Theory – Heteronuclear diatomics With homonuclear diatomic molecules such as H 2 and O 2, the atomic orbitals of the same label, such 2s – 2s and 2p z - 2p z, were symmetry matched and the resulting MOs from their interactions had equal contributions from the atomic orbitals on each atom. With heteronuclear diatomic molecules, such as HF and CO, the set of orbitals available from each atom might be different and the energies of the orbitals are going to be different. How do these atomic orbital symmetry and energy considerations affect the appearance of the molecular orbital energy diagram? With homonuclear diatomic molecules such as H 2 and O 2, the atomic orbitals of the same label, such 2s – 2s and 2p z - 2p z, were symmetry matched and the resulting MOs from their interactions had equal contributions from the atomic orbitals on each atom. With heteronuclear diatomic molecules, such as HF and CO, the set of orbitals available from each atom might be different and the energies of the orbitals are going to be different. How do these atomic orbital symmetry and energy considerations affect the appearance of the molecular orbital energy diagram?

Molecular Orbital Theory – XY molecules The overlap of these two orbitals would be nonbonding, as they are not symmetry compatible The overlap of these two orbitals would be bonding, as they are symmetry compatible

Molecular Orbital Theory – XY molecules When the energies of the atomic orbitals that are interacting (allowed by symmetry) are different, the resulting MOs have different contributions from each atomic orbital, according to the energy difference (  E) between the atomic orbitals. The ψ* MO has more “X” character, while the ψ MO has more “Y” character.

Molecular Orbital Theory - HF The H atom has only one orbital with an electron in it, the 1s orbital. Which F atomic orbital is it going to interact with? In terms of symmetry, it could interact with the 2s or the 2p z atomic orbitals on F. In terms of energy, the F 2p z orbital is closer in energy to the H 1s orbital than is the F 2s orbital The H atom has only one orbital with an electron in it, the 1s orbital. Which F atomic orbital is it going to interact with? In terms of symmetry, it could interact with the 2s or the 2p z atomic orbitals on F. In terms of energy, the F 2p z orbital is closer in energy to the H 1s orbital than is the F 2s orbital

Molecular Orbital Theory - HF The H 1s orbital interacts with the F 2p z orbital to form a  and a  * orbital, with each contributing one electron to fill the  orbital and form a H-F bond. The remaining orbitals on F have no orbitals on H to interact with and form filled nonbonding (n) orbitals at the same energy as the F atomic orbitals The H 1s orbital interacts with the F 2p z orbital to form a  and a  * orbital, with each contributing one electron to fill the  orbital and form a H-F bond. The remaining orbitals on F have no orbitals on H to interact with and form filled nonbonding (n) orbitals at the same energy as the F atomic orbitals  2s 2

Molecular Orbital Theory - CO The Lewis structure and valence bond theory suggest to us that CO has a triple bond, with one lone pair of electrons on the oxygen atom and one lone pair of electrons on the carbon atom: It is important to note that: Z eff (O) > Z eff (C) the energy of the O 2s atomic orbital is lower than that of the C 2s atomic orbital the 2p level in O is at a lower energy than that in C the 2s-2p energy separation in O is greater than that in C The Lewis structure and valence bond theory suggest to us that CO has a triple bond, with one lone pair of electrons on the oxygen atom and one lone pair of electrons on the carbon atom: It is important to note that: Z eff (O) > Z eff (C) the energy of the O 2s atomic orbital is lower than that of the C 2s atomic orbital the 2p level in O is at a lower energy than that in C the 2s-2p energy separation in O is greater than that in C

Molecular Orbital Theory - CO  2s  2p  2p *  2s *  2s 2   2s 2  2p 4  2p 2

Molecular Orbital Theory - CO (doubly degenerate)