Chemistry 445. Lecture 3. Molecular Orbital Theory

1. Chemistry 445. Lecture 3. Molecular Orbital Theory

2. We start by reminding ourselves of the shapes and signs of the wavefunction on the atomic orbitals. Below are the s and three p orbitals, showing boundary surfaces (H&S Fig. 1.9) Note: Pink color indicates sign of wavefunction opposite to that of the white part of the orbital.

3. The five atomic d-orbitals

4. The essence of MO theory is that overlap of two orbitals always occurs in two ways. In one (bottom), the two 1s orbitals shown here overlapping have the same sign of the wavefunction, and so a net overlap occurs. This produces a lower energy bonding orbital. In the upper case, the two orbitals are of opposite sign, and so no net overlap occurs. This produces a higher energy anti-bonding orbital. higher energy anti-bonding orbital Sign of wavefunction is opposite + σ*1s 1s 1s + σ1s 1s 1s lower energy bonding orbital sign of wavefunction is the same

5. Drawing up a Molecular Orbital (MO) diagram for H2 energy arrow represents electron in 1s orbital energy level of 1s orbital of H-atom 1s atomic orbital of H atom 1s atomic orbital of H atom

6. Drawing up a Molecular Orbital (MO) diagram for H2 σ*1s anti-bonding molecular orbital in H2 molecule energy 1s atomic orbital of H atom 1s atomic orbital of H atom σ1s bonding molecular orbital in H2 molecule These are the molecular orbitals of the H2 molecule

7. Molecular Orbital (MO) diagram for H2 molecule (bond order = 1) σ* 1s asterisk denotes anti-bonding orbital arrow = electron 1s atomic orbital of H atom 1s atomic orbital of H atom σ 1s

8. Some observations on MO diagrams: A single bond consists of a shared pair of electrons (Lewis). In MO theory Bond Order (BO) = (No. of e’s in bonding levels – no. of e’s in anti- bonding levels)/2 BO for H2 = (2-0)/2 = 1 in labeling the molecular orbitals, the type of overlap Is specified (σor π), and the atomic orbitals involved indicated. the two arrows are opposite in direction indicating a pair of spin-paired electrons of opposite spin because of the Pauli exclusion Principle each orbital can contain a maximum of two electrons, which must be of opposite spin

9. Some more observations on MO diagrams: The greater the drop in energy the stronger the bond. For the H2 molecule the drop is 218 kJ/mol so the enthalpy of dissociation of the H2 molecule is 436 kJ/mole In MO theory the reason molecules form is because the bonding orbitals formed are lower in energy than the atomic orbitals, and the electrons are lowered in energy by this amount.

10. Even more observations on MO diagrams: Electron excited to anti-bonding level Photon of Energy = hv BO = (1-1)/2 = 0 for excited state MO diagrams show how a photon of energy = hv = the difference in energy between two MO’s, can cause an electron to be excited to the higher energy level MO. In this excited state the bond order = zero and so the H2 molecule can photo-dissociate. Whether the transition can occur is also determined by the parity of the orbitals (g or u) – see later.

11. Identification of bonding and non-bonding molecular orbitals. A bonding MO has no nodal plane between the two atoms forming the bond, i.e. the electron density does not go to zero at a node. An anti-bonding MO has a nodal plane where electron-density = zero: nodal plane σ(1s) bonding orbital σ*(1s) anti-bonding orbital π(2p) bonding orbital π*(2p) anti-bonding orbital