Symmetry III: Molecular Orbital Theory. Reading: Shriver and Atkins and , 6.10

Transcription

1 Lecture 9 Symmetry III: Molecular Orbital Theory Reading: Shriver and Atkins and g , 6.10

2 The orbitals of molecules H H The electron energy in each H atom is ev below vacuum. What happens to the energy levels as the H-atoms approach each other? Technique: Solve Schrodinger equation, using the potential energy for the coupled electrons.

3 Molecular Force Net Force F N =F A +F R Equilibrium E i when F N =0 r 0 =bond length

4 Potential energy, V(r) V 0: bond energy or cohesive energy (energy required to separate the two atoms) V R A B In general: V ( r) n m r r V V 0 V A

5 Bonding & Antibonding orbitals Two H atoms, both in their 1s state. As they approach, their wavefunctions begin to overlap.

6 Bonding & Antibonding orbitals Formation of molecular orbitals - bonding and antibonding ( and * ) when two H atoms approach each other. The two electrons pair their spins and occupy the bonding orbital.

7 H-H bond: Electron probability distribution (a) Electron probability distributions for bonding and antibonding orbitals, and *. (b) Lines representing contours of constant probability (darker lines represent greater relative probability).

8 Linear combination of atomic orbitals Two atomic orbitals 1s on atoms A and B can be combined linearly in two different ways to generate two separate molecular orbitals and * and * generated from a linear combination i of atomic orbitals (LCAO) Wavefunction around A Wavefunction around B ( r ) ( r 1 s A 1 s B ) r ) ( r ) s ( 1s A 1 s B * B

9 Energies using schrodinger s equation Energy of and * found using the time-independent Schrodinger equation (TISE) vs. the interatomic separation R.

10 Molecular orbital energy level diagram antibonding 11.4eV Bonding energy (dissociation bonding energy) = 4.5eV H atom H 2 molecule H atom

11 He-He bond antibonding bonding Two He atoms have four electrons. When He atoms come together, two of the electrons enter the E level and two the E * level, so the overall energy is greater than two isolated He atoms (since E antibonding >> E bonding ). Therefore, He-He does not exist!

12 Key Concepts 1. # molecular orbitals = # atomic orbitals 2. Three types of molecular orbitals: bonding, antibonding, and nonbonding Nonbonding: a MO that neither raises nor lowers the energy of the system. Typically, it consists of a single orbital on one atom (possibly because there is no atomic orbital of the correct symmetry for it to overlap on a neighboring atom) 3. All components of the MO must behave identically under transformation if they are to have non-zero overlap 4. The Pauli exclusion principle limits the number of electrons that can occupy any molecular orbital to two. Those electrons must be paired.

13 Symmetry adapted linear combinations σ Orbitals Molecular orbitals arise from atomic orbitals of the same symmetry (i.e., overlap of s and s or s and p z or d and d)

14 Symmetry adapted linear combinations π Orbital δ Orbital Molecular orbitals arise from atomic orbitals of the same symmetry (i.e., overlap of s and s or s and p z or d and d)

15 Disallowed SACLs The constructive interference between parts of atomic orbitals with the same sign exactly matches the destructive interference between the parts with opposite sign: zero net overlap All components of the molecular orbital must behave identically under transformation if they are to have nonzero overlap

16 Energies of molecular orbitals Generally determined d by number of nodes. The greater the number of nodes in a MO, the greater the antibonding character and the higher the orbital energy. Energy

17 Energies of molecular orbitals Energy Recall: The label g, u indicates the symmetry of the orbital with respect to inversion (and is not necessarily related to the MO energy)

18 Benzene From the six atomic p z orbitals, we can construct six molecular orbitals

19 Benzene