1. Lab schedule
March 28* for Sections 53 and 54
April 4** for Section 57

2. Potential energy surfaces, pt. 2.

3. Various trajectories through the potential energy surface

4. 24.8 Results from experiments and calculations
(a) The direction of the attack and separation

5. Attractive and repulsive surfaces

6. Classical trajectories
Direct mode process:

7. Classical trajectories
The complex mode process: the activated complex survives for an extended period.

8. Quantum mechanical scattering theory
Using wavefunction to represent initially the reactants and finally products.
Need to take into account all the allowed electronic, vibrational, and rotational states populated by each atom and molecules in the system at a given temperature.
Use “channel” to express a group of molecules in well-defined quantum mechanically allowed state.
Many channels can lead to the desired product.
The cumulative reaction probability.

9. 24.9 The investigation of reaction dynamics with ultrafast laser technique
Spectroscopic observation of the activated complex.
pico: ; femto: 10-15
activated complex often survive a few picoseconds.
Controlling chemical reactions with lasers.
using laser to prepare specific states of reactant molecules.
mode-selective chemistry.

10. 24.10 The rate of electron transfer processes in homogeneous systems
Consider electron transfer from a donor D to an acceptor A in solution
D A → D A- v = kobs [D][A]
Assuming that D, A and DA (the complex being formed first) are in equilibrium: D + A ↔ DA KDA = [DA]/([D][A]) = ka/ka’
Next, electron transfer occurs within the DA complex
DA → D+A vet = ket[DA]
D+A- has two fates: D+A- → DA vr = kr[D+A- ]
D+A- → D+ + A- vd = kd[D+A- ]

11. Electron transfer process
For the case kd>> kr:
When ket <<ka’: kobs ≈ (ka/ka’)ket
Using transition state theory:

12. 24.11 Theory of electron transfer processes
Electrons are transferred by tunneling through a potential energy barrier. Electron tunneling affects the magnitude of kv
The complex DA and the solvent molecules surrounding it undergo structural rearrangements prior to electron transfer
The energy associated with these rearrangements and the standard reaction Gibbs energy determine Δ±G

13. 24.11(a) Electron tunneling
An electron migrates from one energy surface, representing the dependence of the energy of DA on its geometry, to another representing the energy of D+A-.
The factor kv is a measure of the probability that the system will convert from DA to D+A- at the intersection by thermal fluctuation.

14. Initially, the electron to be transferred occupies the HOMO of D
Nuclei rearrangement leads to the HOMO of DA and the LUMO of D+A- degenerate and electron transfer becomes energetically feasible.

15. 24.12 Experimental results of electron transfer processes
where λ is the reorganization energy

16. Decrease of electron transfer rate with increasing reaction Gibbs energy

17. Marcus cross-relation
*D + D+ → *D D kDD
*A A → *A A kAA
Kobs = (kDD kAA K)1/2
Examples: Estimate kobs for the reduction by cytochrome c of plastocyanin, a protein containing a copper ion that shuttles between the +2 and +1 oxidation states and for which kAA = 6.6 x 102 M-1s-1 and E0 = V.