Various trajectories through the potential energy surface

24.8 Results from experiments and calculations

(a) The direction of the attack and separation

Attractive and repulsive surfaces

Classical trajectories

• Direct mode process:

Classical trajectories

• The complex mode process: the activated complex survives for an extended period.

24.8(d) Quantum mechanical scattering theory

• Classic trajectory calculations do not recognize the fact that the motion of atoms, electrons, and nuclei is governed by quantum mechanics.

• Using wave function 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, which complicate the quantum mechanical calculations.

• The cumulative reaction probability, N(E), the summation of all possible transitions that leads to products.

24.9 The investigation of reaction dynamics with ultrafast laser technique

• Spectroscopic observation of the activated complex.

pico: 10-12; femto: 10-15

activated complex often survive a few picoseconds.

• Femtosecond spectroscopy (two pulses):

• Controlling chemical reactions with lasers. mode-selective chemistry: using laser to excite the reactants to

different vibrational states: Example: H + HOD reaction. Limitation: energy can be deposited and remains localized.

combination of ultrafast lasers: Overall, it requires more sophisticated knowledge of how stimulation

works.

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- ]

Electron transfer process

• For the case kd>> kr:

• When ket <<ka’: kobs ≈ (ka/ka’)ket

• Using transition state theory:

et

a

aobs k

k

kk

'

111

d

r

eta

a

aobs k

k

kk

k

kk1

11 '

RTGet vek /

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 (the Gibbs energy of activation).

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-. (so fast that they can be regarded as taking place in s stationary nuclear framework)

• 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.

• 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.

24.12 Experimental results of electron transfer processes

where λ is the reorganization energy

tconsRT

G

RT

Gk rret tan

2

1

4

1)ln(

2

Decrease of electron transfer rate with increasing reaction Gibbs energy

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 = 0.350 V.