various trajectories through the potential energy surface

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.