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.
