Physical Chemistry 3: — Chemical Kinetics — - Christian-Albrechts ...

1.2 Time scales for chemical reactions 3
I
Time scale of molecular vibrations:
• The frequencies of the vibrational motions of the atoms in a molecule with respect
to each other determine an upper limit for the rate of a unimolecular reaction.
• Uncertainty principle (Fourier relation between frequency and time domain):
y
With = = ˜:
∆ ∆ ≥ ~ (1.6)
∆ ∆ ≥ 1
2
1
∆ ≈
2 ∆˜
• Application to a C-C stretching vibration:
y
y
(1.7)
(1.8)
˜(C-C) ≈ 1000 cm −1 (1.9)
= = ˜ =3× 10 13 s −1 (1.10)
= −1 =333 × 10 −14 s ≈ 33 fs (1.11)
• Application to slow torsional motions of large molecular groups in solution:
˜ ≈ 100 cm −1 (1.12)
y
∆ ≈ 330 fs (1.13)
I Femtochemistry: We can observe ultrafast chemical reactions directly nowadays by
following the motions of atoms or groups of atoms in the course of a reaction in real
time by femtosecond spectroscopy and femtosecond diffraction techniques. This new
area of “femtochemistry” has grown enormously in importance in the last decade, since
the award of the Nobel prize in chemistry to A.H. Zewail in 1999.
1 femtosecond =1fs=10 −15 s (1.14)
I Timescale of e − -jump processes: Only electron jumps are faster than vibrational
motions (by factor of roughly ).
• Estimated time for − -jump to another orbital due to absorption/emission of a
photon:
∆ ≈ 10 −18 s (1.15)
There are indications that electron correlation may slow this time to some
10 −17 s. 10
10 The group of F. Krausz (MPI for Quantum Optics, Munich) recently used attosecond metrology
based on an interferometric method to measure a delay of 21 ± 5as in the photo-induced emission
of electrons from the 2 orbitals of neon atoms with respect to emission from the 2 orbital by a
100 eV light pulse (Schultze et al, Science 328, 1658 (2010)).