Page 166 - Academic Press Encyclopedia of Physical Science and Technology 3rd Chemical Engineering

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Encyclopedia of Physical Science and Technology EN003H-565 June 13, 2001 20:37

228 Coherent Control of Chemical Reactions

FIGURE 25 Efficiency of the transfer of population in SO 2 by STIRAP as a function of time delay between the pump
and Stokes laser pulses. [Reproduced with permission from Halfmann, T., and Bergmann, K. (1996). J. Chem. Phys.
104, 7068. Copyright American Institute of Physics.]

molecule. In this section we show how the dipole force can K + C 6 H 5 I → C 6 H 5 + KI (68)
be used to manipulate the external motion of a molecule.
was measured by Loesch and coworkers for different ori-
A particle with an electric dipole moment µ and a polar-
entations of phenyl iodide. If a focusing hexapole field is
izability α exposed to an electric field ε has a potential
used instead of a uniform dc field, it is possible to generate
energy
a beam of symmetric top molecules in a single rotational
1 2 2 2
V (θ) =−µε cos θ − ε α cos θ + α ⊥ sin θ , (67) eigenstate.
2
Although the brute force method has produced many
where θ is the angle between µ and ε, and α and α ⊥ are beautiful results, it is limited to molecules with a
the parallel and perpendicular components of the polar- permanent dipole moment and is hampered by the require-
izability tensor, respectively. For a static electric field the ments of high voltages, and, for a multipole focusing field,
first term dominates, and the potential energy has a mini- a complex apparatus. An alternate method of producing
4
mum at θ = 0. Static field strengths on the order of 10 – a strong electric field is to use a focused laser beam. In
5
10 V/cm are typically required to align or orient a the high frequency limit, the time average of the ac elec-
molecule. (Alignment refers to the direction of the molec- 2 1 2
tric field gives
ε(t) = 0 and
ε (t) =
ε , where ε 0
2 0
ular axis without regard to which end is “up,” whereas is the amplitude of the field. The potential energy of the
orientation treats a molecule as a single-headed arrow.) molecule in this case is
For example, Wei Kong used a field strength of 58 kV/cm 1 2 2
V (θ) =− ε α cos θ + α ⊥ , (69)
to orient a molecular beam of BrCN. This “brute force” 4 0
method of orientation has been used to study steric ef- where α = α −α ⊥ is the anisoptropy of the polarizabil-
fects in bimolecular reactions. For example, the differen- ity. A dimensionless quantity that is useful for scaling the
tial cross section for the reaction alignment of different molecules is given by