Principles of Electric-Dipole-Allowed Enantiomeric Control

1 PRINCIPLES OF ELECTRIC-DIPOLE-ALLOWED ENANTIOMERIC CONTROL 

In this chapter we discuss a number of scenarios for manipulating enantiomer, populations via the electric dipole interaction. However, these scenarios are, presumably, a small subset of an entire class of scenarios capable of achieving this goal. The key issue then is to establish the general conditions under which the electric-dipole, electromagnetic field interaction may be used to attain selective control over the, population of a desired enantiomer. These rales [261] are established in this section. . 

Consider a molecule, described by the Hamiltonian (including electrons and nuclei ) f MT. This Hamiltonian has eigenstates describing the L and D enantiomers,. denoted Lt) and Dt) (i = 1,2,3 ) that satisfy % 

The dipole interaction of this molecule with an incident time-dependent electric- field E(f) is described by the total Hamiltonian  

Here d is the total dipole operator, including both electron and nuclear contributiqni and we have explicitly indicated the dependence of the Hamiltonian on the eledplP field. Consider now the effect of inversion on H. Noting that T operates on jhgj coordinates of the molecule, that = 1 and that [//MT, J] = 0, we have [265] 

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