Electromagnetic interactions electric-dipole interaction

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. . 

In addition, there could be a mechanical or electromagnetic interaction of a system with an external entity which may do work on an otherwise isolated system. Such a contact with a work source can be represented by the Hamiltonian U p, q, x) where x is the coordinate (for example, the position of a piston in a box containing a gas, or the magnetic moment if an external magnetic field is present, or the electric dipole moment in the presence of an external electric field) describing the interaction between the system and the external work source. Then the force, canonically conjugate to x, which the system exerts on the outside world is... 

Not only can electronic wavefiinctions tell us about the average values of all the physical properties for any particular state (i.e. above), but they also allow us to tell us how a specific perturbation (e.g. an electric field in the Stark effect, a magnetic field in the Zeeman effect and light s electromagnetic fields in spectroscopy) can alter the specific state of interest. For example, the perturbation arising from the electric field of a photon interacting with the electrons in a molecule is given within die so-called electric dipole approximation [12] by ... 

To see how this result is used, consider the integral that arises in formulating the interaction of electromagnetic radiation with a molecule within the electric-dipole approximation ... 

Thermal effects (dielectric heating) can result from dipolar polarization as a consequence of dipole-dipole interactions of polar molecules with the electromagnetic field. They originate in dissipation of energy as heat, as an outcome of agitation and intermolecular friction of molecules when dipoles change their mutual orientation at each alternation of the electric field at a very high frequency (v = 2450 MHz) [10, 11] (Scheme 3.1). 

Suppose now that the system is subjected to an oscillating electromagnetic field with a representative Fourier component of the electric field F0( >] cos cot. The predominant term in the interaction energy V is usually the electric dipole term Ei , e.g. for an electron in an atom... 

If the field oscillates between the upper and the lower positions, the induced dipole will also oscillate with the frequency of oscillation of the field. The oscillating electric field of the electromagnetic radiation acts in a similar fashion to create an oscillating dipole in the atom or the molecule with Which it is interacting. The dipole is generated in the direction of the electric vector of the incident radiation. 

The probability of a transition being induced by interaction with electromagnetic radiation is proportional to the square of the modulus of a matrix element of the form where the state function that describes the initial state transforms as F, that describing the final state transforms as Tk, and the operator (which depends on the type of transition being considered) transforms as F. The strongest transitions are the El transitions, which occur when Q is the electric dipole moment operator, — er. These transitions are therefore often called electric dipole transitions. The components of the electric dipole operator transform like x, y, and z. Next in importance are the Ml transitions, for which Q is the magnetic dipole operator, which transforms like Rx, Ry, Rz. The weakest transitions are the E2 transitions, which occur when Q is the electric quadrupole operator which, transforms like binary products of x, v, and z. 

Any molecule with a permanent electric dipole moment can interact with an electromagnetic field and increase its rotational energy by absorbing photons. Measuring the separation between rotational levels (for example, by applying a microwave field which can cause transitions between states with different values of /) let us measure the bond length. The selection rule is A/ = +1—the rotational quantum number can only increase by one. So the allowed transition energies are... 

In the first part of this introductory section, we summarize the main collective phenomena acquired by the dipolar exciton from the lattice-symmetry collectivization of molecular properties. The crystal is considered as an assembly of electrically neutral systems, the molecules, physically separated from each other and in electromagnetic interaction. This /V-body problem will be treated quantum-mechanically in the limit of low exciton densities. We redemonstrate the complete equivalence of this treatment with the theories of Lorentz and Ewald, as well as with the semiclassical approximation. In Section I.A, in a more compact but still gradual way, we establish the model of the rigid lattice of dipoles and the general theory of low-exciton-density systems in interaction with the radiation field. Coulombic excitons, photons,... 

This approach clearly distinguishes two ranges of interaction At the scale r < A, where the electrostatic interaction dominates, and at the scale r > /, where the retardation effects dominate. This scale property justifies the separation, implicit in the Coulomb gauge, between instantaneous terms and retarded terms. However, the electric-dipole gauge shows that these two distinct aspects of the electromagnetic interaction are physically undissoci-able, even though it is possible in many problems to omit retardation effects. 

In most of the examples described in this book, the rotational angular momentum is coupled to other angular momenta within the molecule, and the selection rules for transitions are more complicated than for the simplest example described above. Spherical tensor methods, however, offer a powerftd way of determining selection rules and transition intensities. Let us consider, as an example, rotational transitions in a good case (a) molecule. The perturbation due to the oscillating electric component of the electromagnetic radiation, interacting with the permanent electric dipole moment of the molecule, is represented by the operator... 

Equation (79) has the physical meaning that the coherence of the electromagnetic field is lost in a time l/. Models of this kind are frequently used to depict laser light. The electrical dipole of the system interacting with the external field is assumed to have the simple form... 

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