Polarization moments, classical ground state

Following the general approach, as presented in Chapter 2, let us expand the solution (3.5) over spherical functions (2.14) in order to pass from pa(9,(p) to classic ground state polarization moments aPq (2.16). It is important to stress that, since absorption is non-linear with respect to the exciting light, here, unlike in Section 2.3, we obtain polarization moments aPq of rank k > 2 in the ground state. We will denote the rank and the projection by k and q respectively (unlike K and Q for the excited state). We can, however, state that all the produced polarization... 

The charge distribution of neutral polar molecules is characterized by a dipole moment which is defined classically by jx = E, , , where the molecular charge distribution is defined in terms of the residual charges (qt) at the position r,. The observed molecular dipole moment provides useful information about the charge distribution of the ground state and its ionic character. 

Table 3.1. Analytical expressions for classic polarization moments apQ (k < 4) describing optical polarization of angular momenta in the ground (initial) state via light absorption...

Thus, in this section we have described the manner in which absorption of light by a molecule leads to polarization of the angular momenta of the absorbing level. We have also shown how to calculate the multipole moments created on the lower level. It is important to stress that the adopted model of description enables us to obtain precise analytical expressions for the multipole moments, including both cases, namely those for arbitrary values of angular momenta and those for the classic limit J — oo. Our subsequent discussion will concern problems connected with the manifestation of ground state angular momenta anisotropy in experimentally observable quantities. 

In order to obtain the equations of motion of classical polarization moments, we must base our methods on the system of equations of motion of the probability density pa(6, angular momentum vector 3(6, optical pumping. For a number of maximally simplified situations, where the probability density in the ground state pa(6,(p) does not depend on that of the excited state pb(6,(p), we have already encountered such equations in preceding chapters see e.g., (3.4), or (4.5) and (4.6). 

In the same work, the authors performed reactions in open vessel systems, either in the absence of solvent or on silica gel support in dry media . The cycloaddition of ethyl 1,3-cyclohexadiene carboxylate 81 to ethyl propiolate 82 was improved compared with the harsh classical conditions (benzene at 320 °C for 24 h) (Scheme 11.22). No specific microwave effects were observed in this reaction this was in accordance with results from ah initio calculations which indicated a synchronous mechanism with similar polarity (dipole moment) in both ground and transition states. 

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