Rotational strength, determination

The planar C2h and C2V geometries of the 1,3-butadiene moiety are achiral structures and obviously they cannot show optical activity (i.e. ORD and CD). This has, of course, a spectroscopic origin. The optical activity of a transition Pq — Pi is determined by its Rotational Strength (R)1 defined as the scalar product... 

A bloom strength determination is part of the acceptance criteria for each receipt of gelatin raw material. The bloom gelometer numbers range from 125 to 195 for the 12 lots, with a mean of 147. This number was compared to gelatin ribbon thickness and die rotation speed during encapsulation to ascertain whether lot-to-lot differences had to be compensated for. No relationship was found. 

The quantity that connects theory with experiment in CD spectroscopy is the rotational strength R. On an experimental level, R is determined by the area under a resolved CD transition (Figure 1.6b), while from theory the rotational strength is proportional to the projection of the electric dipole moment of a T g —> vPe transition... 

Here i//0 is the ground vibrational wave function and ij/ is the wavefunction corresponding to the first excited vibrational state of the th normal mode /< is the electric dipole moment operator Qj is the normal coordinate for the /th vibrational mode the subscript 0 at derivative indicates that the term is evaluated at the equilibrium geometry. The related rotational strength or VCD intensity is determined by the dot product between the electric dipole and magnetic dipole transition moment vectors, as given in (2) ... 

A quantitative measure of the optical activity of an electronic transition is the rotational strength which can be determined from the CD spectrum by integration over the corresponding band. In units of Debye x Bohr magneton one has... 

The electric and magnetic moments, <01// a> and , are based on the linear and angular momentum of electrons involved in the transition. The angular momentum corresponds to the rotational motion of an electron, while the linear momentum corresponds to the linear motion of the electron. If the electric and magnetic moment vectors, <01// a> and , are parallel to each other in one enantiomer, they should be antiparallel in the other enantiomer. Therefore, the rotational strength R, OR [a]A, and CD spectra of enantiomers are opposite in sign but of equal intensity. The problem of how to determine the ACs of... 

In the ligand polarization mechanism for optical activity, the potential of the electric hexadecapole component, Hxy(x>-y>), produces a determinate correlation of the induced electric dipole moment in each ligand group which does not lie in an octahedral symmetry plane of the [Co Ng] chromophore (Fig. 8). The resultant first-order electric dipole transition moment has a non-vanishing component collinear with the zero-order magnetic moment of the dxy dxj yj transition in chiral complexes, and the scalar product of these two moments affords the z-component of the rotational strength, RJg, of the Aj -> Ti octahedral excitation. 

For intrinsically chiral species that are inert enough to be resolved conventionally, the measurement of natural optical activity in crystals has the same advantages as single crystal absorption measurements. In addition, however, it also affords the opportunity to determine rotational strengths of species which do not exhibit optical activity in solution. There are two classes of such materials 1) intrinsically achiral chromophores which crystallize in enantiomorphous space groups, and 2) intrinsically chiral but labile chromophores which spontaneously resolve on crystallization. 

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