Character matrix production

Molecular point-group symmetry can often be used to determine whether a particular transition s dipole matrix element will vanish and, as a result, the electronic transition will be "forbidden" and thus predicted to have zero intensity. If the direct product of the symmetries of the initial and final electronic states /ei and /ef do not match the symmetry of the electric dipole operator (which has the symmetry of its x, y, and z components these symmetries can be read off the right most column of the character tables given in Appendix E), the matrix element will vanish. 

We have used bold characters to show how the C32 was calculated. C32 is the dot product of the second column of matrix B with the third row of matrix A ... 

Wavefunctions and Non-Adiabatic Character. To the extent that simple TST provides a viable model, one can often avoid detailed consideration of wavefunctions for the reactant and product species (t and t ig), and the corresponding matrix element,... 

The matrix Rij,kl = Rik Rjl represents the effect of R on the orbital products in the same way Rjk represents the effect of R on the orbitals. One says that the orbital products also form a basis for a representation of the point group. The character (i.e., the trace) of the representation matrix Rij,kl appropriate to the orbital product basis is seen to equal the product of the characters of the matrix Rjk appropriate to the orbital basis %e2(R) = Xe(R)%e(R)i which is, of course, why the term "direct product" is used to describe this relationship. 

Oil-off occurs in margarine when the matrix of fine fat crystals is no longer of sufficient size or character to be able to enmesh all of the liquid oil. The problem is most serious for stick products as the outside of the inner wrappers may become oil soaked, and if severe, oil will leak out of the package. Prints are also the most susceptible to oil-off because of the pressures to which the product is subjected when pallets or individual packages are stacked. If the margarine is to be merchandised outside of dairy cases, the 21.1°C (70°F) SFI should be specified as high as... 

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