Transition moment description

Sharf and Fischer14) have developed a new approach to account for the lack of a complete cancellation of intensity at the dip in the Fano line, in terms of the Fano treatment of a discrete state and a number of continua. It was shown that the Bixon-Jortner description of the quasi-continuum as a manifold of equally spaced levels with constant interactions with the discrete state and with constant transition moments from the ground state, does not comply with the quantum-... 

The first term in Equation (1.47) is identical with the expression derived in the last section for electronically allowed transitions. It is presently assumed to be very small or zero. (A/o f - 0 for symmetry-forbidden transitions.) The second term results from vibronic mixing and represents a first-order vibronic contribution to the transition moment. It is seen that in this description the forbidden transition 0->f steals or borrows intensity from the allowed transition 0- b. If A/o f is exactly zero all observed components of the electronic transition will be polarized along the direction of the transition dipole moment A o b. The 0- 0 transition (v = v = 0) will have zero intensity and only vibrational levels of overall symmetry given by the direct product of symmetries of the states % and % will appear. 

Although the description of electronic states by means of the perimeter model is somewhat less satisfactory for molecules that can be derived formally from an antiaromatic AN perimeter than for aromatic molecules, simple statements about MCD signs are still possible. While nothing can be said about the S and D bands, which according to the perimeter model have zero electric transition moments and which experimentally are found to be very weak (the latter is normally inobservable), predictions are possible for the strong absorptions that are referred to as the N, N2, P, and P2 bands according to the nomenclature given in Section 2.2.7. The parameters that are essential for the MCD spectra of systems derived from a 4)V-electron perimeter are... 

These equations are difficult to use to accurately calculate the nonlinear optical properties of molecules because of the need for a complete set of excitation energies and transition moments. For p and 7, the transition moments needed are not only ground to excited state (i.e., normal UV/vis-type data) but also excited state to excited state transtion moments. Alternatively, what is needed is a complete description of the ground and excited states of the molecule. 

The absence of a wave function makes a direct description of excited states with the same symmetry as the ground state problematic. Excited states must be orthogonal to the ground state, which is easy to enforce if the spatial or spin symmetry differ, but difficult to ensure for excited states having the same spatial and spin symmetry. Excited state properties, however, can be calculated by time-dependent DFT (linear response) methods, since the excited state is never needed explicitly. Such calculations can give for example excitation energies and transition moments, as well as gradients of the excited surface, which allows excited states to be optimized. 

The theory for rotational diffusion of ellipsoids, and measurements by fluorescence polarization, can be traced to the classic reports by F. Perrin. Since these seminal reports, the theory has been modified to include a description of expected anisotropy decays. Hiis theory has been summarized in several reviews.For a rigid ellipsoid with three unequal axes, it is now agreed that the anisotropy decays with five correlation times. The correlation times depend on the three rotational diffiision coefficients, and the amplitudes depend on the orientation of the absorption and emission transition moments widiin the fluoroi iore and/or ellipsoid. While the the( predicts five correlation times, it is known diat two pairs of correlation times will be very close in magniOide, so that in practice only three correlation times are expect for a nonsf oical molecule. ... 

A sufficient amount of oriented chiral molecules can be obtained in an induced cholesteric liquid crystal phase if the induced helical structure has been untwisted by an electric field. In the following description tensors are needed for the sake of simplicity (At least there are three tensors required the transition moment tensor (absorption tensor ,y), the rotational strength tensor (circular dichroism tensor A ,y), and the order tensor g,y33 (i,j= 1,2,3). If the molecules do not possess any symmetry, the principal axes of all of these tensors are differently oriented with respect to the molecular frame (the coordinate system in which only the three diagonal elements of a tensor are different from zero).) The only tensorial property, needed here explicitly, is the existence of three coordinates (components) of a tensor with respect to three specially chosen mutually perpendicular axes. This means that three information instead of one information about a molecule are needed instead of one CD value, namely Ae, three CD values, namely As, (i=l, 2, 3), have to be introduced. Ac is then one-third of a sum of the three so-called tensor coordinates of the CD tensor ... 

As will be seen later, this aspect of orientation description is important in some experimental techniques, where for example OA represents a transition moment at an angle ip to the molecular chain axis OB which has a preferred orientation with respect to the director OC. 

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