Quantum optics numerical calculations

The necessary derivations with respect to the small displacements can be performed either numerically, or, more recently, also analytically. These analytical methods have developed very rapidly in the past few years, allowing complete ab initio calculation of the spectra (frequencies and intensities) of medium sized molecules, such as furan, pyrrole, and thiophene (Simandiras et al., 1988) however, with this approach the method has reached its present limit. Similar calculations are obviously possible at the semi-empirical level and can be applied to larger systems. Different comparative studies have shown that the precise calculation of infrared and Raman intensities makes it necessary to consider a large number of excited states (Voisin et al., 1992). The complete quantum chemical calculation of a spectrum will therefore remain an exercise which can only be perfomied for relatively small molecule. For larger systems, the classical electro-optical parameters or polar tensors which are calibrated by quantum chemical methods applied to small molecules, will remain an attractive alternative. For intensity calculations the local density method is also increasing their capabilities and yield accurate results with comparatively reduced computer performance (Dobbs and Dixon, 1994). 

Methods for the description of the optical activity are either based on an estimation of the sum over the rotational strengths of all transitions weighted by a dispersion term as in the case of frequency-dependent optical rotation (ORD denoted as <(> or [M]) or of the rotational strength of one transition in the case of circular dichroism, denoted as Ae or 6 (Eqn [32]). Numerical quantum-mechanical calculations of the rotational strength for a few transitions N) —y K) of a molecule lead nowadays to results of... 

Such processes are obviously dependent on the optical frequency and the resonant frequencies of the liquid crystal constituent molecules. They are also understandably extremely complicated, owing to the complex electronic and energy level stracture of liquid crystal molecules. Even calculating such basic quantities as the Hamiltonian, the starting point for quantum mechanical calcnlations of the electronic wave function and energy levels and linear optical properties, requires very powerful numerical computational techniques. 

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