The possibility of application of the three coupled oscillators model in crystalline optical activity

Abstract

In this paper we generalize the quantum mechanical model of three coupled oscillators because of its usage in the crystal optical activity. Using this model we can include the influence of all essential couplings between single oscillators which represent the molecules or atoms of optically active crystals belonging for example to the space groups of symmetry D 4 3 or D 6 3 . The single oscillators are damped and therefore we can include both parts of the optical activity -optical rotatory dispersion and circular dichroism -into computations. We present more universal formulas for description of the above mentioned parts.

Note on the solutions of the model of coupled oscillators in crystalline optical activity for the direction perpendicular to the optic axis

“…The principles of the three coupled oscillator model have already been discussed [18]. Using the proper corrections of the constants in the results, this model can include all couplings between the adjacent oscillators on one helix and also the couplings between odd oscillators (e.g.…”

“…The term in square brackets, in the above listed relation (13), is considered a small perturbation. In this case, the mean values of the induced displacements of the oscillators can be evaluated using the Kubo theorem [18]. These displacements in the normal coordinates are…”

“…to use the model of three coupled oscillators with some corrections, which enable the inclusion of all substantial couplings between oscillators in the crystal structure. This extension can be considered sufficient for crystals belonging to the space groups of symmetry D 4 3 and D 6 3 [18]. The effect of the CD can also be described using damped oscillators.…”