Raman microscopy of a small uniaxial crystal: Tetragonal aspartame

A general method is presented for determining the shape and orientation of the Raman tensor of a molecule in a uniaxial crystal using a Raman microscope. First, equations are derived to connect the Raman tensor components (α xx , α yy , etc.) of a molecule to the Raman tensor components (α aa , α cc , etc.) of a crystal that is composed of molecules in a uniaxial arrangement, with an orientation specified by the two angles χ and θ. Next, a method is presented to obtain a correct set of values of the intensity ratios I ac / I aa and I cc / I aa from observed values of the intensity ratios measured with a Raman microscope. To augment the experimental data, the depolarization ratio ρ (for a completely random molecular orientation) is plotted as a function of r 1 = α xx /α zz and r 2 = α yy /α zz , so that a possible set of r 1 and r 2 values can be found from an observed value of ρ. The method has been applied to an aspartame IIA crystal ( P 4 1 ). A set of values of r 1 , r 2 , χ and θ has been determined for each of the following Raman fundamentals: 1741 cm −1 (ester CO stretch), 1667 cm −1 (amide I), 1275 cm −1 (amide III) and 1204 cm −1 (CC phenyl stretch), excited at 488.0 nm.