  The orientational dynamics of supercooled glycerol using molecular dynamics
simulations for temperatures ranging from 323 K to 253 K, is probed through
correlation functions of first and second ranks of Legendre polynomials,
pertaining respectively to dielectric spectroscopy (DS) and depolarized dynamic
light scattering (DDLS). The self, cross, and total correlation functions are
compared with relevant experimental data. The computations reveal the low
sensitivity of DDLS to cross-correlations, in agreement with what is found in
experimental work, and strengthen the idea of directly comparing DS and DDLS
data to evaluate the effect of cross-correlations in polar liquids. The
analysis of the net static cross-correlations and their spatial decomposition
shows that, although cross-correlations extend over nanometric distances, their
net magnitude originates, in the case of glycerol, from the first shell of
neighbouring molecules. Accessing the angular dependence of the static
correlation allows us to get a microscopic understanding of why the rank-1
correlation function is more sensitive to cross-correlation than its rank-2
counterpart.
