Direct calculation of the X-ray structure factor of ionic liquids

A conceptually simple and computationally efficient direct method to calculate the total X-ray structure factor of ionic liquids from molecular simulations is advocated to be complementary to the popular Fourier transform (FT) method. The validity of the direct method is well formulated and established by comparison with FT results. The effectiveness is demonstrated through versatile partition schemes using tetradecyltrihexylphosphonium bis(trifluoromethylsulfonyl)amide P14,666 Tf2N as a model system. Three characteristic intermolecular peaks were observed below 2 Å(-1), consistent with experimental X-ray measurements. The prepeak corresponds to the polarity alternation leading to structural heterogeneity and the intermediate shoulder is due to the ubiquitous charge ordering of the ionic liquid. The intense peak is mainly attributed to the adjacent contact of apolar cationic tails. The cationic head-anion correlation function is found to be a unique signature for all three characteristic length scales even if a certain peak is concealed by fortuitous cancellation in the X-ray structure factor. The proposed direct formulation can be readily extended to neutron scattering experiments.