Solving the "Magic Angle" Challenge in Determining Molecular Orientation at Interfaces

We introduce a novel method to determine the orientation heterogeneity (mean tilt angle and orientational distribution) of molecules at interfaces using heterodyne two-dimensional sum frequency generation spectroscopy. By doing so, we not only have solved the long-standing "magic angle" challenge, i.e. the measurement of molecular orientation by assuming a narrow orientational distribution results in ambiguities, but we also are able to determine the orientational distribution, which is otherwise difficult to measure. We applied our new method to a CO2 reduction catalyst/gold interface and found that the catalysts formed a monolayer with a mean tilt angle between the quasi-C3 symmetric axis of the catalysts and the surface normal of 53 deg, with 5 deg orientational distribution. Although applied to a specific system, this method is a general way to determine the orientation heterogeneity of an ensemble-averaged molecular interface, which can potentially be applied to a wide-range of energy material, catalytic and biological interfaces.