Ambiguities in surface nonlinear spectroscopy calculations

Recent molecular simulations of liquid interfaces yield surface sum-frequency vibrational spectra that can be highly sensitive to the seemingly-arbitrary choice of molecular center in the calculation method. We show that the ambiguity arises because widely-used approaches, focusing exclusively on electric-dipole contributions from the surface, neglect coordinate-dependent quadrupole-order contributions of comparable magnitude from the bulk. The correct calculation includes both surface and bulk responses. With a judicious choice of molecular center, however, it may be possible to minimize the bulk contribution, allowing the surface-only calculation to produce a reasonably accurate spectrum. We use water as an example to elucidate the problem.