Boundary effects and quadrupole contribution in sum frequency generation spectroscopy

Calculation of time correlation functions is a primary task in the computational analysis of sum frequency generation spectroscopy. This paper resolved basic issues to extract interface signals from the calculation. These issues stem from the boundary to restrict the bulk region, which renders the practical computation feasible at a finite and affordable cost. The boundary is found to have significant influences on the time correlation functions, which is closely related to the quadrupole contribution in the nonlinear susceptibility. Thus, we thoroughly examined these influences to establish a proper treatment in performing reliable spectroscopic analysis. We elucidated the distinction of the present boundary effects from the quadrupole contribution and also established a proper center of molecule to minimize the quadrupole effect in the time correlation functions. In the case of liquid water, the proper center was found to be close to the center of mass of a water molecule.