We present a combined molecular dynamics simulation and experimental study on the water bending mode at the water-vapor interface using sum-frequency generation (SFG) spectroscopy. The SFG spectrum simulated using an ab initio-based water model shows good agreement with the experimental data. The imaginary part of the SFG response shows a negative peak at ∼1650 cm(-1) and a positive peak at ∼1730 cm(-1). Our results reveal that these widely (∼80 cm(-1)) separated peaks result from the interference of two closely spaced (∼29 cm(-1)) peaks of opposite sign. The positive peak at ∼1689 cm(-1) originates from water with two donor hydrogen atoms with the HOH angular bisector pointing down toward the bulk, and the negative peak at ∼1660 cm(-1) from water with free O-H groups, pointing up. The small frequency difference of 29 cm(-1) indicates that the HOH bending mode frequency of interfacial water is relatively insensitive to the number of hydrogen bonds.

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Two types of diagrammatic approaches for the design and simulation of nonlinear optical experiments (closed-time path loops based on the wave function and doublesided Feynman diagrams for the density matrix) are presented and compared. We give guidelines for the assignment of relevant pathways and provide rules for the interpretation of existing nonlinear experiments in carotenoids.

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