Hydrogen bond (HB) dynamics at the air-water interface is investigated by constructing a new statistical approach to analyze the configuration data obtained from density functional-based molecular dynamics (DFTMD) simulations. To calculate HB dynamics for water molecules at the air-water interface, we combines two different ways to identify interfacial H-bonds. This approach gives two extreme cases of the interfacial HB dynamics: one underestimates the HB breaking rate constant and the other overestimates it. The interfacial HB dynamics in the water layers below the surface in these two extreme cases tends to be the same as the thickness of the water layer increases. The advantage of this approach is that the real HB characteristics, such as the HB lifetime, HB reaction rate constants, and the thickness of the air-water interface, are determined.

In this note, we introduce one basic concept in nonlinear optical spectroscopy: time-dependent Hamiltonian, and give one example of application of the time evolution operator.