Sum Frequency Generation Spectra from Velocity-Velocity Correlation Functions.

We developed an expression for the calculation of the sum frequency generation spectra (SFG) of water interfaces that is based on the projection of the atomic velocities on the local normal modes. Our approach permits one to obtain the SFG signal from suitable velocity-velocity correlation functions, reducing the computational cost to that of the accumulation of a molecular dynamics trajectory, and therefore cutting the overhead costs associated with the explicit calculation of the dipole moment and polarizability tensor. Our method permits to interpret the peaks in the spectrum in terms of local modes, also including the bending region. The results for the water-air interface, obtained using ab initio molecular dynamics simulations, are discussed in connection to recent phase resolved experimental data.