Structure-resolved analysis of OH sum frequency generation spectra at the air/water Interface based on ssVVCF

Vibrational sum-frequency generation (SFG) spectroscopy selectively probes interfacial water, but its signed OH lineshape combines local frequency shifts, orientational projection, spatial selection, and coherent cancellation. Recovering a total spectrum from structural components therefore does not, by itself, validate their molecular interpretation. Here, we develop a structure-resolved analysis of a static, zero-field air/water interface by partitioning the surface-specific velocity-velocity correlation function (ssVVCF) at the correlation-function level and testing the resulting assignments beyond algebraic closure. Five independently initialized 100 ps production trajectories of a flexible SPC/Fw water slab were analyzed using hydrogen-bond donor character, OH orientation, and interfacial depth. The calculated ensemble spectrum showed a negative maximum at 3572.9 ± 2.3 cm^-1 and a positive maximum at 3670.9 ± 2.3 cm^-1 (mean ± between-trajectory SD). Independent radial vibrational density-of-states analysis identified donor character as the principal frequency-related descriptor: the centroid of non-donor OH groups was 31.37 ± 0.13 cm^-1 higher than that of strong donors. Orientation produced smaller frequency differences but controlled the sign and efficiency of the ssVVCF response, whereas depth mainly conditioned spatial enrichment. The structural hierarchy was reproduced across all five trajectories and survived held-out-trajectory prediction, label permutation (p = 0.002), threshold perturbation, and structural-memory analysis. The components are therefore interpreted as initial-state-conditioned structure-response associations rather than directly resolved molecular species. Within this scope, quantitative peak positions and amplitudes remain specific to the classical SPC/Fw model, the finite production trajectories, and the Auto-C ssVVCF approximation, which omits explicit intermolecular cross-correlation terms.