Neural Network-Assisted Analysis of Free O-H Orientational Distribution at the Air-Water Interface: Gaussian or Exponential?

The studies on the orientational distribution of free O-H groups at the air-water interface have sparked an ongoing scientific debate, giving rise to three compelling theoretical frameworks: the first proposes a stepwise angular distribution; the second hypothesizes a Gaussian pattern; while the third suggests an exponential decay in orientation probabilities. The challenges of understanding the orientation of free O-H groups often stem from insufficient consideration of their conformational states. For instance, a free O-H group can adopt one of two distinct configurational states: (1) the "doubly free" state, termed as -HOH-, where neither of the two O-H groups in a water molecule participates in hydrogen bonding, and (2) the "mixed" state, termed as -HOH-, in which one O-H group remains free while the other engages in hydrogen bonding. Our neural network (NN)-based molecular dynamics (MD) simulation has revealed an intriguing finding: the -HOH- state is much more prevalent among the population of free O-H groups than the -HOH- state. Furthermore, our study suggests that the -HOH- state can be categorized as "interfacial ordered water," which is demonstrated by a relatively narrow Gaussian-like distribution with an average tilt angle of approximately 40°. In contrast, the -HOH- state represents "interfacial disordered water," as evidenced by its broad Gaussian distribution around 90°. Considering the significant influence of configurational states on the orientational distribution of free O-H groups, we propose a dual-Gaussian superposition model to reveal intricate features of free O-H orientation, incorporating two Gaussian functions: one with a broad angular distribution, representing the disordered component, and the other featuring a narrow distribution to capture the ordered component. Employing this dual-Gaussian superposition model, we calculated the orientational parameter and the sum frequency generation (SFG) intensity ratio across different polarizations, achieving excellent alignment with the experimental results. Our findings illuminate the crucial role of free O-H groups' ordered state (-HOH-) in shaping SFG signals at 3700 cm. In contrast, the disordered state (-HOH-) may increase the average tilt angle but exerts little influence on the SFG signals. In summary, the insights from our DeePMD simulations, coupled with our pro dual-Gaussian superposition model, provide a perspective on the long-standing debate regarding the orientational distribution of free O-H groups.