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 <i>f</i>-HOH-<i>f</i>, where neither of the two O-H groups in a water molecule participates in hydrogen bonding, and (2) the "mixed" state, termed as <i>f</i>-HOH-<i>h</i>, 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 <i>f</i>-HOH-<i>h</i> state is much more prevalent among the population of free O-H groups than the <i>f</i>-HOH-<i>f</i> state. Furthermore, our study suggests that the <i>f</i>-HOH-<i>h</i> 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 <i>f</i>-HOH-<i>f</i> 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 <i>D</i> 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 (<i>f</i>-HOH-<i>h</i>) in shaping SFG signals at 3700 cm^{- 1}. In contrast, the disordered state (<i>f</i>-HOH-<i>f</i>) 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.