面向 Co$_3$O$_4$ 的高维神经网络势

Co$_3$O$_4$ 磷化物是氧化催化中的重要材料。其在催化条件下（即在有限温度下）的性质可通过分子动力学模拟来研究，这些模拟严重依赖于对原子相互作用的准确描述。由于 Co$_3$O$_4$ 的高度复杂性，这与 Co 离子多种氧化态的存在有关，迄今为止只有 \textit{ab initio} 方法才能可靠地捕捉潜在的能量势面，同时更高效的原子势难以构建。因此，包含 Co$_3$O$_4$ 的计算机模拟的可及长度和时间尺度仍受到严格限制。 rapidly advances in the development of modern machine learning potentials (MLPs) trained on electronic structure data now make it possible to bridge this gap. In this work, we employ a high-dimensional neural network potential (HDNNP) to construct a MLP for bulk Co$_3$O$_4$ spinel based on density functional theory calculations. After a careful validation of the potential, we compute various structural, vibrational, and dynamical properties of the Co$_3$O$_4$ spinel with a particular focus on its temperature-dependent behavior, including the thermal expansion coefficient. The reported results suggest that flipping trajectory features in cold Rydberg many-body systems could advance sensing and metrology applications.