High-dimensional potential energy surface (PES) for van der Waals systems with spectroscopic accuracy, is of great importance for quantum dynamics and an extremely challenge job. CO-N2 is a typical van der Waals system and its high-precision PES may help elucidate weak interaction mechanisms. Taking CO-N2 potential energies calculated by CCSD(T)-F12b/aug-cc-pVQZ as the benchmark, we establish an accurate, robust, and efficient machine learning model by using only four molecular structure descriptors based on 7966 benchmark potential energies. The highest accuracy is obtained by a stacking ensemble DNN (SeDNN). Its evaluation parameters MAE, RMSE, and R2 reach 0.096, 0.163, 0.9999 cm-1 , respectively, and the spectroscopic accuracy for vibration spectrum is achieved with predicted PES, which shows SeDNN superior goodness-of-fit and prediction performance. An elaborated PES with the reported global minimum has been predicted with the model, which perfectly reproduces CCSD(T) potential energies and the analytical MLR PES [PCCP, 2018, 20, 2036]. The critical points (global minimum, TSI, TSII, and their barriers), potential curve, and entire PES profile are remarkably consistent with CCSD(T) calculations. To further improve the usability of constructing PESs in practice, the size of the training set (energy points) for the model is reduced to 50%, 30%, and 20% of the database, respectively. The results show that even training with the smallest training set (1593 points), the PES only differs 2.555 cm-1 with the analytic MLR PES. Therefore, the proposed SeDNN is promisingly an alternative efficient tool to construct subtle PES for van der Waals systems.
Keywords: deep learning ensemble; first-principles; machine learning; potential energy surface (PES); van der Waals systems.
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