Exploring nonlinear correlations among transition metal nanocluster properties using deep learning: a comparative analysis with LOO-CV method and cosine similarity.

A novel approach is introduced for the rapid and accurate correlation analysis of nonlinear properties in Transition Metal (TM) clusters utilizing the Deep Leave-One-Out Cross-Validation technique. This investigation demonstrates that the Deep Neural Network (DNN)-based approach offers a more efficient predictive method for various properties of fourth-row TM nanoclusters compared to conventional Density Functional Theory methods, which are computationally intensive and time-consuming. The feature space, also known as descriptors, is established based on a broad spectrum of electronic and physical characteristics. Leveraging the similarities among these clusters, the DNN-based model is employed to explore the correlations among TM cluster properties. The proposed method, in conjunction with cosine similarity, achieves remarkable accuracy up to 10^-9 for predicting total energy, lowest vibrational mode, binding energy, and HOMO-LUMO energy gap of TM₂, TM₃, and TM₄nanoclusters. By analyzing correlation errors, the most closely coupled TM clusters are identified. Notably, Mn and Ni clusters exhibit the highest and lowest levels of energy coupling with other TMs, respectively. Generally, energy prediction for TM₂, TM₃, and TM₄clusters exhibit similar trends, while an alternating behavior is observed for vibrational modes and binding energies. Furthermore, Ti, V, and Co demonstrate the highest binding energy correlations with TM₂, TM₃, and TM₄sets, respectively. Regarding energy gap predictions, Ni exhibits the strongest correlation in the smallest TM₂clusters, while Cr shows the highest dependence in TM₃and TM₄sets. Lastly, Zn displays the largest error in HOMO-LUMO energy gap across all sets, indicating distinctive independent energy gap characteristics.