Machine-Learning-Integral-Based Density Functional Theory: mi-DFT

Kohn–Sham density functional theory (KS-DFT) has achieved widespread success owing to its favorable balance between computational accuracy and efficiency. However, its application to molecular aggregates remains challenging because the steep increase in the number of atoms leads to an explosive growth in two-electron integral evaluations, with the computational bottleneck manifesting directly in the construction of high-dimensional Kohn–Sham (KS) matrices. To address this issue, we have developed a Machine-Learning-Integral-Based Density Functional Theory (mi-DFT), which is specifically suited for studying molecular aggregates. By leveraging a machine-learning integral strategy, mi-DFT significantly reduces the cost of constructing high-dimensional KS matrices while exhibiting favorable scalability. Benchmarked against the mi-DFT-Bench dataset—which encompasses one- and two-dimensional $CO_2$ and $H_2O$ systems, as well as one-dimensional ethylene and benzene aggregates—mi-DFT was systematically validated for wavefunctions, energies, and electron densities. The results demonstrate that the energy error of mi-DFT relative to standard DFT is less than 0.3 mH. Furthermore, for one-dimensional $CO_2$ and $H_2O$ systems comprising 2520 atomic-orbital (AO) basis functions, mi-DFT achieves a speedup of 2–5 fold over standard KS-DFT. Although the acceleration is modest at this scale, mi-DFT exhibits a near-linear scaling with system size owing to its local-block prediction strategy, enabling the method to be extended to much larger aggregates: DFT calculations with 30000 basis functions can be completed within 10 hours, where conventional methods would require weeks under equivalent hardware. This method provides a practical pathway for large-scale KS-DFT electronic-structure predictions of molecular aggregates that simultaneously preserves accuracy, transferability, and computational efficiency.