Active Learning the High-Dimensional Transferable Hubbard U and V Parameters in the DFT + U + V Scheme

Density functional theory (DFT) is a powerful quantum mechanical computational tool to perform electronic structure calculations for materials. Few DFT methods can ensure accuracy and efficiency simultaneously. DFT + U + V is an alternative effective approach to overcome this drawback. However, the accuracy sensitively depends on the self-consistent estimation of the high-dimensional onsite and intersite Hubbard interaction U and V terms. We propose Bayesian optimization using a dropout (BOD) algorithm, one type of active learning method, to optimize U and V terms. The DFT + U + V with U/V obtained by BOD can produce improved electronic properties for diverse bulk materials of comparable quality to the hybrid functionals with lower computational cost compared to the linear response approach. Note that the band gaps calculated by BOD are somewhat different from that of hybrid functionals by simply applying the same U/V parameters as in the case of surface slabs and interfaces, which suggests that the transferability of U/V from the bulk models to slabs and interfaces is not as well as expected. BOD is extended to calculate the U/V parameters for slabs and interfaces and reach similar results as bulk solids. Moreover, we find that the U/V are reasonably transferable between surface slabs and interfaces with different thicknesses under various effects of quantum confinement, which contributes to fast access to the electronic properties of large-scale systems with higher accuracy.