On the practical applicability of DM21 neural-network DFT functional for chemical calculations: Focus on geometry optimization

Density functional theory is the workhorse of present-day quantum chemistry thanks to its good balance between calculation accuracy and speed. In recent years, several neural network-based exchange-correlation functionals have been developed, with DM21, developed by Google DeepMind, being the most recognizable among them. In this study, we focus on evaluating the efficiency of DM21 functional on the task of optimizing molecular geometries and investigate how the non-smooth behavior of neural network-predicted exchange-correlation energy and potential affects the final geometry precision. We implement geometry optimization for the DM21 functional in PySCF and compare its performance with traditional functionals on various benchmarks. Our findings reveal that numerical noise coming from the neural network outputs contaminates numerical nuclear gradients required for geometry optimization. We also found that a numerical differentiation step in the range of 0.0001-0.001 Å is required to obtain sufficiently smooth nuclear gradients. Furthermore, we show that the non-smoothness of DM21 can be reproduced by adding random normally distributed noise to local energies of an analytical SCAN functional, allowing one to efficiently estimate the optimal numerical differentiation step for geometry optimization of a given molecule. Our findings show that DM21 does not outperform analytical functionals in the accuracy of optimized molecular geometries and is significantly slower, which limits its practical applicability to chemical calculations.