Performance assessment of the effective core potentials under the fermionic neural network: First and second row elements

The rapid development of deep learning techniques has driven the emergence of a neural network-based variational Monte Carlo (VMC) method (referred to as FermiNet), which has manifested high accuracy and strong predictive power in the electronic structure calculations of atoms, molecules, and some periodic systems. Recently, the implementation of the effective core potential (ECP) scheme has further facilitated more efficient calculations in practice. However, there is still a lack of comprehensive assessments of the ECP's performance under the FermiNet. In this work, we set sail to fill this gap by conducting extensive tests on the first two row elements regarding their atomic, spectral, and molecular properties. Our major finding is that, in general, the qualities of ECPs have been correctly reflected under FermiNet. Two recently built ECP tables, namely, correlation consistent ECP (ccECP) and energy consistent correlated electron pseudopotential (eCEPP), seem to prevail in terms of overall performance. In particular, ccECP performs slightly better on spectral precision and covers more elements, while eCEPP is more systematically built from both shape and energy consistency and better treats the core polarization. On the other hand, the high accuracy of the all-electron calculations is hindered by the absence of relativistic effects as well as the numerical instabilities in some heavier elements. Finally, with further in-depth discussions, we generate possible directions for developing and improving FermiNet in the near future.