Fig.1 DeePKS algorithm has been implemented within the self-consistent loop in ABACUS[71] (The Hamiltonian value for the DeePKS and the base methods are depicted as HDeePKS and Hbase, respectively. In addition, the difference of the above two Hamiltonians is labeled as Hδ . The electronic wave function and eigenvalue for the ith state are labeled as ψi and εi, respectively. EDeePKS—is the total energy from the DeePKS method) (a); DeePKS algorithm can achieve the accuracy of Hybrid functionals or more precise quantum chemistry methods by incorporating corrections from deep neural networks on top of LDA or GGA functionals (b); and forces on a given single water molecule were calculated using the PBE functional (FPBE), the Heyd-Scuseria-Ernzerhof (HSE) hybrid functional (FHSE) and the DeePKS model (FDeePKS), and the results showed that the DeePKS method's outcomes correspond well with those from the HSE. The label O refers to the oxygen atom while HA and HB refer to the two hydrogen atoms of a water molecule, respectively (c)
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