Calculate electronic excited states using neural networks with effective core potential

The essence of atomic structure theory, quantum chemistry, and computational materials science is solving the multi-electron stationary Schr\"odinger equation. The Quantum Monte Carlo-based neural network wave function method has surpassed traditional post-Hartree-Fock methods in precision across various systems. However, its energy uncertainty is limited to 0.01%, posing challenges in accurately determining excited states and ionization energies, especially for elements beyond the fourth period. Using effective core potentials to account for inner electrons enhances the precision of vertical excitation and ionization energies. This approach has proved effective in computing ground state energies for elements like Lithium to Gallium and in calculating energy levels and wave functions for atoms and molecules with second and fourth period elements. Additionally, by integrating effective core potentials with Ferminet, we've achieved multiple excited state calculations with a precision comparable to experimental results, marking a significant advancement in practical applications and setting a new standard for theoretical excited state calculations.