We cast the inverse DFT problem as a constrained optimization problem and employ a finite-element basis-a systematically convergent and complete basis-to discretize the problem. This work presents a numerically robust and accurate scheme to evaluate the exact exchange-correlation potentials from correlated ab-initio densities. However, the lack of an accurate and systematically convergent approach has left the problem unresolved, heretofore. The inverse DFT problem of mapping the ground-state density to its exchange-correlation potential is instrumental in aiding functional development in DFT. The quest for accurate exchange-correlation functionals has long remained a grand challenge in density functional theory (DFT), as it describes the many-electron quantum mechanical behavior through a computationally tractable quantity-the electron density-without resorting to multi-electron wave functions. The effects of higher-order non-relativistic interactions as well as the finite nuclear mass of the atoms are also analyzed. The non-relativistic ground-state ionization potentials for atoms with up to 103 electrons generated using the all-electron potential are in reasonable agreement with the existing experimental and theoretical data. With the potential, all atoms are treated in the same way regardless of whether they are open or closed shell using their system specific information. The symmetry dependence in the proposed potential hinges on an empirically determined angular momentum-dependent partitioning fraction for the electron–electron interaction. In an effort to tackle this many-body problem, a symmetry-dependent all-electron potential generalized for an n-electron atom is suggested in this study. Accurate treatment of the electron–electron problem is likely to unravel some nice physical properties of matter embedded in the interaction. Indeed with the finite mass correction, we obtain the groundstate energy of helium atom to be −2.90382769.Įlectron–electron interactions and correlations form the basis of difficulties encountered in the theoretical solution of problems dealing with multi-electron systems. Our results are in reasonable agreement with literature values. With the derived potential, the effects of the local long-range and non-local short-range components, and the finite nuclear mass correction are tested. The higher-order multipole interactions are fully included through the exchange correlation processes where the interacting electrons exchanges their angular momentum via the operator. A non-local component of the potential emanates from the higher-order angular momentum terms of the multipole series expansion. The suggested all-electron potential has a local Coulomb potential with embedded nuclear charge screening effect in the leading term of the multipole potential. We have calculated the non-relativistic groundstate energy for helium atom to be −2.90422284. In this study, we have suggested a symmetry-dependent analytical all-electron potential for helium atom derived using an alternative multipole expansion, a variational technique, and a mean-field approximation. The Schrödinger equation even for such simple systems cannot be solved exactly without resorting to approximate methods. Helium atom and other two-electron systems are the simplest many-body systems in nature. Hyperphysics.Electron–electron interaction is the origin of the many-body problems usually encountered in physics and chemistry. Lehrbuch der Theoretischen Physik (in German). USA: National Center for Biotechnology Information. ^ "Helium - PubChem Public Chemical Database".The theoretic value of Helium atom's second ionization energy is −54.41776311(2) eV. One needs to include relativistic and quantum electrodynamic corrections to get full agreement with experiment to spectroscopic accuracy. Morgan III, Jonathan Baker and Robert Hill using Hylleraas or Frankowski- Pekeris basis functions. The variational approach has been refined to very high accuracy for a comprehensive regime of quantum states by G.W.F. Where again, E 1 represents the ionization energy of hydrogen.īy using more complicated/accurate wave functions, the ground state energy of helium has been calculated closer and closer to the experimental value −78.95 eV.
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