TY - JOUR
T1 - Two-body Schrödinger wave functions in a plane-wave basis via separation of dimensions
AU - Jerke, Jonathan
AU - Poirier, Bill
N1 - Publisher Copyright:
© 2018 Author(s).
PY - 2018/3/14
Y1 - 2018/3/14
N2 - Using a combination of ideas, the ground and several excited electronic states of the helium atom and the hydrogen molecule are computed to chemical accuracy - i.e., to within 1-2 mhartree or better. The basic strategy is very different from the standard electronic structure approach in that the full two-electron six-dimensional (6D) problem is tackled directly, rather than starting from a single-electron Hartree-Fock approximation. Electron correlation is thus treated exactly, even though computational requirements remain modest. The method also allows for exact wave functions to be computed, as well as energy levels. From the full-dimensional 6D wave functions computed here, radial distribution functions and radial correlation functions are extracted - as well as a 2D probability density function exhibiting antisymmetry for a single Cartesian component. These calculations support a more recent interpretation of Hund's rule, which states that the lower energy of the higher spin-multiplicity states is actually due to reduced screening, rather than reduced electron-electron repulsion. Prospects for larger systems and/or electron dynamics applications appear promising.
AB - Using a combination of ideas, the ground and several excited electronic states of the helium atom and the hydrogen molecule are computed to chemical accuracy - i.e., to within 1-2 mhartree or better. The basic strategy is very different from the standard electronic structure approach in that the full two-electron six-dimensional (6D) problem is tackled directly, rather than starting from a single-electron Hartree-Fock approximation. Electron correlation is thus treated exactly, even though computational requirements remain modest. The method also allows for exact wave functions to be computed, as well as energy levels. From the full-dimensional 6D wave functions computed here, radial distribution functions and radial correlation functions are extracted - as well as a 2D probability density function exhibiting antisymmetry for a single Cartesian component. These calculations support a more recent interpretation of Hund's rule, which states that the lower energy of the higher spin-multiplicity states is actually due to reduced screening, rather than reduced electron-electron repulsion. Prospects for larger systems and/or electron dynamics applications appear promising.
UR - http://www.scopus.com/inward/record.url?scp=85043520696&partnerID=8YFLogxK
U2 - 10.1063/1.5017621
DO - 10.1063/1.5017621
M3 - Article
C2 - 29544282
AN - SCOPUS:85043520696
VL - 148
JO - The Journal of Chemical Physics
JF - The Journal of Chemical Physics
SN - 0021-9606
IS - 10
M1 - 104101
ER -