2004/09/30 by Michal Bajdich, Luboš Mitáš, Lubos Mitas +3 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Chemical Physics Studies #Atomic orbital #Coordinate space #Coordinate system #Electron #Geometry #Mathematical physics #Mathematics #Node (physics) #Physics #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #Quantum mechanics #Topology (electrical circuits) #Wave function #cond-mat.other
paper · pdf · doi:10.1103/physrevb.72.075131
7 pages, 7 figures
arxiv created 2005/05/23 · openalex publication_date 2005/08/23 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
A study of fermion nodes for spin-polarized states of a few-electron ions and molecules with s,p,d one-particle orbitals is presented. We find exact nodes for some cases of two-electron atomic and molecular states and also the first exact node for the three-electron atomic system in 4S(p3) state using appropriate coordinate maps and wave function symmetries. We analyze the cases of nodes for larger number of electrons in the Hartree-Fock approximation and for some cases we find transformations for projecting the high-dimensional node manifolds into three-dimensional space. The node topologies and other properties are studied using these projections. We also propose a general coordinate transformation as an extension of Feynman-Cohen backflow coordinates to both simplify the nodal description and as a new variational freedom for quantum Monte Carlo trial wave functions.