A study of fermion nodes for spin-polarized states of a few-electron ions andmolecules with $s,p,d$ one-particle orbitals is presented. We find exact nodesfor some cases of two electron atomic and molecular states and also the firstexact node for the three-electron atomic system in $^4S(p^3)$ state usingappropriate coordinate maps and wavefunction symmetries. We analyze the casesof nodes for larger number of electrons in the Hartree-Fock approximation andfor some cases we find transformations for projecting the high-dimensional nodemanifolds into 3D space. The node topologies and other properties are studiedusing these projections. We also propose a general coordinate transformation asan extension of Feynman-Cohen backflow coordinates to both simplify the nodaldescription and as a new variational freedom for quantum Monte Carlo trialwavefunctions.
展开▼
