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Title: Nodal surfaces and interdimensional degeneracies

The aim of this paper is to shed light on the topology and properties of the nodes (i.e., the zeros of the wave function) in electronic systems. Using the “electrons on a sphere” model, we study the nodes of two-, three-, and four-electron systems in various ferromagnetic configurations (sp, p{sup 2}, sd, pd, p{sup 3}, sp{sup 2}, and sp{sup 3}). In some particular cases (sp, p{sup 2}, sd, pd, and p{sup 3}), we rigorously prove that the non-interacting wave function has the same nodes as the exact (yet unknown) wave function. The number of atomic and molecular systems for which the exact nodes are known analytically is very limited and we show here that this peculiar feature can be attributed to interdimensional degeneracies. Although we have not been able to prove it rigorously, we conjecture that the nodes of the non-interacting wave function for the sp{sup 3} configuration are exact.
Authors:
 [1] ;  [2]
  1. Research School of Chemistry, Australian National University, Canberra ACT 2601 (Australia)
  2. Dipartimento di Scienza e Alta Tecnologia, Università dell’Insubria, Via Lucini 3, I-22100 Como (Italy)
Publication Date:
OSTI Identifier:
22415928
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Chemical Physics; Journal Volume: 142; Journal Issue: 21; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; ATOMS; CONFIGURATION; ELECTRONS; FERROMAGNETISM; MOLECULES; SPHERES; SURFACES; TOPOLOGY; VISIBLE RADIATION; WAVE FUNCTIONS