Related Experiment Video
Updated: May 13, 2026

Writing and Low-Temperature Characterization of Oxide Nanostructures
Published on: July 18, 2014
Types of single particle symmetry breaking in transition metal oxides due to electron correlation
1Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA. lkwagner@illinois.edu
Abstract:
Very accurate wave functions are calculated for small transition metal oxide molecules. These wave functions are decomposed using reduced density matrices to study the underlying correlation of electrons. The correlation is primarily of left-right type between the transition metals and the oxygen atoms, which is mediated by excitations from the nominal single Slater ground state into antibonding and d-type orbitals. In a localized representation, this correlation manifests itself in a 2-electron hopping term that is off-diagonal. This term is of similar magnitude to the commonly considered Hubbard-type on-site interaction.
Related Concept Videos
Crystal Field Theory - Octahedral Complexes
To explain the observed behavior of transition metal complexes (such as colors), a model involving electrostatic interactions between the electrons from the ligands and the electrons in the unhybridized d orbitals of the central metal atom has been developed. This electrostatic model is crystal field theory (CFT). It helps to understand, interpret, and predict the colors, magnetic behavior, and some structures of coordination compounds of transition metals.
CFT focuses on...
Properties of Transition Metals
Crystal Field Theory - Tetrahedral and Square Planar Complexes
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...
Valence Bond Theory
Structural Isomerism
Isomers are different chemical species that have the same chemical formula. Structural isomerism of coordination compounds can be divided into two subcategories, the linkage isomers and coordination-sphere isomers.
Linkage isomers occur when the coordination compound contains a ligand that can bind to the transition metal center through two different atoms. For example, the CN− ligand can bind through the carbon atom or through the nitrogen atom. Similarly, SCN− can be...
Bonding in Metals

