Capping Ligand Vortices as "Atomic Orbitals" in Nanocrystal Self-Assembly
Related Experiment Video
Updated: Feb 20, 2026

Liquid-cell Transmission Electron Microscopy for Tracking Self-assembly of Nanoparticles
Published on: October 16, 2017
Curt Waltmann1, Nathan Horst1, Alex Travesset1,2
1Department of Materials Science and Engineering and Ames Laboratory, Iowa State University , Ames, Iowa 50011, United States.
Abstract:
We present a detailed analysis of the interaction between two nanocrystals capped with ligands consisting of hydrocarbon chains by united atom molecular dynamics simulations. We show that the bonding of two nanocrystals is characterized by ligand textures in the form of vortices. These results are generalized to nanocrystals of different types (differing core and ligand sizes) where the structure of the vortices depends on the softness asymmetry. We provide rigorous calculations for the binding free energy, show that these energies are independent of the chemical composition of the cores, and derive analytical formulas for the equilibrium separation. We discuss the implications of our results for the self-assembly of single-component and binary nanoparticle superlattices. Overall, our results show that the structure of the ligands completely determines the bonding of nanocrystals, fully supporting the predictions of the recently proposed Orbifold topological model.
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...
Valence Bond Theory
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,...
MO Theory and Covalent Bonding
Molecular Orbital Theory I
Valence Bond Theory and Hybridized Orbitals
A σ bond (single bond in a Lewis structure) is a covalent bond in which the electron density is...

