Related Experiment Video
Updated: Oct 3, 2026

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
Published on: May 27, 2020
The extended version of the computer package CST for conversions, standardization and transformations of the spin
1Department of Physics and Materials Science, City University of Hong Kong, Kowloon Tong, SAR, China. apceslaw@cityu.edu.hk
Abstract:
The computer package CST (Conversions, Standardization and Transformations) is useful for general manipulations of the zero-field splitting (ZFS) and crystal field (CF) parameters for various systems, especially for transition ions at orthorhombic and lower symmetry sites in crystals. The ZFS parameters are extensively used in the EMR and related spectroscopic and magnetic studies (e.g. magnetic susceptibility, magnetic anisotropy, Mössbauer spectroscopy), whereas the CF parameters in optical absorption spectroscopy, inelastic neutron scattering, and infrared spectroscopy. An extended version of the CST package developed recently is presented in this paper. The standardization, including the standardization errors, for the five possible non-standard ranges of the 'rhombicity' parameter for monoclinic and triclinic symmetry in the local axis system has been worked out. The handling of the border points in the standardization module has been improved. The rotational invariants used before only for the transformations of the CF parameters have been incorporated into the standardization module for the CF and ZFS parameters expressed in any of the major tensor operator notations. The input option in the Euler angles has been added into the transformation module, and the newest physical constants in the unit conversions module have been adopted. Specific applications of the CST package for the CF and ZFS parameters will be presented elsewhere.
Related Concept Videos
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,...
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...
Spin–Spin Coupling Constant: Overview
Qualitatively, any spin plus-half nucleus polarizes the spins of its electrons to the minus-half state. Consequently, the paired electron in the hydrogen–carbon bond must have a...
Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)
The extent of coupling depends on the C‑C bond length, the two H‑C‑C angles, any electron-withdrawing substituents, and the dihedral angle between the involved orbitals. The...
Crystallographic Point Groups
Spin–Spin Coupling: One-Bond Coupling

