Related Experiment Video
Updated: Oct 25, 2025

Hyperspectral Imaging as a Tool to Study Optical Anisotropy in Lanthanide-Based Molecular Single Crystals
Published on: April 14, 2020
Nonlinear optical properties of the rhombic B4 -cluster
1Institute of Organic and Pharmaceutical Chemistry, National Hellenic Research Foundation, Vasileos Constantinou 48, GR-11635 Athens, Greece.
Multireference methods reveal excited state contributions to the ground state wave function of the rhombic B4 cluster. Correlated methods provide reliable electric properties, though differences exist between CCSD(T) and BD(T).
Area of Science:
- Computational Chemistry
- Quantum Chemistry
- Materials Science
Background:
- Accurate calculation of electronic structure and properties for small clusters is crucial for understanding their behavior.
- The rhombic B4 cluster, with D2h symmetry, presents a computational challenge due to potential multireference character.
Purpose of the Study:
- To investigate the equilibrium geometry, energy, dipole polarizability, and second hyperpolarizability of the rhombic B4 cluster.
- To compare the performance of various quantum chemical methods, including single-reference and multireference approaches.
Main Methods:
- Employed restricted (RHF) and unrestricted (UHF) Hartree-Fock, Møller-Plesset perturbation theory (MPn), coupled-cluster theory [CCSD(T), BD(T)], and complete/restricted active space SCF (CASSCF/RASSCF).
- Utilized three distinct basis sets to assess the impact of basis set size on calculated properties.
- Investigated the influence of excited state configurations on the ground state wave function.
Main Results:
- Multireference methods indicated significant contributions from excited state configurations to the ground state wave function.
- Restricted Hartree-Fock (RHF) results deviated substantially from correlated methods, even for geometry.
- Unrestricted Hartree-Fock (UHF) provided more reliable geometries but exhibited spin contamination; correlated methods yielded comparable electric properties, with notable differences between CCSD(T) and BD(T).
Conclusions:
- The ground state of the B4 cluster possesses multireference character, necessitating the use of advanced correlated or multireference methods for accurate predictions.
- Electric properties are qualitatively similar across different correlated methods, but quantitative differences warrant careful selection of the theoretical approach.
- Basis set extension with f-functions had a minimal impact on the calculated electric properties.
Related Concept Videos
VSEPR Theory and the Effect of Lone Pairs
Stereoisomerism
Isomers are different chemical species that have the same chemical formula.
Transition metal complexes often exist as geometric isomers, in which the same atoms are connected through the same types of bonds but with differences in their orientation in space. Coordination complexes with two different ligands in the cis and trans positions from a ligand of interest form isomers. For example, the octahedral [Co(NH3)4Cl2]+ ion has two isomers (Figure 1) In the cis...
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,...
Radicals: Electronic Structure and Geometry
Accordingly, the structure of a trivalent radical lies between the geometries of carbocations and carbanions. An sp2-hybridized carbocation is trigonal planar, while an sp3-hybridized carbanion is trigonal pyramidal. Here, the difference in geometry is...
Lattice Centering and Coordination Number
Types of Unit Cells
Imagine taking a large number of identical...
Colors and Magnetism
When atoms or molecules absorb light at the proper frequency, their electrons are excited to higher-energy orbitals. For many main group atoms and molecules, the absorbed photons are in the ultraviolet range of the electromagnetic spectrum, which cannot be detected by the human eye. For coordination compounds, the energy difference between the d orbitals often allows photons in the visible range to be absorbed and emitted, which is seen as colors by the human...

