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Related Concept Videos

Lattice Centering and Coordination Number02:33

Lattice Centering and Coordination Number

The structure of a crystalline solid, whether a metal or not, is best described by considering its simplest repeating unit, which is referred to as its unit cell. The unit cell consists of lattice points that represent the locations of atoms or ions. The entire structure then consists of this unit cell repeating in three dimensions. The three different types of unit cells present in the cubic lattice are illustrated in Figure 1.
Types of Unit Cells
Imagine taking a large number of identical...
Crystal Field Theory - Octahedral Complexes02:58

Crystal Field Theory - Octahedral Complexes

Crystal Field Theory
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...
Crystal Field Theory - Tetrahedral and Square Planar Complexes02:46

Crystal Field Theory - Tetrahedral and Square Planar Complexes

Tetrahedral 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,...
Molecular Geometry and Dipole Moments02:36

Molecular Geometry and Dipole Moments

The VSEPR theory can be used to determine the electron pair geometries and molecular structures as follows:
Valence Bond Theory and Hybridized Orbitals02:38

Valence Bond Theory and Hybridized Orbitals

According to valence bond theory, a covalent bond results when: (1) an orbital on one atom overlaps an orbital on a second atom, and (2) the single electrons in each orbital combine to form an electron pair. The strength of a covalent bond depends on the extent of overlap of the orbitals involved. Maximum overlap is possible when the orbitals overlap on a direct line between the two nuclei.
A σ bond (single bond in a Lewis structure) is a covalent bond in which the electron density is...
Crystal Density01:19

Crystal Density

The crystal lattice structure of a material allows us to determine how many molecules exist in its unit cell. With this information, alongside the unit-cell parameters - three distance parameters (a, b, c) and three angular parameters (α, β, γ).Density (ρ) = (Z × M) / (a × b × c × NA)where:Z is the number of formula units per unit cellM is the molar mass of the substancea, b, and c are the edge lengths of the unit cellNA is Avogadro’s numberFor a simple cubic lattice, atoms are located only at...

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Related Experiment Video

Updated: Jun 21, 2026

Spatial Separation of Molecular Conformers and Clusters
10:37

Spatial Separation of Molecular Conformers and Clusters

Published on: January 9, 2014

The conversion among various B4C clusters: a density functional theoretical study.

Chunhui Liu1, Mingsheng Tang, Hongming Wang

  • 1Department of Chemistry, Zhengzhou University, Zhengzhou, Henan, 450052, China.

The Journal of Physical Chemistry. A
|January 26, 2007
PubMed
Summary
This summary is machine-generated.

Boron carbide (B4C) clusters favor structures with three-member boron rings, particularly a five-member ring configuration. These B4C clusters exhibit stability due to three-centered bonds and pi-electron delocalization.

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Last Updated: Jun 21, 2026

Spatial Separation of Molecular Conformers and Clusters
10:37

Spatial Separation of Molecular Conformers and Clusters

Published on: January 9, 2014

Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics
10:52

Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics

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Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
12:11

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

Area of Science:

  • Computational Chemistry
  • Materials Science
  • Quantum Chemistry

Background:

  • Boron carbide (B4C) is a complex material with diverse structural possibilities.
  • Understanding the stability and properties of small B4C clusters is crucial for predicting bulk material behavior.
  • Previous studies on B4C clusters lack detailed energetic and structural analysis of stable isomers.

Purpose of the Study:

  • To identify and characterize stable isomers of B4C clusters using computational methods.
  • To analyze the energetic stability and bonding characteristics of these isomers.
  • To investigate the potential interconversion pathways and energy barriers between isomers.

Main Methods:

  • Geometry optimizations and vibrational frequency calculations were performed using the Becke-3LYP (B3LYP) hybrid functional.
  • The 6-31G(d) and 6-311G+(3df) basis sets were employed for electronic structure calculations.
  • Molecular Orbital (MO) and Natural Bond Orbital (NBO) analyses were conducted to understand bonding.

Main Results:

  • Fourteen stable B4C isomers were identified, with the most stable featuring a five-member ring containing two three-member boron rings.
  • Structures incorporating three-member boron rings were found to be energetically predominant.
  • Three-centered bonding and pi-electron delocalization were identified as key stabilizing factors for planar five-member rings.

Conclusions:

  • The study elucidates the preferred structural motifs and energetic landscape of small B4C clusters.
  • Specific isomers demonstrate low energy barriers for interconversion, suggesting dynamic behavior.
  • High energy barriers for certain isomer conversions indicate distinct stable configurations.