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Related Concept Videos

Hybridization of Atomic Orbitals I03:24

Hybridization of Atomic Orbitals I

The mathematical expression known as the wave function, ψ, contains information about each orbital and the wavelike properties of electrons in an isolated atom. When atoms are bound together in a molecule, the wave functions combine to produce new mathematical descriptions that have different shapes. This process of combining the wave functions for atomic orbitals is called hybridization and is mathematically accomplished by the linear combination of atomic orbitals. The new orbitals that...
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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...
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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,...
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Coordination compounds and complexes exhibit different colors, geometries, and magnetic behavior, depending on the metal atom/ion and ligands from which they are composed. In an attempt to explain the bonding and structure of coordination complexes, Linus Pauling proposed the valence bond theory, or VBT, using the concepts of hybridization and the overlapping of the atomic orbitals. According to VBT, the central metal atom or ion (Lewis acid) hybridizes to provide empty orbitals of suitable...

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Related Experiment Video

Updated: Jun 28, 2026

Construction and Systematical Symmetric Studies of a Series of Supramolecular Clusters with Binary or Ternary Ammonium Triphenylacetates
06:35

Construction and Systematical Symmetric Studies of a Series of Supramolecular Clusters with Binary or Ternary Ammonium Triphenylacetates

Published on: February 15, 2016

Linear augmented Slater-type orbital method for free standing clusters.

K S Kang1, J W Davenport, J Glimm

  • 1Computational Science Center, Brookhaven National Laboratory, Upton, New York, USA.

Journal of Computational Chemistry
|November 7, 2008
PubMed
Summary
This summary is machine-generated.

We developed a Scalable Linear Augmented Slater-Type Orbital (LASTO) method for efficient electronic structure calculations on atomic clusters. This approach enhances computational speed for materials science research.

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Related Experiment Videos

Last Updated: Jun 28, 2026

Construction and Systematical Symmetric Studies of a Series of Supramolecular Clusters with Binary or Ternary Ammonium Triphenylacetates
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Published on: February 15, 2016

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

Spatial Separation of Molecular Conformers and Clusters
10:37

Spatial Separation of Molecular Conformers and Clusters

Published on: January 9, 2014

Area of Science:

  • Computational physics and chemistry
  • Materials science
  • Electronic structure theory

Background:

  • Accurate electronic structure calculations are crucial for understanding material properties.
  • Existing methods face scalability challenges for large atomic systems.
  • Linear scaling methods offer a promising avenue for computational efficiency.

Purpose of the Study:

  • To introduce a novel Scalable Linear Augmented Slater-Type Orbital (LASTO) method.
  • To enable efficient electronic structure calculations for free-standing atomic clusters.
  • To address the computational demands of large-scale materials simulations.

Main Methods:

  • Employs a mixed basis set of numerical functions and Slater-type orbitals.
  • Utilizes a finite difference method with smoothed charge density for the Poisson equation.
  • Incorporates multigrid techniques for solving the Coulomb potential.
  • Leverages ScaLAPACK for efficient solution of the linear eigen-problem.

Main Results:

  • The Scalable Linear Augmented Slater-Type Orbital (LASTO) method has been successfully developed.
  • The method was tested on small clusters of palladium, demonstrating its applicability.
  • The approach combines numerical and analytical functions for improved accuracy and efficiency.

Conclusions:

  • The LASTO method provides a scalable and efficient approach for electronic structure calculations.
  • This method has the potential to advance computational materials science and condensed matter physics.
  • Further applications on larger and more complex systems are warranted.