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Valence Bond Theory02:42

Valence Bond Theory

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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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The molecular orbital theory describes the distribution of electrons in molecules in a manner similar to the distribution of electrons in atomic orbitals. The region of space in which a valence electron in a molecule is likely to be found is called a molecular orbital. Mathematically, the linear combination of atomic orbitals (LCAO) generates molecular orbitals. Combinations of in-phase atomic orbital wave functions result in regions with a high probability of electron density, while...
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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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Updated: Apr 30, 2026

Synthesis and Performance Characterizations of Transition Metal Single Atom Catalyst for Electrochemical CO2 Reduction
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Synthesis and Performance Characterizations of Transition Metal Single Atom Catalyst for Electrochemical CO2 Reduction

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Partial Sigma Covalent Bonding in Transition Metals.

Lam H Nguyen1, Thanh N Truong1

  • 1Department of Chemistry, University of Utah, Salt Lake City, Utah, USA.

Journal of Computational Chemistry
|April 29, 2026
PubMed
Summary
This summary is machine-generated.

This study reveals partial sigma-covalent bonding in transition metals, influenced by ligand type and orbital symmetry. N-donor ligands in frameworks enable tunable metal-metal bonding and band gap engineering.

Keywords:
d8–d8 transition‐metal interactionlantern organic frameworksorbital reorderingpartial sigma covalent bonding

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Area of Science:

  • Computational Chemistry
  • Inorganic Chemistry
  • Materials Science

Background:

  • Partial sigma-covalent bonding is a key phenomenon in chemical bonding.
  • Understanding metal-metal interactions is crucial for designing new materials.
  • Ligand field theory and orbital symmetry play significant roles in electronic structure.

Purpose of the Study:

  • To establish partial sigma-covalent bonding as a general electronic phenomenon.
  • To investigate the influence of ligand field and orbital symmetry on metal-metal bonding.
  • To explore the potential of N-donor lantern organic frameworks (LOFs) for band gap engineering.

Main Methods:

  • Dispersion-corrected Density Functional Theory (DFT) calculations.
  • Wiberg bond index (WBI) analysis to quantify bond order.
  • Frontier molecular orbital (FMO) analysis to understand electronic structure.

Main Results:

  • Partial sigma-bonding is observed in main-group biradicals and d8-d8 transition metal systems.
  • C-donor ligands widen the HOMO-LUMO gap, leading to triplet-dominant metal-metal bonding.
  • N-donor LOFs narrow the HOMO-LUMO gap, enabling substantial sigma-bonding in both spin states and reducing the gap by up to 2.00 eV.

Conclusions:

  • Partial sigma-covalent bonding is a general phenomenon governed by ligand field and orbital symmetry.
  • N-donor LOFs offer a viable strategy for single-unit-cell band gap engineering.
  • The findings provide insights into tuning metal-metal interactions and electronic properties.