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Hybridization of Atomic Orbitals I03:24

Hybridization of Atomic Orbitals I

50.6K
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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Resonance and Hybrid Structures02:16

Resonance and Hybrid Structures

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According to the theory of resonance, if two or more Lewis structures with the same arrangement of atoms can be written for a molecule, ion, or radical, the actual distribution of electrons is an average of that shown by the various Lewis structures.
Resonance Structures and Resonance Hybrids
The Lewis structure of a nitrite anion (NO2−) may actually be drawn in two different ways, distinguished by the locations of the N–O and N=O bonds.
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Chemical Shift: Internal References and Solvent Effects01:17

Chemical Shift: Internal References and Solvent Effects

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In an NMR sample, precise measurement of the absolute absorption frequencies of nuclei is difficult. A standard internal reference compound is added, and the frequency difference between the reference signal and sample signals is measured.
The internal reference compound generally used in NMR spectroscopy is tetramethylsilane (TMS). TMS is preferred because it is chemically inert, soluble in NMR solvents, and easily removable. Also, the highly shielded methyl protons in TMS yield an intense...
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Hybridization of Atomic Orbitals II03:35

Hybridization of Atomic Orbitals II

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sp3d and sp3d 2 Hybridization
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Resonance02:52

Resonance

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The Lewis structure of a nitrite anion (NO2−) may actually be drawn in two different ways, distinguished by the locations of the N-O and N=O bonds. 
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Hybrid Zones02:29

Hybrid Zones

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Hybrid zones are narrow regions where two closely related species interact, mate, and produce hybrids. Relative to either parent species, hybrids may possess distinct phenotypic or genetic differences that impact their survival and reproductive success. The genetic variances introduced by hybridization influence species diversity and speciation processes within the hybrid zone.
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Related Experiment Video

Updated: Oct 11, 2025

Creating and Applying a Reference to Facilitate the Discussion and Classification of Proteins in a Diverse Group
07:49

Creating and Applying a Reference to Facilitate the Discussion and Classification of Proteins in a Diverse Group

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A generalized hybrid scheme for multireference methods.

A Waigum1, J A Black1, A Köhn1

  • 1Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, D-70569 Stuttgart, Germany.

The Journal of Chemical Physics
|December 2, 2021
PubMed
Summary
This summary is machine-generated.

New hybrid methods enhance multireference calculations by combining different theoretical approaches. These advanced computational chemistry techniques offer improved accuracy and efficiency for complex molecular systems.

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Area of Science:

  • Quantum Chemistry
  • Computational Chemistry
  • Theoretical Chemistry

Background:

  • Multireference methods are essential for describing electronic structures with strong electron correlation.
  • Existing hybrid schemes partition excitation spaces for computational efficiency.
  • Recent advancements by Saitow and Yanai introduced a novel hybrid scheme.

Purpose of the Study:

  • To generalize the hybrid scheme for multireference methods.
  • To introduce new hybrid methods by combining various theoretical approaches.
  • To test a new excitation space separation strategy.

Main Methods:

  • Generalization of the hybrid scheme for multireference methods.
  • Development of new hybrid methods using internally contracted multireference coupled-cluster, unshifted multireference coupled electron pair, and multireference perturbation methods.
  • Implementation of a new excitation space separation combining singles and doubles excitations into the external space.

Main Results:

  • The generalized hybrid methods were derived and benchmarked.
  • The new separation of excitation space was tested.
  • Hybrid methods generally show improvement over their non-hybrid counterparts.

Conclusions:

  • The developed hybrid methods offer a favorable balance between computational cost and accuracy.
  • These methods provide a valuable tool for accurate electronic structure calculations.
  • The generalization enhances the applicability of hybrid schemes in computational chemistry.