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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...
Hybridization of Atomic Orbitals II03:35

Hybridization of Atomic Orbitals II

sp3d and sp3d 2 Hybridization
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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...
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π Molecular Orbitals of 1,3-Butadiene

Conjugated dienes have lower heats of hydrogenation than cumulated and isolated dienes, making them more stable. The enhanced stabilization of conjugated systems can be understood from their π molecular orbitals.
The simplest conjugated diene is 1,3-butadiene: a four-carbon system where each carbon is sp2-hybridized and has an unhybridized p orbital that contains an unpaired electron. According to molecular orbital theory, atomic orbitals combine to form molecular orbitals such that the number...
Structure of Benzene: Molecular Orbital Model01:18

Structure of Benzene: Molecular Orbital Model

According to the molecular orbital (MO) model, benzene has a planar structure with a regular hexagon of six sp2 hybridized carbons. As shown in Figure 1, each carbon is bonded to three other atoms with C–C–C and H–C–C bond angles of 120°. The C–H bond length is 109 pm, and the C–C bond length is 139 pm which is midway between the single bond length of sp3 hybridized carbons (154 pm) and sp2 hybridized carbons (133 pm).
Molecular Orbital Theory II03:51

Molecular Orbital Theory II

Molecular Orbital Energy Diagrams

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Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations
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Seeking for parameter-free double-hybrid functionals: the PBE0-DH model.

Eric Brémond1, Carlo Adamo

  • 1Laboratoire d'Electrochimie, Chimie des Interfaces et Modélisation pour l'Energie, CNRS UMR-7575, Chimie ParisTech, 11 rue P. et M. Curie, F-75231 Paris Cedex 05, France.

The Journal of Chemical Physics
|July 20, 2011
PubMed
Summary
This summary is machine-generated.

A new PBE0 Double Hybrid (PBE0-DH) functional was developed using physical principles, not empirical fitting. This computational chemistry tool shows improved performance for molecular properties compared to its parent functional.

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Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Materials Science

Background:

  • Density functional theory (DFT) is a cornerstone of modern computational chemistry.
  • Existing hybrid functionals like PBE0 offer a balance of accuracy and computational cost.
  • Parameterization of double hybrid functionals often relies on empirical fitting, limiting their general applicability.

Purpose of the Study:

  • To introduce a novel double hybrid functional, PBE0 Double Hybrid (PBE0-DH).
  • To determine the ratio of Hartree-Fock, Kohn-Sham, and second-order Møller-Plesset perturbation theory (MP2) terms based on physical considerations.
  • To evaluate the performance of PBE0-DH for various molecular properties without empirical parameterization.

Main Methods:

  • Development of the PBE0 Double Hybrid (PBE0-DH) functional.
  • Theoretical determination of the functional's component ratios.
  • Testing PBE0-DH on atomization energies, weak interactions, and reaction energies.

Main Results:

  • The PBE0-DH functional incorporates a 12.5% MP2 contribution.
  • PBE0-DH demonstrates significant improvements over the parent PBE0 functional.
  • Its performance is comparable to existing parameterized double hybrid functionals.

Conclusions:

  • Reliable, general-purpose double hybrid functionals can be derived from purely theoretical principles.
  • PBE0-DH offers a parameter-free alternative with competitive accuracy.
  • This work supports the development of non-empirical functionals for broader chemical applications.