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Related Concept Videos

Electrostatic Boundary Conditions in Dielectrics01:27

Electrostatic Boundary Conditions in Dielectrics

When an electric field passes from one homogeneous medium to another, crossing the boundary between the two mediums imparts a discontinuity in the electric field. This results in electrostatic boundary conditions that depend on the type of mediums the field propagates through.
Consider a case where both the mediums across a boundary are two different dielectric materials. Recall that the electric field and electric displacement are proportional and related through the material's permittivity.
Spin–Spin Coupling: One-Bond Coupling01:17

Spin–Spin Coupling: One-Bond Coupling

Coupling interactions are strongest between NMR-active nuclei bonded to each other, where spin information can be transmitted directly through the pair of bonding electrons. While nuclei polarize their electrons to the opposite spins, the bonding electron pair has opposite spins. Configurations with antiparallel nuclear spins are expected to be lower in energy. When coupling makes antiparallel states more favorable, J is considered to have a positive value. The one-bond coupling constant, 1J,...
Van der Waals Equation01:10

Van der Waals Equation

The ideal gas law is an approximation that works well at high temperatures and low pressures. The van der Waals equation of state (named after the Dutch physicist Johannes van der Waals, 1837−1923) improves it by considering two factors.
First, the attractive forces between molecules, which are stronger at higher densities and reduce the pressure, are considered by adding to the pressure a term equal to the square of the molar density multiplied by a positive coefficient a. Second, the volume...
Electrostatic Boundary Conditions01:16

Electrostatic Boundary Conditions

Consider an external electric field propagating through a homogeneous medium. When the electric field crosses the surface boundary of the medium, it undergoes a discontinuity. The electric field can be resolved into normal and tangential components. The amount by which the field changes at any boundary is given by the difference between the field components above and below the surface boundary.
The surface integral of an electric field is given by Gauss's law in integral form and is related to...
Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)01:20

Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)

Two NMR-active nuclei bonded to a central atom can be involved in geminal or two-bond coupling. Geminal coupling is commonly seen between diastereotopic protons in chiral molecules and unsymmetrical alkenes, among others.
The central atom need not be NMR-active because its electrons are affected by the electron polarization of the spin-active atoms. However, spin information is transmitted less effectively than in one-bond coupling, and 2J values are usually weaker than 1J values. The energy of...
Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)01:22

Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)

Vicinal or three-bond coupling is commonly observed between protons attached to adjacent carbons. Here, nuclear spin information is primarily transferred via electron spin interactions between adjacent C‑H bond orbitals. This generally favors the antiparallel arrangement of spins, so 3J values are usually positive.
The extent of coupling depends on the C‑C bond length, the two H‑C‑C angles, any electron-withdrawing substituents, and the dihedral angle between the involved orbitals. The...

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Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
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Adiabatic connection for strictly correlated electrons.

Zhen-Fei Liu1, Kieron Burke

  • 1Department of Chemistry, University of California, Irvine, California 92697-2025, USA. zhenfei.liu@uci.edu

The Journal of Chemical Physics
|October 2, 2009
PubMed
Summary

Density functional theory (DFT) can use a strictly correlated electrons reference. A new "decorrelation energy" and adiabatic connection formula offer insights for developing better DFT functionals.

Area of Science:

  • Quantum chemistry
  • Computational physics
  • Materials science

Background:

  • Modern density functional theory (DFT) relies on the Kohn-Sham approach, using a noninteracting electron system as a reference.
  • The exchange-correlation energy (E(XC)) encapsulates the complex many-body interactions.
  • The adiabatic connection (AC) formula provides an exact route to E(XC).

Purpose of the Study:

  • To explore an alternative DFT framework using a strictly correlated electrons (SCE) reference system.
  • To introduce and define a "decorrelation energy" that bridges the SCE reference to the real interacting system.
  • To derive a novel AC formula applicable to the SCE reference system.

Main Methods:

  • Development of theoretical framework for DFT with an SCE reference.

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  • Definition of decorrelation energy.
  • Derivation of the adiabatic connection formula for the SCE reference.
  • Application and illustration of the theory to model systems.

    • Main Results:

    • A new theoretical perspective for DFT calculations based on SCE.
    • Introduction of the decorrelation energy concept.
    • Derivation of the SCE adiabatic connection formula.
    • Demonstration of the theory's applicability to the uniform electron gas, Hooke's atom, and stretched H2.

    Conclusions:

    • The SCE reference and its associated AC formula offer a new viewpoint on DFT.
    • This approach may facilitate the development of improved approximate DFT functionals.
    • The decorrelation energy provides a quantitative measure of the difference between SCE and real systems.