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Related Concept Videos

Valence Bond Theory02:42

Valence Bond Theory

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...
¹H NMR: Interpreting Distorted and Overlapping Signals01:02

¹H NMR: Interpreting Distorted and Overlapping Signals

Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are slanted or...
Oscillations about an Equilibrium Position01:04

Oscillations about an Equilibrium Position

Stability is an important concept in oscillation. If an equilibrium point is stable, a slight disturbance of an object that is initially at the stable equilibrium point will cause the object to oscillate around that point. For an unstable equilibrium point, if the object is disturbed slightly, it will not return to the equilibrium point. There are three conditions for equilibrium points—stable, unstable, and half-stable. A half-stable equilibrium point is also unstable, but is named so because...
Potential-Energy Criterion for Equilibrium01:16

Potential-Energy Criterion for Equilibrium

Potential energy or potential function plays an essential role in determining the stability of a mechanical system. If a system is subjected to both gravitational and elastic forces, the potential function of the system can be expressed as the algebraic sum of gravitational and elastic potential energy. If the system is in equilibrium and is displaced by a small amount, then the work done on the system equals the negative of the change in the system's potential energy from the initial to the...
Crystal Field Theory - Octahedral Complexes02:58

Crystal Field Theory - Octahedral Complexes

Crystal Field Theory
To explain the observed behavior of transition metal complexes (such as colors), a model involving electrostatic interactions between the electrons from the ligands and the electrons in the unhybridized d orbitals of the central metal atom has been developed. This electrostatic model is crystal field theory (CFT). It helps to understand, interpret, and predict the colors, magnetic behavior, and some structures of coordination compounds of transition metals.
CFT focuses on...
Complexation Equilibria: Overview01:23

Complexation Equilibria: Overview

Complexation reactions take place when dative or coordinate covalent bonds form between metal ions and ligands. The compounds formed in these reactions are called coordination compounds. The number of bonds formed between the metal ion and the ligands is called its coordination number. Generally, most metal ions in an aqueous solution are solvated by water molecules and thus exist as aqua complexes.
The equilibrium constant of the complexation reaction is represented as the formation constant...

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Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
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Oscillations in meta-generalized-gradient approximation potential energy surfaces for dispersion-bound complexes.

Erin R Johnson1, Axel D Becke, C David Sherrill

  • 1Department of Chemistry, Duke University, Durham, North Carolina 27708, USA.

The Journal of Chemical Physics
|July 24, 2009
PubMed
Summary

Meta-generalized-gradient approximations (meta-GGAs) can oscillate in dispersion-bound complexes due to grid sensitivity. Careful grid selection is crucial for accurate results when using these density-functional theory methods.

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Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Materials Science

Background:

  • Meta-generalized-gradient approximations (meta-GGAs) are advanced density-functional theory (DFT) functionals.
  • These functionals incorporate local density, density gradient, and kinetic-energy density.
  • Previous studies highlighted potential issues with meta-GGAs in specific systems.

Purpose of the Study:

  • To investigate the origin of spurious oscillations in meta-GGA potential energy curves.
  • To analyze the grid sensitivity of meta-GGAs in dispersion-bound complexes.
  • To provide guidance for the accurate application and development of meta-GGAs.

Main Methods:

  • Analysis of meta-GGA functional behavior in the saddle-point region of the density.
  • Examination of dimensionless ratios involving kinetic-energy density.
  • Assessment of integration grid requirements for accurate potential energy curves.

Main Results:

  • Meta-GGAs exhibit grid sensitivity in dispersion-bound complexes, leading to spurious oscillations.
  • This sensitivity stems from the saddle-point region of the electron density near the intermonomer midpoint.
  • Ill-behaved dimensionless ratios in typical meta-GGAs exacerbate the grid sensitivity issue.

Conclusions:

  • Standard integration grids are often insufficient for accurate meta-GGA calculations.
  • Careful consideration of grid density is necessary to avoid oscillations.
  • Recommendations are provided for users and developers of meta-GGAs to mitigate these problems.