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Related Concept Videos

Hybridization of Atomic Orbitals II03:35

Hybridization of Atomic Orbitals II

sp3d and sp3d 2 Hybridization
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...
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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.
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¹H NMR: Long-Range Coupling01:27

¹H NMR: Long-Range Coupling

The coupling interactions of nuclei across four or more bonds are usually weak, with J values less than 1 Hz. While these are usually not observed in spectra, the presence of multiple bonds along the coupling pathway can result in observable long-range coupling.
In alkenes, spin information is communicated via σ–π overlap, as seen in allylic (four-bond) and homoallylic (five-bond) couplings. These coupling interactions are stronger when the σ bond is parallel to the alkene π orbitals.
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...
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Resonance and Hybrid Structures

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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Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations
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Using optimally tuned range separated hybrid functionals in ground-state calculations: consequences and caveats.

Andreas Karolewski1, Leeor Kronik, Stephan Kümmel

  • 1Theoretical Physics IV, University of Bayreuth, 95440 Bayreuth, Germany.

The Journal of Chemical Physics
|June 8, 2013
PubMed
Summary

Optimally tuned range separated hybrid functionals excel at predicting electronic excitations but fail for ground state properties. Tuning these functionals leads to significant size consistency errors, unreliable binding energies, and incorrect predictions of molecular properties.

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Area of Science:

  • Computational chemistry
  • Quantum chemistry
  • Materials science

Background:

  • Range separated hybrid functionals are implicitly defined, with parameters determined non-empirically.
  • Tuning these parameters has shown success in predicting electronic excitations.

Purpose of the Study:

  • To investigate the application of the tuning approach for predicting ground state properties.
  • To identify and analyze the limitations of this tuning method for ground state calculations.

Main Methods:

  • Iterative tuning of the range separation parameter for individual systems.
  • Analysis of diatomic molecules to assess size consistency and binding energies.
  • Evaluation of potential energy surfaces and spin state predictions.

Main Results:

  • The tuning approach leads to significant size consistency errors (up to several electron volts) for ground state properties.
  • Binding energies of diatomic molecules are not reliably predicted.
  • Potential energy surfaces and spin states are often predicted incorrectly.

Conclusions:

  • The optimal tuning approach, while effective for excitations, is unsuitable for predicting ground state properties due to inherent limitations.
  • Violations of size consistency, unreliable binding energies, and inaccurate potential energy surfaces are key drawbacks.
  • Further research is needed to address these failures and develop robust methods for ground state property prediction.