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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...
Band Theory02:35

Band Theory

When two or more atoms come together to form a molecule, their atomic orbitals combine and molecular orbitals of distinct energies result. In a solid, there are a large number of atoms, and therefore a large number of atomic orbitals that may be combined into molecular orbitals. These groups of molecular orbitals are so closely placed together to form continuous regions of energies, known as the bands.
The energy difference between these bands is known as the band gap.
Conductor, Semiconductor,...
Energy Bands in Solids01:01

Energy Bands in Solids

Isolated atoms have discrete energy levels that are well described by the Bohr model. And, it quantifies the energy of an electron in a hydrogen atom as En. Higher quantum numbers 'n' yield less negative, closer electron energy levels.
 Band Formation:
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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...
Lattice Energies of Ionic Crystals01:27

Lattice Energies of Ionic Crystals

Lattice energy represents the energy released when gaseous cations and anions combine to form an ionic solid, reflecting the strength of electrostatic interactions within the crystal. This process is fundamentally governed by Coulombic attraction between oppositely charged ions, where the potential energy varies inversely with the interionic distance and directly with the product of ionic charges. As ions approach one another, the electrostatic energy becomes increasingly negative, indicating a...
Electronic Structure of Atoms02:28

Electronic Structure of Atoms


An atom comprises protons and neutrons, which are contained inside the dense, central core called the nucleus, with electrons present around the nucleus. Taking into account the wave–particle duality of electrons and the uncertainty in position around the nucleus, quantum mechanics provides a more accurate model for the atomic structure. It describes atomic orbitals as the regions around the nucleus where electrons of discrete energy exist, characterized by four quantum numbers:  n, l, ml, and...

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Related Experiment Video

Updated: May 31, 2026

Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations
13:56

Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations

Published on: October 12, 2019

Electronic minibands in complex basis superlattices: a numerically stable calculation.

W J Hsueh1, J C Lin, H C Chen

  • 1Department of Engineering Science, National Taiwan University, 1, Section 4, Roosevelt Road, Taipei 10660, Taiwan.

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|June 23, 2011
PubMed
Summary
This summary is machine-generated.

This study introduces a stable numerical method for calculating superlattice energy minibands. The new approach avoids potential calculation overflows, offering improved accuracy for complex superlattices.

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Area of Science:

  • Condensed Matter Physics
  • Materials Science
  • Solid-State Physics

Background:

  • Superlattices exhibit energy minibands crucial for electronic properties.
  • Traditional methods for calculating minibands can suffer from numerical instability.
  • Complex superlattices pose significant challenges for accurate energy band determination.

Purpose of the Study:

  • To develop a numerically stable and accurate method for determining superlattice energy minibands.
  • To derive closed-form equations for miniband edge calculations.
  • To enhance the analysis of complex basis superlattices.

Main Methods:

  • Utilized a graph model incorporating tangent and secant functions.
  • Derived concise, closed-form miniband edge equations based on topology theory.
  • Avoided the calculation of the cosine of the Bloch phase to prevent numerical overflow.

Main Results:

  • The developed method demonstrates superior numerical stability compared to traditional approaches.
  • Accurate determination of energy minibands for superlattices with arbitrary layers per cell is achieved.
  • The closed-form equations provide efficient calculation of miniband structures.

Conclusions:

  • The new method offers a robust and accurate solution for superlattice miniband calculations.
  • This approach enhances the study of complex superlattices by improving numerical stability.
  • The derived equations are valuable for condensed matter and materials science research.