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Related Concept Videos

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,...
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...
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:
When atoms are brought close together, as in a solid, these discrete energy levels begin to split due to the overlap of electron orbitals from adjacent atoms. This split occurs because of the Pauli exclusion principle, which states that no two...
The Aufbau Principle and Hund's Rule03:02

The Aufbau Principle and Hund's Rule

To determine the electron configuration for any particular atom, we can build the structures in the order of atomic numbers. Beginning with hydrogen, and continuing across the periods of the periodic table, we add one proton at a time to the nucleus and one electron to the proper subshell until we have described the electron configurations of all the elements. This procedure is called the aufbau principle, from the German word aufbau (“to build up”). Each added electron occupies the subshell of...
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...
Electron Configurations02:46

Electron Configurations

Electron configurations and orbital diagrams can be determined by applying the Aufbau principle (each added electron occupies the subshell of lowest energy available), Pauli exclusion principle (no two electrons can have the same set of four quantum numbers), and Hund’s rule of maximum multiplicity (whenever possible, electrons retain unpaired spins in degenerate orbitals).
The relative energies of the subshells determine the order in which atomic orbitals are filled (1s, 2s, 2p, 3s, 3p, 4s,...

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Related Experiment Video

Updated: Jun 8, 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

Unfolding first-principles band structures.

Wei Ku1, Tom Berlijn, Chi-Cheng Lee

  • 1Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, USA.

Physical Review Letters
|September 28, 2010
PubMed
Summary
This summary is machine-generated.

A new method unfolds electronic band structures from supercell calculations, simplifying visualization and enabling direct comparison with experimental data. This technique efficiently reveals material properties like defects and order.

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Last Updated: Jun 8, 2026

Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations
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Visualizing Uniaxial-strain Manipulation of Antiferromagnetic Domains in Fe1+YTe Using a Spin-polarized Scanning Tunneling Microscope
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Area of Science:

  • Condensed matter physics
  • Materials science
  • Computational materials science

Background:

  • First-principles supercell calculations are crucial for understanding material properties.
  • Visualizing the electronic structure, especially with broken translational symmetry, can be challenging.
  • Direct comparison between theoretical calculations and experimental spectroscopy is vital.

Purpose of the Study:

  • To present a general method for unfolding electronic band structures from supercell calculations.
  • To enable easier visualization of electronic structure and broken translational symmetry.
  • To facilitate direct comparison with experimental techniques like angle-resolved photoemission spectroscopy.

Main Methods:

  • Utilizing first-principles supercell calculations.
  • Applying a method to unfold band structures with proper spectral weight.
  • Employing Wannier functions for computational efficiency.

Main Results:

  • Generated unfolded band structures with enhanced information from Kohn-Sham orbitals.
  • Successfully absorbed the structure factor for experimental comparability.
  • Demonstrated the method's applicability to materials with defects and ordering.

Conclusions:

  • The presented method offers a computationally inexpensive way to analyze complex electronic structures.
  • Unfolded band structures provide valuable insights for materials with imperfections or ordered phases.
  • This technique significantly aids in interpreting experimental results from angle-resolved photoemission spectroscopy.