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Related Concept Videos

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...
The Quantum-Mechanical Model of an Atom02:45

The Quantum-Mechanical Model of an Atom

Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra. Schrödinger...
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,...
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...
Valence Bond Theory and Hybridized Orbitals02:38

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.
A σ bond (single bond in a Lewis structure) is a covalent bond in which the electron density is...
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...

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

Published on: October 12, 2019

Electronic structure via potential functional approximations.

Attila Cangi1, Donghyung Lee, Peter Elliott

  • 1Department of Chemistry, University of California, Irvine, California 92697-2025, USA.

Physical Review Letters
|July 21, 2011
PubMed
Summary
This summary is machine-generated.

This study improves orbital-free Kohn-Sham calculations by developing a variational method for the universal functional. This enhances the accuracy of the noninteracting kinetic energy, crucial for density functional theory. Keywords: Kohn-Sham, density functional theory, kinetic energy.

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Area of Science:

  • Computational physics
  • Quantum chemistry
  • Materials science

Background:

  • The Hohenberg-Kohn theorems are foundational to density functional theory (DFT).
  • Accurate calculation of the noninteracting kinetic energy is essential for orbital-free Kohn-Sham methods.
  • Approximations in DFT can lead to inaccuracies, particularly in kinetic energy functionals.

Purpose of the Study:

  • To derive conditions for variational potential-functional approximations.
  • To improve the accuracy of the noninteracting kinetic energy in orbital-free Kohn-Sham calculations.
  • To provide a more robust framework for density functional theory.

Main Methods:

  • The universal functional was expressed as a coupling-constant integral.
  • Conditions for variational potential-functional approximations were derived.
  • A construction method incorporating these conditions was developed.

Main Results:

  • Potential-functional approximations were shown to be variational under derived conditions.
  • The developed method significantly improves the accuracy of the noninteracting kinetic energy.
  • This advancement is particularly beneficial for orbital-free Kohn-Sham calculations.

Conclusions:

  • The derived conditions and construction method offer a more accurate approach to kinetic energy functionals.
  • This work enhances the reliability of orbital-free density functional theory.
  • The findings pave the way for more efficient and accurate electronic structure calculations.