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Related Concept Videos

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...
Debye–Huckel–Onsager Conductance Equation01:28

Debye–Huckel–Onsager Conductance Equation

The Debye-Hückel-Onsager equation is a cornerstone of physical chemistry, providing a method to determine the molar conductance (Λm) and molar conductance at infinite dilution (Λ°m) for uni-univalent electrolytes.Uni-univalent electrolytes are electrolytes that dissociate in solution to produce one cation with a +1 charge and one anion with a –1 charge per formula unit.This equation addresses two crucial phenomena: the asymmetry effect and the electrophoretic effect. According to this equation,...
Crystal Density01:19

Crystal Density

The crystal lattice structure of a material allows us to determine how many molecules exist in its unit cell. With this information, alongside the unit-cell parameters - three distance parameters (a, b, c) and three angular parameters (α, β, γ).Density (ρ) = (Z × M) / (a × b × c × NA)where:Z is the number of formula units per unit cellM is the molar mass of the substancea, b, and c are the edge lengths of the unit cellNA is Avogadro’s numberFor a simple cubic lattice, atoms are located only at...
The de Broglie Wavelength02:32

The de Broglie Wavelength

In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a table will behave like a particle; it will continue traveling in a straight line unless it collides with another ball, or it is acted on by some other force, such as friction. The ball has a well-defined position and velocity or well-defined momentum, p = mv, which is defined by mass m and velocity v at any given moment. This is the typical...
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...
Boundary Conditions for Current Density01:25

Boundary Conditions for Current Density

Current density becomes discontinuous across an interface of materials with different electrical conductivities. The normal component of the current density is continuous across the boundary.

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Related Experiment Video

Updated: May 18, 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

One-dimensional continuum electronic structure with the density-matrix renormalization group and its implications for

E M Stoudenmire1, Lucas O Wagner, Steven R White

  • 1Department of Physics and Astronomy, University of California, Irvine, 92697, USA.

Physical Review Letters
|September 26, 2012
PubMed
Summary

We developed a new method to find exact ground states for one-dimensional many-electron systems. This approach accurately simulates strongly correlated atoms and aids in understanding density-functional theory.

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Last Updated: May 18, 2026

Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations
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Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Published on: May 27, 2020

Area of Science:

  • Quantum Many-Body Physics
  • Condensed Matter Physics
  • Computational Chemistry

Background:

  • Accurate computation of ground states for many-electron systems is crucial for understanding material properties.
  • Continuum models with long-range interactions present significant computational challenges.
  • Density-functional theory (DFT) provides a framework but requires accurate methods for its exact study.

Purpose of the Study:

  • To extend the density matrix renormalization group (DMRG) for computing exact ground states of one-dimensional continuum many-electron systems with long-range interactions.
  • To apply the extended DMRG method to a specific system of 100 strongly correlated artificial hydrogen atoms.
  • To demonstrate the utility of the method for simulating cold atom systems and for studying DFT in an exact setting.

Main Methods:

  • Extension of the density matrix renormalization group (DMRG) algorithm.
  • Application to one-dimensional continuum many-electron systems.
  • Simulation of a chain of 100 strongly correlated artificial hydrogen atoms.

Main Results:

  • The exact ground state of a 100-site chain of strongly correlated artificial hydrogen atoms was successfully computed.
  • The extended DMRG method proved capable of simulating 1D cold atom systems.
  • An example was provided where an interacting, extended system behaves as an insulator, while its corresponding Kohn-Sham system is metallic, highlighting a DFT insight.

Conclusions:

  • The extended DMRG is a powerful tool for obtaining exact ground states of complex 1D quantum systems.
  • This method offers a valuable platform for investigating cold atom physics and for rigorously testing density-functional theory approximations.
  • The findings demonstrate the potential for discrepancies between true interacting systems and their DFT descriptions.