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Electron Carriers01:24

Electron Carriers

91.8K
Electron carriers can be thought of as electron shuttles. These compounds can easily accept electrons (i.e., be reduced) or lose them (i.e., be oxidized). They play an essential role in energy production because cellular respiration is contingent on the flow of electrons.
Over the many stages of cellular respiration, glucose breaks down into carbon dioxide and water. Electron carriers pick up electrons lost by glucose in these reactions, temporarily storing and releasing them into the electron...
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Electron Affinity03:07

Electron Affinity

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The electron affinity (EA) is the energy change for adding an electron to a gaseous atom to form an anion (negative ion).
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Electron Behavior00:54

Electron Behavior

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Overview
Electrons are negatively charged subatomic particles that are attracted to an orbit around the positively-charged nucleus of an atom. They reside in locations that are associated with energy levels called shells and are further organized into sub-shells and orbitals within each shell.
Electrons Orbit the Nucleus
Electrons are found in specific locations outside of the nucleus. The shell in which an electron resides indicates the general energy level of the electron: those closer to the...
108.5K
Electron Transport Chains01:28

Electron Transport Chains

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The final stage of cellular respiration is oxidative phosphorylation that consists of two steps: the electron transport chain and chemiosmosis. The electron transport chain is a set of proteins found in the inner mitochondrial membrane in eukaryotic cells. Its primary function is to establish a proton gradient that can be used during chemiosmosis to produce ATP and generate electron carriers, such as NAD+ and FAD, that are used in glycolysis and the citric acid cycle.
The ETC is comprised of...
112.1K
Electron Orbital Model01:18

Electron Orbital Model

72.1K
Orbitals are the areas outside of the atomic nucleus where electrons are most likely to reside. They are characterized by different energy levels, shapes, and three-dimensional orientations. The location of electrons is described most generally by a shell or principal energy level, then by a subshell within each shell, and finally, by individual orbitals found within the subshells.
The first shell is closest to the nucleus, and it has only one subshell with a single spherical orbital called the...
72.1K
Second Order systems II01:18

Second Order systems II

406
In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
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Related Experiment Video

Updated: Jan 30, 2026

A Technique to Functionalize and Self-assemble Macroscopic Nanoparticle-ligand Monolayer Films onto Template-free Substrates
08:09

A Technique to Functionalize and Self-assemble Macroscopic Nanoparticle-ligand Monolayer Films onto Template-free Substrates

Published on: May 9, 2014

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Wavefunctions of macroscopic electron systems.

P Fulde1

  • 1Max-Planck-Institut für Physik Komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany.

The Journal of Chemical Physics
|January 21, 2019
PubMed
Summary

The Exponential Wall Problem (EWP) hinders electronic structure calculations for large systems. This study resolves the EWP by reformulating wavefunctions as additive quantities in Liouville space, enabling accurate calculations for macroscopic solids.

Area of Science:

  • Quantum chemistry
  • Computational physics
  • Materials science

Background:

  • The Exponential Wall Problem (EWP) arises from the multiplicative nature of wavefunctions for large electron numbers, limiting their use in macroscopic systems.
  • Existing wavefunction-based methods struggle with the exponential scaling of Hilbert space dimensions with electron number N.
  • A robust theoretical foundation is needed for electronic structure calculations of solids.

Purpose of the Study:

  • To resolve the Exponential Wall Problem (EWP) in electronic structure calculations for macroscopic systems.
  • To provide a basis for wavefunction-based methods applicable to solids.
  • To develop a formalism for handling large electron numbers in quantum systems.

Main Methods:

  • Reformulating wavefunctions from multiplicative to additive quantities by taking logarithms.

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  • Transitioning from Hilbert space to operator- or Liouville space with a cumulant-based metric.
  • Utilizing a mean-field state as a vacuum, with fluctuations treated via cluster expansion.

    • Main Results:

    • A method is presented to overcome the EWP for ground-state electronic structure calculations of macroscopic electron systems.
    • The approach establishes a solid foundation for electronic structure calculations in solids.
    • The formalism accommodates matrix product states, demonstrating their connection to Liouville space operators.

    Conclusions:

    • The developed scheme provides a rigorous basis for electronic structure calculations of solids, overcoming the EWP.
    • The method's applicability has been experimentally validated.
    • The formalism offers a unified framework for diverse quantum many-body techniques.