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Related Concept Videos

Van der Waals Equation01:10

Van der Waals Equation

The ideal gas law is an approximation that works well at high temperatures and low pressures. The van der Waals equation of state (named after the Dutch physicist Johannes van der Waals, 1837−1923) improves it by considering two factors.
First, the attractive forces between molecules, which are stronger at higher densities and reduce the pressure, are considered by adding to the pressure a term equal to the square of the molar density multiplied by a positive coefficient a. Second, the volume...
Van der Waals Interactions01:24

Van der Waals Interactions

Atoms and molecules interact with each other through intermolecular forces. These electrostatic forces arise from attractive or repulsive interactions between particles with permanent, partial, or temporary charges. The intermolecular forces between neutral atoms and molecules are ion–dipole, dipole–dipole, and dispersion forces, collectively known as van der Waals forces.Polar molecules have a partial positive charge on one end and a partial negative charge on the other end of the molecule,...
The Van der Waals Equation01:26

The Van der Waals Equation

The ideal gas law is based on two simplifying assumptions: first, that there are no intermolecular attractions between gas molecules, and second, that the volume occupied by the molecules themselves is negligible compared with the volume of the container. However, these assumptions don't hold up under all conditions - specifically, at high pressures and low temperatures, as gas tends to deviate from ideal gas behavior.The van der Waals equation is an enhanced version of the ideal gas law,...
IR Spectroscopy: Hooke's Law Approximation of Molecular Vibration01:16

IR Spectroscopy: Hooke's Law Approximation of Molecular Vibration

A covalently bonded heteronuclear diatomic molecule can be modeled as two vibrating masses connected by a spring. The vibrational frequency of the bond can be expressed using an equation derived from Hooke's law, which describes how the force applied to stretch or compress a spring is proportional to the displacement of the spring. In this case, the atoms behave like masses, and the bond acts like a spring.
According to Hooke's law, the vibrational frequency is directly proportional to the...
Spin–Spin Coupling: One-Bond Coupling01:17

Spin–Spin Coupling: One-Bond Coupling

Coupling interactions are strongest between NMR-active nuclei bonded to each other, where spin information can be transmitted directly through the pair of bonding electrons. While nuclei polarize their electrons to the opposite spins, the bonding electron pair has opposite spins. Configurations with antiparallel nuclear spins are expected to be lower in energy. When coupling makes antiparallel states more favorable, J is considered to have a positive value. The one-bond coupling constant, 1J,...
Intermolecular Forces03:13

Intermolecular Forces

Atoms and molecules interact through bonds (or forces): intramolecular and intermolecular. The forces are electrostatic as they arise from interactions (attractive or repulsive) between charged species (permanent, partial, or temporary charges) and exist with varying strengths between ions, polar, nonpolar, and neutral molecules. The different types of intermolecular forces are ion–dipole, dipole–dipole, hydrogen bonds, and dispersion; among these, dipole–dipole, hydrogen bonds, and dispersion...

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Updated: Jul 7, 2026

Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations
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Published on: October 12, 2019

Carbynes phonons: a tight binding force field.

Alberto Milani1, Matteo Tommasini, Giuseppe Zerbi

  • 1Center for NanoEngineered Materials and Surfaces (NEMAS), Dipartimento di Chimica, Materiali e Ingegneria Chimica, G. Natta, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133 Milan, Italy. alberto.milani@chem.polimi.it

The Journal of Chemical Physics
|February 20, 2008
PubMed
Summary
This summary is machine-generated.

A new tight-binding model accurately predicts vibrational properties of linear carbon chains, overcoming limitations of first-principles calculations for experimental data interpretation.

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Area of Science:

  • Condensed Matter Physics
  • Materials Science
  • Computational Chemistry

Background:

  • First-principles calculations struggle to model vibrational structures of linear carbon chains.
  • This limits interpretation of experimental data, like Raman scattering on carbon chains in nanotubes.

Purpose of the Study:

  • To develop a simplified model for calculating longitudinal phonon dispersion in linear carbon chains.
  • To overcome limitations of current computational methods for vibrational analysis.

Main Methods:

  • A tight-binding scheme for pi-electrons was employed.
  • A force field based on bond-bond polarizabilities and three parameters was developed.
  • Longitudinal phonon dispersion branches were calculated.

Main Results:

  • The model shows excellent agreement with experimental data for carbynes and polyynes.
  • It accurately describes long-range vibrational interactions in carbynes.
  • The approach analytically captures phenomena like Kohn anomaly and electron-phonon coupling.

Conclusions:

  • The developed tight-binding model provides an accurate and efficient method for studying vibrational properties of linear carbon chains.
  • This model enhances the interpretation of experimental data, particularly in spectroscopy.
  • It offers analytical insights into fundamental physical phenomena governing vibrational behavior.