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Related Concept Videos

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...
The Bohr Model02:18

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Following the work of Ernest Rutherford and his colleagues in the early twentieth century, the picture of atoms consisting of tiny dense nuclei surrounded by lighter and even tinier electrons continually moving about the nucleus was well established. This picture was called the planetary model since it pictured the atom as a miniature “solar system” with the electrons orbiting the nucleus like planets orbiting the sun. The simplest atom is hydrogen, consisting of a single proton as the nucleus...
Atomic Orbitals02:44

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Emission Spectra02:39

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The Uncertainty Principle04:08

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Updated: May 30, 2026

Spatial Separation of Molecular Conformers and Clusters
10:37

Spatial Separation of Molecular Conformers and Clusters

Published on: January 9, 2014

Classical and quantum physics of hydrogen clusters.

Fabio Mezzacapo, Massimo Boninsegni

    Journal of Physics. Condensed Matter : an Institute of Physics Journal
    |August 10, 2011
    PubMed
    Summary
    This summary is machine-generated.

    We investigated para-hydrogen (p-H(2)) clusters using quantum simulations. At low temperatures, pristine clusters exhibit superfluidity, while larger clusters show solid-like behavior, with some undergoing quantum melting into a liquid state.

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    Area of Science:

    • Quantum physics
    • Low-temperature condensed matter physics
    • Cluster science

    Background:

    • Understanding the quantum behavior of molecular clusters is crucial for condensed matter physics.
    • Para-hydrogen (p-H(2)) and its isotopes are model systems for studying quantum phenomena in finite systems.
    • Previous studies have explored the properties of hydrogen clusters, but a comprehensive theoretical investigation at very low temperatures was needed.

    Purpose of the Study:

    • To theoretically investigate the low-temperature properties of pristine para-hydrogen (p-H(2)) clusters.
    • To examine the influence of isotopic impurities, such as ortho-deuterium (o-D(2)), on cluster behavior.
    • To explore the transition between liquid-like and solid-like phases in these clusters.

    Main Methods:

    • Utilizing quantum simulations, specifically the continuous-space Worm algorithm.
    • Studying clusters of para-hydrogen molecules up to N = 40.
    • Analyzing both pristine and isotopically doped (ortho-deuterium) clusters.

    Main Results:

    • Pristine p-H(2) clusters exhibit liquid-like and superfluid properties in the low-temperature limit.
    • Superfluidity in these clusters is uniform and associated with long molecular permutation cycles.
    • Clusters with over 22 molecules show solid-like, classical behavior down to approximately 1 Kelvin.
    • Some larger clusters demonstrate a transition to a liquid-like state at sufficiently low temperatures, indicating quantum melting.

    Conclusions:

    • Para-hydrogen clusters display rich low-temperature phase behavior, including superfluidity and quantum melting.
    • Cluster size plays a critical role in determining the transition from quantum liquid to classical solid.
    • The study provides valuable insights into the quantum nature of finite systems and the behavior of hydrogen isotopes at low temperatures.