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Related Concept Videos

Atomic Orbitals02:44

Atomic Orbitals

An atomic orbital represents the three-dimensional regions in an atom where an electron has the highest probability to reside. The radial distribution function indicates the total probability of finding an electron within the thin shell at a distance r from the nucleus. The atomic orbitals have distinct shapes which are determined by l, the angular momentum quantum number. The orbitals are often drawn with a boundary surface, enclosing densest regions of the cloud.
Predicting Molecular Geometry02:27

Predicting Molecular Geometry

VSEPR Theory for Determination of Electron Pair Geometries
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 Uncertainty Principle04:08

The Uncertainty Principle

Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He mathematically...
VSEPR Theory02:37

VSEPR Theory

Valence shell electron-pair repulsion theory (VSEPR theory) enables us to predict the molecular structure around a central atom from an examination of the number of bonds and lone electron pairs in its Lewis structure. The VSEPR model assumes that electron pairs in the valence shell of a central atom will adopt an arrangement that minimizes repulsions between these electron pairs by maximizing the distance between them. The electrons in the valence shell of a central atom form either bonding...
Structure of Benzene: Molecular Orbital Model01:18

Structure of Benzene: Molecular Orbital Model

According to the molecular orbital (MO) model, benzene has a planar structure with a regular hexagon of six sp2 hybridized carbons. As shown in Figure 1, each carbon is bonded to three other atoms with C–C–C and H–C–C bond angles of 120°. The C–H bond length is 109 pm, and the C–C bond length is 139 pm which is midway between the single bond length of sp3 hybridized carbons (154 pm) and sp2 hybridized carbons (133 pm).

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Related Experiment Videos

Geometry-Based Neural-Network Prediction of Electron Localization Function Topology in Dense Hydrogen.

Xiaoyu Wang1, Miriam Marqués2, Sergio Gómez3,4

  • 1Sorbonne Université, CNRS, Laboratoire de Chimie Théorique, LCT, Paris, France.

Chemistry (Weinheim an Der Bergstrasse, Germany)
|July 6, 2026
PubMed
Summary
This summary is machine-generated.

We created a machine-learning model to predict electron localization function (ELF) in dense hydrogen from atomic structure, bypassing complex calculations. This framework accurately models hydrogen bonding and network characteristics, enabling faster materials discovery.

Keywords:
dense hydrogenelectron localization functionhigh‐pressure physicshydrogen networksmachine learning

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Area of Science:

  • Computational materials science
  • Quantum chemistry
  • Machine learning applications

Background:

  • Predicting electron localization function (ELF) in dense hydrogen is crucial for understanding its unique properties.
  • Traditional electronic-structure calculations are computationally expensive, limiting high-throughput studies.

Purpose of the Study:

  • To develop a machine-learning framework for predicting ELF directly from atomic geometry.
  • To bypass computationally intensive electronic-structure calculations for dense hydrogen.

Main Methods:

  • Developed a machine-learning model trained on first-principles data of dense fluid hydrogen.
  • Utilized a combined real- and reciprocal-space analysis to evaluate model accuracy and error sources.
  • Tested the model's transferability to crystalline hydrogen configurations.

Main Results:

  • The machine-learning model achieved high accuracy (R² > 0.99) in predicting ELF.
  • Residual errors were analyzed, revealing long-wavelength components that increase with pressure.
  • The model demonstrated robust transferability to crystalline hydrogen, preserving topological features.

Conclusions:

  • The developed framework offers a computationally efficient route for evaluating hydrogen-networking characteristics.
  • This approach enables high-throughput analysis of both fluid and crystalline hydrogen.
  • The study highlights the potential of machine learning in accelerating materials science research.