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The Quantum-Mechanical Model of an Atom

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.

Hybridization of Atomic Orbitals I

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The mathematical expression known as the wave function, ψ, contains information about each orbital and the wavelike properties of electrons in an isolated atom. When atoms are bound together in a molecule, the wave functions combine to produce new mathematical descriptions that have different shapes. This process of combining the wave functions for atomic orbitals is called hybridization and is mathematically accomplished by the linear combination of atomic orbitals. The new orbitals that...

Van der Waals Interactions

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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.

Electronic Structure of Atoms

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...

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sp3d and sp3d 2 Hybridization

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Updated: Jan 8, 2026

Isotopic Effect in Double Proton Transfer Process of Porphycene Investigated by Enhanced QM/MM Method

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Published on: July 19, 2019

Machine learning interatomic potentials at the centennial crossroads of quantum mechanics.

Bhupalee Kalita¹, Hatice Gokcan¹, Olexandr Isayev^2,3

¹Department of Chemistry, Mellon College of Science, Carnegie Mellon University, Pittsburgh, PA, USA.

Nature Computational Science

|December 22, 2025

Summary

Machine learning interatomic potentials combine quantum accuracy with classical speed for molecular modeling. Future frameworks aim for predictive, transferable, and physically grounded computational chemistry.

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Area of Science:

Computational chemistry
Materials science
Quantum mechanics

Background:

Machine learning interatomic potentials (MLIPs) are emerging tools in molecular modeling.
They bridge the gap between quantum mechanical accuracy and classical computational efficiency.
The centennial of quantum mechanics in 2025 highlights the importance of these advancements.

Purpose of the Study:

To examine the development of MLIPs.
To address key challenges in their application.
To outline future directions for next-generation computational chemistry.

Main Methods:

Reviewing architectural innovations in MLIPs.
Exploring physics-informed machine learning approaches.
Analyzing foundation models trained on extensive datasets.

Main Results:

Significant progress has been made in achieving chemical accuracy with MLIPs.
Computational efficiency has been maintained and improved.
Interpretability and generalizability are active areas of research and development.

Conclusions:

MLIPs are rapidly advancing computational chemistry.
Innovations focus on accuracy, efficiency, interpretability, and generalizability.
Future MLIP frameworks will be predictive, transferable, and physically grounded.