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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.

Valence Bond Theory and Hybridized Orbitals

Valence Bond Theory and Hybridized Orbitals

According to valence bond theory, a covalent bond results when: (1) an orbital on one atom overlaps an orbital on a second atom, and (2) the single electrons in each orbital combine to form an electron pair. The strength of a covalent bond depends on the extent of overlap of the orbitals involved. Maximum overlap is possible when the orbitals overlap on a direct line between the two nuclei.
A σ bond (single bond in a Lewis structure) is a covalent bond in which the electron density is...

Hybridization of Atomic Orbitals I

Hybridization of Atomic Orbitals I

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...

Hybridization of Atomic Orbitals II

Hybridization of Atomic Orbitals II

sp3d and sp3d 2 Hybridization

Molecular Orbital Theory I

Molecular Orbital Theory I

Overview of Molecular Orbital Theory

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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Related Experiment Video

Updated: Jul 19, 2025

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Published on: September 8, 2023

Ab initio quantum chemistry with neural-network wavefunctions.

Jan Hermann^1,2, James Spencer³, Kenny Choo^4,5

¹Microsoft Research AI4Science, Berlin, Germany.

Nature Reviews. Chemistry

|August 9, 2023

Summary

This summary is machine-generated.

Machine learning, specifically neural networks, is revolutionizing quantum chemistry by directly solving the electronic Schrödinger equation. This approach offers accurate solutions for molecular systems, complementing traditional quantum chemistry methods.

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Last Updated: Jul 19, 2025

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

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Published on: September 8, 2023

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

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Published on: April 8, 2020

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

Area of Science:

Computational chemistry
Quantum mechanics
Machine learning applications in science

Background:

Deep learning excels at pattern recognition and data processing, driving scientific discovery.
Machine learning is used in molecular science to learn potential energy surfaces from quantum chemistry calculations.
Conventional quantum chemistry methods can be computationally intensive.

Purpose of the Study:

To review a complementary machine learning approach for solving quantum chemistry problems directly.
To focus on quantum Monte Carlo methods utilizing neural-network wave function ansatzes.
To explore the application of these methods in solving the electronic Schrödinger equation.

Main Methods:

Utilizing neural-network ansatzes within quantum Monte Carlo frameworks.
Solving the electronic Schrödinger equation in first and second quantization.
Generalizing solutions over multiple nuclear configurations for ground and excited states.

Main Results:

Neural network quantum Monte Carlo methods can provide highly accurate solutions to the electronic Schrödinger equation.
These methods are beginning to rival advanced conventional quantum chemistry techniques.
The approach shows promise for systems up to a few dozen electrons.

Conclusions:

Machine learning offers a powerful new paradigm for tackling fundamental quantum chemistry problems.
Neural network quantum Monte Carlo methods represent an emerging and promising area of research.
This approach has the potential to accelerate molecular simulations and scientific discovery.