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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.
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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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Quantum chemistry - from the first steps to linear-scaling electronic structure methods.

Daniel Graf1, Viktoria Drontschenko1, Alexandra Stan-Bernhardt1

  • 1Theoretical Chemistry, Department of Chemistry, Ludwig-Maximilians-Universität München (LMU Munich), D-81377 München, Germany.

Pure and Applied Chemistry. Chimie Pure Et Appliquee
|November 27, 2025
PubMed
Summary
This summary is machine-generated.

This study reviews quantum chemistry's history, focusing on approximations to the Schrödinger equation and methods to overcome computational scaling challenges for larger systems. It also explores future directions in reaction network exploration.

Keywords:
Density functional theoryelectronic structure theoryquantum chemistryquantum science and technologyreaction network explorationwavefunction theory

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Area of Science:

  • Quantum Chemistry
  • Computational Chemistry

Background:

  • The development of quantum chemistry traces back to early atomic models and the Schrödinger equation.
  • Efficient approximations to the Schrödinger equation are crucial due to computational cost scaling.

Purpose of the Study:

  • To provide a historical overview of quantum chemistry.
  • To discuss methods for overcoming computational scaling issues in quantum chemistry.
  • To explore future directions in reaction network exploration.

Main Methods:

  • Historical review of quantum chemistry milestones.
  • Discussion of computational techniques to address scaling problems.
  • Exploration of reaction network analysis.

Main Results:

  • Quantum chemistry has evolved significantly since the 19th century.
  • Approximations are essential for solving the Schrödinger equation computationally.
  • Techniques to mitigate computational cost scaling are actively researched.

Conclusions:

  • Quantum chemistry requires efficient approximations to handle complex systems.
  • Overcoming computational scaling is key to advancing the field.
  • Reaction network exploration represents a promising future avenue.