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The Quantum-Mechanical Model of an Atom02:45

The Quantum-Mechanical Model of an Atom

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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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Orbitals are the areas outside of the atomic nucleus where electrons are most likely to reside. They are characterized by different energy levels, shapes, and three-dimensional orientations. The location of electrons is described most generally by a shell or principal energy level, then by a subshell within each shell, and finally, by individual orbitals found within the subshells.
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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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In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a table will behave like a particle; it will continue traveling in a straight line unless it collides with another ball, or it is acted on by some other force, such as friction. The ball has a well-defined position and velocity or well-defined momentum, p = mv, which is defined by mass m and velocity v at any given moment. This is the typical...
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Updated: Oct 31, 2025

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
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Quantum Chemical Models (Nobel Lecture).

John A Pople1

  • 1Department of Chemistry, Northwestern University, Evanston, IL (USA), Fax: (+1) 847-491-7713.

Angewandte Chemie (International Ed. in English)
|June 29, 2021
PubMed
Summary
This summary is machine-generated.

Quantum chemistry, specifically the ab initio (GAUSSIAN) method, offers accurate solutions for complex chemical problems. High-precision calculations of binding energies for small molecules are now within reach.

Keywords:
Ab initio calculationsComputer chemistryNobel lectureTheoretical chemistry

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Area of Science:

  • Quantum chemistry
  • Theoretical chemistry
  • Computational chemistry

Background:

  • Theoretical models aim to solve complex chemical problems with unknown or disputed answers.
  • The ab initio concept, widely recognized as GAUSSIAN, is a key theoretical approach in chemistry.

Purpose of the Study:

  • To describe the advancements in quantum chemistry, particularly the ab initio method.
  • To highlight the capability of ab initio methods in achieving highly accurate computational results.

Main Methods:

  • Utilizing the ab initio computational chemistry approach.
  • Focusing on the GAUSSIAN implementation for theoretical modeling.

Main Results:

  • Ab initio methods provide a pathway to significantly improve the accuracy of chemical calculations.
  • The precision of 1 kcal/mol for binding energies is achievable for small molecules (up to 50 electrons).

Conclusions:

  • Quantum chemistry, via ab initio methods, is increasingly capable of solving challenging chemical problems.
  • Highly accurate predictions of molecular properties are becoming standard for small chemical systems.