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Related Concept Videos

Electronic Structure of Atoms02:28

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 numbers:  n, l, ml, and...
The Energies of Atomic Orbitals03:21

The Energies of Atomic Orbitals

In an atom, the negatively charged electrons are attracted to the positively charged nucleus. In a multielectron atom, electron-electron repulsions are also observed. The attractive and repulsive forces are dependent on the distance between the particles, as well as the sign and magnitude of the charges on the individual particles. When the charges on the particles are opposite, they attract each other. If both particles have the same charge, they repel each other.
π Electron Effects on Chemical Shift: Overview01:27

π Electron Effects on Chemical Shift: Overview

An applied magnetic field causes loosely bound π-electrons in organic molecules to circulate, producing a local or induced diamagnetic field over a large spatial volume. As the molecules tumble in solution, the field generated by π-electrons in spherical substituents results in a zero net field. However, the net field generated by π-electrons in non-spherical substituents is not zero. The effect of this induced field depends on the orientation of the molecule with respect to B0, resulting in...
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.
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...
Valence Bond Theory and Hybridized Orbitals02:38

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...

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Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
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Completeness-optimized basis sets: application to ground-state electron momentum densities.

Jussi Lehtola1, Pekka Manninen, Mikko Hakala

  • 1Department of Physics, University of Helsinki, P.O. Box 64, FI-00014 University of Helsinki, Finland. jussi.lehtola@helsinki.fi

The Journal of Chemical Physics
|September 18, 2012
PubMed
Summary

This study introduces a new algorithm for optimizing basis sets in electronic structure calculations. It enables more efficient and cost-effective computation of electron momentum density properties, reaching complete basis set limits.

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Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Theoretical Chemistry

Background:

  • Basis set convergence is crucial for accurate electronic structure calculations.
  • Achieving the complete basis set (CBS) limit is computationally demanding.
  • Electron momentum density provides insights into electronic structure.

Purpose of the Study:

  • To investigate basis set convergence for electron momentum density moments.
  • To develop a computationally efficient method for reaching the CBS limit.
  • To present a black-box completeness-optimization algorithm.

Main Methods:

  • Application of the completeness-optimization paradigm.
  • Development of a black-box completeness-optimization algorithm.
  • Comparison with conventional energy-optimized Gaussian basis sets.

Main Results:

  • Demonstration of a cost-effective approach to reach the CBS limit for electron momentum density.
  • Generation of computationally efficient, completeness-optimized basis sets.
  • Validation against established CBS limits.

Conclusions:

  • Completeness-optimized basis sets offer a more efficient route to CBS limits than energy-optimized sets.
  • The developed algorithm facilitates accurate calculations for larger systems.
  • This method enhances the computational feasibility of studying electron momentum density.