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Related Concept Videos

Atomic Radii and Effective Nuclear Charge03:08

Atomic Radii and Effective Nuclear Charge

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The elements in groups of the periodic table exhibit similar chemical behavior. This similarity occurs because the members of a group have the same number and distribution of electrons in their valence shells.
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Atomic Nuclei: Nuclear Magnetic Moment00:59

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All atomic nuclei are positively charged. When they have a nonzero spin, they behave like rotating charges. As a consequence of their charge and spin, these nuclei generate a magnetic field (B). This, in turn, gives rise to a magnetic moment (μ), which is randomly oriented in the absence of an external magnetic field. When an external magnetic field (B0) is applied, the magnetic moment vectors can align with the field or against it in 2 + 1 orientations. A hydrogen nucleus, which is just a...
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Nuclear Stability03:18

Nuclear Stability

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Protons and neutrons, collectively called nucleons, are packed together tightly in a nucleus. With a radius of about 10−15 meters, a nucleus is quite small compared to the radius of the entire atom, which is about 10−10 meters. Nuclei are extremely dense compared to bulk matter, averaging 1.8 × 1014 grams per cubic centimeter. If the earth’s density were equal to the average nuclear density, the earth’s radius would be only about 200 meters.
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Atomic Nuclei: Nuclear Relaxation Processes01:23

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In the absence of an external magnetic field, nuclear spin states are degenerate and randomly oriented. When a magnetic field is applied, the spins begin to precess and orient themselves along (lower energy) or against (higher energy) the direction of the field. At equilibrium, a slight excess population of spins exists in the lower energy state. Because the direction of the magnetic field is fixed as the z-axis,  the precessing magnetic moments are randomly oriented around the z-axis.
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Atomic Nuclei: Nuclear Spin01:08

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All atomic particles possess an intrinsic angular momentum, or 'spin'. Electrons, protons, and neutrons each have a spin value of ½, although protons and neutrons in nuclei may have higher half-integer spins owing to energetic factors.
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Atomic Nuclei: Nuclear Spin State Population Distribution01:14

Atomic Nuclei: Nuclear Spin State Population Distribution

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Near absolute zero temperatures, in the presence of a magnetic field, the majority of nuclei prefer the lower energy spin-up state to the higher energy spin-down state. As temperatures increase, the energy from thermal collisions distributes the spins more equally between the two states. The Boltzmann distribution equation gives the ratio of the number of spins predicted in the spin −½ (N−) and spin +½ (N+) states.
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Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
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Realistic nuclear charge distribution model function for analytic nuclear attraction integrals in Gaussian basis

Nobuki Inoue1, Takahito Nakajima1

  • 1RIKEN Center for Computational Science, Kobe, Hyogo, Japan.

Journal of Computational Chemistry
|January 16, 2023
PubMed
Summary

A new Augmented Gaussian 12 (AG12) model provides accurate nuclear charge distributions, improving electronic structure calculations. This method offers analytical formulas for nuclear attraction integrals, overcoming limitations of simpler models for heavy nuclei.

Keywords:
Gaussian basis functionsnuclear attraction integralnuclear charge distributionrelativistic quantum chemistrysuperheavy elements

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Area of Science:

  • Computational chemistry
  • Atomic physics
  • Quantum mechanics

Background:

  • Accurate nuclear charge distribution is crucial for electronic structure theory.
  • Common models like point charge and Gaussian functions lack accuracy for heavy nuclei.
  • Realistic models such as the two-parameter Fermi (2pF) distribution lack analytical nuclear attraction integral (NAI) formulas.

Purpose of the Study:

  • Introduce the Augmented Gaussian 12 (AG12) model for nuclear charge distribution.
  • Develop a fitting scheme to optimize the AG12 model.
  • Evaluate the performance of AG12 against existing models.

Main Methods:

  • Developed the Augmented Gaussian 12 (AG12) function model with adjustable parameters.
  • Implemented a fitting scheme to reproduce established nuclear charge distributions (2pF and realistic models).
  • Performed calculations for hydrogen-like ions to compare energy differences.

Main Results:

  • The AG12 model, with its fitting scheme, accurately reproduces 2pF and more realistic nuclear charge distributions.
  • AG12 fitted to the 2pF model successfully replicates energy differences in hydrogen-like ions.
  • Calculations highlight the need for realistic nuclear charge distributions beyond the 2pF model.

Conclusions:

  • The AG12 model offers a balance of flexibility and analytical tractability for nuclear charge distributions.
  • AG12 provides a superior alternative to traditional models for electronic structure calculations, especially for heavy nuclei.
  • The study underscores the importance of employing realistic nuclear charge models for high-accuracy atomic and molecular calculations.