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Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...
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CFT focuses on...
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The ideal gas law is an approximation that works well at high temperatures and low pressures. The van der Waals equation of state (named after the Dutch physicist Johannes van der Waals, 1837−1923) improves it by considering two factors.
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Updated: Oct 4, 2025

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
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Basis-set correction based on density-functional theory: Rigorous framework for a one-dimensional model.

Diata Traore1, Emmanuel Giner1, Julien Toulouse1

  • 1Laboratoire de Chimie Théorique, Sorbonne Université and CNRS, F-75005 Paris, France.

The Journal of Chemical Physics
|February 2, 2022
PubMed
Summary
This summary is machine-generated.

We introduce a new density-functional theory method to fix basis-set errors in wave-function calculations. This approach improves accuracy for quantum chemistry and materials science simulations.

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Area of Science:

  • Quantum Chemistry
  • Computational Physics
  • Theoretical Chemistry

Background:

  • Basis-set incompleteness is a significant error source in wave-function methods.
  • Density-functional theory (DFT) offers a potential route to correct these errors.
  • Existing methods require complex adaptations, limiting their applicability.

Purpose of the Study:

  • To re-examine and refine basis-set correction theory using DFT.
  • To develop a novel, adapted local-density approximation for basis-set correction.
  • To provide a more robust theoretical foundation for basis-set correction methods.

Main Methods:

  • Utilized a one-dimensional model Hamiltonian with delta-potential interactions for systematic analysis.
  • Derived mathematical details of the basis-set correction theory.
  • Developed a new local-density approximation by projecting electron-electron interactions onto the basis set using a finite uniform electron gas.

Main Results:

  • Demonstrated the feasibility of developing an adapted local-density approximation for basis-set correction.
  • Showcased a method that automatically adapts to the employed basis set.
  • Established a more rigorous foundation for basis-set correction theory.

Conclusions:

  • The proposed variant of basis-set correction offers an improved and adaptable strategy.
  • This work strengthens the theoretical basis of DFT-based corrections for wave-function methods.
  • The findings pave the way for more accurate and efficient quantum mechanical calculations.