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¹H NMR: Long-Range Coupling01:27

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The coupling interactions of nuclei across four or more bonds are usually weak, with J values less than 1 Hz. While these are usually not observed in spectra, the presence of multiple bonds along the coupling pathway can result in observable long-range coupling.
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In Ultraviolet–Visible (UV–Vis) spectroscopy, the absorption of electromagnetic radiation is used to probe the electronic structure of molecules. This technique provides insights into molecular electronic transitions, particularly the movement of electrons between different molecular orbitals. Radiation is absorbed if the energy of the electromagnetic radiation passing through the molecule is precisely equal to the energy difference between the excited and ground states. During this...
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Piecewise linearity and spectroscopic properties from Koopmans-compliant functionals.

Ismaila Dabo1, Andrea Ferretti, Nicola Marzari

  • 1Department of Materials Science and Engineering, Materials Research Institute, The Pennsylvania State University, University Park, PA, 16802, USA, dabo@matse.psu.edu.

Topics in Current Chemistry
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Density-functional theory (DFT) approximations often fail to accurately predict spectroscopic properties. This study introduces orbital-density-dependent functionals that enforce piecewise linearity, improving predictions of electron removal energies and spectroscopic data.

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Area of Science:

  • Computational Physics
  • Quantum Chemistry
  • Materials Science

Background:

  • Density-functional theory (DFT) is a cornerstone of quantum simulations for electronic structure.
  • Standard DFT approximations struggle to accurately predict quasiparticle energy levels and spectroscopic properties.
  • A key theoretical property, piecewise linearity of the energy functional at fractional electron occupations, is often violated by common DFT approximations.

Purpose of the Study:

  • To investigate the impact of enforcing piecewise linearity in DFT energy functionals.
  • To develop new DFT approximations that accurately describe spectroscopic properties.
  • To bridge the gap between theoretical calculations and experimental spectroscopic measurements.

Main Methods:

  • Reformulation of the electronic-structure problem using DFT.
  • Imposition of the piecewise linearity constraint on the total energy functional.
  • Development of orbital-density-dependent functionals.
  • Validation against spectroscopic properties and generalized Koopmans' theorem.

Main Results:

  • The developed functionals closely satisfy a generalized Koopmans condition.
  • Spectroscopic properties are described with significantly improved accuracy compared to standard DFT.
  • The discrepancy between total and partial electron removal energies is resolved.

Conclusions:

  • Enforcing piecewise linearity is crucial for accurate DFT predictions of spectroscopic properties.
  • Orbital-density-dependent functionals offer a promising route to overcome limitations of current DFT methods.
  • This approach enhances the predictive power of DFT for materials and molecular science.