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Nuclear Binding Energy02:13

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The difference between the calculated and experimentally measured masses is known as the mass defect of the atom. In the case of helium-4, the mass defect indicates a “loss” in mass of 4.0331 amu – 4.0026 amu = 0.0305 amu. The loss in mass accompanying the formation of an atom from protons, neutrons, and electrons is due to the conversion of that mass into energy that is evolved as the atom forms. The nuclear binding energy is the energy produced when the atoms’ nucleons are bound...
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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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The equilibrium binding constant (Kb) quantifies the strength of a protein-ligand interaction. Kb can be calculated as follows when the reaction is at equilibrium:
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Stable molecules exist because covalent bonds hold the atoms together. The strength of a covalent bond is measured by the energy required to break it, that is, the energy necessary to separate the bonded atoms. Separating any pair of bonded atoms requires energy — the stronger a bond, the greater the energy required to break it.
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The free energy change for a process taking place with reactants and products present under nonstandard conditions (pressures other than 1 bar; concentrations other than 1 M) is related to the standard free energy change according to this equation:
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Related Experiment Video

Updated: Dec 8, 2025

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
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Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

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Relativistic correction scheme for core-level binding energies from GW.

Levi Keller1, Volker Blum2, Patrick Rinke1

  • 1Department of Applied Physics, Aalto University, Otakaari 1, FI-02150 Espoo, Finland.

The Journal of Chemical Physics
|September 23, 2020
PubMed
Summary
This summary is machine-generated.

We developed a relativistic correction to accurately calculate core-level binding energies using Green's function theory (GW approximation). This method significantly reduces errors and improves accuracy without increasing computational cost.

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Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Relativistic Quantum Mechanics

Background:

  • Accurate calculation of core-level binding energies is crucial for understanding chemical environments and electronic structure.
  • Existing methods, such as Green's function theory in the GW approximation, often struggle with relativistic effects, particularly for heavier elements.
  • Relativistic effects become significant for core-level electrons and can lead to substantial errors in calculated binding energies.

Purpose of the Study:

  • To introduce a novel, computationally inexpensive relativistic correction scheme for improving 1s core-level binding energies.
  • To enhance the accuracy of calculations performed using Green's function theory within the GW approximation.
  • To reduce the mean absolute error (MAE) and eliminate species dependence in calculated core-level binding energies.

Main Methods:

  • Derivation of an element-specific relativistic corrective term based on the difference between non-relativistic/scalar-relativistic and four-component relativistic calculations for free atoms.
  • Application of this corrective term as a perturbation to quasiparticle energies obtained from partially self-consistent and single-shot GW calculations.
  • Investigation of the corrective term's dependence on molecular environment and exact exchange in hybrid functionals.

Main Results:

  • The relativistic correction reduced the MAE of 65 core-state excitations from 0.55 eV to 0.30 eV compared to experimental data.
  • The correction successfully eliminated the species dependence of the MAE, which previously increased with atomic number.
  • Reduced species dependence was also observed for the optimal amount of exact exchange in hybrid functionals for G0W0 calculations.

Conclusions:

  • The proposed element-specific relativistic correction scheme significantly enhances the accuracy of 1s core-level binding energies calculated with GW theory.
  • The method is computationally efficient, adding no overhead, and effectively addresses relativistic effects, improving predictions across different elements.
  • The correction scheme's transferability is demonstrated for the delta self-consistent field (ΔSCF) method, indicating broad applicability.