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The Van der Waals Equation01:26

The Van der Waals Equation

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The ideal gas law is based on two simplifying assumptions: first, that there are no intermolecular attractions between gas molecules, and second, that the volume occupied by the molecules themselves is negligible compared with the volume of the container. However, these assumptions don't hold up under all conditions - specifically, at high pressures and low temperatures, as gas tends to deviate from ideal gas behavior.The van der Waals equation is an enhanced version of the ideal gas law,...
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Van der Waals Equation01:10

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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.
First, the attractive forces between molecules, which are stronger at higher densities and reduce the pressure, are considered by adding to the pressure a term equal to the square of the molar density multiplied by a positive coefficient a. Second, the volume...
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Trends in Lattice Energy: Ion Size and Charge02:54

Trends in Lattice Energy: Ion Size and Charge

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An ionic compound is stable because of the electrostatic attraction between its positive and negative ions. The lattice energy of a compound is a measure of the strength of this attraction. The lattice energy (ΔHlattice) of an ionic compound is defined as the energy required to separate one mole of the solid into its component gaseous ions. For the ionic solid sodium chloride, the lattice energy is the enthalpy change of the process:
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Electronic Structure of Atoms02:28

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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...
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Real Gases: Effects of Intermolecular Forces and Molecular Volume Deriving Van der Waals Equation04:01

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Thus far, the ideal gas law, PV = nRT, has been applied to a variety of different types of problems, ranging from reaction stoichiometry and empirical and molecular formula problems to determining the density and molar mass of a gas. However, the behavior of a gas is often non-ideal, meaning that the observed relationships between its pressure, volume, and temperature are not accurately described by the gas laws.
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The Pauli Exclusion Principle03:06

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The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that contains three pieces of information:
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Scrutinizing "Invisible" astatine: A challenge for modern density functionals.

Dumitru-Claudiu Sergentu1,2, Grégoire David2, Gilles Montavon1

  • 1Laboratoire SUBATECH, UMR CNRS 6457, IN2P3/EMN Nantes/Université De Nantes, 4 Rue Alfred Kastler, BP 20722, Nantes Cedex 3, 44307, France.

Journal of Computational Chemistry
|April 10, 2016
PubMed
Summary

This study benchmarks density functional theory methods for astatine (At) properties. The PW6B95 functional is recommended for accurate calculations of astatine species and its chemistry in solution.

Keywords:
astatinebenchmarkdensity functional theoryequilibrium constantsspin-orbit coupling

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Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Astatine Chemistry

Background:

  • Main-group 6p elements, including astatine, are underrepresented in density functional development.
  • Selecting appropriate density functionals for accurate predictions remains challenging.

Purpose of the Study:

  • To conduct a comprehensive benchmark study of density functional theory (DFT) methods for astatine (At) species.
  • To evaluate the performance of various functionals for predicting astatine properties.

Main Methods:

  • Relativistic (two-component) density functional theory calculations were performed.
  • An extensive set of widely used density functionals were employed.
  • Geometries, transition energies, and thermodynamic properties of 19 astatine species were investigated.

Main Results:

  • The hybrid meta-generalized gradient approximation (meta-GGA) PW6B95 functional demonstrated the best overall performance.
  • Range-separated HSE06 and hybrid-GGA functionals (B3LYP, PBE0) also showed good accuracy.
  • Implicit solvent models can accurately predict astatine chemistry in solution with specific cavity parameters.

Conclusions:

  • PW6B95 is a highly recommended functional for astatine-related calculations.
  • Several other functionals offer reliable predictions for astatine properties.
  • Accurate prediction of astatine solution chemistry is achievable with appropriate solvent models.