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Ion Exchange01:17

Ion Exchange

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Ion exchange chromatography separates charged molecules from a solution by reversibly exchanging them with mobile, or 'active', ions associated with the oppositely charged stationary phase. This method can be used to separate ions, soften and deionize water, and purify solutions. The polymers comprising the ion-exchange column are high-molecular-weight and chemically stable polymers, crosslinked to be porous and essentially insoluble. They are also functionalized with either acidic or...
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Metallic solids such as crystals of copper, aluminum, and iron are formed by metal atoms. The structure of metallic crystals is often described as a uniform distribution of atomic nuclei within a “sea” of delocalized electrons. The atoms within such a metallic solid are held together by a unique force known as metallic bonding that gives rise to many useful and varied bulk properties.
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Homogeneous Equilibria for Gaseous Reactions
For gas-phase reactions, the equilibrium constant may be expressed in terms of either the molar concentrations (Kc) or partial pressures (Kp) of the reactants and products. A relation between these two K values may be simply derived from the ideal gas equation and the definition of molarity. According to the ideal gas equation:
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What is the optimal mGGA exchange functional for solids?

Péter Kovács1, Fabien Tran1, Peter Blaha1

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The Journal of Chemical Physics
|September 8, 2022
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Summary
This summary is machine-generated.

Twenty-five new generalized gradient approximation (GGA) and meta-generalized gradient approximation (mGGA) functionals were trained to improve predictions of material properties. Some trained functionals match specialized ones for bandgaps while exceeding them for lattice parameters and cohesive energy.

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Area of Science:

  • Solid-state physics
  • Computational materials science
  • Quantum chemistry

Background:

  • Generalized gradient approximation (GGA) and meta-generalized gradient approximation (mGGA) are essential methods for approximating electron exchange-correlation energy in materials science.
  • Existing functionals often face trade-offs between accuracy for different material properties like lattice parameters, cohesive energy, and bandgaps.
  • Systematic exploration of the functional space is needed to develop more accurate and versatile approximations.

Purpose of the Study:

  • To systematically explore the space of GGA and mGGA exchange approximations.
  • To train new functionals that optimize predictions for lattice parameters, cohesive energy, and bandgaps.
  • To understand the accuracy trade-offs and the influence of enhancement factor maps on predictive performance.

Main Methods:

  • Training of 25 new GGA and mGGA exchange functionals using a data-driven approach.
  • Evaluation of trained functionals against established benchmarks for lattice parameter, cohesive energy, and bandgap predictions.
  • Comparison of newly trained functionals with notable existing mGGA functionals, focusing on enhancement factor maps.

Main Results:

  • Several newly trained functionals demonstrate high accuracy for lattice parameters, cohesive energy, and bandgaps.
  • Some functionals achieve performance comparable to specialized functionals for bandgap prediction.
  • The trained functionals outperform specialized functionals in predicting lattice parameters and cohesive energy simultaneously.
  • Analysis reveals how modifications in enhancement factor landscapes impact prediction accuracy across properties.

Conclusions:

  • The developed functionals offer improved accuracy and reduced trade-offs for key material properties.
  • The study provides insights into the fundamental limits and capabilities of mGGA functionals.
  • The error surface of the trained functionals serves as a benchmark for future mGGA development.