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Adiabatic Processes for an Ideal Gas01:18

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When an ideal gas is compressed adiabatically, that is, without adding heat, work is done on it, and its temperature increases. In an adiabatic expansion, the gas does work, and its temperature drops. Adiabatic compressions actually occur in the cylinders of a car, where the compressions of the gas-air mixture take place so quickly that there is no time for the mixture to exchange heat with its environment. Nevertheless, because work is done on the mixture during the compression, its...
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The equilibrium between a liquid and its vapor depends on the temperature of the system; a rise in temperature causes a corresponding rise in the vapor pressure of its liquid. The Clausius-Clapeyron equation gives the quantitative relation between a substance’s vapor pressure (P) and its temperature (T); it predicts the rate at which vapor pressure increases per unit increase in temperature.
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The Clausius-Clapeyron equation is a fundamental principle in physical chemistry and thermodynamics that describes the relationship between a substance's vapor pressure and temperature. Named after Rudolf Clausius and Benoît Paul Émile Clapeyron, the equation is integral in predicting a substance's behavior under different temperature conditions.The Clausius-Clapeyron equation allows us to calculate how the pressure at which a liquid boils (its vapor pressure) changes as the...
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Exchange-Correlation Functionals via Local Interpolation along the Adiabatic Connection.

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This study introduces local models for density-functional approximations, improving size consistency. These models accurately capture strong correlation effects, offering a new path for developing better computational chemistry tools.

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Area of Science:

  • Quantum Chemistry
  • Computational Physics
  • Materials Science

Background:

  • Density-functional approximations (DFAs) are crucial for electronic structure calculations.
  • Existing global models face challenges with size consistency and strong correlation.
  • Local modeling of the adiabatic connection offers a promising alternative.

Purpose of the Study:

  • To explore the construction of density-functional approximations using local adiabatic connection modeling.
  • To assess the accuracy of local interpolation models against accurate exchange-correlation energy densities.
  • To investigate the treatment of strong correlation effects using strictly correlated electrons (SCE) functionals.

Main Methods:

  • Modeling the adiabatic connection locally using energy densities of the exchange-correlation hole.
  • Utilizing accurate local input ingredients for model assessment.
  • Developing an approximate analytic model for the local adiabatic connection's initial slope.

Main Results:

  • Local models demonstrate improved size consistency compared to global counterparts.
  • Accurate exchange-correlation energy densities validate the performance of local interpolation models.
  • The study successfully incorporates strictly correlated electrons (SCE) functional for strong correlation effects.

Conclusions:

  • Local adiabatic connection modeling provides a robust framework for constructing accurate density-functional approximations.
  • The developed models show promise for treating systems with strong correlation.
  • Further development based on local adiabatic connection holds potential for advancing computational chemistry methods.