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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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Fluid flow analysis is critical in many scientific and engineering disciplines, and two principal approaches are used to describe this flow: the Eulerian and Lagrangian methods. These methods offer different perspectives on monitoring and analyzing the motion of fluids, each with distinct advantages depending on the scenario.
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Phase Transitions: Melting and Freezing02:39

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Heating a crystalline solid increases the average energy of its atoms, molecules, or ions, and the solid gets hotter. At some point, the added energy becomes large enough to partially overcome the forces holding the molecules or ions of the solid in their fixed positions, and the solid begins the process of transitioning to the liquid state or melting. At this point, the temperature of the solid stops rising, despite the continual input of heat, and it remains constant until all of the solid is...
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Pressure and Volume in an Adiabatic Process01:27

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Free expansion of a gas is an adiabatic process. However, there are few differences between free expansion and adiabatic expansion. During free expansion, no work is done, and there is no change in internal energy. But, for an adiabatic expansion, work is done, and there is a change in internal energy. During an adiabatic process, the relation between the pressure and volume is obtained from the condition for the adiabatic process, that is, 
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Consider the adiabatic compression of an ideal gas in the cylinder of an automobile diesel engine. The gasoline vapor is injected into the cylinder of an automobile engine when the piston is in its expanded position. The temperature, pressure, and volume of the resulting gas-air mixture are 20 °C, 1.00 x 105 N/m2, and 240 cm3 , respectively. The mixture is then compressed adiabatically to a volume of 40 cm3. Note that, in the actual operation of an automobile engine, the compression is not...
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Whether solid, liquid, or gas, a substance's state depends on the order and arrangement of its particles (atoms, molecules, or ions). Particles in the solid pack closely together, generally in a pattern. The particles vibrate about their fixed positions but do not move or squeeze past their neighbors. In liquids, although the particles are closely spaced, they are randomly arranged. The position of the particles are not fixed—that is, they are free to move past their neighbors to...
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Frozen-Core Analytical Gradients within the Adiabatic Connection Random-Phase Approximation from an Extended

Jefferson E Bates1, Henk Eshuis2

  • 1Department of Chemistry and Fermentation Sciences, Appalachian State University, Boone, North Carolina 28608-2021, United States.

Journal of Chemical Theory and Computation
|March 6, 2025
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Summary
This summary is machine-generated.

A new frozen-core option for random-phase approximation (RPA) calculations significantly speeds up computations. This method efficiently yields accurate molecular properties for various compounds, extending the applicability of RPA calculations.

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Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Theoretical Chemistry

Background:

  • The random-phase approximation (RPA) is a powerful method for calculating electron correlation.
  • Accurate RPA calculations can be computationally expensive, limiting their application to smaller systems.
  • Developing efficient computational methods is crucial for advancing theoretical chemistry.

Purpose of the Study:

  • To implement and evaluate a frozen-core option for analytic gradient calculations within the RPA framework.
  • To assess the computational speedup and accuracy of the frozen-core RPA method.
  • To extend the applicability of RPA calculations to larger and more complex molecular systems.

Main Methods:

  • Implementation of a frozen-core option combined with the analytic gradient of RPA.
  • Utilized density functional theory reference determinants and resolution-of-the-identity techniques.
  • Employed an extended Lagrangian and Curtis-Clenshaw quadratures for correlation contributions.

Main Results:

  • The frozen-core option significantly reduces computational cost by decreasing matrix dimensionality and grid size.
  • Optimized geometries, vibrational frequencies, and dipole moments show only modest deviations from all-electron results.
  • Achieved computational speedups of 35-55% for various molecular systems, including alkanes and metal complexes.

Conclusions:

  • The combination of the frozen-core option and RPA provides an efficient and accurate method for calculating molecular properties.
  • This approach broadens the scope of systems amenable to high-accuracy RPA calculations.
  • The developed method offers a practical solution for computational chemists seeking to balance accuracy and efficiency.