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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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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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A thermodynamic process that occurs at constant volume is called an isochoric process. According to the first law of thermodynamics, heat supplied or removed from the system is partially utilized to perform work and change the internal energy of the system. However, in an isochoric process, the volume remains constant. Hence, the work done by the system is zero. Therefore, the exchange of heat changes the internal energy of the system only. 
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Effective Two-State Model Based on Adiabatic-to-Diabatic Transformation.

Hangjing Zheng1, Huizhu Zhang1, Tengwei Chen1

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A new two-state model simplifies analyzing complex chemical reactions. This effective model aids in calculating diabatic properties and understanding electronic coupling effects in multistate systems.

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Area of Science:

  • Computational Chemistry
  • Theoretical Chemistry
  • Quantum Chemistry

Background:

  • Multistate interacting systems present challenges in accurately modeling chemical dynamics.
  • Understanding electronic coupling is crucial for reactions like electron transfer and bond formation/breaking.

Purpose of the Study:

  • To propose and validate a novel, effective two-state model for analyzing multistate interacting systems.
  • To demonstrate the model's utility in calculating diabatic properties and assessing electronic coupling effects.

Main Methods:

  • Deriving two effective diabatic states from adiabatic wave functions.
  • Utilizing configuration interaction and partitioning coefficients for the adiabatic-to-diabatic (ATD) transformation.
  • Applying the model to various molecular systems and reactions.

Main Results:

  • The model successfully constructs effective diabatic wave functions.
  • Accurate evaluation of diabatic properties including energy, electronic coupling, and potential energy surfaces (PESs).
  • Demonstrated versatility across diverse chemical reactions, including electron transfer and Diels-Alder reactions.

Conclusions:

  • The effective two-state model is a simple yet powerful tool for theoretical analysis.
  • It provides insights into electronic coupling's influence on reaction barriers and reactivity.
  • The model is practical for studying bridge-assisted multistate electron transfer and complex chemical reactions.