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Thermodynamics: Activity Coefficient01:24

Thermodynamics: Activity Coefficient

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Activity is the measure of the effective concentration of the species in solution. It can be expressed as the product of the molar concentration of the species and its activity coefficient. The activity coefficient is a dimensionless quantity and depends on the total ionic strength of the solution.
The activity coefficient is a measure of the deviation from ideal behavior. When the ionic strength of the solution is minimal, the activity coefficient of an ionic species is close to unity, making...
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Thermodynamic Potentials

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Thermodynamic potentials are state functions that are extremely useful in analyzing a thermodynamic system. They have dimensions of energy. The four important thermodynamic potentials are internal energy, enthalpy, Helmholtz free energy, and Gibbs free energy. These thermodynamic potentials can be expressed using two of the following variables: pressure, volume, temperature, and entropy. These two variables are expressed as the rate of change of the thermodynamic potential with respect to other...
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Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
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Thermodynamics: Chemical Potential and Activity01:10

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The effective concentration of a species in a solution can be expressed precisely in terms of its activity. Activity considers the effect of electrolytes present in the vicinity of the species of interest and depends on the ionic strength of the solution. The activity of a species is expressed as the product of molar concentration and the activity coefficient of the species.
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Sigmatropic rearrangements are a class of pericyclic reactions in which a σ bond migrates from one part of a π system to another. These are intramolecular rearrangements where the total number of σ and π bonds remain unchanged.
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Debye–Huckel–Onsager Conductance Equation01:28

Debye–Huckel–Onsager Conductance Equation

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The Debye-Hückel-Onsager equation is a cornerstone of physical chemistry, providing a method to determine the molar conductance (Λm) and molar conductance at infinite dilution (Λ°m) for uni-univalent electrolytes.Uni-univalent electrolytes are electrolytes that dissociate in solution to produce one cation with a +1 charge and one anion with a –1 charge per formula unit.This equation addresses two crucial phenomena: the asymmetry effect and the electrophoretic effect.
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Optimization of B97-Type Density Functional Approximation, Global Hybrid, and Range-Separated Hybrid Energy Functionals with the D4 Dispersion Corrections in TAO-DFT.

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Thermally-assisted-occupation density functional theory with generalized-gradient approximations.

Jeng-Da Chai1

  • 1Department of Physics, Center for Theoretical Sciences, and Center for Quantum Science and Engineering, National Taiwan University, Taipei 10617, Taiwan.

The Journal of Chemical Physics
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Thermally-assisted-occupation generalized gradient approximation (TAO-GGA) methods improve calculations for thermochemistry and kinetics. These methods efficiently study electronic properties of large acene molecules, revealing trends in energy gaps and radical character.

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Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Materials Science

Background:

  • Density Functional Theory (DFT) is a cornerstone of modern electronic structure calculations.
  • Thermally-Assisted-Occupation DFT (TAO-DFT) offers a novel approach to handle systems with strong static correlation.
  • Previous TAO-DFT implementations were limited to the Local Density Approximation (LDA).

Purpose of the Study:

  • To extend TAO-DFT to Generalized Gradient Approximation (GGA) functionals, creating TAO-GGAs.
  • To evaluate the performance of TAO-GGAs for various chemical properties.
  • To investigate the electronic properties of large acene systems using TAO-LDA and TAO-GGAs.

Main Methods:

  • Development and implementation of TAO-GGA exchange-correlation functionals.
  • Benchmarking TAO-GGAs against established methods for thermochemistry, kinetics, and reaction energies.
  • Application of TAO-LDA and TAO-GGAs to study electronic properties of acenes up to 100 rings.

Main Results:

  • TAO-GGAs demonstrate significant improvements over TAO-LDA for thermochemistry and kinetics.
  • TAO-GGAs with dispersion corrections show excellent performance for noncovalent interactions.
  • Electronic properties of acenes, including energy gaps and radical character, were systematically studied for large systems.

Conclusions:

  • TAO-GGAs represent a substantial advancement over TAO-LDA for a broad range of chemical applications.
  • TAO-LDA and TAO-GGAs are computationally efficient for systems with strong static correlation.
  • Acene electronic properties exhibit monotonic trends with increasing chain length, with ground states remaining singlets.