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Entropy02:39

Entropy

37.9K
Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...
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Entropy01:18

Entropy

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The first law of thermodynamics is quantitatively formulated via an equation relating the internal energy of a system, the heat exchanged by it, and the work done on it. A quantitative formulation of the second law of thermodynamics leads to defining a state function, the entropy.
When an ideal gas expands isothermally, the disorder in the gas increases. From the molecular perspective, the gas molecules have more volume to move around in.
Consider an infinitesimal step in the expansion, which...
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Third Law of Thermodynamics02:38

Third Law of Thermodynamics

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A pure, perfectly crystalline solid possessing no kinetic energy (that is, at a temperature of absolute zero, 0 K) may be described by a single microstate, as its purity, perfect crystallinity,and complete lack of motion means there is but one possible location for each identical atom or molecule comprising the crystal (W = 1). According to the Boltzmann equation, the entropy of this system is zero.
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Entropy and Solvation02:05

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The process of surrounding a solute with solvent is called solvation. It involves evenly distributing the solute within the solvent. The rule of thumb for determining a solvent for a given compound is that like dissolves like. A good solvent has molecular characteristics similar to those of the compound to be dissolved. For example, polar solutions dissolve polar solutes, and apolar solvents dissolve apolar solutes. A polar solvent is a solvent that has a high dielectric constant (ϵ...
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Entropy and the Second Law of Thermodynamics01:20

Entropy and the Second Law of Thermodynamics

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The second law of thermodynamics can be stated quantitatively using the concept of entropy. Entropy is the measure of disorder of the system.
The relation  between entropy and disorder can be illustrated with the example of the phase change of ice to water. In ice, the molecules are located at specific sites giving a solid state, whereas, in a liquid form, these molecules are much freer to move. The molecular arrangement has therefore become more randomized. Although the change in average...
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Entropy and the Second Law of Thermodynamics01:26

Entropy and the Second Law of Thermodynamics

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Consider an isolated system in which a hot object is placed in contact with a cold one. This is an irreversible process that eventually leads both objects to reach the same equilibrium temperature. It is crucial to note that the constituents of any substance exhibit increased disorder at higher temperatures. As a cold substance absorbs heat, its constituents become more disordered. The energy transfer from a hotter object to a cooler one increases the system's disorder or randomness. This...
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Macromolecular Entropy Can Be Accurately Computed from Force.

Ulf Hensen1, Frauke Gräter2, Richard H Henchman3,4

  • 1ETH Zürich , Biosystems Science and Engineering, Mattenstrasse 26, 4058 Basel, Switzerland.

Journal of Chemical Theory and Computation
|November 20, 2015
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Summary
This summary is machine-generated.

This study introduces a new method to calculate molecular entropy using atomic forces from molecular dynamics simulations. This approach offers improved accuracy and efficiency compared to existing quasiharmonic analysis for molecular systems.

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Area of Science:

  • Computational Chemistry
  • Molecular Dynamics
  • Statistical Mechanics

Background:

  • Calculating molecular entropy is crucial for understanding chemical reactions and molecular behavior.
  • Existing methods like quasiharmonic analysis have limitations in accuracy and computational efficiency.
  • Molecular dynamics simulations provide rich data on atomic motion and forces.

Purpose of the Study:

  • To develop a novel method for accurately calculating molecular entropy from atomic forces obtained via molecular dynamics simulations.
  • To compare the performance of the new method against established quasiharmonic analysis.
  • To demonstrate the applicability of the new method to various molecular systems.

Main Methods:

  • Calculating atomic forces during molecular dynamics simulations.
  • Diagonalizing the mass-weighted force covariance matrix to obtain eigenvalues.
  • Relating eigenvalues to vibrational frequencies within the harmonic approximation.
  • Summing harmonic oscillator entropies for each vibrational mode to determine total entropy.

Main Results:

  • The proposed method demonstrated superior agreement with thermodynamic integration results for hydrocarbons, dialanine, and a beta hairpin compared to quasiharmonic analysis.
  • Atomic forces were found to exhibit a more harmonic distribution than coordinate displacements, better reflecting the potential energy surface.
  • The method requires force trajectories as input, computationally similar to quasiharmonic analysis.

Conclusions:

  • The new method provides a more accurate and robust way to calculate molecular entropy.
  • Atomic force analysis offers a better representation of the underlying molecular potential energy surface.
  • The method's simplicity and computational efficiency make it broadly applicable to diverse molecular systems in computational chemistry.