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Related Concept Videos

Calculating Standard Free Energy Changes02:49

Calculating Standard Free Energy Changes

The free energy change for a reaction that occurs under the standard conditions of 1 bar pressure and at 298 K is called the standard free energy change. Since free energy is a state function, its value depends only on the conditions of the initial and final states of the system. A convenient and common approach to the calculation of free energy changes for physical and chemical reactions is by use of widely available compilations of standard state thermodynamic data. One method involves the...
Free Energy Changes for Nonstandard States03:25

Free Energy Changes for Nonstandard States

The free energy change for a process taking place with reactants and products present under nonstandard conditions (pressures other than 1 bar; concentrations other than 1 M) is related to the standard free energy change according to this equation:
Gibbs Free Energy02:39

Gibbs Free Energy

One of the challenges of using the second law of thermodynamics to determine if a process is spontaneous is that it requires measurements of the entropy change for the system and the entropy change for the surroundings. An alternative approach involving a new thermodynamic property defined in terms of system properties only was introduced in the late nineteenth century by American mathematician Josiah Willard Gibbs. This new property is called the Gibbs free energy (G) (or simply the free...
Standard Entropy Change for a Reaction03:00

Standard Entropy Change for a Reaction

Entropy is a state function, so the standard entropy change for a chemical reaction (ΔS°rxn) can be calculated from the difference in standard entropy between the products and the reactants.
Enthalpy of Solution02:39

Enthalpy of Solution

There are two criteria that favor, but do not guarantee, the spontaneous formation of a solution:
Entropy Change in Reversible Processes01:10

Entropy Change in Reversible Processes

In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.

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Related Experiment Video

Updated: Jul 15, 2026

Isotopic Effect in Double Proton Transfer Process of Porphycene Investigated by Enhanced QM/MM Method
05:51

Isotopic Effect in Double Proton Transfer Process of Porphycene Investigated by Enhanced QM/MM Method

Published on: July 19, 2019

Smoother Alchemical Transformations via Enveloping Distribution Sampling for Free-Energy Estimation.

Shu-Yu Chen1, Enrico Ruijsenaars1, Philippe H Hünenberger1

  • 1Department of Chemistry and Applied Biosciences, ETH Zurich, Vladimir-Prelog-Weg 2, Zurich 8093, Switzerland.

Journal of Chemical Theory and Computation
|July 13, 2026
PubMed
Summary

The enveloping distribution sampling (EDS) scheme improves computational free energy calculations by creating smoother phase-space transformations. This method enhances accuracy and robustness in simulations, outperforming traditional energy interpolation.

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Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics
10:52

Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics

Published on: April 12, 2019

Area of Science:

  • Computational Chemistry
  • Statistical Mechanics
  • Biophysics

Background:

  • Accurate relative free energy calculations are crucial for molecular modeling.
  • Current methods like energy interpolation (EI) can suffer from insufficient phase-space overlap.
  • This limits accuracy in equilibrium (EQ) and nonequilibrium (NEQ) simulations.

Purpose of the Study:

  • To introduce and validate the enveloping distribution sampling (EDS) coupling scheme.
  • To demonstrate EDS as a more flexible and accurate alternative to EI.
  • To improve the smoothness of alchemical transformations in free energy calculations.

Main Methods:

  • Generalized energy interpolation using linear combination of Boltzmann factors.
  • Introduction of a negative smoothing parameter in EDS to enhance phase-space curvature.
  • Validation across model systems (harmonic oscillators, Ising models) and absolute hydration free-energy (AHFE) calculations.

Main Results:

  • EDS demonstrated superior accuracy and statistical robustness compared to EI in model systems.
  • EDS significantly improved AHFE calculations in the NEQ regime.
  • The negative smoothing parameter in EDS effectively avoided phase transitions, ensuring smoother transformations.

Conclusions:

  • The EDS scheme offers a more flexible and effective approach for free energy calculations.
  • EDS enhances simulation accuracy and reliability, particularly in NEQ scenarios.
  • This method holds promise for advancing computational predictions in solvation and binding energies.