Free energy
Free-energy perturbation (FEP) is a method based on statistical mechanics that is used in computational chemistry for computing free-energy differences from molecular dynamics or Metropolis Monte Carlo simulations.
The FEP method was introduced by Robert W. Zwanzig in 1954. According to the free-energy perturbation method, the free-energy difference for going from state A to state B is obtained from the following equation, known as the Zwanzig equation: ${\displaystyle \Delta F(\mathbf {A} \to \mathbf {B} )=F_{\mathbf {B} }-F_{\mathbf {A} }=-k_{\text{B}}T\ln \left\langle \exp \left(-{\frac {E_{\mathbf {B} }-E_{\mathbf {A} }}{k_{\text{B}}T}}\right)\right\rangle _{\mathbf {A} },}$ where T is the temperature, kB is the Boltzmann constant, and the angular brackets denote an average over a simulation run for state A. In practice, one runs a normal simulation for state A, but each time a new configuration is accepted, the energy for state B is also computed. The difference between states A and B may be in the atom types involved, in which case the ΔF obtained is for “mutating” one molecule onto another, or it may be a difference of geometry, in which case one obtains a free-energy map along one or more reaction coordinates. This free-energy map is also known as a potential of mean force (PMF).
Free-energy perturbation calculations only converge properly when the difference between the two states is small enough; therefore it is usually necessary to divide a perturbation into a series of smaller “windows”, which are computed independently. Since there is no need for constant communication between the simulation for one window and the next, the process can be trivially parallelized by running each window on a different CPU, in what is known as an “embarrassingly parallel” setup.
Free energy is the energy in a system that is available to do work, and its change () predicts if a chemical reaction will happen spontaneously. There are two main types: Gibbs free energy (G), which is used at constant pressure, and Helmholtz free energy (F or A), used at constant temperature. In thermodynamics, the sign of the change in free energy is crucial: a negative value indicates a spontaneous reaction (exergonic), while a positive value indicates the reaction requires energy (endergonic).
Thermodynamic free energy
- Gibbs free energy: Often used in chemistry and biology, it combines enthalpy () and entropy () with temperature () using the formula .
- Negative : The reaction is spontaneous and will release energy (exergonic).
- Positive : The reaction is non-spontaneous and requires an input of energy (endergonic).
- Helmholtz free energy: Used in physics, it’s the energy available to do work at constant temperature. The formula is , where is internal energy.
- A negative change in Helmholtz free energy indicates a spontaneous process, while a positive change indicates a non-spontaneous one.
Other contexts
- Free energy principle: In biophysics and cognitive science, this is a mathematical principle that suggests systems (like the brain) act to minimize free energy, which corresponds to minimizing surprise or prediction error.
- Free energy machines: These are often conflated with “perpetual motion” machines and are not scientifically viable. A system cannot produce more energy than it receives, and any device that claims to do so violates the laws of thermodynamics. [4, 5, 6, 7, 8]
Key takeaways
- Free energy is the energy available to do work.
- The change in free energy ( or ) determines the spontaneity of a process.
- A negative change () means the process is spontaneous.
- A positive change () means the process is non-spontaneous and requires energy input.
- The two main types are Gibbs free energy (for constant pressure) and Helmholtz free energy (for constant temperature). [1, 2]
AI responses may include mistakes.
[4] https://www.britannica.com/science/free-energy
[5] https://www.wtamu.edu/~cbaird/sq/2013/03/24/how-do-free-energy-machines-work/
[6] wikipedia/en/Gibbs_free_energy