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Category:Advanced molecular-dynamics sampling

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In a molecular-dynamics (MD) calculation, we are often interested in rare events or specific transitions. Advanced molecular-dynamics sampling helps to capture these during an MD run within a feasible simulation time. There are several different available methods:

Constrained molecular dynamics

Selected geometric parameters in this hydrogen cyanide isomerization to hydrogen isocyanide reaction are constrained to model the transition state. R1 is the C-H bond, R2 is the C-N bond, and R3 is the N-H bond.

In constrained molecular dynamics selected geometric parameters are constrained during the calculations using the ICONST file. This is achieved by extending the Lagrangian with a term incorporating the desired constraints (SHAKE algorithm[1]) directly. This method can be used on its own to support molecular dynamics calculations but some of the methods on this page also incorporate constraints via the same methodology.

Biased molecular dynamics

In biased MD, a biased potential can be used to pin the system to given configuration (i.e., uncommon configurations), e.g., in umbrella sampling.

Biased molecular dynamics refers to methods introducing a biased potential [2]. In one of this method's most popular representatives, the umbrella sampling or umbrella integration, the biased potential is used to pin the system to given configurations. This way the sampling of a system is greatly enhanced and thermodynamic methods with proper statistics become accessible. Although some of the methods on this page also use biased potentials they have differences in the usage of the potential and hence belong in their categories.

Biased molecular dynamics are often used to calculate free energies or free energy differences.

Thermodynamic integration

Thermodynamic integration allows integration from a non-interacting system (λ = 0) to an interacting system (λ = 1). E.g., between a harmonic and an anharmonic system.

In the thermodynamic integration method,[3][4] the energy differences of a fully interacting and non-interacting system are calculated. This is achieved by making the potential energy depend on a coupling parameter and defining the free energy as a smooth integral over the potential energy along this coupling parameter. As the reference state for a non-interacting system, usually an ideal gas or a harmonic solid is chosen.

Thermodynamic integration is usually used to compute free energy differences between different phases.

Metadynamics

In metadynamics, a biased potential (coloured lines) is applied along selected collective variables (x), cf. potential V, to gradually fill free-energy minima and allows the system to cross barriers and explore the potential energy surface, including other minima.

In metadynamics,[5][6] a biased potential that acts on a few selected geometric parameters (collective variables) is added to the Hamiltonian of a system. The biased potential is constantly built up during a molecular dynamics run by adding Gaussian hills at selected time increments. This way even deep potential minima can be filled and overcome.

This method is good for exploring new phases of a given system.

Blue moon ensemble

In the Blue moon ensemble method, the free energy profile along a chosen reaction coordiante (x) can be calculated by calculating the unbiased free-energy derivative.

The blue moon ensemble method[7] is designed to calculate the free energy profile along the path of selected reaction coordinates. It also employs constraining of the atoms during molecular dynamics (SHAKE algorithm[1]). The term "blue moon" refers to rare events such as the "moon turning blue".

The method is often used to calculate free energy differences for systems where the profile is characterized by a few barriers that are high enough that they would not be crossed within regular thermostatted molecular dynamics.

Slow-growth approach

In the slow-growth approach, a reaction pathway can be followed linearly on a reaction coordinate (x) from the reactant state (λ = 0) to the target state (λ = 1).

In the slow-growth approach,[8] the free energy profile is scanned along a reaction coordinate. The scanning is done by linearly changing the reaction coordinate from that of the reactant state to that of a transition or product state via constrained molecular dynamics (SHAKE algorithm[1]).

Like in the blue moon ensemble, this method is also designed to calculate free energy differences for systems where the profile is characterized by a few barriers that are high enough that they would not be crossed within regular thermostatted molecular dynamics.

Interface pinning

Interface pinning is used to model two different phases on the same system in the same cell, e.g., the water-ice interface.

In interface pinning,[9] two different phases of the same system are simulated in a single simulation box. The goal of this method is to look for the right conditions where both phases would coexist, which corresponds to a phase transition point. Above a transition point, the whole system would quickly turn into one phase and below the point into the other phase. With this, the transition point could be searched via bi-sectioning, but this would involve a huge effort. To accelerate the search for a phase transition point the order parameters are used to control the composition of the box and the force that would drive the system towards equilibrium is used to estimate the phase transition point.

Interface pinning is usually used to determine melting points (solid-liquid interface).

Additional resources

Books

  • Statistical Mechanics: Theory and Molecular Simulation by M. Tuckerman [10].
  • Understanding Molecular Simulation - From Algorithms to Applications by D. Frenkel and B. Smit [11].

How to

Tutorials

Lectures

References

  1. ↑ a b c J. P. Ryckaert, G. Ciccotti, and H. J. C. Berendsen, J. Comp. Phys. 23, 327 (1977).
  2. ↑ D. Frenkel and B. Smit, Understanding molecular simulations: from algorithms to applications, Academic Press: San Diego, 2002.
  3. ↑ F. Dorner, Z. Sukurma, C. Dellago, and G. Kresse, Phys. Rev. Lett. 121, 195701 (2018).
  4. ↑ J. Kirkwood, Statistical Mechanics of Fluid Mixtures, J. Chem. Phys. 3, 300–313 (1935).
  5. ↑ R. A. Laio and M. Parrinello, Proc. Natl. Acad, Sci. USA 99, 12562 (2002).
  6. ↑ M. Iannuzzi, A. Laio, and M. Parrinello, Phys. Rev. Lett. 90, 238302 (2003).
  7. ↑ E. Carter, G. Ciccotti, J. Hynes, R. Kapral, Chem. Phys. Lett., 156, 472 (1989).
  8. ↑ T. Woo, P. Margl, P. Blöchl, T. Ziegler. J. Phys. Chem., 101, 40 (1997)
  9. ↑ U. R. Pedersen, F. Hummel, G. Kresse, G. Kahl, and C. Dellago, Phys. Rev. B 88, 094101 (2013).
  10. ↑ M. Tuckerman, Statistical Mechanics: Theory and Molecular Simulation (2nd edn), Oxford University Press (2023).
  11. ↑ D. Frenkel, B. Smit, Understanding Molecular Simulation - From Algorithms to Applications (2nd edn), Elsevier Science (2023).

Subcategories

This category has the following 2 subcategories, out of 2 total.

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