Path integral molecular dynamics (PIMD) is a method of incorporating
quantum mechanics
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistr ...
into
molecular dynamics
Molecular dynamics (MD) is a computer simulation method for analyzing the physical movements of atoms and molecules. The atoms and molecules are allowed to interact for a fixed period of time, giving a view of the dynamic "evolution" of t ...
simulations using
Feynman path integrals. In PIMD, one uses the
Born–Oppenheimer approximation
In quantum chemistry and molecular physics, the Born–Oppenheimer (BO) approximation is the best-known mathematical approximation in molecular dynamics. Specifically, it is the assumption that the wave functions of atomic nuclei and elect ...
to separate the
wavefunction
A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system. The wave function is a complex-valued probability amplitude, and the probabilities for the possible results of measurements ...
into a nuclear part and an electronic part. The nuclei are treated quantum mechanically by mapping each quantum nucleus onto a classical system of several fictitious particles connected by springs (harmonic potentials) governed by an effective Hamiltonian, which is derived from Feynman's path integral. The resulting classical system, although complex, can be solved relatively quickly. There are now a number of commonly used condensed matter computer simulation techniques that make use of the path integral formulation including Centroid Molecular Dynamics (CMD), Ring Polymer Molecular Dynamics (RPMD), and the Feynman-Kleinert Quasi-Classical Wigner (FK-QCW) method. The same techniques are also used in
path integral Monte Carlo
Path integral Monte Carlo (PIMC) is a quantum Monte Carlo method used to solve quantum statistical mechanics problems numerically within the path integral formulation. The application of Monte Carlo methods to path integral simulations of condens ...
(PIMC).
Combination with other simulation techniques
Applications
The technique has been used to calculate time correlation functions.
References
Further reading
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External links
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* {{cite journal, author=John Shumway; Matthew Gilbert , year=2008, title=Path Integral Monte Carlo Simulation, doi=10.4231/D3T43J39D , url=http://nanohub.org/resources/pimc
Molecular dynamics
Quantum chemistry
Quantum Monte Carlo