Path integral molecular dynamics

<p>Path integral molecular dynamics (PIMD) is a method of incorporating <a href="/facts/Quantum_mechanics/BRc3Mzgr">quantum mechanics</a> into <a href="/facts/Molecular_dynamics/yR3DNt6U">molecular dynamics</a> simulations using <a href="/facts/Feynman_path_integral/6lt2MHkW">Feynman path integrals</a>. In PIMD, one uses the <a href="/facts/Born%25E2%2580%2593Oppenheimer_approximation/hxlUcBrX">Born–Oppenheimer approximation</a> to separate the <a href="/facts/Wavefunction/KgM5ykjY">wavefunction</a> 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 <a href="/facts/Path_integral_Monte_Carlo/rB8tELce">path integral Monte Carlo</a> (PIMC).
</p><p>There are two ways to calculate the dynamics calculations of PIMD. The first one is the non-Hamiltonian phase space analysis theory, which has been updated to create an "extended system" of isokinetic equations of motion which overcomes the properties of a system that created issues within the community. The second way is by using <a href="/facts/Nos%25C3%25A9%25E2%2580%2593Hoover_thermostat/2VxMtN1o">Nosé–Hoover chain</a>, which is a chain of variables instead of a single <a href="/facts/Thermostatics/tLILkepz">thermostat</a> of variable. 
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Path integral molecular dynamics open-in-new

Path integral molecular dynamics