Path integral molecular dynamics

Path integral molecular dynamics (PIMD) is a method of incorporating quantum mechanics into molecular dynamics simulations using Feynman path integrals. In PIMD, one uses the Born–Oppenheimer approximation to separate the wavefunction 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 (PIMC).

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 Nosé–Hoover chain, which is a chain of variables instead of a single thermostat of variable.

The simulations done my PIMD can broadly characterize the biomolecular systems, covering the entire structure and organization of the membrane, including the permeability, protein-lipid interactions, along with "lipid-drug interactions, protein–ligand interactions, and protein structure and dynamics."

PIMD is "widely used to describe nuclear quantum effects in chemistry and physics".

Path Integral Molecular Dynamics can be applied to polymer physics, both field theories, quantum and not, string theory, stochastic dynamics, quantum mechanics, and quantum gravity. PIMD can also be used to calculate time correlation functions

• Feynman, R. P. (1972). "Chapter 3". Statistical Mechanics. Reading, Massachusetts: Benjamin. ISBN 0-201-36076-4.
• Morita, T. (1973). "Solution of the Bloch Equation for Many-Particle Systems in Terms of the Path Integral". Journal of the Physical Society of Japan. 35 (4): 980–984. Bibcode:1973JPSJ...35..980M. doi:10.1143/JPSJ.35.980.
• Wiegel, F. W. (1975). "Path integral methods in statistical mechanics". Physics Reports. 16 (2): 57–114. Bibcode:1975PhR....16...57W. doi:10.1016/0370-1573(75)90030-7.
• Barker, J. A. (1979). "A quantum-statistical Monte Carlo method; path integrals with boundary conditions". The Journal of Chemical Physics. 70 (6): 2914–2918. Bibcode:1979JChPh..70.2914B. doi:10.1063/1.437829.
• Ceperley, D. M. (1995). "Path integrals in the theory of condensed helium". Reviews of Modern Physics. 67 (2): 279–355. Bibcode:1995RvMP...67..279C. doi:10.1103/RevModPhys.67.279.
• Chakravarty, C. (1997). "Path integral simulations of atomic and molecular systems". International Reviews in Physical Chemistry. 16 (4): 421–444. Bibcode:1997IRPC...16..421C. doi:10.1080/014423597230190.

• "Density matrices and path integrals". SMAC-wiki. Archived from the original (computer code) on May 1, 2016. Retrieved May 12, 2012.
• John Shumway; Matthew Gilbert (2008). "Path Integral Monte Carlo Simulation". doi:10.4231/D3T43J39D. {{cite journal}}: Cite journal requires |journal= (help)CS1 maint: multiple names: authors list (link)