Path integral molecular dynamics (PIMD) is a method of incorporating
quantum mechanics
Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is ...
into
molecular dynamics
Molecular dynamics (MD) is a computer simulation method for analyzing the Motion (physics), 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 dynamics ( ...
simulations using
Feynman path integral
The path integral formulation is a description in quantum mechanics that generalizes the stationary action principle of classical mechanics. It replaces the classical notion of a single, unique classical trajectory for a system with a sum, or ...
s. In PIMD, one uses the
Born–Oppenheimer approximation
In quantum chemistry and molecular physics, the Born–Oppenheimer (BO) approximation is the assumption that the wave functions of atomic nuclei and electrons in a molecule can be treated separately, based on the fact that the nuclei are much h ...
to separate the
wavefunction
In quantum physics, a wave function (or wavefunction) is a mathematical description of the quantum state of an isolated quantum system. The most common symbols for a wave function are the Greek letters and (lower-case and capital psi (letter) ...
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).
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
A thermostat is a regulating device component which senses the temperature of a physical system and performs actions so that the system's temperature is maintained near a desired setpoint.
Thermostats are used in any device or system tha ...
of variable.
Combination with other simulation techniques
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."
Applications
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
References
Further reading
*
*
*
*
*
*
External links
*
* {{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