Path Integral Molecular Dynamics Methods

Which Algorithm Best Propagates the Meyer–Miller–Stock–Thoss Mapping Hamiltonian for Non-Adiabatic Dynamics?

“…An alternative method that can capture nuclear quantum effects is to use a ring of multiple classical system replicas (beads) attached by harmonic springs, known as a ring polymer. − While the path-integral representation leads to an exact method for static equilibrium properties, the dynamics of the ring polymer can yield short-time approximations to quantum real-time dynamics through methods such as ring-polymer molecular dynamics (RPMD), ,− centroid molecular dynamics (CMD), − and thermostatted (T)-RPMD. − Specifically, RPMD provides, for a single (adiabatic) potential, an approximation to Kubo-transformed time correlation functions while preserving the Boltzmann distribution and is exact in the short-time and classical limits. ,, The Kubo-transformed correlation functions allow short-time quantum effects to be included, although the long-time quantum coherence effects are neglected. RPMD can be derived from exact quantum dynamics through a series of approximations via Matsubara dynamics, , and RPMD transition-state theory is equivalent to true quantum transition-state theory. ,− Many extensions have been suggested for multiple states, including mean-field RPMD, nonadiabatic RPMD (NRPMD), and mapping-variable RPMD (MVRPMD). ,,,− As NRPMD utilizes the Meyer–Miller Hamiltonian, the algorithms discussed in this work are directly applicable.…”

“…An alternative method that can capture nuclear quantum effects is to use a ring of multiple classical system replicas (beads) attached by harmonic springs, known as a ring polymer. 53 − 56 While the path-integral representation leads to an exact method for static equilibrium properties, the dynamics of the ring polymer can yield short-time approximations to quantum real-time dynamics through methods such as ring-polymer molecular dynamics (RPMD), 53 , 57 − 59 centroid molecular dynamics (CMD), 60 − 63 and thermostatted (T)-RPMD. 64 − 66 Specifically, RPMD provides, for a single (adiabatic) potential, an approximation to Kubo-transformed time correlation functions while preserving the Boltzmann distribution and is exact in the short-time and classical limits.…”

Small Matrix Decomposition of Feynman Path Amplitudes

“…6 Monte Carlo methods 7 can efficiently sample the large space of path integral variables in this case, 8 and the quantum-classical isomorphism also allows the use of molecular dynamics tools. 9,10 On the other hand, these approaches are not successful for calculating dynamical properties because of the highly oscillatory nature of quantum mechanical amplitudes, which leads to a sign problem. Numerical evaluation of the real-time path integral for system-bath dynamics is based on iterative tensor decompositions.…”

“…Since the Boltzmann operator is identical to the time evolution operator in imaginary time, the path integral formulation also gives rise to an exact description of equilibrium properties in many-particle systems, where each quantum particle becomes isomorphic to a necklace of fictitious classical particles . Monte Carlo methods can efficiently sample the large space of path integral variables in this case, and the quantum-classical isomorphism also allows the use of molecular dynamics tools. , On the other hand, these approaches are not successful for calculating dynamical properties because of the highly oscillatory nature of quantum mechanical amplitudes, which leads to a sign problem. Numerical evaluation of the real-time path integral for system-bath dynamics is based on iterative tensor decompositions …”

Nanocomposites based on halloysite as carriers for anticancer drugs

“…The bases for MD are the atoms or defined particles of the systems and the force influence on each one can be examined as a derivative of the total potential energy Etotal with respect in the particle's position's changes. By knowing the positions, the masses and the forces of each particle, it is easy to investigate new positions by numerical integration of motion's equations over the selected time (Deymier et al, 2016). MD have several steps:…”