Communication: Constant uncertainty molecular dynamics: A simple and efficient algorithm to incorporate quantum nature into a real-time molecular dynamics simulation

Abstract

We propose a novel molecular dynamics (MD) algorithm for approximately dealing with a nuclear quantum dynamics in a real-time MD simulation. We have found that real-time dynamics of the ensemble of classical particles acquires quantum nature by introducing a constant quantum mechanical uncertainty constraint on its classical dynamics. The constant uncertainty constraint is handled by the Lagrange multiplier method and implemented into a conventional MD algorithm. The resulting constant uncertainty molecular dynamics (CUMD) is applied to the calculation of quantum position autocorrelation functions on quartic and Morse potentials. The test calculations show that CUMD gives better performance than ring-polymer MD because of the inclusion of the quantum zero-point energy during real-time evolution as well as the quantum imaginary-time statistical effect stored in an initial condition. The CUMD approach will be a possible starting point for new real-time quantum dynamics simulation in condensed phase.

Thermal quantum time-correlation functions from classical-like dynamics

“…There may also be other classical-like approximations to quantum dynamics (and maybe Matsubara dynamics) that for some systems are more accurate [145]. Very recent research has obtained out-of-equilibrium RPMD and CMD from Matsubara dynamics [20], which should be useful tools for excited state quantum dynamics.…”

“…One can re-insert N momentum identities [152] 1 = β N 2πm dp e β N p 2 /2m (145) in p i , i = 1, . .…”

“…There may also be the possibility of applying Matsubara dynamics (or a similar approximate quantum dynamics) to the computation of nonlinear response functions [143] which can diverge in a purely classical calculation [144]. There may also be other classical-like approximations to quantum dynamics (and maybe Matsubara dynamics) that for some systems are more accurate [145]. Very recent research has obtained out-of-equilibrium RPMD and CMD from Matsubara dynamics [20], which should be useful tools for excited state quantum dynamics.…”

Nuclear Quantum Dynamics of Three-Dimensional Condensed-Phase Systems by Constant Uncertainty Molecular Dynamics

“…Furthermore, the CUMD is expected to simulate the quantum dynamics more precisely than the PI-based methods as shown in the previous work. 27 On the contrary, the CUMD simulation is currently disadvantageous in terms of the computational costs compared to CMD and (T)RPMD. For example, the time step of the CUMD simulations must be smaller and the number of beads (replicated atoms) should be larger than those of the CMD and (T)RPMD simulations.…”

“…Subsequently, the applicability of the developed method is verified through simulations of the radial distribution functions, momentum distribution, and IR spectra of bulk water and ice Ih using the q-TIP4P/F water model, which has often been used as the benchmark model to check the properties of new simulation methods. In our previous study, the RPMD simulation was used in the preparation of the initial conditions of the positions and momenta for the time correlation function . However, we emphasize that the present CUMD simulations are independent of the imaginary-time PI technique, because the initial conditions were prepared by the equilibration runs of the CUMD simulations like standard classical MD simulations.…”