Accelerating ab initio molecular dynamics simulations by linear prediction methods

Abstract

Acceleration of ab initio molecular dynamics (AIMD) simulations can be reliably achieved by extrapolation of electronic data from previous timesteps. Existing techniques utilize polynomial least-squares regression to fit previous steps' Fock or density matrix elements. In this work, the recursive Burg "linear prediction" technique is shown to be a viable alternative to polynomial regression, and the extrapolation-predicted Fock matrix elements were three orders of magnitude closer to converged elements. Accelerations of 1.8-3.4x were observed in test systems, and in all cases, linear prediction outperformed polynomial extrapolation. Importantly, these accelerations were achieved without reducing the MD integration timestep.

Vibrational spectroscopy by means of first‐principles molecular dynamics simulations

“…Polack et al for instance, recently published an efficient method for extrapolating the density matrix guess between MD steps for faster convergence, especially with tight convergence requirements 234 . Other extrapolation techniques have been proposed, for instance, by Herr and Steele 235 . Another example for accelerating FPMD simulations is the use of multiple time steps 236 .…”

Adiabatic Molecular Orbital Tracking in Ab Initio Molecular Dynamics

“…Other approaches to orbital-tracking schemes are, of course, also possible. Our own recent application of so-called “linear prediction” techniques enabled robust extrapolation of Fock matrix elements for AIMD-acceleration purposes . Similar techniques could potentially be used to extrapolate the orbital eigenvalues directly to resolve ambiguous assignments in crossing regions.…”

“…Our own recent application of so-called "linear prediction" techniques enabled robust extrapolation of Fock matrix elements for AIMD-acceleration purposes. 35 Similar techniques could potentially be used to extrapolate the orbital eigenvalues directly to resolve ambiguous assignments in crossing regions. As a merging of these two methods, the present approach could also enable the use of extrapolation/ propagation techniques 36−44 in the MO, rather than AO, basis, which has previously been ill-advised due to the presence of eigenvalue crossings.…”

Nuclear Motion in the Intramolecular Dihydrogen-Bound Regime of an Aminoborane Complex

“…101−104 A recently developed linear-prediction algorithm was additionally used to accelerate the SCF convergence within each bead's trajectory. 105 The classical MD and quantum PIMD simulations were performed in the NVT ensemble using a stochastic Langevin thermostat of each centroid degree of freedom (time constant of 100 fs) and, for PIMD, an optimally tuned analogous thermostat for each internal bead normal mode. 87 The PIMD simulations contained 32 path integral replicas at a temperature of 300 K and were integrated with a time step of 0.5 fs.…”

“…The degree of nuclear motion in NBNB was assessed via classical and quantum (path integral) molecular dynamics (PIMD − ) methods. These PIMD simulations capture full quantum effects in a classical-like formalism, in which the delocalization of harmonically coupled replicas of a molecule allows the molecule to sample the quantum, thermal distribution. ,− Simulations with 32 replicas (beads) have been shown to sufficiently capture quantum properties for hydrogen-containing systems at room temperature within the second-order Trotter expansion. − A recently developed linear-prediction algorithm was additionally used to accelerate the SCF convergence within each bead’s trajectory . The classical MD and quantum PIMD simulations were performed in the NVT ensemble using a stochastic Langevin thermostat of each centroid degree of freedom (time constant of 100 fs) and, for PIMD, an optimally tuned analogous thermostat for each internal bead normal mode .…”