On the theory underlying the Car-Parrinello method and the role of the fictitious mass parameter

TL;DR

This paper reviews the theoretical foundations of the Car-Parrinello method, emphasizing the role of the fictitious mass parameter and analyzing how it affects systematic errors in force calculations, with implications for comparing CPMD and BOMD efficiencies.

Contribution

It clarifies the nature of adiabatic decoupling in CPMD and investigates the impact of the fictitious mass on force accuracy, providing insights for better method comparisons.

Findings

Large fictitious mass leads to systematic force errors in CPMD.

Accuracy comparisons should consider similar error levels for CPMD and BOMD.

BOMD may be more efficient than CPMD when comparable accuracy is maintained.

Abstract

The theory underlying the Car-Parrinello extended-lagrangian approach to {\em ab initio} molecular dynamics (CPMD) is reviewed and reexamined using 'heavy' ice as a test system. It is emphasized that the adiabatic decoupling in CPMD is not a decoupling of electronic orbitals from the ions but only a decoupling of a subset of the orbital vibrational modes from the rest of the necessarily-coupled system of orbitals and ions. Recent work (J. Chem. Phys. {\bf 116}, 14 (2002)) has pointed out that, due to the orbital-ion coupling that remains once adiabatic-decoupling has been achieved, a large value of the fictitious mass $\mu$ can lead to systematic errors in the computed forces in CPMD. These errors are further investigated in the present work with a focus on those parts of these errors that are not corrected simply by rescaling the masses of the ions. It is suggested that any comparison of the efficiencies of Born-Oppenheimer molecular dynamics (BOMD) and CPMD should be performed at a similar level of accuracy. If accuracy is judged according to the average magnitude of the systematic errors in the computed forces, the efficiency of BOMD compares more favorably to that of CPMD than previous comparisons have suggested.