CarParrinello

The Car-Parrinello method is a computational approach to ab initio molecular dynamics that combines quantum mechanics for electrons with classical dynamics for atomic nuclei. It was introduced in 1985 by Carlo Car and Michele Parrinello and has since become a widely used framework in chemistry, physics, and materials science.

In Car-Parrinello molecular dynamics, the electronic degrees of freedom, described by a set of wavefunctions or Kohn-Sham orbitals, are propagated in time together with the nuclear coordinates. A fictitious mass parameter assigns inertia to the electronic states, allowing them to follow the instantaneous ground state as the nuclei evolve without performing a full self-consistent field optimization at every step.

The nuclear forces are derived from the evolving electronic structure, and the method aims to approximate Born–Oppenheimer dynamics by maintaining the electrons near the ground state throughout the trajectory. The choice of the fictitious mass and the integration time step are crucial: too large a mass or too large a step can cause deviations from true ground-state behavior.

Car-Parrinello dynamics has enabled efficient simulation of complex systems with quantum mechanical accuracy, including liquids, solids, surfaces, and enzymatic reactions, using density functional theory or other quantum mechanical models. It is implemented in several software packages and has driven advances in computational materials science and chemistry.

Variants and related approaches include pure Born–Oppenheimer molecular dynamics and extensions that improve stability and efficiency, with ongoing methodological developments addressing electrons in excited states, long-range interactions, and improved pseudopotentials.