The Car–Parrinello Molecular Dynamics,[1], also known as CPMD, is a method to follow the classical motion of point-like atomic nuclei in time, i.e. for performing molecular dynamics (MD), while at the same time solving ab-initio and efficiently the quantum mechanical motion of electrons. Unlike classical MD, CPMD includes the motion of electrons in the calculations of energy, forces and motion.
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In CPMD the core electrons are usually described by a pseudopotential, and the wavefunction of the valence electrons are approximated by a plane wave basis set.
The ground state electronic density (for fixed nuclei) is calculated self-consistently, usually using the density functional theory method. Then, using that density, forces on the nuclei can be computed, to update the trajectories (using, e.g. the Verlet integration algorithm). In addition, however, the coefficients used to obtain the electronic orbital functions can be treated as a set of extra spatial dimensions, and trajectories for the orbitals can be calculated in this context.
CPMD is an approximation of the Born-Oppenheimer MD (BOMD) method. In BOMD the electrons must be minimized via matrix diagonalization at every step in the trajectory. CPMD uses fictitious dynamics to keep the electrons in the ground state, preventing the need for a costly self-consistent iterative minimization at each time step. The fictitious dynamics relies on the use of a fictitious electron mass (usually in the range of 400 - 800 a.u.) to ensure that there is very little energy transfer from nuclei to electrons, i.e. to ensure adiabaticity. Any increase in the fictitious electron mass resulting in energy transfer would cause the system to leave the ground-state BOMD surface. [2]