CP2K Open Source Molecular Dynamics

Finite temperature molecular dynamics simulation methods that are driven by the forces obtained “on-the-fly” with an electronic structure theory such as density functional theory are so-called ab-initio molecular dynamics (AIMD). With the pioneering contributions of Roberto Car and Michele Parrinello, the field of AIMD started and became a landmark of computational science. The Car-Parrinello molecular dynamics (CPMD) made AIMD possible to study realistic systems such as dynamics of the solution, phase transition and mass-transportation, etc.

In Born-Oppenheimer molecular dynamics, it solves the energies or forces from the electronic structure theory via minimization or diagonalization methods. At each molecular dynamics step, the electronic structure only relies on the given fixed nuclear positions, namely the electron and nuclei are not coupled. Therefore, the electronic structure problem can be solved by time-independent Schrodinger's equation. And the nuclei are propagated according to classical mechanics or quantum mechanics. The resulting Born-Oppenheimer molecular dynamics method is defined as:

\begin{equation} {\displaystyle M_{I}{\ddot {\mathbf {R} }}_{I}=-\nabla _{I}\,\underset{\{ \psi_0 \}}{\mathrm {min}}\{\langle \psi_0 \mid \mathcal{H}_e \mid \psi_0 \rangle\}} \end{equation} \begin{equation} E_0 \psi_0 = \mathcal{H}_e \psi_0 \end{equation}

The ground state energy can be obtained from any variational method such as density functional theory.

\emph{Ab-initio} Molecular dynamics simulations are most commonly carried out according to the Born-Oppenheimer procedure, i.e., by optimizing the electronic structure at each step along with the integration of the equations of motion for the atomic coordinates. This protocol can be significantly accelerated by properly propagating the electronic density by ad hoc extrapolation schemes. However, when metallic electronic structures are involved, the efficiency of the electronic structure optimization as well as of the extrapolation algorithms rapidly degrades, due to the infamous charge sloshing problem. The convergence difficulties become even worse by increasing the system size, due to the divergent eigenvalue spectrum of the charge dielectric function of metallic systems. This is the reason why \emph{ab-initio} Molecular dynamics simulations of metals are often excessively demanding.