IBRION=3

If a damping factor, is supplied in the INCAR file by means of the SMASS tag, a damped second order equation of motion is used for the update of the ionic degrees of freedom:

$${\ddot {\vec x}} = - 2* \alpha {\vec F} - \mu {\dot {\vec x}},$$

where SMASS supplies the damping factor $\mu$, and POTIM controls $\alpha$. In fact, a simple velocity Verlet algorithm is used to integrate the equation, the discretised equation reads:

$${\vec v_{N+1/2}} = \Big((1-\mu/2) {\vec v_{N-1/2}} - 2* \alpha {\vec F_N} \Big)/(1+\mu/2)$$

$${\vec x_{N+1}} = {\vec x_{N+1}} + {\vec v_{N+1/2}}$$

It is immediately recognized, that $\mu=2$ is equivalent to a simple steepest descent algorithm (of course without line optimization). Hence, $\mu=2$ corresponds to maximal damping, $\mu=0$ corresponds to no damping. The optimal damping factor depends on the Hessian matrix (matrix of the second derivatives of the energy with respect to the atomic positions). A reasonable first guess for $\mu$ is usually 0.4. Mind that our implementation is particular user-friendly, since changing $\mu$ usually does not require to re-adjust the time step (POTIM). To chose an optimal time step and damping factor, we recommend the following two step procedure: First fix $\mu$ (for instance to 1) and adjust POTIM. POTIM should be chosen as large as possible without getting divergence in the total energy. Than decrease $\mu$ and keep POTIM fixed. If POTIM and SMASS are chose correctly, the damped molecular dynamics mode usually outperforms the conjugate gradient method by a factor of two.

If SMASS is not set in the INCAR file (respectively SMASS$<$0), a velocity quench algorithm is used. In this case ions are updated according using the following algorithm: Here ${\vec F}$ are the current forces, and $\alpha$ corresponds to POTIM. This equation implies that, if the forces are antiparallel to the velocities, the velocities are quenched to zero. Otherwise the velocities are made parallel to the present forces, and they are increased by an amount that is proportional to the forces.

Mind: For IBRION=3, a reasonable time step must be supplied by the POTIM parameter. Too large time steps will result in divergence, too small ones will slow down the convergence. The stable time step is usually twice the smallest line minimization step in the conjugate gradient algorithm.