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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:
where SMASS supplies the damping
factor , and POTIM controls
In fact, a simple velocity Verlet algorithm is used to integrate the
equation, the discretised equation reads:
It is immediately recognized, that is equivalent to a simple steepest descent
algorithm (of course without line optimization). Hence, corresponds
to maximal damping, 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 is usually 0.4.
Mind that our implementation is particular user-friendly,
since changing usually does not require to re-adjust the time step (POTIM).
To choose an optimal time step and damping factor, we recommend the
following two step procedure: First fix (for instance to
1) and adjust POTIM. POTIM should be chosen as large as possible
without getting divergence in the total energy.
Then decrease and keep POTIM fixed.
If POTIM and SMASS are chosen correctly, the damped molecular dynamics mode
usually outperforms the conjugate gradient method by a factor of
If SMASS is not set in the INCAR file (respectively SMASS0),
a velocity quench algorithm
is used. In this case ions are updated according using the following algorithm:
Here are the current forces, and 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
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
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