The perpendicular relaxation

After the push, ARTn algorithm performs a perpendicular relaxation. That is, a relaxation constrained to the direction perpendicular to the push.

The perpendicular relaxation is often abbreviated as “perp relax”, or just “perp”.

The number of perp relax steps

Depending on the current position on the PES, the goal of perp relax differs:

  1. in the initial basin, the goal of perp relax is to avoid atomic collisions which can happen due to a randomized push vector;

  2. near a saddle point, the goal is to minimize the force, and converge the system to the saddle.

We can see that in case 1), the goal can be achieved with only a few steps of perp relax, but in case 2) we might need more steps.

This is regulated with nperp_limitation, which is an array of integer values. For example, the specification:

nperp_limitation = 4, 8, 12, 12, 12, 18

means that within the basin, the number of perp relax steps will be 4 (the first integer). Once the system reaches a negative eigenvalue, the number of perp relax steps will be progressively increased from 4 to 18. Specifically, the number of perp relax steps will first increase to 8, then it will be held at 12 for 3 steps, and finally increased to 18. If the saddle is still not reached, the number will be kept at 18.

It is also possible to specify the last value as -1:

nperp_limitation = 4, 8, 12, 12, 18, -1

which signifies that the number of perp relax steps is unlimited. That means perp relax will continue until some Stopping criteria is met.

FIRE parameters

The perp relax is mainly controlled by the FIRE parameters, such as the timestep, alpha, and inc/dec factors. The modification of these parameters depends upon your E/F engine, and the mode of execution. See also: Relaxation to minima.

Stopping criteria

While the system is within the starting basin, the only criterion to stop the perp relax is:

  • number of perp relax steps has reached the limit according to current value of nperp_limitation;

When outside of the basin, any of the following criteria will stop the perp relax block:

  • system has converged to saddle point;

  • number of perp relax steps has reached the limit according to current value of nperp_limitation;

  • parallel component of the force is larger in magnitude than the perpendicular component;

  • perpendicluar component of the force is aligned in the direction such that relaxation along it, would bring the system back toward the initial minimum;