FORCE BASED OPTIMIZERS

The NEB and min-mode following (dimer/Lanczos) saddle point finding methods use a force projection in order to direct the optimizers towards minimum energy paths and saddle points. These modifications to the force mean that the energy is no longer consistent with the force being optimized. Because of this, we can only use optimizers that are solely based upon the force (and not the energy). The quasi-Newton and quick-min (IBRION=1 and 3 respectively) optimizers that are built into VASP are both force-based, but the conjugate-gradient method (IBRION=2) is not.

Here, we present a set of optimizers that are all force-based so they can be used with the NEB and min-mode following methods. To use them, the INCAR must set IBRION=3 and POTIM=0, to disable the built in optimizers. Then, the IOPT parameter will select one of the following methods.

This version of quick-min is essential the same as what has been implemented in vasp. The conjugate-gradient method is different in that is uses a Newton’s line optimizer, and are entirely force based. The LBFGS is also different in that the NEB can be optimized globally, instead of image-by-image. The FIRE optimizer is an interesting new optimizer which has similarities to quick-min, but tends to be faster. The steepest descent method is provided primarily for testing. We recommend using CG or LBFGS when accurate forces are available. This is essential for evaluating curvatures. For high forces (far from the minimum) or inaccurate forces (close to the minimum) the quick-min or FIRE methods are recommended. These two methods do not rely on curvatures, and tend to be less aggressive, better behaved, but also less efficient than CG/LBFGS.

Here is a recent paper discussing the performance of these different optimizers with the NEB.

The min-mode following methods can only be used with one of these methods. If IOPT is not set in a dimer run, the job with die with a corresponding error message.


Optimizer input parameters

The following parameters are read from the INCAR file.

(IOPT = 0) Use VASP optimizers specified from IBRION (default)

(IOPT = 1) LBFGS = Limited-memory Broyden-Fletcher-Goldfarb-Shanno

(IOPT = 2) CG = Conjugate Gradient

(IOPT = 3) QM = Quick-Min

(IOPT = 4) SD = Steepest Descent

(IOPT = 7) FIRE = Fast Inertial Relaxation Engine


Required Parameters

Parameter

Default

Description

IOPT

0

Default is to use the VASP optimizers

IBRION

3

pecify that VASP do molecular dynamics (with zero time step)

POTIM

0

Zero time step so that VASP does not move the ions


LBFGS Parameters (IOPT = 1)

Parameter

Default

Description

MAXMOVE

0.2

Maximum allowed step size for translation

ILBFGSMEM

20

Number of steps saved when building the inverse Hessian matrix

LGLOBAL

.TRUE.

Optimize the NEB globally instead of image-by-image

LAUTOSCALE

.TRUE.

Automatically determines INVCURV

INVCURV

0.01

Initial inverse curvature, used to construct the inverse Hessian matrix

LLINEOPT

.FALSE.

Use a force based line minimizer for translation

FDSTEP

5E-3

Finite difference step size for line optimizer


CG Parameters (IOPT = 2)

Parameter

Default

Description

MAXMOVE

0.2

Maximum allowed step size for translation

FDSTEP

5E-3

Finite difference step size to calculate curvature


QM Parameters (IOPT = 3)

Parameter

Default

Description

MAXMOVE

0.2

Maximum allowed step size for translation

TIMESTEP

0.1

Dynamical time step


SD Parameters (IOPT = 4)

Parameter

Default

Description

MAXMOVE

0.2

Maximum allowed step size for translation

SDALPHA

0.01

Ratio between force and step size


FIRE Parameters (IOPT = 7)

Parameter

Default

Description

MAXMOVE

0.2

Maximum allowed step size for translation

TIMESTEP

0.1

Dynamical time step

FTIMEMAX

1.0

Maximum dynamical time step allowed

FTIMEDEC

0.5

Factor to decrease dt

FTIMEINC

1.1

Factor to increase dt

FALPHA

0.1

Parameter that controls velocity damping

FNMIN

5

Minimum number of iterations before adjusting alpha and dt