LANCZOS

There have been several similar but distinct methods published to locate lowest (or minimum) eigenmodes. We prefer to call them collectively Min-Mode following methods. The most successful ones are the Lagrange multiplier approach, Phys. Rev. B 59, 3969 (1999), the ARTn method, Phys. Rev. E 62, 7723 (2000), and the Dimer method.

The use of a Lanczos type scheme in this field was pioneered by N. Mousseau et al. in their ARTn method. This method is is similar in spirit to the Dimer method in that it can be used to search for nearby saddle points from a local minimum or any other starting configuration, and it has recently been shown that the convergence properties are comparible between the two methods (see J. Chem. Phys. 121, 9776, (2004)).

The difference between the two methods is how the lowest curvature mode is found. The Dimer method rotates a dimer to find the lowest modes, and the Lanczos method finds an approximation to the Hessian eigenvector by expansion in a systematically increasing dimensional Krylov subspace. After the lowest mode is found, the two method proceed in an identical manner.

Lanczos input parameter set

The following parameters are read from the INCAR file. All parameters specific to the Lanczos method start with S.

Required Parameters

Parameter Default Value Description
ICHAIN 3 Use the Lanczos method
IBRION 3 Specify that VASP do MD with a zero time step
POTIM 0 Zero time step so that VASP does not move the ions
EDIFF 1E-8 Strict force criteria to accurately find force differences (curvature)

Standard Parameters (default values given)

Parameter Default Value Description
SLTOL 0.01 Use the Lanczos method
Sdr 0.001 Specify that VASP do MD with a zero time step
SNL 20 Zero time step so that VASP does not move the ions

Lanczos Output

All output related to the Lanczos procedure is directed to the LANCAR file. A combination of the unix commands grep/cut/head/tail can be used to extract the results.

Keywords to “grep” for in the LANCAR file:

Keyword Description
For Gets the force components for each central point, i.e. points after translating the system
Coo Gets the coordinate components for each central point
Low Gets the lowest mode at each central point
eig Gets the lowest eigenvalue convergence sequence at each central point
conv Gets the size of the Lanczos matrix, energy, maximum force and lowest eigenvalue at each central point