Climbing-Image Nudged Elastic Band¶

The reaction path can be found by simultaneous optimization of a number of replicas of the system in question starting from some rough approximation [159]. In the simplest case, implemented in ADF, the initial approximation is just a polynomial interpolation between initial and final states (see keyword geovar). The images are optimized not independently of each other but, in fact, forces on each image depend on its neighbors. At each step the forces parallel to the reaction path are eliminated and a so-called spring force is added which keeps the image in the middle between its neighbors. This does not let images slide to the initial or final reaction state and ensures that they are evenly distributed along the reaction path. There are also options to distribute images more densely near the transition state (energy-dependent spring force).

Below is the list of NEB options:

GEOMETRY
  CINEB {NumImages}
  {NEBSPRING  Nspring  Spring Spring2 Spower}
  {NEBOPT OptMethod}
  {NEBECONO}
  {NOCLIMB}
  {NONEBOPTENDS}
End

CINEB

The runtype. Nudged will also be recognized.

NumImages

The number of NEB images excluding initial and final stated. The default is 8.

NEBSPRING Nspring  Spring Spring2 Spower

Nspring determines the type of spring used, which, in turn, determines which of the spring parameters are used:

1. constant spring, spring=Spring
2. exponential scaling, spring = Spring+Spring2*exp((dE-dEmax)**Spower)
3. power scaling, spring = Spring+Spring2*(dE/dEmax)**Spower
4. another exponential with different meaning of Spower, spring = Spring+Spring2*exp((dE-dEmax)*Spower)
5. another exponential scaling very close to #4, spring = Spring+Spring2*(2**(dE-dEmax))**Spower)

Units for Spring and Spring2 are Hartree/bohr. Default values, when NEBSPRING is not present in the input, are 1 for Nspring and 0.1 for Spring. If NEBSPRING is specified with Nspring 1 then the Spring parameter is required. If Nspring>1 is specified then also Spring2 and Spower are required.

NEBOPT OptMethod

Specifies the optimization procedure. Since NEB is conceptually different from simple optimization, not all or not always options used in simple geometry optimization applicable to NEB. There are two optimization modes available for NEB: global (covering all images simultaneously) and local (that is, local to each image). Each method has its pro’s and con’s. The global method usually converges in fewer steps than local because its Hessian takes into account all degrees of freedom at once. On the other hand, the size of the matrix may become too large for moderate-size system, which might lead to problems (one dimension of the Hessian matrix may be as large as N(atoms)*3*N(images)). There are two geometry update methods available for both global and local optimization: Quasi-Newton and Conjugate-Gradient. Quasi-Newton is the preferred method at all times. NEB optimization in Z-matrix coordinates is not available at this time.

OptMethod can take any of the following values:

GLOBALQN: global Quasi-Newton.

QN: Local Quasi-Newton. The preferred (and default) method.

NEBECONO

(local optimization only) Requests that when at some point an image’s geometry converges this image will not be recalculated in subsequent steps. This option can be used to speed up calculation in the end when some images have already converged. Please note though that even if an image has converged at one point it may become “un-converged” at a subsequent point due to increase in spring force (which is determined by position of the image with respect to its neighbors). This option is irrelevant in case of the global optimization because then the convergence state of a single image is not determined.

NOCLIMB

Switches off the climbing-image feature. This option is generally not recommended and exists for debugging and troubleshooting purposes.

NONEBOPTENDS

Do not optimize geometries the initial and final reaction states during NEB optimization.