NEB — Nudged Elastic Band

Henkelman–Jónsson (2000) NEB with climbing-image (CI-NEB):

Algorithm

1. Linear interpolation of $N$ images between start and end endpoints

2. Energy-weighted tangent selection: uphill images use max-energy neighbor, downhill use min-energy neighbor; blended at energy crossings

3. Spring force along tangent: $$F_{\text{spring}}=k_{\text{spring}}\times (|R_{i+1}-R_i|-|R_i-R_{i-1}|)\times \hat{\tau }$$

4. CI-NEB activates after $N/3$ iterations: highest-energy image climbs by inverting the gradient component along the tangent

5. Gradient-descent relaxation of the full image band; convergence by max force across all moveable images

6. Output includes per-image energies, geometries, and a formatted path summary

Usage

task: RHF STO-3G

GEOMETRY
  # Start geometry
  O   0.000000   0.000000   0.100000
  H   0.750000   0.000000  -0.450000
  H  -0.750000   0.000000  -0.450000

  # End geometry
  O   0.000000   0.000000   0.100000
  H   0.750000   0.100000  -0.450000
  H  -0.750000  -0.100000  -0.450000
END

OPT
  NEB     true
  Images  8
END

The start and end geometries are provided as consecutive blocks in the GEOMETRY section separated by a blank line. Images N controls the number of interpolating images (default 8).