Transition State Method: Dimer

Local transition-state search algorithm based on minimum-mode following.

The Dimer method is a local transition-state search algorithm based on minimum-mode following. Starting from a single initial geometry, it rotates a trial direction to follow the lowest-curvature mode and then translates the structure along this mode under a trust region, climbing efficiently toward a first-order saddle point.

I. Adjustable Parameters

use_hvp

Hessian–vector backend. If true, the Dimer uses an analytic Hessian–vector product H·n when available; otherwise H·n is evaluated by finite differences controlled by delta.

  • =false (default)
  • =true

delta

Finite-difference step (Å). Step length Δ along the dimer direction when approximating curvature from forces at R ± Δn.

(default: delta=0.005)

rot_max_iter

Maximum rotation iterations. Maximum number of inner rotation steps per outer Dimer iteration used to minimize κ = n†Hn.

(default: rot_max_iter=5)

rot_alpha

Rotation step factor. Controls the step size for updating the dimer orientation along the rotational force; smaller values give more conservative rotations.

(default: rot_alpha=0.5)

rot_fmax_th

Rotation max-force threshold. Convergence threshold on the maximum component of the rotational force |F_rot| (Eh/Å) during orientation optimization.

(default: rot_fmax_th=1.0e-3)

rot_frms_th

Rotation RMS-force threshold. Convergence threshold on the RMS rotational force |F_rot|_rms (Eh/Å).

(default: rot_frms_th=5.0e-4)

step0

Initial step scale. Initial scaling factor for the translational step along the TS search direction.

(default: step0=0.2)

step_max

Maximum Cartesian displacement (Å). Hard upper limit on the per-iteration atomic displacement; prevents unstable, overly large steps.

(default: step_max=0.15)

trust_radius

Trust-region radius (Å). Effective maximum step size in the chosen metric; the actual step is restricted by min(trust_radius, step_max) in each iteration.

(default: trust_radius=0.15)

fmax_th

Max-force threshold. Target convergence threshold on the maximum (Eh/Å) translational force component.

(default: fmax_th=5.0e-3)

frms_th

RMS-force threshold. Target convergence threshold on the RMS (Eh/Å) translational force.

(default: frms_th=1.0e-3)

kappa_to_flip

Curvature flip threshold. When κ = n†Hn falls below this value, the parallel force component is flipped so that the Dimer climbs along the negative-curvature mode toward the saddle.

(default: kappa_to_flip=0.0)

max_iter

Maximum Dimer iterations. Maximum number of outer Dimer steps allowed in the TS search.

(default: max_iter=200)

use_mass_weight

Mass-weighted metric. If true, dot products and norms are evaluated in a mass-weighted metric, which can improve mode localization in systems with very different masses.

  • =false (default)
  • =true

remove_rigid

Remove rigid-body motion. If true, global translation and rotation are projected out of the dimer direction so that the search follows purely internal modes.

(default: remove_rigid=true)

n_init

Initial orientation mode. Choice of how to construct the initial dimer direction n:

  • =random (default) – random vector
  • =force – aligned with the force
  • =given – use the user-specified n_given

n_given

User-defined initial n. Optional user-specified initial direction used when n_init="given". Its length must match 3N.

(default: n_given=None)

save_traj

Write Dimer trajectory. Controls whether all intermediate structures are written to an XYZ trajectory file (*_dimer_traj.xyz).

(default: save_traj=true)

II. Output Files

The Dimer method produces several output files containing information about the transition state search process.

Main Output File: *.out

Contains detailed information about the dimer search process, including rotation and translation steps, convergence diagnostics, and final transition state properties.

Trajectory File: *_dimer_traj.xyz

XYZ trajectory file containing all intermediate structures generated during the dimer search, useful for visualizing the search path.

Final Structure

The final optimized transition state structure is written to output files for further analysis.