Optimization Method: RFO

Rational Function Optimization with trust-region strategy for enhanced stability.

RFO (Rational Function Optimization) is an alternative geometry optimization method available in the Optimization (opt) module. It employs a trust-region strategy that compares the predicted model energy change with the actual energy change to accept or reject steps, offering enhanced stability for systems with strong curvature or sensitive potential energy surfaces.

I. Default Parameters

#opt(method=rfo, maxiter=256, trust_radius_init=0.2, trust_radius_min=1e-3, trust_radius_max=1.0, eta_shrink=0.75, eta_expand=1.75, evals_eps=1e-10, mu_margin=1e-8, max_bisect_it=60, write_traj=true, traj_every=1)

II. Adjustable Parameters

maxiter

Maximum number of optimization steps. Sets the upper limit for the optimization cycles. If convergence is not reached within this limit, the calculation stops and writes the final geometry.

trust_radius_init

Initial trust radius (Å). Defines the initial maximum allowed step size in mass-weighted coordinates. Larger values allow more aggressive first steps; smaller values are more conservative.

trust_radius_min

Minimum trust radius (Å). Sets the lower bound to which the trust radius may shrink. Prevents the optimizer from reducing the step size to an impractically small level.

trust_radius_max

Maximum trust radius (Å). The largest allowed trust-region size during optimization. Controls the upper limit for step expansion after successful iterations.

eta_shrink

Shrink threshold. The threshold for the quality ratio ρ (actual/predicted change) below which the step is rejected. If ρ < eta_shrink, the step is rejected and the trust radius is reduced.

eta_expand

Expand threshold. The threshold for ρ above which the trust radius is expanded. If ρ > eta_expand and the step lies on the boundary, the trust radius is increased to allow larger subsequent steps.

evals_eps

Eigenvalue regularization threshold. A small stabilizing value applied to very small Hessian eigenvalues. Prevents numerical instabilities in RFO step construction when eigenvalues are near zero.

mu_margin

Eigenvalue shift margin. Defines a safety margin below the minimum eigenvalue when determining the shift parameter μ.

max_bisect_it

Maximum bisection iterations. Sets the maximum iterations for solving the trust-region equation via bisection.

write_traj

Output optimization trajectory. Controls whether optimization snapshots are written to a trajectory file.

  • =true (default)
  • =false

traj_every

Trajectory output frequency (steps). Determines how often trajectory frames are written when write_traj = true. A value of 1 records every step; larger values record every N steps.

III. Output Files

The RFO optimization method produces output files containing information about the trust-region optimization process and final results.

Main Output File: *.out

Contains detailed information about the RFO optimization process, including trust radius adjustments and convergence diagnostics.

Trajectory File

When write_traj=true, intermediate geometries are saved at the specified frequency for visualization of the optimization path.

Final Optimized Structure

The final optimized geometry is written to output files for further analysis.