PES Scan with RFO Optimization

Overview

RFO (Rational Function Optimization) is available as a relaxed PES scan optimizer through #scan(method=rfo). At each scan point, MAPLE constrains the requested internal coordinates and reuses the same RFO minimizer used by #opt(method=rfo) to relax the remaining degrees of freedom.

RFO is more expensive than L-BFGS because it uses Hessian information and a trust-region step, but it can be more stable when the scan passes through regions with strong curvature changes or difficult convergence.

Parameters

Per-point RFO settings reuse the same controls as #opt(method=rfo). The shared level preset on #scan supplies the scan-point convergence thresholds; the scan driver sets per-point optimizer verbosity to quiet by default.

Parameter	Type	Default	Description
`max_iter`	int	`256`	Maximum number of RFO iterations per scan point.
`trust_radius_init`	float	`0.2`	Initial trust radius in Angstrom.
`trust_radius_min`	float	`1e-3`	Minimum trust radius.
`trust_radius_max`	float	`1.0`	Maximum trust radius.
`eta_shrink`	float	`0.75`	Trust radius shrink factor when step quality is poor.
`eta_expand`	float	`1.75`	Trust radius expansion factor when step quality is good.
`evals_eps`	float	`1e-10`	Eigenvalue epsilon for numerical stability.
`mu_margin`	float	`1e-8`	Margin for the level-shift parameter mu.
`max_bisect_it`	int	`60`	Maximum bisection iterations for level-shift optimization.
`verbose`	int	`0` in scans	Per-point optimizer verbosity. Scan keeps this low so the scan log stays readable.

Input Example

Checked-in MAPLE example: example/scan/rfo/methanol_oh_torsion.inp. This is the relaxed methanol O-H torsion scan shown in the visualization below:

#model=aimnet2nse
#scan(method=rfo,mode=relaxed)
#device=gpu0

C     -0.46276972     1.15067867     0.42624477
O     -0.32124714    -0.24861552     0.26422771
H     -1.51133868     1.39211728     0.61684893
H     -0.13712321     1.64920740    -0.48974849
H      0.15713375     1.48625319     1.26124710
H     -0.61759765    -0.66356677     1.09214997

S 3 1 2 6 5.0 72

The final S line is a dihedral scan: four atom indices followed by a 5.0 degree step and 72 increments, producing 73 scan points including the initial geometry.

Scan Visualization

The animation below pairs the generated scan geometries with the energy profile for a relaxed methanol torsion scan using RFO.

Fig. 1 — Methanol torsion relaxed scan (RFO)

When to Use RFO Scans

L-BFGS struggles at selected scan points: RFO's Hessian-based trust-region step accepts/rejects per step, providing a built-in safeguard against bad moves through strong curvature regions.
Smaller systems or high-value scan regions: RFO stores and manipulates the full Hessian, so its cost is worth it only where the added robustness pays off.
Routine large scans: Start with L-BFGS scan and switch to RFO only at scan points or regions where convergence fails.

Tip

For large systems where per-point RFO is too expensive, fall back to L-BFGS scan with a reduced max_step as a compromise between robustness and efficiency.