PES Scan with RFO Optimization

Overview

The RFO (Rational Function Optimization) method is a Hessian-based geometry optimizer that can be used within the PES Scan workflow as an alternative to the default L-BFGS optimizer. At each scan point, RFO builds the full Hessian matrix, diagonalizes it, and determines a shift parameter using Brent's root-finding algorithm to compute a trust-region step. This approach provides more robust convergence in regions of the PES where the curvature changes rapidly or where L-BFGS may struggle.

Parameters

The RFO scan optimizer uses its own standalone parameters with trust-radius control. Like the scan L-BFGS, these are hardcoded in the standalone scan function.

Warning

The scan IMPLEMENTATION_MAP only registers "lbfgs" and "cg" as valid methods. RFO scan support may not be available in all versions of MAPLE. Check your version's release notes before using #scan(method=rfo).

Parameter	Type	Default	Description
`maxiter`	int	256	Maximum number of RFO iterations per scan point.
`max_step_size`	float	0.1	Upper bound on step displacement to prevent unphysical jumps.
`tol`	float	1.0e-5	Convergence tolerance for the Brent root-search of the shift parameter.
`lambda_max_iter`	int	64	Maximum Brent iterations for solving the rational-function shift equation.

Standard convergence thresholds (maximum force, RMS force, maximum displacement, RMS displacement) are evaluated at each scan point.

Input Example

A relaxed 1D bond scan using the RFO optimizer:

#model=uma
#scan(method=rfo)
#device=gpu0

C   0.0  0.0  0.0
H   1.0  0.0  0.0
O   2.0  0.0  0.0

S 1 2 -0.1 15

When to Use

Consider using the RFO optimizer for PES scans when:

The default L-BFGS optimizer has difficulty converging at certain scan points, particularly near stationary points or in flat regions of the PES.
The scan path passes through regions with strong curvature changes where Hessian information is valuable for determining step directions.
You need more robust convergence and are willing to accept the additional cost of Hessian computation at each optimization step.

For routine scans on well-behaved surfaces, the default L-BFGS method is generally preferred due to its lower per-step cost.