Growing String Method (GSM)

Overview

The Growing String Method (GSM) is an adaptive path-based algorithm for finding minimum energy paths and transition states between a given reactant and product. Unlike NEB, which creates all images at once, GSM grows the path incrementally from both endpoints, adding new nodes only where needed. This adaptive growth strategy can be significantly more efficient than NEB for large molecular systems.

MAPLE's GSM implementation features Kabsch alignment of endpoints, two-ended adaptive growth with constrained mini-relaxation in the hyperplane orthogonal to the local path direction, energy-weighted tangents, a dynamic growth policy (including side pausing and forced connector pulls), and CI-STRING refinement followed by P-RFO TS optimization from the highest-energy image.

Parameters

Parameter	Type	Default	Description
`grow_step`	float	0.12	Step size for growing new nodes (Angstrom).
`grow_step_min`	float	0.02	Minimum growing step size.
`grow_backtrack`	float	0.5	Backtracking factor during growth.
`grow_relax_iters`	int	10	Relaxation iterations after each growth step.
`grow_relax_tol`	float	2.5e-3	Force tolerance for growth relaxation.
`grow_energy_tol`	float	1.0e-3	Energy tolerance for growth relaxation (Eh).
`pause_imbalance`	int	2	Pause growth from one end if it leads the other by this many nodes.
`refine_end_every`	int	3	Re-optimize endpoint images every N growth steps.
`merge_threshold`	float	0.5	Distance threshold for merging approaching fronts (Angstrom).
`n_images`	int	9	Target number of string images.
`max_iter_relax`	int	300	Maximum iterations for full string relaxation.
`string_f_max_th`	float	5.0e-3	Max force convergence threshold for string.
`string_f_rms_th`	float	1.0e-3	RMS force convergence threshold for string.
`lbfgs_memory`	int	7	L-BFGS memory for string relaxation.
`lbfgs_curvature`	float	70.0	L-BFGS initial curvature estimate.
`lbfgs_max_step`	float	0.2	L-BFGS maximum step.
`reparam_every`	int	3	Reparametrize string every N iterations.
`refine`	str	None	Post-string refinement: None, "cistring", or "stringts".
`cistring_f_max_th`	float	4.0e-3	Max force threshold for CI-String refinement.
`cistring_f_rms_th`	float	2.0e-3	RMS force threshold for CI-String refinement.
`max_iter_grow`	int	100	Maximum iterations for the growing phase.
`log_every`	int	1	Log progress every N iterations.
`guide_conn_min`	float	0.3	Minimum connectivity for geodesic guiding.
`guide_d_switch`	float	4.0	Distance switch for geodesic guidance.
`guide_inc_trigger`	int	2	Trigger for increasing guidance strength.

Input Example

#model=ani1xnr
#ts(method=string,refine=stringts)
#device=gpu0

XYZ /path/to/reactant.xyz
XYZ /path/to/product.xyz

Output

*_gsm_grow_final.xyz — The final path after the growth phase is complete, before reparameterization and refinement.
*_gsm_mep.xyz — The reparameterized minimum energy path with equally spaced images.
*_stringts_ts.xyz — The final optimized TS geometry obtained from P-RFO refinement of the highest-energy image along the string.

Comparison with NEB

Both GSM and NEB are path-based methods that require reactant and product endpoints. The key differences are:

Aspect	NEB	String/GSM
Path construction	All images created at once via interpolation	Images grown adaptively from both ends
Computational cost	All images evaluated at every iteration	Only frontier images evaluated during growth
Large systems	Can be expensive due to many simultaneous images	More efficient; fewer evaluations needed during growth
Path resolution	Uniform resolution along entire path	Adaptive resolution; concentrates images where needed
Robustness	Well-established; generally robust	Can stall for very large structural differences

For small to medium systems with modest structural changes, NEB and GSM typically perform comparably. For large systems (hundreds of atoms) or reactions with large geometric rearrangements, GSM's adaptive growth can provide significant computational savings.