Choosing an algorithm

This page helps you select the right eOn algorithm for your task.

Finding transition states

Method	Use when	Configuration
NEB	You know both reactant and product	Nudged elastic band
Dimer	One known minimum; search nearby saddles	Dimer method
Process Search	Automated saddle point exploration from one state	Process search
Saddle Search	Single saddle point search with displacement	Saddle search

NEB vs Dimer

Use NEB when both endpoint structures are known and the minimum-energy path is the target. NEB optimizes the entire path simultaneously and identifies the transition state as the highest-energy image.

Use the Dimer method from a single minimum to locate nearby saddle points. The dimer walks uphill along the lowest curvature direction without the product state.

Process Search combines both: it uses the dimer to find saddle points, then minimizes from the saddle to identify the product.

Accelerated dynamics

Method	Acceleration type	Use when	Page
Parallel Replica	Spatial parallelism	You have many replicas available	Parallel replica
TAD	Temperature extrapolation	Barriers are known to follow Arrhenius	Temperature accelerated dynamics
Hyperdynamics	Bias potential	Barriers are localized (bond-boost)	Hyperdynamics
AKMC	Kinetic Monte Carlo	Long timescale evolution with rare events	Adaptive kinetic Monte Carlo

The client job for hyperdynamics is safe_hyperdynamics. The server job for adaptive kinetic Monte Carlo is akmc.

Optimization

Optimizer	Convergence	Failure mode	Memory
LBFGS	Fast near minima	Can fail far from min	O(memory * N)
FIRE	Moderate	Tolerant of poor guesses	O(N)
CG	Moderate	Good	O(N)
QuickMin	Slow	Tolerant of poor guesses	O(N)
SD	Very slow	Guaranteed descent	O(N)
xtsci	rgmin engine: L-BFGS, BFGS, SR1/SR2, Newton, RFO, NLCG, Adam, PSO	Needs a build with rgmin (-Dwith_rgmin)	O(N) or O(N²) pair Hessian

For most tasks, start with LBFGS. If it fails to converge, try FIRE or the refinement feature (start with FIRE, switch to LBFGS at threshold). In a build with rgmin, [Optimizer] opt_backend = rgmin runs the same opt_method through rgmin instead of eOn’s own solver.

See Optimizer for configuration details.

Global optimization

Method	Use when	Page
Basin Hopping	Finding global minimum of a cluster or surface	Basin hopping
Minima hopping	Short constant-energy escapes between minima	Minima hopping
Monte Carlo	Sampling configurations at finite temperature	Monte Carlo
Replica Exchange	Overcoming barriers via temperature exchange	Replica exchange