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Key Concepts🔗

This section explains the fundamental concepts behind NEB Dynamics.

Nodes and Chains🔗

Nodes🔗

A Node represents a single molecular structure (geometry) along a reaction path. The main node types are:

  • StructureNode: Represents a molecular structure with geometry, symbols, charge, and multiplicity. Stores cached energy and gradient data.
  • XYNode: A simplified node for 2D coordinates (useful for model systems).

Nodes are containers for molecular structures that also hold computational results: 

from neb_dynamics import StructureNode
from qcio import Structure

# Create a node from a structure
structure = Structure.from_smiles("C=O")
node = StructureNode(structure=structure)

# Update coordinates
new_coords = node.coords + 0.1  # Slight displacement
new_node = node.update_coords(new_coords)

Chains🔗

A Chain is a collection of Nodes representing a reaction pathway. It contains: - A list of Node objects (images along the path) - Chain parameters (spring constants, interpolation settings)

from neb_dynamics import Chain, ChainInputs
from neb_dynamics.nodes import StructureNode
from qcio import Structure

# Create a chain from nodes
nodes = [StructureNode(structure=Structure.from_smiles(s)) for s in ["C=O", "C[O]"]]
chain = Chain(nodes=nodes, parameters=ChainInputs())

# Access chain properties
print(chain.energies)       # Energy of each node
print(chain.gradients)      # Gradient of each node
print(chain.coordinates)    # Atomic coordinates
print(chain.path_length)    # Integrated path length

The Nudged Elastic Band Method🔗

How NEB Works🔗

NEB finds the minimum energy path by: 1. Creating a chain of images between reactant and product 2. Optimizing images simultaneously using spring forces (to keep them spaced) and perpendicular forces (to push toward the MEP)

Key Equations🔗

The total force on each image consists of two components:

Spring Force (parallel to path): 

F_spring = k * (|R_i+1 - R_i| - d) * t
where t is the tangent direction.

Perpendicular Gradient (perpendicular to path): 

F_perp = -∇E + (∇E · t) * t

The "nudging" removes the component of the spring force perpendicular to the path, ensuring images don't climb barriers.

Climbing Image NEB🔗

Enable with NEBInputs(climb=True) - the image with highest energy climbs to the saddle point.

nbi = NEBInputs(climb=True)

Geodesic Interpolation🔗

Geodesic interpolation provides better initial path guesses than linear interpolation, especially for reactions involving bond breaking/forming.

How It Works🔗

  1. Calculate pairwise distances between all atoms
  2. Find a path that minimizes the sum of geodesic distances
  3. Generate images along this path
import neb_dynamics.chainhelpers as ch
from neb_dynamics.inputs import ChainInputs, GIInputs

# Geodesic interpolation
gi_inputs = GIInputs(nimages=15, friction=0.001, nudge=0.1)
initial_chain = ch.run_geodesic([start_node, end_node],
                                 chain_inputs=ChainInputs(),
                                 nimages=15)

Parameters🔗

  • nimages: Number of images in the chain
  • friction: Controls penalty for large pairwise distances (lower = more flexible)
  • nudge: Nudge parameter for path optimization

Multi-Step MEP (MSMEP)🔗

MSMEP automatically handles complex reactions with multiple elementary steps:

  1. Run NEB on initial path
  2. Check if the path represents a single elementary step
  3. If not, split the path at intermediate minima
  4. Recursively minimize each segment
  5. Build a tree of all pathways found
from neb_dynamics import MSMEP, RunInputs

# Run recursive minimization
inputs = RunInputs(path_min_method='NEB')
m = MSMEP(inputs=inputs)

# This will automatically split if needed
history = m.run_recursive_minimize(initial_chain)

Convergence Criteria🔗

NEB Dynamics uses multiple convergence criteria:

Parameter Description Default
en_thre Energy difference threshold (Ha) 1e-4
rms_grad_thre RMS perpendicular gradient threshold 0.02 Ha/Bohr
max_rms_grad_thre Maximum RMS gradient threshold 0.05 Ha/Bohr
ts_grad_thre Transition state gradient threshold 0.05 Ha/Bohr
ts_spring_thre TS spring force threshold 0.02 Ha/Bohr
barrier_thre Barrier height change threshold (kcal/mol) 0.1
max_steps Maximum optimization steps 500

Visualization🔗

NEB Dynamics provides several visualization tools:

import neb_dynamics.chainhelpers as ch

# Plot energy profile
chain.plot_chain()

# Plot optimization history
n.plot_opt_history(1)

# Plot convergence metrics
n.plot_convergence_metrics()

# Visualize chain in 3D
ch.visualize_chain(chain)