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calculate_neb_force

omecp::reaction_path

Function calculate_neb_force 

Source 
fn calculate_neb_force(
    path: &[Geometry],
    image_index: usize,
    spring_constant: f64,
) -> Vec<f64>
Expand description

Calculates the NEB force for a specific image in the reaction path.

This function computes the spring forces that maintain proper spacing between images in the NEB method. It implements the core force calculation that drives the path optimization toward the minimum energy pathway.

§Theoretical Background

The NEB force on image i consists of spring forces along the path tangent:

F_i^spring = k × [(d_{i+1} - d_avg) - (d_i - d_avg)] × τ̂_i

where:

  • k is the spring constant
  • d_i is the distance from image i to image i-1
  • d_avg is the average spacing between all images
  • τ̂_i is the normalized tangent vector at image i

§Algorithm Steps

  1. Neighbor Identification: Get previous and next images
  2. Tangent Calculation: Compute path tangent at current image
  3. Distance Measurement: Calculate distances to neighboring images
  4. Spring Force: Apply Hooke’s law along the tangent direction
  5. Force Balancing: Ensure forces maintain even spacing

§Arguments

  • path - Complete reaction path as array of geometries
  • image_index - Index of the current image (0 = first, n-1 = last)
  • spring_constant - Spring stiffness parameter (typically 0.1-1.0)

§Returns

Vector of forces with length 3×N_atoms, representing [Fx, Fy, Fz] components for each atom in the molecule.

§Force Direction Logic

§Interior Images (i = 1, 2, …, n-2)

  • Previous spring: Pulls toward image i-1 if too far apart
  • Next spring: Pulls toward image i+1 if too far apart
  • Net effect: Maintains even spacing along path

§Endpoint Images (i = 0, n-1)

  • Fixed positions: No forces applied (endpoints don’t move)
  • Boundary conditions: Provide reference for neighboring images

§Spring Constant Effects

  • High k (stiff springs): Images stay evenly spaced but may resist optimization
  • Low k (soft springs): Images can cluster but may lose path resolution
  • Typical values: k = 0.1-0.5 eV/Angstrom² for most chemical systems

§Implementation Notes

§Current Limitations

  • Spring forces only: True energy gradients not included
  • Simple spacing: Uses RMSD rather than arc length
  • No adaptive springs: Constant spring constant throughout

§Distance Metrics

  • RMSD: Root mean square deviation between geometries
  • Average spacing: Mean distance between consecutive images
  • Force scaling: Proportional to deviation from average spacing