Function get_average_spacing 

fn get_average_spacing(path: &[Geometry]) -> f64

Calculates the average spacing between consecutive images in a reaction path.

This function computes the mean distance between neighboring geometries along a reaction path. It’s used in NEB to determine the reference spacing for spring force calculations and to assess path quality.

Mathematical Definition

Average spacing is calculated as:

d_avg = (1/(n-1)) × Σᵢ₌₁ⁿ⁻¹ RMSD(Rᵢ₊₁, Rᵢ)

where:

• n is the number of images in the path
• RMSD(Rᵢ₊₁, Rᵢ) is the distance between consecutive images
• The sum is over all adjacent image pairs

Arguments

• path - Array of geometries representing the reaction path

Returns

Average spacing in the same units as coordinates (typically Angstroms). Returns 0.0 for paths with fewer than 2 images.

Applications in NEB

Spring Force Reference

The average spacing serves as the equilibrium length for NEB springs:

F_spring ∝ (d_actual - d_avg)

Path Quality Assessment

• Uniform spacing: d_avg ≈ individual spacings (good path)
• Non-uniform spacing: Large variation in spacings (needs optimization)

Convergence Monitoring

• Stable d_avg: Path spacing has converged
• Changing d_avg: Path still optimizing

Ideal Path Properties

• Even spacing: All consecutive distances ≈ d_avg
• Smooth progression: No large jumps between adjacent images
• Appropriate resolution: d_avg small enough to capture path features