Function calculate_path_length 

pub fn calculate_path_length(geometries: &[Geometry]) -> f64

Calculates the total path length along an interpolated reaction coordinate.

This function computes the cumulative Euclidean distance between consecutive geometries in the interpolation path. The path length provides a measure of the total geometric change along the reaction coordinate and can be useful for analyzing reaction paths and comparing different interpolation methods.

Arguments

• geometries - A slice of geometries representing the interpolation path

Returns

Returns the total path length as a f64 value in the same units as the input coordinates (typically Angstroms).

Algorithm

The path length is calculated as:

L = Σᵢ √(Σⱼ (xᵢ₊₁,ⱼ - xᵢ,ⱼ)²)

where the outer sum is over geometry pairs and the inner sum is over all coordinate components.

Examples

use omecp::lst::{interpolate_linear, calculate_path_length};
use omecp::geometry::Geometry;

let elements = vec!["H".to_string(), "H".to_string()];
let coords1 = vec![0.0, 0.0, 0.0, 0.0, 0.0, 0.0];
let coords2 = vec![1.0, 0.0, 0.0, 1.0, 0.0, 0.0];

let geom1 = Geometry::new(elements.clone(), coords1);
let geom2 = Geometry::new(elements, coords2);

let path = interpolate_linear(&geom1, &geom2, 1);
let length = calculate_path_length(&path);
// Length should be approximately sqrt(2) ≈ 1.414

Notes

• Returns 0.0 for empty or single-geometry paths
• The path length depends on the coordinate system and units used
• Longer paths may indicate more significant structural changes
• Can be used to compare the “smoothness” of different interpolation methods