Function calculate_rmsd 

fn calculate_rmsd(geom1: &Geometry, geom2: &Geometry) -> f64

Calculates the Root Mean Square Deviation (RMSD) between two molecular geometries.

RMSD is a standard metric for measuring the similarity between molecular structures. It quantifies the average distance between corresponding atoms in two geometries, providing a single number that represents structural similarity.

Mathematical Definition

RMSD is calculated as:

RMSD = √[(1/N) × Σᵢ(rᵢ₁ - rᵢ₂)²]

where:

• N is the total number of coordinate components (3 × number of atoms)
• rᵢ₁, rᵢ₂ are corresponding coordinate components in the two geometries
• The sum is over all x, y, z coordinates of all atoms

Arguments

• geom1 - First molecular geometry
• geom2 - Second molecular geometry (must have same number of atoms)

Returns

RMSD value in the same units as the input coordinates (typically Angstroms).

Interpretation

• RMSD ≈ 0: Geometries are nearly identical
• RMSD < 0.1 Angstrom: Very similar structures (small conformational changes)
• RMSD 0.1-0.5 Angstrom: Moderate structural differences
• RMSD > 0.5 Angstrom: Significant structural changes

Applications in Path Methods

• Image spacing: Measure distances between path images
• Convergence criteria: Check if optimization has converged
• Path length calculation: Sum of RMSD values along path
• Quality assessment: Evaluate path smoothness