v.0.1 updates

• Initial release
• .xlsx export: x, y cartesian coordinates are calculated, and each column is separated by PCS values.

v.0.2 updates

• Tensor values, PCS range, and intervals can now be inputted for calculations.
• Molar susceptibility tensor calculation
  ∆χ_ax = χ_zz - ((χ_xx + χ_yy))/2
  ∆χ_rh = χ_xx - χ_yy

v.0.3 updates

• XYZ file import and plot, coordinate rotation, atom coordinate table added, geometrical parameter analysis plot

v.0.3.1 updates

• Clicking on an atom point on the PCS plot to highlight the corresponding table entry, enhancing data visualization and interaction.

v.0.4 updates

• Added 3D molecule scatter plot

v.0.5 updates

• Reorganized GUI
• Added Mollweide projection plot

v.0.6 updates

• PCS polar plot: Half/Quarter view toggle function added

v.0.7 updates

• Bug fix

v.1.0.0 updates

• Code refactoring
• PCS fitting

v.1.0.1 updates

• Added table δ_exp data export/import

• Axis:
  • For two donors: normalize(v₁ + v₂) — the internal angle bisector
  • For three or more donors: practically equivalent to average
• When to use: Especially useful for bidentate ligands.
• Pros: Physically intuitive for bidentate geometries.
• Caution: If v₁ ≈ −v₂, the axis becomes ill-defined (like average).

• Axis: Normal vector to the least-squares plane through the donor set (e.g., the PC3 direction from PCA/SVD).
• When to use: For planar donor arrangements (e.g., tridentates), where the perpendicular axis is meaningful.
• Pros: Captures the out-of-plane direction of planar ligands.
• Caution: For only 2 donors or collinear donors, the plane is ill-defined → fallback to average or bisector is recommended.

• Axis: Principal component of maximum variance in the donor distribution (usually PC1).
• When to use: For elongated, chain-like, or non-planar donor arrays.
• Pros: Captures the dominant elongation axis of donor geometry.
• Caution: For planar sets, the normal (PC3) may be more intuitive.

• Axis: normalize(mean(Dᵢ) − M) — vector from the metal center M to the centroid of the donor coordinates
• When to use: When donor positions (including distances) should influence the axis.
• Pros: Naturally incorporates distance effects; geometric center-based.
• Caution: A single distant donor can dominate the direction.

• Axis: normalize(Σ vᵢ) — normalized vector sum of all donor directions
• When to use: To equally account for multiple donor directions.
• Pros: Straightforward; reflects all donors equally.
• Caution: Nearly opposite donors may cancel out, making the axis unstable.

• Axis: v₁ (the first donor direction itself)
• When to use: When only one donor should define the axis (e.g., monodentate, or a specific donor chosen as reference).
• Pros: Simple and intuitive.
• Caution: If multiple donors exist, the other directions are not reflected in the axis definition.

• Bidentate: bisector (recommended), or average
• Planar tridentate (or similar): normal is most intuitive
• Chain-like / elongated donor arrays: pca
• Single donor focus: first
• Equal weighting of all donors: average
• Distance-sensitive cases: centroid