cylindrical_molecular_shape_checks.py

IDWT's physical premise is one infinite-dimensional manifold with all sectors nested as submanifolds. Particle depth counts macroscopic spatial dimensions; matrix and field-component counts in a calculation add no physical dimensions.

Calculation record

Full ligand-shape Hessians for prescribed cylindrical electron routes.

This is a frozen-route energy diagnostic: the electron route and central nucleus
are held fixed while every Cartesian coordinate of every outer nucleus varies.
It therefore tests considerably more than the common-radius force balance, but
is not a self-consistent electron--nuclear periodic-orbit calculation or a
derived Born--Oppenheimer surface. Nuclear repulsion uses point centres even
when the finite profiles used for electron attraction overlap.

Research context

Cylindrical molecular shape stability
The prescribed three-petal route gives a strict trigonal ligand minimum, while the nominal tetrahedral quarter-turn rays carry transverse force and relax to a strict disphenoidal minimum.

Interpret numerical checks within the assumptions and limitations documented in these notes.