Hückel Molecular Orbitals & the Frost Circle (2D)

This 2D companion to the 3D Hückel simulator builds the same physics from scratch with an independent, general-purpose method: it assembles the N×N Hückel Hamiltonian matrix for a cyclic π-conjugated ring of 3 to 8 carbons and diagonalizes it with a Jacobi eigenvalue algorithm running live in the browser, rather than relying only on the closed-form cyclic solution. The Frost circle panel places each computed energy level on a circle of radius 2|β|, groups degenerate orbitals side by side, and fills them by the Aufbau principle with Hund's rule for degenerate pairs, so aromaticity or antiaromaticity falls out of the actual computed electron configuration for whatever ring size and charge you pick — never a hardcoded per-molecule answer. The ring panel renders the real eigenvector coefficients as coloured, sized lobes so you can watch node count grow with orbital energy exactly as the diagonalization computes it.