Exciton ECD Explorer — Cn symmetric oligomers
Coupled-oscillator (matrix-exciton) model: ECD, UV–Vis and dissymmetry g-factor of a dimer, trimer and tetramer of one chromophore.
Model after Castro-Fernández, Peña-Gallego, Mosquera & Alonso-Gómez, Molecules 2019, 24, 141 — chiroptical responses of Cn/Dn systems. Δε and ε share one arbitrary cgs scale (∝ rotational / dipole strength, 10⁻⁴⁰ esu²cm²), so ε ≫ |Δε| and g = 4·Δε/ε is dimensionless (~10⁻³). Geometry knobs are live.
| oligomer | geometry · drag to rotate | ECD Δε (rotational strengths) | UV–Vis ε (dipole strengths) | dissymmetry g = 4R/D |
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How it works. Each oligomer is a Cn ring of identical chromophores (n = 2, 3, 4). Transition dipoles are placed by symmetry, the
point-dipole coupling matrix Vij = 5034·[μ̂i·μ̂j − 3(μ̂i·n̂)(μ̂j·n̂)]·|μ|²/Rij³ (cm⁻¹, μ in D, R in Å) is diagonalized,
and for every exciton state k: dipole strength Dk=|Σckiμi|² (→ UV–Vis), rotational strength
Rk ∝ ν̃k·Σi<jckickj(ri−rj)·(μi×μj) (→ ECD). The ECD and UV–Vis curves are sums of Gaussians
(ΣRk·G and ΣDk·G); the dissymmetry factor is their pointwise ratio g(λ) = 4·ECD(λ)/UV(λ), masked where the UV
curve falls below 3% of its peak. ECD is conservative (ΣkRk ≈ 0). Set θ = 0° (dipoles in plane) and the CD vanishes; flip the sign of θ and the couplet inverts.
