Cyanine DFT
Live Animations
Four real DFT geometry optimisations. 14 hours 29 minutes of wall time. Every animation on this page runs on the actual numbers from the ORCA output files.
The Polymethine Chain
BLA = mean(long C-C) minus mean(short C=C). In cyanine dyes the chain alternates between compressed and extended bonds. The animation shows each molecule's actual BLA from the DFT output, scaled to δ = 0.013643 (the Pythagorean comma).
BLA = 0.04715 Å = 3.456δ
14 SCF cycles · 2h 33min
E = -1231.098644523 Eh
BLA = 0.04901 Å = 3.592δ
14 SCF cycles · 3h 02min
E = -1308.453858270 Eh
BLA = 0.05406 Å = 3.963δ
31 SCF cycles · 7h 25min
E = -1385.900699281 Eh
BLA = 0.05054 Å = 3.704δ
8 SCF cycles · 1h 29min
E = -1385.809303280 Eh
LUMO Pinning
The most striking result from the calculations: LUMO energy stays nearly constant across the cation series (σ = 0.013 eV). The chain-length red-shift is HOMO-dominated. The LUMO has a node at the meso position; adding carbons at the ends does not perturb it.
| Molecule | HOMO (eV) | LUMO (eV) | Gap (eV) | LUMO deviation |
|---|---|---|---|---|
| Cy7+ | -7.734 | -4.184 | 3.550 | +0.003 eV |
| Cy9+ | -7.462 | -4.183 | 3.280 | +0.002 eV |
| Cy11(0) | -3.906 | -1.243 | 2.663 | neutral (UKS) |
| Cy11+ | -7.250 | -4.156 | 3.094 | -0.025 eV |
The CPCS Correction
Standard PIB: RMSE = 107 nm. CPCS-corrected PIB using y(n) = 2.67ⁿ + 2.535 Å: RMSE = 0.73 nm. A 146× improvement with zero free parameters. The animation shows both models against the experimental absorption wavelengths from your midterm exam (k = 0,1,2,3).
67 Cycles · 14h 29min Total
Every SCF cycle from the ORCA 6.1.1 output files. Cy9+ shows a +10.33 mHartree spike at cycle 8 (the trust-radius algorithm accepted an uphill step, self-corrected at cycle 9). Cy11(0) required 31 cycles due to near-degeneracy between the SOMO and low-lying virtual orbitals.
BLA / δ = 3.678
The observation: mean BLA = 0.05019 Å = 3.678 × δ. All four values lie in (3δ, 4δ). Base-rate probability of coincidence: ~18% at N=4. Stated honestly: recorded because real data does something unexpected, not because it is proven. The animation places each BLA on the comma number line.
BLA values, orbital energies, LUMO pinning (σ = 0.013 eV), convergence data. Real numbers from real calculations.
BLA/δ = 3.678. All four in (3δ, 4δ). 18% base-rate probability. N=4. Interesting. Unproven.
Any causal link between δ and BLA physics. The connection to CAM-B3LYP μ = 0.33 bohr⁻¹ remains open.