66th International Molecular Spectroscopy Symposium June 24, 2011 Time-dependent density-functional description of the 1La state in polycyclic aromatic hydrocarbons: Charge-transfer character in disguise? Ryan M. Richard 66th International Molecular Spectroscopy Symposium June 24, 2011

Background *Grimme, S.; Parac, M. ChemPhysChem 2003, 4, 292. Studies* show traditional TD-DFT has problems with some polycyclic aromatic hydrocarbons (PAHs) Particular focus on 1ππ* states 1La and 1Lb States differ by: Polarization Excitation character *Grimme, S.; Parac, M. ChemPhysChem 2003, 4, 292. Parac, M.; Grimme, S. Chem. Phys. 2003, 292, 11. Wong, B. M.; Hsieh, T. H. JCTC. 2010, 6, 3704.

Results: LCAs Non-LRC-TD-DFT: Errors worse with system size Underestimation of vertical excitation energy Errors relative to experiment Corrected for vertical excitation

Results: LCAs

CT and TD-DFT If excitation goes from i on A to a on B (i and a do not overlap): The proper CT energy is:

CT and TD-DFT One way to mitigate this problem is via long- range corrected (LRC) TDDFT Partition Coulomb operator as: Makes A element:

CT metric Tozer's CT metric: 0≤Λ≤1, closer to 1, the less CT character Established that TD-B3LYP excitation errors are unreliable when Λ<0.3

CT Metric CT metric predicts: Localization is expected from NTOs 1La state more localized Both significantly more than 0.3 Localization is expected from NTOs

Difference Densities Calculated by subtracting ground state density from excited state density LRC-TD-DFT and TD- DFT predict similar densities 90% isocontours

Mulliken Charge Differences Possible to decompose transition density matrix into a particle and hole contribution Sum of these two densities is the 1 electron difference density matrix

Mulliken Charge Differences If the electron and hole densities are in the atomic orbital basis: By restricting the summation to AOs on a given atom, this is analogous to a Mulliken charge for the given atom Can also be done for Löwdin charges

Mulliken Charge Differences Charge alternation: Expect for 1La Also see for 1Lb Difference: 1La has charge build-up at the extremities of the molecule Magnitudes smaller for 1La

Valence Bond Theory + + + Ionic Covalent - + + - H H H H H-H H-H States linear combinations of bonding arrangements: Ionic φI>=(|1sa(1)1sa(2)>+|1sb(1)1sb(2)>) Covalent φC>=(|1sa(1)1sb(2)>+|1sb(1)1sa(2)>) Ionic Covalent - + + - H H + + H H H-H + H-H + +

Results: Nonlinear PAHs Extrapolation of LRC- TD-DFT to nonlinear PAHs has not been studied before Previous study for this series -------------------> Also reported large errors for the 1La state

Results: Nonlinear PAHs 1 L a s t a t e : TD-B3LYP: Underestimates energy Worst error large molecules LRC-TD-DFT: Overestimate Worst when TD-B3LYP does well

Results: Nonlinear PAHs 1Lb state Errors not size dependent LRC-TD-DFT exhibits large errors (~0.5 eV) Overestimation by all TD-DFTs Not Corrected Suggested to be ~0.03 eV

Metrics CT metric still fails to predict CT character NTOs still consistent with large spatial overlap

Metrics Difference densities are still similar Mulliken charge differences even more subtle

Conclusions Tozer CT metric fails to predict the failure of B3LYP Other simple metrics (NTOs, Mulliken Charge diffrences, and Diffrence Densities) also fail Is there a simple metric capable of predicting when B3LYP will fail?