1. 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

2. 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 , 292, 11.
Wong, B. M.; Hsieh, T. H. JCTC. 2010, 6, 3704.

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

4. Results: LCAs

5. 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:

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

7. 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

8. 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

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

10. 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

11. 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

12. 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

13. 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 + +

14. 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

15. 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

16. 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

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

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

19. 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?