Failures of TDDFT in describing the lowest intramolecular charge-transfer excitation in para-nitroaniline

Abstract

We investigate the failure of time-dependent density functional theory (TDDFT) with the CAM-B3LYP exchange-correlation (xc) functional coupled to the polarisable embedding (PE) scheme (PE-CAM-B3LYP) in reproducing the solvatochromic shift of the lowest intense charge-transfer excitation in para-nitroaniline (pNA) in water by comparing with results obtained with the coupled cluster singles and doubles (CCSD) model also coupled to the polarisable embedding scheme (PE-CCSD). We determine the amount of charge separation in the ground and excited charge-transfer state with both methods by calculating the electric dipole moments in the gas phase and for 100 solvent configurations. We find that CAM-B3LYP overestimates the amount of charge separation inherent in the ground state and TDDFT/CAM-B3LYP drastically underestimates this amount in the excited charge-transfer state. As the errors in the solvatochromatic shift are found to be inverse proportional to the change in dipole moment upon excitation, we conclude that the flaws in the description of the solvatochromic shift of this excitation are related to TDDFT itself and how it responds to the solvent effects modelled by the PE scheme. We recommend therefore to benchmark results of TDDFT calculations with CAM-B3LYP for intramolecular charge-transfer excitations in molecular systems similar to pNA against higher level ab initio wave function methods, like, e.g. CCSD, prior to their use. Using the calculated change in dipole moment upon excitation as a measure for charge-transfer character, we furthermore confirm that the difference between excitation energies calculated with TDDFT and with the Tamm–Dancoff approximation (TDA) to TDDFT is indeed correlated with the charge-transfer character of a given electronic transition both in vacuo and in solution. This is supported by a corresponding correlation between the change in dipole moment and the size of the Λ index diagnostic for the investigated CT excitation.

Keywords:

• time-dependent density functional theory
• TDDFT
• CAM-B3LYP
• para-nitroaniline
• solvatochromic shift
• charge-transfer excitation
• lambda diagnostic
• Tamm–Dancoff approximation

Acknowledgements

The authors would all like to congratulate Professor Dr. Trygve Helgaker on the occasion of his 60th birthday. In this work, we have used many features of the dalton program written by Prof. Helgaker, and we have been inspired by his thorough analyses of the application of DFT/TDDFT to molecular systems, his results in the literature and the Λ diagnostic. Furthermore, the authors wish to express their most sincere acknowledgments to the immense impact he has had on the scientific community for decades, as a mentor as well as a collaborator.

 The authors also thank Dr. Kristian Sneskov for fruitful discussions regarding the experimental PE-CCSD code and the journal referees for insightful comments.

 The authors thank the Danish Center for Scientific Computing. J.K. thanks The Danish Councils for Independent Research (STENO and Sapere Aude programmes), The Lundbeck Foundation, and The Willum Foundation for financial support.

Additional information

Notes on contributors

Janus J. Eriksen

Present address: qLEAP Center for Theoretical Chemistry, Department of Chemistry, Aarhus University, Langelandsgade 140, DK-8000 Aarhus C, Denmark