A revised electronic Hessian for approximate time-dependent density functional theory.

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Theoretical Physics

Background:

• Time-dependent density functional theory (TD-DFT) with generalized gradient approximation (GGA) exhibits systematic errors in calculating excitation energies.
• These errors are particularly pronounced for electronic transitions involving spatially separated regions or orbitals of differing extents.
• The limitations are linked to the electronic ground state Hessian within GGA (G(GGA)).

Purpose of the Study:

• To investigate the limitations of G(GGA) in TD-DFT for calculating excitation energies.
• To demonstrate that G(GGA) is unsuitable for one-electron excitations involving significant density rearrangement.
• To develop an improved theoretical framework for accurate excitation energy calculations in TD-DFT.

Main Methods:

• Analysis of the electronic ground state Hessian in Hartree-Fock (HF) and GGA functionals.
• Derivation of a new Hessian matrix, G(R-DFT), accounting for incomplete self-interaction cancellation (ISIC).
• Application of TD-DFT with G(R-DFT) to calculate state-to-state transition energies, specifically for charge-transfer excitations.

Main Results:

• G(GGA) is accurate for small density perturbations but fails for one-electron excitations with full charge rearrangement.
• Hartree-Fock theory's G(HF) has a larger trust region due to complete self-interaction cancellation (CSIC).
• The new G(R-DFT) matrix demonstrates a trust region comparable to G(HF) by properly including ISIC terms.
• TD-DFT calculations using G(R-DFT) provide accurate approximations for charge-transfer excitation energies.

Conclusions:

• Approximate TD-DFT methods require higher-order response theory, including ISIC terms, to accurately describe charge-transfer excitations.
• The developed G(R-DFT) offers a more reliable approach for excitation energy calculations in TD-DFT.
• This work highlights the importance of addressing self-interaction errors in DFT for accurate electronic excitation predictions.