How Do Virtual Orbitals Influence Charge-Transfer Excitations in ΔSCF Calculations? Insights from Constricted...

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Spectroscopy

Background:

• Accurate calculation of excited states, especially those involving charge transfer (CT), is crucial in computational chemistry.
• Traditional methods may struggle with the variational instability of excited states with significant charge separation.
• The role of virtual orbitals in variational excited-state calculations needs further clarification.

Purpose of the Study:

• To comprehensively evaluate constricted variational density functional theory (CV-DFT) for intra- and intermolecular singlet-singlet excitations.
• To understand the influence of virtual orbitals and initial guess methods on CV-DFT robustness for charge-transfer excitations.
• To identify suitable CV-DFT schemes for different degrees of charge transfer (CT).

Main Methods:

• Evaluation of constricted variational density functional theory (CV-DFT) for excited states with varying charge transfer (CT) distances (dCT).
• Investigation of different initial guess methods: TDDFT, sTDDFT, and TDDFT+TB.
• Application of SCF-CV(∞)-DFT with orbital relaxation and SOR-R-CV(∞)-DFT with frozen natural transition orbitals (NTOs).

Main Results:

• Mild CT states (dCT ≤ 1.50 Å) do not require variational calculations.
• Strong CT states (dCT ≥ 1.50 Å) benefit from CV-DFT, with SCF-CV(∞)-DFT yielding improved excitation energies (RMSE ≈ 0.33 eV with hybrid functionals).
• For fully charge-separated states (dCT ≥ 2.50 Å), SCF-CV(∞)-DFT becomes unstable; SOR-R-CV(∞)-DFT with frozen NTOs provides accurate results.

Conclusions:

• CV-DFT is a robust method for excited states with varying degrees of charge transfer.
• SCF-CV(∞)-DFT with orbital relaxation is effective for strong CT states, while SOR-R-CV(∞)-DFT is necessary for charge-separated states.
• Optimizing and relaxing virtual orbitals within CV-DFT enables accurate variational calculations of excited states.