Combining extrapolation with ghost interaction correction in range-separated ensemble density functional theory for...

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Range-separated density-functional theory (DFT) is used for ground-state calculations.
• Extrapolation techniques improve convergence of calculated energies.
• Existing methods are adapted for excited-state calculations in ensemble DFT.

Purpose of the Study:

• To adapt Savin's extrapolation technique for ghost-interaction-corrected (GIC) range-separated ensemble DFT (eDFT) for excited states.
• To analytically show faster convergence (μ^-3) of GIC eDFT energies compared to standard methods (μ^-2).
• To improve the accuracy of excitation energies at finite range-separation parameters.

Main Methods:

• Adaptation of Savin's extrapolation technique to GIC range-separated eDFT.
• Analytical derivation of the convergence rate for GIC ensemble energies.
• Application to He, H₂, HeH⁺, and LiH systems for various excitation types.

Main Results:

• Demonstrated faster convergence (μ^-3) of GIC eDFT excited-state energies towards wavefunction theory limits.
• Successfully applied the adapted extrapolation method to small atomic and molecular systems.
• Analyzed potential energy profiles and avoided crossings for singlet Σ⁺ excitations in HeH⁺ and H₂.

Conclusions:

• The adapted extrapolation method provides a more efficient route to accurate excited-state energies in GIC range-separated eDFT.
• Faster convergence allows for improved accuracy at practical, smaller values of the range-separation parameter.
• Future work may involve extracting individual state energies from ensemble calculations.