Long-range corrected functionals satisfy Koopmans' theorem: calculation of correlation and relaxation energies

Area of Science:

• Computational Chemistry
• Quantum Chemistry

Background:

• Accurate prediction of molecular electronic properties like frontier orbital energies and HOMO-LUMO gaps is crucial in chemistry.
• Traditional density functionals often struggle to accurately describe these properties, particularly for systems requiring long-range electron interactions.

Purpose of the Study:

• To evaluate the performance of long-range-corrected (LC) density functionals, specifically LC-BOP and LCgau-BOP, in reproducing frontier orbital energies and HOMO-LUMO gaps.
• To compare the accuracy of LC-BOP and LCgau-BOP against other density functionals, including the recently proposed ωM05-D.
• To analyze orbital relaxation and correlation energies in relation to density functional approximations.

Main Methods:

• Calculated vertical ionization potentials (IPs) and electron affinities for 113 molecules using the CCSD(T)/6-311++G(3df,3pd) high-level theoretical method.
• Compared the negative of highest-occupied molecular orbital (HOMO) and lowest-unoccupied molecular orbital (LUMO) energies from LC-BOP and LCgau-BOP with calculated IPs and electron affinities.
• Investigated orbital relaxation and correlation energies for the test set of molecules.

Main Results:

• LC-BOP and LCgau-BOP demonstrate superior accuracy in reproducing frontier orbital energies and HOMO-LUMO gaps compared to other tested density functionals.
• LC functionals were found to satisfy Koopmans' theorem, relating orbital energies to IPs and electron affinities.
• LC functionals incorporate more relaxation and correlation effects than Hartree-Fock and non-LC density functionals, respectively.
• An optimal parameter value (μ = 0.47 bohr⁻¹) for the LC-BOP functional was identified and validated across the tested molecular systems.

Conclusions:

• Long-range-corrected density functionals, LC-BOP and LCgau-BOP, offer significant improvements for predicting key electronic properties.
• These findings highlight the utility of LC functionals in computational chemistry for accurate molecular electronic structure analysis.
• The optimized LC-BOP functional with a specific μ parameter provides a reliable tool for future electronic structure calculations.