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

In this article, we show that the long-range-corrected (LC) density functionals LC-BOP and LCgau-BOP reproduce frontier orbital energies and highest-occupied molecular orbital (HOMO)-lowest-unoccupied molecular orbital (LUMO) gaps better than other density functionals. The negative of HOMO and LUMO energies are compared with the vertical ionization potentials (IPs) and electron affinities, respectively, using CCSD(T)/6-311++G(3df,3pd) for 113 molecules, and we found LC functionals to satisfy Koopmans' theorem. We also report that the frontier orbital energies and the HOMO-LUMO gaps of LC-BOP and LCgau-BOP are better than those of recently proposed ωM05-D (Lin et al., J. Chem. Phys. 2012, 136, 154109). We express the exact IP in terms of orbital relaxation, and correlation energies and hence calculate the relaxation and correlation energies for the same set of molecules. It is found that the LC functionals, in general, includes more relaxation effect than Hartree-Fock and more correlation effect than the other density functionals without LC scheme. Finally, we scan μ parameter in LC scheme from 0.1 to 0.6 bohr(-1) for the above test set molecules with LC-BOP functional and found our parameter value, 0.47 bohr(-1), is usefully applicable to our tested systems.