An improved long-range corrected hybrid functional with vanishing Hartree–Fock exchange at zero interelectronic distance (LC2gau-BOP)

We present a new long-range corrected (LC) density functional theory (DFT) scheme, named "LC2gau," which combines the best features of our two recently developed hybrid functionals, "LCgau" [J.-W. Song et al., J. Chem. Phys. 127, 154109 (2007)] and "LCgau-core" [J.-W. Song et al., J. Chem. Phys. 129, 184113 (2008)]. By introducing a flexible mixing of Hartree-Fock and DFT exchange in the LCgau scheme, we showed that a DFT functional could simultaneously achieve high accuracy in the reproduction of thermochemical properties, molecular geometries, as well as charge transfer and valence-Rydberg excitation energies. With an alternative mixing of short-range exchange, LCgau-core can reproduce core excitations with high accuracy, especially in the C, N, and O atoms, but at the expense of slightly higher atomization energy errors. We now show that LC2gau can simultaneously perform well for all types of excitations, as well as thermochemistry. In contrast to the previously proposed LC functionals, a notable feature is the inclusion of 100% DFT exchange as the interelectronic distance vanishes, showing that pure DFT approximations can be successfully used at short range, and the importance of including an appropriate correction in the midrange. This is achieved using two Gaussian functions in combination with the error function to describe the exchange partitioning. We rationalize the success of LC2gau by demonstrating a near-linear behavior of the total energies of the C atom as a function of the fractional number of electrons, both in the valence and core regions, which indicates an alleviation of significant self-interaction errors observed with other functionals.