We report the calculations of core-excitation energies of first-row atoms using the time-dependent density functional theory (DFT) and the long-range correction (LC) scheme for exchange-correlation functionals, including LC-BOP, Coulomb-attenuated method BLYP, and our recently developed LCgau-BOP method, which includes a flexible portion of short-range Hartree-Fock (HF) exchange through the inclusion of a Gaussian function in the LC scheme. We show that the LC scheme completely fails to improve the poor accuracy of conventional generalized gradient approximation functionals, while the LCgau scheme gives an accuracy which is an order of magnitude better than BLYP and significantly better than B3LYP. A reoptimization of the two parameters controlling the inclusion of short-range HF exchange in the LCgau method enables the errors to be reduced to the order of 0.1 eV which is competitive with the best DFT methods we are aware of. This reparametrization does not affect the LC scheme and therefore maintains the high accuracy of predicted reaction barrier heights. Moreover, while there is some loss in accuracy in thermochemical predictions compared to the previously optimized LCgau-BOP, rms errors in the atomization energies over the G2 test set are found to be comparable to B3LYP. Finally, we attempt to rationalize the success of the LC and LCgau schemes in terms of the well-known self-interaction error (SIE) of conventional functionals. To estimate the role of the SIE, we examine the total energy calculations for systems with a fractional number of electrons, not only in the highest occupied molecular orbital but also in the 1s-characterized core orbital. Our conclusion is that the inclusion of short-range HF exchange in LC-type functionals can significantly alleviate the problems of the SIE in the core region. In particular, we confirm that the absence of the SIE diagnostics in the core orbital energies correlates with the accurate prediction of core-excitation energies using the newly optimized LCgau approach.

The core-valence-Rydberg Becke's three-parameter exchange (B3)+Lee-Yang-Parr (LYP) correlation functional (CVR-B3LYP) is proposed as a means to improve descriptions of Rydberg excitations of core-valence B3LYP (CV-B3LYP). CV-B3LYP describes excitations from both core and occupied valence orbitals to unoccupied valence orbitals with high accuracy but fails to describe those to Rydberg orbitals. CVR-B3LYP, which adopts the appropriate portions of Hartree-Fock exchange for unoccupied valence and Rydberg regions separately, overcomes the disadvantage of CV-B3LYP. Numerical assessment confirms that time-dependent density functional theory calculations with CVR-B3LYP succeed in describing not only core excitations but also Rydberg excitations with reasonable accuracy.

A new hybrid functional for accurate descriptions of core and valence excitations, the core-valence Becke's three-parameter exchange (B3)+Lee-Yang-Paar (LYP) correlation functional (CV-B3LYP), is proposed. The construction of the new hybrid functional is based on the assessment that B3LYP performs well for properties concerning valence electrons and Becke's half-and-half exchange+LYP functional (BHHLYP), which includes 50% portion of Hartree-Fock exchange, performs well for core excitations. By using the appropriate portions of Hartree-Fock exchange for core and valence regions separately, CV-B3LYP overcomes the disadvantages of BHHLYP and B3LYP, which give inferior descriptions of valence and core excitations, respectively. Density functional theory (DFT) calculations with the CV-B3LYP functional reproduce core- and valence-orbital energies close to those of BHHLYP and B3LYP, respectively. Time-dependent DFT calculations with the CV-B3LYP functional yield both core- and valence-excitation energies with reasonable accuracy.

A well-defined nano-cobalt phosphide serves as an air-stable, highly active and reusable heterogeneous catalyst for the selective hydrogenation of nitriles to primary amines under mild reaction conditions.