Reliability of Density Functional and Perturbation Theories for Calculating Core-Ionization Spectra of Free Radicals.

The C 1s, N 1s, and O 1s ionization energies were calculated for the three stable nitroxide free radicals, viz., tempo and its two analogues, and compared to their most recent high-resolution core photoelectron spectra. We compare the performance of unrestricted and restricted open shell based ΔHF, ΔMP2, and ΔB3LYP methods. A mixed basis set is employed in all cases, which consists of the core-valence correlation-consistent triple-ζ basis set (cc-pCVTZ or cc-pwCVTZ) on the atom whose core-electron binding energy is calculated, model core potentials on the remaining first row atoms, and the cc-pVDZ basis set on the hydrogen atoms. The best overall performance for the three free radicals is offered by the restricted open shell based ΔB3LYP method. Surprisingly, both the restricted open and unrestricted second-order perturbation theories perform relatively poorly and typically do not warrant additional computational effort over the reference ΔHF methods. This is particularly true of the ΔZAPT method, which exhibits a number of grave failures that render it unsuitable for calculating the core-ionization spectra.