Density-functional methods give accurate vibrational frequencies and spin densities for phenoxyl radical

Abstract

The structure, electronic spin density ratios, harmonic vibrational frequencies, and deuterium isotopic vibrational frequency shifts for phenoxyl radical, C6H5Ȯ, were calculated by using spin unrestricted Hartree–Fock (UHF), second-order Mo/ller–Plesset perturbation (UMP2), and various density functional (DF) and hybrid Hartree–Fock/density functional (HF/DF) methods with a 6–31G(d) basis set. Computed results are compared with experiment and with recently published complete active space self-consistent field (CASSCF) and unrestricted natural orbital-complete active space (UNO-CAS) calculations to evaluate the accuracy of DF and HF/DF methods for the highly delocalized, strongly correlated phenoxyl radical. Bond lengths and angles calculated by using DF and HF/DF methods appear as accurate as those obtained by using the UMP2 method. The correlation functional of Vosko, Wilk, and Nusair combined with Slater’s exchange functional (SVWN) gives a structure closest to the best available CASSCF calculations, with the structures from three parameter hybrid HF/DF methods (B3P86 and B3LYP) nearly as good. Electronic spin density ratios computed by using DF methods are closest to experimentally derived spin density ratios, UHF spin densities are the worst, and the hybrid HF/DF methods give intermediate quality spin density ratios. Unscaled vibrational frequencies from the DF and HF/DF methods are closer to experimentally measured frequencies than uniformly scaled UHF or UMP2 frequencies. Unscaled frequencies calculated by using the B3LYP method, for example, differ from the nine experimentally observed frequencies by an average of only 22 cm−1. The vibrational mode of phenoxyl radical observed experimentally at 1552 cm−1 is confirmed to correspond to a C=C stretching vibration and the band observed at 1505 cm−1 is primarily a C–O stretch. Vibrational modes of phenoxyl radical shift to lower frequencies upon deuteration and the larger shift of the C=C stretch, compared to the C–O stretch, confirms their assignment. Thus density functional methods give electronic spin density ratios, vibrational frequencies, mode assignments, and isotopic frequency shifts in good agreement with experiment and with more expensive UNO-CAS//CASSCF calculations for phenoxyl radical.