Approximately spin-projected Hessian for broken symmetry method and stretching frequencies of F2 and singlet O2



An approximate spin projection (AP) method is applied to a second derivative of energy (Hessian) of the broken-symmetry (BS) method in order to eliminate a spin contamination error. Stretching frequencies of F2 (X1math image) and singlet molecular oxygen (a1Δg) are calculated by using the spin-projected Hessian (AP Hessian). In case of F2 molecule, a potential curve of an unrestricted Hartree-Fock (UHF) method does not have an energy minimum but the stretching frequency can be calculated by the AP UHF method. The difference in the calculated stretching frequencies between a restricted HF (RHF) and the AP UHF methods is 650–700 cm−1, and indicates that a static correlation correction is a crucial to consider the frequency. On the other hand, we cannot find a significant difference in calculated frequencies of RHF and AP-BS HF in case of 1O2 molecule within the HF method. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009