Vibrational Frequencies of Fractionally Charged Molecular Species: Benchmarking DFT Results against ab Initio Calculations

Recent advances in nano/molecular electronics and electro-chemistry made it possible to continuously tune the fractional charge q of single molecules and to use vibrational spectroscopic methods to monitor such changes. Approaches to compute vibrational frequencies omega(q) of fractionally charged species based on the density functional theory (DFT) are faced with an important issue: the basic quantity used in these calculations, the total energy, should exhibit piecewise linearity with respect to the fractional charge, but approximate, commonly utilized exchange correlation functionals do not obey this condition. In this paper, with the aid of a simple and representative example, we benchmark results for omega(q) obtained within the DFT against ab initio methods, namely, coupled cluster singles and doubles and also second- and third-order Moller-Plesset perturbation) expansions. These results indicate that, in spite of missing the aforementioned piecewise linearity, DFT-based values omega(q) can reasonably be trusted.