Ascorbic acid is a well-known antioxidant and radical scavenger. It can be oxidized by losing two protons and two electrons, but normally loses only one electron at a time. The reactivity of the ascorbate radical is unusual, in that it can either disproportionate or react with other radicals, but it reacts poorly with non-radical species. To explore the oxidation mechanism of ascorbic acid, the pK_a's and reduction potentials have been calculated using the B3LYP/6-31+G(d,p) and CBS-QB3 levels of theory with the SMD implicit solvent model and explicit waters. Calculations show that the most stable form of dehydroascorbic acid in water is the bicyclic hydrated structure, in agreement with NMR studies. The possible oxidation reactions at different pH conditions can be understood by constructing a potential-pH (Pourbaix) diagram from the calculated pK_a's and standard reduction potentials. At physiological pH disproportionation of the intermediate radical is thermodynamically favored. The calculations show that disproportionation proceeds via dimerization of ascorbate radical and internal electron transfer, as suggested by Bielski. In the dimer, one of the ascorbate units cyclizes. Then protonation and dissociation yields the fully reduced and bicyclic fully oxidized structures. Calculations show that this mechanism also explains the reaction of the ascorbic acid radical with other radical species such as superoxide. Ascorbate radical combines with the radical, and intramolecular electron transfer followed by cyclization and hydrolysis yields dehydroascorbic acid and converts the radical to its reduced form.

The geometry optimization using direct inversion in the iterative subspace (GDIIS) has been implemented in a number of computer programs and is found to be quite efficient in the quadratic vicinity of a minimum. However, far from a minimum, the original method may fail in three typical ways: (a) convergence to a nearby critical point of higher order (e.g. transition structure), (b) oscillation around an inflection point on the potential energy surface, (c) numerical instability problems in determining the GDIIS coefficients. An improved algorithm is presented that overcomes these difficulties. The modifications include: (a) a series of tests to control the construction of an acceptable GDIIS step, (b) use of a full Hessian update rather than a fixed Hessian, (c) a more stable method for calculating the DIIS coefficients. For a set of small molecules used to test geometry optimization algorithms, the controlled GDIIS method overcomes all of the problems of the original GDIIS method, and performs as well as a quasi-Newton RFO (rational function optimization) method. For larger molecules and very tight convergence, the controlled GDIIS method shows some improvement over an RFO method. With a properly chosen Hessian update method, the present algorithm can also be used in the same form to optimize higher order critical points.