Locating saddle points of any index on potential energy surfaces by the generalized gentlest ascent dynamics
Locating saddle points of any index on potential energy surfaces by the generalized gentlest ascent dynamics
W. Quapp, J. M. Bofill
Theor. Chem. Acc., 133 (2014) 1510.
Energy profile over an index-4-GAD trajectory beginning at a LJ7-SP of index 3, to a LJ7-SP of index 4. R is an abstract ’reaction coordinate’, the inlet is the shape of the SPi4.
The system of ordinary differential equations for the method of the gentlest ascent dynamics (GAD) has been derived which was previously proposed [W. E and X. Zhou, Nonlinearity 24, 1831 (2011)]. For this purpose we use diverse projection operators to a given initial direction. Using simple examples we explain the two possibilities of a GAD curve: it can directly find the transition state by a gentlest ascent, or it can go the roundabout way over a turning point and then find the transition state going downhill along its ridge. An outlook to generalised formulas for higher order saddle-points is added.