To optimize the geometry of a molecule to a first order saddle point, some information about the curvature of the potential energy surface is required. This information is contained within the Hessian matrix, some (or all) of which must be known to step towards a saddle point. Optimization to a first order saddle point requires stepping uphill on the potential energy surface in the direction of the reaction coordinate and downhill in all other directions. We define the reaction coordinate as the direction in which the curvature is smallest (most negative or least positive), which is by construction the leftmost eigenvector of the Hessian matrix. Therefore it is at least necessary to know this eigenvector to step towards a first order saddle point.