Figure : An illustration of the null-space SQP method. The initial point q has gradient g (red) and does not lie on the constraint manifold (green). The constraint-correction displacement vector s P leads to the closest point on the constraint manifold. The extrapolated gradient g ex (orange) is the sum of the original gradient g and the approximate gradient Bs P (yellow) created by the displacement assuming constant curvature of the potential energy surface. The optimization displacement s Q is calculated with this extrapolated gradient in the space tangent to the constraint manifold and orthogonal to s P . These two displacement vectors are combined into the overall displacement vector s.