On the potential energy surface, the gradient, g(x), vanishes at a stationary point, g(x) ≡ ∇E = 0. Hence, in the local quadratic approximation of the potential energy surface, the displacement to the minimum at the stationary point is given by: △x = -H -1 0 g 0 This is known as the Newton-Raphson step. It is an integral part of almost all quantum chemistry geometry optimization approaches. The gradient here can be obtained by differentiation of the energy with respect to the coordinates, and the Hessian can be obtained using numerical or analytical methods of the second derivative of the energy with respect to the coordinates.