This updated Hessian can be used to determine the step, △x. The Hessian can be updated in a number of ways, and several algorithmic schemes can be used to determine the step and the new coordinate system along the minimum to get at the optimized geometry. Additionally, the initial estimate of the Hessian or second derivative matrix does have an effect on the performance of geometry optimization with quasi-Newton methods; the more precise the initial estimate, the faster the convergence. One can use an exact Hessian, which is expensive. However, often the estimate does not have to be extremely precise since the Hessian matrix gradually improves in quality as it is updated using gradient information during the search for the minimum. The unit matrix is the most basic and popular approximation, in which case the first optimization step corresponds to a gradient descent. The nature of the atoms, the bonds connecting them, and other pertinent structural information about the molecule are all ignored in this case despite the fact that this is an unbiased choice. All connection between coordinates is initially ignored, and flexible coordinates (such as torsion and ring deformation) are not separated from stiff modes (such as bond stretching). At the price of additional optimization steps, this data must be gathered during the optimization process. For cyclic compounds, whose coordinates are by nature strongly coupled, this is a poor approximation. Simple schemes to approximate the initial Hessian based on parameterized values for bond, angle and dihedral force constants have thus been proposed to reduce the number of required geometry optimization steps. Recently, the integration of machine learning techniques into traditional methods for calculating potential energy surfaces (PES) has led to even more efficient optimization approaches. In particular, machine learning can accelerate the location of minima and transition states. Further discussion on this topic will be presented later in the paper.