Since the Cartesian coordinate system is the easiest approach to define the molecular geom-etry, it is usually used for the evaluation of the energy and gradient. However, the potential energy surface is strongly nonlinear and coordinates are coupled, so only small steps can be taken downhill. Cartesian coordinates perform significantly worse for flexible, acyclic systems than they do for constrained, cyclic molecules. In Cartesian coordinates, it is also much harder to impose constraints. Internal coordinates on the other hand are better at reflecting the overall atomic motions. Internal coordinates can describe displacements along curved pathways and decouple various types of molecular displacements. As a result, the optimization algorithm can proceed with greater efficiency. It is possible to calculate the entire Hessian matrix analytically for each step at the current point on the potential energy surface. Only one step is needed to get to the minimum of the energy if the local potential energy surface is quadratic. Since actual potential energy surfaces are rarely quadratic, one must take several Newton-Raphson steps to get at a stationary point. It is thus often impractical or undesirable to directly calculate the full Hessian due to the amount of computational work this typically involves. Instead one can resort to quasi-Newton techniques, whose foundation is a computationally cheap approximation of the Hessian. At each stage of a quasi-Newton optimization, the Hessian is improved using the difference between the calculated gradient change and the change anticipated by the approximate Hessian.