Atomistic studies are of interest for a variety of stationary points, such as minima, transition states, and conical intersections. The most effective and extensively used techniques for identifying these stationary points are Newton and quasi-Newton techniques, which typically employ a sequential optimization cycle, in which a guess optimal geometry is steadily enhanced by employing the gradient and either an exact or an approximate Hessian. For minimization, the Hessian must contain exclusively positive eigenvalues (i.e., positive definite). If one or more eigenvalues are negative, the step will be in the direction of a first-order or higher-order saddle point, which can be useful when locating a transition state.