For molecular saddle point optimization, it is common to evaluate the full Hessian matrix at least once at the beginning of optimization. Many electronic structure theory methods such as Hartree-Fock and DFT have efficient analytical Hessian implementations. Additionally, transformation of Cartesian Hessians into internal coordinates is straightforward. When using a level of theory for which efficient analytical second derivatives are not available, the Hessian matrix is usually evaluated in full using finite difference. For computationally expensive levels of theory or for very large molecules, the evaluation of the initial Hessian matrix may become more costly than all subsequent geometry optimization steps. Even when using levels of theory with efficient analytical second derivatives, evaluation of the Hessian matrix will eventually dominate the overall cost of optimization as system sizes grow larger due to the higher computational scaling of Hessian evaluations relative to gradient evaluations. For this reason, saddle point optimization methods which do not require full evaluation of the Hessian matrix may be useful for expensive levels of theory and for large systems.