The use of machine learning models such as GPR with efficient kernel functions 24 in conjunction with different internal coordinate systems can also reduce the number of required optimization cycles. For instance, Meyer and Hauser achieved 225 steps for the Baker test set by using reduced redundancy Z-matrix-derived internal coordinates with HF/STO-3G. Raggi et al. introduced a restricted-variance optimization (RVO) scheme that utilizes a Hessian model function to generate a non-redundant set of internal coordinates for molecular geometries, making the surrogate model invariant to translations and rotations. With the HF/6-31G basis set, they achieved 225 steps using RVO, while with DFT(B3LYP)/def2-SVP, they obtained 241 steps. Teng, Huang, and Bao demonstrated that combining the gradient-enhanced universal kriging (GEUK) algorithm with an adaptive ab initio prior mean function, which incorporates prior physical knowledge into surrogate-based optimization, and incomplete internal/incomplete Cartesian methods can reduce the number of steps to 165 as shown for the BP86/def2-SVP level of theory. Herein we explored several different open-source quasi-Newton approaches (L-BFGS and some modified BFGS algorithms) and available machine learning (GPR) models, utilizing various internal coordinate systems with either the unit matrix as the starting Hessian (as in the L-BFGS approaches) or a more sophisticated first estimate (geomeTRIC, ASE/Berny, ASE/Sella). In all cases, not unexpectedly, internal coordinates outperformed methods using Cartesian coordinates, but the numerical details of the implementation of the internal coordinate methods make a significant difference (e.g., ASE/Berny versus geomeTRIC).