Constraints as in Table can be used to enforce e.g. symmetry or certain paths in the search of a transition state. If there are no constraints and all internal degrees of freedom are to be optimized, our method is unfortunately inferior to the unconstrained optimization in the common non-hierarchical internal coordinates. More detailed results for the comparison of unconstrained geometry optimizations on the Baker test set 48 of 30 molecules can be found in the supporting information. One explanation for the worse performance is that in general the Hessian in Z-matrix coordinates will have a larger variation in the diagonal elements, because those coordinates at the top of the table greatly affect the overall structure and will in general have a larger gradient and hessian diagonal element. For this reason the usual approximations and perfomance enhancements such as a model Hessian or step restrictions based on chemical knowledge cannot be applied. If we also allow arbitrary differentiable expressions for constrained optimisations then there cannot be a "one size fits all" approximation.