  We use energies and forces predicted within response operator based quantum
machine learning (OQML) to perform geometry optimization and transition state
search calculations with legacy optimizers. For randomly sampled initial
coordinates of small organic query molecules we report systematic improvement
of equilibrium and transition state geometry output as training set sizes
increase. Out-of-sample S$_\mathrm{N}$2 reactant complexes and transition state
geometries have been predicted using the LBFGS and the QST2 algorithm with an
RMSD of 0.16 and 0.4 \r{A} -- after training on up to 200 reactant complexes
relaxations and transition state search trajectories from the QMrxn20 data-set,
respectively. For geometry optimizations, we have also considered relaxation
paths up to 5'500 constitutional isomers with sum formula C$_7$H$_{10}$O$_2$
from the QM9-database. Using the resulting OQML models with an LBFGS optimizer
reproduces the minimum geometry with an RMSD of 0.14~\r{A}. For converged
equilibrium and transition state geometries subsequent vibrational normal mode
frequency analysis indicates deviation from MP2 reference results by on average
14 and 26\,cm$^{-1}$, respectively. While the numerical cost for OQML
predictions is negligible in comparison to DFT or MP2, the number of steps
until convergence is typically larger in either case. The success rate for
reaching convergence, however, improves systematically with training set size,
underscoring OQML's potential for universal applicability.
