LoFi samples are distributed equidistantly, whereas HiFi samples are manually selected based on knowledge from LoFi scans. Both strategies are intuitive but not very efficient. The main challenge is the unknown functional form of the to-be-determined PES. We use GPR as explained before as PES surrogate, which we then use to guide our search. This is possible because the GPR also provides the variance. In addition, an acquisition function is needed to allow decision making about where to sample next. In the present application, not only the global minimum of the unknown function is important, but also local minima. Conventional Bayesian optimization acquisition functions can in principle learn to deal with such situations when hyperparameters within these acquisition functions are tailored adjusted to weight between exploration and exploitation. These hyperparameters are difficult to estimate and tend to be problem-specific. Hyperparameter-free solutions in turn are either designed to exploit minima or to explore the whole space equally. In this study, we develop a problem-oriented acquisition function inspired by thermodynamic functional relations. It uses the fact that different features of the PES influence different thermochemical results: from the Boltzmann distribution it follows that low energies are generally more important to thermochemistry than high energies. From experience, the internal energy is strongly dominated by potential energy, i.e. U ≈ E, while entropies may be strongly affected by number of local minima. Such minima are easily overseen or only revealed after many iterations with standard exploitative acquisition functions as they are usually designed to exploit global minima. Of course, it is not possible to represent the thermochemical behaviour emerging from solving the Schrödinger Equation and evaluating all energy levels within a simple function. Instead, inspired by U = A + T S, we design an acquisition function composed of two terms: one term that reflects the importance of low energies and one term that reflects the importance of the curvature and further minima: