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The design of chemical compounds with specific physical, chemical, or biological properties is a central goal of many fundamental as well as industrially relevant research fields. Due to the combinatorial nature of chemical compound space, however, even /in silico/ a systematic screening for interesting properties is beyond any current capacity. Consequently, when it comes to properties that require first principles calculations with atomistic resolution, optimization algorithm must find the ideal compromise between convergence and number of compounds "visited". Analytical gradients in chemical space promise significant speedup in predicting properties of compounds without the need to visit them. In this talk I will present analytical potential energy difference derivatives, based on the Hellmann-Feynman theorem, for any pair of iso-electronic compounds. The energies not being a monotonic function between compounds, these derivatives are insufficient to predict the right trends of the effect of alchemical mutation. Quantitative estimates without additional self-consistency calculations can be made when the Hellmann-Feynman derivative is multiplied with a linearization coefficient that is defined for a reference pair of compounds. These results suggest that accurate predictions can be made regarding any molecule's energetic properties as long as energies and gradients of three other molecules have been provided. Presented numerical evidence includes predictions of electronic eigenvalues of saturated and aromatic molecular hydrocarbons.
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