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We show that even order contributions to energy differences between any twoiso-electronic compounds vanish when using perturbation theory around anaveraged electronic reference Hamiltonian. This finding generalizes thepreviously introduced alchemical chirality concept [von Rudorff, vonLilienfeld, Science Advances 7 (2021)] by lifting the symmetry requirements fortransmutating atoms in the iso-electronic reference system. The leading orderterm corresponds to twice the Hellmann-Feynman derivative evaluated using theelectron density of the averaged Hamiltonian. Analogous analysis reveals MelLevy's formula for relative energies [J. Chem. Phys. 70, 1573 (1979)] toinclude the first order contribution while overestimating the higher odd orderenergy contributions by a factor linearly increasing in order. Using densityfunctional theory, we illustrate the predictive power of the leading order termfor estimating relative energies among diatomics in the charge-neutraliso-electronic 14 proton series N2, CO, BF, BeNe, LiNa, HeMg, HAl, and theunited atom, Si. The framework's potential for the simultaneous exploration ofmultiple dimensions in chemical space is demonstrated for toluene by evaluatingrelative energies between all the possible 35 antisymmetric BN doped isomers(dubbed ``alchemical diastereomers''). Based solely on toluene's electrondensity, necessary to evaluate all the respective Hellmann-Feynman derivatives,mean absolute errors of predicted total potential energy differences betweenthe alchemical diastereomers are on the scale of mHa.

Even order contributions to relative energies vanish for antisymmetric perturbations