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