Evaluating quantum alchemy of atoms with thermodynamic cycles: Beyond ground electronic states

Due to the sheer size of chemical and materials space, high-throughput computational screening thereof will require the development of new computational methods that are accurate, efficient, and transferable. These methods need to be applicable to electron configurations beyond ground states. To this end, we have systematically studied the applicability of quantum alchemy predictions using a Taylor series expansion on quantum mechanics (QM) calculations for single atoms with different electronic structures arising from different net charges and electron spin multiplicities. We first compare QM method accuracy to experimental quantities, including first and second ionization energies, electron affinities, and spin multiplet energy gaps, for a baseline understanding of QM reference data. Next, we investigate the intrinsic accuracy of "manual" quantum alchemy. This method uses QM calculations involving nuclear charge perturbations of one atom's basis set to model another. We then discuss the reliability of quantum alchemy based on Taylor series approximations at different orders of truncation. Overall, we find that the errors from finite basis set treatments in quantum alchemy are significantly reduced when thermodynamic cycles are employed, which highlights a route to improve quantum alchemy in explorations of chemical space. This work establishes important technical aspects that impact the accuracy of quantum alchemy predictions using a Taylor series and provides a foundation for further quantum alchemy studies.