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 multiplet spin energy gaps for a baseline understanding of QM reference data. We then investigate the intrinsic accuracy of an approach we call "manual" quantum alchemy schemes compared to the same QM reference data, which employ QM calculations where the basis set of a different element is used for an atom as the limit case of quantum alchemy. 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 points out 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.