Simplifying inverse material design problems for fixed lattices with alchemical chirality

Abstract: Massive brute-force compute campaigns relying on demanding ab initio calculations routinely search for novel materials in chemical compound space, the vast virtual set of all conceivable stable combinations of elements and structural configurations which form matter. Here we demonstrate that 4-dimensional chirality, arising from anti-symmetry of alchemical perturbations, dissects that space and defines approximate ranks which effectively reduce its formal dimensionality, and enable us to break down its combinatorial scaling. The resulting distinct alchemical' enantiomers must share the exact same electronic energy up to third order -- independent of respective covalent bond topology, and imposing relevant constraints on chemical bonding. Alchemical chirality deepens our understanding of chemical compound space and enables theon-the-fly' establishment of new trends without empiricism for any materials with fixed lattices. We demonstrate its efficacy for three such cases: i) new formulas for estimating electronic energy contributions to chemical bonding; ii) analysis of the perturbed electron density of BN doped benzene; and iii) ranking stability estimates for BN doping in over 2,000 naphthalene and over 400 million picene derivatives.