Interpolating between Hamiltonians of different isoelectronic systems connects points in chemical space and allows for a series expansion not only in the Hamiltonian but also in the solution of Schrödinger's equation, also called Quantum Alchemy. Truncating this expansion yields a closed-form expression for the energy and one-electron properties for many close-by systems [1] which can be systematically improved within the substantial convergence radius of the expansion[2]. This expression allows to identify alchemical enantiomers [3] which are pairs of compounds that need to be degenerate in their electronic energy up to third order of the perturbative expansion. Most interestingly, this new and fundamental constraint on chemical space is independent of bond topology, which simplifies material design problems due to the effectively reduced dimensionality of the search space. This is exemplified by using alchemical enantiomers to obtain new rules for electronic energy contributions to chemical bonding and for ranking 400 million BN-doped picene derivatives, respectively.
Typically, the Quantum Alchemy expansion requires the evaluation of electron density derivatives. A new approach, the Alchemical Integral Transform, [4] allows to trade derivatives of the electron density for derivatives of the perturbing potential which is known analytically. This improves over the 2n+1 textbook statement that the n-th order perturbation of the wavefunction is sufficient to obtain the 2n+1-th energy perturbation. Demonstrated here for single atoms, this approach might be extendable to molecules, allowing to approximate chemical space more efficiently based on unperturbed densities alone.
[1] Alchemical Perturbation Density Functional Theory, GF von Rudorff, OA von Lilienfeld, Phys. Rev. Res. 2020, 2, 023220.
[2] Arbitrarily accurate quantum alchemy, GF von Rudorff, J. Chem. Phys. 2021, 155(22), 224103.
[3] Simplifying inverse materials design problems for fixed lattices with alchemical chirality, GF von Rudorff, OA von Lilienfeld, Sci. Adv. 2021, 7, eabf1173.
[4] Relative energies without electronic perturbations via integral transform, SL Krug, GF von Rudorff, OA von Lilienfeld, arXiv 2022, 2203.13794.
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