Simplifying inverse materials design problems for fixed lattices with alchemical chirality

Rudorff, Guido Falk von; Lilienfeld, O. Anatole von

doi:10.1126/sciadv.abf1173

Cited by 15 publications

(15 citation statements)

References 84 publications

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“…In Figure 1 (a), clear steps can be observed since all odd orders to not contribute to the final accuracy. This is due to the symmetry [2,8] of the system and can also be observed for the case of N 2 → CO in panel (b) of the same figure. Since this behaviour is a consequence of the symmetry of the perturbation, this step-wise convergence is a necessary criterion for numerical stability.…”

Section: Resultssupporting

confidence: 72%

“…While some formulations even allow for a change in numbers of electrons [6,7], this work considers isoelectronic changes only. * guido.vonrudorff@univie.ac.at Even though these pen-and-paper formulations already allow for fundamental insights such as quasisymmetries [8] in chemical space or tests of the nearsightedness of the electron density [9], the underlying assumption-the convergence of the Taylor series-has only been postulated and motivated. Numerical tests so far are limited by the numerical accuracy and the finite number of expansion terms that could be calculated.…”

Section: Introductionmentioning

confidence: 99%

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Arbitrarily Precise Quantum Alchemy

Rudorff¹

2021

Preprint

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Doping compounds can be considered a perturbation to the nuclear charges in a molecular Hamiltonian. Expansions of this perturbation in a Taylor series, i.e. quantum alchemy, has been used in literature to assess millions of derivative compounds at once rather than enumerating them in costly quantum chemistry calculations. So far, it was unclear whether this series even converges for small molecules, whether it can be used for geometry relaxation and how strong this perturbation may be to still obtain convergent numbers. This work provides numerical evidence that this expansion converges and recovers the self-consistent energy of Hartree-Fock calculations. The convergence radius of this expansion is quantified for dimer examples and systematically evaluated for different basis sets, allowing for estimates of the chemical space that can be covered by perturbing one reference calculation alone. Besides electronic energy, convergence is shown for density matrix elements, molecular orbital energies, and density profiles, even for large changes in electronic structure, e.g. transforming He3 into H6. Subsequently, mixed alchemical and spatial derivatives are used to relax H2 from the electronic structure of He alone, highlighting a path to spatially relaxed quantum alchemy. Finally, the underlying code (APHF) which allows for arbitrary precision evaluation of restricted Hartree-Fock energies and arbitrary-order derivatives is made available to support future method development.

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Section: Resultssupporting

confidence: 72%

Section: Introductionmentioning

confidence: 99%

Arbitrarily Precise Quantum Alchemy

Rudorff¹

2021

Preprint

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“…86,87 We note, however, that these trends change upon removal of the nuclear repulsion terms which do not affect the electronics. The predicted energy ordering is the same, both for the vertical and the relaxed energies, the relaxation calculated only with the first order alchemical force is in fact not able to discriminate alchemical enantiomers 88 and does not change the energy order.…”

Section: B-n Doping Of Benzenementioning

confidence: 63%

Alchemical geometry relaxation

Domenichini¹,

Lilienfeld²

2022

Preprint

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We propose to relax geometries throughout chemical compound space (CCS) using alchemical perturbation density functional theory (APDFT). APDFT refers to perturbation theory involving changes in nuclear charges within approximate solutions to Schrödinger's equation. We give an analytical formula to calculate the mixed second order energy derivatives with respect to both, nuclear charges and nuclear positions (named "alchemical force"), within the restricted Hartree-Fock case. We have implemented and studied the formula for its use in geometry relaxation of various reference and target molecules. We have also analysed the convergence of the alchemical force perturbation series, as well as basis set effects. Interpolating alchemically predicted energies, forces, and Hessian to a Morse potential yields more accurate geometries and equilibrium energies than when performing a standard Newton Raphson step. Our numerical predictions for small molecules including BF, CO, N2, CH 4 , NH 3 , H 2 O, and HF yield mean absolute errors of of equilibrium energies and bond lengths smaller than 10 mHa and 0.01 Bohr for 4 th order APDFT predictions, respectively. Our alchemical geometry relaxation still preserves the combinatorial efficiency of APDFT: Based on a single coupled perturbed Hartree Fock derivative for benzene we provide numerical predictions of equilibrium energies and relaxed structures of all the 17 iso-electronic charge-netural BN-doped mutants with averaged absolute deviations of ∼27 mHa and ∼0.12 Bohr, respectively.

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“…For this endeavor to be successful, it was necessary to improve on the representation of chemical structures [ 314 , 315 ] and desired properties [ 316 ]. It was also shown that the new concept of alchemical chirality [ 317 ] might allow one to draw direct energy relations across the chemical compound space to accelerate design processes.…”

Section: Conceptual Considerationsmentioning

confidence: 99%

Autonomous Reaction Network Exploration in Homogeneous and Heterogeneous Catalysis

Steiner

Reiher

2022

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Autonomous computations that rely on automated reaction network elucidation algorithms may pave the way to make computational catalysis on a par with experimental research in the field. Several advantages of this approach are key to catalysis: (i) automation allows one to consider orders of magnitude more structures in a systematic and open-ended fashion than what would be accessible by manual inspection. Eventually, full resolution in terms of structural varieties and conformations as well as with respect to the type and number of potentially important elementary reaction steps (including decomposition reactions that determine turnover numbers) may be achieved. (ii) Fast electronic structure methods with uncertainty quantification warrant high efficiency and reliability in order to not only deliver results quickly, but also to allow for predictive work. (iii) A high degree of autonomy reduces the amount of manual human work, processing errors, and human bias. Although being inherently unbiased, it is still steerable with respect to specific regions of an emerging network and with respect to the addition of new reactant species. This allows for a high fidelity of the formalization of some catalytic process and for surprising in silico discoveries. In this work, we first review the state of the art in computational catalysis to embed autonomous explorations into the general field from which it draws its ingredients. We then elaborate on the specific conceptual issues that arise in the context of autonomous computational procedures, some of which we discuss at an example catalytic system. Graphical Abstract

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Simplifying inverse materials design problems for fixed lattices with alchemical chirality

Cited by 15 publications

References 84 publications

Arbitrarily Precise Quantum Alchemy

Arbitrarily Precise Quantum Alchemy

Alchemical geometry relaxation

Autonomous Reaction Network Exploration in Homogeneous and Heterogeneous Catalysis

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