Simplifying inverse materials design problems for fixed lattices with alchemical chirality

Extending the definition of atomic basis sets to atoms with fractional nuclear charge

Alchemical transformations showed that perturbation theory can be applied also to changes in the atomic nuclear charges of a molecule. The alchemical path that connects two different chemical species involves the conceptualization of a non-physical system in which an atom possess a non-integer nuclear charge. A correct quantum mechanical treatment of these systems is limited by the fact that finite size atomic basis sets do not define exponents and contraction coefficients for fractional charge atoms. This paper proposes a solution to this problem and shows that a smooth interpolation of the atomic orbital coefficients and exponents across the periodic table is a convenient way to produce accurate alchemical predictions, even using small size basis sets.

Quantum Alchemy Based Bonding Trends and Their Link to Hammett's Equation and Pauling's Electronegativity Model

We present an intuitive and general analytical approximation estimating the energy of covalent single and double bonds between participating atoms in terms of their respective nuclear charges with just three parameters, [E_AB ≈ a - bZ_AZ_B + c(Z_A^7/3 + Z_B^7/3) ]. The functional form of our expression models an alchemical atomic energy decomposition between participating atoms A and B. After calibration, reasonably accurate bond dissociation energy estimates are obtained for hydrogen-saturated diatomics composed of p-block elements coming from the same row 2 ≤ n ≤ 4 in the periodic table. Corresponding changes in bond dissociation energies due to substitution of atom B by C can be obtained via simple formulas. While being of different functional form and origin, our model is as simple and accurate as Pauling's well-known electronegativity model. Analysis indicates that the model's response in covalent bonding to variation in nuclear charge is near-linear, which is consistent with Hammett's equation.

Alchemical geometry relaxation

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 Schr\"odinger'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$^\text{th}$ 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 $\sim$27 mHa and $\sim$0.12 Bohr, respectively.

Autonomous Reaction Network Exploration in Homogeneous and Heterogeneous Catalysis

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.

Arbitrarily accurate quantum alchemy

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, have been used in the 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 that allows for arbitrarily accurate evaluation of restricted Hartree-Fock energies and arbitrary order derivatives is made available to support future method development.

Ab Initio Machine Learning in Chemical Compound Space

Chemical compound space (CCS), the set of all theoretically conceivable combinations of chemical elements and (meta-)stable geometries that make up matter, is colossal. The first-principles based virtual sampling of this space, for example, in search of novel molecules or materials which exhibit desirable properties, is therefore prohibitive for all but the smallest subsets and simplest properties. We review studies aimed at tackling this challenge using modern machine learning techniques based on (i) synthetic data, typically generated using quantum mechanics based methods, and (ii) model architectures inspired by quantum mechanics. Such Quantum mechanics based Machine Learning (QML) approaches combine the numerical efficiency of statistical surrogate models with an ab initio view on matter. They rigorously reflect the underlying physics in order to reach universality and transferability across CCS. While state-of-the-art approximations to quantum problems impose severe computational bottlenecks, recent QML based developments indicate the possibility of substantial acceleration without sacrificing the predictive power of quantum mechanics.