Predicting Deprotonation Sites Using Alchemical Derivatives

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.

Transferability of atomic energies from alchemical decomposition

We study alchemical atomic energy partitioning as a method to estimate atomization energies from atomic contributions, which are defined in physically rigorous and general ways through the use of the uniform electron gas as a joint reference. We analyze quantitatively the relation between atomic energies and their local environment using a dataset of 1325 organic molecules. The atomic energies are transferable across various molecules, enabling the prediction of atomization energies with a mean absolute error of 23 kcal/mol, comparable to simple statistical estimates but potentially more robust given their grounding in the physics-based decomposition scheme. A comparative analysis with other decomposition methods highlights its sensitivity to electrostatic variations, underlining its potential as a representation of the environment as well as in studying processes like diffusion in solids characterized by significant electrostatic shifts.

Optimization of General Molecular Properties in the Equilibrium Geometry Using Quantum Alchemy: An Inverse Molecular Design Approach

Inverse molecular design allows the optimization of molecules in chemical space and is promising for accelerating the development of functional molecules and materials. To design realistic molecules, it is necessary to consider geometric stability during optimization. In this work, we introduce an inverse design method that optimizes molecular properties by changing the chemical composition in the equilibrium geometry. The optimization algorithm of our recently developed molecular design method has been modified to allow molecular design for general properties at a low computational cost. The proposed method is based on quantum alchemy and does not require empirical data. We demonstrate the applicability and limitations of the present method in the optimization of the electric dipole moment and atomization energy in small chemical spaces for (BF, CO), (N₂, CO), BN-doped benzene derivatives, and BN-doped butane derivatives. It was found that the optimality criteria scheme adopted for updating the molecular species yields faster convergence of the optimization and requires a less computational cost. Moreover, we also investigate and discuss the applicability of quantum alchemy to the electric dipole moment.

On the Prediction of Lattice Energy with the Fukui Potential: Some Supports on Hardness Maximization in Inorganic Solids

Using perturbation theory within the framework of conceptual density functional theory, we derive a lower bound for the lattice energy of the ionic solids. The main element of the lower bound is the Fukui potential in the nuclei of the molecule corresponding to the unit formula of the solid. Thus, we propose a model to calculate the lattice energy in terms of the Fukui potential. Our method, which is extremely simple, performs well as other methods using the crystal structure information of alkali halide solids. The method proposed here correlates surprisingly well with the experimental data on the lattice energy of a diverse series of solids having even a non-negligible covalent characteristic. Finally, the validity of the maximum hardness principle (MHP) is assessed, showing that in this case, the MHP is limited.

Molecular Interactions From the Density Functional Theory for Chemical Reactivity: The Interaction Energy Between Two-Reagents

Reactivity descriptors indicate where a reagent is most reactive and how it is most likely to react. However, a reaction will only occur when the reagent encounters a suitable reaction partner. Determining whether a pair of reagents is well-matched requires developing reactivity rules that depend on both reagents. This can be achieved using the expression for the minimum-interaction-energy obtained from the density functional reactivity theory. Different terms in this expression will be dominant in different circumstances; depending on which terms control the reactivity, different reactivity indicators will be preferred.

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.

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.

Links among the Fukui potential, the alchemical hardness and the local hardness of an atom in a molecule

This paper presents a brief summary of the difficulty that resides in the definition of the elusive concept of local chemical hardness. We argue that a definition of local hardness should be useful to a reactivity principle and not just as a mere definition. We then continue with a formal discussion about the benefits and difficulties of using the Fukui potential, which is interpreted as an alchemical derivative (alchemical hardness), as descriptor of local hardness of molecules. Computational evidence shows that the alchemical hardness is at least as good a descriptor as the combination of other two well-stabilized descriptors of local hardness, such as the Fukui function and grand canonical local hardness. Although our results are auspicious for the alchemical hardness as descriptor of local hardness, we finish by calling the attention of the community on the importance of discussing the raison d'être of a local hardness function and its main characteristics. We suggest that an axiomatic construction of local hardness could be they way of constructing a local hardness which is both useful and free of arbitrariness.

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.

Effects of perturbation order and basis set on alchemical predictions

Alchemical perturbation density functional theory has been shown to be an efficient and computationally inexpensive way to explore chemical compound space. We investigate approximations made, in terms of atomic basis sets and the perturbation order, introduce an electron-density based estimate of errors of the alchemical prediction, and propose a correction for effects due to basis set incompleteness. Our numerical analysis of potential energy estimates, and resulting binding curves, is based on coupled-cluster single double (CCSD) reference results and is limited to all neutral diatomics with 14 electrons (AlH⋯NN). The method predicts binding energy, equilibrium distance, and vibrational frequencies of neighboring out-of-sample diatomics with near CCSD quality using perturbations up to the fifth order. We also discuss simultaneous alchemical mutations at multiple sites in benzene.