Guiding ab initio calculations by alchemical derivatives

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.

Simplifying inverse materials design problems for fixed lattices with alchemical chirality

Brute-force compute campaigns relying on demanding ab initio calculations routinely search for previously unknown materials in chemical compound space (CCS), the vast set of all conceivable stable combinations of elements and structural configurations. Here, we demonstrate that four-dimensional chirality arising from antisymmetry of alchemical perturbations dissects CCS and defines approximate ranks, which reduce its formal dimensionality and break down its combinatorial scaling. The resulting "alchemical" enantiomers have the same electronic energy up to the third order, independent of respective covalent bond topology, imposing relevant constraints on chemical bonding. Alchemical chirality deepens our understanding of CCS and enables the establishment of trends without empiricism for any materials with fixed lattices. We demonstrate the efficacy for three cases: (i) new rules for electronic energy contributions to chemical bonding; (ii) analysis of the electron density of BN-doped benzene; and (iii) ranking over 2000 and 4 million BN-doped naphthalene and picene derivatives, respectively.

Predicting Deprotonation Sites Using Alchemical Derivatives

An alchemical transformation is any process, physical or fictitious, that connects two points in the chemical space. A particularly important transformation is the vanishing of a proton, whose energy can be linked to the proton dissociation enthalpy of acids. In this work we assess the reliability of alchemical derivatives in predicting the proton dissociation enthalpy of a diverse series of mono- and polyprotic molecules. Alchemical derivatives perform remarkably well in ranking the proton affinity of all molecules. Additionally, alchemical derivatives could be use also as a predictive tool because their predictions correlate quite well with calculations based on energy differences and experimental values. Although second-order alchemical derivatives underestimate the dissociation enthalpy, the deviation seems to be almost constant. This makes alchemical derivatives extremely accurate to evaluate the difference in proton affinity between two acid sites of polyprotic molecule. Finally, we show that the reason for the underestimation of the dissociation enthalpy is most likely the contribution of higher-order derivatives.

Unifying machine learning and quantum chemistry with a deep neural network for molecular wavefunctions

Machine learning advances chemistry and materials science by enabling large-scale exploration of chemical space based on quantum chemical calculations. While these models supply fast and accurate predictions of atomistic chemical properties, they do not explicitly capture the electronic degrees of freedom of a molecule, which limits their applicability for reactive chemistry and chemical analysis. Here we present a deep learning framework for the prediction of the quantum mechanical wavefunction in a local basis of atomic orbitals from which all other ground-state properties can be derived. This approach retains full access to the electronic structure via the wavefunction at force-field-like efficiency and captures quantum mechanics in an analytically differentiable representation. On several examples, we demonstrate that this opens promising avenues to perform inverse design of molecular structures for targeting electronic property optimisation and a clear path towards increased synergy of machine learning and quantum chemistry.

Atoms in Molecules from Alchemical Perturbation Density Functional Theory

Based on thermodynamic integration, we introduce atoms in molecules (AIM) using the orbital-free framework of alchemical perturbation density functional theory (APDFT). Within APDFT, atomic energies and electron densities in molecules are arbitrary because any reference system and integration path can be selected as long as it meets the boundary conditions. We choose the uniform electron gas (jellium) as a reference and linearly scale up all nuclear charges, situated at any query molecule's atomic coordinates. Within the approximations made when calculating one-particle electron densities, this universal choice affords unambiguous and exact definitions of energies and electron densities of AIMs. Numerical results are presented for neutral small molecules (CO, N₂, BF, CO₂), various small molecules with different electronic hybridization states of carbon (CH₄, C₂H₆, C₂H₄, C₂H₂, HCN), and all of the possible BN-doped mutants connecting benzene to borazine (C_2nB_3-nN_3-nH₆, 0 ≤ n ≤ 3). Our results, as well as comparison to atomic energy estimates resulting from either DFT trained neural network models or atomic basis set overlap within CCSD, suggest that APDFT based AIMs enable meaningful, interesting, and counterintuitive interpretations of chemical bonding and molecular electron densities.

Search for Catalysts by Inverse Design: Artificial Intelligence, Mountain Climbers, and Alchemists

In silico catalyst design is a grand challenge of chemistry. Traditional computational approaches have been limited by the need to compute properties for an intractably large number of possible catalysts. Recently, inverse design methods have emerged, starting from a desired property and optimizing a corresponding chemical structure. Techniques used for exploring chemical space include gradient-based optimization, alchemical transformations, and machine learning. Though the application of these methods to catalysis is in its early stages, further development will allow for robust computational catalyst design. This review provides an overview of the evolution of inverse design approaches and their relevance to catalysis. The strengths and limitations of existing techniques are highlighted, and suggestions for future research are provided.

Alchemical Normal Modes Unify Chemical Space

In silico design of new molecules and materials with desirable quantum properties by high-throughput screening is a major challenge due to the high dimensionality of chemical space. To facilitate its navigation, we present a unification of coordinate and composition space in terms of alchemical normal modes (ANMs) which result from second order perturbation theory. ANMs assume a predominantly smooth nature of chemical space and form a basis in which new compounds can be expanded and identified. We showcase the use of ANMs for the energetics of the isoelectronic series of diatomics with 14 electrons, BN doped benzene derivatives (C_{6-2 x}(BN) _xH₆ with x = 0,1,2,3), predictions for over 1.8 million BN doped coronene derivatives, and genetic energy optimizations in the entire BN-doped coronene space. Using Ge lattice scans as reference, the applicability of ANMs across the periodic table is demonstrated for III-V and IV-IV semiconductors Si, Sn, SiGe, SnGe, SiSn, as well as AlP, AlAs, AlSb, GaP, GaAs, GaSb, InP, InAs, and InSb. Analysis of our results indicates simple qualitative structure property rules for estimating energetic rankings among isomers. Useful quantitative estimates can also be obtained when few atoms are changed to neighboring or lower lying elements in the periodic table. The quality of the predictions often increases with the symmetry of system chosen as reference due to cancellation of odd order terms. Rooted in perturbation theory, the ANM approach promises to generally enable unbiased compound exploration campaigns at reduced computational cost.

Exploring dissociative water adsorption on isoelectronically BN doped graphene using alchemical derivatives

The design and production of novel 2-dimensional materials have seen great progress in the last decade, prompting further exploration of the chemistry of such materials. Doping and hydrogenating graphene are an experimentally realised method of changing its surface chemistry, but there is still a great deal to be understood on how doping impacts on the adsorption of molecules. Developing this understanding is key to unlocking the potential applications of these materials. High throughput screening methods can provide particularly effective ways to explore vast chemical compositions of materials. Here, alchemical derivatives are used as a method to screen the dissociative adsorption energy of water molecules on various BN doped topologies of hydrogenated graphene. The predictions from alchemical derivatives are assessed by comparison to density functional theory. This screening method is found to predict dissociative adsorption energies that span a range of more than 2 eV, with a mean absolute error <0.1 eV. In addition, we show that the quality of such predictions can be readily assessed by examination of the Kohn-Sham highest occupied molecular orbital in the initial states. In this way, the root mean square error in the dissociative adsorption energies of water is reduced by almost an order of magnitude (down to ∼0.02 eV) after filtering out poor predictions. The findings point the way towards a reliable use of first order alchemical derivatives for efficient screening procedures.

How predictive could alchemical derivatives be?

The chemical space contains all possible compounds that can be imagined. Its size easily equals the number of fundamental particles in the observable universe. Rational design of compounds aims to find those sectors of the chemical space where compounds optimize a set of desired properties. Then, rational design demands tools to efficiently navigate the chemical space. Ab initio alchemical derivatives offer the possibility to navigate, without empiricism, the energy landscape through alchemical transformations. An alchemical transformation is any process, physical or fictitious, that connects to points in the chemical space. In this work, those transformations are constructed as a perturbative expansion of the energy with respect to perturbations in the stoichiometry. The response functions of that expansion are what is called alchemical derivatives. In this work we assess how effective alchemical derivatives are in predicting energy changes associated to changes in the composition. We do this by including in the expansion, for the first time, electrostatic, polarization and electron-transfer effects. The system we chose is one that challenges alchemical derivatives because none of these effects dominates its behavior. The transmutations studied here correspond to substitutional doping of Al₁₃ with up to four atoms of Si, Al_13-nSi_n. Two types of transformations are considered, those in which the number of electrons remains constant and those in which the number of electrons also changes. It is found that contrary to what has been reported before, polarization cannot be neglected. If polarization is not included, alchemical derivatives fail to predict the change of energy and the relative energy between isomers. For isoelectronic substitution of four or more atoms, the perturbative approach collapses because the strength of the perturbation becomes too strong to guarantee convergence of the series. It is shown, however, that if only one atom is mutated at a time, alchemical derivatives rank pretty well the isomers of Al_13-nSi_n according to their energy. In the case of non-isoelectronic transformations, it is observed that the series rapidly diverges with increasing number of electrons. In this situation, it becomes more important to keep the degree of transmutation of the parent system small.

Exploring Chemical Space with Alchemical Derivatives: BN-Simultaneous Substitution Patterns in C60

With the idea of using alchemical derivatives to explore in an efficient, computer- and cost-effective way Chemical Space was launched several years ago. In the context of Conceptual DFT response functions, these energies vs nuclear charge derivatives permit the estimatation of the energy of transmutants of a given starting or reference molecule showing different nuclear compositions. After an explorative study on small and planar molecules ( Balawender et al. J. Chem. Theory Comput. 2013 , 9 , 5327 ) by the present authors of this paper, the present study fully exploits the computational advantages of the alchemical derivatives in larger three-dimensional systems. Starting from a single reference calculation on C₆₀, the complete BN substitution pattern, from single substituted C₅₈BN via the belt (C₂₀(BN)₂₀ and the ball C₁₂(BN)₂₄ structures to the fully substituted (BN)₃₀, is explored. Successive and simultaneous substitution strategies are followed and compared, indicating that both techniques yield identical results up to 13 substitutions but that for higher substitutions the simultaneous approach needs to be taken. Due to the cost-efficiency of the algorithm this path can indeed be followed as opposed to earlier work in the literature where for each step a full SCF calculation was at stake leading to prohibitively large computational demands for adopting the simultaneous approach. Previously formulated rules governing the substitution pattern by Kar and co-workers are scrutinized in this context and reformulated giving chemical insight in the gradual substitution process and the relative energies of the isomers. In its present form the method offers an interesting venue to study BN substitution patterns in higher fullerenes and graphene and in general paves the way for more efficient exploration of the Chemical Space.

Alchemical Predictions for Computational Catalysis: Potential and Limitations

Kohn-Sham density functional theory (DFT) is the workhorse method for calculating adsorbate binding energies relevant for catalysis. Unfortunately, this method is too computationally expensive to methodically and broadly search through catalyst candidate space. Here, we assess the promise of computational alchemy, a perturbation theory approach that allows for predictions of binding energies thousands of times faster than DFT. We first benchmark the binding energy predictions of oxygen reduction reaction intermediates on alloys of Pt, Pd, and Ni using alchemy against predictions from DFT. Far faster alchemical estimates yield binding energies within 0.1 eV of DFT values in many cases. We also identify distinct cases where alchemy performs significantly worse, indicating areas where modeling improvements are needed. Our results suggest that computational alchemy is a very promising tool that warrants further consideration for high-throughput screening of heterogeneous catalysts.

Alchemical screening of ionic crystals

We introduce alchemical perturbations as a rapid and accurate tool to estimate fundamental structural and energetic properties in pure and mixed ionic crystals.