Variational particle number approach for rational compound design

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.

Combining Deep Learning Neural Networks with Genetic Algorithms to Map Nanocluster Configuration Spaces with Quantum Accuracy at Low Computational Cost

The configuration spaces for bimetallic AuPd nanoclusters of various sizes are explored efficiently and analyzed accurately by combining genetic algorithms with neural networks trained on density functional theory. The methodology demonstrated herein provides an optimizable solution to the problem of searching vast configuration spaces with quantum accuracy in a way that is computationally practical. We implement a machine learning algorithm which learns the density functional theory potential with increasing performance while simultaneously generating and relaxing structures within the system's global configuration space unbiasedly. As a result, the algorithm naturally converges onto the system's energy minima while mapping the configuration space as a function of energy. The algorithm's simple design applies not only to nanocluster configurations, as demonstrated, but to bulk, substrate, and adsorption sites as well, and it is designed to scale. To demonstrate its computational efficiency, we work with AuPd nanoclusters of sizes 15, 20, and 25 atoms. Results focus primarily on evaluating the algorithm's performance; however, several physical insights into possible configurations for these nanoclusters naturally emerge as well, such as geometric Au surface segregation and stoichiometric Au minimization as a function of stability.

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.

Relative energies without electronic perturbations via alchemical integral transform

We show that the energy of a perturbed system can be fully recovered from the unperturbed system’s electron density. We derive an alchemical integral transform by parametrizing space in terms of transmutations, the chain rule, and integration by parts. Within the radius of convergence, the zeroth order yields the energy expansion at all orders, restricting the textbook statement by Wigner that the p-th order wave function derivative is necessary to describe the (2 p + 1)-th energy derivative. Without the need for derivatives of the electron density, this allows us to cover entire chemical neighborhoods from just one quantum calculation instead of single systems one by one. Numerical evidence presented indicates that predictive accuracy is achieved in the range of mHa for the harmonic oscillator or the Morse potential and in the range of machine accuracy for hydrogen-like atoms. Considering isoelectronic nuclear charge variations by one proton in all multi-electron atoms from He to Ne, alchemical integral transform based estimates of the relative energy deviate by only few mHa from corresponding Hartree–Fock reference numbers.

Molecular-orbital-based machine learning for open-shell and multi-reference systems with kernel addition Gaussian process regression

We introduce a novel machine learning strategy, kernel addition Gaussian process regression (KA-GPR), in molecular-orbital-based machine learning (MOB-ML) to learn the total correlation energies of general electronic structure theories for closed- and open-shell systems by introducing a machine learning strategy. The learning efficiency of MOB-ML(KA-GPR) is the same as the original MOB-ML method for the smallest criegee molecule, which is a closed-shell molecule with multi-reference characters. In addition, the prediction accuracies of different small free radicals could reach the chemical accuracy of 1 kcal/mol by training on one example structure. Accurate potential energy surfaces for the H₁₀ chain (closed-shell) and water OH bond dissociation (open-shell) could also be generated by MOB-ML(KA-GPR). To explore the breadth of chemical systems that KA-GPR can describe, we further apply MOB-ML to accurately predict the large benchmark datasets for closed- (QM9, QM7b-T, and GDB-13-T) and open-shell (QMSpin) molecules.

Inverse design of molecule-metal nanoparticle systems interacting with light for desired photophysical properties

Molecules close to a metal nanoparticle (NP) have significantly different photophysical properties from those of the isolated one. In order to harness the potential of the molecule-NP system, appropriate design guidelines are required. Here, we propose an inverse design method of the optimal molecule-NP systems and incident electric field for desired photophysical properties. It is based on a gradient-based optimization search within the time-dependent quantum chemical description for the molecule and the continuum model for the metal NP. We designed the optimal molecule, relative molecule-NP spatial conformation, and incident electric field of a molecule-NP system to maximize the population transfer to the target electronic state of the molecule. The design results were presented and discussed. The present method is promising as the basis for designing molecule-NP systems and incident fields and accelerates discoveries of efficient molecular plasmonics systems.

Exploration of Chemical Space for Designing Functional Molecules Accounting for Geometric Stability

The design of functional molecules is regarded as searching for molecules with desired functionalities in chemical space populated by candidate molecules. Considering the geometric stability of molecules during the search process is crucial for designing realistic molecules. Here, we propose a method for designing functional molecules by exploring chemical space while explicitly accounting for geometric stability based on computational quantum alchemy. The proposed design method allows the simultaneous prediction of functional molecule in the equilibrium structure and its target desired property in an inverse design fashion without preparing the molecular geometries and performing brute-force screening. The applicability of the design method is proven by obtaining molecules with the desired atomization and electronic energies in various chemical spaces: (BF, CO), (CH₄, NH₃), 18 BN-doped benzene derivatives, and 3.1 × 10⁵ BN-doped phenanthrene derivatives.

Molecular Dipole Moment Learning via Rotationally Equivariant Gaussian Process Regression with Derivatives in Molecular-orbital-based Machine Learning

This study extends the accurate and transferable molecular-orbital-based machine learning (MOB-ML) approach to modeling the contribution of electron correlation to dipole moments at the cost of Hartree--Fock computations. A molecular-orbital-based (MOB) pairwise decomposition of the correlation part of the dipole moment is applied, and these pair dipole moments could be further regressed as a universal function of molecular orbitals (MOs).The dipole MOB features consist of the energy MOB features and their responses to electric fields. An interpretable and rotationally equivariant Gaussian process regression (GPR) with derivatives algorithm is introduced to learn the dipole moment more efficiently. The proposed problem setup, feature design, and ML algorithm are shown to provide highly-accurate models for both dipole moment and energies on water and fourteen small molecules. To demonstrate the ability of MOB-ML to function as generalized density-matrix functionals for molecular dipole moments and energies of organic molecules, we further apply the proposed MOB-ML approach to train and test the molecules from the QM9 dataset. The application of local scalable GPR with Gaussian mixture model unsupervised clustering (GMM/GPR) scales up MOB-ML to a large-data regime while retaining the prediction accuracy. In addition, compared with literature results, MOB-ML provides the best test MAEs of 4.21 mDebye and 0.045 kcal/mol for dipole moment and energy models, respectively, when training on 110000 QM9 molecules. The excellent transferability of the resulting QM9 models is also illustrated by the accurate predictions for four different series of peptides.

Atomic Structure Optimization with Machine-Learning Enabled Interpolation between Chemical Elements

We introduce a computational method for global optimization of structure and ordering in atomic systems. The method relies on interpolation between chemical elements, which is incorporated in a machine-learning structural fingerprint. The method is based on Bayesian optimization with Gaussian processes and is applied to the global optimization of Au-Cu bulk systems, Cu-Ni surfaces with CO adsorption, and Cu-Ni clusters. The method consistently identifies low-energy structures, which are likely to be the global minima of the energy. For the investigated systems with 23-66 atoms, the number of required energy and force calculations is in the range 3-75.

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.

Perspective on integrating machine learning into computational chemistry and materials science

Machine learning (ML) methods are being used in almost every conceivable area of electronic structure theory and molecular simulation. In particular, ML has become firmly established in the construction of high-dimensional interatomic potentials. Not a day goes by without another proof of principle being published on how ML methods can represent and predict quantum mechanical properties-be they observable, such as molecular polarizabilities, or not, such as atomic charges. As ML is becoming pervasive in electronic structure theory and molecular simulation, we provide an overview of how atomistic computational modeling is being transformed by the incorporation of ML approaches. From the perspective of the practitioner in the field, we assess how common workflows to predict structure, dynamics, and spectroscopy are affected by ML. Finally, we discuss how a tighter and lasting integration of ML methods with computational chemistry and materials science can be achieved and what it will mean for research practice, software development, and postgraduate training.

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.

Exploring chemical compound space with quantum-based machine learning

Rational design of compounds with specific properties requires understanding and fast evaluation of molecular properties throughout chemical compound space - the huge set of all potentially stable molecules. Recent advances in combining quantum-mechanical calculations with machine learning provide powerful tools for exploring wide swathes of chemical compound space. We present our perspective on this exciting and quickly developing field by discussing key advances in the development and applications of quantum-mechanics-based machine-learning methods to diverse compounds and properties, and outlining the challenges ahead. We argue that significant progress in the exploration and understanding of chemical compound space can be made through a systematic combination of rigorous physical theories, comprehensive synthetic data sets of microscopic and macroscopic properties, and modern machine-learning methods that account for physical and chemical knowledge.

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.

Understanding Chemical Selectivity through Well Selected Excited States

In this publication, we propose a new set of reactivity/selectivity descriptors, derived within a Rayleigh-Schrödinger perturbation theory framework, for chemical systems undergoing an electrostatic (point-charge) perturbation. From the electron density polarization at first order, qualitative insight on reactivity is retrieved, while more quantitative information (noteworthy selectivity) can be obtained from either the second-order energy response or the number of shifted electrons under perturbation. Noteworthily, only a small number of excitations contribute significantly to the overall responses to perturbation, suggesting chemical reactivity could be foreseen by a careful scrutiny of the electron density reorganization upon excitation.

Rapid and accurate molecular deprotonation energies from quantum alchemy

We assess the applicability of alchemical perturbation density functional theory (APDFT) for quickly and accurately estimating deprotonation energies. We have considered all possible single and double deprotonations in one hundred small organic molecules drawn at random from QM9 [Ramakrishnan et al., JCTC, 2015]. Numerical evidence is presented for 5160 deprotonated species at both HF/def2-TZVP and CCSD/6-31G* levels of theory. We show that the perturbation expansion formalism of APDFT quickly converges to reliable results: using CCSD electron densities and derivatives, regular Hartree-Fock calculations are outperformed at the second or third order for ranking all possible doubly or singly deprotonated molecules, respectively. CCSD single deprotonation energies are reproduced within 1.4 kcal mol^-1 on average within third order APDFT. We introduce a hybrid approach where the computational cost of APDFT is reduced even further by mixing first order terms at a higher level of theory (CCSD) with higher order terms at a lower level of theory only (HF). We find that this approach reaches 2 kcal mol^-1 accuracy in absolute deprotonation energies compared to CCSD at 2% of the computational cost of third order APDFT.

Designing Catalytic Sites on Surfaces with Optimal H-Atom Binding via Atom Doping Using the Inverse Molecular Design Approach

It remains a general challenge to computationally design optimal catalytic structures based on earth-abundant metals for hydrogenation. Here, we demonstrate an effective computational approach based on inverse molecular design to deterministically design optimal catalytic sites on the Cu(100) surface through the doping of Fe and/or Zn, and a stable Zn-doped Cu(100) surface was found with minimal binding energy to H atoms. By the calculations at the level of density functional theory, the optimized catalyst sites are verified to be valid on the Cu(100) surface in an infinite periodic system. We analyze the electronic structure cause of the optimal binding sites using the analysis of the density of states. In addition, we use a Cu₂₉Zn₃ atomic cluster, where such an optimum catalytic site is valid on the Cu(100) surface, to understand the role of doped Zn atoms on lowering the H atom binding energy. We found that in the atomic cluster, the atomic orbitals of surface Zn-atoms show less participation in the binding of H atoms, compared to the atomic orbitals of surface Cu atoms. Our study provides valuable chemistry insights on designing catalytic structures using earth-abundant metals, and it may lead to the development of novel Cu-based earth-abundant alloys in bulk, nanoparticles, atomic clusters, or single-atom catalysts for important catalytic applications such as lignin degradation or CO₂ conversion.

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 chemical space with alchemical derivatives: alchemical transformations of H through Ar and their ions as a proof of concept

Alchemical derivatives have been used previously to obtain information about transformations in which the number of electrons is unchanged. Here an approach for combining changes in both the number of electrons and the nuclear charge is presented.

Globally Optimal Catalytic Fields - Inverse Design of Abstract Embeddings for Maximum Reaction Rate Acceleration

The search for, and understanding of, good catalysts for chemical reactions is a central issue for chemists. Here, we present first steps toward developing a general computational framework to better support this task. This framework combines efficient, unbiased global optimization techniques with an abstract representation of the catalytic environment, to shrink the search space. To analyze the resulting catalytic embeddings, we employ dimensionality reduction and clustering techniques. This not only provides an inverse design approach to new catalytic embeddings but also illuminates the actual interactions behind catalytic effects. All this is illustrated here with a strictly electrostatic model for the environment and with two versions of a selected example reaction. We close with detailed discussions of future improvements of our framework.

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.

Chemical transferability of functional groups follows from the nearsightedness of electronic matter

We establish the physical origins of chemical transferability from the perspective of the nearsightedness of electronic matter. To do this, we explicitly evaluate the response of electron density to a change in the system, at constant chemical potential, by computing the softness kernel, [Formula: see text] The softness kernel is nearsighted, indicating that under constant-chemical-potential conditions like dilute solutions changing the composition of the molecule at [Formula: see text] has only local effects and does not have any significant impact on the reactivity at positions [Formula: see text] far away from point [Formula: see text] This locality principle elucidates the transferability of functional groups in chemistry.

Tuning the HOMO-LUMO Energy Gap of Small Diamondoids Using Inverse Molecular Design

Functionalized diamondoids show great potential as building blocks for various new optoelectronic applications. However, until now, only simple mono and double substitutions were investigated. In this work, we considered up to 10 and 6 sites for functionalization of the two smallest diamondoids, adamantane and diamantane, respectively, in search for diamondoid derivatives with a minimal and maximal HOMO-LUMO energy gap. To this end, the energy gap was optimized systematically using an inverse molecular design methodology based on the best-first search algorithm combined with a Monte Carlo component to escape local optima. Adamantane derivatives were found with HOMO-LUMO gaps ranging from 2.42 to 10.63 eV, with 9.45 eV being the energy gap of pure adamantane. For diamantane, similar values were obtained. The structures with the lowest HOMO-LUMO gaps showed apparent push-pull character. The push character is mainly formed by sulfur or nitrogen dopants and thiol groups, whereas the pull character is predominantly determined by the presence of electron-withdrawing nitro or carbonyl groups assisted by amino and hydroxyl groups via the formation of intramolecular hydrogen bonds. In contrast, maximal HOMO-LUMO gaps were obtained by introducing numerous electronegative groups.

Fast and accurate predictions of covalent bonds in chemical space

We assess the predictive accuracy of perturbation theory based estimates of changes in covalent bonding due to linear alchemical interpolations among molecules. We have investigated σ bonding to hydrogen, as well as σ and π bonding between main-group elements, occurring in small sets of iso-valence-electronic molecules with elements drawn from second to fourth rows in the p-block of the periodic table. Numerical evidence suggests that first order Taylor expansions of covalent bonding potentials can achieve high accuracy if (i) the alchemical interpolation is vertical (fixed geometry), (ii) it involves elements from the third and fourth rows of the periodic table, and (iii) an optimal reference geometry is used. This leads to near linear changes in the bonding potential, resulting in analytical predictions with chemical accuracy (∼1 kcal/mol). Second order estimates deteriorate the prediction. If initial and final molecules differ not only in composition but also in geometry, all estimates become substantially worse, with second order being slightly more accurate than first order. The independent particle approximation based second order perturbation theory performs poorly when compared to the coupled perturbed or finite difference approach. Taylor series expansions up to fourth order of the potential energy curve of highly symmetric systems indicate a finite radius of convergence, as illustrated for the alchemical stretching of H2 (+). Results are presented for (i) covalent bonds to hydrogen in 12 molecules with 8 valence electrons (CH4, NH3, H2O, HF, SiH4, PH3, H2S, HCl, GeH4, AsH3, H2Se, HBr); (ii) main-group single bonds in 9 molecules with 14 valence electrons (CH3F, CH3Cl, CH3Br, SiH3F, SiH3Cl, SiH3Br, GeH3F, GeH3Cl, GeH3Br); (iii) main-group double bonds in 9 molecules with 12 valence electrons (CH2O, CH2S, CH2Se, SiH2O, SiH2S, SiH2Se, GeH2O, GeH2S, GeH2Se); (iv) main-group triple bonds in 9 molecules with 10 valence electrons (HCN, HCP, HCAs, HSiN, HSiP, HSiAs, HGeN, HGeP, HGeAs); and (v) H2 (+) single bond with 1 electron.

Guiding ab initio calculations by alchemical derivatives

We assess the concept of alchemical transformations for predicting how a further and not-tested change in composition would change materials properties. This might help to guide ab initio calculations through multidimensional property-composition spaces. Equilibrium volumes, bulk moduli, and relative lattice stability of fcc and bcc 4d transition metals Zr, Nb, Mo, Tc, Ru, Rh, Pd, and Ag are calculated using density functional theory. Alchemical derivatives predict qualitative trends in lattice stability while equilibrium volumes and bulk moduli are predicted with less than 9% and 28% deviation, respectively. Predicted changes in equilibrium volume and bulk moduli for binary and ternary mixtures of Rh-Pd-Ag are in qualitative agreement even for predicted bulk modulus changes as large as +100% or -50%. Based on these results, it is suggested that alchemical transformations could be meaningful for enhanced sampling in the context of virtual high-throughput materials screening projects.

Optimizing molecular properties using a relative index of thermodynamic stability and global optimization techniques

We devised a global optimization (GO) strategy for optimizing molecular properties with respect to both geometry and chemical composition. A relative index of thermodynamic stability (RITS) is introduced to allow meaningful energy comparisons between different chemical species. We use the RITS by itself, or in combination with another calculated property, to create an objective function F to be minimized. Including the RITS in the definition of F ensures that the solutions have some degree of thermodynamic stability. We illustrate how the GO strategy works with three test applications, with F calculated in the framework of Kohn-Sham Density Functional Theory (KS-DFT) with the Perdew-Burke-Ernzerhof exchange-correlation. First, we searched the composition and configuration space of CmHnNpOq (m = 0-4, n = 0-10, p = 0-2, q = 0-2, and 2 ≤ m + n + p + q ≤ 12) for stable molecules. The GO discovered familiar molecules like N2, CO2, acetic acid, acetonitrile, ethane, and many others, after a small number (5000) of KS-DFT energy evaluations. Second, we carried out a GO of the geometry of CumSnn (+) (m = 1, 2 and n = 9-12). A single GO run produced the same low-energy structures found in an earlier study where each CumSnn (+) species had been optimized separately. Finally, we searched bimetallic clusters AmBn (3 ≤ m + n ≤ 6, A,B= Li, Na, Al, Cu, Ag, In, Sn, Pb) for species and configurations having a low RITS and large highest occupied Molecular Orbital (MO) to lowest unoccupied MO energy gap (Eg). We found seven bimetallic clusters with Eg > 1.5 eV.

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.

Alchemical Variations of Intermolecular Energies According to Molecular Grand-Canonical Ensemble Density Functional Theory

Molecular grand-canonical density functional theory [J. Chem. Phys. 2006, 125, 154104] is employed for the alchemical variation of intermolecular energies due to changes in the chemical composition of small molecules. We investigate the interaction of a fixed binding target, formic acid, with a restricted chemical space, corresponding to an isoelectronic 10-proton system which includes molecules such as CH4, NH3, H2O, and HF. Differential expressions involving the nuclear chemical potential are derived, numerically evaluated, tested with respect to finite difference results, and discussed regarding their suitability as gradients of the intermolecular energy with respect to compositional variations.

Smooth heuristic optimization on a complex chemical subspace

In the present work, several heuristic reordering algorithms for deterministic optimization on a combinatorial chemical compound space are evaluated for performance and efficiency.

Conceptual DFT: chemistry from the linear response function

Within the context of reactivity descriptors known in conceptual DFT, the linear response function (χ(r,r')) remained nearly unexploited. Although well known, in its time dependent form, in the solid state physics and time-dependent DFT communities the study of the "chemistry" present in the kernel was, until recently, relatively unexplored. The evaluation of the linear response function as such and its study in the time independent form are highlighted in the present review. On the fundamental side, the focus is on the approaches of increasing complexity to compute and represent χ(r,r'), its visualisation going from plots of the unintegrated χ(r,r') to an atom condensed matrix. The study on atoms reveals its physical significance, retrieving atomic shell structure, while the results on molecules illustrate that a variety of chemical concepts are retrieved: inductive and mesomeric effects, electron delocalisation, aromaticity and anti-aromaticity, σ and π aromaticity,…. The applications show that the chemistry of aliphatic (saturated and unsaturated) chains, saturated and aromatic/anti-aromatic rings, organic, inorganic or metallic in nature, can be retrieved via the linear response function, including the variation of the electronic structure of the reagents along a reaction path. The connection of the linear response function with the concept of nearsightedness and the alchemical derivatives is also highlighted.