On Quantum Chemical Topology

Explainable chemical artificial intelligence from accurate machine learning of real-space chemical descriptors

Machine-learned computational chemistry has led to a paradoxical situation in which molecular properties can be accurately predicted, but they are difficult to interpret. Explainable AI (XAI) tools can be used to analyze complex models, but they are highly dependent on the AI technique and the origin of the reference data. Alternatively, interpretable real-space tools can be employed directly, but they are often expensive to compute. To address this dilemma between explainability and accuracy, we developed SchNet4AIM, a SchNet-based architecture capable of dealing with local one-body (atomic) and two-body (interatomic) descriptors. The performance of SchNet4AIM is tested by predicting a wide collection of real-space quantities ranging from atomic charges and delocalization indices to pairwise interaction energies. The accuracy and speed of SchNet4AIM breaks the bottleneck that has prevented the use of real-space chemical descriptors in complex systems. We show that the group delocalization indices, arising from our physically rigorous atomistic predictions, provide reliable indicators of supramolecular binding events, thus contributing to the development of Explainable Chemical Artificial Intelligence (XCAI) models.

Distinguishing the Geometric and Electronic Structures of Actinide Carbides AnxC8 (An = Th, U; x = 2, 3) through Exchange Interactions

Global-minimum optimizations combined with relativistic quantum chemistry calculations have been performed to characterize the ground-state stable structures of four titled compounds and to analyze the bonding properties. Th2C8 was identified as being a ThC4-Th(C2)2 structure, U2C8 has been found to favor the U-U(C8) structure, and both Th3C8 and U3C8 adopt the (AnC3)2-(AnC2) structure. Then, the wave function analyses reveal that the interactions between the Th 7s-based orbital and the σg molecular orbital of the C2 unit compensate for the excitation energy of 7s16d1 → 6d2 and lead to the stabilization of two Th(IV)s in the ThC4-Th(C2)2 structure. It also reveals that the U species exhibit magnetic exchange coupling behavior in UxC8, for instance, as seen in the direct interaction of U2C8 and the superexchange pathway of U3C8, which effectively stabilizes their low-spin states. This interpretation indicates that the geometric and electronic structures of AnxC8 species are largely influenced by the local magnetic moment and spin correlation.

Revisiting the Nature of Chemical Bonding in Chalcogenides to Explain and Design their Properties

Quantum chemical bonding descriptors have recently been utilized to design materials with tailored properties. Their usage to facilitate a quantitative description of bonding in chalcogenides as well as the transition between different bonding mechanisms is reviewed. More importantly, these descriptors can also be employed as property predictors for several important material characteristics, including optical and transport properties. Hence, these quantum chemical bonding descriptors can be utilized to tailor material properties of chalcogenides relevant for thermoelectrics, photovoltaics, and phase-change memories. Relating material properties to bonding mechanisms also shows that there is a class of materials, which are characterized by unconventional properties such as a pronounced anharmonicity, a large chemical bond polarizability, and strong optical absorption. This unusual property portfolio is attributed to a novel bonding mechanism, fundamentally different from ionic, metallic, and covalent bonding, which is called "metavalent." In the concluding section, a number of promising research directions are sketched, which explore the nature of the property changes upon changing bonding mechanism and extend the concept of quantum chemical property predictors to more complex compounds.

Atomic charges in molecules defined by molecular real space partition into atomic subspaces

Atomic charge (AC), which is the charge distribution of a molecule, is an important property that is closely associated with structures, reactivities, and intra- and inter-molecular interactions among molecules. Several theoretical models or methods can be used to obtain the magnitudes of AC with different characteristics. These models can be classified into fuzzy-atoms models and models partitioning a molecule into individual atoms with sharp boundaries. The first category includes Mulliken, natural population analysis (NPA), Hirshfeld, Merz-Kollman-Singh (MK), CHELPG, the electronegativity equalization method (EEM), the atom-bond electronegativity equalization method (ABEEM), and atomic polar tensor (APT). The second category is derived from quantum chemical topology (QCT) and includes the quantum theory of atoms in molecules (QTAIM) and QCT analysis based on the potential acting on one electron in a molecule (PAEMQCT). Herein, after giving a bird's-eye view of the population methods of the first category, we specifically describe some features of the second category. We only present the basic framework of QCT for obtaining ACs from QTAIM and PAEMQCT and show their important characteristics. QCT establishes the basis of the following chemical concept: a molecule is spatially partitioned into individual atoms with sharp boundaries. The ACs from QTAIM are close to the atomic valence in chemistry, and ACs from PAEMQCT may be practically suitable for modeling intra- and inter-molecular interactions.

Topological Analysis of Functions on Arbitrary Grids: Applications to Quantum Chemistry

Algorithms are presented for performing a topological analysis of an arbitrary function, evaluated on an arbitrary grid of points. These algorithms work strictly by post-processing the data and require no additional function evaluations. This is achieved by connecting the grid points with a neighborhood graph, allowing the topological analysis to be recast as a problem in the graph theory. The flexibility of the approach is demonstrated for various applications involving analysis of the charge and magnetically induced current densities in molecules, where features of the neighborhood graph are found to correspond to chemically relevant topographical properties, such as Bader charges. These properties converge using orders of magnitude fewer grid points than uniform-grid approaches while exhibiting an appealing O[N log(N)] scaling of the computational cost. The issue of grid bias is discussed in the context of graph-based algorithms and strategies for avoiding this bias are presented. Python implementations of the algorithms are provided.

Non-covalent interactions from a Quantum Chemical Topology perspective

About half a century after its little-known beginnings, the quantum topological approach called QTAIM has grown into a widespread, but still not mainstream, methodology of interpretational quantum chemistry. Although often confused in textbooks with yet another population analysis, be it perhaps an elegant but somewhat esoteric one, QTAIM has been enriched with about a dozen other research areas sharing its main mathematical language, such as Interacting Quantum Atoms (IQA) or Electron Localisation Function (ELF), to form an overarching approach called Quantum Chemical Topology (QCT). Instead of reviewing the latter’s role in understanding non-covalent interactions, we propose a number of ideas emerging from the full consequences of the space-filling nature of topological atoms, and discuss how they (will) impact on interatomic interactions, including non-covalent ones. The architecture of a force field called FFLUX, which is based on these ideas, is outlined. A new method called Relative Energy Gradient (REG) is put forward, which is able, by computation, to detect which fragments of a given molecular assembly govern the energetic behaviour of this whole assembly. This method can offer insight into the typical balance of competing atomic energies both in covalent and non-covalent case studies. A brief discussion on so-called bond critical points is given, highlighting concerns about their meaning, mainly in the arena of non-covalent interactions.

New insights in chemical reactivity from quantum chemical topology

Based on the quantum chemical topology of the modified electron localization function ELF_x , an efficient and robust mechanistic methodology designed to identify the favorable reaction pathway between two reactants is proposed. We first recall and reshape how the supermolecular interaction energy can be evaluated from only three distinct terms, namely the intermolecular coulomb energy, the intermolecular exchange-correlation energy and the intramolecular energies of reactants. Thereafter, we show that the reactivity between the reactants is driven by the first-order variation in the coulomb intermolecular energy defined in terms of the response to changes in the number of electrons. Illustrative examples with the formation of the dative bond B-N involved in the BH₃ NH₃ molecule and the typical formation of the hydrogen bond in the canonical water dimer are presented. For these selected systems, our approach unveils a noticeable mimicking of E_dual onto the DFT intermolecular interaction energy surface calculated between the both reactants. An automated reaction-path algorithm aimed to determine the most favorable relative orientations when the two molecules approach each other is also outlined.

On the strength of hydrogen bonding within water clusters on the coordination limit

Hydrogen bonds (HB) are arguably the most important noncovalent interactions in chemistry. We study herein how differences in connectivity alter the strength of HBs within water clusters of different sizes. We used for this purpose the interacting quantum atoms energy partition, which allows for the quantification of HB formation energies within a molecular cluster. We could expand our previously reported hierarchy of HB strength in these systems (Phys. Chem. Chem. Phys., 2016, 18, 19557) to include tetracoordinated monomers. Surprisingly, the HBs between tetracoordinated water molecules are not the strongest HBs despite the widespread occurrence of these motifs (e.g., in ice I_h ). The strongest HBs within H₂ O clusters involve tricoordinated monomers. Nonetheless, HB tetracoordination is preferred in large water clusters because (a) it reduces HB anticooperativity associated with double HB donors and acceptors and (b) it results in a larger number of favorable interactions in the system. Finally, we also discuss (a) the importance of exchange-correlation to discriminate among the different examined types of HBs within H₂ O clusters, (b) the use of the above-mentioned scale to quickly assess the relative stability of different isomers of a given water cluster, and (c) how the findings of this research can be exploited to indagate about the formation of polymorphs in crystallography. Overall, we expect that this investigation will provide valuable insights into the subtle interplay of tri- and tetracoordination in HB donors and acceptors as well as the ensuing interaction energies within H₂ O clusters.

Partitioning a Molecule into the Atomic Basins and the Resultant Atomic Charges from Quantum Chemical Topology Analysis of the Kohn-Sham Potential

Quantum chemical topology (QCT) solidifies the chemical basic concepts demonstrating how a molecular system is intrinsically partitioned into its components and what the interaction lines between them are. Here, QCT analysis using a Kohn-Sham one-electron potential (KSpot) in KS equation as a scalar function is initiated and explored, showing KSpot and its resultant electron force lines have novel spatial features which reveal that an atom in a molecule is a spatial basin governed by its nucleus as a 3D-attractor that terminates all the electron force lines defined by the negative gradient of KSpot and that a chemical bond line is just a minimum path of KSpot for the electron motion. Particularly, the atomic charges from this KSpot QCT analysis are moderate and good, having much lower dependence on basis sets chosen for computation. This may provide a platform for the study of molecular structures and properties, intra- and intermolecular electrostatic interaction, energy decomposition, and construction of force field.

Quantitative Assessment of B-B-B, B-Hb -B, and B-Ht Bonds: From BH3 to B12 H12 2

We report the thermodynamic stabilities and the intrinsic strengths of three-center-two-electron B-B-B and B-H_b -B bonds ( H b : bridging hydrogen), and two-center-two-electron B-H_t bonds ( H t : terminal hydrogen) which can be served as a new, effective tool to determine the decisive role of the intermediates of hydrogenation/dehydrogenation reactions of borohydride. The calculated heats of formation were obtained with the G4 composite method and the intrinsic strengths of B-B-B, B-H_b -B, and B-H_t bonds were derived from local stretching force constants obtained at the B3LYP-D2/cc-pVTZ level of theory for 21 boron-hydrogen compounds, including 19 intermediates. The Quantum Theory of Atoms in Molecules (QTAIM) was used to deepen the inside into the nature of B-B-B, B-H_b -B, and B-H_t bonds. We found that all of the experimentally identified intermediates hindering the reversibility of the decomposition reactions are thermodynamically stable and possess strong B-B-B, B-H_b -B, and B-H_t bonds. This proves that thermodynamic data and intrinsic B-B-B, B-H_b -B, and B-H_t bond strengths form a new, effective tool to characterize new (potential) intermediates and to predict their role for the reversibility of the hydrogenation/dehydrogenation reactions.

Quantum Crystallography: Current Developments and Future Perspectives

Crystallography and quantum mechanics have always been tightly connected because reliable quantum mechanical models are needed to determine crystal structures. Due to this natural synergy, nowadays accurate distributions of electrons in space can be obtained from diffraction and scattering experiments. In the original definition of quantum crystallography (QCr) given by Massa, Karle and Huang, direct extraction of wavefunctions or density matrices from measured intensities of reflections or, conversely, ad hoc quantum mechanical calculations to enhance the accuracy of the crystallographic refinement are implicated. Nevertheless, many other active and emerging research areas involving quantum mechanics and scattering experiments are not covered by the original definition although they enable to observe and explain quantum phenomena as accurately and successfully as the original strategies. Therefore, we give an overview over current research that is related to a broader notion of QCr, and discuss options how QCr can evolve to become a complete and independent domain of natural sciences. The goal of this paper is to initiate discussions around QCr, but not to find a final definition of the field.