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C[C4H4], the simplest compound of the [4]-pyramidane family, has so far eluded experimental characterization, although several of its analogs E[C4(SiMe3)4], in which the E apex atom is a tetrel group element, have been successfully prepared. The non-classical bonding mode of E, similar to that found in propellanes, has prompted a considerable number of theoretical studies to unravel the nature of the apex-base interaction. Here, we contribute to this knowledge by analyzing the electron localization function (ELF) and classical QTAIM descriptors; as well the statistical distribution of electrons in atomic regions by means of the so-called electron distribution functions (EDFs), calculation of multicenter indices (MCI) as aromaticity descriptors and by performing orbital invariant energy decompositions with the interacting quantum atoms (IQA) approach on a series of E[C4(SiMe3)4] compounds. We find that the bonding evolves from covalent to electrostatic as E changes from C to Pb, with an anomaly when E=Si, which is shown to be the most charged moiety, compatible with an aromatic [C4(SiMe3)4]2- scaffold in the pyramidane base.

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Quantum crystallography is an emerging research field of science that has its origin in the early days of quantum physics and modern crystallography when it was almost immediately envisaged that X-ray radiation could be somehow exploited to determine the electron distribution of atoms and molecules. Today it can be seen as a composite research area at the intersection of crystallography, quantum chemistry, solid-state physics, applied mathematics and computer science, with the goal of investigating quantum problems, phenomena and features of the crystalline state. In this article, the state-of-the-art of quantum crystallography will be described by presenting developments and applications of novel techniques that have been introduced in the last 15 years. The focus will be on advances in the framework of multipole model strategies, wavefunction-/density matrix-based approaches and quantum chemical topological techniques. Finally, possible future improvements and expansions in the field will be discussed, also considering new emerging experimental and computational technologies.

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The interaction energies of two series of molecular balances (1-X with X = H, Me, OMe, NMe2 and 2-Y with Y = H, CN, NO2, OMe, NMe2) designed to probe carbonyl…carbonyl interactions were analysed at the B3LYP/6-311++G(d,p)-D3 level of theory using the energy partitioning method of Interacting Quantum Atoms/Fragments (IQA/IQF). The partitioned energies are analysed by the Relative Energy Gradient (REG) method, which calculates the correlation between these energies and the total energy of a system, thereby explaining the role atoms have in the energetic behaviour of the total system. The traditional "back-of-the-envelope" open and closed conformations of molecular balances do not correspond to those of the lowest energy. Hence, more care needs to be taken when considering which geometries to use for comparison with the experiment. The REG-IQA method shows that the 1-H and 1-OMe balances behave differently to the 1-Me and 1-NMe2 balances because the latter show more prominent electrostatics between carbonyl groups and undergoes a larger dihedral rotation due to the bulkiness of the functional groups. For the 2-Y balance, REG-IQA shows the same behaviour across the series as the 1-H and 1-OMe balances. From an atomistic point of view, the formation of the closed conformer is favoured by polarisation and charge-transfer effects on the amide bond across all balances and is counterbalanced by a de-pyramidalisation of the amide nitrogen. Moreover, focusing on the oxygen of the amide carbonyl and the α-carbon of the remaining carbonyl group, electrostatics have a major role in the formation of the closed conformer, which goes against the well-known n-π* interaction orbital overlap concept. However, REG-IQF shows that exchange-correlation energies overtake electrostatics for all the 2-Y balances when working with fragments around the carbonyl groups, while they act on par with electrostatics for the 1-OMe and 1-NMe2. REG-IQF also shows that exchange-correlation energies in the 2-Y balance are correlated to the inductive electron-donating and -withdrawing trends on aromatic groups. We demonstrate that methods such as REG-IQA/IQF can help with the fine-tuning of molecular balances prior to the experiment and that the energies that govern the probed interactions are highly dependent on the atoms and functional groups involved.

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Machine learning (ML) force fields are revolutionizing molecular dynamics (MD) simulations as they bypass the computational cost associated with ab initio methods but do not sacrifice accuracy in the process. In this work, the GPyTorch library is used to create Gaussian process regression (GPR) models that are interfaced with the next-generation ML force field FFLUX. These models predict atomic properties of different molecular configurations that appear in a progressing MD simulation. An improved kernel function is utilized to correctly capture the periodicity of the input descriptors. The first FFLUX molecular simulations of ammonia, methanol, and malondialdehyde with the updated kernel are performed. Geometry optimizations with the GPR models result in highly accurate final structures with a maximum root-mean-squared deviation of 0.064 Å and sub-kJ mol-1 total energy predictions. Additionally, the models are tested in 298 K MD simulations with FFLUX to benchmark for robustness. The resulting energy and force predictions throughout the simulation are in excellent agreement with ab initio data for ammonia and methanol but decrease in quality for malondialdehyde due to the increased system complexity. GPR model improvements are discussed, which will ensure the future scalability to larger systems.

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We considered it timely to test the applicability of transferable multipole pseudo-atoms for restoring inner-crystal electronic force density fields. The procedure was carried out on the crystal of 1,3-bis(2-hydroxyethyl)-6-methyluracil, and some derived properties of the scalar potential and vector force fields were compared with those obtained from the experimental multipole model and from the aspherical pseudo-atom model with parameters fitted to the calculated structure factors. The procedure was shown to accurately replicate the general vector-field behavior, the peculiarities of the quantum potentials and the characteristics of the force-field pseudoatoms, such as charge, shape and volume, as well as to reproduce the relative arrangement of atomic and pseudoatomic zero-flux surfaces along internuclear regions. It was found that, in addition to the quantum-topological atoms, the force-field pseudoatoms are spatially reproduced within a single structural fragment and similar environment. In addition, the classical and nonclassical hydrogen bonds in the uracil derivative crystal, as well as the H...O, N...O and N...C interactions in the free π-stacked dimer of the uracil derivative molecules, were studied using the potential and force fields within the concepts of interatomic charge transfer and electron lone pair donation-acceptance. Remarkably, the nitrogen atoms in the N...O and N...C interactions behave rather like a Lewis base and an electron contributor. At the same time, the hydrogen atom in the H...O interaction, being a Lewis acid, also participates in the interatomic electron transfer by acting as a contributor. Thus, it has been argued that, when describing polar interatomic interactions within orbital-free considerations, it makes more physical sense to identify electronegative (electron occupier) and electropositive (electron contributor) atoms or subatomic fragments rather than nucleophilic and electrophilic sites.

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We establish a robust protocol for materials innovation based on our proposed transmutation engineering strategy combined with combinatorial chemistry and hierarchical high-throughput screening to make a large class of layered 2D A3BX2 materials. After several rounds of efficient screening, 60 types of easily exfoliable and highly stable A3BX2 monolayers have been obtained. Excitingly, four representative monolayers (ferromagnetic Fe3SiS2 and Fe3GeS2, antiferromagnetic Mn3PbTe2 and Co3GeSe2) demonstrate quite high magnetic critical temperatures of 600 (TC), 630 (TC), 770 (TN), and 510 K (TN), respectively. Through electronic fingerprint identification, the magnetic exchange mechanism is fundamentally unveiled at the atomic level in combination with a local chemical topology environment and crystal/exchange field. Furthermore, two simple and effective unified descriptors are proposed to perfectly explain the origin of magnetic strain regulation. Some intriguing materials (featuring double Dirac cones, node-loops, and ultrahigh Fermi velocities) are expected to be used in high-speed and low-dissipation nanodevices. This material family forms a dataset, which establishes a platform to discover and explore unexpected physicochemcial properties and develop promising applications under different circumstances. The chemical trends of diverse properties for this class of materials are revealed, which offers guiding insights for the development of spintronics and nanoelectronics with the target of exploiting both spin and charge degrees of freedom directed functional materials design and screening.

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A single-domain protein catenane refers to two mechanically interlocked polypeptide rings that fold synergistically into a compact and integrated structure, which is extremely rare in nature. Here, we report a single-domain protein catenane of dihydrofolate reductase (cat-DHFR). This design was achieved by rewiring the connectivity between secondary motifs to introduce artificial entanglement and synthesis was readily accomplished through a series of programmed and streamlined post-translational processing events in cells without any additional in vitro reactions. The target molecule contained few exogenous motifs and was thoroughly characterized using a combination of ultra-performance liquid chromatography-mass spectrometry, sodium dodecyl sulfate-polyacrylamide gel electrophoresis, protease cleavage experiments and ion mobility spectrometry-mass spectrometry. Compared with the linear control, cat-DHFR retained its catalytic capability and exhibited enhanced stability against thermal or chemical denaturation due to conformational restriction. These results suggest that linear proteins may be converted into their concatenated single-domain counterparts with almost identical chemical compositions, well-preserved functions and elevated stabilities, representing an entirely new horizon in protein science.

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The interaction of the thumb site II of the NS5B protein of hepatitis C virus and a pair of drug candidates was studied using a topological energy decomposition method called interacting quantum atoms (IQA). The atomic energies were then processed by the relative energy gradient (REG) method, which extracts chemical insight by computation based on minimal assumptions. REG reveals the most important IQA energy contributions, by atom and energy type (electrostatics, sterics, and exchange-correlation), that are responsible for the behaviour of the whole system, systematically from a short-range ligand-pocket interaction until a distance of approximately 22 Å. The degree of covalency in various key interatomic interactions can be quantified. No exchange-correlation contribution is responsible for the changes in the energy profile of both pocket-ligand systems investigated in the ligand-pocket distances equal to or greater than that of the global minimum. Regarding the hydrogen bonds in the system, a "neighbour effect" was observed thanks to the REG method, which states that a carbon atom would rather not have its covalent neighbour oxygen form a hydrogen bond. The combination of IQA and REG enables the automatic identification of the pharmacophore in the ligands. The coarser Interacting Quantum Fragments (IQF) enables the determination of which amino acids of the pocket contribute most to the binding and the type of energy of said binding. This work is an example of the contribution topological energy decomposition methods can make to fragment-based drug design.

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Machine learning is becoming increasingly more important in the field of force field development. Never has it been more vital to have chemically accurate machine learning potentials because force fields become more sophisticated and their applications expand. In this study a method for developing chemically accurate Gaussian process regression models is demonstrated for an increasingly complex set of molecules. This work is an extension to previous work showing the progression of the active learning technique in producing more accurate models in much less CPU time than ever before. The per-atom active learning approach has unlocked the potential to generate chemically accurate models for molecules such as peptide-capped glycine.

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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.

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One challenge in chemistry is the plethora of often disparate models for rationalizing the electronic structure of molecules. Chemical concepts abound, but their connections are often frail. This work describes a quantum-mechanical framework that enables a combination of ideas from three approaches common for the analysis of chemical bonds: energy decomposition analysis (EDA), quantum chemical topology, and molecular orbital (MO) theory. The glue to our theory is the electron energy density, interpretable as one part electrons and one part electronegativity. We present a three-dimensional analysis of the electron energy density and use it to redefine what constitutes an atom in a molecule. Definitions of atomic partial charge and electronegativity follow in a way that connects these concepts to the total energy of a molecule. The formation of polar bonds is predicted to cause inversion of electronegativity, and a new perspective of bonding in diborane and guanine-cytosine base-pairing is presented. The electronegativity of atoms inside molecules is shown to be predictive of pKa .

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Force fields are actively used to study RNA. Development of accurate force fields relies on a knowledge of how the variation of properties of molecules depends on their structure. Detailed scrutiny of RNA's conformational preferences is needed to guide such development. Towards this end, minimum energy structures for each of a set of 16 small RNA-derived molecules were obtained by geometry optimization at the HF/6-31G(d,p), B3LYP/apc-1, and MP2/cc-pVDZ levels of theory. The number of minima computed for a given fragment was found to be related to both its size and flexibility. Atomic electrostatic multipole moments of atoms occurring in the [HO-P(O3)-CH2-] fragment of 30 sugar-phosphate-sugar geometries were calculated at the HF/6-31G(d,p) and B3LYP/apc-1 levels of theory, and the transferability of these properties between different conformations was investigated. The atomic multipole moments were found to be highly transferable between different conformations with small standard deviations. These results indicate necessary elements of the development of accurate RNA force fields.

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Based on the quantum chemical topology of the modified electron localization function ELFx , 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 Edual 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.

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FFLUX is a biomolecular force field under construction, based on Quantum Chemical Topology (QCT) and machine learning (kriging), with a minimalistic and physically motivated design. A detailed analysis of the forces within the kriging models as treated in FFLUX is presented, taking as a test example a liquid water model. The energies of topological atoms are modeled as 3Natoms -6 dimensional potential energy surfaces, using atomic local frames to represent the internal degrees of freedom. As a result, the forces within the kriging models in FFLUX are inherently N-body in nature where N refers to Natoms . This provides a fuller picture that is closer to a true quantum mechanical representation of interactions between atoms. The presented computational example quantitatively showcases the non-negligible (as much as 9%) three-body nature of bonded forces and angular forces in a water molecule. We discuss the practical impact on the pressure calculation with N-body forces and periodic boundary conditions (PBC) in molecular dynamics, as opposed to classical force fields with two-body forces. The equivalence between the PBC-related correction terms in the general virial equation is shown mathematically.

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Despite its role in spin density functional theory and it being the basic observable for describing and understanding magnetic phenomena, few studies have appeared on the electron spin density subtleties thus far. A systematic full topological analysis of this function is lacking, seemingly in contrast to the blossoming in the last 20 years of many studies on the topological features of other scalar fields of chemical interest. We aim to fill this gap by unveiling the kind of information hidden in the spin density distribution that only its topology can disclose. The significance of the spin density critical points, the 18 different ways in which they can be realized and the peculiar topological constraints on their number and kind, arising from the presence of positive and negative spin density regions, is addressed. The notion of molecular spin graphs, spin maxima (minima) joining paths, spin basins and of their valence is introduced. We show that two kinds of structures are associated with a spin-polarized molecule: the usual one, defined through the electron density gradient, and the magnetic structure, defined through the spin density gradient and composed in general by at least two independent spin graphs, related to spin density maxima and minima. Several descriptors, such as the spin polarization index, are introduced to characterize the properties of spin density critical points and basins. The study on the general features of the spin density topology is followed by the specific example of the water molecule in the 3B1 triplet state, using spin density distributions of increasing accuracy.

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Energy profiles of seven halogen-bonded complexes were analysed with the topological energy partitioning called Interacting Quantum Atoms (IQA) at MP4(SDQ)/6-31+G(2d,2p) level of theory. Explicit interatomic electron correlation energies are included in the analysis. Four complexes combine X2 (X = Cl or F) with HCN or NH3, while the remaining three combine ClF with HCN, NH3 or N2. Each complex was systematically deformed by translating the constituent molecules along its central axis linking X and N, and reoptimising its remaining geometry. The Relative Energy Gradient (REG) method (Theor. Chem. Acc. 2017, 136, 86) then computes which IQA energies most correlate with the total energy during the process of complex formation and further compression beyond the respective equilibrium geometries. It turns out that the covalent energy (i.e., exchange) of the halogen bond, X…N, itself drives the complex formation. When the complexes are compressed from their equilibrium to shorter X…N distance then the intra-atomic energy of N is in charge. When the REG analysis is restricted to electron correlation then the interatomic correlation energy between X and N again drives the complex formation, and the complex compression is best described by the destabilisation of the through-space correlation energy between N and the "outer" halogen.

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Based on parametrized tight Gaussian functions, an efficient and robust methodology designed to restore the effective core potentials electron densities and the inner shells of the electron localization function is introduced and tested. Attention is focused on the underlying effects of augmented coreless electron densities on selected quantum topological descriptors computed for a test set of species containing heavy elements such as the emblematic uranyl cation. Also, this article shows how a proper topology of the electron density can be recovered from semi-empirical Hückel calculations where core densities are missing.

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The formation of C70O from C70O3 monomolozonide is a three-step process with the isomer dependent last step leading either to c,c-C70O epoxide or d,d-C70O oxidoannulene. The process involves the open intermediate (first O-O then Cc-Cc/Cd-Cd bonds broken), oxidoannulene-like structure intermediate (new Cc-O/Cd-O bond formed) and finally the oxide product. On the formation of c,c-C70O isomer, the final release of O2 is followed by the restoration of Cc-Cc bond, which stabilizes the product. Neither Cd-Cd bond is restored nor the total energy essentially lowered upon d,d-C70O formation. At all steps of the studied process, the four CC bonds adjacent to Cc-Cc or Cd-Cd bond, respectively, play a crucial role donating or withdrawing the necessary electron density. C70(O)O2 products, with O2 bridging one of the bonds adjacent to the parent Cc-Cc/Cd-Cd one, may compete with the oxide products. The OO bond in such structures is weak as suggested by its low electron population. For both c,c-C70O3 and d,d-C70O3, the shape of the potential energy surfaces (0 K) and the related, reported earlier, room temperature-free energy surfaces differ. Graphical abstract.

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The nature of halogen-bond interactions has been analysed from the perspective of the astatine element, which is potentially the strongest halogen-bond donor. Relativistic quantum calculations on complexes formed between halide anions and a series of Y3 C-X (Y=F to X, X=I, At) halogen-bond donors disclosed unexpected trends, e. g., At3 C-At revealing a weaker donating ability than I3 C-I despite a stronger polarizability. All the observed peculiarities have their origin in a specific component of C-Y bonds: the charge-shift bonding. Descriptors of the Quantum Chemical Topology show that the halogen-bond strength can be quantitatively anticipated from the magnitude of charge-shift bonding operating in Y3 C-X. The charge-shift mechanism weakens the ability of the halogen atom X to engage in halogen bonds. This outcome provides rationales for outlier halogen-bond complexes, which are at variance with the consensus that the halogen-bond strength scales with the polarizability of the halogen atom.

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Key to progress in molecular simulation is the development of advanced models that go beyond the limitations of traditional force fields that employ a fixed, point charge-based description of electrostatics. Taking water as an example system, the FFLUX framework is shown capable of producing models that are flexible, polarizable and have a multipolar description of the electrostatics. The kriging machine-learning methods used in FFLUX are able to reproduce the intramolecular potential energy surface and multipole moments of a single water molecule with chemical accuracy using as few as 50 training configurations. Molecular dynamics simulations of water clusters (25-216 molecules) using the new FFLUX model reveal that incorporating charge-quadrupole, dipole-dipole, and quadrupole-charge interactions into the description of the electrostatics results in significant changes to the intermolecular structuring of the water molecules. © 2019 The Authors. Journal of Computational Chemistry published by Wiley Periodicals, Inc.