Synergy of semiempirical models and machine learning in computational chemistry.

Catalyzed by enormous success in the industrial sector, many research programs have been exploring data-driven, machine learning approaches. Performance can be poor when the model is extrapolated to new regions of chemical space, e.g., new bonding types, new many-body interactions. Another important limitation is the spatial locality assumption in model architecture, and this limitation cannot be overcome with larger or more diverse datasets. The outlined challenges are primarily associated with the lack of electronic structure information in surrogate models such as interatomic potentials. Given the fast development of machine learning and computational chemistry methods, we expect some limitations of surrogate models to be addressed in the near future; nevertheless spatial locality assumption will likely remain a limiting factor for their transferability. Here, we suggest focusing on an equally important effort-design of physics-informed models that leverage the domain knowledge and employ machine learning only as a corrective tool. In the context of material science, we will focus on semi-empirical quantum mechanics, using machine learning to predict corrections to the reduced-order Hamiltonian model parameters. The resulting models are broadly applicable, retain the speed of semiempirical chemistry, and frequently achieve accuracy on par with much more expensive ab initio calculations. These early results indicate that future work, in which machine learning and quantum chemistry methods are developed jointly, may provide the best of all worlds for chemistry applications that demand both high accuracy and high numerical efficiency.

NEXMD v2.0 Software Package for Nonadiabatic Excited State Molecular Dynamics Simulations.

We present NEXMD version 2.0, the second release of the NEXMD (Nonadiabatic EXcited-state Molecular Dynamics) software package. Across a variety of new features, NEXMD v2.0 incorporates new implementations of two hybrid quantum-classical dynamics methods, namely, Ehrenfest dynamics (EHR) and the Ab-Initio Multiple Cloning sampling technique for Multiconfigurational Ehrenfest quantum dynamics (MCE-AIMC or simply AIMC), which are alternative options to the previously implemented trajectory surface hopping (TSH) method. To illustrate these methodologies, we outline a direct comparison of these three hybrid quantum-classical dynamics methods as implemented in the same NEXMD framework, discussing their weaknesses and strengths, using the modeled photodynamics of a polyphenylene ethylene dendrimer building block as a representative example. We also describe the expanded normal-mode analysis and constraints for both the ground and excited states, newly implemented in the NEXMD v2.0 framework, which allow for a deeper analysis of the main vibrational motions involved in vibronic dynamics. Overall, NEXMD v2.0 expands the range of applications of NEXMD to a larger variety of multichromophore organic molecules and photophysical processes involving quantum coherences and persistent couplings between electronic excited states and nuclear velocity.

Semi-Empirical Shadow Molecular Dynamics: A PyTorch Implementation.

Extended Lagrangian Born-Oppenheimer molecular dynamics (XL-BOMD) in its most recent shadow potential energy version has been implemented in the semiempirical PyTorch-based software PySeQM. The implementation includes finite electronic temperatures, canonical density matrix perturbation theory, and an adaptive Krylov subspace approximation for the integration of the electronic equations of motion within the XL-BOMB approach (KSA-XL-BOMD). The PyTorch implementation leverages the use of GPU and machine learning hardware accelerators for the simulations. The new XL-BOMD formulation allows studying more challenging chemical systems with charge instabilities and low electronic energy gaps. The current public release of PySeQM continues our development of modular architecture for large-scale simulations employing semi-empirical quantum-mechanical treatment. Applied to molecular dynamics, simulation of 840 carbon atoms, one integration time step executes in 4 s on a single Nvidia RTX A6000 GPU.

Extending machine learning beyond interatomic potentials for predicting molecular properties.

Machine learning (ML) is becoming a method of choice for modelling complex chemical processes and materials. ML provides a surrogate model trained on a reference dataset that can be used to establish a relationship between a molecular structure and its chemical properties. This Review highlights developments in the use of ML to evaluate chemical properties such as partial atomic charges, dipole moments, spin and electron densities, and chemical bonding, as well as to obtain a reduced quantum-mechanical description. We overview several modern neural network architectures, their predictive capabilities, generality and transferability, and illustrate their applicability to various chemical properties. We emphasize that learned molecular representations resemble quantum-mechanical analogues, demonstrating the ability of the models to capture the underlying physics. We also discuss how ML models can describe non-local quantum effects. Finally, we conclude by compiling a list of available ML toolboxes, summarizing the unresolved challenges and presenting an outlook for future development. The observed trends demonstrate that this field is evolving towards physics-based models augmented by ML, which is accompanied by the development of new methods and the rapid growth of user-friendly ML frameworks for chemistry.

Mechanisms of nitric oxide generation in living systems.

In modern chemical and biochemical studies, special attention is paid to molecular systems capable of generating nitric oxide (NO), which is one of the most important signalling molecules in the body and can trigger a whole cascade of reactions. Despite the importance of this molecule, the mechanisms of its formation in living organisms remain a subject of debate. This review combines the most important methods of releasing NO from endogenous and exogenous sources. The history of endogenous NO donors dates back more than 150 years, since the synthesis of nitroglycerin, which remains the standard vasodilator today, even though it is known that it and many other similar compounds lead to the development of a nitrate tolerance. Particular awareness is devoted to the mechanisms of NO formation without the participation of enzymes, since these methods are most important for creating exogenous sources of NO as drugs. The study of NO formation methods is centred on both the creation of new NO donors and understanding the mechanisms of tolerance to them.

The Rise of Neural Networks for Materials and Chemical Dynamics.

Machine learning (ML) is quickly becoming a premier tool for modeling chemical processes and materials. ML-based force fields, trained on large data sets of high-quality electron structure calculations, are particularly attractive due their unique combination of computational efficiency and physical accuracy. This Perspective summarizes some recent advances in the development of neural network-based interatomic potentials. Designing high-quality training data sets is crucial to overall model accuracy. One strategy is active learning, in which new data are automatically collected for atomic configurations that produce large ML uncertainties. Another strategy is to use the highest levels of quantum theory possible. Transfer learning allows training to a data set of mixed fidelity. A model initially trained to a large data set of density functional theory calculations can be significantly improved by retraining to a relatively small data set of expensive coupled cluster theory calculations. These advances are exemplified by applications to molecules and materials.

Reply to the Comment on "Realization of Lewis Basic Sodium Anion in the NaBH3 - Cluster".

We reply to the comment by S. Pan and G. Frenking who challenged our interpretation of the Na- :→BH3 dative bond in the recently synthesized NaBH3 - cluster. Our conclusion remains the same as that in our original paper (https://doi.org/10.1002/anie.201907089 and https://doi.org/10.1002/ange.201907089). This conclusion is additionally supported by the energetic pathways and NBO charges calculated at UCCSD and CASMP2(4,4) levels of theory. We also discussed the suitability of the Laplacian of electron density (QTAIM) and Adaptive Natural Density Partitioning (AdNDP) method for bond type assignment. It seems that AdNDP yields more sensible results. This discussion reveals that the complex realm of bonding is full of semantic inconsistencies, and we invite experimentalists and theoreticians to elaborate this topic and find solutions incorporating different views on the dative bond.

Boron-Made N2 : Realization of a B≡B Triple Bond in the B2 Al3 - Cluster.

Until now, all B≡B triple bonds have been achieved by adopting two ligands in the L→B≡B←L manner. Herein, we report an alternative route of designing the B≡B bonds based on the assumption that by acquiring two extra electrons, an element with the atomic number Z can have properties similar to those of the element with the atomic number Z+2. Specifically, we show that due to the electron donation from Al to B, the negatively charged B≡B kernel in the B2 Al3 - cluster mimics a triple N≡N bond. Comprehensive computational searches reveal that the global minimum structure of B2 Al3 - exhibits a direct B-B distance of 1.553 Å, and its calculated electron vertical detachment energies are in excellent agreement with the corresponding values of the experimental photoelectron spectrum. Chemical bonding analysis revealed one σ and two π bonds between the two B atoms, thus confirming a classical textbook B≡B triple bond, similar to that of N2 .

Correction: Can aromaticity be a kinetic trap? Example of mechanically interlocked aromatic [2-5]catenanes built from cyclo[18]carbon.

Correction for 'Can aromaticity be a kinetic trap? Example of mechanically interlocked aromatic [2-5]catenanes built from cyclo[18]carbon' by Nikita Fedik et al., Chem. Commun., 2020, 56, 2711-2714.

Can aromaticity be a kinetic trap? Example of mechanically interlocked aromatic [2-5]catenanes built from cyclo[18]carbon.

The unusual stability of cyclo[18]carbon arising from its aromaticity might be used to provide the kinetic trapping needed in the design of interlocked systems. The kinetic barrier separating the interlocked rings and the chemically bonded complex is about 30 kcal mol-1. In addition, the rings can slide freely, which is a promising property for the design of molecular gears and motors.

"Bottled" spiro-doubly aromatic trinuclear [Pd2Ru]+ complexes.

Following an ongoing interest in the study of transition metal complexes with exotic bonding networks, we report herein the synthesis of a family of heterobimetallic triangular clusters involving Ru and Pd atoms. These are the first examples of trinuclear complexes combining these nuclei. Structural and bonding analyses revealed both analogies and unexpected differences for these [Pd2Ru]+ complexes compared to their parent [Pd3]+ peers. Noticeably, participation of the Ru atom in the π-aromaticity of the coordinated benzene ring makes the synthesized compound the second reported example of 'bottled' double aromaticity. This can also be referred to as spiroaromaticity due to the participation of Ru in two aromatic systems at a time. Moreover, the [Pd2Ru]+ kernel exhibits unprecedented orbital overlap of Ru d z 2 AO and two Pd d xy or d x 2-y 2 AOs. The present findings reveal the possibility of synthesizing stable clusters with delocalized metal-metal bonding from the combination of non-adjacent elements of the periodic table which has not been reported previously.

Expansion of Magnetic Aromaticity Criteria to Multilayer Structures: Magnetic Response and Spherical Aromaticity of Matryoshka-Like Cluster [Sn@Cu12 @Sn20 ]12.

Structural characterization of the discrete [Sn@Cu12 @Sn20 ]12- cluster exposed a fascinating architecture composed of three concentric structural layers in which an endohedral Sn atom is enclosed in a Cu12 icosahedron, which in turn is embedded in an Sn20 dodecahedron. Herein, the possibility of sustaining aromatic behavior for this prototypical multilayered species was evaluated, in order to extend this concept to more complex clusters on the basis of magnetic response and bonding analysis by the AdNDP approach. This revealed characteristic features of spherical aromatics, given by the ability to sustain the shielding cone property, similar to archetypal aromatics. The favorable bonding pattern in the [Sn@Cu12 @Sn20 ]12- cluster fulfills the 2(N+1)2 Hirsch rule for aromaticity; thus, the cluster could be regarded as a first member of aromatic multilayered structures. The set of four 13c-2e aromatic bonds that was identified in the internal SnCu12 structure results in spherical aromatic character of this multilayered cluster. This insight builds a bridge between the traditional concept of Hückel's aromaticity and the aromaticity of complex and stable 3D systems that may be explored on the basis of magnetic response and bonding analysis. It also may open a way to novel findings in bottled clusters displaying aromatic behavior in multilayer structures, which are of great interest for inorganic nano- and material sciences due to their unprecedented stability.

Aromatic character of [Au13]5+ and [MAu12]4+/6+ (M = Pd, Pt) cores in ligand protected gold nanoclusters - interplay between spherical and planar σ-aromatics.

The most characteristic feature of planar π-aromatics is the ability to sustain a long-range shielding cone under a magnetic field oriented in a specific direction. In this article, we showed that similar magnetic responses can be found in σ-aromatic and spherical aromatic systems. For [Au13]5+, long-range characteristics of the induced magnetic field in the bare icosahedral core are revealed, which are also found in the ligand protected [Au25(SH)18]- model, proving its spherical aromatic properties, also supported by the AdNDP analysis. Such properties are given by the 8-ve of the structural core satisfying the Hirsch 2(N + 1)2 rule, which is also found in the isoelectronic [M@Au12]4+ core, a part of the [MAu24(SR)18]2- (M = Pd, Pt) cluster. This contrasts with the [M@Au12]6+ core in [MAu24(SR)18]0 (M = Pd, Pt), representing 6-ve superatoms, which exhibit characteristics of planar σ-aromatics. Our results support the spherical aromatic character of stable superatoms, whereas the 6-ve intermediate electron counts satisfy the 4N + 2 rule (applicable for both π- and σ-aromatics), showing the reversable and controlled interplay between 3D spherical and 2D σ-aromatic clusters.

Superoctahedral two-dimensional metallic boron with peculiar magnetic properties.

Among the diversity of new materials, two-dimensional crystal structures have been attracting significant attention from the broad scientific community due to their promising applications in nanoscience. In this study we predict a novel two-dimensional ferromagnetic boron material, which has been exhaustively studied with DFT methods. The relaxed structure of the 2D-B6 monolayer consists of slightly flattened octahedral units connected with 2c-2e B-B σ-bonds. The calculated phonon spectrum and ab initio molecular dynamics simulations reveal the thermal and dynamical stability of the designed material. The calculation of the mechanical properties indicate a relatively high Young's modulus of 149 N m-1. Moreover, the electronic structure indicates the metallic nature of the 2D-B6 sheets, whereas the magnetic moment per unit cell is found to be 1.59 µB. The magnetism in the 2D-B6 monolayer can be described by the presence of two unpaired delocalized bonding elements inside every distorted octahedron. Interestingly, the nature of the magnetism does not lie in the presence of half-occupied atomic orbitals, as was shown for previously studied magnetic materials based on boron. We hope that our predictions will provide promising new ideas for the further fabrication of boron-based two-dimensional magnetic materials.

Comprehensive study of nitrofuroxanoquinolines. New perspective donors of NO molecules.

The goal of present work is the study of NO releasing mechanisms in nitrofuroxanoquinoline (NFQ) derivatives. Mechanisms of their structural non-rigidity and pathways of NO donation - spontaneous or under the action of sulfanyl radicals or photoirradiation - were considered in details, both experimentally and quantum chemically. Furoxan-containing systems of the discussed type are not capable of spontaneous or photoinduced decomposition under mild conditions, and sulfanyl (radical) induced processes are the most preferable. It was shown that appropriate modification of NFQ through [3 + 2] cycloaddition and subsequent aromatization is a powerful tool to design new prospective donors of NO molecule. Two newly obtained NFQ derivatives were proven to have unusually high NO activity in full accordance with the theoretical model. We hope that these examples will encourage community to seek for new NO active molecules among cycloadducts and modified furoxanes.

Realization of Lewis Basic Sodium Anion in the NaBH3 - Cluster.

We report a Na:- →B dative bond in the NaBH3 - cluster, which was designed on the principle of minimum-energy rupture, prepared by laser vaporization, and characterized by a synergy of anion photoelectron spectroscopy and electronic structure calculations. The global minimum of NaBH3 - features a Na-B bond. Its preferred heterolytic dissociation conforms with the IUPAC definition of dative bond. The lone electron pair revealed on Na and the negative Laplacian of electron density at the bond critical point further confirm the dative nature of the Na-B bond. This study represents the first example of a Lewis adduct with an alkalide as the Lewis base.

Hydrated Sulfate Clusters SO42-(H2O) n ( n = 1-40): Charge Distribution Through Solvation Shells and Stabilization.

Investigations of inorganic anion SO42- interactions with water are crucial for understanding the chemistry of its aqueous solutions. It is known that the isolated SO42- dianion is unstable, and three H2O molecules are required for its stabilization. In the current work, we report our  computational study of hydrated sulfate clusters SO42-(H2O) n ( n = 1-40) in order to understand the nature of stabilization of this important anion by water molecules. We showed that the most significant charge transfer from dianion SO42- to H2O takes place at a number of H2O molecules n ≤ 7. The SO42- directly donates its charge only to the first solvation shell and surprisingly, a small amount of electron density of 0.15| e| is enough to be transferred in order to stabilize the dianion. Upon further addition of H2O molecules, we found that the cage effect played an essential role at n ≤ 12, where the first solvation shell closes. During this process, SO42- continues to lose density up to 0.25| e| at n = 12. From this point, additional water molecules do not take any significant amount of electron density from the dianion. These results can help in development of understanding how other solvent molecules could stabilize the SO42- anion as well as other multicharged unstable anions.

Structure and Bonding in [Sb@In8 Sb12 ]3- and [Sb@In8 Sb12 ]5.

We report the characterization of the compound [K([2.2.2]crypt)]4 [In8 Sb13 ], which proves to contain a 1:1 mixture of [Sb@In8 Sb12 ]3- and [Sb@In8 Sb12 ]5- . The tri-anion displays perfect Th symmetry, the first completely inorganic molecule to do so, and contains eight equivalent In3+ centers in a cube. The gas-phase potential energy surface of the penta-anion has eight equivalent minima where the extra pair of electrons is localized on one In+ center, and these minima are linked by low-lying transition states where the electron pair is delocalized over two adjacent centers. The best fit to the electron density is obtained from a model where the structure of the 5- cluster lies close to the gas-phase transition state.

Inorganic Molecular Electride Mg4 O3 : Structure, Bonding, and Nonlinear Optical Properties.

Growing demands of material science and, in particular, in the field of nonlinear optics (NLO) encourage us to look for stable highly polarizable molecules with excess diffuse electrons. An unusual class of compounds called electrides comply with these requirements. Many attempts have been made, yet only few electrides have been synthesized as solids and none of them as molecular species. In this paper, a new theoretically designed molecular species with electride characteristics is reported. The idea of this molecular electride comes from the formation of electride-like features in the MgO crystal with defect F-centers. The geometry of the investigated molecule can be described as a Mg4 O4 cube with one oxygen atom removed. In Mg4 O3 , two 3s electrons are pushed out from the inner area of the molecule forming a diffuse electride multicentered bond. Our calculations show that this electride-like cluster possesses a noticeably large first hyperpolarizability ß=5733 au. At the same time, a complete cube Mg4 O4 and Mg4 O3 2+ without electride electron pair have much smaller ß: 0 au and 741 au, respectively. This fact indicates the decisive role of the electride electron pair in NLO properties. Additionally, vertical detachment energies of isomers (VDE), excitation energies ΔE, polarizabilities α, and IR spectra were calculated. These properties, including ß, are supposed to be observable experimentally and can serve as indirect evidence of the stable molecular electride formation.

Insight into The Nature of Rim Bonds in Coronene.

Coronene is known in chemistry as an aromatic or even superaromatic molecule while it has 24 π-electrons which does not conform to the 4 n + 2 Huckel's rule. Chemical bonding description of it is not settled in chemistry and five models were reported in the literature. According to our model, coronene has two concentric π-systems responsible for aromaticity inside of the molecule. In addition to that there are six peripheral 2c-2e π-bonds, which makes coronene aliphatic/aromatic at the same time. However, recent experiments and calculations put in question the presence of peripheral π-bonds. In order to resolve this issue, we computationally studied reaction mechanism of the Cl2 molecule with C2H4, C6H6, and C24H12. As it turned out, coronene behaves in a way similar to ethylene by adding Cl2 molecule. Thus, it proves that coronene indeed has peripheral double bonds which is also consistent with its experimental geometrical features. Our chemical bonding model allows to identify the most reactive atoms in coronene and other PAHs; therefore, it is a matter of importance for combustion and soot formation studies.