Photoelectron Spectroscopy and Theoretical Study of Di-Copper-Boron Clusters: Cu2B3- and Cu2B4.

Copper has been found to be able to mediate the formation of bilayer borophenes. Copper-boron binary clusters are ideal model systems to probe the copper-boron interactions, which are essential to understand the growth mechanisms of borophenes on copper substrates. Here, we report a joint photoelectron spectroscopy and theoretical study on two di-copper-doped boron clusters: Cu2B3- and Cu2B4-. Well-resolved photoelectron spectra are obtained, revealing the presence of a low-lying isomer in both cases. Theoretical calculations show that the global minimum of Cu2B3- (C2v, 1A1) contains a doubly aromatic B3- unit weakly interacting with a Cu2 dimer, while the low-lying isomer (C2v, 1A1) consists of a B3 triangle with the two Cu atoms covalently bonded to two B atoms at two vertexes. The global minimum of Cu2B4- (D2h, 2Ag) is found to consist of a rhombus B4 unit covalently bonded to the two Cu atoms at two opposite vertexes, whereas in the low-lying isomer (Cs, 2A'), one of the two Cu atoms is bonded to two B atoms.

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.

Double σ-Aromaticity in a Planar Zinc-Doped Gold Cluster: Au9Zn.

The strong relativistic effects result in many interesting chemical and physical properties for gold and gold compounds. One of the most surprising findings has been that small gold clusters prefer planar structures. Dopants can be used to tune the electronic and structural properties of gold nanoclusters. Here we report an experimental and theoretical investigation of a Zn-doped gold cluster, Au9Zn-. Photoelectron spectroscopy reveals that Au9Zn- is a highly stable electronic system with an electron binding energy of 4.27 eV. Quantum chemical studies show that the global minimum of Au9Zn- has a D3h structure with a closed-shell electron configuration (1A1'), which can be viewed as replacing the central Au atom by Zn in the open-shell parent Au10- cluster. The high electronic stability of Au9Zn- is corroborated by its extremely large HOMO-LUMO gap of 3.3 eV. Chemical bonding analyses revealed that the D3h Au9Zn- are bonded by two sets of delocalized σ bonds, giving rise to double σ aromaticity and its remarkable stability. Two planar low-lying isomers are also observed, corresponding to a similar triangular structure with the Zn atom on the edge and another one with one of the corner Au atoms moved to the edge of the triangle.

Photoelectron Spectroscopy of Size-Selected Bismuth-Boron Clusters: BiBn- (n = 6-8).

Because of its low toxicity, bismuth is considered to be a "green metal" and has received increasing attention in chemistry and materials science. To understand the chemical bonding of bismuth, here we report a joint experimental and theoretical study on a series of bismuth-doped boron clusters, BiBn- (n = 6-8). Well-resolved photoelectron spectra are obtained and are used to understand the structures and bonding of BiBn- in conjunction with theoretical calculations. Global minimum searches find that all three BiBn- clusters have planar structures with the Bi atom bonded to the edge of the planar Bn moiety via two Bi-B σ bonds as well as π bonding by the 6pz orbital. BiB6- is found to consist of a double-chain B6 with a terminal Bi atom. Both BiB7- and BiB8- are composed of a Bi atom bonded to the planar global minima of the B7- and B8- clusters. Chemical bonding analyses reveal that BiB6- is doubly antiaromatic, whereas BiB7- and BiB8- are doubly aromatic. In the neutral BiBn (n = 6-8) clusters, except BiB6 which has a planar structure similar to the anion, the global minima of both BiB7 and BiB8 are found to be half-sandwich-type structures due to the high stability of the doubly aromatic B73- and B82- molecular wheel ligands.

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.

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.

High-Resolution Photoelectron Imaging of IrB3 - : Observation of a π-Aromatic B3 + Ring Coordinated to a Transition Metal.

In a high-resolution photoelectron imaging and theoretical study of the IrB3 - cluster, two isomers were observed experimentally with electron affinities (EAs) of 1.3147(8) and 1.937(4) eV. Quantum calculations revealed two nearly degenerate isomers competing for the global minimum, both with a B3 ring coordinated with the Ir atom. The isomer with the higher EA consists of a B3 ring with a bridge-bonded Ir atom (Cs , 2 A'), and the second isomer features a tetrahedral structure (C3v , 2 A1 ). The neutral tetrahedral structure was predicted to be considerably more stable than all other isomers. Chemical bonding analysis showed that the neutral C3v isomer involves significant covalent Ir-B bonding and weak ionic bonding with charge transfer from B3 to Ir, and can be viewed as an Ir-(η3 -B3 + ) complex. This study provides the first example of a boron-to-metal charge-transfer complex and evidence of a π-aromatic B3 + ring coordinated to a transition metal.

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.

Uncertainty-driven dynamics for active learning of interatomic potentials.

Machine learning (ML) models, if trained to data sets of high-fidelity quantum simulations, produce accurate and efficient interatomic potentials. Active learning (AL) is a powerful tool to iteratively generate diverse data sets. In this approach, the ML model provides an uncertainty estimate along with its prediction for each new atomic configuration. If the uncertainty estimate passes a certain threshold, then the configuration is included in the data set. Here we develop a strategy to more rapidly discover configurations that meaningfully augment the training data set. The approach, uncertainty-driven dynamics for active learning (UDD-AL), modifies the potential energy surface used in molecular dynamics simulations to favor regions of configuration space for which there is large model uncertainty. The performance of UDD-AL is demonstrated for two AL tasks: sampling the conformational space of glycine and sampling the promotion of proton transfer in acetylacetone. The method is shown to efficiently explore the chemically relevant configuration space, which may be inaccessible using regular dynamical sampling at target temperature conditions.

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.

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.

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.

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.

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.