Adaptive Density Partitioning Research Articles

Concentric dual π delocalisation and conflicting aromaticity in bowl-like B56 cluster: an all-boron analogue of circumbiphenyl C38H16

We present computational evidence for concentric dual π delocalisation and conflicting aromaticity in an elongated quasi-planar bowl-like B56 (C 2v, 1A1) cluster, using the canonical molecular orbital (CMO) and the adaptive natural density partitioning (AdNDP) analyses at the density functional theory (DFT) level. The first B12 and second B18 rings constitute an inner BDR ribbon, and the second B18 and third B24 rings form an outer BDR ribbon. Chemical bonding analyses indicate that the 19 delocalised π bonds can be divided into two separate π subsystems, with inner 14π and outer 24π delocalised electrons. The bonding pattern is consistent with conflicting π aromaticity, which leads to an elongated geometry. A refined bonding model is also proposed for circumbiphenyl molecule C38H16, of which the B56 cluster is an inorganic analogue. The updated bonding pictures differ from that reported in prior studies on the system. It is further unravelled the mechanism as to why the two hexagonal holes prefer to be located at the centre. This research enriches the analogous relationship between quasi-planar boron clusters and their polycyclic hydrocarbons counterparts.

The Aromaticity of Osmapentalenes Derivatives. An Analysis Based on Electron-delocalization Indices.

A systematic investigation of the aromatic features of the electronic structures of a family of recently synthesized osmapentalene derivatives has been carried by means of indices derived from the calculated one-electron density matrix of the corresponding geometry optimized compounds, and complemented by the analysis of the valence molecular orbitals and the delocalized bonding units emerging from the adaptive natural density partitioning method. The calculated delocalization indices between consecutive atom pairs, and normalized multicenter indices are very suggestive of the aromatic character of the equatorial fused carbon rings (except triangular ones) for all the members of the family. Since the electron-delocalization based indices allow precise quantification of the aromaticity, differences of the aromatic character among the various members have also been highlighted, and have been found to be consistent with the magnetic based criteria indices reported earlier. Finally, the valence molecular orbitals along with the delocalized bonding units of the adaptive natural density partitioning indicate that the aromaticity of these compounds is sustained by either 10 or 14 π electrons, which satisfy the Hückel aromatic electron counting rule.

Three-fold π delocalisation bonding pattern in bowl-like B70 cluster: an all-boron analogue of the nanographene molecule C48H18

A chemical bonding model for the quasi-planar bowl-like B70 cluster has been presented using the canonical molecular orbital (CMO) and the adaptive natural density partitioning (AdNDP) analyses at the density functional theory (DFT) level. Chemical bonding analysis indicates that the bowl-like B70 is an all-boron analogues of one planar nanographene molecule (C48H18) featuring concentric triple π delocalisation with 6π, 12π and 30π electrons for the inner, middle and outer boron ribbons, respectively. The bonding nature of C48H18 is fully elucidated herein firstly. The infrared spectra of B70 are predicted to facilitate the future experimental characterisations. This research enriches the analogous relationship between planar boron clusters and their polycyclic aromatic hydrocarbons (PAHs) counterparts. The bowl-shaped B70 is the largest boron analogue of PAH reported to date. The unique bonding picture of concentric, three-fold π delocalisation has not been discussed previously in the literature.

Structural evolution and electronic properties of anionic plutonium-doped oxygen clusters

Plutonium oxides are important in actinide chemistry and nuclear industry activities, and the demand and interest in enriching knowledge of plutonium chemistry is growing increasingly significant. However, unlike uranium oxide clusters, few studies related to the geometry and bonding properties of anionic plutonium oxide clusters have been reported. Here we explored the geometries, photoelectron spectra, and electronic properties of anionic plutonium oxide clusters by means of unbiased structural searches coupled with density-functional theory (DFT). The results show that the PuO6− cluster with a high D2h symmetry formed by a linear O-Pu-O plutonyl unit with two O2 units exhibits excellent stability. In addition, the HOMO–LUMO gap value of PuO6− cluster are 4.35 eV and 3.41 eV for the α- and β-orbitals, respectively, as well as the vertical detachment energy (VDE) of 4.20 eV. In the analysis of molecular orbitals and adaptive natural density partitioning in oxygen-rich systems, the σ bonds between plutonium atom and oxygen ligands, primarily from the Pu-5f and O-2p orbitals, are responsible for the goodish stability of PuO6− cluster. We hope that the current work can enrich the geometrical configuration of plutonium oxide oxygen clusters and provide reference information for the subsequent research work.

Structural Evolution of Small-Sized Phosphorus-Doped Boron Clusters: A Half-Sandwich-Structured PB15 Cluster.

The present study is a theoretical investigation into the structural evolution, electronic properties, and photoelectron spectra of phosphorus-doped boron clusters PBn0/- (n = 3-17). The results of this study revealed that the lowest energy structures of PBn- (n = 3-17) clusters, except for PB17-, exhibit planar or quasi-planar structures. The lowest energy structures of PBn (n = 3-17), with the exceptions of PB7, PB9, and PB15, are planar or quasi-planar. The ground state of PB7 has an umbrella-shaped structure, with C6V symmetry. Interestingly, the neutral cluster PB15 has a half-sandwich-like structure, in which the P atom is attached to three B atoms at one end of the sandwich, exhibiting excellent relative and chemical stability due to its higher second-order energy difference and larger HOMO-LUMO energy gap of 4.31 eV. Subsequently, adaptive natural density partitioning (AdNDP) and electron localization function (ELF) analyses demonstrate the bonding characteristics of PB7 and PB15, providing support for the validity of their stability. The calculated photoelectron spectra show distinct characteristic peaks of PBn- (n = 3-17) clusters, thus providing theoretical evidence for the future identification of doped boron clusters. In summary, our work has significant implications for understanding the structural evolution of doped boron clusters PBn0/- (n = 3-17), motivating further experiments regarding doped boron clusters.

Exploration of Free Energy Surface of the Au10 Nanocluster at Finite Temperature.

The first step in comprehending the properties of Au10 clusters is understanding the lowest energy structure at low and high temperatures. Functional materials operate at finite temperatures; however, energy computations employing density functional theory (DFT) methodology are typically carried out at zero temperature, leaving many properties unexplored. This study explored the potential and free energy surface of the neutral Au10 nanocluster at a finite temperature, employing a genetic algorithm coupled with DFT and nanothermodynamics. Furthermore, we computed the thermal population and infrared Boltzmann spectrum at a finite temperature and compared it with the validated experimental data. Moreover, we performed the chemical bonding analysis using the quantum theory of atoms in molecules (QTAIM) approach and the adaptive natural density partitioning method (AdNDP) to shed light on the bonding of Au atoms in the low-energy structures. In the calculations, we take into consideration the relativistic effects through the zero-order regular approximation (ZORA), the dispersion through Grimme's dispersion with Becke-Johnson damping (D3BJ), and we employed nanothermodynamics to consider temperature contributions. Small Au clusters prefer the planar shape, and the transition from 2D to 3D could take place at atomic clusters consisting of ten atoms, which could be affected by temperature, relativistic effects, and dispersion. We analyzed the energetic ordering of structures calculated using DFT with ZORA and single-point energy calculation employing the DLPNO-CCSD(T) methodology. Our findings indicate that the planar lowest energy structure computed with DFT is not the lowest energy structure computed at the DLPN0-CCSD(T) level of theory. The computed thermal population indicates that the 2D elongated hexagon configuration strongly dominates at a temperature range of 50-800 K. Based on the thermal population, at a temperature of 100 K, the computed IR Boltzmann spectrum agrees with the experimental IR spectrum. The chemical bonding analysis on the lowest energy structure indicates that the cluster bond is due only to the electrons of the 6 s orbital, and the Au d orbitals do not participate in the bonding of this system.

Probing the Structural and Electronic Properties of the Anionic and Neutral Tellurium-Doped Boron Clusters TeBnq (n = 3-16, q = 0, -1).

In this study, we employ density functional theory along with the artificial bee colony algorithm for cluster global optimization to explore the low-lying structures of TeBnq (n = 3-16, q = 0, -1). The primary focus is on reporting the structural properties of these clusters. The results reveal a consistent doping pattern of the tellurium atom onto the in-plane edges of planar or quasi-planar boron clusters in the most energetically stable isomers. Additionally, we simulate the photoelectron spectra of the cluster anions. Through relative stability analysis, we identify three clusters with magic numbers -TeB7-, TeB10, and TeB12. The aromaticity of these clusters is elucidated using adaptive natural density partitioning (AdNDP) and magnetic properties analysis. Notably, TeB7- exhibits a perfect σ-π doubly aromatic structure, while TeB12 demonstrates strong island aromaticity. These findings significantly contribute to our understanding of the structural and electronic properties of these clusters.

Nonplanar Aromaticity of Dinuclear Rare-Earth Metallacycles.

While the concept of metalla-aromaticity has well been extended to transition organometallic compounds in diverse geometries, aromatic rare-earth organometallic complexes are rare due to the special (n - 1)d0 configuration and high-lying (n - 1)d orbitals of rare-earth centers. In particular, nonplanar cases of rare-earth complexes have not been reported so far. Here, we disclose the nonplanar aromaticity of dinuclear scandium and samarium metallacycles characterized by various aromaticity indices (nucleus-independent chemical shift, isochemical shielding surface, anisotropy of induced current density, and isomerization stabilization energy). Bonding analyses (Kohn-Sham molecular orbital, adaptive natural density partitioning, multicenter bond indices, and principal interacting orbital) reveal that three delocalized π orbitals, predominantly contributed by the 2-butene tetraanion ligand, result in the formation of six-electron conjugated systems. Guided by these findings, we predicted that the lutetium and gadolinium analogues of dinuclear rare-earth metallacycles should be aromatic, which have been verified by the successful synthesis of real molecules. This work extends the concept of nonplanar aromaticity to the field of rare-earth metallacycles and illuminates the path for designing and synthesizing various rare-earth metalla-aromatics.

Restriction on molecular fluxionality by substitution: A case study for the 1,10-dicyanobullvalene.

We show herein that 1,10-dicyano substitution restricts the paragon fluxionality of bullvalene to just 14 isomers which isomerize along a single cycle. The restricted fluxionality of 1,10-dicyanobullvalene (DCB) is investigated by means of: (i) Bonding analyses of the isomer structures using the adaptive natural density partitioning (AdNDP). (ii) Quantum dynamical simulations of the isomerizations along the cyclic intrinsic reaction coordinate of the potential energy surface (PES). The PES possesses 14 equivalent potential wells supporting 14 isomers which are separated by 14 equivalent potential barriers supporting 14 transition states. Accordingly, at low temperatures, DCB appears as a hindered molecular rotor, without any delocalization of the wavefunction in the 14 potential wells, without any nuclear spin isomers, and with completely negligible tunneling. These results are compared and found to differ from those for molecular boron rotors. (iii) Born-Oppenheimer molecular dynamics (BOMD) simulations of thermally activated isomerizations. (iv) Calculations of the rate constants in the frame of transition state theory (TST) with reasonable agreement achieved with the BOMD results. (v) Simulations of the equilibration dynamics using rate equations for the isomerizations with TST rate coefficients. Accordingly, in the long-time limit, isomerizations of the 14 isomers, each with Cs symmetry, approach the "14 Cs → C7v" thermally averaged structure. This is a superposition of the 14 equally populated isomer structures with an overall C7v symmetry. By extrapolation, the results for DCB yield working hypotheses for so far un-explored properties e.g. for the equilibration dynamics of C10H10.

Introducing hafnium to atomically small- and medium-sized tin clusters (HfSnn0/-/2- (n = 4–17)): A computational investigation of geometrical and growth behavior, spectral properties, electronic configuration and thermochemistry

The global and local minimum configurations of single Hf atom doped Sn clusters are conducted via density function theory (DFT) combined with artificial bee colony algorithm (ABCluster). Furthermore, DFT method is also used to systematically investigate on their structural growth evolution, spectral and electronic information, thermochemical properties following the size of tin clusters doped Hf atom. Structurally, the ground-state geometries of neutral, anion and di-anion are discovered that, from n = 4, the number of Sn atoms in cluster, HfSnn0/-/2- adsorb additional Sn atom on the prior architecture one by one until forming n = 17 for HfSnn-10/-, as well as forming n = 16 for HfSnn-12-. And for the HfSn110/- and HfSn102- as beginning the species veritably develop sealed architectures. The strongest vibrational modes of sealed nanoclusters are stretching modes of Hf atom with infrared actives and breathing modes of the Sn cage framework with Raman actives, respectively. The natural population analysis (NPA) elucidates the stronger relationship between the Hf atoms and the tin frameworks in sealed clusters than that in unsealed clusters. The results of thermochemical properties, molecular orbital shell (MOs), adaptive natural density partitioning (AdNDP) and ultraviolet visible absorption spectrum (UV–Vis) indicate that, the HfSn16 with high symmetry of Td exhibits thermochemical stability and optoelectronic properties, which is utilized potentially as zero-dimensional unit of self-assembling fluorescent nanomaterials.

Unveiling the structural and bonding properties of AuSi2- and AuSi3- clusters: A comprehensive analysis of anion photoelectron spectroscopy and abinitio calculations.

Silicon clusters infused with transition metals, notably gold, exhibit distinct characteristics crucial for advancing microelectronics, catalysts, and energy storage technologies. This investigation delves into the structural and bonding attributes of gold-infused silicon clusters, specifically AuSi2- and AuSi3-. Utilizing anion photoelectron spectroscopy and abinitio computations, we explored the most stable isomers of these clusters. The analysis incorporated Natural Population Analysis, electron localization function, molecular orbital diagrams, adaptive natural density partitioning, and Wiberg bond index for a comprehensive bond assessment. Our discoveries reveal that cyclic configurations with the Au atom atop the Si-Si linkage within the fundamental Si2 and Si3 clusters offer the most energetically favorable structures for AuSi2- and AuSi3- anions, alongside their neutral counterparts. These anions exhibit notable highest occupied molecular orbital-lowest unoccupied molecular orbital gaps and significant σ and π bonding patterns, contributing to their chemical stability. Furthermore, AuSi2- demonstrates π aromaticity, while AuSi3- showcases a distinctive blend of σ antiaromaticity and π aromaticity, crucial for their structural robustness. These revelations expand our comprehension of gold-infused silicon clusters, laying a theoretical groundwork for their potential applications in high-performance solar cells and advanced functional materials.

The geometry, electronic and magnetic properties of Zr n Ni (n = 2-14) clusters: A first-principles jointed particle-swarm-optimization investigation

Zirconium-nickel binary alloys and metal glass have superior performance like ultrahigh fracture strength, good toughness. In this paper, the structures of small-sized Zr n Ni (n = 2–14) clusters have been searched using the particle swarm algorithm in combination with density-functional theory (DFT). The geometrical configuration tends to form a three-dimensional structure as the number of atoms in the cluster increases. By calculating the average binding energy per atom, second-order difference of energy, and dissociation energy of Zr n Ni (n = 2–14) clusters, it is demonstrated that Zr n Ni (n = 7, 12) clusters are more stable than their neighbors, and can be used as a candidate structure for magic number clusters. The electron localization function (ELF) calculations reveal those metallic bonds of Zr-Ni and Zr-Zr atoms. The Adaptive natural density partitioning results show that there are 20 three-center and 7 seven-center two-electron orbitals which make the quenching of magnetic moments of Zr12Ni atoms.

FeC4H22+ Encompassing Planar Tetracoordinate Iron: Structure and Bonding Patterns

The singlet, triplet, and quintet electronic states of the FeC4H22+ system are theoretically explored using quantum chemical methods, and 39 isomers are identified in the singlet electronic state and 4 isomers in both triplet and quintet electronic states. A molecule with a planar tetracoordinate iron (ptFe) is found on the potential energy surface of singlet and triplet electronic states. The bonding features of ptFe in the singlet electronic state are analyzed with natural bond orbital (NBO) analysis, adaptive natural density partitioning (AdNDP), and molecular orbital analysis. The resultant data delineate that the ptFe is stabilized through electron delocalization in the ptFe system.

The structural and electronic split: Boron vs aluminum hydrides

We systematically investigated the structural evolution of boron (B) and aluminum (Al) hydrides using various DFT and ab initio methods, aiming to reveal the similarities and differences in their geometric and electronic structures. While B hydrides have been extensively studied both experimentally and theoretically, less is known about its group 13 heavier congener, Al. Extensive global minimum searches of the B2Hx (Al2Hx) and B3Hy (Al3Hy) hydrides (x = [0–6], y = [0–9]) were performed to identify the most stable geometric structures for each stoichiometry. In most of the series, B and Al hydrides exhibit qualitatively different structures, except for the most saturated X2H5 and X2H6 stoichiometries. Chemical bonding analyses employing adaptive natural density partitioning and electron localization function methods identified notable differences between B and Al hydrides in most of the compositions. B hydrides predominantly possess two-center (2c) and three-center (3c) bonding elements, suggesting a relatively balanced electron distribution. On the contrary, Al hydrides tend to retain unpaired electrons or lone pairs on Al atoms, forming a large number of closely lying isomers with various combinations of 1c, 2c, 3c, and 4c bonding elements. Thermodynamic stability analyses revealed that all studied clusters demonstrated stability toward various H/H2 dissociation pathways, with Al hydrides being less stable than B counterparts.

Large-size gold–aluminum alloy cluster Al12Au60 stabilized by an encapsulating B12 icosahedron: a first-principles study

The investigation of novel clusters incorporating gold (Au) has attracted increasing attention due to their intriguing architecture and feasibility of experimental synthesis. In this study, a large-size gold–aluminum alloy cluster with icosahedral B12 as its core, specifically a B12@Al12Au60 cluster, is proposed and demonstrated to have remarkable stability as ascertained through first-principles calculations. The core–shell assembly, B12@Al12Au60, exhibiting I symmetry, is characterized by the incorporation of an icosahedral B12 motif within the outer shell of the Al12Au60 framework. By thorough analysis encompassing vibrational frequency and molecular dynamics simulations, the structural stability of the core–shell B12@Al12Au60 is investigated. The electronic characteristics are probed through adaptive natural density partitioning analysis, revealing the presence of 66 multi-center two-electron σ bonds distributed across the entirety of the core–shell configuration. Furthermore, scrutiny of distinct dimeric configurations composed of core–shell B12@Al12Au60 underscores their relative autonomy and potential prospects for applications within cluster-assembled materials.

Global minimum and a heap of low-lying isomers with planar tetracoordinate carbon in the CAl3MgH2- system.

A global minimum and a heap of low-lying isomers with planar tetracoordinate carbon (ptC) are identified in the CAl3MgH2- system by computational quantum chemical investigations. The nature of the chemical bonding in the global minimum ptC isomer is examined using the conceptual quantum chemical tools. The atoms in molecule (AIM) analysis reveals that the global minimum isomer possesses a ptC geometry. Additionally, the adaptive natural density partitioning (AdNDP), electron localization function (ELF), and nucleus-independent chemical shifts (NICS) analysis corroborate the presence of delocalization in the ptC isomer. The delocalization of electron density in the global minimum ptC isomer contributes to attaining structural stability. The results also suggest that the bridging hydrogen plays a crucial role in stabilizing the ptC system. Furthermore, the ab initio molecular dynamics study supports the structural stability of the ptC isomer.

Exploring the stability and aromaticity of rare earth doped tin cluster MSn16- (M = Sc, Y, La).

Rare earth elements have high chemical reactivity, and doping them into semiconductor clusters can induce novel physicochemical properties. The study of the physicochemical mechanisms of interactions between rare earth and tin atoms will enhance our understanding of rare earth functional materials from a microscopic perspective. Hence, the structure, electronic characteristics, stability, and aromaticity of endohedral cages MSn16- (M = Sc, Y, La) have been investigated using a combination of the hybrid PBE0 functional, stochastic kicking, and artificial bee colony global search technology. By comparing the simulated results with experimental photoelectron spectra, it is determined that the most stable structure of these clusters is the Frank-Kasper polyhedron. The doping of atoms has a minimal influence on density of states of the pure tin system, except for causing a widening of the energy gap. Various methods such as ab initio molecular dynamics simulations, the spherical jellium model, adaptive natural density partitioning, localized orbital locator, and electron density difference are employed to analyze the stability of these clusters. The aromaticity of the clusters is examined using iso-chemical shielding surfaces and the gauge-including magnetically induced currents. This study demonstrates that the stability and aromaticity of a tin cage can be systematically adjusted through doping.

Four-membered heterocyclic molecules featuring boron and heavy group 14 elements that exhibit both σ-aromatic and π-aromatic properties: a new synthetic target.

In this study, we present a series of theoretically designed B2G14G14' molecules, featuring four-membered-ring heterocycles containing boron and heavy group 14 elements (G14 and G14' = Si, Ge, Sn, and Pb). Through the use of density functional theory (DFT), natural bond orbital (NBO) analysis, quantum theory of atoms in molecules (QTAIM), and electron localization function (ELF), our studies demonstrate a strong π single bond between the bridgehead G14 and G14' atoms, with minimal participation from a very weak G14-G14' σ bond. Additionally, the nucleus independent chemical shift (NICS), anisotropy of current-induced density (ACID), and adaptive natural density partitioning (AdNDP) analyses definitively establish the presence of both σ-aromaticity and π-aromaticity in these inorganic four-membered heterocyclic neutral molecules.

Chemical bonding misnomer in AeF- (Ae = Be-Ca) anions.

Chemical bonding is the fundamental concept in chemistry and multiple bonding holds a special position. Recent quantum chemical calculations predicted the presence of triple dative bonds in BeF- and MgF- and quadruple dative bonds in CaF- anions. The present quantum chemical calculations based on quantum theory of atoms in molecules (QTAIM), electron localization function (ELF) and adaptive density partitioning (AdNDP) analyses find no sign of multiple dative bonding in these anions. In fact, the bond is actually an electron-sharing covalent one, rather than dative. Charge distribution analysis and comparison with a neutral AeF molecule reveal no difference in bonding between the neutral AeF molecule and its anion.

Exploring the potential energy surface of B4H42-: an exception of the Wade-Mingos rules.

An analysis of the potential energy surface of B4H42- which, according to Wade-Mingos rules should have a tetrahedral structure, is presented. Our results indicate that the global minimum has a planar diamond-like boron skeleton and that the nearest local minimum lies 7.8 kcal mol-1 above it. This isomer corresponds to a Jahn-Teller distorted tetrahedral B4H4 structure as a result of the gain of two electrons. Furthermore, the analysis of the bonding pattern using the Adaptive Natural Density Partitioning method indicates a double σ and π delocalization providing high stability. These results show that B4H42- is an exception to the Wade-Mingos rules and open the door to future experimental characterization of this compound.