Adaptive Natural Density Partitioning Analyses Research Articles

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.

Electric field-driven up-and-down motion of the flexible tail of Al13+ cluster system-a nano-scale flipper.

Dynamic metal nanoclusters have become a hot area of research in the field of nanoscience and nanotechnology due to their potential applications in micro devices. One such dynamic cluster is a quasi-planar ground state (GS) Al13+ cluster which exhibits anelectric field driven up and down flipping motion of the flexible tail which oscillates with respect to the mean plane. A Car-Parrinello molecular dynamics (CPMD) simulation has been carried out to understand the nature of dynamics of the cluster. CPMD simulation study reveals that the flexible tail region of the Al13+ isomeric system (two ground states M1, M2 and a transition state TS connecting them) can be engaged in a systematic up down flipping motion by the application of a transverse electric field. A saw tooth electric field of amplitude 5.19V/nm is sufficient to induce the up-and-down flipping oscillation of the cluster, which has an average oscillation frequency of around 20 THz. AIM, NICS and AdNDP analyses also have been carried out to understand the fluxional nature of the cluster from the electronic structural perspective. Electronic structural analysis of selected optimized intermediate states in the presence of transverse electric field has also been analyzed to correlate the electronic structure with the dynamic nature of the cluster. Single-point energies of all intermediate states between two minima of Al13+ clusters connected through a transition state cluster. Optimized geometries of Al13+ clusters in the presence of electric field of different strengths have been carried out by using the Gaussian 03 package. 6-311 + G(d) basis set and B3LYP hybrid density functional have been utilized for these studies. To establish the flipping motion, Car-Parrinello molecular dynamics (CPMD) has been performed using the cp.x module of the Quantum ESPRESSO 6.3.0 program package using the Perdew-Burke-Ernzerhof (PBE) functional, plane-wave basis set and ultrasoft pseudopotentials. ORTEP-3 and POV ray-3.7 software packages have been used for visualization and graphics generation. Atoms in molecule (AIM), Adaptive Natural Density Partitioning (AdNDP) analysis have been carried out using Multiwfn 3.7 program package.

Five Bonds to Carbon through Tri-Coordination in 
 Al3C3−/0

Here, five bonds to carbon through tri-coordination are theoretically established in the global minimum energy isomers of Al3C3− anion (1a) and Al3C3 neutral (1n) for the first time. Various isomers of Al3C3−/0 are theoretically identified using density functional theory at the PBE0-D3/def2-TZVP level. Chemical bonding features are thoroughly analyzed for these two isomers (1a and 1n) with different bonding and topological quantum chemical tools, such as adaptive natural density partitioning (AdNDP), Wiberg Bond Indices (WBIs), nucleus-independent chemical shifts (NICS), and atoms in molecules (AIM) analyses. The structure of isomer 1a is planar with C2v symmetry, whereas its neutral counterpart 1n is non-planar with C2 symmetry, in which its terminal aluminum atoms are out of the plane. The central allenic carbon atom of isomers 1a and 1n exhibits tri-coordination and thus makes it a case of five bonds to carbon, which is confirmed through their total bond order as observed in WBI. Both the isomers show σ- and π-aromaticity and are predicted with the NICS and AdNDP analyses. Further, the results of ab initio molecular dynamics simulations reveal their kinetic stability at room temperature; thus, they are experimentally viable systems.

Structural evolution and electronic properties of neutral and anionic TiASil (A = Sc, Ti; l ≤ 12): relatively stable TiASi4 as a structural unit.

Simulated photoelectron spectroscopy was conducted to investigate the structural evolution and electronic properties of TiASil (A = Sc, Ti; l ≤ 12) clusters and their anions via the Perdew-Burke-Enzerhof scheme and extensive cluster search using the ABCluster software. The results revealed that the ground-state structures of the TiASil (A = Sc, Ti) clusters generally exhibited similar configurations except for the Ti2Si3, ScTiSi3, and TiScSi10 clusters. Furthermore, the TiASil clusters exhibited an adsorptive evolution pattern, and the TiASi4 unit was considered the basic constituent framework of the structure, excluding several distortions and minor changes. With the increase in the cluster size, the lowest-energy structures varied from the exohedral to the cage structures of the single-metal atom at the center. Regarding the second energy difference data, the neutral TiASi4 clusters exhibited better stability among the neutral and anionic TiASil (A = Sc, Ti; l ≤ 12) clusters. Furthermore, the chemical bonding in the TiASi4 clusters was analyzed by molecular orbitals (MOs), highest occupied MO-lowest unoccupied MO gaps, and adaptive natural density partitioning analyses for the best Ti2Si4 cluster especially, and the results were combined with the natural population analysis data. The hybridization of the spd orbital of the metal atoms, eight localized bonds, and four delocalized bonds may primarily account for the relative stabilities of the neutral, square bipyramidal structure of Ti2Si4. Thus, the TiASi4 clusters may be assembled as the basic units of silicon-based semiconductor clusters of large-size neutral and anionic TiASil.

Understanding electronic structures, chemical bonding, and fluxional behavior of Lu2@C2n (2n = 76-88) by a theoretical study.

Endohedral metal-metal-bonding fullerenes, in which encapsulated metals form covalent metal-metal bonds inside, are an emerging class of endohedral metallofullerenes. Herein, we reported quantum-chemical studies on the electronic structures, chemical bonding, and dynamic fluxionality behavior of endohedral metal-metal-bonding fullerenes Lu2@C2n (2n = 76-88). Multiple bonding analysis approaches, including molecular orbital analysis, the natural bond orbital analysis, electron localization function, adaptive natural density partitioning analysis, and quantum theory of atoms in molecules, have unambiguously revealed one two-center two-electron σ covalent bond between two Lu ions in fullerenes. Energy decomposition analysis with the natural orbitals for chemical valence method on the bonding nature between the encapsulated metal dimer and the fullerene cage suggested the existence of two covalent bonds between the metal dimer and fullerenes, giving rise to a covalent bonding nature between the metal dimer and fullerene cage and a formal charge model of [Lu2]2+@[C2n]2-. For Lu2@C76, the dynamic fluxionality behavior of the metal dimer Lu2 inside fullerene C76 has been revealed via locating the transition state with an energy barrier of 5 kcal/mol. Further energy decomposition analysis calculations indicate that the energy barrier is controlled by a series of terms, including the geometric deformation energy, electrostatic interaction, and orbital interactions.

Pentacoordinate Carbon Atoms in a Ferrocene Dication Derivative—[Fe(Si2-η5-C5H2)2]2+

Pentacoordinate carbon atoms are theoretically predicted here in a ferrocene dication derivative in the eclipsed-(1; C2v), gauche-(2; C2) and staggered-[Fe(Si2-η5-C5H2)2]2+(3; C2h) forms for the first time. Energetically, the relative energy gaps for 2 and 3 range from −3.06 to 16.74 and −2.78 to 40.34 kJ mol−1, respectively, when compared to the singlet electronic state of 1 at different levels. The planar tetracoordinate carbon (ptC) atom in the ligand Si2C5H2 becomes a pentacoordinate carbon upon complexation. The ligand with a ptC atom was predicted to be both a thermodynamically and kinetically stable molecule by some of us in our earlier theoretical works. Natural bond orbital and adaptive natural density partitioning analyses confirm the pentacoordinate nature of carbon in these three complexes (1–3). Although they are hypothetical at the moment, they support the idea of “hypercoordinate metallocenes” within organometallic chemistry. Moreover, ab initio molecular dynamics simulations carried out at 298 K temperature for 2000 fs suggest that these molecules are kinetically stable.

Structural evolution and relative stability of vanadium-doped boron clusters

Cluster is the intermediate of individual atom and larger agglomeration. The structural evolutions of clusters are critically important to explore the physical properties of bulk solids. Here, we carry out systematic structure predictions of medium-sized vanadium-doped boron clusters by using crystal structure analysis by particle swarm optimization method combined with density function theory calculations. A great deal of low-lying isomers with attractive geometries are discovered, such as the crown-like VB18 − cluster and the drum-like VB20 − cluster. Interestingly, the VB12 − cluster possesses excellently relative stability due to its higher second-order difference and larger highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) energy gap. The molecular orbitals (MOs) and adaptive natural density partitioning (AdNDP) analysis indicate that the 3d orbitals of V atom and the 2p and 2s orbitals of B atoms are the primary constituents of the MOs, and the interactions between V and B atoms are the main factor for the robust stabilization of the anionic VB12 − cluster. The present findings advance the understanding of the structural evolution of transition metal doped boron clusters and offer crucial insights for future experiments.

Au12@Au30: Core-Shell Molecule Constituted of an Icosahedron and an Icosidodecahedron

A stable core-shell structure with Ih symmetry, Au12@Au30, has been investigated by first-principles calculations. It is composed of an icosahedron core and an icosidodecahedron shell. The stability of the core-shell Au42 structure is verified by vibrational frequency analysis and molecular dynamics NVT simulations. Both the frontier molecular orbitals and the spin density of states show obvious s-d hybridization characteristics. The adaptive natural density partitioning analysis demonstrate multi-center bonds, twenty 6-center {\sigma} bonds ,and one 12-center {\sigma} bond, which are of great importance for the core-shell structural stability. In this core-shell nanostructure, there are also a large number of one-center valence lone electron pairs with the characteristics of d-like orbitals, so that the proposed Au12@Au30 could be used in medicine and catalysis fields.

New insight into the electronic structure of SiF4: synergistic back-donation and the eighteen-electron rule.

SiF4 demonstrated high thermal stability in dry air or vacuum, and a Si-F bond length of 1.554 Å is close to the second period element C-C bond length (1.54 Å) of C2H6. To determine which factors confer this property of SiF4, here we conduct a comparative study of a series of molecules SiHnF4-n (n = 0, 1, 2, 3), SiX4 (X = Cl, Br, I), CF4 and TiF4 in terms of bond length and energy, molecular orbitals, and adaptive natural density partitioning (AdNDP) analysis. The AdNDP analysis shows that there are five 5c-2c bonds in SiF4, here named synergistic back-donation (SBD) bonds. These SBD bonds together with the Si-F σ bonds and the eighteen-electron rule are demonstrated as the main factors contributing to the short Si-F bond length and the high thermal stability of SiF4 in dry air or vacuum. Moreover, the SBD bonds exist widely in other isoelectronic species of SiF4 such as ClO4-, SO42-, PO43- and XeO4.

Strong Be-Be bonds in double-aromatic bridged Be2(μ-SO) molecules.

A bridged Be2(μ-SO) molecule is formed by stabilizing the Be2 dimer using a SO ligand. In this molecule, which is thermodynamically stable, the Be2 moiety behaves as an efficient electron donor toward the SO fragment. The ionic character of Be2δ+ and SOδ- in this molecule is confirmed by NBO analysis. Energy decomposition analysis shows that the strongest attractive interactions in this molecule are the polarization and exchange interactions. Also, Adaptive Natural Density Partitioning (AdNDP) analysis indicates the stability of this molecule, which could be due to the double-aromatic character of this system. Therefore, it seems that the title molecule could be experimentally detected.

In Silico Studies on Selected Neutral Molecules, CGa2Ge2, CAlGaGe2, and CSiGa2Ge Containing Planar Tetracoordinate Carbon

Density functional theory (DFT) was used to study the structure, stability, and bonding in some selected neutral pentaatomic systems, viz., CGa2Ge2, CAlGaGe2, and CSiGa2Ge containing planar tetracoordinate carbon. The systems are kinetically stable, as predicted from the ab initio molecular dynamics simulations. The natural bond orbital (NBO) analysis showed that strong electron donation occurs to the central planar carbon atom by the peripheral atoms in all the studied systems. From the nucleus independent chemical shift (NICS) analysis, it is shown that the systems possess both σ- and π- aromaticity. The presence of 18 valence electrons in these systems, in their neutral form, appears to be important for their stability with planar geometries rather than tetrahedral structures. The nature of bonding is understood through the adaptive natural density partitioning analysis (AdNDP), quantum theory of atoms in molecules (QTAIM) analysis, and also via Wiberg bond index (WBI) and electron localization function (ELF).

C−C Bond Formation between the μ‐Alkylidyne Ligands in a Diruthenium Bis(μ‐alkylidyne) Complex; σ‐ and π‐Aromaticity of the Ru2C2 Core

AbstractZn‐free μ‐ethylidyne‐μ‐propylidyne complex, [(Cp*Ru)2(μ‐CMe)(μ‐CEt)] (2 b; Cp*=C5Me5) was synthesized by the treatment of [(Cp*Ru)2(μ‐CMe)(μ‐CEt)(μ‐ZnCl2)] (1 b) with ethylenediamine. Similarly, bis(μ‐ethylidyne) complex [Cp*Ru(μ‐CMe)]2 (2 a) was synthesized from [Cp*RuCl2]2. Although the bis(μ‐alkylidyne) complexes 2 a, b adopted a coordinatively unsaturated 32‐electron configuration, these complexes were unreactive toward acetylene, ethylene, and H2. Adaptive natural density partitioning (AdNDP) analysis suggested that the enhanced stability of 2 a and 2 b was due to the dual aromaticity of the planar Ru2C2 core, viz. σ‐ and π‐aromaticity. On the other hand, complexes 2 a and 2 b reacted with π‐acidic CO to yield a μ‐η2:η2‐alkyne complex, [(Cp*Ru)2(μ‐η2:η2‐MeCCR)(μ‐CO)] (6 a, R=Me; 6 b, R=Et) via C−C bond formation between the μ‐alkylidyne ligands, along with Ru−Ru bond formation. Dearomatization of the Ru2C2 core is crucial for this transformation. Complex 6 a further reacted with CO in the presence of methanol to yield [Cp*Ru(CO)(μ‐CO)]2 (7) by liberating 2‐butyne.

A joint experimental and theoretical study on structural, electronic, and magnetic properties of MnGen - (n = 3-14) clusters.

A systematic structure and property investigation of MnGen - (n = 3-14) was conducted by means of density functional theory coupled with mass-selected anion photoelectron spectroscopy. This combined theoretical and experimental study allows global minimum and coexistence structures to be identified. It is found that the pentagonal bipyramid shape is the basic framework for the nascent growth process of MnGen - (n = 3-10), and from n = 10, the endohedral structures can be found. For n = 12, the anion MnGe12 - cluster probably includes two isomers: a major isomer with a puckered hexagonal prism geometry and a minor isomer with a distorted icosahedron geometry. Specifically, the puckered hexagonal prism isomer follows the Wade-Mingos rules and can be suggested as a new kind of superatom with the magnetic property. Furthermore, the results of adaptive natural density partitioning and deformation density analyses suggest a polar covalent interaction between Ge and Mn for endohedral clusters of MnGe12 -. The spin density and natural population analysis indicate that MnGen - clusters have high magnetic moments localized on Mn. The density of states diagram visually shows the significant spin polarization for endohedral structures and reveals the weak interaction between the Ge 4p orbital and the 4s, 3d orbitals of Mn.

Umbrella-shaped vs planar; evolutionary search for BnQ, Be©BnQ (n = 6–12, Q = 0, −1) clusters

We used the universal structure predictor: evolutionary xtallography (USPEX) method conjugated with density functional theory (DFT) calculations to investigate the global search of the neutral and anionic BnQ and Be©BnQ (n = 6–12, Q = 0,−1) clusters. The lowest- energy structures of BnQ, Be©BnQ clusters mainly featured planar or quasi-planar for all clusters, except for Be©B70/−and Be©B80/− (umbrella-shaped) clusters. Based on obtained data, it can be seen that the most stable structure of neutral and anionic clusters are the same except for B60/− and Be©B110/− clusters. Based on our calculations, the Be©B8 cluster with umbrella-shaped (heptagonal bi-pyramidal) can be observed as a magic cluster, which is extremely thermodynamic and kinetic stability. A net charge transfer from the Be metal atom to the boron motif demonstrated that the electrostatic interactions has an essential role in the stability of boron-doped clusters. Furthermore, molecular orbital (MO) and adaptive natural density partitioning (AdNDP) analyses ascertained that the enhanced stability of Be©B8 resulted from strong interactions between the 2 s orbital of Be atom and the 2s2p orbitals of the B atoms. Moreover, the B–B σ bonds in the B8 shell, which can be considered σ-anti-aromaticity and π-aromaticity, contribute to the stabilization of the Be©B8 cluster.

TM4B18 0/- (TM = Hf, Ta, W, Re, Os): new structure construction with TM doped B wheel units.

We report the global search for the lowest energy structures of the transition metal (TM) doped B clusters, TM4B180/− (TM = Hf, Ta, W, Re, Os) and their electronic properties. A combination of the comprehensive genetic algorithm (CGA) method with density functional theory (DFT) calculations shows that they are composed of four planar TM@B9 wheel units by sharing B atoms, except for Os4B180/−, which consists of two types of planar molecular wheels of Os@B7 and Os@B8. Among these nanoclusters, it is found that the Ta4B18 cluster has a closed-shell with a large HOMO–LUMO gap of 2.61 eV. Adaptive natural density partitioning analysis (AdNDP) reveals that the Ta4B18 cluster has σ antiaromaticity and π aromaticity, i.e., a conflicting aromaticity. The simulated photoelectron spectra (PES) of all anionic clusters are also provided for future experimental investigations.

Structural and bonding properties of AlnC4−/0 (n = 2–4) clusters: Anion photoelectron spectroscopy and theoretical calculations

We measured the photoelectron spectra of AlnC4− (n=2-4) clusters by using size-selected anion photoelectron spectroscopy. The structures of AlnC4−/0 (n = 2–4) clusters were explored with quantum chemistry calculations and were determined by comparing the theoretical results with the experimental spectra. It is found that the most stable structure of Al2C4− anion is a C2v symmetry planar structure with two Al atoms interacting with two C2 units. In addition, Al2C4− anion also has a D∞h symmetry linear structure with two Al atoms located at the two ends of a C4 chain, which is slightly higher in energy than the planar structure. The most stable structure of neutral Al2C4 has a D∞h symmetry linear structure. The most stable structure of Al3C4− anion is a planar structure with three Al atoms interacting with two C2 units. Whereas neutral Al3C4 cluster has a C2v symmetric V-shaped bent structure. The global minima structures of both Al4C4− and neutral Al4C4 are C2h symmetry planar structures with four Al atoms interacting with the ends of two C2 units. Adaptive natural density partitioning analyses of AlnC4− (n=2−4) clusters show that the interactions between the Al atoms and C2 units have both σ and π characters.

Structural evolution in boron-based clusters B5Aln0/-/+ (n = 1–4): Al atoms transition from the periphery of the planar W-shaped B5 ring to the vertex of the bipyramid

The structures and properties of binary boron-aluminum B5Aln0/-/+ (n = 1–4) clusters have been systematically explored using the density functional theory method at the B3LYP/6–311+G(d) level and the coupled cluster method at the CCSD(T)/6–311+G(2df)//B3LYP/6–311+G(d) level. Lowest-energy structures, stabilities, growth behaviors and chemical bonding of these clusters were analyzed. Our results show that when the number of doped Al atoms is one or two, the Al atoms are located at the periphery, and the host B5 cluster preferentially forms a W-shape core, which is only slightly affected by the Al atoms. When there are three or four Al atoms, the B5Aln0/-/+ (n = 3, 4) clusters have their lowest energy structures preferentially in capped bipyramid configurations. Neutral B5Aln (n = 1, 3) clusters are somewhat more stable than their neighboring n clusters, while anionic and cationic B5Aln-/+ (n = 2, 4) clusters tend to be somewhat more stable. We also simulated the infrared (IR) spectrum and photoelectron spectroscopy (PES) of these clusters for future experimental comparison. Adaptive natural density partitioning (AdNDP) analysis shows that a variety of delocalized multicenter bonds appear in these clusters, which may enhance the stability of the clusters.

Tuning of Structure Evolution and Electronic Properties through Palladium-Doped Boron Clusters: PdB16 as a Motif for Boron-Based Nanotubes.

Transition metal-doped electronic deficiency boron clusters have led to a vast variety of electronic bonding properties in chemistry and materials science. We have determined the ground state structures of PdBn0/- (n = 10-20) clusters by performing CALYPSO search and density functional theory (DFT) optimization. The identified lowest energy structures for both neutral and anionic Pd-doped boron clusters follow the structure evolution from two dimensional (2D) planar configurations to 3D distorted Pd-centered drum-like or tubular structures. Photoelectron spectra are simulated by time-dependent DFT theoretical calculations, which is a powerful method to validate our obtained ground-state structures. More interestingly, two "magic" number clusters, PdB12 and PdB16, are found with enhanced stability in the middle size regime studied. Subsequently, molecular orbital and adaptive natural density partitioning analyses reveal that the high stability of the PdB16 cluster originates from doubly σ π aromatic and bonding interactions of d-type atomic orbitals of the Pd atom with tubular B16 units. The tubular C8v PdB16 cluster, with robust relative stability, is an ideal embryo for forming finite and infinite nanotube nanomaterials.

LiB13: A New Member of Tetrahedral-Typed B13 Ligand Half-Surround Cluster

It will get entirely unusual derivatives with gratifying chemical bonding schemes for boron clusters by doping with lithium, the lightest alkalis. The geometric structures and electronic properties of the LiBn0/− (n = 10−20) clusters have been studied through Crystal structure AnaLYsis by Particle Swarm Optimization (CALYPSO) structural search approach along with the density functional theory (DFT) calculations. The low-lying candidates of LiBn0/− (n = 10–20) are reoptimized at the B3LYP functional in conjunction with 6–311 + G(d) basis set. Three forms of geometric configurations are identified for the ground-state structures of LiBn0/− clusters: half-sandwich-type, quasi-planar and drum-type structures. The photoelectron spectra (PES) of the LiBn− clusters have been calculated through time-dependent density functional theory (TD-DFT). A promising LiB13 with tetrahedral-typed B13 ligand half-surround cluster and robust stability is uncovered. The molecular orbital and adaptive natural density partitioning (AdNDP) analysis show that B-B bonds in the B13 moiety combined with the interaction between the B13 shell and Li atom stabilize the C2v LiB13 cluster. Our results advance the fundamental understanding about the alkali metal doped boron clusters.

Modular bonding picture for aromatic borometallic molecular wheels

Borometallic molecular wheel is a special class of clusters with a planar ring of boron atoms surrounding a transition metal center, and its distinctive geometry and atypical electronic structure make this class of clusters an interesting target for theoretical analysis. Previous adaptive natural density partitioning analyses have provided a bonding picture for them. In this work, we take a slightly different perspective on their bonding, by considering such clusters as coordination complexes. We find that these clusters can be understood through a simple modular bonding picture, which could be applied to a number of related complexes/clusters.