The Boron conundrum: the case of cationic clusters B n + with n?=?2–20

We investigate the molecular and electronic structure and thermochemical properties of the cationic boron clusters B _n ⁺ with n?=?2–20, using both MO and DFT methods. Several functionals are used along with the MP2, G3, G3B3, G4, and CCSD(T)/CBS methods. The latter is the high accuracy reference. While the TPSS, TPSSh, PW91, PB86, and PBE functionals show results comparable to high-accuracy MO methods, both BLYP and B3LYP functionals are not accurate enough for three-dimensional (3D) structures. A negligible difference is observed between the B3LYP, MP2, and CCSD(T) geometries. A transition between 2D and 3D structures occurs for this series at the B₁₆ ⁺–B₁₉ ⁺ sizes. While smaller clusters B _n ⁺ with n?≤?15 are planar or quasi-planar, a structural competition takes place in the intermediate sizes of B _16–19 ⁺ . The B₂₀ ⁺ cation has a 3D tubular shape. The standard heats of formation are determined and used to evaluate the cluster stability. The average binding energy tends to increase with increasing size toward a limit. All closed-shell species B _n ⁺ has an aromatic character, but an enhanced stability is found for B₅ ⁺ and B₁₃ ⁺ whose aromaticity and electron delocalization are analyzed using the LOL technique.     

Cover Feature: Rare Spin Avoided σ-σ Diradical Planar Tetracoordinate Boron Cluster: A Proto-Star for Planar Pentacoordination (ChemPhysChem 18/2023)

We report a global planar star-like cluster B₃Li₃ featuring three planar tetracoordinate boron centres with a rare spin avoided σ-σ diradical character. The cluster was found to be stable towards dissociation into different fragments. The spin density was found to be localized solely on the three boron atoms in the molecular plane. This spin avoided σ-σ diradical character leads to the extension of the coordination number to yield a neutral B₃Li₃H₃ and a cationic B₃Li₃H₃⁺ cluster with three planar pentacoordinate boron centres in their global minimum structures. The planar geometry of the aninonic B₃Li₃H₃⁻ cluster is slightly higher in energy. The planar global clusters were found to maintain planarity in their ligand protected benzene bound complexes, B₃Li₃(Bz)₃, B₃Li₃H₃(Bz)₃ and B₃Li₃H₃(Bz)₃⁺ with high ligand dissociation energies offering candidature for experimental detection.     

High Magnetic Moments in Manganese‐Doped Silicon Clusters

We report on the structural, electronic, and magnetic properties of manganese‐doped silicon clusters cations, Si_nMn⁺ with n=6–10, 12–14, and 16, using mass spectrometry and infrared spectroscopy in combination with density functional theory computations. This combined experimental and theoretical study allows several structures to be identified. All the exohedral Si_nMn⁺ (n=6–10) clusters are found to be substitutive derivatives of the bare Si_n+1⁺ cations, while the endohedral Si_nMn⁺ (n=12–14 and 16) clusters adopt fullerene‐like structures. The hybrid B3P86 functional is shown to be appropriate in predicting the ground electronic states of the clusters and in reproducing their infrared spectra. The clusters turn out to have high magnetic moments localized on Mn. In particular the Mn atoms in the exohedral Si_nMn⁺ (n=6–10) clusters have local magnetic moments of 4 μ_B or 6 μ_B and can be considered as magnetic copies of the silicon atoms. Opposed to other 3d transition‐metal dopants, the local magnetic moment of the Mn atom is not completely quenched when encapsulated in a silicon cage.     

[B30]−: A Quasiplanar Chiral Boron Cluster

Chirality is vital in chemistry. Its importance in atomic clusters has been recognized since the discovery of the first chiral fullerene, the D₂ symmetric C₇₆. ¹ A number of gold clusters have been found to be chiral, ² raising the possibility to use them as asymmetric catalysts. The discovery of clusters with enantiomeric structures is essential to design new chiral materials with tailored chemical and physical properties. ³ Herein we report the first inherently chiral boron cluster of [B₃₀]^? in a joint photoelectron spectroscopy and theoretical study. The most stable structure of [B₃₀]^? is found to be quasiplanar with a hexagonal hole. Interestingly, a pair of enantiomers arising from different positions of the hexagonal hole are found to be degenerate in our global minimum searches and both should co‐exist experimentally because they have identical electronic structures and give rise to identical simulated photoelectron spectra.     

Analysis of Why Boron Avoids sp2 Hybridization and Classical Structures in the BnHn+2 Series

We performed global minimum searches for the B_nH_n+2 (n=2‐5) series and found that classical structures composed of 2c–2e B? H and B? B bonds become progressively less stable along the series. Relative energies increase from 2.9 kcal mol^?1 in B₂H₄ to 62.3 kcal mol^?1 in B₅H₇. We believe this occurs because boron atoms in the studied molecules are trying to avoid sp² hybridization and trigonal structure at the boron atoms, as in that case one 2p‐AO is empty, which is highly unfavorable. This affinity of boron to have some electron density on all 2p‐AOs and avoiding having one 2p‐AO empty is a main reason why classical structures are not the most stable configurations and why multicenter bonding is so important for the studied boron–hydride clusters as well as for pure boron clusters and boron compounds in general.     

Density functional theory study of BnC clusters

B_nC clusters (n = 3–10) were studied at the density functional theory (DFT) (B3LYP)/6‐311G** level of theory. The calculations predicted that the most stable configurations of the B_nC clusters are the (n + 1)‐membered cyclic structures. For boron–carbon clusters, the configurations containing greater numbers of three‐membered boron rings are more favorable, except for the B₇C and B₉C clusters. Through molecular orbital analysis of these B_nC clusters, we have concluded that π‐electron delocalization plays a crucial role in the stability of n + 1‐membered cyclic structures. In this paper, the relative stability of each cluster is discussed based on their single atomic‐binding energies. The capability of clusters to obtain or lose an electron was also discussed, based on their vertical electron detachment energies (VDEs), adiabatic electron detachment energies (ADEs), vertical electron affinities (VEAs) and adiabatic electron affinities (AEAs). Copyright © 2011 John Wiley & Sons, Ltd.     

Structure and energetic of Bn (n = 2–12) clusters: Electronic structure calculations

The electronic and geometric structures, total and binding energies, first and second energy differences, harmonic frequencies, point symmetries, and highest occupied molecular orbital–lowest unoccupied molecular orbital (HOMO–LUMO) gaps of small and neutral B_n (n = 2–12) clusters have been investigated using density functional theory (DFT), B3LYP with 6‐311++G(d,p) basis set. Linear, planar, convex, quasi‐planar, three‐dimensional (3D) cage, and open‐cage structures have been found. None of the lowest energy structures and their isomers has an inner atom; i.e., all the atoms are positioned at the surface. Within this size range, the planar and quasi‐planar (convex) structures have the lowest energies. The first and the second energy differences are used to obtain the most stable sizes. A simple growth path is also discussed with the studied sizes and isomers. The results have been compared with previously available theoretical and experimental works. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Hexagonal Bipyramidal [Ta2B6]−/0 Clusters: B6 Rings as Structural Motifs

It has been a long‐sought goal in cluster science to discover stable atomic clusters as building blocks for cluster‐assembled nanomaterials, as exemplified by the fullerenes and their subsequent bulk syntheses. ¹ , ² Clusters have also been considered as models to understand bulk properties, providing a bridge between molecular and solid‐state chemistry. ³ Because of its electron deficiency, boron is an interesting element with unusual polymorphism. While bulk boron is known to be dominated by the three‐dimensional (3D) B₁₂ icosahedral motifs, ⁴ new forms of elemental boron are continuing to be discovered. ⁵ In contrast to the 3D cages commonly found in bulk boron, in the gas phase two‐dimensional (2D) boron clusters are prevalent. ⁶ – ⁸ The unusual planar boron clusters have been suggested as potential new bulking blocks or ligands in chemistry. ^6a Herein we report a joint experimental and theoretical study on the [Ta₂B₆]⁻ and [Ta₂B₆] clusters. We found that the most stable structures of both the neutral and anion are D_6h bipyramidal, similar to the recently discovered MB₆M structural motif in the Ti₇Rh₄Ir₂B₈ solid compound. ⁹      

Structure and Fluxionality of B13+ Probed by Infrared Photodissociation Spectroscopy

We use cryogenic ion vibrational spectroscopy to characterize the structure and fluxionality of the magic number boron cluster B₁₃⁺. The infrared photodissociation (IRPD) spectrum of the D₂‐tagged all‐¹¹B isotopologue of B₁₃⁺ is reported in the spectral range from 435 to 1790 cm⁻¹ and unambiguously assigned to a planar boron double wheel structure based on a comparison to simulated IR spectra of low energy isomers from density‐functional‐theory (DFT) computations. Born–Oppenheimer DFT molecular dynamics simulations show that B₁₃⁺ exhibits internal quasi‐rotation already at 100 K. Vibrational spectra derived from these simulations allow extracting the first spectroscopic evidence from the IRPD spectrum for the exceptional fluxionality of B₁₃⁺.     

Density functional study of structural and electronic properties of maximum‐spin n+1Aun−1Ag clusters

The structures and relative stabilities of high‐spin ⁿ⁺¹Au_n?1Ag and ⁿAu_n?1Ag⁺ (n = 2–8) clusters have been studied with density functional calculation. We predicted the existence of a number of previously unknown isomers. Our results revealed that all structures of high‐spin neutral or cationic Au_n?1Ag clusters can be understood as a substitution of an Au atom by an Ag atom in the high‐spin neutral or cationic Au_n clusters. The properties of mixed gold–silver clusters are strongly sized and structural dependence. The high‐spin bimetallic clusters tend to be holding three‐dimensional geometry rather than planar form represented in their low‐spin situations. Silver atom prefers to occupy those peripheral positions until to n = 8 for high‐spin clusters, which is different from its position occupied by light atom in the low‐spin situations. Our theoretical calculations indicated that in various high‐spin Au_n?1Ag neutral and cationic species, ⁵Au₃Ag, ³AuAg and ⁵Au₄Ag⁺ hold high stability, which can be explained by valence bond theory. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Construction and applications of symmetrized valence bond wave functions

A method constructing symmetry-adapted bonded Young tableau bases is proposed, based on the symmetry properties of bonded tableaus and the projection operator associated with a point group. Several examples including the ground states and π excited states of O₃⁻, O₃, O₃⁺, and C₃⁻ are shown for instruction to construct the symmetrized valence bond (VB) wave function. Excitation energies of transitions from the ground states to π excited states of O₃⁻, C₃H₅, and C₃⁻ are calculated with an optimized symmetrized valence bond wave function in the σ–π separation approximation. Good agreement between the VB and experimental excitation energies is observed. The bonding features of the ground state and the first π excited singlet and triplet states for S₃ are discussed according to bonding populations from VB calculations. Both the singlet-biradical and the dipole structures have significant contributions to the ground state X ¹A₁ of S₃, while the excited state 1 ¹B₂ is essentially composed of the dipole structures, and the 1 ³B₂ excited state is comprised from a triplet-biradical structure. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 66 : 1–7, 1998     

Structural and Electronic Properties in Titanium-Doped Stannum Clusters: Comparison with Their Anions and Cations

The neutral, anionic, and cationic Sn_nTi^{(0, ±1)} (n?=?1–10) units are researched computationally using a density functional theory. The optimized geometries of Sn_nTi^{(0, ±1)} clusters illustrate that the most stable structures between the neutral, anionic, and cationic clusters keep the similar structures when n?=?1, 2, 4, 5, 9,10, however, we find that the obtained most stable clusters of the size n?=?3, 6, 7, 8 are different. From the optimized results a systematic analysis is carried out to obtain the relative stabilities, electronic properties, and natural population analysis of Sn_nTi^{(0, ±1)} clusters. The relative stabilities are investigated by analyzing the binding energies, fragmentation energies, and the second order energies difference of Sn_nTi^{(0, ±1)} clusters, the results show that the binding energies of anionic clusters are obviously larger than those of neutral and cationic clusters. The HOMO–LUMO gap, the adiabatic electron affinity, vertical electron detachment energy, adiabatic ionization potential energy, and vertical ionization potential energy respond the electronic property, we obtain that the Ti atom changes the electron structures of stannum clusters. To discuss reliable charge transfer information from Sn_nTi clusters to Sn_nTi^? clusters and Sn_nTi⁺ clusters, the natural population analysis of neutral, anionic, and cationic Sn_nTi^(0,±1) clusters are calculated.     

Isomerization of B6, B6 − and B6 + clusters

The interconversions between isomers with the same spin multiplicity of neutral B₆ and charged B₆ ^? and B₆ ⁺ clusters have been investigated at the B3LYP/6-311+G* level of theory, including determination of the minimum energy pathways with transition states connecting the corresponding reactants and products. In dynamic calculations, 26 isomers were optimized, including 11 novel isomers. In order to further refine the energies, single-point B3LYP/6-311+G(3df) calculations were carried out on the corresponding B3LYP/6-311+G* geometries of all isomers of B₆, B₆ ^? and B₆ ⁺ and the corresponding isomerization transition states. The stability of each isomer of B₆ (singlet and triplet states), B₆ ^? (doublet state) and B₆ ⁺ (doublet state) was analyzed from both thermodynamic and dynamic viewpoints.     

Theoretical Studies on the Structures and Stabilities of Charged, Titanium-Doped, Small Silicon Clusters, TiSi n ? /TiSi n + (n?=?1–8)

The structures and stabilities of charged, titanium-doped, small silicon clusters TiSi _n ⁺ /TiSi _n ^? (n?=?1–8) have been systematically investigated using the density functional theory method at the B3LYP/6-311+G* level. For comparison, the geometries of neutral TiSi_n clusters were also optimized at the same level, although most of them have been reported previously (Guo et al., J Chem Phys 126: 234704, 2007). Our results indicate that all neutral TiSi_n clusters favor Si-capped TiSi_n?1 structures, with the lowest energy structure of TiSi₂, TiSi₃, TiSi₄, TiSi₅, TiSi₆, TiSi₇ and TiSi₈ being Si-side-on TiSi adduct, Si-face-capped TiSi₂ triangle, Si-face-capped TiSi₃ trigonal pyramid, Si-face-capped TiSi₄ trigonal bipyramid, Si-face-capped TiSi₅ square bipyramid, Si-face-capped TiSi₆ pentagonal bipyramid, and Si-face-capped TiSi₇ capped pentagonal bipyramid, respectively. The ground state structures obtained herein for the neutral TiSi_n clusters agree well with those of Guo et al. except for TiSi₃ and TiSi₈. Adding or removing an electron greatly changes some ground state structures, i.e. for TiSi₃ ^?/TiSi₃ ⁺, TiSi₅ ^?, TiSi₆ ^?/TiSi₆ ⁺ TiSi₇ ^? and TiSi₈ ^?/TiSi₈ ⁺; others are almost unchanged, e.g. TiSi₂ ^?/TiSi₂ ⁺, TiSi₄ ^?/TiSi₄ ⁺, TiSi₅ ⁺ and TiSi₇ ⁺. Based on the optimized geometries, various energetic properties, including binding energies, fragmentation energies, second-order difference energies, HOMO–LUMO energy gaps, ionization potentials and electron affinities, were calculated for all the most stable isomers. The average binding energies reveal that all of TiSi_n/TiSi _n ⁺ /TiSi _n ^? (n?=?1–8) clusters can continue to gain energy as the size increasing. The fragmentation energies and second-order energy differences suggest that neutral TiSi₅, anionic TiSi₅ ^? and cationic TiSi₆ ⁺ are relatively stable.     

Defect clusters in wustite,Fe1−xO

A quantum chemical approach based on predominantly covalent “normalized ion energies” has been developed for estimating structures and energies for defect clusters in quenched nonstoichiometric wustite (Fe_1?xO). Small defect clusters of zinc blende structure show special stability over other clusters considered. Of these, either a 13:5 or a 16:7 defect cluster (13 or 16 Fe³⁺ vacancies and 5 or 7 tetrahedral Fe³⁺ interstitials) have the proper structure and composition to account for the observed P′ and P″ phases in wustite.     

A density functional study for the isomers of anionic sulfur clusters Sn− (n=3–20)

The signals of anionic sulfur clusters are intense in the mass spectrum of sulfur clusters generated in direct laser vaporization. We have acquired numerous isomers of sulfur clusters by means of the B3LYP DFT method. According to total energies, the most stable S_n⁻ (n=3–13) isomers are predicted. The helical S_n (n=14–20) structures are also calculated. Most of the anionic clusters are with chain configurations; the ring clusters with threefold atom(s) are higher in total energy. The most stable forms of isomers, from S₉⁻ to S₁₃⁻, show helical configurations that are completely different from those of the corresponding neutral and cationic clusters.     

硼碳团簇BnC2 (n＝1～6)的理论研究

应用密度泛函理论在B3LYP/6-311＋G(d)水平上研究了硼碳团簇B_nC₂ (n＝1～6)的几何结构、生长机制和相对稳定性. 计算结果表明, 对于n＝2～6的簇, 平面多环状构型为最稳定的结构, 其中C原子分布于环的顶点、有尽可能多的三配位硼原子和尽可能多的B—C键. 碳原子作为杂原子倾向掺杂于团簇的顶点位置, 它的掺杂不改变硼团簇的主体结构. 与平面多环状结构相比, 随着簇尺寸的增大, 三维结构和线性链结构更不稳定. 在低能线性结构中, C原子位于链两侧的第二个位置. 计算的碎片分裂能、递增键能以及HOMO-LUMO能隙表明, B₄C₂为幻数簇.     

The adduction behavior of water reactant ions with mobility shift reagents in ion mobility spectrometry is determined by the number of locations for adduction,interaction energies,proton affinities,and steric hindrance of these species

The introduction of mobility shift reagents (SRs) into the buffer gas of mobility spectrometers yields SR-ion clusters that decrease ion mobilities and allow the separation of overlapping ions. With a large amount of papers on the introduction of SRs in ion mobility spectrometry (IMS) few investigations explain the behavior of the adducts of reactant ions with SRs and it is not clear what type of peaks to expect which obscures the interpretation of spectra. Electrospray-ionization IMS was coupled to quadrupole mass spectrometry, and 2-butanol (B), ethyl lactate (L), and methanol were introduced as SRs into the buffer gas. The hybrid functional X3LYP/6–311++(d,p) with Gaussian 09 was used for theoretical calculations of SR-ion interaction energies. Adducts of the reactant ions with B and L presented different behaviors; even at low flow rates, L consumed all sodium, reactant ions, and water by adduction, because a) in the experimental conditions, SRs were more concentrated in the buffer gas than reactant ions, b) L’s high proton affinity and c) L’s three electron-donor oxygens, increases adduction. Therefore, chemical equilibria in the buffer gas were only between L and L_nH⁺, L_mH₃O⁺, or L_xNa⁺ adducts and, consequently, these sets of adducts had different mobilities. The lower mobility of L_mH₃O⁺ compared to L_nH⁺ was explained on the base of the lower steric hindrance in LH₃O⁺ for attachment of L molecules. The behavior of reactant ions with B was different: B_nH₃O⁺ and B_nH⁺ overlapped because the relatively low proton affinity and the single and weaker interaction site in B allowed protons and water to be exchanged between species. Finally, L₄H⁺, L₄H₃O⁺, B₄H⁺ and B₅H⁺ ions, not reported before, were seen for large SR concentrations. This study explains two different behaviors of the adducts of SRs with reactant ions using interaction energies, proton affinities, steric hindrance, and the number of locations for adduction.     

Ab initio calculations on (SiH3)2F+: stability in the gas phase and model for bridging fluorine atom in ion-implanted amorphous silicon

Ab initio calculations have been performed on model molecular clusters simulating bridging fluorine configurations in fluorinated amorphous silicon. Optimized geometries, total energies and vibrational frequencies have been computed for (SiH₃)₂F⁺ clusters with the terminal SiH₃ groups eclipsed or staggered. The stable minimum on the potential energy surface corresponds to a linear, but very flexible, Si-F-Si bridging configuration. (SiH₃)₂F⁺ appears to be stable with respect to unimolecular decomposition. The calculated vibrational frequencies include a strongly infrared-active antisymmetric stretch mode at 740 cm⁻¹, similar to the metastable “Bband” experimentally observed at 750 cm⁻¹ in the ion-implanted samples. These results are compared with calculated geometries and vibrational frequencies of SiH₃F, SiH₃F⁺, SiH₂F⁺ and Si₂H₅F.     

The Geometric Structure of Silver‐Doped Silicon Clusters

Cationic silver‐doped silicon clusters, Si_nAg⁺ (n=6–15), are studied using infrared multiple photon dissociation in combination with density functional theory computations. Candidate structures are identified using a basin‐hopping global optimizations method. Based on the comparison of experimental and calculated IR spectra for the identified low‐energy isomers, structures are assigned. It is found that all investigated clusters have exohedral structures, that is, the Ag atom is located at the surface. This is a surprising result because many transition‐metal dopant atoms have been shown to induce the formation of endohedral silicon clusters. The silicon framework of Si_nAg⁺ (n=7–9) has a pentagonal bipyramidal building block, whereas the larger Si_nAg⁺ (n=10–12, 14, 15) clusters have trigonal prism‐based structures. On comparing the structures of Si_nAg⁺ with those of Si_nCu⁺ (for n=6–11) it is found that both Cu and Ag adsorb on a surface site of bare Si_n⁺ clusters. However, the Ag dopant atom takes a lower coordinated site and is more weakly bound to the Si_n⁺ framework than the Cu dopant atom.