The nature of the chemical bond in Be2+, Be2, Be2−, and Be3

A nucleophilic beryllyl complex via metathesis at [Be-Be]2

Owing to its high toxicity, the chemistry of element number four, beryllium, is poorly understood. However, as the lightest elements provide the basis for fundamental models of chemical bonding, there is a need for greater insight into the properties of beryllium. In this context, the chemistry of the homo-elemental Be-Be bond is of fundamental interest. Here the ligand metathesis chemistry of diberyllocene (1; CpBeBeCp)-a stable complex with a Be-Be bond-has been investigated. These studies yield two complexes with Be-Be bonds: Cp*BeBeCp (2) and [K{(HCDippN)2BO}2]BeBeCp (3; Dipp = 2,6-diisopropylphenyl). Quantum chemical calculations indicate that the Be-Be bond in 3 is polarized to such an extent that the complex could be formulated as a mixed-oxidation state Be0/BeII complex. Correspondingly, it is demonstrated that 3 can transfer the 'beryllyl' anion, [BeCp]-, to an organic substrate, by analogy with the reactivity of sp2-sp3 diboranes. Indeed, this work reveals striking similarities between the homo-elemental bonding linkages of beryllium and boron, despite the respective metallic and non-metallic natures of these elements.

BeM(CO)3- (M = Co, Rh, Ir) and BeM(CO)3 (M = Ni, Pd, Pt): Triply bonded terminal beryllium in zero oxidation state

We perform detailed potential energy surface explorations of BeM(CO)3- (M = Co, Rh, Ir) and BeM(CO)3 (M = Ni, Pd, Pt) using both single-reference and multireference-based methods. The present results at the CASPT2(12,12)/def2-QZVPD//M06-D3/def2-TZVPPD level reveal that the global minimum of BeM(CO)3- (M = Co, Rh, Ir) and BePt(CO)3 is a C3v symmetric structure with an 1A1 electronic state, where Be is located in a terminal position bonded to M along the center axis. For other cases, the C3v symmetric structure is a low-lying local minimum. Although the present complexes are isoelectronic with the recently reported BFe(CO)3- complex having a B-Fe quadruple bond, radial orbital-energy slope (ROS) analysis reveals that the highest occupied molecular orbital (HOMO) in the title complexes is slightly antibonding in nature, which bars a quadruple bonding assignment. Similar weak antibonding nature of HOMO in the previously reported BeM(CO)4 (M = Ru, Os) complexes is also noted in ROS analysis. The bonding analysis through energy decomposition analysis in combination with the natural orbital for chemical valence shows that the bonding between Be and M(CO)3q (q = -1 for M = Co, Rh, Ir and q = 0 for M = Ni, Pd, Pt) can be best described as Be in the ground state (1S) interacting with M(CO)30/- via dative bonds. The Be(spσ) → M(CO)3q σ-donation and the complementary Be(spσ) ← M(CO)3q σ-back donation make the overall σ bond, which is accompanied by two weak Be(pπ) ← M(CO)3q π-bonds. These complexes represent triply bonded terminal beryllium in an unusual zero oxidation state.

Beryllium Dimer Reactions with Acetonitrile: Formation of Strong Be-Be Bonds

Laser ablated Be atoms have been reacted with acetonitrile molecules in 4 K solid neon matrix. The diberyllium products BeBeNCCH3 and CNBeBeCH3 have been identified by D and 13C isotopic substitutions and quantum chemical calculations. The stabilization of the diberyllium species is rationalized from the formation of the real Be-Be single bonds with bond distances as 2.077 and 2.058 Å and binding energies as -27.1 and -77.2 kcal/mol calculated at CCSD (T)/aug-cc-pVTZ level of theory for BeBeNCCH3 and CNBeBeCH3, respectively. EDA-NOCV analysis described the interaction between Be2 and NC···CH3 fragments as Lewis "acid-base" interactions. In the complexes, the Be2 moiety carries positive charges which transfer from antibonding orbital of Be2 to the bonding fragments significantly strengthen the Be-Be bonds that are corroborated by AIM, LOL and NBO analyses. In addition, mono beryllium products BeNCCH3, CNBeCH3, HBeCH2CN and HBeNCCH2 have also been observed in our experiments.

Photoelectron Velocity Map Imaging Spectroscopy of the Beryllium Trimer and Tetramer

Computational studies of small beryllium clusters (BeN) predict dramatic, nonmonotonic changes in the bonding mechanisms and per-atom cohesion energies with increasing N. To date, experimental tests of these quantum chemistry models are lacking for all but the Be2 molecule. In the present study, we report spectroscopic data for Be3 and Be4 obtained via anion photodetachment spectroscopy. The trimer is predicted to have D3h symmetric equilibrium structures for both the neutral molecule and the anion. Photodetachment spectra reveal transitions that originate from the X2A2″ ground state and the 12A1' electronically excited state. The state symmetries were assigned on the basis of anisotropic photoelectron angular distributions. The neutral and anionic forms of Be4 are predicted to be tetrahedral. Franck-Condon diagonal photodetachment was observed with a photoelectron angular distribution consistent with the expected Be4-X2A1 → Be4X1A1 transition. The electron affinities of Be3 and Be4 were determined to be 11363 ± 60 and 13052 ± 50 cm-1, respectively.

Three-membered beryllium ring, Be3: not just a hydrogen bond acceptor

Quantum chemical calculations predict that the three-membered beryllium ring, Be3 is not just a hydrogen bond acceptor. It is a bond breaker. Calculations reveal that the global minimum geometry of Be3HX (X = F, Cl, OH, CN) features a linear geometry with complete cleavage of the H-X bond along with linearization of the Be3 unit. The linear geometry is radical stabilized Be trimer, R-Be-Be-Be-R. Thus, the present study clearly reveals that the Be3 ring has more to offer than just showing hydrogen bond accepting ability.

Diberyllocene, a stable compound of Be(I) with a Be-Be bond

The complex diberyllocene, CpBeBeCp (Cp, cyclopentadienyl anion), has been the subject of numerous chemical investigations over the past five decades yet has eluded experimental characterization. We report the preparation and isolation of the compound by the reduction of beryllocene (BeCp₂) with a dimeric magnesium(I) complex and determination of its structure in the solid state by means of x-ray crystallography. Diberyllocene acts as a reductant in reactions that form beryllium-aluminum and beryllium-zinc bonds. Quantum chemical calculations indicate parallels between the electronic structure of diberyllocene and the simple homodiatomic species diberyllium (Be₂).

Beryllium bonding with noble gas atoms

Quantum chemical calculations were carried out to investigate the nature of the bonding between a neutral Be₃ ring and noble gas atom. Electronic structure calculation for these complexes was carried out at different computational levels in association with natural bond orbital, quantum theory of atoms in molecules, electron localization function, symmetry adapted perturbation theory, and molecular electrostatic potential surface analysis of Be₃ complexes. The Be atoms in the Be₃ moiety are chemically bonded to one another, with the BeBe bond dissociation energy being ~125 kJ mol^-1 . The Be₃ ring interacts with the noble gases through non-covalent interactions. The binding energies of the noble gas atoms with the Be₃ ring increases with increase in their atomic number. The non-covalent interaction index, density overlap region indicator and independent gradient model analyses reveal the presence of non-covalent inter-fragment interactions in the complexes. Energy decomposition analysis reveals that dispersion plays the major role towards stabilizing these systems.

More about properties of Morse oscillator

Using Birge-Sponer extrapolation we have analyzed the approximation of the potential of a real diatomic molecule by the Morse model, which implies a constant value of anharmonicity ωx. The real values of ωx*(v) for each vibrational level are estimated from transition frequencies between neighboring levels. The dependence of ωx* on the vibrational quantum number v up to dissociation is calculated from the literature data for the ground electronic state of H₂, O₂, Be₂, Li₂, ArXe, Xe₂, Kr₂ and the excited state of Li₂. Characteristic features of deviations of the anharmonicity parameter x* - x from the Morse model are described.

Exploration of interlacing and avoided crossings in a manifold of potential energy curves by a unitary group adapted state specific multi-reference perturbation theory (UGA-SSMRPT)

The Unitary Group Adapted State-Specific Multi-Reference Perturbation Theory (UGA-SSMRPT2) developed by Mukherjee et al. [J. Comput. Chem. 36, 670 (2015)] has successfully realized the goal of studying bond dissociation in a numerically stable, spin-preserving, and size-consistent manner. We explore and analyze here the efficacy of the UGA-SSMRPT2 theory in the description of the avoided crossings and interlacings between a manifold of potential energy curves for states belonging to the same space-spin symmetry. Three different aspects of UGA-SSMRPT2 have been studied: (a) We introduce and develop the most rigorous version of UGA-SSMRPT2 that emerges from the rigorous version of UGA-SSMRCC utilizing a linearly independent virtual manifold; we call this the "projection" version of UGA-SSMRPT2 (UGA-SSMRPT2 scheme P). We compare and contrast this approach with our earlier formulation that used extra sufficiency conditions via amplitude equations (UGA-SSMRPT2 scheme A). (b) We present the results for a variety of electronic states of a set of molecules, which display the striking accuracy of both the two versions of UGA-SSMRPT2 with respect to three different situations involving weakly avoided crossings, moderate/strongly avoided crossings, and interlacing in a manifold of potential energy curves (PECs) of the same symmetry. Accuracy of our results has been benchmarked against IC-MRCISD + Q.

Bond dissociation energies of low-valent lanthanide hydroxides: lower limits from ion-molecule reactions and comparisons with fluorides

Despite that bond dissociation energies (BDEs) are among the most fundamental and relevant chemical properties they remain poorly characterized for most elementary lanthanide hydroxides and halides. Lanthanide ions Ln+ = Eu+, Tm+ and Yb+ are here shown to react with H2O to yield hydroxides LnOH+. Under low-energy conditions such reactions must be exothermic, which implies a lower limit of 499 kJ mol-1 for the Ln+-OH BDEs. This limit is significantly higher than previously reported for YbOH+ and is unexpectedly similar to the BDE for Yb+-F. To explain this apparent anomaly, it is considered feasible that the inefficient hydrolysis reactions observed here in a quadrupole ion trap mass spectrometer may actually be endothermic. More definitive and broad-based evaluations and comparisons require additional and more reliable BDEs and ionization energies for key lanthanide molecules, and/or energies for ligand-exchange reactions like LnF + OH ↔ LnOH + F. The hydroxide results motivated an assessment of currently available lanthanide monohalide BDEs. Among several intriguing relationships is the distinctively higher BDE for neutral LuF versus cationic LuF+, though quantifying this comparison awaits a more accurate value for the anomalously high ionization energy of LuF.

Spontaneous bond dissociation cascades induced by Ben clusters (n = 2,4)

High-level single and multireference ab initio calculations show that the Be₄ cluster behaves as a very efficient Lewis acid when interacting with conventional Lewis bases such as ammonia, water or hydrogen fluoride, to the point that the corresponding acid-base interaction triggers a sequential dissociation of all the bonds of the Lewis base. Notably, this behavior is already found for the simplest beryllium cluster, the Be₂ dimer. However, whereas for Be₂ the first dissociation process involves a low activation barrier which is above the reactants, for Be₄ all the bond dissociation processes involve barriers below the entrance channel leading to a cascade of successive exothermic processes, which end up spontaneously in a global minimum in which the bonding patterns of both the base and the Lewis acid are completely destroyed. Indeed, the global minimum, in all cases, is stabilized by three-center Be-H-Be bonds and covalent interactions between the Be atoms and the basic center of the base, which replace the initial metallic bond stabilizing the Be₄ cluster. As a consequence, in the global minimum the basic atoms (N, O and F) behave as hyper-coordinated centers. Also importantly, the Be₄ cluster and its complexes present RHF-UHF instabilities (not reported before for Be₄), which require the use of multireference methods to correctly describe them.

Anchoring a bow-shaped boron single chain in binary Be6B7- cluster: hybrid octagonal ring, multifold π/σ aromaticity, and dual electronic transmutation

Elemental boron clusters do not form linear chain or monocyclic ring structures, which is in contrast to carbon. Based on computer global searches and quantum chemical calculations, we report on the viability of a curved boron single chain in binary Be6B7- cluster. The boron motif assumes a bow shape, being anchored on a Be6 prism. Such a motif, which appears to be highly strained in its free-standing form, is exotic in boron-based clusters and nanostructures. Chemically, the cluster is analogous to a "clam-and-pearl-chain" system at the nanoscale (about 1 nm in size), in which a Be6 clam moderately opens its mouth, except that a B7 pearl chain is too large to be encapsulated inside. The picture differs from a three-layered sandwich. This cluster features a hybrid Be2B7 monocyclic ring, which is octagonal in nature and supports double 10π/6σ aromaticity. The number of π bonds substantially surpasses that in bare boron clusters of similar sizes. Two Be3 rings in the prism are also σ aromatic, albeit with effective 1σ/1σ electron-counting only. The unique multifold 1σ/10π/6σ/1σ aromaticity governs the geometry of the Be6B7- cluster, which can also be rationalized using the concept of dual electronic transmutation.

Double aromaticity in a BBe6H6+ cluster with a planar hexacoordinate boron structure

Aromaticity is one of the central concepts in chemistry and stabilizes many clusters that have interesting structural motifs. Herein, a cationic BBe6H6 cluster featuring a planar hexacoordinate boron structure stabilized by 2π/6σ double aromaticity was predicted theoretically. The cluster was predicted to be dynamically stable well above room temperature.

Computational Study of spx (x=1-3)-Hybridized Be-Be Bonds Stabilized by Amidinate Ligands

Complexes containing odd-electron Be-Be bonds are still rare until now. Hereby, a series of neutral di-beryllium amidinate complexes containing a Be-Be bond were explored theoretically. The complexes with direct chelation with the Be₂ dimer by the bidentate amidinate (AMD) ligands are always corresponding to their global minimum structures. The detailed bonding analyses reveal that the localized electrons of the Be-Be fragment can be adjusted by the amount of AMD ligands because each AMD ligand only takes one electron from the Be₂ fragment. Meanwhile, the hybridization of the central Be atom also changes as the number of AMD ligands increases. In particular, the sp³ -hybridized single-electron Be-Be bond is firstly identified in the tri-AMD-ligands-chelated neutral D_3h -Be₂ (AMD)₃ complex, which also possesses the higher stability compared to its monoanionic D_3h -Be₂ (AMD)₃ ^- and monocationic C₃ -Be₂ (AMD)₃ ⁺ analogues. Importantly, our study provides a new approach to obtain a neutral odd-electron Be-Be bond, namely by the use of radical ligands through side-on chelation.

Planar or tetrahedral? A ternary 17-electron CBe5H4+ cluster with planar pentacoordinate carbon

A 17-electron CBe₅H₄⁺ cluster features planar pentacoordinate carbon, owing to the 2π/6σ double aromaticity. The neutral CBe₅H₄ cluster has a tetrahedral configuration despite its 18-electron counting. The latter species is governed by σ conjugation.

A designer 32-electron superatomic CBe8H12 cluster: core–shell geometry, octacoordinate carbon, and cubic aromaticity

A 32-electron CBe₈H₁₂ cluster is designed with cubic octacoordinate carbon. It features core–shell geometry, two-fold superatomic bonding, and cubic aromaticity.

Ternary 12-electron CBe3X3+ (X = H, Li, Na, Cu, Ag) clusters: planar tetracoordinate carbons and superalkali cations

Molecules with planar tetracoordinate carbons (ptCs) are exotic in chemical bonding, and they are normally designed according to the 18-electron rule. Here we report on the viability of ptC clusters with as few as 12 valence electrons, which represent the lower limit in terms of electron counting. Specifically, we have computationally designed a class of ternary 12-electron ptC clusters, CBe3X3+ (X = H, Li, Na, Cu, Ag), based on a rhombic CBe32- unit. Computer structural searches reveal that the ptC species are global minima, whose C center is coordinated in-plane by three Be atoms and a terminal X atom via robust C-Be/C-X bonding, either covalent or ionic. The other two X atoms are on the periphery and each bridge two Be atoms. Bonding analyses show that the ptC core is governed by delocalized 2π/6σ bonding, that is, double π/σ aromaticity, which collectively conforms to the 8-electron counting. Additional 4 electrons contribute to peripheral Be-X-Be and Be-Be σ bonding. The delocalized 2π/6σ frameworks appear to be universal for all ptC clusters, ranging from 18-electron down to 12-electron systems. In other words, the ptC species are dictated entirely by the 8-electron counting. Predicted vertical electron affinities of these ptC clusters range from 3.13 to 5.48 eV, indicative of superalkali or pseudoalkali cations.

Bond orders of the diatomic molecules

Bond order quantifies the number of electrons dressed-exchanged between two atoms in a material and is important for understanding many chemical properties. Diatomic molecules are the smallest molecules possessing chemical bonds and play key roles in atmospheric chemistry, biochemistry, lab chemistry, and chemical manufacturing. Here we quantum-mechanically calculate bond orders for 288 diatomic molecules and ions. For homodiatomics, we show bond orders correlate to bond energies for elements within the same chemical group. We quantify and discuss how semicore electrons weaken bond orders for elements having diffuse semicore electrons. Lots of chemistry is effected by this. We introduce a first-principles method to represent orbital-independent bond order as a sum of orbital-dependent bond order components. This bond order component analysis (BOCA) applies to any spin-orbitals that are unitary transformations of the natural spin-orbitals, with or without periodic boundary conditions, and to non-magnetic and (collinear or non-collinear) magnetic materials. We use this BOCA to study all period 2 homodiatomics plus Mo₂, Cr₂, ClO, ClO⁻, and Mo₂(acetate)₄. Using Manz's bond order equation with DDEC6 partitioning, the Mo–Mo bond order was 4.12 in Mo₂ and 1.46 in Mo₂(acetate)₄ with a sum of bond orders for each Mo atom of ∼4. Our study informs both chemistry research and education. As a learning aid, we introduce an analogy between bond orders in materials and message transmission in computer networks. We also introduce the first working quantitative heuristic model for all period 2 homodiatomic bond orders. This heuristic model incorporates s–p mixing to give heuristic bond orders of ¾ (Be₂), 1¾ (B₂), 2¾ (C₂), and whole number bond orders for the remaining period 2 homodiatomics.

Bond orders were computed for 288 diatomics, and a new bond order component analysis (BOCA) was applied to selected diatomics.

The Nature of the Chemical Bond in BeF- and Related Species

The beryllium atom represents a curiosity. Its ground state valency is zero, so it should not form chemical bonds. Nevertheless Be is a metal and can form stable chemical species largely due to the participation of its excited ³P (2s¹2p¹) state as shown in the cases of Be₂ and Be₃. BeF^- is a stable ( D₀ ≥ 81.4 kcal/mol) closed shell molecule that has been studied experimentally quite recently. Although it dissociates adiabatically to two closed shell atoms, Be (¹S) and F^-(¹S), the bonding is due to the excited ³P (2s¹2p¹) and ¹D (2p²) Be states.

Planar Pentacoordinate versus Tetracoordinate Carbons in Ternary CBe4Li4 and CBe4Li42- Clusters

Planar hypercoordinate carbon molecules are exotic species, for which the 18-electron counting has been considered a rule. We report herein computational evidence of perfectly planar C_{2 v} CBe₄Li₄ (1) and D_{4 h} CBe₄Li₄^2- (3) clusters. These ternary species contain 16 and 18 electrons, respectively. The dianion is highly symmetric with a planar tetracoordinate carbon (ptC), whereas the neutral features a planar pentacoordinate carbon (ppC). Thus, charge-state alters the coordination environments of a cluster. Chemical bonding analysis shows that both clusters have 2π and 6σ delocalization around the C center, suggesting that ppC or ptC clusters are governed by double π/σ aromaticity, rather than the 18-electron rule. The outer Be₄Li₄ ring in 1 and 3 also supports 2σ aromaticity, collectively leading to 3-fold π/σ aromaticity for these ppC/ptC clusters. Structural transformation from ptC (3) to ppC (1) is discussed, in which the 16-electron quasi-ptC CBe₄Li₄ (2) cluster serves as an intermediate. Cluster 2 as a local minimum has severe out-of-plane distortion. Flattening of 2 leads to reorganization of Be₄ ring around the C center, which offers space for the fifth atom to coordinate and facilitates ppC formation. The latter arrangement optimizes π aromaticity and better manages intramolecular Coulomb repulsion. This work highlights the geometric factor (and unconventional electron counting) in the design of planar hypercoordinate carbons.

Boron-based binary Be6B102- cluster: three-layered aromatic sandwich, electronic transmutation, and dynamic structural fluxionality

Boron-based nanoclusters have unique structures, bonding, and dynamic properties, which originate from boron's electron-deficiency. We demonstrate here that pouring in extra electrons can alter such systems fundamentally. A coaxial triple-layered Be6B102- sandwich cluster is designed via global structural searches and quantum chemical calculations. It is well defined as the global minimum, which consists of a slightly elongated B10 monocyclic ring and two Be3 rings, the latter forming a Be6 trigonal-prism albeit without interlayer Be-Be bonding. The B10 ring shows structural and chemical integrity with respect to the Be3 rings, and yet it differs markedly from the free B10 cluster and closely resembles the C10 cluster. The present data testify to the idea of electronic transmutation, in which a B- is equivalent to C and a B10 cluster, upon charge-transfer, is converted to and stabilized as a monocyclic ring analogous to C10. Chemical bonding analyses reveal that the B10 ring in the Be6B102- cluster has 10π and 10σ delocalization and each Be3 ring is held together by 2σ electrons, collectively rendering four-fold π/σ aromaticity. The bonding pattern is in line with the formula of [Be3]4+[B10]10-[Be3]4+, suggesting a highly charged electron-transfer complex. Furthermore, the Be6B102- cluster is dynamically fluxional with dual modes of revolution (orbiting) and rotation (twisting), being structurally robust at least up to a temperature of 1500 K.

Dative Bonding between Closed-Shell Atoms: The BeF- Anion

Beryllium can exhibit unusually strong attractive interactions under conditions where it is nominally a closed-shell atom. Two prominent examples are the Be₂ dimer and the He-BeO complex. In the present study, we examine the bonding of the closed-shell Be-F^- anion. This molecule preserves the closed-shell character of the individual atoms as the electron affinity of F is high (328.16 kJ mol^-1) while that of Be is negative. Photodetachment spectroscopy was used to determine the vibrational frequency for BeF^- and the electron affinity of BeF (104.2 kJ mol^-1). The latter has been used to determine a lower bound of 343 kJ mol^-1 for the bond energy of BeF^-. Electronic structure calculations yielded predictions that were in good agreement with the observed data. A natural bond orbital analysis shows that BeF^- is primarily bound by a dative interaction.

Novel strategy to implement active-space coupled-cluster methods

A new approach is presented for the efficient implementation of coupled-cluster (CC) methods including higher excitations based on a molecular orbital space partitioned into active and inactive orbitals. In the new framework, the string representation of amplitudes and intermediates is used as long as it is beneficial, but the contractions are evaluated as matrix products. Using a new diagrammatic technique, the CC equations are represented in a compact form due to the string notations we introduced. As an application of these ideas, a new automated implementation of the single-reference-based multi-reference CC equations is presented for arbitrary excitation levels. The new program can be considered as an improvement over the previous implementations in many respects; e.g., diagram contributions are evaluated by efficient vectorized subroutines. Timings for test calculations for various complete active-space problems are presented. As an application of the new code, the weak interactions in the Be dimer were studied.

Hypervalent Bonding in the OF(a4Σ-), SF(a4Σ-), SF5/SF6, and OSF4 Species

Hypervalency has struggled the conventional wisdom of too many chemists for so many years. Numerous theories and bonding models have been introduced but the so-called "hypervalency" mystery remains. We offer a simple and appealing explanation for the bonding mechanism of OF(a⁴Σ^-), SF(a⁴Σ^-), SF₅/SF₆, and OSF₄ based solely on the fact that excited and/or ionic states of the constituent fragments may and actually do occur in the ground states of so many "every day" molecules. In particular, and through multireference methods, we have found that the bonding in all the studied species is ionic in nature, perhaps contrary to the present status of our chemical beliefs. Although the "atoms in molecules" hypothesis is certainly not the only way to explain the formation of the chemical bond, we strongly believe that it is the simplest and most economical conceptual principle that should guide our chemical thinking.

Hydrogen-Bonding Acceptor Character of Be3, the Beryllium Three-Membered Ring

The ability of Be₃ as a hydrogen bond acceptor has been explored by studying the potential complexes between this molecule and a set of hydrogen bond donors (HF, HCl, HNC, HCN, H₂O, and HCCH). The electronic structure calculations for these complexes were carried out at the MP2 and CCSD(T) computational levels together with an extensive NBO, ELF, AIM, and electrostatic potential characterization of the isolated Be₃ system. In all the complexes, the Be-Be σ bond acts as electron donor, with binding energies between 19 and 6 kJ mol^-1. A comparison with the analogous cyclopropane:HX complexes shows similar binding energies and contributions of the DFT-SAPT energetic terms. A blue-shift of the harmonic frequencies of Be₃ is observed upon complexation.

Can Popular DFT Approximations and Truncated Coupled Cluster Theory Describe the Potential Energy Surface of the Beryllium Dimer?

The potential energy surface (PES) of the ground state of the beryllium dimer poses a significant challenge for high-level ab initio electronic structure methods. Here, we present a systematic study of basis set effects over the entire PES of Be2 calculated at the full configuration interaction (FCI) level. The reference PES is calculated at the valence FCI/cc-pV{5,6}Z level of theory. We find that the FCI/cc-pV{T,Q}Z basis set extrapolation reproduces the shape of the FCI/cc-pV{5,6}Z PES as well as the binding energy and vibrational transition frequencies to within ~10 cm−1. We also use the FCI/cc-pV{5,6}Z PES to evaluate the performance of truncated coupled cluster methods (CCSD, CCSD(T), CCSDT, and CCSDT(Q)) and contemporary density functional theory methods (DFT) methods for the entire PES of Be2. Of the truncated coupled cluster methods, CCSDT(Q)/cc-pV{5,6}Z provides a good representation of the FCI/cc-pV{5,6}Z PES. The GGA functionals, as well as the HGGA and HMGGA functionals with low percentages of exact exchange tend to severely overbind the Be2 dimer, whereas BH&HLYP and M06-HF tend to underbind it. Range-separated DFT functionals tend to underbind the dimer. Double-hybrid DFT functionals show surprisingly good performance, with DSD-PBEP86 being the best performer. Møller–Plesset perturbation theory converges smoothly up to fourth order; however, fifth-order corrections have practically no effect on the PES.

Ternary CBe4Au4 cluster: a 16-electron system with quasi-planar tetracoordinate carbon

A ternary CBe₄Au₄ cluster contains quasi-planar tetracoordinate carbon (quasi-ptC). It adds the new 16-electron counting to ptC complexes, featuring 2π and 6σ double aromaticity.

Beryllium–beryllium double-π bonds in the octahedral cluster of Be2(μ2-X)4 (X = Li, Cu, BeF)

Double π_Be–Be bonds formed by the help of s¹-type electron donating ligand.

Coaxial Triple-Layered versus Helical Be6 B11- Clusters: Dual Structural Fluxionality and Multifold Aromaticity

Two low-lying structures are unveiled for the Be₆ B₁₁^- nanocluster system that are virtually isoenergetic. The first, triple-layered cluster has a peripheral B₁₁ ring as central layer, being sandwiched by two Be₃ rings in a coaxial fashion, albeit with no discernible interlayer Be-Be bonding. The B₁₁ ring revolves like a flexible chain even at room temperature, gliding freely around the Be₆ prism. At elevated temperatures (1000 K), the Be₆ core itself also rotates; that is, two Be₃ rings undergo relative rotation or twisting with respect to each other. Bonding analyses suggest four-fold (π and σ) aromaticity, offering a dilute and fluxional electron cloud that lubricates the dynamics. The second, helix-type cluster contains a B₁₁ helical skeleton encompassing a distorted Be₆ prism. It is chiral and is the first nanosystem with a boron helix. Molecular dynamics also shows that at high temperature the helix cluster readily converts into the triple-layered one.

The nature of the chemical bond in BeO0,-, BeOBe+,0,-, and in their hydrogenated products HBeO0,-, BeOH, HBeOH, BeOBeH+,0,-, and HBeOBeH

The nature of the chemical bond in BeO^0,-, BeOBe^+,0,-, and in their hydrogenated products HBeO^0,-, BeOH, HBeOH, BeOBeH^+,0,-, and HBeOBeH has been studied through single and multi reference correlation methods. In all these species, excited and ionized atomic states participate in a resonant way making chemically possible molecules that have been termed hypervalent and explain also the "incompatible" geometrical structure of some species.