Low-lying electronic states of Ben clusters (n = 7, 10, 13) and of the Be7H system

Self-consistent-field (SCF) calculations have been performed by means of a pseudopotential (PP) technique on medium-size Be_n clusters (n = 7, 10, 13). Correlation effects have been taken into account through multireference double-excitation configuration-interaction (MRD CI) procedure. Particular attention has been paid to the existence of Be clusters with many nearly degenerated states of singlet and triplet spin multiplicity. The SCF ordering of these states is frequently reversed in CI. Planar and non-planar Be clusters show comparable high stabilities caused by a strong sp hybridization. Two sections of the potential energy surface for the interaction of a H atom with the Be₇(7,0) cluster have been determined. Two regions of low energy found in this energy surface: one inside and the second outside the cluster border, are separated by an energy barrier. The CI results, indicating the directly overhead position as the absolute minimum of the surface, are in qualitative agreement with previous SCF studies on similar systems. The modifications of the cluster geometry (shrinkage or relaxation) caused by the interaction with the H atom in the directly overhead position are found to be very small.     

From Very Strong to Inexistent Be−Be Bonds in the Interactions of Be2 with π-Systems

Isolated Be₂ is a typical example of a weakly bound system, but interaction with other systems may give rise to surprising bonding features. The interactions between Be₂ and a set of selected neutral C_nH_n (n=2–8) π-systems have been analyzed through the use of G4 and G4MP2 ab initio methods, along with multireference CASPT2//CASPT2 calculations. Our results systematically show that the C_nH_n−Be₂−C_nH_n clusters formed are always very stable. However, the nature of this interaction is completely different when the π-system involved is a closed shell species (n=2, 4, 6, 8), or a radical (n=3, 5, 7). In the first case, the interaction does not occur with the π-system as a whole, but with specific C centers yielding rather polar but strong C−Be bonds. Nonetheless, although the Be−Be distances in these complexes are similar to the ones in compounds with ultra-strong Be−Be bonds, a close examination of their electron density distribution reveals that no Be−Be bonds exist. The situation is totally different when the interaction involves two π-radicals, C_nH_n−Be₂−C_nH_n (n=3, 5, 7). In these cases, a strong Be−Be bond is formed. Indeed, even though Be is electron deficient, the Be₂ moiety behaves as an efficient electron donor towards the two π-radicals, so that the different C_nH_n−Be₂−C_nH_n (n=3, 5, 7) clusters are the result of the interaction between Be₂²⁺ and two L⁻ anions. The characteristics of these two scenarios do not change when dealing with bicyclic π-compounds, such as naphthalene and pentalene, because the interaction with the Be₂ moiety is localized on one of the unsaturated cycles, the other being almost a spectator.     

Searching new structures of beryllium-doped in small-sized magnesium clusters: Be2MgnQ (Q = 0, −1; n = 1–11) clusters DFT study

Using CALYPSO method to search new structures of neutral and anionic beryllium-doped magnesium clusters followed by density functional theory (DFT) calculations, an extensive study of the structures, electronic and spectral properties of Be₂Mg_n^Q (Q = 0, −1; n = 2–11) clusters is performed. Based on the structural optimization, it is found that the Be₂Mg_n^Q (Q = 0, −1) clusters are shown by tetrahedral-based geometries at n = 2–6 and tower-like-based geometries at n = 7–11. The calculations of stability indicate that Be₂Mg₅^Q=0, Be₂Mg₅^Q=−1, and Be₂Mg₈^Q=−1 clusters are “magic” clusters with high stability. The NCP shows that the charges are transferred from Mg atoms to Be atoms. The s- and p-orbitals interactions of Mg and Be atoms are main responsible for their NEC. In particular, chemical bond analysis including molecular orbitals (MOs) and chemical bonding composition for magic clusters to further study their stability. The results confirmed that the high stability of these clusters is due to the interactions between the Be atom and the Mg₅ or Mg₈ host. Finally, theoretical calculations of infrared and Raman spectra of the ground state of Be₂Mg_n^Q (Q = 0, −1; n = 1–11) clusters were performed, which will be absolutely useful for future experiments to identify these clusters.     

Ab Initio Study on the Stability of NgnBe2N2, NgnBe3N2 and NgBeSiN2 Clusters

The global minima of Be₂N₂, Be₃N₂ and BeSiN₂ clusters are identified using a modified stochastic kick methodology. The structure, stability and bonding nature of these clusters bound to noble gas (Ng) atoms are studied at the MP2/def2‐QZVPPD level of theory. Positive Be?Ng bond dissociation energy, which gradually increases down Group 18 from He to Rn, indicates the bound nature of Ng atoms. All of the Ng‐binding processes are exothermic in nature. The Xe and Rn binding to Be₂N₂ and Be₃N₂ clusters and Ar?Rn binding to BeSiN₂ are exergonic processes at room temperature; however, for the lighter Ng atoms, lower temperatures are needed. Natural population analysis, Wiberg bond index computations, electron density analysis, and energy decomposition analysis are performed to better understand the nature of Be?Ng bonds.     

Structure and Stability of (NG)nCN3Be3+ Clusters and Comparison with (NG)BeY0/+

The noble gas binding ability of CN₃Be₃⁺ clusters was assessed both by ab intio and density functional studies. The global minimum structure of the CN₃Be₃⁺ cluster binds with four noble‐gas (NG) atoms, in which the Be atoms are acting as active centers. The electron transfer from the noble gas to the Be atom plays a key role in binding. The dissociation energy of the Be? NG bond gradually increases from He to Rn, maintaining the periodic trend. The HOMO–LUMO gap, an indicator for stability, gives additional insight into these NG‐bound clusters. The temperature at which the NG‐binding process is thermodynamically feasible was identified. In addition, we investigated the stability of two new neutral NG compounds, (NG)BeSe and (NG)BeTe, and found them to be suitable candidates to be detected experimentally such as (NG)BeO and (NG)BeS. The dissociation energies of the Be? NG bond in monocationic analogues of (NG)BeY (Y=O, S, Se, Te) were found to be larger than in the corresponding neutral counter‐parts. Finally, the higher the positive charge on the Be atoms, the higher the dissociation energy for the Be? NG bond becomes.     

Boron‐Based Chiral Helix Be6B102− and Be6B11− Clusters: Structures,Chemical Bonding,and Formation Mechanism

Boron forms a rich variety of low‐dimensional nanosystems, including the newly discovered helix Be₆B₁₀^2? ( 1 ) and Be₆B₁₁^? ( 2 ) clusters. We report herein on the elucidation of chemical bonding in clusters 1 / 2 , using the modern quantum chemistry tools of canonical molecular orbital analyses and adaptive natural density partitioning (AdNDP). It is shown that clusters 1 / 2 contain a chiral helix Be₂B₁₀Be₂ or Be₂B₁₁Be₂ skeleton with a total of 11 and 12 segments, respectively, which effectively curve into “helical pseudo rings” and chemically consist of two “quasicircles” as defined by their anchoring Be centers. The helix skeleton is connected via Lewis‐type B?B and Be?B?Be σ bonds, being further stabilized by island π/σ bonds and a loose π bond at the junction. The Be₆ component in 1 / 2 assumes a distorted prism shape only physically, and it is fragmented into four parts: two terminal Be₂ dimers and two isolated Be centers. A Be₂ dimer at the far end manages to bend over and cap a quasicircle from one side of B plane. Consequently, each quasicircle of a helical pseudo ring is capped from opposite sides by two Be₂/Be units, facilitating intramolecular charge‐transfers of 5 electrons from Be to B. Overall, the folding of B helix involves as many as 10 electrons. The enormous electrostatics offers the ultimate driving forces for B helix formation.     

The Beryllium Pentamer: Trailing an Uneven Sequence of Dissociation Energies

Recent high‐resolution spectroscopic studies by Merritt, Bondybey, and Heaven (Science 2009 , 324, 1548) have heightened the anticipation that small beryllium clusters will soon be observed in the laboratory. Beryllium clusters are important discrete models for the theoretical study of metals. The trigonal bipyramidal Be₅ molecule is studied using high‐level coupled cluster methods. We obtain the optimized geometry, atomization and dissociation energies, and vibrational frequencies. The c～CCSDT(Q) method is employed to compute the atomization and dissociation energies. In this approach, complete basis set (CBS) extrapolations at the CCSD(T) level of theory are combined with an additive correction for the effect of iterative triple and perturbative quadruple excitations. Harmonic vibrational frequencies are obtained using analytic gradients computed at the CCSD(T) level of theory. We report an atomization energy of 129.6 kcal mol^?1 at the trigonal bipyramid global minimum geometry. The Be₅→Be₄+Be dissociation energy is predicted to be 39.5 kcal mol^?1. The analogous dissociation energies for the smaller beryllium clusters are 64.0 kcal mol^?1 (Be₄→Be₃+Be), 24.2 kcal mol^?1 (Be₃→Be₂+Be), and 2.7 kcal mol^?1 (Be₂→Be+Be). The trigonal bipyramidal Be₅ structure has an equatorial–equatorial bond length of 2.000 Å and an axial–equatorial distance of 2.060 Å. Harmonic frequencies of 730, 611, 456, 583, 488, and 338 cm^?1 are obtained at the CCSD(T)/cc‐pCVQZ level of theory. Quadruple excitations are found to make noticeable contributions to the energetics of the pentamer, which exhibits a significant level of static correlation.     

Beryllium-9 NMR Spectroscopy and Molecular Orbital Studies of Hydrogen-Bonding Interaction of Tetraaquaberyllium(II) Ion with Water in the Second Solvation Sphere in Propiononitrile

The equilibrium constants of the hydrogen-bonding interactions between the tetraaqua-beryllium(II) ion ([Be(H₂O)₄]²⁺) and water in the second solvation sphere were determined from the dependence of the ⁹Be NMR chemical shift (δ_Be) on the water concentration (C _W) in propiononitrile (PN). The ⁹Be NMR line assigned to [Be(H₂O)₄]²⁺ is downfield shifted with the increasing C _W, and the change in δ_Be as a function of C _W is explained in terms of a two-step hydrogen-bonding interaction to form [Be(H₂O)₄](H₂O) _n ²⁺ (n = 1, 2). Molecular orbital calculations for [Be(H₂O)₄](H₂O) _n ²⁺ (n = 0?2) revealed that the electron density on the Be(II) ion increases with an increase in n due to an enhanced polarization of the bound water molecules accompanied by the hydrogen bonding in the second solvation sphere. The observed downfield shift of δ_Be is interpreted as a significant compensation of the diamagnetic upfield shift by the paramagnetic contribution due to the mixing of the vacant s and p orbitals of Be with the σ-type lone-pair orbitals of the coordinating water molecules.     

Unprecedented Bonding Situation in Viable E2(NHBMe)2 (E=Be,Mg; NHBMe=(HCNMe)2B) Complexes: Neutral E2 Forms a Single E−E Covalent Bond

Is it possible to facilitate the formation of a genuine Be?Be or Mg?Mg single bond for the E₂ species while it is in its neutral state? So far, (NHC^R)Be?Be(NHC^R) (R=H, Me, Ph) have been reported where Be₂ is in ¹Δ_g excited state imposing a formal Be?Be bond order of two. Herein, we present the formation of a single E?E (E=Be, Mg) covalent bond in E₂(NHB^Me)₂ (E=Be, Mg; NHB^Me=(HCN^Me)₂B) complexes where E₂ is in ³∑_u⁺ excited state having (nσ_g⁺)²(nσ_u⁺)¹((n+1)σ_g⁺)¹ (n=2 for Be and n=4 for Mg) valence electron configuration and it forms electron‐shared bonding with two NHB^Me radicals. The effects of bonding with nσ_u⁺ and (n+1)σ_g⁺ orbitals will cancel each other, providing the former E?E bond order as one. Be₂(NHB^Me)₂ complex is thermochemically stable with respect to possible dissociation channels at room temperature, whereas the two exergonic channels, Mg₂(NHB^Me)₂ → Mg + Mg(NHB^Me)₂ and Mg₂(NHB^Me)₂ → Mg₂ + (NHB^Me)₂, are kinetically inhibited by a free energy barrier of 15.7 and 18.7 kcal mol^?1, respectively, which would likely to be further enhanced in cases of bulkier substituents attached to the NHB ligands. Therefore, the title complexes are first viable systems which feature a neutral E₂ moiety with a single E?E covalent bond.     

Unprecedented Bonding Situation in Viable E2(NHBMe)2 (E=Be,Mg; NHBMe=(HCNMe)2B) Complexes: Neutral E2 Forms a Single E−E Covalent Bond

Is it possible to facilitate the formation of a genuine Be?Be or Mg?Mg single bond for the E₂ species while it is in its neutral state? So far, (NHC^R)Be?Be(NHC^R) (R=H, Me, Ph) have been reported where Be₂ is in ¹Δ_g excited state imposing a formal Be?Be bond order of two. Herein, we present the formation of a single E?E (E=Be, Mg) covalent bond in E₂(NHB^Me)₂ (E=Be, Mg; NHB^Me=(HCN^Me)₂B) complexes where E₂ is in ³∑_u⁺ excited state having (nσ_g⁺)²(nσ_u⁺)¹((n+1)σ_g⁺)¹ (n=2 for Be and n=4 for Mg) valence electron configuration and it forms electron‐shared bonding with two NHB^Me radicals. The effects of bonding with nσ_u⁺ and (n+1)σ_g⁺ orbitals will cancel each other, providing the former E?E bond order as one. Be₂(NHB^Me)₂ complex is thermochemically stable with respect to possible dissociation channels at room temperature, whereas the two exergonic channels, Mg₂(NHB^Me)₂ → Mg + Mg(NHB^Me)₂ and Mg₂(NHB^Me)₂ → Mg₂ + (NHB^Me)₂, are kinetically inhibited by a free energy barrier of 15.7 and 18.7 kcal mol^?1, respectively, which would likely to be further enhanced in cases of bulkier substituents attached to the NHB ligands. Therefore, the title complexes are first viable systems which feature a neutral E₂ moiety with a single E?E covalent bond.     

The energy optimized configurations of Be18 and Be20 clusters and the effect of He atom in these clusters

The optimized configurations of Be₁₈ (D_3d) and Be₂₀ (D_3h) clusters which are considered as the smallest subunits of Be crystal are calculated by the ab initio STO-3G SCF energy gradient method. The characteristics of these optimized geometries are discussed. The impurity effect caused by a He atom in the center of these clusters is also discussed.     

Novel Barium Beryllates Ba[Be2N2] and Ba3[Be5O8]: Syntheses,Crystal Structures and Bonding Properties

Ba[Be₂N₂] was prepared as a yellow‐green microcrystalline powder by reaction of Ba₂N with Be₃N₂ under nitrogen atmosphere. The crystal structure Rietfeld refinements (space group I4/mcm, a = 566.46(5) pm, c = 839.42(9) pm, R_int = 4.73 %, R_prof = 9.16 %) reveal the compound to crystallize as an isotype of the nitridoberyllates A[Be₂N₂] (A = Ca, Sr) consisting of planar 4.8² nets of mutually trigonal planar coordinated Be and N species. Averaged magnetic susceptibility values for the anion [(Be₂N₂)^2?] determined from measurements on A[Be₂N₂] with A = Mg, Ca, Ba allow to derive a diamagnetic increment for N^3? χ_dia = (?13±1stat.) · 10^?6emu mol^?1. Colorless Ba₃[Be₅O₈] was first obtained as an oxidation product of Ba[Be₂N₂] in air. The crystal structure was solved and refined from single crystal X‐ray diffaction data (space group Pnma, a = 942.9(1) pm, b = 1163.47(7) pm, c = 742.1(1) pm, R1 = 2.99 %, wR2 = 7.15 %) and contains infinite rods of Be in trigonal planar, tetrahedral and 3 + 1 coordination by O. The crystal structure is discussed in context with other known oxoberyllates. Electronic structure calculations and electron localization function diagrams for both compounds support the classification as nitrido‐ and oxoberyllate, respectively.     

Jahn-teller effects in the MNDO approximation: structures of the molecular cations of some simple organoberyllium compounds

The MNDO method gives geometries for the molecular cations of organoberyllium compounds of types BeR₂ and HBeR (R = CH₃, CHCH₂, CCH, CN, C₅H₅), of C₄H₄Be and CH₃BeBeH₃ and of the series CH_4?n(BeH)_n (n = 0–4) which have symmetries in precise accord with the predictions of the Jahn-Teller theorem. In the series CH_4?n(BeH)_n and CH_4?n(BeH)_n⁺, the barriers to inversion via a planar intermediate decrease with increasing n, are significantly smaller for the cations than for the neutral molecules, and are zero for CH(BeH)₃⁺ and C(BeH)₄⁺, both of which have their minimum energy when strictly planar at carbon.     

Electronic structure and stability of charged beryllium clusters

Electronic structure studies on neutral, singly and doubly ionized Be _n clusters (n≤5) have been carried out in order to investigate the stability and observability of charged clusters. Our studies employ wave function expansion in terms of gaussian type orbitals and have been carried out within local spin density formalism. It is shown that although small doubly ionized clusters are unstable, they are protected from fragmentation by energy barriers. We illustrate this explicitly for trimers by presenting a Born-Oppenheimer surface of Be₃, Be ₃ ⁺ and Be ₃ ⁺⁺ . It is argued that depending on their geometries, the observable doubly charged clusters can be generated through a one or two photons ionization. We also present results on the distribution of “hole charge” in doubly ionized clusters and show that a small cluster exhibits metallic like behaviour in regard to distribution of missing electronic charge.     

Dismantlement of ammonia upon interaction with Ben (n ≤ 10) clusters

The interaction of ammonia with Be_n (n < 1–10) clusters has been investigated by density functional theory and ab initio calculations. The main conclusion is that, regardless of the size of the Be cluster, neither the structure of ammonia nor that of the Be clusters are preserved due to a systematic dissociation of its N H bonds and a spontaneous H-shift toward the available Be atoms. This H migration not only leads to rather stable Be H bonds, but dramatically enhances the strength of the Be N bonds as well. Accordingly, the maximum stability is found for the interaction with the beryllium trimer, leading to a complex with three N Be and three Be H bonds. Another maximum in stability, although lower than that reached for n = 3, is found for the Be heptamer, since from n = 6, a new N Be bond is formed, so that complexes from n = 6 to n = 10 are characterized by the formation of a NBe₄ moiety, whose stability reaches a maximum at n = 7. The bonding characteristics of the different species formed are analyzed by means of AIM, NBO, ELF and AdNDP approaches.     

Wellenmechanische Untersuchungen an der Wasserstoffbrücke zwischen zwei Berylliumatomen

The systems Be₂H⁺ and Be₂H^? have been investigated for different nuclear positions, the H atom being situated between the Be atoms, taking all electrons into account, using the Allgemeines Programmsystem/SCF –MO –LC (LCGO ) Verfahren. For Be₂H⁺ there results a minimum total energy of ?29.3824 a.u. in the linear symmetric configuration with a bond distance of 1.609 Å. The ionization energy was estimated to be 12.37 eV. The formation of Be₂H⁺ can be interpreted as an addition of Be to BeH⁺ with an exotherm heat of reaction of 7.0 kcal/mole. The electron affinity of BeH⁺ (ionization energy of BeH) was estimated to be approximately 7.24 eV. All force constants of Be₂H⁺ and BeH⁺ have been computed. Using SCF results, the Be₂H^? was found to be unstable.     

Extraction liquide-liquide par des esters alkylphosphoriques. II. Extraction des nitrates de béryllium et des autres alcalino-terreux par le tri-n-butylphosphate

The solvent extraction systems Be(NO₃)₂? HNO₃? H₂O? TBP/kerosene and M(NO₃)₂? H₂O? TBP/kerosene (TBP = tri-n-butylphosphate, M = Be, Mg, Ca and Sr) have been studied. The alkaline earths elements are poorly extracted. Only very high acidities allow better extraction of beryllium. The sequence of extraction of the alkaline earths elements by the TBP depends on the concentration of the cations and is Ca > Be > Sr > Mg if the metal concentration is lower than 2 M.     

Theoretical study of hydrated Be2+ ions

Hydrated Be²⁺ ions [Be(H₂O)_n]²⁺, n = 1−4 and 6, were examined theoretically. The structure of the hydrated ions was determined and the hydration energy estimated with and without electron correlation. The bond between the Be²⁺ ion and the oxygen of water is very strong and has the nature of a dative bond. The non-additivity of the binding energy is so profound that without taking it into account the structure and dynamics of Be²⁺ ions cannot be explained. The hydration number in water is found to be 4. The fifth and sixth water molecules prefer forming the second coordination shell to the Be²⁺ ion. The result is in agreement with X-ray analysis of the aqueous solution, but not with a recent molecular dynamics simulation. In addition, the harmonic vibrational frequencies for the complexes are evaluated and compared with some experiments.     

Tuning aromaticity in trigonal alkaline earth metal clusters and their alkali metal salts

In this work, we analyze the geometry and electronic structure of the [X_nM₃]^n?2 species (M = Be, Mg, and Ca; X = Li, Na, and K; n = 0, 1, and 2), with special emphasis on the electron delocalization properties and aromaticity of the cyclo‐[M₃]^2? unit. The cyclo‐[M₃]^2? ring is held together through a three‐center two‐electron bond of σ‐character. Interestingly, the interaction of these small clusters with alkali metals stabilizes the cyclo‐[M₃]^2? ring and leads to a change from σ‐aromaticity in the bound state of the cyclo‐[M₃]^2? to π‐aromaticity in the XM₃^? and X₂M₃ metallic clusters. Our results also show that the aromaticity of the cyclo‐[M₃]^2? unit in the X₂M₃ metallic clusters depends on the nature of X and M. Moreover, we explored the possibility for tuning the aromaticity by simply moving X perpendicularly to the center of the M₃ ring. The Na₂Mg₃, Li₂Mg₃, and X₂Ca₃ clusters undergo drastic aromaticity alterations when changing the distance from X to the center of the M₃ ring, whereas X₂Be₃ and K₂Mg₃ keep its aromaticity relatively constant along this process. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

General principles governing structures of small clusters

General rules which govern electronic and geometric structures of small clusters are formulated, and their validity is documented with the results of the MRD - CI investigations for Li _n , BeLi _k , Be _l (n=2?14,k=2?6,l=2?13) as well as on IIa and IVa tetramers. The MRD - CI results are compared with investigations performed with other methods.