The beryllium bond. Computational Chemistry. Elsevier; 2019. pp. 73-121. [DOI: 10.1016/bs.adioch.2018.10.003]

A Personal Account on Inorganic Reaction Mechanisms

The presented Review is focused on the latest research in the field of inorganic chemistry performed by the van Eldik group and his collaborators. The first part of the manuscript concentrates on the interaction of nitric oxide and its derivatives with biologically important compounds. We summarized mechanistic information on the interaction between model porphyrin systems (microperoxidase) and NO as well as the recent studies on the formation of nitrosylcobalamin (CblNO). The following sections cover the characterization of the Ru(II)/Ru(III) mixed-valence ion-pair complexes, including Ru(II)/Ru(III)(edta) complexes. The last part concerns the latest mechanistic information on the DFT techniques applications. Each section presents the most important results with the mechanistic interpretations.

Strong Be-N Interaction Induced Complementary Chemical Tuning to Design a Dual-gated Single Molecule Junction

The interaction between pyridines and the π-hole of BeH2 leads to the formation of strong beryllium-bonded complexes. Theoretical investigations demonstrate that the Be-N bonding interaction can effectively regulate the electronic current through a molecular junction. The electronic conductance exhibits distinct switching behavior depending on the substituent groups at the para position of pyridine, highlighting the role of Be-N interaction as a potent chemical gate in the proposed device. The complexes exhibit short intermolecular distances ranging from 1.724 to 1.752 Å, emphasizing their strong binding. Detailed analysis of electronic rearrangements and geometric perturbations upon complex formation provides insights into the underlying reasons for the formation of such strong Be-N bonds, with bond strengths varying from -116.25 to -92.96 kJ/mol. Moreover, the influence of chemical substituents on the local electronic transmission of the beryllium-bonded complex offers valuable insights for the implementation of a secondary chemical gate in single-molecule devices. This study paves the way for the development of chemically gateable, functional single-molecule transistors, advancing the design and fabrication of multifunctional single-molecule devices in the nanoscale regime.

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.

Nature of Beryllium, Magnesium, and Zinc Bonds in Carbene⋯MX2 (M = Be, Mg, Zn; X = H, Br) Dimers Revealed by the IQA, ETS-NOCV and LED Methods

The nature of beryllium−, magnesium− and zinc−carbene bonds in the cyclopropenylidene⋯MX2 (M = Be, Mg, Zn; X = H, Br) and imidazol-2-ylidene⋯MBr2 dimers is investigated by the joint use of the topological QTAIM-based IQA decomposition scheme, the molecular orbital-based ETS-NOCV charge and energy decomposition method, and the LED energy decomposition approach based on the state-of-the-art DLPNO-CCSD(T) method. All these methods show that the C⋯M bond strengthens according to the following order: Zn < Mg << Be. Electrostatics is proved to be the dominant bond component, whereas the orbital component is far less important. It is shown that QTAIM/IQA underestimates electrostatic contribution for zinc bonds with respect to both ETS-NOCV and LED schemes. The σ carbene→MX2 donation appears to be much more important than the MX2→ carbene back-donation of π symmetry. The substitution of hydrogen atoms by bromine (X in MX2) strengthens the metal−carbene bond in all cases. The physical origin of rotational barriers has been unveiled by the ETS-NOCV approach.

Open questions on toxic heavy metals Cd, Hg and Pb binding small components of DNA and nucleobases. Are there any predictable trends?

In this perspective article, we provide a bibliographic compilation of experimental and theoretical work on Cd, Hg, and Pb, and analyze in detail the bonding of M²⁺ and CH₃M⁺ (M = Zn, Cd, Hg, Pb) with urea and thiourea as suitable models for larger biochemical bases. Through the use of DFT calculations, we have found that although in principle binding energies decrease according to ionic size (Zn²⁺ > Cd²⁺ > Pb²⁺), Hg²⁺ largely breaks the trend. Through the use of EDA (Energy Decomposition Analysis) it is possible to explain this behavior, which is essentially due to the strong contribution of polarization to the binding. This conclusion is ratified by the NEDA (Natural Energy Decomposition Analysis) formalism, showing that the charge transfer term is very large in all cases, but particularly in the case of the mercury-thiourea system. The general trends observed for the interactions with CH₃M⁺ monocations show however CH₃Hg⁺ binding energies systematically smaller than the CH₃Zn⁺ ones, likely because the relativistic contraction of the Hg orbitals is very much attenuated by the attachment to the methyl group. Finally, we have investigated the gas-phase reactivity between EtHg⁺ and uracil to compare it with that exhibited by CH₃Hg⁺ and n-ButHg⁺ previously described in the literature. This comparison gathers new information that highlights the importance of the length of the alkyl chain attached to the metal on the mechanisms of these reactions. For methyl mercury, only the alkyl transfer process is allowed; for butyl mercury, protonation is clearly favored, and for ethyl mercury, both paths are competitive experimentally.

Malonaldehyde-like Systems: BeF2 Clusters—A Subtle Balance between Hydrogen Bonds, Beryllium Bonds, and Resonance

The stability of malonaldehyde is governed by intramolecular hydrogen bonds (IMHBs) as well as in malonaldehyde-like systems where oxygen is replaced by N or S at any of the basic sites. As beryllium bonds have been shown to strongly cooperate with hydrogen bonds, this work explores at the high level ab initio G4 level of theory the effect of including this non-covalent interaction in the system through its association with BeF2. Although malonaldehyde follows the expected trends, where the formation of a pseudocyclic form is favored also when IMHB and Be bonds are present, the subtle balance between both non-covalent interactions leads to some surprising results when other heteroatoms are involved, to the point that interaction energies can be much larger than expected or even cyclization is not favored. A complete analysis using different computational tools gives an answer to those cases escaping the predictable trends.

Noble-gas compounds: A general procedure of bonding analysis

This paper accounts for a general procedure of bonding analysis that is, expectedly, adequate to describe any type of interaction involving the noble-gas (Ng) atoms. Building on our recently proposed classification of the Ng-X bonds (X = binding partner) [New J. Chem. 44, 15536 (2020)], these contacts are first distinguished into three types, namely, A, B, or C, based on the topology of the electron energy density H(r) and on the shape of its plotted form. Bonds of type B or C are, then, further assigned as B-loose (B^l) or B-tight (B^t) and C-loose (C^l) or C-tight (C^t) depending on the sign that H(r) takes along the Ng-X bond path located from the topological analysis of ρ(r), particularly at around the bond critical point (BCP). Any bond of type A, B^l/B^t, or C^l/C^t is, finally, assayed in terms of contribution of covalency. This is accomplished by studying the maximum, minimum, and average value of H(r) over the volume enclosed by the low-density reduced density gradient (RDG) isosurface associated with the bond (typically, the RDG isosurface including the BCP) and the average ρ(r) over the same volume. The bond assignment is also corroborated by calculating the values of quantitative indices specifically defined for the various types of interactions (A, B, or C). The generality of our taken approach should encourage its wide application to the study of Ng compounds.

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.

Theoretical Study of N-Heterocyclic-Carbene-ZnX2 (X = H, Me, Et) Complexes

This article discusses the properties of as many as 30 carbene–ZnX2 (X = H, Me, Et) complexes featuring a zinc bond C⋯Zn. The group of carbenes is represented by imidazol-2-ylidene and its nine derivatives (labeled as IR), in which both hydrogen atoms of N-H bonds have been substituted by R groups with various spatial hindrances, from the smallest Me, iPr, tBu through Ph, Tol, and Xyl to the bulkiest Mes, Dipp, and Ad. The main goal is to study the relationship between type and size of R and X and both the strength of C⋯Zn and the torsional angle of the ZnX2 plane with respect to the plane of the imidazol-2-ylidene ring. Despite the considerable diversity of R and X, the range of dC⋯Zn is quite narrow: 2.12–2.20 Å. On the contrary, D0 is characterized by a fairly wide range of 18.5–27.4 kcal/mol. For the smallest carbenes, the ZnX2 molecule is either in the plane of the carbene or is only slightly twisted with respect to it. The twist angle becomes larger and more varied with the bulkier R. However, the value of this angle is not easy to predict because it results not only from the presence of steric effects but also from the possible presence of various interatomic interactions, such as dihydrogen bonds, tetrel bonds, agostic bonds, and hydrogen bonds. It has been shown that at least some of these interactions may have a non-negligible influence on the structure of the IR–ZnX2 complex. This fact should be taken into account in addition to the commonly discussed R⋯X steric repulsion.

Prediction of beryllium clusters (Ben; n = 3-25) from first principles

Evolutionary searches using the USPEX method (Universal Structure Predictor: Evolutionary Xtallography) combined with density functional theory (DFT) calculations were performed to obtain the global minimum structures of beryllium (Be_n, n = 3-25) clusters. The thermodynamic stability, optoelectronic and photocatalytic properties as well as the nature of bonding are considered for the most stable clusters. It is found that the cluster with n = 15 is the transition point at which the configurations change from 3D hollow cages to filled cage structures (with an interior atom appearing in the structure). All the ground state structures are energetically favorable with negative binding energies, suggesting good synthetic feasibility for these structures. The calculated relative stabilities and electronic structure show that the Be₄, Be₁₀ and, Be₁₇ clusters are the most stable structures and can be considered as superatoms. The electron configurations of Be₄, Be₁₀ and Be₁₇ clusters with 8, 20 and 34 electrons are identified as 1S² 1P⁶, 1S² 1P⁶ 1D¹⁰ 2S², 1S² 1P⁶ 1D¹⁰ 2S² 1F¹⁴, respectively. Theoretical simulations determined that all the ground state structures exhibit excellent thermal stability, where the upper-limit temperature that the structures can tolerate is 900 K. During AIMD simulation of O₂ adsorption onto the Be₁₇ cluster an interesting phenomenon was happening in which the pristine Be₁₇ cluster becomes a new stable Be₁₇O₁₆ cluster. Based on ELF (electron localization function) analysis, it can be concluded that the Be-Be bonds in the small clusters are primarily of van der Waals type, while for the larger clusters, the bonds are of metallic nature. The Be_n clusters show very strong absorption in the UV and visible regions with absorption coefficients larger than 10⁵ cm^-1, which suggests a wide range of potential advanced optoelectronics applications. The Be₁₇ cluster has a suitable band alignment in the visible-light excitation region which will produce enhanced photocatalytic activities (making it a promising material for water splitting).

Group 12 Carbonates and their Binary Complexes with Nitrogen Bases and FH2 Z Molecules (Z=P, As, Sb): Synergism in Forming Ternary Complexes

MCO₃ (M=Zn, Cd, Hg) forms a spodium bond with nitrogen-containing bases (HCN, NHCH₂ , NH₃ ) and a pnicogen bond with FH₂ Z (Z=P, As, Sb). The spodium bond is very strong with the interaction energy ranging from -31 kcal/mol to -56 kcal/mol. Both NHCH₂ and NH₃ have an equal electrostatic potential on the N atom, but the corresponding interaction energy is differentiated by 1.5-4 kcal/mol due to the existence of spodium and hydrogen bonds in the complex with NHCH₂ as the electron donor. The spodium bond is weakest in the HCN complex, which is not consistent with the change of the binding distance. The spodium bond becomes stronger in the CdCO₃ <ZnCO₃ <HgCO₃ sequence although the positive electrostatic potential on the Hg atom is smallest. This is because the electrostatic interaction is dominant in the spodium-bonded complexes of CdCO₃ and ZnCO₃ but the polarization interaction in that of HgCO₃ . The pnicogen bond is much weaker than the spodium bond and the former has a larger enhancement than the latter in the FH₂ Z⋅⋅⋅OCO₂ M⋅⋅⋅N-base ternary complexes.

Study of Beryllium, Magnesium, and Spodium Bonds to Carbenes and Carbodiphosphoranes

The aim of this article is to present results of theoretical study on the properties of C⋯M bonds, where C is either a carbene or carbodiphosphorane carbon atom and M is an acidic center of MX2 (M = Be, Mg, Zn). Due to the rarity of theoretical data regarding the C⋯Zn bond (i.e., the zinc bond), the main focus is placed on comparing the characteristics of this interaction with C⋯Be (beryllium bond) and C⋯Mg (magnesium bond). For this purpose, theoretical studies (ωB97X-D/6-311++G(2df,2p)) have been performed for a large group of dimers formed by MX2 (X = H, F, Cl, Br, Me) and either a carbene ((NH2)2C, imidazol-2-ylidene, imidazolidin-2-ylidene, tetrahydropyrymid-2-ylidene, cyclopropenylidene) or carbodiphosphorane ((PH3)2C, (NH3)2C) molecule. The investigated dimers are characterized by a very strong charge transfer effect from either the carbene or carbodiphosphorane molecule to the MX2 one. This may even be over six times as strong as in the water dimer. According to the QTAIM and NCI method, the zinc bond is not very different than the beryllium bond, with both featuring a significant covalent contribution. However, the zinc bond should be definitely stronger if delocalization index is considered.

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.

Significant bonding rearrangements triggered by Mg4 clusters

The structure, stability, and bonding of the complexes formed by the interaction of Mg₄ clusters and first row Lewis bases, namely, ammonia, water, and hydrogen fluoride, have been investigated through the use of high-level G4 single-reference and CASPT2 multireference formalisms. The adducts formed reflect the high electrophilicity of the Mg₄ cluster through electron density holes in the neighborhood of each metallic center. After the adduct formation, the metallic bonding of the Mg₄ moiety is not significantly altered so that the hydrogen shifts from the Lewis base toward the Mg atoms lead to new local minima with enhanced stability. For the particular case of ammonia and water, the global minima obtained when all the hydrogens of the Lewis base are shifted to the Mg₄ moiety have in common a very stable scaffold with a N or an O center covalently tetracoordinated to the four Mg atoms, so the initial bonding arrangements of both reactants have completely disappeared. The reactivity features exhibited by these Mg₄ clusters suggest that nanostructures of this metal might have an interesting catalytic behavior.

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_n H_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_n H_n -Be₂ -C_n H_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_n H_n -Be₂ -C_n H_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_n H_n -Be₂ -C_n H_n (n=3, 5, 7) clusters are the result of the interaction between Be₂ ²⁺ 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.

The Importance of Strain (Preorganization) in Beryllium Bonds

In order to explore the angular strain role on the ability of Be to form strong beryllium bonds, a theoretical study of the complexes of four beryllium derivatives of orthocloso-carboranes with eight molecules (CO, N₂, NCH, CNH, OH₂, SH₂, NH₃, and PH₃) acting as Lewis bases has been carried out at the G4 computational level. The results for these complexes, which contain besides Be other electron-deficient elements, such as B, have been compared with the analogous ones formed by three beryllium salts (BeCl₂, CO₃Be and SO₄Be) with the same set of Lewis bases. The results show the presence of large and positive values of the electrostatic potential associated to the beryllium atoms in the isolated four beryllium derivatives of ortho-carboranes, evidencing an intrinsically strong acidic nature. In addition, the LUMO orbital in these systems is also associated to the beryllium atom. These features led to short intermolecular distances and large dissociation energies in the complexes of the beryllium derivatives of ortho-carboranes with the Lewis bases. Notably, as a consequence of the special framework provided by the ortho-carboranes, some of these dissociation energies are larger than the corresponding beryllium bonds in the already strongly bound SO₄Be complexes, in particular for N₂ and CO bases. The localized molecular orbital energy decomposition analysis (LMOEDA) shows that among the attractive terms associated with the dissociation energy, the electrostatic term is the most important one, except for the complexes with the two previously mentioned weakest bases (N₂ and CO), where the polarization term dominates. Hence, these results contribute to further confirm the importance of bending on the beryllium environment leading to strong interactions through the formation of beryllium bonds.

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.

Mutual Influence of Pnicogen Bonds and Beryllium Bonds: Energies and Structures in the Spotlight

Pnicogen bonds, which are weak noncovalent interactions (NCIs), can be significantly modified by the presence of beryllium bonds, one of the strongest NCIs known. We demonstrate the importance of this influence by studying ternary complexes in which both NCIs are present, that is, the ternary complexes formed by a nitrogen base (NH₃, NHCH₂, and NCH), a phosphine (fluorophosphane, PH₂F) and a beryllium derivative (BeH₂, BeF₂, BeCl₂, BeCO₃, and BeSO₄). Energies, structures, and nature of the chemical bonding in these complexes are studied by means of ab initio computational methods. The pnicogen bond between the nitrogen base and the phosphine and the beryllium bond between the fluorine atom of fluorophosphane and the beryllium derivative show large cooperativity effects both on energies and geometries, with dissociation energies up to 296 kJ mol^-1 and cooperativity up to 104 kJ mol^-1 in the most strongly bound complex, CH₂HN:PH₂F:BeSO₄. In the complexes between the strongest nitrogen bases and the strongest beryllium donors, phosphorus-shared and phosphorus-transfer bonds are found.

Some interesting features of the rich chemistry around electron-deficient systems

In this short review, different phenomena that are triggered by the interaction of different compounds or clusters of compounds with electron-deficient systems, in particular beryllium and boron compounds, have been discussed in some detail. Particular attention was devoted to the huge acidity enhancements that can be induced through the interaction of conventional bases with B or Be containing compounds, which change these conventional bases in extremely strong proton donors. We have paid also attention to the cooperativity between Be bonds with other weak interactions, which results in a substantial increase of their strength, that can lead in some specific cases to the spontaneous formation of ion-pairs in the gas phase. Finally, the behavior of different Be derivatives as electron and anion sponges is discussed as well as the conditions needed to have clusters exhibiting rather strong Be–Be bonds, even though the Be–Be interaction in Be2 dimer is extremely weak. Finally, some attention was paid to systems with extremely short Be–Be distances but without a bond.

Not Only Hydrogen Bonds: Other Noncovalent Interactions

In this review, we provide a consistent description of noncovalent interactions, covering most groups of the Periodic Table. Different types of bonds are discussed using their trivial names. Moreover, the new name “Spodium bonds” is proposed for group 12 since noncovalent interactions involving this group of elements as electron acceptors have not yet been named. Excluding hydrogen bonds, the following noncovalent interactions will be discussed: alkali, alkaline earth, regium, spodium, triel, tetrel, pnictogen, chalcogen, halogen, and aerogen, which almost covers the Periodic Table entirely. Other interactions, such as orthogonal interactions and π-π stacking, will also be considered. Research and applications of σ-hole and π-hole interactions involving the p-block element is growing exponentially. The important applications include supramolecular chemistry, crystal engineering, catalysis, enzymatic chemistry molecular machines, membrane ion transport, etc. Despite the fact that this review is not intended to be comprehensive, a number of representative works for each type of interaction is provided. The possibility of modeling the dissociation energies of the complexes using different models (HSAB, ECW, Alkorta-Legon) was analyzed. Finally, the extension of Cahn-Ingold-Prelog priority rules to noncovalent is proposed.

Regium Bonds between Silver(I) Pyrazolates Dinuclear Complexes and Lewis Bases (N2, OH2, NCH, SH2, NH3, PH3, CO and CNH)

A theoretical study and Cambridge Structural Database (CSD) search of dinuclear Ag(I) pyrazolates interactions with Lewis bases were carried out and the effect of the substituents and ligands on the structure and on the aromaticity were analyzed. A relationship between the intramolecular Ag–Ag distance and stability was found in the unsubstituted system, which indicates a destabilization at longer distances compensated by ligands upon complexation. It was also observed that the asymmetrical interaction with phosphines as ligands increases the Ag–Ag distance. This increase is dramatically higher when two simultaneous PH3 ligands are taken into account. The calculated 109Ag chemical shielding shows variation up to 1200 ppm due to the complexation. Calculations showed that six-membered rings possessed non-aromatic character while pyrazole rings do not change their aromatic character significantly upon complexation.

Bonding between electron-deficient atoms: strong Lewis-acid character preserved in X–Y–X (X = B, Al; Y = Be, Mg) bridges

Beryllium bis(diazaborolyl) derivatives and their Mg and Al-containing analogues are stable compounds stabilized through covalent bonds between electron-deficient atoms, and behave as good Lewis acids.

N-Derivatives of Shannon entropy density as response functions

The exact first and second order partial derivatives of Shannon entropy density with respect to the number of electrons at constant external potential are introduced as new descriptors for prediction of the active sites of a molecule. The derivatives, which are a measure of the inhomogeneity of electron density, are calculated both exactly (from analytical forms) and approximately (using the finite difference method) for some molecular systems. According to the maximum entropy principle, the extreme value of the first order derivative on the surface of a given molecule should determine the active sites of the molecule in electrophilic and nucleophilic attack. The second order derivative indicates where the Shannon entropy is more concentrated or depleted during the electron exchange. Although these derivatives on the surfaces of helium and neon atoms are uniform, the corresponding values for argon, krypton and xenon atoms are not. This could explain the greater tendency of heavy noble gas atoms to form stable compounds. A dual descriptor is also defined as the difference between the left and right first order derivatives of Shannon entropy density, which allows one to simultaneously predict the preferable sites for electrophilic and nucleophilic attack over the system at point r. Therefore, the reactivity of an atom in a molecule requires the non-uniformity of the first and second order derivatives of Shannon entropy density on the surface of that atom.

Weak Interactions Get Strong: Synergy between Tetrel and Alkaline-Earth Bonds

Weak and strong noncovalent interactions such as tetrel bonds and alkaline-earth bonds, respectively, cooperate and get reinforced when acting together in ternary complexes of general formula RN··· SiH₃F···MY, where MY is a Be or Mg derivative and RN is a N-containing Lewis base with different hybridization patterns. Cooperativity has been studied in the optimized MP2/aug'-cc-pVTZ ternary complexes by looking at changes on geometries, binding energies, ²⁹Si NMR chemical shifts, and topological features according to the atoms in molecules theoretical framework. Our study shows that cooperativity in terms of energy is in general significant: more than 40 kJ/mol, and up to 83.6 kJ/mol in the most favorable case. The weakest the isolated interaction, the strongest the reinforcement in the ternary complex; in this sense, the tetrel bond is shortened enormously, between 0.3 and 0.6 Å. This dramatic reinforcement of the tetrel bond is also nicely reflected in the positive variations of the ²⁹Si chemical shifts in all the ternary complexes. At the same time the ternary complexes are characterized by the presence of totally planar silyl group, due to the pentacoordination of the Si atom. Both the hybridization of the N base and the geometry imposed by the alkaline-earth ligands have a strong influence on the binding energies, as they modify the donor ability of N and the Lewis acid character of the alkaline-earth metal.