Non-nuclear Attractor Research Articles

Prediction of Covalent Metal-Metal Bonding in Cp-M-M'-Nacnac Complexes of Group 2 and 12 Metals (Be, Mg, Ca, Zn, Cd, Hg).

Bimetallic CpMM'Nacnac molecules with group 2 and 12 metals (M=Be, Mg, Ca, Zn, Cd, Hg) that contain novel metal-metal bonding have been investigated in a theoretical study of their molecular and electronic structure, thermodynamic stability, and metal-metal bonding. In all cases the metal-metal bonds are characterized as electron-sharing covalent single bonds from natural bond orbital (NBO) and energy-decomposition analysis with natural orbitals of chemical valence (EDA-NOCV) analysis. The sum of [MM'] charges is relatively constant, with all complexes exhibiting a [MM']2+ core. Quantum theory of atoms in molecules (QTAIM) analysis indicates the presence of non-nuclear attractors (NNA) in the metal-metal bonds of the BeBe, MgMg, and CaCa complexes. There is substantial electron density (0.75-1.33 e) associated with the NNAs, which indicates that these metal-metal bonds, while classified as covalent electron-sharing bonds, retain significant metallic character that can be associated with reducing reactivity of the complex. The predicted stability of these complexes, combined with their novel covalent metal-metal bonding and potential as reducing agents, make them appealing targets for the synthesis of new metal-metal bonds.

The Ehrenfest force field: A perspective based on electron density functions

The topology of the Ehrenfest force field (EhF) is investigated as a tool for describing local interactions in molecules and intermolecular complexes. The EhF is obtained by integrating the electronic force operator over the coordinates of all but one electron, which requires knowledge of both the electron density and the reduced pair density. For stationary states, the EhF can also be obtained as minus the divergence of the kinetic stress tensor, although this approach leads to well-documented erroneous asymptotic behavior at large distances from the nuclei. It is shown that these pathologies disappear using the electron density functions and that the EhF thus obtained displays the correct behavior in real space, with no spurious critical points or attractors. Therefore, its critical points can be unambiguously obtained and classified. Test cases, including strained molecules, isomerization reactions, and intermolecular interactions, were analyzed. Various chemically relevant facts are highlighted: for example, non-nuclear attractors are generally absent, potential hydrogen–hydrogen interactions are detected in crowded systems, and a bifurcation mechanism is observed in the isomerization of HCN. Moreover, the EhF atomic basins are less charged than those of the electron density. Although integration of the EhF over regions of real space can also be performed to yield the corresponding atomic forces, several numerical drawbacks still need to be solved if electron density functions are to be used for that purpose. Overall, the results obtained support the Ehrenfest force field as a reliable descriptor for the definition of atomic basins and molecular structure.

Influence of an electric‐field on the topological stability of the neutral lithium dimer

AbstractIn this investigation, we seek to understand the role of non‐nuclear attractors (NNAs) of the neutral Li2 dimer subjected to an electric (±E) field that is directed parallel (±Ex) and perpendicular (±Ey) to the bond‐path. The ±Ex‐fields and ±Ey‐fields are separately applied to the Li2 molecular graph until the bond ruptures. The next generation quantum theory of atoms in molecules (NG‐QTAIM) interpretation of bonding was constructed with the stress tensor σ(r) eigenvectors on the Hessian of ρ(r) molecular graph. The asymmetry induced by both the ±Ey‐field and ±Ex‐field was detected in terms of the rotation of the orthogonal triad of stress tensor σ(r) eigenvectors {e1σ, e2σ, e3σ} relative to the Cartesian coordinate frame. The orthogonal triad of Hessian of ρ(r) eigenvectors {e1, e2, e3} however, were only able to detect rotation induced by the high degree of asymmetry present for bent bond‐paths induced by the ±Ey‐fields. Larger movement of the NNAs along the bond‐path correlated with greater bond critical point (BCP) bond metallicity ξ(rb). The effect of applying the ±Ex‐field was compared with unpublished results on neutral Li2 subject to a stretching distortion. The lack of NNA motion along the bond‐path for the stretching distortion correlated with a lower degree of bond metallicity ξ(rb). The stress tensor σ(r) eigenvectors have a unique ability to detect rotation relative to the Cartesian coordinate frame for high bond‐path symmetry occurring for the bond‐stretching distortion and application of the ±Ex‐field. Suggestions for future work are provided.

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The cover image is based on the Research Article Bonding in the high spin lithium clusters: Non-nuclear attractors play a crucial role by Sara Sadat Karachi and Kiamars Eskandariet, https://doi.org/10.1002/jcc.27056

Inducing Nucleophilic Reactivity at Beryllium with an Aluminyl Ligand.

The reactions of anionic aluminium or gallium nucleophiles {K[E(NON)]}2 (E = Al, 1; Ga, 2; NON = 4,5-bis(2,6-diisopropylanilido)-2,7-ditert-butyl-9,9-dimethylxanthene) with beryllocene (BeCp2) led to the displacement of one cyclopentadienyl ligand at beryllium and the formation of compounds containing Be-Al or Be-Ga bonds (NON)EBeCp (E = Al, 3; Ga, 4). The Be-Al bond in the beryllium-aluminyl complex [2.310(4) Å] is much shorter than that found in the small number of previous examples [2.368(2) to 2.432(6) Å], and quantum chemical calculations suggest the existence of a non-nuclear attractor (NNA) for the Be-Al interaction. This represents the first example of a NNA for a heteroatomic interaction in an isolated molecular complex. As a result of this unusual electronic structure and the similarity in the Pauling electronegativities of beryllium and aluminium, the charge at the beryllium center (+1.39) in 3 is calculated to be less positive than that of the aluminium center (+1.88). This calculated charge distribution suggests the possibility for nucleophilic behavior at beryllium and correlates with the observed reactivity of the beryllium-aluminyl complex with N,N'-diisopropylcarbodiimide─the electrophilic carbon center of the carbodiimide undergoes nucleophilic attack by beryllium, thereby yielding a beryllium-diaminocarbene complex.

New kind of electride sandwich complexes based on the cyclooctatetraene ligand M12(η8-C8H8)2M22 (M1 = Na, K and M2 = Ca, Mg): a theoretical study.

In the present study, the electronic structures of a series of binuclear sandwich complexes based on the cyclooctatetraene ligand M12(η8-C8H8)2M22 (M1 = Na, K and M2 = Ca, Mg) are studied theoretically. Each cyclooctatetraene ligand binds with the metal in the η8 binding mode. The M2-M2 bond length agrees well with the reported bimetallic covalent Ca2 and Mg2 bond lengths. The Wiberg bond index (WBI) also indicates the presence of covalent M2-M2 bonds, which gives additional stability to the complex. A non-nuclear attractor (NNA) is found in-between the M2-M2 bond and the negative Laplacian of the electron density is found at the NNA. Noncovalent interaction (NCI) plot shows that electron density is localized at the M2-M2 bond. Based on the performed analysis, we have concluded that the designed sandwich complexes are electrides. We herein report, for the first time, the electride sandwich complexes of the cyclooctatetraene ligand. Due to the presence of a diffuse electron system, the electride complexes exhibit higher values of the static second hyperpolarizability within the range of 2.6 × 105 to 1.4 × 106 a.u. Among the studied complexes, M12(η8-C8H8)2Ca2 exhibit a higher value of static second hyperpolarizability.

Bonding in the high spin lithium clusters:Non‐nuclearattractors play a crucial role

The bonding in lithium high-spin clusters contradicts the usual chemical bonding concept since there are no electron pairs between the atoms, and they are bound with parallel spin electrons. Quantum theory of atoms in molecules and interacting quantum atom analysis (IQA) were used to investigate the nature of bonding in the high-spin clusters. Our findings demonstrate that the non-nuclear attractors (NNAs) are an essential component of the high-spin lithium clusters and play a key role in keeping them stable. Based on IQA energy terms, an electrostatic destabilizing interaction between the lithium atoms works against the cluster formation. On the other hand, the interactions between lithium atoms and NNA basins are stabilizing and outweigh the lithium-lithium destabilizing effects. In fact, NNAs tend to draw lithium atoms together and stabilize the resulting cluster. The high-spin clusters of lithium can be regarded as electrostatically driven compounds since the electrostatic components are primarily responsible for the stabilizing interactions between NNAs and Li atoms. The only exception is 3 Li2 , which lacks NNA and has a non-repellent lithium-lithium interaction. Indeed, in the 3 Li2 , the interatomic electrostatic component is negligibly small, and the exchange-correlation term leads to a weak bonding interaction.

Stabilisation of Li(0)-Li(0) bond by normal and mesoionic carbenes and electride characteristics of the complexes

Density functional theory (DFT) has been used to study the structure, stability, and bonding in the Li2L2 complexes containing Li(0)-Li(0) bond using both normal and mesoionic carbenes (MICs) as binding ligands (L) with Li2 molecule. The geometries and the nature of bonding of Li2(SNHCMe)2 and Li2(cAACMe)2 normal carbene complexes and Li2(MIC1)2 and Li2(MIC2)2 mesoionic carbene complexes have been compared with the previously reported Li2(NHC)2 normal carbene complex. The stability of the designed complexes is determined by positive Gibbs’ free energy changes (ΔG) towards the dissociation of the complexes into different fragments. Both normal and mesoionic carbenes stabilise the Li2 moiety and both the types of complexes are almost equally stable. From the natural bond orbital (NBO) analysis and the atoms in molecule (AIM) analysis, it is shown that two Li atoms are bonded by a single covalent bond with the oxidation state of zero on each Li. Again, the electron density analysis confirmed that each Li-Li bond has a non-nuclear attractor (NNA) at the middle of the bonds and the values of Laplacian of electron density (∇2 ρ(r)) are negative therein. Both the types of complexes show electride characteristics. The reactivity descriptors of all the studied complexes have been analyzed.

Substituent Effects on Electride Characteristics of Mg2(η5-C5H5)2: A Theoretical Study.

An ab initio study has been carried out on the substituted binuclear sandwich complexes of Mg2(η5-C5H5)2. We have checked whether the substitution destroys the electride properties of a complex, as it needs to satisfy several stringent criteria to obtain the status of an electride. The thermochemical results show that the complexes are stable at room temperature and 1 atm pressure. From the analysis of the various electron density descriptors and the natural bond orbital (NBO) for all the complexes, it is confirmed that the Mg-Mg bonds are covalent and the metal-ligand bonds are ionic in nature. The charges on each Mg atom in the studied complexes are +1. Analysis of the electron density descriptors shows the presence of a non-nuclear attractor (NNA) at the middle of the bond formed by the two Mg atoms when attached to the ligands. The electride characteristics are exhibited by all of the designed complexes. We also report the aromaticity behavior and reactivity descriptors of these complexes. The electride characteristics of Mg2(η5-C5H5)2 complex get affected on substitution, as both the NNA population and the nonlinear optical properties (NLO) of the complexes are changed.

How Many Electrons Does a Molecular Electride Hold?

Electrides are very peculiar ionic compounds where electrons occupy the anionic positions. In a crystal lattice, these isolated electrons often form channels or surfaces, furnishing electrides with many traits with promising technological applications. Despite their huge potential, thus far, only a few stable electrides have been produced because of the intricate synthesis they entail. Due to the difficulty in assessing the presence of isolated electrons, the characterization of electrides also poses some serious challenges. In fact, their properties are expected to depend on the arrangement of these electrons in the molecule. Among the criteria that we can use to characterize electrides, the presence of a non-nuclear attractor (NNA) of the electron density is both the rarest and the most salient feature. Therefore, a correct description of the NNA is crucial to determine the properties of electrides. In this paper, we analyze the NNA and the surrounding region of nine molecular electrides to determine the number of isolated electrons held in the electride. We have seen that the correct description of a molecular electride hinges on the electronic structure method employed for the analyses. In particular, one should employ a basis set with sufficient flexibility to describe the region close to the NNA and a density functional approximation that does not suffer from large delocalization errors. Finally, we have classified these nine molecular electrides according to the most likely number of electrons that we can find in the NNA. We believe this classification highlights the strength of the electride character and will prove useful in designing new electrides.

Electride characteristics of M2(η5-E5)2 (M = Be, Mg; E = Sb5-)

Ab initio computation is performed on the binuclear sandwich complexes, M2(η5-Sb5)2. Eclipsed and staggered conformations are generated due to the η5 mode of binding by Sb5- ligand with the alkaline earth metals (Be and Mg metals). The complexes are thermodynamically stable at room temperature. The electron density descriptors and the natural bond orbital (NBO) analysis confirmed the covalent nature of the M-M bond. Both Be2(η5-Sb5)2 and Mg2(η5-Sb5)2 complexes have one non-nuclear attractor (NNA) at the center of the M-M bond which is predicted and confirmed by the electron density analysis. At the NNA, the values of the Laplacian of electron density are negative and an electron localization function basin (ELF) is present at the center of the M-M bond for localized electrons. Both the complexes show large values of nonlinear optical (NLO) properties. Both the designed binuclear sandwich complexes Be2(η5-Sb5)2 and Mg2(η5-Sb5)2 behave as electride.

Comparison Between Electride Characteristics of Li3@B40 and Li3@C60.

Density functional theory (DFT) based computation is performed on the endohedrally encapsulated Li3 cluster inside the B40 and C60 cages namely, Li3@B40 and Li3@C60. For both these systems, the Li-Li bond lengths are shorter than that in the free Li3 cluster. Due to confinement, the Li-Li vibrational frequencies increase in both the systems as compared to that in the free Li3 cluster. Thermodynamically, the formation of these two systems is spontaneous in nature as predicted by the negative values of Gibbs’ free energy changes (ΔG). For both the systems one non-nuclear attractor (NNA) is present on the middle of the Li3 cluster which is predicted and confirmed by the electron density analysis. The NNA population and the percentage localization of electron density at the NNA of the Li3@C60 system are higher than that in the Li3@B40 system. At the NNA the values of the Laplacian of electron density are negative and an electron localization function basin is present at the center of the Li3 cluster for localized electrons. Both systems show large values of nonlinear optical properties (NLO). Both the Li3 encapsulated endohedral systems behave as electrides. Electrides have low work function and hence have a great potential in catalytic activity toward the activation of small molecules (such as CO2, N2). Even some electrides have greater catalytic activity than some well-studied metal-loaded catalysts. As the systems under study behave as electrides, they have the power to show catalytic activity and can be used in catalyzing the activation of small molecules.

Bonding and Aromaticity in Electron-Rich Boron and Aluminum Clusters.

In this work bonding and aromaticity of triply bonded atoms of group 13 elements (M≡M, M = B and Al) in recently characterized B2Al3-, Na3Al2-, and Na4Al2 are studied. Here, I show that although molecular orbital-based analyses characterize triple bonds, the electropositive nature of group 13 elements gives these bonds unique characteristics. The bond orders derived from the delocalization index, topology of the electron density, and local characteristics of (3, -1) critical points, as defined within the context of quantum theory of atoms in molecules, do not conform with those of ordinary triple bonds. In Na3Al2- and Na4Al2 clusters non-nuclear attractors form between the electropositive Al atoms acting like pseudo atoms. The bond between boron atoms in B2Al3- is more similar to an ordinary triple covalent bond benefiting from the exchange-correlation component of the interatomic interaction energy as defined via interacting quantum atom theory. However, extreme electrostatic repulsion between negatively charged boron atoms attenuates this bond. Finally, current density analysis suggests that B2Al3- is a magnetic aromatic system, nearly 50% more aromatic compared to benzene.

Electride Characteristics of Some Binuclear Sandwich Complexes of Alkaline Earth Metals, M2(η5-L)2 (M = Be, Mg; L = C5H5-, N5-, P5-, As5-).

Ab initio calculations have been performed for a series of binuclear sandwich complexes, M2(η5-L)2. It has been observed that the eclipsed and staggered conformations have almost equal amount of energies. The M-M bond lengths are comparable with those in the free M2 molecules (M = Be, Mg). The nuclear-independent chemical shift (NICS) values indicate the aromaticity of these complexes. The stability of Be2(η5-L)2 complexes is higher than that of the Mg2(η5-L)2 complexes. The natural bond orbital (NBO) analysis and electron density descriptors proved the existence of a single covalent M-M bond in an M22+ fragment. It has been observed that each M-M bond contains a non-nuclear attractor (NNA) at the center of the respective bond. The Laplacian of electron density [∇2ρ(r)] is negative at the NNAs. The energy decomposition analysis (EDA) showed that M22+ and 2L- represent the bonding interaction in the complexes. All of the designed binuclear sandwich complexes behave as electrides.

The nature of the triple B[tbnd]B, double, B[dbnd]B, single, B–B, and one-electron, B.B boron-boron bonds from the topological analysis of electron localisation function (ELF) perspective

Local nature of the boron-boron (BB) bond has been investigated in 23 molecules using the topological analysis of Electron Localisation Function (ELF) and the electron density (AIM) frameworks. The wave function has been approximated using the CCSD//CCSD(T), CASSCF and DFT(M062x) methods and triple-zeta basis sets. The calculations yielded a formally triple bond, BB, with population of 5.87–4.67e, a double bond BB with population of 4.39–3.58e, a single bond, B–B with population of 2.49–2.04e and one electron bond, B.B with 0.38e. Topological analysis of ρ(r) field has shown the non-nuclear attractor, NNA, for the BB bond in ten molecules (CCSD, DFT) with ropt(B,B) smaller than 1.6 Å. Population of the pseudo-atom basin ranges from 0.28e to 1.42e (CCSD) and from 0.32e to 1.27e (DFT). An overview of the results from topological analysis of ELF together with a detailed discussion of electronic structure for 14 small molecules has been presented.

Encapsulation of Mg2 inside a C60 cage forms an electride.

Density functional theory (DFT) based calculations have been carried out for the endohedral encapsulation of magnesium dimer inside fullerene, that is, Mg2 @C60 . It is observed that the minimum energy structure of the Mg2 @C60 system is C2h symmetry. The MgMg bond distance in the Mg2 @C60 system is much shorter than that in the free Mg2 and Mg2 2+ ion. The formation of the endohedral Mg2 @C60 system is thermochemically spontaneous in nature. The natural bond orbital (NBO) analysis showed the presence of an Mg2 2+ fragment with an MgMg bond inside the C60 cage. The electron density descriptors have identified the covalency in the MgMg bond. A non-nuclear attractor (NNA) is present in the middle of the two Mg-atoms. The bonding interaction between the Mg2 and C60 fragments is ionic in nature and the [Mg2 2+ ] and [C60 2- ] represent the bonding pattern in the Mg2 @C60 system. The designed endohedrally encapsulated system behaves as an electride.

New lithium-electride design: material properties of Lin@porphyrin

The material with electride features have cavity-trapped electrons in the molecular structure. In this work, we select the porphyrin species as backbone to design new electrides. In this regard, addition of Li-atoms to porphyrin backbone (Li@porphyrin species) has been investigated at density functional theory (DFT) framework, systematically. According to our results, the Li@porphyrin systems have high thermodynamic stability and can be incorporated in either lithium electride (Li10Pr species) or lithium salt (Li1Pr and Li5Pr species) categories. This categorization is in terms of the computational study of four factors, non nuclear attractor (NNA), electron density laplacian (), electron localization function (ELF) and non linear optical (NLO) property. Therefore, Lithium:porphyrin ratio in the Li@porphyrin systems is very important criterion to provide porphyrin based lithium electride.

The nature of the T=T double bond (T\u2009=\u2009B, Al, Ga, In) in dialumene and its derivatives: topological study of the electron localization function (ELF)

The local electronic structure of the Al=Al bond was studied in dialumene and derivatives of dialumene in which the Al atoms were substituted by B, Ga, or In atoms. DFT calculations were performed using the B3LYP, B3PW91, PBE0, M06-L, and M06-2X functionals. Topological analysis of the electron localization function described the covalent bonds mentioned above using the disynaptic basins Vi=1,2(B,B), Vi=1,2(Al,Al), V(Ga,Ga), and Vi=1,2(In,In). The basin populations were smaller than 4 e, as expected for a double bond: B=B 2.97 e, Al=Al 3.44–3.5 e, Ga=Ga 3.58 e, and In=In 3.86 e. The Al=Al, Ga=Ga, and In=In bonds were found to be intermediate in character between single and double bonds. Topological analysis of the ρ(r) field for dialumene showed a non-nuclear attractor along the Al=Al bond, with a pseudoatom basin population of 0.937 e. NBO analysis suggested that a double bond occurred only in the molecules containing Al, Ga, or In atoms. The character of the Ga=Ga bond was observed to be strongly dependent on the effective core potential used in the calculations.

Lin@Tetracyanoethylene (n = 1–4) systems: Lithium salt vs lithium electride

Electrides are interesting and promising materials with cavity-trapped electrons which can be used as source of electron donor in different systems. Hereby, we have explored the possible formation of electride materials based on tetracyanoethylene (TCNE) backbone at MP2 computational level. This is achieved by systematic addition of up to four Li atoms to TCNE backbone. Our results predict high thermodynamic stability in the Lin@TCNE (n = 1–4) systems. Moreover, based on the evaluation of four criteria, non-nuclear attractor (NNA), electron localization function (ELF), electron density laplacian (∇2ρ(r)), and non-linear optical (NLO), TCNE-Li1 and TCNE-Li2 and TCNE-Li4 species are conventional donor-acceptor systems (lithium salt). In contrast, the TCNE-Li3 species can be introduced as lithium electride with cavity-trapped electrons. Therefore, Li:TCNE ratio is very significant factor to provide species with electride feature through the addition of Li atoms to TCNE backbone.

Activation of Small Molecules (H2, CO2, N2O, CH4, and C6H6) by a Porphyrinoid-Based Dimagnesium(I) Complex, an Electride.

A density functional theory-based computation has been carried out to reveal the geometrical and electronic structures of Mg2EP (1), where EP is an extended (3.1.3.1) porphyrinoid system. EP is a 22 π electronic system and is aromatic in nature. Here, we have studied the thermodynamic and kinetic stabilities of EP2–-supported Mg22+ ion. The nature of bonding has been studied using natural bond orbital and atoms in molecule schemes. The presence of a covalent Mg(I)–Mg(I) σ-bond in Mg2EP is confirmed. The occurrence of a non-nuclear attractor (NNA) with large electron population, negative Laplacian of electron density at NNA, and presence of an electron localization function basin along with large nonlinear optical properties prompt us to classify Mg2EP as the first porphyrinoid-based organic electride. Further five small molecules, viz., dihydrogen (H2), carbon dioxide (CO2), nitrous oxide (N2O), methane (CH4), and benzene (C6H6), are found to be activated by the electron density between the two Mg atoms in Mg2EP.