Topological Analysis of Multiple Metal−Metal Bonds in Dimers of the M2(Formamidinate)4Type with M = Nb, Mo, Tc, Ru, Rh, and Pd

Three-Dimensional Convolutional Neural Networks Utilizing Molecular Topological Features for Accurate Atomization Energy Predictions

Deep learning methods provide a novel way to establish a correlation between two quantities. In this context, computer vision techniques such as three-dimensional (3D)-convolutional neural networks become a natural choice to associate a molecular property with its structure due to the inherent 3D nature of a molecule. However, traditional 3D input data structures are intrinsically sparse in nature, which tend to induce instabilities during the learning process, which in turn may lead to underfitted results. To address this deficiency, in this project, we propose to use quantum-chemically derived molecular topological features, namely, localized orbital locator and electron localization function, as molecular descriptors, which provide a relatively denser input representation in a 3D space. Such topological features provide a detailed picture of the atomic and electronic configuration and interatomic interactions in the molecule and hence are ideal for predicting properties that are highly dependent on the physical or electronic structure of the molecule. Herein, we demonstrate the efficacy of our proposed model by applying it to the task of predicting atomization energies for the QM9-G4MP2 data set, which contains ∼134k molecules. Furthermore, we incorporated the Δ-machine learning approach into our model, which enabled us to reach beyond benchmark accuracy levels (∼1.0 kJ mol^-1). As a result, we consistently obtain impressive mean absolute errors of the order 0.1 kcal mol^-1 (∼0.42 kJ mol^-1) versus the G4(MP2) theory using relatively modest models, which could potentially be improved further in a systematic manner using additional compute resources.

Polyhedral [M2B5] Metallaborane Clusters and Derivatives: An Overview of Their Structural Features and Chemical Bonding

A large number of metallaborane clusters and their derivatives with various structural arrangements are known. Among them, M2B5 clusters and derivatives constitute a significant class. Transition metals present in these species span from group 4 to group 7. Their structure can vary from oblatonido, oblatoarachno, to arachno type open structures. Many of these clusters appear to be hypoelectronic and are often considered as 'rule breakers' with respect to the classical Wade-Mingos electron counting rules. This is due to their unique highly oblate (flattened) deltahedral structures featuring a cross-cluster M-M interaction. Many theoretical calculations were performed to elucidate their electronic structure and chemical bonding properties. In this review, the synthesis, structure, and electronic aspects of the transition metal M2B5 clusters known in the literature are discussed. The chosen examples illustrate how, in synergy with experiments, computational results can provide additional valuable information to better understand the electronic properties and electronic requirements which govern their architecture and thermodynamic stability.

Covalent vs Charge-Shift Nature of the Metal-Metal Bond in Transition Metal Complexes: A Unified Understanding

We present here a general conceptualization of the nature of metal-metal (M-M) bonding in transition-metal (TM) complexes across the periods of TM elements, by use of ab initio valence-bond theory. The calculations reveal a dual-trend: For M-M bonds in groups 7 and 9, the 3d-series forms charge-shift bonds (CSB), while upon moving down to the 5d-series, the bonds become gradually covalent. In contrast, M-M bonds of metals having filled d-orbitals (groups 11 and 12) behave oppositely; initially the M-M bond is covalent, but upon moving down the Periodic Table, the CSB character increases. These trends originate in the radial-distribution-functions of the atomic orbitals, which determine the compactness of the valence-orbitals vis-à-vis the filled semicore orbitals. Key factors that gauge this compactness are the presence/absence of a radial-node in the valence-orbital and relativistic contraction/expansion of the valence/semicore orbitals. Whenever these orbital-types are spatially coincident, the covalent bond-pairing is weakened by Pauli-repulsion with the semicore electrons, and CSB takes over. Thus, for groups 3-10, which possess (n - 1)s²(n - 1)p⁶ semicores, this spatial-coincidence is maximal at the 3d-transition-metals which consequently form charge-shift M-M bonds. However, in groups 11 and 12, the relativistic effects maximize spatial-coincidence in the third series, wherein the 5d¹⁰ core approaches the valence 6s orbital, and the respective Pauli repulsion generates M-M bonds with CSB character. These considerations create a generalized paradigm for M-M bonding in the transition-elements periods, and Pauli repulsion emerges as the factor that unifies CSB over the periods of main-group and transition elements.

How to understand very weak Cr-Cr double bonds and negative spin populations in trinuclear Cr complexes: theoretical insight

Trinuclear Cr(ii) complex [Cr3(dpa)4Cl2] 1 (Hdpa = dipyridylamine) has two Cr-Cr double bonds linked with each other. DMRG-CASPT2 calculations reproduced its symmetrical structure. The Cr-Cr effective bond order (EBO) was evaluated to be only 0.59 based on the density matrix based on localized orbitals from DMRG-CASSCF orbitals. The CASCI calculations showed a significantly large α-spin population on the terminal Cr atoms as expected but a significantly large β-spin population on the central Cr atom against expectations. The very small EBO and the presence of a large β-spin population are not consistent with the simple understanding that 1 has two Cr-Cr double bonds and a quintet ground state, which requests correct understanding of 1 from the viewpoint of chemical bond theory. Comparison of 1 with the allene molecule and allyl radical disclosed that the linked Cr-Cr bonds of 1 resembled the C-C bond of the allyl radical but completely differed from the linked C-C double bonds of allene despite the similar molecular structure. Its N3 analogue [Cr3(dpa)4(N3)2] 2 has non-symmetrical structure with shorter Cr1-Cr2 and longer Cr2-Cr3 bonds unlike 1, indicating that 2 is a valence tautomer of 1. DMRG-CASPT2 could reproduce its non-symmetrical structure but DFT/B3PW91 could not. In 2, the EBO is 0.95 for the shorter Cr1-Cr2 bond and 0.47 for the longer Cr2-Cr3 one. The terminal Cr3 has a very large α spin population, and the other terminal Cr1 has a somewhat large α spin population, but the central Cr2 has a considerably large β spin population. These results indicate that the Cr1-Cr2 bond conjugates with the Cr2-Cr3 bond, which is inconsistent with the simple understanding that 2 has a quadruple bond between Cr1 and Cr2 and no bond between Cr2 and Cr3. The symmetrical structure has a stronger Cr-X coordinate bond (X = Cl or N3) but less stable Cr3 core than does the non-symmetrical one. The relative stabilities of the symmetrical and the non-symmetrical structures are determined by the balance between stabilization energies from the Cr3 core and the Cr-X coordinate bond. All these findings show that electronic structures and Cr-Cr bonds of 1 and 2 are interesting from the viewpoint of molecular science.

The scandium doped boron cluster B27Sc2+: a fruit can-like structure

A systematic exploration of the potential energy surface through evolutionary search algorithms was carried out to identify the most stable B₂₇Sc₂⁺ structure.

Metal-metal bonding and aromaticity in [M2(NHCHNH)3]2 (μ-E)2 (E = O, S; M = Nb, Mo, Tc, Ru, Rh)

The nature of M-M bonding and aromaticity of [M2(NHCHNH)3]2(μ-E)2 (E = O, S; M = Nb, Mo, Tc, Ru, Rh) was investigated using atoms in molecules (AIM) theory, electron localization function (ELF), natural bond orbital (NBO) and molecular orbital analysis. These analyses led to the following main conclusions: in [M2(NHCHNH)3]2(μ-E)2 (E = O, S; M = Nb, Mo, Tc, Ru, Rh), the Nb-Nb, Ru-Ru, and Rh-Rh bonds belong to "metallic" bonds, whereas Mo-Mo and Tc-Tc drifted toward the "dative" side; all these bonds are partially covalent in character. The Nb-Nb, Mo-Mo, and Tc-Tc bonds are stronger than Ru-Ru and Rh-Rh bonds. The M-M bonds in [M2(NHCHNH)3]2(μ-S)2 are stronger than those in [M2(NHCHNH)3]2(μ-O)2 for M = Nb, Mo, Tc, and Ru. The NICS(1)ZZ values show that all of the studied molecules, except [Ru2(NHCHNH)3]2(μ-O)2, are aromaticity molecules. O-bridged compounds have more aromaticity than S-bridged compounds. Graphical Abstract Left Molecular graph, and right electron localization function (ELF) isosurface of [M2(NHCHNH)3]2(μ-E)2(E = O, S; M = Nb, Mo, Tc, Ru, Rh).

Dinuclear first-row transition metal–(C8Me6)2complexes: metal–metal and metal–ligand bonds determined by the d electron configuration of the metal atom

The nature and strength of the metal–metal and metal–ligand bonds depend on the d electron configuration of the transition metal.

Nature of the bonding in the AuNgX (Ng = Ar, Kr, Xe; X = F, Cl, Br, I) molecules. Topological study on electron density and the electron localization function (ELF)

Topological analysis of the electron localization function (ELF) has been carried out for the AuNgX (Ng = Ar, Kr, Xe; X = F, Cl, Br, I) molecules using the wave function approximated by the CCSD, MP2, and DFT(B3LYP, M062X) methods including zero-order regular approximation (ZORA). In the Ng-F bond, the bonding disynaptic attractor V(Ng,F) is missing; therefore, there are no signs of the covalent binding. The nature of the Au-Ng bond depends on the computational method used. Analysis of the ELF carried out for the AuArF and AuXeF molecules, with the wave function approximated by the CCSD and MP2 methods, shows the V(Au,Ng) attractor possibly corresponding to a partially covalent binding between the gold and noble gas atom. However, its very small basin population (<1e) and a very large value of the variance of the basin population suggest that the Au-Ng bond has a very delocalized character. Such bond nature may be related to the charge shift concept with a resonance of the Au(-+)NgX, Au(+-)NgX hybrids. The weakest Au-Ng bond, in terms of the smallest amount of electron density for the V(Au,Ng) basin, is found for the AuKrF molecule with the CCSD method (0.13e). The MP2 method, however, does not yield any V(Au, Ng) population; hence, the covalent Au-Kr bond is not confirmed. Because the V(Au,Ng) attractor is also not observed with the DFT method, the proper characterization of the Au-Ng bond requires proper description of correlation effects. Additional studies on the Au2 and [AuXe](+) molecules, performed at the CCSD and B3LYP levels, exhibit no V(Au,Au) and V(Au,Xe) bonding basins either.

Bonding analysis of the donor-acceptor sandwiches CpE-MCp (E = B, Al, Ga; M = Li, Na, K; Cp = η⁵-C₅H₅)

The nature of E-M bonds in CpE-MCp (E = B, Al, Ga; M = Li, Na, K; Cp = η (5)-C5H5) donor-acceptor sandwiches was studied using the atoms in molecules (AIM) theory, electron localization function (ELF), energy decomposition analysis (EDA), and natural bond orbital analysis (NBO) methods. Both topological and orbital analysis show that the E atom determines the bond strength of the E-M bonds, while the M atom has little influence on it. E-M bond strength decreases in the order E = B, Al, and Ga. The EDA analysis shows that the electrostatic character decreases following the sequence E = B > Al > Ga. Not only the s orbital, but also the p orbital of the E/M atom participates in formation of the E-M bond. The interactions of E and M with Cp are different. The M-Cp interaction is purely electrostatic while the E-Cp interaction has a partly covalent character.

The important role of the Mo–Mo quintuple bond in catalytic synthesis of benzene from alkynes. A theoretical study

The reaction mechanism of catalytic synthesis of benzene from alkynes by the Mo–Mo quintuple bond and the electronic structure and bonding nature of dimetallacyclobutadiene and dimetallabenzyne were studied theoretically.

Bonding between strongly repulsive metal atoms: an oxymoron made real in a confined space of endohedral metallofullerenes

Endohedral metallofullerenes (EMFs) are able to encapsulate up to four metal atoms. In EMFs, metal atoms are positively charged because of the electron transfer from the endohedral metal atoms to the carbon cage. It results in the strong Coulomb repulsion between the positively charged ions trapped in the confined inner space of the fullerene. At the same time, in many EMFs, such as Lu(2)@C(76), Y(2)@C(79)N, M(2)@C(82) (M = Sc, Y, Lu, etc.), Y(3)@C(80), or Sc(4)O(2)@C(80), metals do not adopt their highest oxidation states, thus yielding a possibility of the covalent metal-metal bonding. In some other EMFs (e.g., La(2)@C(80)), metal-metal bonding evolves as the result of the electrochemical or chemical reduction, which leads to the population of the metal-based LUMO with pronounced metal-metal bonding character. This article highlights different aspects of the metal-metal bonding in EMFs. It is concluded that the valence state of the metal atoms in dimetallofullerenes is not dependent on their third ionization potential, but is determined by their ns(2)(n- 1)d(1)→ns(1)(n- 1)d(2) excitation energies. Peculiarities of the metal-metal bonding in EMFs are described in terms of molecular orbital analysis as well as topological approaches such as Quantum Theory of Atoms in Molecules and Electron Localization Function. Interplay of Coulomb repulsion and covalent bonding is analyzed in the framework of the Interacting Quantum Atom approach.

Charge-shift bonding and its manifestations in chemistry

Electron-pair bonding is a central chemical paradigm. Here, we show that alongside the two classical covalent and ionic bond families, there exists a class of charge-shift (CS) bonds wherein the electron-pair fluctuation has the dominant role. Charge-shift bonding shows large covalent-ionic resonance interaction energy, and depleted charge densities, and features typical to repulsive interactions, albeit the bond itself may well be strong. This bonding type is rooted in a mechanism whereby the bond achieves equilibrium defined by the virial ratio. The CS bonding territory involves, for example, homopolar bonds of compact electronegative and/or lone-pair-rich elements, heteropolar bonds of these elements among themselves and with other atoms (for example, the metalloids, such as silicon and germanium), hypercoordinated molecules, and bonds whose covalent components are weakened by exchange-repulsion strain (as in [1.1.1]propellane). Here, we discuss experimental manifestations of CS bonding in chemistry, and outline new directions demonstrating the portability of the new concept.

Source function description of metal–metal bonding in d-block organometallic compounds

The Source Function (SF) analysis is applied to a set of saturated [M2(CO)x, M = Mn, Fe, Co, Ni, x = 10, 9, 8, 7] and unsaturated [Co2(CO)x, x = 8-5] binuclear 3d metal carbonyls, and to the M2(formamidinate)4 (M = Nb, Mo, Tc, Ru, Rh, and Pd) binuclear 4d metal complexes, using ab initio electron densities. A description of the metal-metal (M-M) bonding closely related to that provided by the localization/delocalization indices is afforded. The agreement persists even when the M-M bond is lacking and the internuclear M-M midpoint is taken as a reference point for evaluating the SF contributions. However, use of the local form of the SF unveils interesting differences in how the charge density originates at the M-M midpoint when the system is metal-metal bonded or not. Most of the topological indices conventionally adopted to describe M-M bonds fail in reproducing the expected chemical trends for the set of investigated systems, with the adimensional [ V(b)]/G(b) ratio and the delta2rhob value being particularly inadequate.

The Electronic Structure of Alkali Aurides. A Four-Component Dirac−Kohn−Sham Study

Spectroscopic constants, including dissociation energies, harmonic and anharmonic vibrational frequencies, and dipole moments, are calculated for the complete alkali auride series (LiAu, NaAu, KAu, RbAu, CsAu). The four-component formulation of relativistic density functional theory has been employed in this study, using the G-spinor basis sets implemented recently in the program BERTHA. The performance of four standard nonrelativistic density functionals employed is investigated by comparing the results with the best available theoretical and experimental data. The present work provides the first theoretical predictions on the molecular properties of RbAu. The intermetallic bond that occurs in the alkali auride series is highly polar and is characterized by a large charge transfer from the alkali metals to gold. The extent of this electron transfer has been investigated using several different charge analysis methods, enabling us to reach some general conclusions on their relative performance. We further report a detailed analysis of the topological properties of relativistic electron density in the bonding region, discussing the features of this approach which characterize the nature of the chemical bond. We have also computed the fully relativistic density for the alkali halides MBr and MI (M = Li, Na, K, Rb, and Cs). The comparative study shows that, on the basis of several topological properties and the variation in bond lengths, the gold atom behaves similarly to a halogen intermediate between Br and I.

On the Nature of Metal−Carbon Bonding: AIM and ELF Analyses of MCHn (n = 1−3) Compounds Containing Early Transition Metals

Ab initio and DFT calculations have been performed on a series of organometallic compounds, according to the formula MCH(n), where M = K, Ca, Sc, Ti, V, Cr, or Mn and n = 1-3. Various theoretical methods are compared, the B3LYP level yielding the same agreement with the experimental geometries available as the correlated MP2 and CISD methods, with the 6-311++G(3df,2p) basis set for C and H and Wachter's (15s11p6d3f1g)/[10s7p4d3f1g] basis set for transition metals. The main geometric and electronic features of the molecules studied are described, analyzing the M-C bonding characteristics in terms of the atoms in molecules theory (AIM) and the electron localization function (ELF). Although multiple bonding is expected from the Lewis bonding scheme, the results indicate an almost pure ionic bond for all of the systems studied. The net charge transfer from the metal to the carbon atom ranges from 0.5 to 1 e(-), and the electronic structure of the CH(n)(-) moiety is unaltered after the interaction with the metal cation, showing little or no effect on the shape of the electron pairing. The bond paths corresponding to a possible alpha-agostic bond for these systems are not present.

On the Nature of the Lowest Triplet Excited State of the [Rh2(1,3-diisocyanopropane)4]2+ Ion

The nature of the ground state and the lowest triplet excited state of the [Rh(2)(1,3-diisocyanopropane)(4)](2+) ion have been investigated by the density functional theory. Two locally stable geometrical conformations are found on the potential energy surfaces of both the ground and excited states, corresponding to the eclipsed and twisted conformations, the eclipsed conformation being more stable and having the shorter Rh-Rh bond length. While the Rh-Rh distances of the two conformations differ by approximately 0.4 A, they shorten to the same value upon excitation ( approximately 3.1 A). The excited state originates from the d(z)()()2 (metal antibonding) to p(z)() (ligand-metal bonding) electronic transition. The Mayer Rh-Rh bond order increases from approximately 0.2 to more than 0.8 upon excitation, while the Rh-C(N) bond order shows a slight decrease. A topological bond path between the Rh atoms is found in both the ground and excited states, while the electron localization function (ELF) indicates weak Rh-Rh covalent bonding for the excited state only.