Are One-Electron Bonds Any Different from Standard Two-Electron Covalent Bonds?

Unveiling distinct bonding patterns in noble gas hydrides via interference energy analysis

Despite their apparent simplicity, the helium hydride ion (HeH+) and its analogues with heavier noble gas (Ng) atoms present intriguing challenges due to their unusual electronic structures and distinct ground-state heterolytic bond dissociation profiles. In this work, we employ modern valence bond calculations and the interference energy analysis to investigate the nature of the chemical bond in NgH+ (Ng = He, Ne, Ar). Our findings reveal that the energy well formation in their ground-state potential energy curves is driven by a reduction in kinetic energy caused by quantum interference, identical to cases of homolytic bond dissociation. However, clear differences in bonding situation emerge: in HeH+ and ArH+, electron charge transfer leads to Ng+-H covalent bonds, while in NeH+, a preferred Ne + H+ valence bond structure suggests the formation of a dative bond. This study highlights the distinct bonding mechanisms within the NgH+ series, showcasing the interplay between quantum interference and quasi-classical effects in molecules featuring noble gases.

Chemical Aristocracy: He3 Dication and Analogous Noble-Gas-Exclusive Covalent Compounds

Herein, we predict the first set of covalently bonded triatomic molecular compounds composed exclusively of noble gases. Using a combination of double-hybrid DFT, CCSD(T), and MRCI+Q calculations and a range of bonding analyses, we explored a set of 270 doubly charged triatomics, which included various combinations of noble gases and main group elements. This extensive exploration uncovered nine noble-gas-exclusive covalent compounds incorporating helium, neon, argon, or combinations thereof, exemplified by cases such as He32+ and related systems. This work brings to light a previously uncharted domain of noble gas chemistry, demonstrating the potential of noble gases in forming covalent molecular clusters.

One-Electron (2c/1e) Tin···Tin Bond Stabilized by ortho-Phenylenediamido Ligands

Odd-electron bonds, i.e., the two-center, three-electron (2c/3e), or one-electron (2c/1e) bonds, have attracted tremendous interest owing to their novel bonding nature and radical properties. Herein, complex [K(THF)6][LSn:···Sn:L] (1), featuring the first and unsupported 2c/1e Sn···Sn σ-bond with a long distance (3.2155(9) Å), was synthesized by reduction of stannylene [LSn:] (L = N,N-dpp-o-phenylene diamide) with KC8. The one-electron Sn-Sn bond in 1 was confirmed by the crystal structure, DFT calculations, EPR spectroscopy, and reactivity studies. This compound can be viewed as a stabilized radical by delocalizing to two metal centers and can readily mediate radical reactions such as C-C coupling of benzaldehyde.

The borderless world of chemical bonding across the van der Waals crust and the valence region

The definition of the van der Waals crust as the spherical section between the atomic radius and the van der Waals radius of an element is discussed and a survey of the application of the penetration index between two interacting atoms in a wide variety of covalent, polar, coordinative or noncovalent bonding situations is presented. It is shown that this newly defined parameter permits the comparison of bonding between pairs of atoms in structural and computational studies independently of the atom sizes.

Orbital contraction and covalent bonding

According to Ruedenberg's classic treatise on the theory of chemical bonding [K. Ruedenberg, Rev. Mod. Phys. 34, 326-376 (1962)], orbital contraction is an integral consequence of covalent bonding. While the concept is clear, its quantification by quantum chemical calculations is not straightforward, except for the simplest of molecules, such as H₂ ⁺ and H₂. This paper proposes a new, yet simple, approach to the problem, utilizing the modified atomic orbital (MAO) method of Ehrhardt and Ahlrichs [Theor. Chim. Acta 68, 231 (1985)]. Through the use of MAOs, which are an atom-centered minimal basis formed from the molecular and atomic density operators, the wave functions of the species of interest are re-expanded, allowing the computation of the kinetic energy (and any other expectation value) of free and bonded fragments. Thus, it is possible to quantify the intra- and interfragment changes in kinetic energy, i.e., the effects of contraction. Computations are reported for a number of diatomic molecules H₂, Li₂, B₂, C₂, N₂, O₂, F₂, CO, P₂, and Cl₂ and the polyatomics CH₃-CH₃, CH₃-SiH₃, CH₃-OH, and C₂H₅-C₂H₅ (where the single bonds between the heavy atoms are studied) as well as dimers of He, Ne, Ar, and the archetypal ionic molecule NaCl. In all cases, it is found that the formation of a covalent bond is accompanied by an increase in the intra-fragment kinetic energy, an indication of orbital contraction and/or deformation.

Why an integrated approach between search algorithms and chemical intuition is necessary?

Though search algorithms are appropriate tools for identifying low-energy isomers, fixing several constraints seems to be a fundamental prerequisite to successfully running any structural search program. This causes some potential setbacks as far as identifying all possible isomers, close to the lowest-energy isomer, for any elemental composition. The number of explored candidates, the choice of method, basis set, and availability of CPU time needed to analyze the various initial test structures become necessary restrictions in resolving the issues of structural isomerism reasonably. While one could arrive at new structures through chemical intuition, reproducing or achieving those exact same structures requires increasing the number of variables in any given program, which causes further constraints in exploring the potential energy surface in a reasonable amount of time. Thus, it is emphasized here that an integrated approach between search algorithms and chemical intuition is necessary by taking the C₁₂O₂Mg₂ system as an example. Our initial search through the AUTOMATON program yielded 1450 different geometries. However, through chemical intuition, we found eighteen new geometries within 40.0 kcal mol^-1 at the PBE0-D3/def2-TZVP level. These results indirectly emphasize that an integrated approach between search algorithms and chemical intuition is necessary to further our knowledge in chemical space for any given elemental composition.

Correlated Wave Functions for Electron-Positron Interactions in Atoms and Molecules

The positron, as the antiparticle of the electron, can form metastable states with atoms and molecules before its annihilation with an electron. Such metastable matter-positron complexes are stabilized by a variety of mechanisms, which can have both covalent and noncovalent character. Specifically, electron-positron binding often involves strong many-body correlation effects, posing a substantial challenge for quantum-chemical methods based on atomic orbitals. Here we propose an accurate, efficient, and transferable variational ansatz based on a combination of electron-positron geminal orbitals and a Jastrow factor that explicitly includes the electron-positron correlations in the field of the nuclei, which are optimized at the level of variational Monte Carlo (VMC). We apply this approach in combination with diffusion Monte Carlo (DMC) to calculate binding energies for a positron e+ and a positronium Ps (the pseudoatomic electron-positron pair), bound to a set of atomic systems (H-, Li+, Li, Li-, Be+, Be, B-, C-, O- and F-). For PsB, PsC, PsO, and PsF, our VMC and DMC total energies are lower than that from previous calculations; hence, we redefine the state of the art for these systems. To assess our approach for molecules, we study the potential-energy surfaces (PES) of two hydrogen anions H- mediated by a positron (e+H22-), for which we calculate accurate spectroscopic properties by using a dense interpolation of the PES. We demonstrate the reliability and transferability of our correlated wave functions for electron-positron interactions with respect to state-of-the-art calculations reported in the literature.

Three-center two-electron bonds from the quantum interference perspective

The nature of the three-center two-electron (3c2e) chemical bond is investigated by the Interference Energy Analysis (IEA) method and using of a SC(2, 3) (spin coupled wave function with two...

One-electron Bonds in Copper-Aluminum and Copper-Gallium Complexes

Odd-electron bonds have unique electronic structures and are often encountered as transiently stable, homonuclear species. In this study, a pair of copper complexes supported by Group 13 metalloligands, M[N((o-C6H4)NCH2PiPr2)3] (M...

The Valence-Bond (VB) Model and Its Intimate Relationship to the Symmetric or Permutation Group

VB and molecular orbital (MO) models are normally distinguished by the fact the first looks at molecules as a collection of atoms held together by chemical bonds while the latter adopts the view that each molecule should be regarded as an independent entity built up of electrons and nuclei and characterized by its molecular structure. Nevertheless, there is a much more fundamental difference between these two models which is only revealed when the symmetries of the many-electron Hamiltonian are fully taken into account: while the VB and MO wave functions exhibit the point-group symmetry, whenever present in the many-electron Hamiltonian, only VB wave functions exhibit the permutation symmetry, which is always present in the many-electron Hamiltonian. Practically all the conflicts among the practitioners of the two models can be traced down to the lack of permutation symmetry in the MO wave functions. Moreover, when examined from the permutation group perspective, it becomes clear that the concepts introduced by Pauling to deal with molecules can be equally applied to the study of the atomic structure. In other words, as strange as it may sound, VB can be extended to the study of atoms and, therefore, is a much more general model than MO.

Substituent Effects on the Quantum Interference of Two-Center One-Electron Bonds: [B2X6]- (X = H, F, Cl, CN, OH, CH3, and OCH3)

The interference energy analysis (IEA) provided by the generalized product function energy partitioning (GPF-EP) method was applied to investigate the influence of the neighboring atoms on the nature of the two-center one-electron (2c1e) bonds in the anion dimers of BX₃ species (X = H, F, Cl, CN, OH, CH₃, and OCH₃). The species were studied at the GVB-PP(6/12).SC(1,2)/6-31**G++ level of calculation. The IEA has revealed that there is a balance between two main factors determining the chemical stability of the species. Quantum interference acts as the sole stabilizing effect in the formation of the chemical bonds, particularly as the result of the drop in kinetic energy, and the electronegativity of the substituent has a direct influence on the magnitude of this effect. The quasi-classical energy is responsible for the destabilizing factors, mainly the group bulkiness, and the "electron-withdrawing" effect in the case of the cyano group.

Neither too Classic nor too Exotic: One-Electron Na⋅B Bond in NaBH3 - Cluster

It is here reported that the NaBH₃ ^- cluster exhibits a Na⋅B one-electron bond, a well-established type of electron-deficient bonding in the literature. The topological analysis of the electron localization function, at the correlated level, reveals that Na^- , when approaching the bonding distance, fairly distributes its valence electron pair between two lobes. One of these electrons is used to bond with BH₃ , which participates through its boron empty p-orbital. Furthermore, the bonding situation of LiBH₃ ^- , KBH₃ ^- , MgBH₃ , and CaBH₃ global minima structures are similar to that of NaBH₃ ^- , extending the family of these new one-electron bond systems with biradicaloid character.

Quantifying bond strengths via a Coulombic force model: application to the impact sensitivity of nitrobenzene, nitrogen-rich nitroazole, and non-aromatic nitramine molecules

The quantification of bond strengths is a useful and general concept in chemistry. In this work, a Coulombic force model based on atomic electric charges computed using the accurate distributed multipole analysis (DMA) partition of the molecular charge density was employed to quantify the weakest N-NO₂ and C-NO₂ bond strengths of 19 nitrobenzene, 11 nitroazole, and 10 nitramine molecules. These bonds are known as trigger linkages because they are usually related to the initiation of an explosive. The three families of explosives combine different types of molecular properties and structures ranging from essentially aromatic molecules (nitrobenzenes) to others with moderate aromaticity (nitroazoles) and non-aromatic molecules with cyclic and acyclic skeletons (nitramines). We used the results to investigate the impact sensitivity of the corresponding explosives employing the trigger linkage concept. For this purpose, the computed Coulombic bond strength of the trigger linkages was used to build four sensitivity models that lead to an overall good agreement between the predicted values and available experimental sensitivity values even when the model included the three chemical families simultaneously. We discussed the role of the trigger linkages for determining the sensitivity of the explosives and rationalized eventual discrepancies in the models by examining alternative decomposition mechanisms and features of the molecular structures.

Ca2+ mediated mechanism of octa-brominated dioxin/furan formation via BDE-209 thermolysis: Introducing the Mayer bond order difference

Polybrominated dibenzo-p-dioxins/dibenzofurans (PBDD/Fs) that form during industrial thermal processes, such as the cement kiln co-processing of BDE-209, are highly toxic contaminants. Nevertheless, the formation mechanisms of octa-brominated dioxins/furans (OBDD/Fs), most PBDD/F congeners, and one precursor of the more toxic lower PBDD/Fs from BDE-209 have received little attention. In cement kiln co-processes, the Ca²⁺-mediated regulation of OBDD/F formation is still debated. In this study, simulation experiments revealed that the average brominating degree of PBDD/Fs was 7.8, indicating that OBDD/Fs are dominant congeners (93.6 % median). Density functional theory (DFT) calculations found a new transition state (TS1) with a lower energy barrier than that found in a previous study. Three major OBDD/F formation reactions suggested that the presence of Ca²⁺ was thermodynamically beneficial to the formation of OBDD/Fs. This promotion effect can be attributed to the transfer of electron density leading to a change in the Mayer bond order (MBO) among elements when Ca²⁺ was bound. Intriguingly, in the transition state structures of the Ca²⁺-bound and Ca²⁺-free systems, the MBO difference among the old and new bonds can reveal the difficulty of Ca²⁺-mediated OBDD/F formation reactions from BDE-209.

Clarifying the quantum mechanical origin of the covalent chemical bond

Lowering of the electron kinetic energy (KE) upon initial encounter of radical fragments has long been cited as the primary origin of the covalent chemical bond based on Ruedenberg's pioneering analysis of H[Formula: see text] and H₂ and presumed generalization to other bonds. This work reports KE changes during the initial encounter corresponding to bond formation for a range of different bonds; the results demand a re-evaluation of the role of the KE. Bonds between heavier elements, such as H₃C-CH₃, F-F, H₃C-OH, H₃C-SiH₃, and F-SiF₃ behave in the opposite way to H[Formula: see text] and H₂, with KE often increasing on bringing radical fragments together (though the total energy change is substantially stabilizing). The origin of this difference is Pauli repulsion between the electrons forming the bond and core electrons. These results highlight the fundamental role of constructive quantum interference (or resonance) as the origin of chemical bonding. Differences between the interfering states distinguish one type of bond from another.

On generalized partition methods for interaction energies

The breakdown of interaction energy has always been a very important means to understand chemical bonding and it has become a seamlessly useful tool for modern supramolecular chemistry.

Unexpected reversal of stability in strained systems containing one-electron bonds

Ring strain energy is a very well documented feature of neutral cycloalkanes, and influences their structural, thermochemical and reactivity properties. In this work, we apply density functional theory and high-level coupled cluster calculations to describe the geometry and relative stability of C₆H₁₂⁺˙ radical cations, whose cyclic isomers are prototypes of singly-charged cycloalkanes. Molecular ions with the mentioned stoichiometry were produced via electron impact experiments using a gaseous cyclohexane sample (20-2000 eV). From our calculations, in addition to structures that resemble linear and branched alkenes as well as distinct conformers of cyclohexane, we have found low-lying species containing three-, four- and five-membered rings with the presence of an elongated C-C bond. Remarkably, the stability trend of these ring-bearing radical cations is anomalous, and the three-membered species are up to 11.3 kcal mol^-1 more stable than the six-membered chair structure. Generalized Valence Bond calculations and the Spin Coupled theory with N electrons and M orbitals were used in conjunction with the Generalized Product Function Energy Partitioning (GPF-EP) method and Interference Energy Analysis (IEA) to describe the chemical bonding in such moieties. Our results confirm that these elongated C-C motifs are one-electron sigma bonds. Our calculations also reveal the effects that drive thermochemical preference of strained systems over their strained-free isomers, and the origin of the unusual stability trend observed for cycloalkane radical cations.

Non-classical covalent bonds

The possibility of multiple bond formation between Periodic Table Group 13 – 15 elements is considered. The ways of triple bond formation between these elements are discussed; particular attention is paid to the B≡B triple bonds. New non-linear compounds with triple bonds and their molecular structures are considered. The causes are given for the formation of compounds with unusually short distances between chemically non-bonded atoms. The grounds of the theory of two-centre three-electron bonds are presented and conditions of existence of isolated square planar carbon clusters are analyzed.

The bibliography includes 181 references.

One-electron bonds are not "half-bonds"

Despite the success of the molecular orbital (MO) and valence-bond (VB) models to describe the electronic structure and properties of molecules, neither MO nor VB provides an explanation for the nature of the chemical bond. The first to address this problem was Ruedenberg, who showed that chemical bonds result from quantum interference. He developed a method to calculate the interference contribution to the total electronic energy and density and applied it to molecules containing typical two-centre two-electron (2c-2e) covalent bonds. To test the generality of Ruedenberg's hypothesis, we developed a powerful Interference Energy Analysis (IEA) method to calculate the interference contributions of individual chemical bonds to the total energy of diatomic and polyatomic molecules, and showed that any two-electron bond, despite its polarity, results from quantum interference. Nevertheless, many stable molecules are experimentally known whose chemical structures clearly indicate the existence of two-centre one-electron bonds (2c-1e). Therefore, the question remains if quantum interference will be the dominant effect for these systems. This work describes the extension of the IEA for treating two-centre one-electron bonds, making use of a Generalised Product Function (GPF) built from spin coupled wave functions of N electrons in M orbitals, SC(N,M). Several diatomic and polyatomic molecules were analysed and whenever possible the results were compared with the analogous case of a two-electron bond. The results indicate that interference is the dominant effect for the one-electron bonds, which reinforces the role of quantum interference as the central element in chemical bonding theory.

Zerovalent Rhodium and Iridium Silatranes Featuring Two-Center, Three-Electron Polar σ Bonds

Species with 2-center, 3-electron (2c/3e^- ) σ bonds are of interest owing to their fascinating electronic structures and potential for interesting reactivity patterns. Report here is the synthesis and characterization of a pair of zerovalent (d⁹ ) trigonal pyramidal Rh and Ir complexes that feature 2c/3e^- σ bonds to the Si atom of a tripodal tris(phosphine)silatrane ligand. X-ray diffraction, continuous wave and pulse electron paramagnetic resonance, density-functional theory calculations, and reactivity studies have been used to characterize these electronically distinctive compounds. The data available highlight a 2c/3e^- bonding framework with a σ*-SOMO of metal 4- or 5d_z ² parentage that is partially stabilized by significant mixing with Si (3p_z ) and metal (5- or 6p_z ) orbitals. Metal-ligand covalency thus buffers the expected destabilization of transition-metal (TM)-silyl σ*-orbitals by d-p mixing, affording well-characterized examples of TM-main group, and hence polar, 2c/3e^- σ "half-bonds".

On the Nature of the Positronic Bond

Recently it has been proposed that the positron, the anti-particle analog of the electron, is capable of forming an anti-matter bond in a composite system consists of two hydride anions and a positron [Angew. Chem. Int. Ed. 57, 8859-8864 (2018)]. In order to dig into the nature of this novel bond the newly developed multi-component quantum theory of atoms in molecules (MC-QTAIM) is applied to this positronic system. The topological analysis reveals that this species is composed of two atoms in molecules, each containing a proton and half of the electronic and the positronic populations. Further analysis elucidates that the electron exchange phenomenon is virtually non-existent between the two atoms and no electronic covalent bond is conceivable in between. On the other hand, it is demonstrated that the positron density enclosed in each atom is capable of stabilizing interactions with the electron density of the neighboring atom. This electrostatic interaction suffices to make the whole system bonded against all dissociation channels. Thus, the positron indeed acts like an anti-matter glue between the two atoms.

Formal Nickelate(-I) Complexes Supported by Group 13 Ions

Formal nickelate(-I) complexes bearing Group 13 metalloligands (M=Al and Ga) were isolated. These 17 e^- complexes were synthesized by one-electron reduction of the corresponding Ni⁰ →M^III precursors, and were investigated by single-crystal X-ray diffraction, EPR spectroscopy, and quantum chemical calculations. Collectively, the experimental and computational data support: 1) the strengthening of the Ni-M bond upon one-electron reduction, and 2) the delocalization of the unpaired spin across the Ni and M atoms. An intriguing electronic configuration is revealed where three valence electrons occupy two σ-type bonding interactions: Ni(3dz2 )² →M and σ-(Ni-M)¹ . The latter is an unusual Ni-M σ-bonding molecular orbital that comprises primarily the Ni 4p_z and M np_z /ns atomic orbitals.

Polarization, donor-acceptor interactions, and covalent contributions in weak interactions: a clarification

The concepts of polarization (induction), charge transfer and covalent bonding contributions are discussed in terms of weak interactions. They are shown to be different incarnations of the same phenomenon, so that using polarization to describe them is most consistent as it is the only real, measurable and uniquely defined quantity of the three. Dispersion is discussed as a form of polarization within the Feynman description. Model calculations are described. Graphical abstract The electron density of a hydride ion (nucleus white) polarized by a single positive point charge (brown).