One-electron Bond Research Articles

On the existence of intramolecular one-electron Be-Be bonds.

Although the Be-Be bond is extremely weak in Be2 dimers, we have shown that rather stable Be-Be one-electron sigma bonds are formed upon electron attachment to 1,8-diBeX-naphthalene derivatives. Wavefunction analyses corroborate the formation of Be-Be covalent linkages in which the extra electron is accommodated between the Be atoms as reflected in the dramatic shortening of the Be-Be distance with respect to the corresponding neutral molecule.

Hybrid DFT calculation ofFe57NMR resonances and orbital order in magnetite

The crystal structure and charge and orbital order of magnetite below the Verwey temperature are calculated using a first-principles hybrid density functional theory (DFT) method. The initial atomic positions in the crystal-structure calculation are those recently refined from x-ray diffraction data for the $Cc$ space-group unit cell [Senn, Wright, and Attfield, Nature (London) 481, 173 (2012)]. Fermi contact and magnetic dipolar contributions to hyperfine fields at $^{57}\mathrm{Fe}$ nuclei obtained from hybrid DFT calculations are used to obtain NMR resonance frequencies for magnetite for a range of external magnetic field directions in a relatively weak field. NMR frequencies from hybrid density functional theory calculations are compared to NMR data [M. Mizoguchi, J. Phys. Soc. Jpn. 70, 2333 (2001)] for a range of applied magnetic field directions. NMR resonance frequencies of $B$-site Fe ions show large relative variations with applied field direction owing to anisotropic hyperfine fields from charge and orbital ordered Fe $3d$ minority-spin electrons at those sites. Good agreement between computed and measured NMR resonance frequencies confirms the pattern of charge and orbital order obtained from calculations. The charge and orbital order of magne-tite in its low-temperature phase obtained from hybrid DFT calculations is analyzed in terms of one-electron bonds between Fe ions. The Verwey transition in magnetite therefore resembles Mott-Peierls transitions in vanadium oxides which undergo symmetry-breaking transitions owing to electron-pair bond formation.

The Genesis of the Quantum Theory of the Chemical Bond

An historical overview is given of the relevant steps that allowed the genesis of the quantum theory of the chemical bond, starting from the appearance of the new quantum mechanics and following later developments till approximately 1931. General ideas and some important details are discussed concerning molecular spectroscopy, as well as quantum computations for simple molecular systems performed within perturbative and variational approaches, for which the Born-Oppenheimer method provided a quantitative theory accounting for rotational, vibrational and electronic states. The novel concepts introduced by the Heitler-London theory, complemented by those underlying the method of the molecular orbitals, are critically analyzed along with some of their relevant applications. Further improvements in the understanding of the nature of the chemical bond are also considered, including the ideas of one-electron and three-electron bonds introduced by Pauling, as well as the generalizations of the Heitler-London theory firstly performed by Majorana, which allowed the presence of ionic structures into homopolar compounds and provided the theoretical proof of the stability of the helium molecular ion. The study of intermolecular interactions, as developed by London, is finally examined.

Theoretical Design of Strong Neutral Radical–Boron Adducts: Trisubstituted Boranes as Potential Radical Scavengers

The conditions of formation of strong two-center one-electron bonds in neutral compounds are discussed. Both molecular orbital and valence bond analyses show that good candidates are adducts of radicals ˙AR3 (A=C, Si, Ge) of low ionization energy (IE) with boranes BX3 of high electron affinity (EA). This is confirmed by ab initio calculations. The bond energy of adducts of B(CF3)3 with various radicals ranges from 18 kcal mol(-1) for ˙CH3 to approximately 40 kcal mol(-1) for Me3Si˙, and a clear correlation with IE-EA difference is found. This allows one to expect B(CF3)3, among other fluoroboranes, to be an efficient radical scavenger.

Notes on Valence Bond Structures for S2N2 and Related Systems

For the D2h E2N2 and D4h E4(2+) (E=S, Se and Te) systems with one valence-shell π-electron atomic orbital per atomic centre, the ground-state resonance between two increased-valence structures with one-electron and fractional electron-pair π bonds is equivalent to resonance between the six Lewis-type valence-bond structures considered in this journal (B. Braïda, A. Lo, P. C. Hiberty, ChemPhysChem 2012, 13, 811-819). Approximate values are deduced for the one-electron bond polarity parameters. Three types of electron transfer processes are used to convert one increased-valence structure into the other. Theory is developed to show that one component of the associated electron transfer matrix element is not dependent on atomic orbital overlap. Brief consideration is also given to other types of VB descriptions for the S2N2 ground state.

A Polar Copper–Boron One-Electron σ-Bond

Virtually all chemical bonds consist of one or several pairs of electrons shared by two atoms. Examples of σ-bonds made of a single electron delocalized over two neighboring atoms were until recently found only in gas-phase cations such as H2(+) and Li2(+) and in highly unstable species generated in solid matrices. Only in the past decade was bona fide one-electron bonding observed for molecules in fluid solution. Here we report the isolation and structural characterization of a thermally stable compound featuring a Cu-B one-electron bond, as well as its oxidized (nonbonded) and reduced (two-electrons-bonded) congeners. This triad provides an excellent opportunity to study the degree of σ-bonding in a metalloboratrane as a function of electron count.

On the nature of spin- and orbital-resolved Cu+–NO charge transfer in the gas phase and at Cu(I) sites in zeolites

Electronic factors essential for NO activation by Cu(I) sites in zeolites are investigated within spin-resolved analysis of electron transfer channels (natural orbitals for chemical valence). NOCV analysis is performed for three DFT-optimized models of Cu(I)–NO site in ZSM-5: [CuNO]+, (T1)CuNO, and (M7)CuNO. NO as a non-innocent, open-shell ligand reveals significant differences between independent deformation density components for α and β spins. Four distinct components are identified: (i) unpaired electron donation from NO π‖* antibonding orbital to Cus,d; (ii) backdonation from copper d yz to π⊥* antibonding orbital; (iii) donation from occupied π‖ and Cu d xz to bonding region, and (iv) donation from nitrogen lone-pair to Cus,d. Channel (i), corresponding to one-electron bond, shows-up solely for spin majority and is effective only in the interaction of NO with naked Cu+. Channel (ii) dominates for models b and c: it strongly activates NO bond by populating antibonding π* orbital and weakens the N–O bond in contrast to channel (i), depopulating the antibonding orbital and strengthening N–O bond. This picture perfectly agrees with IR experiment: interaction with naked Cu+ imposes small blue-shift of NO stretching frequency while it becomes strongly red-shifted for Cu(I) site in ZSM-5 due to enhanced backdonation.

Electronic structure and bonding of HBeLi, HmgLi, and HCaLi in their bent equilibrium geometries

Compact, yet accurate, non-orthogonal multi-configuration wavefunctions have been computed for HBeLi, HMgLi, and HCaLi in their respective nonlinear equilibrium geometries. They appear to be dominated by just two configurations, "orbitally relaxed" versions of the single-configuration spin-coupled and generalized valence bond (GVB) wavefunctions, respectively, with a smaller contribution from a self-consistent field (SCF)-like configuration. Double excitations out of the main configurations, while required for quantitative accuracy, enter the wavefunction with such small weights that they do not alter the qualitative picture that emerges from the orbital structure of the two main configurations. For comparison, calculations have also been carried out with two orthogonality-free configurations as reference, and no GVB-like or SCF-like configuration. Atoms-in-molecules (AIM) topological analyses of the overall electron densities, and considerations of local energetics in the differential neighbourhood of the equilibrium geometries, have been used to provide independent assessments of the nature of bonding in these molecules. Orbital structure and AIM results together suggest the existence of three-centre two-electron M-H-M' bonds through hydrogen in all three molecules. Orbital pictures suggest these bonds are at least partially covalent, while a strict interpretation of values of the electron density Laplacian at AIM bond critical points would imply closed-shell interactions. Also for all three molecules, the orbital structures of the two main configurations suggest the presence of a one-electron two-centre bond between Li and the alkaline-earth atom. This bond may provide at least a partial explanation for the relative shortness of the inter-metallic distances, but is apparently too spread out to show up in AIM analyses of the total electron density. Considerations of local energetics support the more nuanced description of bonding that emerges, for these three molecules, from their orbital structure.

One-, two-, and three-electron bonding: An “in vitro” theoretical study using noninteger nuclear charges evidences the crucial role of electronegativity in the strength of symmetrical bonds

Fictitious hydrogen atoms H*A of variable nuclear charge 0.5 ≤ ZA ≤ 2 (and thus of variable electronegativity) are used to study the intrinsic dependency of chemical bonding on electronegativity. Dissociation energy and equilibrium distance are reported for symmetrical 1-, 2- and 3-electron H*AH*A systems and 2-electron dissymmetrical H*A-H ones. Dealing with symmetrical systems, the strongest two-electron bonds are found for ZA ≈ 1.2. Oneelectron and three-electron strongest bonds occur respectively with low (ca. 0.7) and high (ca. 1.7) ZA values and can become stronger than the corresponding 2-electron system. Comparison with data on real systems leads to conclude that electronegativity is a prevailing atomic property in the control of the dissociation energy of symmetrical 1-, 2- and 3-electron bonds. A simplified mathematical model at Hartree-Fock or Heitler-London level with a minimal basis set reproduces these trends semi-quantitatively and provides the overall shape of the dissociation curves. Finally some points are qualitatively discussed from MO analysis, which emphasize the dependence of the bonding/antibonding properties on the nucleus charge ZA and their occupancy number. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011

Metal-organic charge transfer can produce biradical states and is mediated by conical intersections

The present paper illustrates key features of charge transfer between calcium atoms and prototype conjugated hydrocarbons (ethylene, benzene, and coronene) as elucidated by electronic structure calculations. One- and two-electron charge transfer is controlled by two sequential conical intersections. The two lowest electronic states that undergo a conical intersection have closed-shell and open-shell dominant configurations correlating with the 4 s 2 and 4 s 1 3 d 1 states of Ca, respectively. Unlike the neutral-ionic state crossing in, for example, hydrogen halides or alkali halides, the path from separated reactants to the conical intersection region is uphill and the charge-transferred state is a biradical. The lowest-energy adiabatic singlet state shows at least two minima along a single approach path of Ca to the π system: ( i ) a van der Waals complex with a doubly occupied highest molecular orbital, denoted , and a small negative charge on Ca and ( ii ) an open-shell singlet (biradical) at intermediate approach (Ca⋯C distance ≈2.5–2.7 Å ) with molecular orbital structure ϕ 1 ϕ 2 , where ϕ 2 is an orbital showing significant charge transfer form Ca to the π-system, leading to a one-electron multicentered bond. A third minimum ( iii ) at shorter distances along the same path corresponding to a closed-shell state with molecular orbital structure has also been found; however, it does not necessarily represent the ground state at a given Ca⋯C distance in all three systems. The topography of the lowest adiabatic singlet potential energy surface is due to the one- and two-electron bonding patterns in Ca-π complexes.

Valence Bond Structures for Three-Electron Three-Center and Four-Electron Three-Center Bonding Units: Some Further Examples†

A formula is derived for the R-atom valence in the valence bond structure X.R:Y, with one overlapping atomic orbital per atomic center. Using this formula, the results of STO-6G valence bond calculations for linear H(3), HFH, FHF, and F(3) transition states show that for each molecule, the R-atom exhibits increased-valence or electronic hypervalence, that is, its valence exceeds that for the Lewis structure X R:Y, with no one-electron bond. Consideration is also given to (a) valence bond formulations for the conversion of the excited states of the reactants into the excited states of the products for the X(*) + R:Y --> X:R + Y(*) and X(:(-)) + R:Y --> X:R + Y(:(-)) reactions and the state correlation diagram for X(*) + R:Y --> X:R + Y(*), (b) Kekule and Dewar increased-valence structures for D(6h) symmetry systems, and (c) the three-center molecular orbital interaction of the X(*) electron with the antibonding molecular orbital of R:Y, to form the one-electron X-R bond of X.R:Y.

Comments on charge density waves

Charge density waves (CDWs) in transition-metal compounds are shown to be a consequence of the first-order character of the crossover from localized to itinerant d-electron behavior; they are formed as this crossover is approached from either the localized-electron or the itinerant-electron side. Opening of a gap at the Fermi energy by changing the periodicity of the electron potential energy is a description that is only applicable on the approach from the itinerant-electron side. At crossover, single-valent transition-metal compounds with metal–metal d-electron bonding form cation clusters in which d-electrons are confined to molecular orbitals; normally, the individual bonds of a cluster are electron-pair bonds. However, in Zn[V2]O4, orbital ordering of a localized 3d-electron in an xy-orbital lowers the V–V separation in [011] and [101] chains sufficiently that the yz ± izx orbitals approach crossover from the localized-electron side. To resolve the magnetic frustration associated with the antiferromagnetic coupling between the localized spins in neighboring xy orbitals, the yz ± izx electrons become confined to one-electron bonds in a zigzag chain rather than an electron-pair bond within a dimer. The itinerant d-electrons of the zigzag chains are spin-polarized by intra-atomic exchange with xy-orbital spins. At crossover, compounds with cation–anion–cation bonding segregate into cations of an anion complex and cations with localized-electron spins; these segregations commonly result in a disproportionation electron transfer between cations that result in a static “negative-U” CDW in either single-valent or mixed-valent systems, but the perovskite HoNiO3 demonstrates that this electron transfer does not always occur. The insertion of interstitial Oi atoms in the \( {\hbox{L}}{{\hbox{a}}_2}{\hbox{Cu}}{{\hbox{O}}_{{\rm{4}} + \delta }} \) system allows monitoring of the formation of a dynamic phase segregation into mobile multihole polarons in a hole-free matrix that order into a thermodynamically distinct superconductive phase. The polarons may either order into pinned metallic stripes or as two-hole, two-electron bosonic polarons that become pinned to phonons in a superconductive phase that masks a quantum critical point.

One-Electron Metal−Metal Bond Stabilized in Dinuclear Metallocenes: Theoretical Prediction of DBe-LiCp (D = C5H5 or C5Me5)

Recently, stimulated by the unexpected synthesis and isolation of a bis-metallic sandwich compound Cp*ZnZnCp* (Cp* = eta(5)-C(5)Me(5)), many studies have focused on various dinuclear metallocenes involving a direct metal-metal (single or multiple) bond. However, we are not aware of any report on the metallocenes incorporating a "one-electron metal-metal bond". Herein, through the good steric and electronic stabilization effect of Cp and Cp*, we for the first time theoretically design a new type of sandwich-like compounds DBe-LiCp (D = Cp or Cp*) associated by an "unaided" one-electron metal-metal bond. Bonding characteristics of CpBe-LiCp were analyzed by natural bond orbital (NBO) theory. To shed more light on the stability of sandwich complexes, the dissociation energies (DBe-LiCp --> DBe + CpLi) and extrusion energies (DBe-LiCp --> DBeCp + Li) were calculated. Through calculation of thermodynamic standard entropies, we predict that these new compounds may be detected in the gaseous phase at appropriate experiment conditions.

The electronic structure of the two lowest states of CuC

State-of-the-art ab initio quantum mechanical methods and large basis sets are employed for the study of the electronic structure of the first two states of CuC, (4)Sigma(-) and (2)Pi. A one-electron sigma bond state ((4)Sigma(-)) competes with a two-electron sigma-bond state ((2)Pi) for the ground state of the CuC system. The combined effects of core-valence correlation and relativity point to an X-state of (2)Pi symmetry with D(e)=51.9 kcal/mol and r(e)=1.772 A. The (4)Sigma(-) state is predicted to lie 2.1 kcal/mol higher at r(e)=1.787 A.

Stabilisation of reactive intermediates in molecular sieves

This paper presents studies on paramagnetic intermediates, free atoms and radicals produced in γ-irradiated molecular sieves and their reactions with adsorbate molecules or exchangeable cations. Four different systems have been investigated using EPR spectroscopy, Na-A/CH4, AgNa-A/CH3OH, Ag-SAPO-11/C2H4 and AgCs-rho/NH3. It was found that methyl radicals are formed in two different sites in Na-A/CH4 and in one of them they are stable at room temperature. The formation of Ag·CH2OH+ radical cation with one-electron bond between silver and carbon has been established in AgNa-A/CH3OH by EPR experiments with [13C]CH3OH and DFT calculations. In Ag-SAPO-11/C2H4 the stabilisation of biligand silver/ethylene complex, Ag0(C2H4)2 was postulated based on EPR and DFT results. Tetrameric silver clusters (Ag 4 3+ ) produced radiolytically in AgCs-rho/NH3 strongly interact with two ammonia molecules as was deduced from the changes in superhyperfine structure of high-field EPR line of Ag 4 3+ pentet for zeolite exposed to [14N]NH3 and [15N]NH3. The presented examples clearly show that the combination of radiation methods with EPR technique is very useful to study the structure and reactivity of paramagnetic intermediates.

Unpaired and σ Bond Electrons as H, Cl, and Li Bond Acceptors: An Anomalous One-Electron Blue-Shifting Chlorine Bond

Ab initio, DFT, and AIM theoretical studies on H-, Cl-, and Li-bonded complexes have been carried out with typical lone pair (H2O), pi (C2H4) and sigma (H2) bonded pairs, and unpaired (CH3) electrons as acceptors and HF, ClF, and LiF as donors. Optimization and frequency calculations have been carried out at reasonably high levels (MP2, DFT(B3LYP), and QCISD) with large basis sets up to aug-cc-pVTZ. Not surprisingly, all HF complexes show red shift in stretching frequency and the shift is correlated to the binding energy. However, the FCl...CH3 complex shows a large blue shift (about 200 cm-1), which appears to be the largest blue shift predicted for any weakly bound complex yet. Analysis of the normal modes of the complex indicates that the shift is due to the mixing of modes between donor and acceptor and it is qualitatively different from the blue shifts reported thus far in hydrogen-bonded complexes. For Cl- and Li-bonded complexes, a correlation between frequency shift and binding energy is not found. However, AIM theoretical analysis shows the similarity in all these interactions. The electron density at the bond critical point shows a strong correlation with the binding energy for H-, Cl-, and Li-bonded complexes. This appears to be the first report on a one-electron chlorine bond.

Classical and Distonic Radical Cations: A Valence Bond Approach

The conventional radical cations arising from the ionization of CH(3)CH(2)X (X=F, OH, NH(2), Cl, SH, PH(2)), and their distonic isomers, CH(2)CH(2)XH(.+), were studied by means of standard Møller-Plesset and G2 methods, and by an ab initio valence bond method. Among the conventional structures, two distinct states are considered. In the so-called c' states, the unpaired electron is in an orbital that lies in the plane of the heavy atoms, while the c'' states have their unpaired electron in an orbital lying out of the plane. It is shown that c' states are, as a rule, more stable than the c'' states, by up to approximately 20 kJ mol(-1) depending on the nature of X, owing to a stabilizing interplay of resonating structures. While the geometries of the c'' states are rather similar to those of the neutral molecules, some of the c' states display very different geometries, characterized by elongated C--C bonds, particularly when X=F or, to a lesser extent, when X=OH or Cl. These peculiar geometric features are rationalized by the valence bond analysis, which reveals that the C--C bond in these species is better viewed as a two-center, one-electron bond. The distonic radical cations are generally more stable than the conventional ones (by 20-100 kJ mol(-1)), except for the less electronegative X groups of the series, namely X=SH and PH(2). In these two cases, together with X=NH(2), the radical cation displays a classical distonic structure, as regards the geometry and electronic state. On the other hand, considerable C--X elongation is found for X=F or Cl. In these last cases, the valence bond analysis shows that the radical cation is better viewed as an ion-molecule complex between an ionized ethylene and a neutral HX molecule. The electronic structure of the distonic radical cation with X=OH lies between the two previous limiting descriptions.

Valence Bond Formulations of Mechanisms for the Formation and Decomposition of N2O5

Environmental Context. N2O5 is an important nitrogen reservoir in polar stratospheric clouds found in Antarctica and involved with the ozone hole. Here we provide valence bond representations for the gas-phase formation and decomposition of this molecule. Abstract. Qualitative valence bond considerations are used to suggest how electronic reorganization could proceed for (a) the formation of N2O5 via the reactions NO2 + O3 → NO3 + O2, and NO2 + NO3 → N2O5, and (b) the thermal decomposition of N2O5 via the following sets of reactions: (i) N2O5 → NO2 + NO3, 2NO3 → O2NOONO2 →2NO2 + O2; (ii) NO2 + NO3 → ONOONO2 → NO + O2 + NO2, NO + NO3 → 2NO2. Increased-valence structures, which possess one-electron bonds and fractional electron-pair bonds as well as ‘normal’ electron-pair bonds, are used to represent the electronic structures of the molecules.

Corrigendum to: Valence Bond Formulations of Mechanisms for the Formation and Decomposition of N2O5

Environmental Context. N2O5 is an important nitrogen reservoir in polar stratospheric clouds found in Antarctica and involved with the ozone hole. Here we provide valence bond representations for the gas-phase formation and decomposition of this molecule. Abstract. Qualitative valence bond considerations are used to suggest how electronic reorganization could proceed for (a) the formation of N2O5 via the reactions NO2 + O3 → NO3 + O2, and NO2 + NO3 → N2O5, and (b) the thermal decomposition of N2O5 via the following sets of reactions: (i) N2O5 → NO2 + NO3, 2NO3 → O2NOONO2 → 2NO2 + O2; (ii) NO2 + NO3 → ONOONO2 → NO + O2 + NO2, NO + NO3 → 2NO2. Increased-valence structures, which possess one-electron bonds and fractional electron-pair bonds as well as 'normal' electron-pair bonds, are used to represent the electronic structures of the molecules.

Characterizing the Dimerizations of Phenalenyl Radicals by ab Initio Calculations and Spectroscopy: σ-Bond Formation versus Resonance π-Stabilization

Electronic-structure calculations for the self-association of phenalenyl radical (P*) predict the formation of dimeric species (sigma-P2) in which both moieties are connected by a sigma-bond with rP-P approximately 1.59 A and bond dissociation enthalpy of DeltaH(D) approximately 16 kcal mol(-1). Such an unusually weak sigma-bond is related to the loss of aromatic stabilization energy of approximately 34 kcal mol(-1) per phenalenyl moiety, largely owing to rehybridization. Ab initio calculations also reveal that the corresponding (one-electron) bond between phenalenyl radical and its closed-shell cation in sigma-P2+* is unstable relative to dissociation. Time-dependent DFT computations indicate the absence of any (strongly allowed) electronic transition in the visible region of the absorption spectrum of phenalenyl sigma-dimer. Such theoretical predictions are supported by experimental (ESR and UV-NIR) spectroscopic studies, in which the availability of a series of sterically hindered phenalenyl radicals allows definitive separations of the sigma-dimerization process from interference by pi-dimerization. As such, the thermodynamic parameters (determined from the temperature dependence of the ESR signals) with DeltaH(D) = 14 kcal mol(-1) and DeltaS(D) = 52 e.u. can be assigned to the formation of the colorless sigma-dimer. Similar results are obtained for all phenalenyl derivatives (provided their substitution patterns allow sigma-bond formation) to confirm the energetic preference of sigma-dimerization over pi-dimerization.