Barriers of Hydrogen Abstraction vs Halogen Exchange: An Experimental Manifestation of Charge-Shift Bonding

Identifying a real space measure of charge-shift bonding with probability density analysis

Charge-shift bonds have been hypothesized as a third type of chemical bonds in addition to covalent and ionic bonds. They have first been described with valence bond theory where they are identified by the resonance energy resulting from ionic contributions. While other indicators have been described, a clear real space fingerprint for charge-shift bonding is still lacking. Probability density analysis has been developed as a real space method, allowing chemical bonding to be identified from the many-electron probability density |Ψ|2 where the wave function Ψ can be obtained from any quantum chemical method. Recently, barriers of a probability potential, which depends on this density, have proven to be good measures for delocalization and covalent bonding. In this work, we employ many examples to demonstrate that a well-suited measure for charge-shift bonding can be defined within the framework of probability density analysis. This measure correlates well with the charge-shift resonance energy from valence bond theory and thus strongly supports the charge-shift bonding concept. It is, unlike the charge-shift resonance energy, not dependent on a reference state. Moreover, it is independent of the polarity of the bond, suggesting to characterize bonds in molecules by both their polarity and their charge-shift character.

A Theoretical Study on the Medicinal Properties and Eletronic Structures of Platinum(IV) Anticancer Agents With Cl Substituents

In this paper, we selected Pt(en)Cl4, Pt(dach)Cl4, and Pt(bipy)Cl4 with gradually increasing ligands to explore the ligand effect on the properties of platinum(IV) anticancer drugs. The electronic structures and multiple drug properties of these three complexes were studied at the LSDA/SDD level using the density functional theory (DFT) method. By comparing the gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), electron affinity, atomic charge population, and natural bond orbital (NBO), we found that the order of reducibility is Pt(bipy)Cl4 > Pt(en)Cl4 > Pt(dach)Cl4. Our research can provide the theoretical basis for the development of anticancer drugs.

Exploring the nature of electron-pair bonds: an energy decomposition analysis perspective

In this paper, the nature of electron-pair bonds is explored from an energy decomposition perspective. The recently developed valence bond energy decomposition analysis (VB-EDA) scheme is extended for the classification of electron-pair bonds, which divides the bond dissociation energy into frozen, reference state switch, quasi-resonance and polarization terms. VB-EDA investigations are devoted to a series of electron-pair bonds, including the covalent bonds (H-H, H₃C-CH₃, H₃C-H, and H₂N-NH₂), the ionic bonds (Na-Cl, Li-F), the charge-shift (CS) bonds (HO-OH, F-F, Cl-Cl, Br-Br, H-F, F-Cl, H₃Si-F and H₃Si-Cl), and the inverted central carbon-carbon bond in [1.1.1] propallene. It is shown that the VB-EDA approach at the VBSCF level is capable of predicting the characters of the electron-pair bonds. The perspective from VB-EDA illustrates that a relatively high value of quasi-resonance term indicates a CS bond while a large portion of polarization term suggests a classical covalent bond.

Nature of the Trigger Linkage in Explosive Materials Is a Charge-Shift Bond

Explosion begins by rupture of a specific bond, in the explosive, called a trigger linkage. We characterize this bond in nitro-containing explosives. Valence-bond (VB) investigations of X-NO₂ linkages in alkyl nitrates, nitramines, and nitro esters establish the existence of Pauli repulsion that destabilizes the covalent structure of these bonds. The trigger linkages are mainly stabilized by covalent-ionic resonance and are therefore charge-shift bonds (CSBs). The source of Pauli repulsion in nitro explosives is unique. It is traced to the hyperconjugative interaction from the oxygen lone pairs of NO₂ into the σ_(X-N)^* orbital, which thereby weakens the X-NO₂ bond, and depletes its electron density as X becomes more electronegative. Weaker trigger bonds have higher CSB characters. In turn, weaker bonds increase the sensitivity of the explosive to impacts/shocks which lead to detonation. Application of the analysis to realistic explosives supports the CSB character of their X-NO₂ bonds by independent criteria. Furthermore, other families of explosives also involve CSBs as trigger linkages (O-O, N-O, Cl-O, N-I, etc. bonds). In all of these, detonation is initiated selectively at the CSB of the molecule. A connection is made between the CSB bond-weakening and the surface-electrostatic potential diagnosis in the trigger bonds.

Unifying Conceptual Density Functional and Valence Bond Theory: The Hardness-Softness Conundrum Associated with Protonation Reactions and Uncovering Complementary Reactivity Modes

In this study, we address the long-standing issue-arising prominently from conceptual density functional theory (CDFT)-of the relative importance of electrostatic, i.e., "hard-hard", versus spin-pairing, i.e., "soft-soft", interactions in determining regiochemical preferences. We do so from a valence bond (VB) perspective and demonstrate that VB theory readily enables a clear-cut resolution of both of these contributions to the bond formation/breaking process. Our calculations indicate that appropriate local reactivity descriptors can be used to gauge the magnitude of both interactions individually, e.g., Fukui functions or HOMO/LUMO orbitals for the spin-pairing/(frontier) orbital interactions and molecular electrostatic potentials (and/or partial charges) for the electrostatic interactions. In contrast to previous reports, we find that protonation reactions cannot generally be classified as either charge- or frontier orbital-controlled; instead, our results indicate that these two bonding contributions generally interplay in more subtle patterns, only giving the impression of a clear-cut dichotomy. Finally, we demonstrate that important covalent, i.e., spin pairing, reactivity modes can be missed when only a single spin-pairing/orbital interaction descriptor is considered. This study constitutes an important step in the unification of CDFT and VB theory.

Overlap properties of chemical bonds in generic systems including unusual bonding situations

Chemical bond is a ubiquitous and fundamental concept in chemistry, in which the overlap plays a defining role. By using a new approach based on localized molecular orbitals, the overlap properties, e.g., polarizability [Formula: see text], population p_OP, intra [Formula: see text], and inter [Formula: see text] repulsions, and density ρ_OP, of polyatomic systems were calculated, analyzed, and correlated. Several trends are shown for these properties, which are rationalized by the balance of some well-known effects, such as, electron donor/withdrawing character and electronegativity. The overlap properties of unusual bonds are also analyzed, revealing an OZn₄(OOCH)₆ structure with four equivalent Zn-O chemical bonds with overlap properties like the O-O bond in H₂O₂, while in protonated methane [Formula: see text], it is observed that a CH₃⋯[Formula: see text] bond pattern at the equilibrium structure changes to a [Formula: see text]⋯H₂ pattern upon dissociation. Charge-shift resonance energies, atom-in-molecule properties, and the lone-pair-bond-weakening effects are related to the overlap properties, which can provide alternative views and insights into chemical bonds. Graphical abstract A chemical bond analysis approach based on its overlap properties is presented for the first time. The model was applied directly to 25 diatomics and for 28 bonds in polytomics employing localized molecular orbitals. Correlations of the overlap properties with the charge-shift resonance energies and with atom-in-molecule (AIM) properties were uncovered. In addition, it provided insights into the Zn-O bonds in the unusual OZn₄(OOCH)₆ system as well as in the bonding patterns of [Formula: see text] at equilibrium and upon dissociation.

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.

Globally optimal catalytic fields for a Diels-Alder reaction

In a previous paper [M. Dittner and B. Hartke, J. Chem. Theory Comput. 14, 3547 (2018)], we introduced a preliminary version of our GOCAT (globally optimal catalyst) concept in which electrostatic catalysts are designed for arbitrary reactions by global optimization of distributed point charges that surround the reaction. In this first version, a pre-defined reaction path was kept fixed. This unrealistic assumption allowed for only small catalytic effects. In the present work, we extend our GOCAT framework by a sophisticated and robust on-the-fly reaction path optimization, plus further concomitant algorithm adaptions. This allows smaller and larger excursions from a pre-defined reaction path under the influence of the GOCAT point-charge surrounding, all the way to drastic mechanistic changes. In contrast to the restricted first GOCAT version, this new version is able to address real-life catalysis. We demonstrate this by applying it to the electrostatic catalysis of a prototypical Diels-Alder reaction. Without using any prior information, this procedure re-discovers theoretically and experimentally established features of electrostatic catalysis of this very reaction, including a field-dependent transition from the synchronous, concerted textbook mechanism to a zwitterionic two-step mechanism, and diastereomeric discrimination by suitable electric field components.

Charge-Shift Bonding: A New and Unique Form of Bonding

Charge-shift bonds (CSBs) constitute a new class of bonds different than covalent/polar-covalent and ionic bonds. Bonding in CSBs does not arise from either the covalent or the ionic structures of the bond, but rather from the resonance interaction between the structures. This Essay describes the reasons why the CSB family was overlooked by valence-bond pioneers and then demonstrates that the unique status of CSBs is not theory-dependent. Thus, valence bond (VB), molecular orbital (MO), and energy decomposition analysis (EDA), as well as a variety of electron density theories all show the distinction of CSBs vis-à-vis covalent and ionic bonds. Furthermore, the covalent-ionic resonance energy can be quantified from experiment, and hence has the same essential status as resonance energies of organic molecules, e.g., benzene. The Essay ends by arguing that CSBs are a distinct family of bonding, with a potential to bring about a Renaissance in the mental map of the chemical bond, and to contribute to productive chemical diversity.

Dynamic Electric Field Complicates Chemical Reactions in Solutions

Chemical reactions can be strongly influenced by an external electric field (EEF), but because the EEF is often time-dependent and in case it does not adapt quickly enough to the reaction progress, especially during fast barrier crossing processes, dynamic effects could be important. Here we find that electrostatic interactions can reduce the height of the reaction barrier for a Claissen rearrangement reaction and accelerate the key motions for bonding. Meanwhile, strong electrostatic interactions can modify the barrier into an effective potential well, confining the system into the barrier until solvents adjust themselves to provide an appropriate EEF for charge redistribution. In this case, the otherwise concerted mechanism becomes a stepwise one. Consequently, the motion of solvents modulates the reaction dynamics and leads to heterogeneous reaction paths, even in a seemingly homogeneous aqueous solution. In addition, an excessive stabilization of transition state retards the barrier crossing process, making the thermodynamically favorable pathway less favored dynamically.

Structure and reactivity/selectivity control by oriented-external electric fields

This is a tutorial on use of external-electric-fields (EEFs) as effectors of chemical change. The tutorial instructs readers how to conceptualize and design electric-field effects on bonds, structures, and reactions. Most effects can be comprehended as the field-induced stabilization of ionic structures. Thus, orienting the field along the "bond axis" will facilitate bond breaking. Similarly, orienting the field along the "reaction axis", the direction in which "electron pairs transform" from reactants- to products-like, will catalyse the reaction. Flipping the field's orientation along the reaction-axis will cause inhibition. Orienting the field off-reaction-axis will control stereo-selectivity and remove forbidden-orbital mixing. Two-directional fields may control both reactivity and selectivity. Increasing the field strength for concerted reactions (e.g., Diels-Alder's) will cause mechanistic-switchover to stepwise mechanisms with ionic intermediates. Examples of bond breaking and control of reactivity/selectivity and mechanisms are presented and analysed from the "ionic perspective". The tutorial projects the unity of EEF effects, "giving insight and numbers".

Electronic Effects on Room-Temperature, Gas-Phase C-H Bond Activations by Cluster Oxides and Metal Carbides: The Methane Challenge

This Perspective discusses a story of one molecule (methane), a few metal-oxide cationic clusters (MOCCs), dopants, metal-carbide cations, oriented-electric fields (OEFs), and a dizzying mechanistic landscape of methane activation! One mechanism is hydrogen atom transfer (HAT), which occurs whenever the MOCC possesses a localized oxyl radical (M-O^•). Whenever the radical is delocalized, e.g., in [MgO]_n^•+ the HAT barrier increases due to the penalty of radical localization. Adding a dopant (Ga₂O₃) to [MgO]₂^•+ localizes the radical and HAT transpires. Whenever the radical is located on the metal centers as in [Al₂O₂]^•+ the mechanism crosses over to proton-coupled electron transfer (PCET), wherein the positive Al center acts as a Lewis acid that coordinates the methane molecule, while one of the bridging oxygen atoms abstracts a proton, and the negatively charged CH₃ moiety relocates to the metal fragment. We provide a diagnostic plot of barriers vs reactants' distortion energies, which allows the chemist to distinguish HAT from PCET. Thus, doping of [MgO]₂^•+ by Al₂O₃ enables HAT and PCET to compete. Similarly, [ZnO]^•+ activates methane by PCET generating many products. Adding a CH₃CN ligand to form [(CH₃CN)ZnO]^•+ leads to a single HAT product. The CH₃CN dipole acts as an OEF that switches off PCET. [MC]⁺ cations (M = Au, Cu) act by different mechanisms, dictated by the M⁺-C bond covalence. For example, Cu⁺, which bonds the carbon atom mostly electrostatically, performs coupling of C to methane to yield ethylene, in a single almost barrier-free step, with an unprecedented atomic choreography catalyzed by the OEF of Cu⁺.

Charge-Shift Corrected Electronegativities and the Effect of Bond Polarity and Substituents on Covalent-Ionic Resonance Energy

Bond dissociation energies and resonance energies for H_nA-BH_m molecules (A, B = H, C, N, O, F, Cl, Li, and Na) have been determined in order to re-evaluate the concept of electronegativity in the context of modern valence bond theory. Following Pauling's original scheme and using the rigorous definition of the covalent-ionic resonance energy provided by the breathing orbital valence bond method, we have derived a charge-shift corrected electronegativity scale for H, C, N, O, F, Cl, Li, and Na. Atomic charge shift character is defined using a similar approach resulting in values of 0.42, 1.06, 1.43, 1.62, 1.64, 1.44, 0.46, and 0.34 for H, C, N, O, F, Cl, Li, and Na, respectively. The charge-shift corrected electronegativity values presented herein follow the same general trends as Pauling's original values with the exception of Li having a smaller value than Na (1.57 and 1.91 for Li and Na respectively). The resonance energy is then broken down into components derived from the atomic charge shift character and polarization effects. It is then shown that most of the resonance energy in the charge-shift bonds H-F, H₃C-F, and Li-CH₃ and borderline charge-shift H-OH is associated with polarity rather than the intrinsic atomic charge-shift character of the bonding species. This suggests a rebranding of these bonds as "polar charge-shift" rather than simply "charge-shift". Lastly, using a similar breakdown method, it is shown that the small effect the substituents -CH₃, -NH₂, -OH, and -F have on the resonance energy (<10%) is mostly due to changes in the charge-shift character of the bonding atom.

Directionality and the Role of Polarization in Electric Field Effects on Radical Stability

Accurate quantum-chemical calculations are used to analyze the effects of charges on the kinetics and thermodynamics of radical reactions, with specific attention given to the origin and directionality of the effects. Conventionally, large effects of the charges are expected to occur in systems with pronounced charge-separated resonance contributors. The nature (stabilization or destabilization) and magnitude of these effects thus depend on the orientation of the interacting multipoles. However, we show that a significant component of the stabilizing effects of the external electric field is largely independent of the orientation of external electric field (e.g. a charged functional group, a point charge, or an electrode) and occurs even in the absence of any pre-existing charge separation. This effect arises from polarization of the electron density of the molecule induced by the electric field. This polarization effect is greater for highly delocalized species such as resonance-stabilized radicals and transition states of radical reactions. We show that this effect on the stability of such species is preserved in chemical reaction energies, leading to lower bond-dissociation energies and barrier heights. Finally, our simplified modelling of the diol dehydratase-catalyzed 1,2-hydroxyl shift indicates that such stabilizing polarization is likely to contribute to the catalytic activity of enzymes.

Charge-Shift Bonding Emerges as a Distinct Electron-Pair Bonding Family from Both Valence Bond and Molecular Orbital Theories

The charge-shift bonding (CSB) concept was originally discovered through valence bond (VB) calculations. Later, CSB was found to have signatures in atoms-in-molecules and electron-localization-function and in experimental electron density measurements. However, the CSB concept has never been derived from a molecular orbital (MO)-based theory. We now provide a proof of principle that an MO-based approach enables one to derive the CSB family alongside the distinctly different classical family of covalent bonds. In this bridging energy decomposition analysis, the covalent-ionic resonance energy, RECS, of a bond is extracted by cloning an MO-based purely covalent reference state, which is a constrained two-configuration wave function. The energy gap between this reference state and the variational TCSCF ground state yields numerical values for RECS, which correlate with the values obtained at the VBSCF level. This simple MO-based method, which only takes care of static electron correlation, is already sufficient for distinguishing the classical covalent or polar-covalent bonds from charge-shift bonds. The equivalence of the VB and MO-based methods is further demonstrated when both methods are augmented by dynamic correlation. Thus, it is shown from both MO and VB perspectives that the bonding in the CSB family does not arise from electron correlation. Considering that the existence of the CSB family is associated also with quite a few experimental observations that we already reviewed ( Shaik , S. , Danovich , D. , Wu , W. , and Hiberty , P. C. Nat. Chem. , 2009 , 1 , 443 - 449 ), the new bonding concept has passed by now two stringent tests. This derivation, on the one hand, supports the new concept and on the other, it creates bridges between the two main theories of electronic structure.

Direct, catalytic monofluorination of sp³ C-H bonds: a radical-based mechanism with ionic selectivity

Recently, our group unveiled a system in which an unusual interplay between copper(I) and Selectfluor effects mild, catalytic sp(3) C-H fluorination. Herein, we report a detailed reaction mechanism based on exhaustive EPR, (19)F NMR, UV-vis, electrochemical, kinetic, synthetic, and computational studies that, to our surprise, was revealed to be a radical chain mechanism in which copper acts as an initiator. Furthermore, we offer an explanation for the notable but curious preference for monofluorination by ascribing an ionic character to the transition state.

Chloroform as a hydrogen atom donor in Barton reductive decarboxylation reactions

The utility of chloroform as both a solvent and a hydrogen atom donor in Barton reductive decarboxylation of a range of carboxylic acids was recently demonstrated (Ko, E. J. et al. Org. Lett. 2011, 13, 1944). In the present work, a combination of electronic structure calculations, direct dynamics calculations, and experimental studies was carried out to investigate how chloroform acts as a hydrogen atom donor in Barton reductive decarboxylations and to determine the scope of this process. The results from this study show that hydrogen atom transfer from chloroform occurs directly under kinetic control and is aided by a combination of polar effects and quantum mechanical tunneling. Chloroform acts as an effective hydrogen atom donor for primary, secondary, and tertiary alkyl radicals, although significant chlorination was also observed with unstrained tertiary carboxylic acids.

SPIN DENSITY OF SPIN-FREE VALENCE BOND WAVE FUNCTIONS AND ITS IMPLEMENTATION IN VB2000

The expressions for computing the spin density of spin-free valence bond wave functions are derived based on the bonded tableaux approach. The new expressions, although similar to the original forms given by Cooper and McWeeny in the 1960s, are simpler and thus easier for coding. The new formulation was implemented in VB2000, an ab initio valence bond program based on algebrant algorithm and group function theory. The spin density calculation for multi-group VB wave functions is also briefly discussed. As examples of applications, the spin densities of allyl radical and diazide anion [Formula: see text] were computed at different VB levels.

Hydrogen atom abstraction selectivity in the reactions of alkylamines with the benzyloxyl and cumyloxyl radicals. The importance of structure and of substrate radical hydrogen bonding

A time-resolved kinetic study on the hydrogen abstraction reactions from a series of primary and secondary amines by the cumyloxyl (CumO(•)) and benzyloxyl (BnO(•)) radicals was carried out. The results were compared with those obtained previously for the corresponding reactions with tertiary amines. Very different hydrogen abstraction rate constants (k(H)) and intermolecular selectivities were observed for the reactions of the two radicals. With CumO(•), k(H) was observed to decrease on going from the tertiary to the secondary and primary amines. The lowest k(H) values were measured for the reactions with 2,2,6,6-tetramethylpiperidine (TMP) and tert-octylamine (TOA), substrates that can only undergo N-H abstraction. The opposite behavior was observed for the reactions of BnO(•), where the k(H) values increased in the order tertiary < secondary < primary. The k(H) values for the reactions of BnO(•) were in all cases significantly higher than those measured for the corresponding reactions of CumO(•), and no significant difference in reactivity was observed between structurally related substrates that could undergo exclusive α-C-H and N-H abstraction. This different behavior is evidenced by the k(H)(BnO(•))/k(H)(CumO(•)) ratios that range from 55-85 and 267-673 for secondary and primary alkylamines up to 1182 and 3388 for TMP and TOA. The reactions of CumO(•) were described in all cases as direct hydrogen atom abstractions. With BnO(•) the results were interpreted in terms of the rate-determining formation of a hydrogen-bonded prereaction complex between the radical α-C-H and the amine lone pair wherein hydrogen abstraction occurs. Steric effects and amine HBA ability play a major role, whereas the strength of the substrate α-C-H and N-H bonds involved appears to be relatively unimportant. The implications of these different mechanistic pictures are discussed.

The bondons: the quantum particles of the chemical bond

By employing the combined Bohmian quantum formalism with the U(1) and SU(2) gauge transformations of the non-relativistic wave-function and the relativistic spinor, within the Schrödinger and Dirac quantum pictures of electron motions, the existence of the chemical field is revealed along the associate bondon particle B̶ characterized by its mass (m_B̶), velocity (v_B̶), charge (e_B̶), and life-time (t_B̶). This is quantized either in ground or excited states of the chemical bond in terms of reduced Planck constant ħ, the bond energy E_bond and length X_bond, respectively. The mass-velocity-charge-time quaternion properties of bondons’ particles were used in discussing various paradigmatic types of chemical bond towards assessing their covalent, multiple bonding, metallic and ionic features. The bondonic picture was completed by discussing the relativistic charge and life-time (the actual zitterbewegung) problem, i.e., showing that the bondon equals the benchmark electronic charge through moving with almost light velocity. It carries negligible, although non-zero, mass in special bonding conditions and towards observable femtosecond life-time as the bonding length increases in the nanosystems and bonding energy decreases according with the bonding length-energy relationship Ebond[kcal/mol]×Xbond[A0]=182019, providing this way the predictive framework in which the B̶ particle may be observed. Finally, its role in establishing the virtual states in Raman scattering was also established.

Application of the valence bond mixing configuration diagrams to hypervalency in trihalide anions: a challenge to the Rundle-Pimentel model

The X(3)(-) hypercoordinated anions (H, F, Cl, Br, I) are studied by means of the breathing-orbital valence bond ab initio method. The valence bond wave functions describe the different X(3)(-) complexes in terms of only six valence bond structures and yield energies relative to the two exit channels, X(2) + X(-) and X(2)(-) + X(*), in very good agreement with reference CCSD(T) calculations. Although H(3)(-) is unstable and dissociates to H(2) + H(-), all the trihalogen anions are stable intermediates, Br(3)(-) and I(3)(-) being more stable than F(3)(-) and Cl(3)(-). As a challenge to the traditional Rundle-Pimentel model, the different energies of the hypercoordinated species relative to the normal-valent dissociation products X(2) + X(-) are interpreted in terms of valence bond configuration mixing diagrams and found to correlate with a single parameter of the X(2) molecule, its singlet-triplet energy gap. Examination of the six-structure wave functions show that H(3)(-), Cl(3)(-), Br(3)(-), and I(3)(-) share the same bonding picture and can be mainly described in terms of the interplay of two Lewis structures. On the other hand, F(3)(-) is bonded in a different way and possesses a significant three-electron bonding character that is responsible for the dissociation of this complex to F(2)(-) + F(*), instead of the more stable products F(2) + F(-). This counterintuitive preference for the thermodynamically disfavored exit channel is found to be an experimental manifestation of the large charge-shift resonance energy that generally characterizes fluorine-containing bonds.

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.

An efficient generalized polyelectron population analysis in orbital spaces: the hole-expansion methodology

We present relations leading to an efficient generalized population analysis in orbital spaces of usual delocalized molecular orbital wave functions. Besides the calculation of the diagonal elements of the reduced density matrices of any order, one can also calculate efficiently the probabilities (or, in general, the weights) of various occupation schemes of local electronic structures, by using generalized density operators referring to both electrons and electron holes. Within this population analysis, correlated molecular orbital wave functions can be used, and there are no restrictions to the number of the analyzed electrons and electron holes. It is based on the hole-expansion methodology, according to which a given electronic population is expanded in terms involving only electron holes, which as shown, can be calculated very efficiently; usual difficulties arising from the necessity to handle extremely large local determinantal basis sets are avoided, without introducing approximations. Although an emphasis is given for populations in the basis of orthogonal orbital spaces (providing probabilities), the case of nonorthogonal ones is also considered in order to show the connection of the generalized populations and the traditional weights obtained from valence-bond wave functions. Physically meaningful populations can be obtained by using natural orbitals, such as the natural atomic orbitals (NAOs) (orthogonal orbitals) or the pre-NAO's (nonorthogonal orbitals); numerical applications for pyrrole molecule are presented in the basis of these natural orbitals.

Topology of electron charge density for chemical bonds from valence bond theory: a probe of bonding types

To characterize the nature of bonding we derive the topological properties of the electron charge density of a variety of bonds based on ab initio valence bond methods. The electron density and its associated Laplacian are partitioned into covalent, ionic, and resonance components in the valence bond spirit. The analysis provides a density-based signature of bonding types and reveals, along with the classical covalent and ionic bonds, the existence of two-electron bonds in which most of the bonding arises from the covalent-ionic resonance energy, so-called charge-shift bonds. As expected, the covalent component of the Laplacian at the bond critical point is found to be largely negative for classical covalent bonds. In contrast, for charge-shift bonds, the covalent part of the Laplacian is small or positive, in agreement with the weakly attractive or repulsive character of the covalent interaction in these bonds. On the other hand, the resonance component of the Laplacian is always negative or nearly zero, and it increases in absolute value with the charge-shift character of the bond, in agreement with the decrease of kinetic energy associated with covalent-ionic mixing. A new interpretation of the topology of the total density at the bond critical point is proposed to characterize covalent, ionic, and charge-shift bonding from the density point of view.

The inverted bond in [1.1.1]propellane is a charge-shift bond

Bonded or not bonded? An ab initio valence bond study of [1.1.1]propellane shows that the two bridgehead carbons are linked by a strong and direct sigma bond that is neither classically covalent nor classically ionic, but rather a charge-shift bond, in which the covalent-ionic resonance energy plays the major role. As such, the central bond of [1.1.1]propellane closely resembles the single bond of difluorine.