Energetic and topological analysis of the reaction of Mo and Mo2 with NH3, C2H2, and C2H4 molecules

The Density functional theory has been applied to characterize the structural features of Mo(1,2)-NH(3),-C(2)H(4), and -C(2)H(2) compounds. Coordination modes, geometrical structures, and binding energies have been calculated for several spin multiplets. It has been shown that in contrast to the conserved spin cases (Mo(1,2)-NH(3)), the interaction between Mo (or Mo(2)) and C(2)H(4) (or C(2)H(2)) are the low-spin (Mo-C(2)H(4) and -C(2)H(2)) and high-spin (Mo(2)-C(2)H(4) and -C(2)H(2)) complexes. In the ground state of Mo(1,2)-C(2)H(4) and -C(2)H(2), the metal-center always reacts with the C-C center. The spontaneous formation of the global minima is found to be possible due to the crossing between the potential energy surfaces (ground and excited states with respect to the metallic center). The bonding characterization has been performed using the topological analysis of the Electron Localization Function. It has been shown that the most stable electronic structure for a pi-acceptor ligand correlates with a maximum charge transfer from the metal center to the C-C bond of the unsaturated hydrocarbons, resulting in the formation of two new basins located on the carbon atoms (away from hydrogen atoms) and the reduction of the number of attractors of the C-C basin. The interaction between Mo(1,2) and C(2)H(4) (or C(2)H(2)) should be considered as a chemical reaction, which causes the multiplicity change. Contrarily, there is no charge transfer between Mo(1,2) and NH(3), and the partners are bound by an electrostatic interaction.     

When Is a Bond Broken? The Polarizability Perspective.

The question of when a chemical bond can be said to be broken is of fundamental chemical interest but has not been widely studied. Herein we propose that the maxima of static polarizability along bond dissociation coordinates naturally define cutoff points for bond rupture, as they represent the onset of localization of shared electron density into constituent fragments. Examples of computed polarizability maxima over the course of bond cleavage in main-group and transition metal compounds are provided, across covalent, dative and charge-shift bonds. The behavior along reaction paths is also considered. Overall, the static polarizability is found to be a sensitive reporter of electronic structure reorganization associated with bond stretching, and thus can serve as a metric for describing bond cleavage (or diagnose the absence of a chemical bond).     

Charge-shift bonding--a class of electron-pair bonds that emerges from valence bond theory and is supported by the electron localization function approach

This paper deals with a central paradigm of chemistry, the electron-pair bond. Valence bond (VB) theory and electron-localization function (ELF) calculations of 21 single bonds demonstrate that along the two classical bond families of covalent and ionic bonds, there exists a class of charge-shift bonds (CS bonds) in which the fluctuation of the electron pair density plays a dominant role. In VB theory, CS bonding manifests by way of a large covalent-ionic resonance energy, RE(CS), and in ELF by a depleted basin population with large variances (fluctuations). CS bonding is shown to be a fundamental mechanism that is necessary to satisfy the equilibrium condition, namely the virial ratio of the kinetic and potential energy contributions to the bond energy. The paper defines the atomic propensity and territory for CS bonding: Atoms (fragments) that are prone to CS bonding are compact electronegative and/or lone-pair-rich species. As such, the territory of CS bonding transcends considerations of static charge distribution, and involves: a) homopolar bonds of heteroatoms with zero static ionicity, b) heteropolar sigma and pi bonds of the electronegative and/or electron-pair-rich elements among themselves and to other atoms (e.g., the higher metalloids, Si, Ge, Sn, etc), c) all hypercoordinate molecules. Several experimental manifestations of charge-shift bonding are discussed, such as depleted bonding density, the rarity of ionic chemistry of silicon in condensed phases, and the high barriers of halogen-transfer reactions as compared to hydrogen-transfers.     

Advancing beyond charge analysis using the electronic localization function: Chemically intuitive distribution of electrostatic moments

We propose here an evaluation of chemically intuitive distributed electrostatic moments using the topological analysis of the electron localization function (ELF). As this partition of the total charge density provides an accurate representation of the molecular dipole, the distributed electrostatic moments based on the ELF partition (DEMEP) allows computing of local moments located at non atomic centers such as lone pairs, sigma bonds and pi systems. As the local dipole contribution can be decomposed in polarization and charge transfer components, our results indicate that local dipolar polarization of the lone pairs and chemical reactivity are closely related whereas the charge transfer contribution is the key factor driving the local bond dipole. Results on relevant molecules show that local dipole contributions can be used to rationalize inductive polarization effects in alcohols derivatives and typical hydrogen bond interactions. Moreover, bond quadrupole polarization moments being related to a pi character enable to discuss bond multiplicities, and to sort families of molecules according to their bond order. That way, the nature of the C-O bond has been revisited for several typical systems by means of the DEMEP analysis which appears also helpful to discuss aromaticity. Special attention has been given to the carbon monoxide molecule, to the CuCO complex and to a weak intramolecular N|-CO interaction involved in several biological systems. In this latter case, it is confirmed that the bond formation is mainly linked to the CO bond polarization. Transferability tests show that the approach is suitable for the design of advanced force fields.     

Charge decomposition analysis of the electron localizability indicator: a bridge between the orbital and direct space representation of the chemical bond

The novel functional electron localizability indicator is a useful tool for investigating chemical bonding in molecules and solids. In contrast to the traditional electron localization function (ELF), the electron localizability indicator is shown to be exactly decomposable into partial orbital contributions even though it displays at the single-determinantal level of theory the same topology as the ELF. This approach is generally valid for molecules and crystals at either the single-determinantal or the explicitly correlated level of theory. The advantages of the new approach are illustrated for the argon atom, homonuclear dimers N2 and F2, unsaturated hydrocarbons C2H4 and C6H6, and the transition-metal-containing molecules Sc(2)2+ and TiF4.     

Understanding lead chemistry from topological insights: the transition between holo- and hemidirected structures within the [Pb(CO)n]2+ model series

In this contribution, we focus to the currently unknown [Pb(CO)(n)](2+) model series (n=1 to 10), a set of compounds which allows us to investigate in-depth the holo- and hemidirectional character that lead complexes can exhibit. By means of DFT computations performed using either relativistic four-component formalisms coupled to all-electron basis sets for [Pb(CO)](2+), [Pb(OC)](2+) and [Pb(CO)(2)](2+), or scalar relativistic pseudopotentials for higher n values, the structure and the energetics of these species are investigated. The results are complemented by Constrained Space Orbital Variations (CSOV) and Electron Localization Function (ELF) comprehensive analyses in order to get better insights into the poorly documented chemical fundamentals of the Pb(2+) cation. Whereas the discrimination between holo- and hemidirected structures is usually done according to the geometry, we here provide a quantitative indicator grounded on (V(Pb)), the mean charge density of the valence monosynaptic V(Pb) ELFic basin associated to the metal cation. Free-enthalpy relying discussions show, moreover, that those gas-phase complexes having n=7, 8 or 9 may be experimentally instable and should dissociate into [Pb(CO)(6)](2+) and a number of CO ligands. According to second-order differences in energy, it is anticipated that the n=3 or 6 structures should be the most probable structures in the gas phase. Gathering all data from the present theoretical study allows us to propose some concepts that the versatile structural chemistry of Pb(2+) complexes could rely on.     

The chemical bond in polyphosphides: crystal structures, the electron localization function, and a new view of aromaticity in P4(2-) and P5(-)

The incongruent solvation of M(I)4P6 species (M(I) = K, Rb, Cs) in liquid ammonia leads to a broad variety of polyphosphides such as P7(3-), P11(3-), and the putatively aromatic P4(2-) and P5(-), which we investigated by using NMR spectroscopy and single-crystal X-ray structure analysis. The structures of Cs2P4 x 2 NH3, (K@[18]crown-6)3K3(P7)2 x 10 NH3, Rb3P7 x 7 NH3, and (Rb@[18]crown-6)3P7 x 6 NH3 are discussed and compared. The electron localization function ELF is used in a comparison of the chemical bonding of various phosphorus species. The variances of the basin populations provide a well-established measure for electron delocalization and therefore aromaticity. While comparable variance is calculated for P4(2-) and P5(-) it is observed in the lone pairs rather than in the basin populations of the bonds as in the prototypical aromatic hydrocarbons such as benzene or the cyclopentadienide anion. For this behavior, the term "lone pair aromaticity" is proposed.     

A joint study based on the electron localization function and catastrophe theory of the chameleonic and centauric models for the Cope rearrangement of 1,5-hexadiene and its cyano derivatives

A novel interpretation of the chameleonic and centauric models for the Cope rearrangements of 1,5-hexadiene (A) and different cyano derivatives (B: 2,5-dicyano, C: 1,3,4,6-tetracyano, and D: 1,3,5-tricyano) is presented by using the topological analysis of the electron localization function (ELF) and Thom's catastrophe theory (CT) on the reaction paths calculated at the B3LYP/6-31G(d,p) level. The progress of the reaction is monitorized by the changes of the ELF structural stability domains (SSD), each being change controlled by a turning point derived from CT. The reaction mechanism of the parent reaction A is characterized by nine ELF SSDs. All processes occur in the vicinity of the transition structure and corresponding to a concerted formation/breaking of C(1)-C(6) and C(3)-C(4) bonds, respectively, together with an accumulation of charge density onto C(2) and C(5) atoms. Reaction B presents the same number of ELF SSDs as A, but a different order appears; the presence of 2,5-dicyano substituents favors the formation of C(1)-C(6) bonds over the breaking of C(3)-C(4) bond process, changing the reaction mechanism from a concerted towards a stepwise, via a cyclohexane biradical intermediate. On the other side, reaction C presents the same type of turning points but two ELF SSD less than A or B; there is an enhancement of the C(3)-C(4) bond breaking process at an earlier stage of the reaction by delocalizing the electrons from the C(3)-C(4) bond among the cyano groups. In the case of competitive effects of cyano subsituents on each moiety, as it is for reaction D, seven different ELF SSDs have been identified separated by eight turning points (two of them occur simultaneously). Both processes, formation/breaking of C(1)-C(6) and C(3)-C(4) bonds, are slightly favored with respect to the parent reaction (A), and the TS presents mixed electronic features of both B and C. The employed methodology provides theoretical support for the centauric nature (half-allyl, half-radical) for the TS of D.     

On Electrostatics,Covalency, and Chemical Dashes: Physical Interactions versus Chemical Bonds

The increasing availability of real-space interaction energies between quantum atoms or fragments that provide a chemically intuitive decomposition of intrinsic bond energies into electrostatic and covalent terms [see, for instance, Chem. Eur. J. 2018 , 24, 9101] provides evidence for differences between the physicist's concept of interaction and the chemist's concept of a bond. Herein, it is argued that, for the former, all types of interactions are treated equally, whereas, for the latter, only the covalent short-range interactions have actually been used to build intuition about chemical graphs and chemical bonds. This has led to the bonding role of long-range Coulombic terms in molecular chemistry being overlooked. Simultaneously, blind consideration of electrostatic terms in chemical bonding parlance may lead to confusion. The relationship between these concepts is examined herein, and some notes of caution on how to merge them are proposed.     

A topological assessment of the electronic structure of mesoionic compounds

Mesoionic compounds belonging to the 1,3‐oxazol‐5‐one, 1,3‐diazole‐4‐thione and 1,3‐thiazole‐5‐thione rings have been evaluated by a combination of Density Functional Theory, Quantum Theory of Atoms in Molecules, Electron Localization Function, Natural Bond Orbitals and Geodesic Electrostatic Potential Charge calculations. Atomic, bond, and ring properties have been considered to describe the electronic structure of mesoionic compounds. The results show that not only the ring type, but also the substituent groups have great influence on these properties. In addition, there is a significant and heterogeneous π‐bonding contribution throughout the mesoionic rings. Finally, we conclude that some classical conceptions of charge localization and π‐bonding contribution in these compounds are misleading or incomplete. © 2015 Wiley Periodicals, Inc.     

Nature of the Ga-Ga bonding in Na2[Arx*GaGaArx*]（Arx*=C6H3 -2,6-（C6H5）2）:Electron localization function analysis

The nature of the Ga-Ga bonding in Na2[Arx*GaGaArx*](Arx* = C6H3-2,6-(C6H5)2) has been investigated and compared with that of in H2[Arx*GaGaArx*] using electron localization function(ELF) and orbital analysis.The calculation results show that in Na2[Arx*GaGaArx*],the Ga-Ga interaction is a non-classical triple bond,the heart of Na2[Arx*GaGaArx*] is the Ga2Na2 cluster rather than a simple Ga-Ga bond,and the contribution of the sodium atoms to the short Ga-Ga bond length is considerable.As the two sodium atoms are substituted by two hydrogen atoms,the Ga-Ga bond is replaced by two 3-center,2-electron(3c-2e) Ga-H-Ga covalent bridged bonding.     

A model of the chemical bond must be rooted in quantum mechanics, provide insight, and possess predictive power

In this response to the preceding paper by Bader, we show that the core arguments and statements presented in the latter are flawed. We argue that it is insufficient for a model of the chemical bond to be rooted in quantum mechanics. A good model must in addition provide insight and possess predictive power. Our molecular orbital (MO) model of the chemical bond, in particular, the associated energy-decomposition approach satisfies all these conditions. On the other hand, Atoms-in-Molecules (AIM) theory is only rooted in quantum mechanics as far as its mathematical framework is concerned. The physical status of its central concepts is not so clear. In particular, "bond paths" and "bond critical points" are once more confirmed not to be indicators of a stabilizing interaction. Moreover, AIM theory lacks any predictive power. We also address specific questions raised in the preceding paper. Finally, interpreting chemical bonding implies choosing a perspective on this phenomenon. That there are many perspectives is a matter of fact and this is in no way unphysical. What is unscientific is to claim uniqueness and truth for one of these choices, namely AIM, and to dismiss on this ground all other approaches.     

Electronic fluxes during diels‐alder reactions involving 1,2‐benzoquinones: mechanistic insights from the analysis of electron localization function and catastrophe theory

By means of the joint use of electron localization function (ELF) and Thom's catastrophe theory, a theoretical analysis of the energy profile for the hetero‐Diels‐Alder reaction of 4‐methoxy‐1,2‐benzoquinone 1 and methoxyethylene 2 has been carried out. The 12 different structural stability domains obtained by the bonding evolution theory have been identified as well as the bifurcation catastrophes (fold and cusp) responsible for the changes in the topology of the system. This analysis permits finding a relationship between the ELF topology and the evolution of the bond breaking/forming processes and electron pair rearrangements through the reaction progress in terms of the different ways of pairing up the electrons. The reaction mechanism corresponds to an asynchronous electronic flux; first, the O1? C5 bond is formed by the nucleophilic attack of the C5 carbon of the electron rich ethylene 2 on the most electrophilically activated carbonyl O1 oxygen of 1 , and once the σ bond has been completed, the formation process of the second O4? C6 bond takes place. In addition, the values of the local electrophilicity and local nucleophilcity indices in the framework of conceptual density functional theory accounts for the asychronicity of the process as well as for the observed regioselectivity. © 2012 Wiley Periodicals, Inc.     

Electron localization function and electron localizability indicator applied to study the bonding in the peroxynitrous acid HOONO

The ground‐state electronic structure of peroxynitrous acid (HOONO) and its singlet biradicaloid form (HO ··· ONO) have been studied using topological analysis of the electron localization function (ELF), together with the electron localizability indicator (ELI‐D), at the DFT (B3LYP, M05, M052X, and M06), CCSD, and CASSCF levels. Three isomers of HOONO (cis‐cis, cis‐perp, and trans‐perp) have been considered. The results show that from all functionals applied, only B3LYP yields the correct geometrical structure. The ELF and ELI‐D‐topology of the O? O and central N? O bonds strongly depends on the wave function used for analysis. Calculations carried out at CAS (14,12)/aug‐cc‐pVTZ//CCSD(T)/aug‐cc‐pVTZ level reveal two bonds of the charge‐shift type: a protocovalent N? O bond with a basin population of 0.82–1.08e, and a more electron depleted O? O bond with a population of 0.66–0.71e. The most favorable dissociation channel (HOONO → HO + ONO) corresponds to breaking of the most electron‐deficient bond (O? O). In the case of cis‐ and trans‐HO ··· ONO, the ELF, ELI‐D, and electron density fields results demonstrate a closed‐shell O ··· O interaction. The α‐spin electrons are found mainly (0.64e) in the lone pairs of oxygen V_{i = 1,2} (O) from the OH group. The β‐spin electrons are delocalized over the ONO group, with the largest concentration (0.34e) on the lone pair of nitrogen V(N). © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

Investigation of substituent effects in aerogen‐bonding interaction between ZO3 (Z=Kr,Xe) and nitrogen bases

The substituent effects in aerogen bond interactions between ZO₃ (Z = Kr, Xe) and different nitrogen bases are studied at the MP2/aug‐cc‐pVTZ level of theory. The nitrogen bases include the sp bases NCH, NCF, NCCl, NCBr, NCCN, NCOH, NCCH₃ and the sp³ bases NH₃, NH₂F, NH₂Cl, NH₂Br, NH₂CN, NH₂OH, and NH₂CH₃. The nature of aerogen bonds in these complexes is analyzed by means of molecular electrostatic potential, electron localization function, quantum theory atoms in molecules, noncovalent interaction index, and natural bond orbital analyses. The interaction energy (E_int) ranges from ?4.59 to ?9.65 kcal/mol in the O₃Z···NCX complexes and from ?5.30 to ?13.57 kcal/mol in the O₃Z···NH₂X ones. The dominant charge‐transfer interaction in these complexes occurs across the aerogen bond from the nitrogen lone‐pair (n_N) of the Lewis base to the σ*_Z‐O antibonding orbital of the ZO₃. Besides, the formation of aerogen bond tends to decrease the ⁸³Kr or ¹³¹Xe chemical shielding values in these complexes. © 2016 Wiley Periodicals, Inc.     

Computational study of the process of hydrogen bond breaking: the case of the formamide-formic acid complex

MP2/6-311++G(d,p) and B3LYP/6-311++G(d,p) quantum calculations are used to study the formamide-formic acid complex (FFAC), a system bound by two hydrogen bonds, N--H...O and O--H...O, that forms a bond ring at equilibrium. When the intermolecular separation between monomers R increases, this ring opens at a distance for which the weaker N--H...O bond breaks remaining the stronger O--H...O bond. The computational study characterizes that process addressing changes of interaction energy DeltaE, structure and properties of the electron density rho(r) as well as spatial distributions of rho(r), the electrostatic potential U(r), and the electron localization function eta(r). It is shown that the spatial derivatives of DeltaE, the topology of rho(r), and qualitative changes noticed in U(r) = 0 isocontours allow to identify a precise distance R for which one can say the N--H...O hydrogen bond has broken. Both levels of theory predict essentially the same changes of structure and electron properties associated to the process of breaking and virtually identical distances at which it takes place.