Electron group localization in atoms and molecules.

Partitioning atomic and molecular charge densities in non-overlapping chemically significant regions is a challenging problem for quantum chemists. The present method aims to build a tool that enables the determination of "good boundaries" with the help of elementary statistical methods or information theory. This is done by minimizing an objective function with respect to the boundaries of the localization regions, the choice of this function being guided by a clarity requirement. With the sum of the indices of dispersion (ΣD) or the mutual information as the objective function, the method yields partitions in good agreement with the Aufbau rules for Li-Rn atoms and with Lewis's pairing model for molecules.

Nine questions on energy decomposition analysis.

The paper collects the answers of the authors to the following questions: Is the lack of precision in the definition of many chemical concepts one of the reasons for the coexistence of many partition schemes? Does the adoption of a given partition scheme imply a set of more precise definitions of the underlying chemical concepts? How can one use the results of a partition scheme to improve the clarity of definitions of concepts? Are partition schemes subject to scientific Darwinism? If so, what is the influence of a community's sociological pressure in the "natural selection" process? To what extent does/can/should investigated systems influence the choice of a particular partition scheme? Do we need more focused chemical validation of Energy Decomposition Analysis (EDA) methodology and descriptors/terms in general? Is there any interest in developing common benchmarks and test sets for cross-validation of methods? Is it possible to contemplate a unified partition scheme (let us call it the "standard model" of partitioning), that is proper for all applications in chemistry, in the foreseeable future or even in principle? In the end, science is about experiments and the real world. Can one, therefore, use any experiment or experimental data be used to favor one partition scheme over another? © 2019 Wiley Periodicals, Inc.

Curly arrows, electron flow, and reaction mechanisms from the perspective of the bonding evolution theory.

Despite the usefulness of curly arrows in chemistry, their relationship with real electron density flows is still imprecise, and even their direct connection to quantum chemistry is still controversial. The paradigmatic description - from first principles - of the mechanistic aspects of a given chemical process is based mainly on the relative energies and geometrical changes at the stationary points of the potential energy surface along the reaction pathway; however, it is not sufficient to describe chemical systems in terms of bonding aspects. Probing the electron density distribution during a chemical reaction can provide important insights, enabling us to understand and control chemical reactions. This aim has required an extension of the relationships between the concepts of traditional chemistry and those of quantum mechanics. Bonding evolution theory (BET), which combines the topological analysis of the electron localization function (ELF) and Thom's catastrophe theory (CT), provides a powerful method that offers insight into the molecular mechanism of chemical rearrangements. In agreement with the laws of physical and aspects of quantum theory, BET can be considered an appropriate tool to tackle chemical reactivity with a wide range of possible applications. In this work, BET is applied to address a long-standing problem: the ability to monitor the flow of electron density. BET analysis shows a connection between quantum mechanics and bond making/forming processes. Likewise, the present approach retrieves the classical curly arrows used to describe the rearrangements of chemical bonds and provides detailed physical grounds for this type of representation. We demonstrate this procedure using the test set of prototypical examples of thermal ring apertures, and the degenerated Cope rearrangement of semibullvalene.

Theoretical strategies toward stabilization of singlet remote N-heterocyclic carbenes.

Theoretical investigations predict that the singlet states of ylide-substituted remote carbenes are significantly stable and comparable to those of experimentally known NHCs. They are also found to be strongly σ-donating in nature as evident from an evaluation of the carbonyl stretching frequencies (νCO ) of their complexes with the [Rh(CO)2 Cl] fragment. NICS and QTAIM based bond magnetizability calculations indicate the presence of cyclic electron delocalization in majority of the molecules. © 2016 Wiley Periodicals, Inc.

Hydrogen bonding and delocalization in the ELF analysis approach.

Delocalization of the electron density in the proton donor fragment has been studied for 21 complexes, A-HB (A = F, Cl; B = Ne, Ar, CO2, N2, FH, ClH, H2O, PH3, NH3, Cl-, F-, covering the whole range of hydrogen bond strength. The proton donor and proton acceptor fragments are defined by a minimum variance principle achieved by the ELF partition. It is shown that the variance of the proton donor population as well as the charge transfer between the fragments calculated from the ELF partition is always smaller than that evaluated within the QTAIM framework. For both partition schemes, the variance and the charge transfer are correlated with the hydrogen bond strength. It is shown that the variance varies as the square root of the value of the ELF at the hydrogen bond interaction point (i.e. the saddle point at the boundary of the proton donor and proton acceptor moieties)ηvv' providing a numerical proof of the conjecture that the ELF partition satisfies a minimum variance condition and an explanation of the success of the core valence bifurcation index as an indicator of the hydrogen bond strength. The ELF technique has been then applied to the study of hydrogen bonded crystals for which the variance of the fragment population has been estimated from ηvv'. The systems investigated are KHF2, KDP and ice VIII. The results are consistent with very strong hydrogen bonds in the two former crystals and medium-weak bonding in ice. In ice VIII the variance, and therefore the hydrogen bond strength, increases with pressure yielding a phase transition toward ice X in which the hydrogen bond is characterized as very strong. Our study emphasizes the importance of the partition scheme which defines the proton donor fragment and the role of electron density delocalization between the fragments which is, according to us, often improperly termed as covalence.

The missing entry in the agostic-anagostic series: Rh(I)-η(1)-C interactions in P(CH)P pincer complexes.

The missing entry, namely, the "C-anagostic" or η(1)-C interaction, closing the agostic-anagostic series of metal-CH(aryl) interactions is found in a bis(amidiniophosphine) P(CH)P pincer rhodium complex. The three entries, namely, agostic η(2)-(C,H), anagostic (related to hydrogen bonding, thus recoined here as "H-anagostic"), and C-anagostic interactions, are unambiguously characterized by electron localization function (ELF) topological analysis. Other theoretical tools such as noncovalent interaction (NCI) analysis and multicenter electron delocalization indices (MCIs) support the ELF characterization. A η(2)-(C,H) agostic interaction is evidenced by a disynaptic V(C,H) or trisynaptic V(M,C,H) ELF basin with a significant quantum topological atoms in molecules (QTAIM) atomic contribution of the metal M and a large covariance (in absolute value) with the metal core basin C(M). The C-anagostic η(1)-C interaction is characterized by a disynaptic V(M,C) basin, a weak covariance (in absolute value) of V(C,H) and C(M) populations, and a negligible QTAIM atomic contribution of M to V(C,H). The relevance of these ELF signatures is evidenced in a selected series of related rhodium and osmium complexes.

Activation of C-H and B-H bonds through agostic bonding: an ELF/QTAIM insight.

Agostic bonding is of paramount importance in C-H bond activation processes. The reactivity of the σ C-H bond thus activated will depend on the nature of the metallic center, the nature of the ligand involved in the interaction and co-ligands, as well as on geometric parameters. Because of their importance in organometallic chemistry, a qualitative classification of agostic bonding could be very much helpful. Herein we propose descriptors of the agostic character of bonding based on the electron localization function (ELF) and Quantum Theory of Atoms in Molecules (QTAIM) topological analysis. A set of 31 metallic complexes taken, or derived, from the literature was chosen to illustrate our methodology. First, some criteria should prove that an interaction between a metallic center and a σ X-H bond can indeed be described as "agostic" bonding. Then, the contribution of the metallic center in the protonated agostic basin, in the ELF topological description, may be used to evaluate the agostic character of bonding. A σ X-H bond is in agostic interaction with a metal center when the protonated X-H basin is a trisynaptic basin with a metal contribution strictly larger than the numerical uncertainty, i.e. 0.01 e. In addition, it was shown that the weakening of the electron density at the X-Hagostic bond critical point with respect to that of X-Hfree well correlates with the lengthening of the agostic X-H bond distance as well as with the shift of the vibrational frequency associated with the νX-H stretching mode. Furthermore, the use of a normalized parameter that takes into account the total population of the protonated basin, allows the comparison of the agostic character of bonding involved in different complexes.

Carbolithiation of chloro-substituted alkynes: a new access to vinyl carbenoids.

The intramolecular carbolithiation of a series of chloro-substituted alkynes leads to exocyclic alkylidene carbenoids of which both nucleophilic and electrophilic characters can be drove. A sole stereoselective 5-exo-dig addition takes place, probably because of a strong and persisting Li-Cl interaction arising before the transition state.

Microsolvation of cobalt, nickel, and copper atoms with ammonia: a theoretical study of the solvated electron precursors.

CONTEXT: The s-block metals dissolved in ammonia form metal-ammonia complexes with diffuse electrons which could be used for redox catalysis. In this theoretical paper, we investigated the possibility of the d-bloc transition metals (Mn, Fe, Co, Ni, and Cu) solvated by ammonia. It has been demonstrated that both Mn and Fe atoms undergo into an oxidative reaction with NH3 forming an inserted species, HMNH2. On the contrary, the Co, Ni, and Cu atoms can accommodate four NH3, via the coordination bond, to form the first solvation sphere within C2v, D2d, and Td point groups, respectively. Addition of a fifth NH3 constitute the second solvation shell by forming hydrogen bond with the other NH3s. Interestingly, M(NH3)4 (M = Co, Ni, and Cu) is a so-called solvated electron precursor and should be considered as a monocation M(NH3)4+ kernel in tight contact with one electron distributed over its periphery. This nearly free electron could be used to capture a CO2 molecule and engages in a reduction reaction. METHODS: Geometry optimization of the stationary points on the potential energy surface was performed using density functional theory - CAM-B3LYP functional including the GD3BJ dispersion contribution - in combination with the 6-311 + + G(2d, 2p) basis set for all the atoms. All first-principles calculations were performed using the Gaussian 09 quantum chemical packages. The natural electron configuration of transition atom engaged in the compounds has been found using the natural bond orbital (NBO) method. We used the EDR (electron delocalization range) approach to analyze the structure of solvated electrons in real space. We also used the electron localization function (ELF) to measure the degree of electronic localization within a chemical compound. The EDR and ELF analyses are done using the TopMod and Multiwfn packages, respectively.

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.

N, P, and As ylides and aza- and arsa-Wittig reactions from topological analyses of electron density.

The nature of bonding between N, P, and As constituent atoms in ylide systems with the R(3)XYR' formula (X = N, P, As; Y = N, P, As; R = F, H; R' = H, CH(3)) has been characterized by ab initio (MP2/6-311++G**) and density functional theory (B3LYP/6-311++G**) calculations. Its electronic structure has been analyzed through electron density with the quantum theory of atoms in molecules and the electron localization function (ELF). The characteristics of the central bond are inspected with the calculated rotational barriers. The results show that N has a behavior different from that of the remaining pnicogen atoms (P, As), where the bond is much stronger. Fluorine substituents strengthen the X-Y bond, reduce the bond distance, and increase the electron density in the central bond so that the substituent pulls charge from the bond in the pnicogen X atom. For the N-pnicogen ylides, the results showed different bonding characters between F and X atoms; depending on the position of the F atom, the difference of the bond character is sensed by the basin synaptic order, as it is deduced from the analysis of the ELF basins. The energy profiles of the rotational barriers have been calculated at the MP2/6-311++G** level, indicating that the electronegativity of the substituents is a relevant factor that has consequences in the characteristics of the X-Y bond.

A rare example of a krypton difluoride coordination compound: [BrOF2][AsF6] x 2 KrF2.

The synthesis of [BrOF(2)][AsF(6)] x 2 KrF(2), its structural characterization, and bonding are described in this study. Although several KrF(2) adducts with transition metal centers have been previously reported, none have been crystallographically characterized. The solid-state Raman spectrum of [BrOF(2)][AsF(6)] x 2 KrF(2) has been assigned with the aid of quantum-chemical calculations. The low-temperature (-173 degrees C) X-ray crystal structure of [BrOF(2)][AsF(6)] x 2 KrF(2) consists of isolated molecular units and represents an example of KrF(2) coordinated to a main-group atom. The coordination geometry around the BrOF(2)(+) cation renders the free valence electron lone pair more compact than in free BrOF(2)(+). The KrF(2) ligands are coordinated trans to the fluorine atoms of BrOF(2)(+) with the AsF(6)(-) anion coordinated trans to oxygen. The quantum theory of atoms in molecules (QTAIM) and electron localization function (ELF) analyses have been carried out in order to define the nature of the bonding in the complex. A significant amount of charge (0.25 e) is transferred to BrOF(2)(+) from the two KrF(2) ligands (0.10 e each) and from the AsF(6)(-) anion (0.05 e). Significant polarization also occurs within the KrF(2) ligands, which enhances the anionic characters of the fluorine bridges. The interaction energy is mostly governed by the electrostatic interaction of the positively charged bromine atom with the surrounding fluorine atoms.

XeF(2) coordination to a halogen center; Raman spectra (n = 1, 2) and X-ray crystal structures (n = 2) of [BrOF(2)][AsF(6)].nXeF(2) and [XOF(2)][AsF(6)] (X = Cl, Br).

The syntheses and structural characterizations of the [XOF(2)][AsF(6)] (X = Cl, Br) salts and the XeF(2) adduct-salts, [BrOF(2)][AsF(6)].nXeF(2) (n = 1, 2), are described. Although the [XOF(2)][AsF(6)] salts have been known for some time, their crystal structures had not been reported until the present study. The crystal structure of [BrOF(2)][AsF(6)] shows a positional disorder among the oxygen atom and the fluorine atoms. Both ClOF(2)(+) and BrOF(2)(+) have pseudo-octahedral coordination with a primary tripodal coordination sphere consisting of an oxygen atom and two fluorine atoms and a secondary coordination sphere consisting of three long contacts to fluorine atoms of different AsF(6)(-) anions. The low-temperature Raman spectra of [XOF(2)][AsF(6)] have been assigned on the basis of the crystal structures and with the aid of quantum-chemical calculations using [XOF(2)][AsF(6)](3)(2-) as a model for the crystallographic environment of XOF(2)(+). Several examples of XeF(2) coordinated through fluorine to transition metal centers are known, but no crystallographically characterized examples of XeF(2) coordinated to a nonmetal center other than xenon are known. The complex cation salts, [BrOF(2)][AsF(6)].nXeF(2) (n = 1, 2), were synthesized, and their Raman spectra have been assigned with the aid of quantum-chemical calculations. Although the structure of [BrOF(2)][AsF(6)].2XeF(2) is similar to that of the recently reported krypton analogue, notable differences occur. The contact distances between bromine and the fluorine atoms of NgF(2) (Ng = Kr, Xe) are shorter in [BrOF(2)][AsF(6)].2XeF(2) than in the KrF(2) analogue, which is attributed to the more polar natures of the Xe-F bonds. Unlike [BrOF(2)][AsF(6)].2KrF(2), which has been shown in the prior study to be stable in HF solution at room temperature, [BrOF(2)][AsF(6)].2XeF(2) enters into a dissociative equilibrium in which fluoride ion abstraction by BrOF(2)(+) occurs to give Xe(2)F(3)(+) and BrOF(3). The ELF and QTAIM analyses of [BrOF(2)][AsF(6)](3)(2-) and [BrOF(2)][AsF(6)].2XeF(2) were carried out and are compared with those of [BrOF(2)][AsF(6)].2KrF(2) and for free BrOF(2)(+) to better understand the effect of Br(V) coordination number on the localization domain of the Br(V) valence electron lone pair.

Understanding reaction mechanisms in organic chemistry from catastrophe theory: ozone addition on benzene.

The potential energy profiles of the endo and exo additions of ozone on benzene have been theoretically investigated within the framework provided by the electron localization function (ELF). This has been done by carrying out hybrid Hartree-Fock DFT B3LYP calculation followed by a bonding evolution theory (BET) analysis. For both approaches, the reaction is exothermic by ~98 kJ mol(-1). However, the activation energy is calculated to 10 kJ mol(-1) lower in the endo channel than in the exo one; therefore the formation of the endo C(6)H(6)O(3) adduct is kinetically favored. Six structural stability domains are identified along both reaction pathways as well as the bifurcation catastrophes responsible for the changes in the topology of the system. This provides a chemical description of the reaction mechanism in terms of heterolytic synchronous bond formation.

Towards an unified chemical model of secondary bonding.

The concept of secondary bond covers a wide range of non-covalent interactions involving an acceptor (or electrophilic) molecule and an electron donor (or nucleophilic) one. It involves triel, tetrel, pnictogen, chalcogen, halogen, and aerogen bonds as well as hydrogen bonds. Such interactions yield complexes in which the internuclear distance of the electrophilic and nucleophilic centers is intermediate between the sums of the covalent and van der Waals radii of these atoms. These complexes can be considered as precursors of hypothetical nucleophilic substitution or addition reactions. As a consequence of the least motion principle, in the complex, the arrangement of the ligands around the electrophilic center should look like that of the hypothetical transition state or addition product. In a same fashion, the geometry around the nucleophilic center is determined by the location of the lone pair or of the bond involved in the interaction. In this picture of secondary bonding, the structure of the valence shell of the electrophilic atoms determines the geometry of the complex rather than the group to which belongs the elemental atom. The reorganization of the complexes in terms of the arrangement of the bonding and non-bonding electronic domains around the electrophilic center enables to rationalize the geometries in a systematic fashion. A set of VSEPR inspired rules enabling the building up of secondary bonded isomers are proposed and checked by quantum chemical calculations performed on representative test systems of the AX4-nEn type. Graphical Abstract An example of secondary interaction: FClO[Formula: see text].

Topological analysis of the reaction of uranium ions (U+, U2+) with N2O in the gas phase.

Density functional theory calculations were performed to study the ability of uranium cations, U(+) and U(2+), to activate the N-N and N-O bonds of N(2)O. A close description of the reaction pathways leading to different reaction products is presented. The obtained results are compared with previous experimental works. The nature of the bonding of all the involved species and the bonding evolution along the reaction pathways was studied by means of the topological analysis of the ELF function.

Understanding reaction mechanisms in organic chemistry from catastrophe theory applied to the electron localization function topology.

Thom's catastrophe theory applied to the evolution of the topology of the electron localization function (ELF) gradient field constitutes a way to rationalize the reorganization of electron pairing and a powerful tool for the unambiguous determination of the molecular mechanisms of a given chemical reaction. The identification of the turning points connecting the ELF structural stability domains along the reaction pathway allows a rigorous characterization of the sequence of electron pair rearrangements taking place during a chemical transformation, such as multiple bond forming/breaking processes, ring closure processes, creation/annihilation of lone pairs, transformations of C-C multiple bonds into single ones. The reaction mechanism of some relevant organic reactions: Diels-Alder, 1,3-dipolar cycloaddition and Cope rearrangement are reviewed to illustrate the potential of the present approach.

Curly arrows meet electron density transfers in chemical reaction mechanisms: from electron localization function (ELF) analysis to valence-shell electron-pair repulsion (VSEPR) inspired interpretation.

Probing the electron density transfers during a chemical reaction can provide important insights, making possible to understand and control chemical reactions. This aim has required extensions of the relationships between the traditional chemical concepts and the quantum mechanical ones. The present work examines the detailed chemical insights that have been generated through 100 years of work worldwide on G. N. Lewis's ground breaking paper on The Atom and the Molecule (Lewis, G. N. The Atom and the Molecule, J. Am. Chem. Soc. 1916, 38, 762-785), with a focus on how the determination of reaction mechanisms can be reached applying the bonding evolution theory (BET), emphasizing how curly arrows meet electron density transfers in chemical reaction mechanisms and how the Lewis structure can be recovered. BET that combines the topological analysis of the electron localization function (ELF) and Thom's catastrophe theory (CT) provides a powerful tool providing insight into molecular mechanisms of chemical rearrangements. In agreement with physical laws and quantum theoretical insights, BET can be considered as an appropriate tool to tackle chemical reactivity with a wide range of possible applications. Likewise, the present approach retrieves the classical curly arrows used to describe the rearrangements of chemical bonds for a given reaction mechanism, providing detailed physical grounds for this type of representation. The ideas underlying the valence-shell-electron pair-repulsion (VSEPR) model applied to non-equilibrium geometries provide simple chemical explanations of density transfers. For a given geometry around a central atom, the arrangement of the electronic domain may comply or not with the VSEPR rules according with the valence shell population of the considered atom. A deformation yields arrangements which are either VSEPR defective (at least a domain is missing to match the VSEPR arrangement corresponding to the geometry of the ligands), VSEPR compliant or pseudo VSEPR when the position of bonding and non-bonding domains are interchanged. VSEPR defective arrangements increase the electrophilic character of the site whereas the VSEPR compliant arrangements anticipate the formation of a new covalent bond. The frequencies of the normal modes which account for the reaction coordinate provide additional information on the succession of the density transfers. This simple model is shown to yield results in very good agreement with those obtained by BET.

Coupling quantum interpretative techniques: another look at chemical mechanisms in organic reactions.

A cross ELF-NCI analysis is tested over prototypical organic reactions. The synergetic use of ELF and NCI enables the understanding of reaction mechanisms since each method can respectively identify regions of strong and weak electron pairing. Chemically intuitive results are recovered and enriched by the identification of new features. Non covalent interactions are found to foresee the evolution of the reaction from the initial steps. Within NCI, no topological catastrophe is observed as changes are continuous to such an extent that future reaction steps can be predicted from the evolution of the initial NCI critical points. Indeed, strong convergences through the reaction paths between ELF and NCI critical points enable to identify key interactions at the origin of the bond formation. VMD scripts enabling the automatic generation of movies depicting the cross NCI/ELF analysis along a reaction path (or following a Born-Oppenheimer molecular dynamics trajectory) are provided as S.I.

Is delocalization a prerequisite for stability of ring systems? A case study of some inorganic rings.

A combined DFT, AIM and ELF study has been carried out on borazine and its heavier analogs containing both the pnictogens and chalcogens as the ring constituent. Compared to the pnictogen substituted rings, chalcogen substituted rings are found to be less aromatic. Except for a few systems, the computed aromatic stabilization energies (ASE) do not correlate with the NICS values. For these ring systems, NICS and bond length equalization are found to be better indicators of aromaticity than ASE. It was found that bulky electronegative substituents at the metal atom dramatically increases the stability and aromaticity of these molecules. AIM and ELF analysis predicts that boron and gallium based heterocycles are moderately aromatic while the aluminium analogs are significantly less aromatic.