Electron localization and delocalization in open-shell molecules

Localization and delocalization indices derived in the framework of the quantum Atoms in Molecules theory have recently been used to analyze the electron-pair structure of closed-shell molecules. Here we report calculations of localization and delocalization indices for open-shell molecules at the Hartree-Fock (HF) level. Several simple doublet and triplet radical molecules are studied. In general, interatomic delocalization between bonded atoms is heavily dependent on the order and polarity of the bond. Unpaired electrons also have a significant effect on the interatomic delocalization indices. Indeed, for many radicals, the analysis of the spin components reveals that the interatomic delocalization is very different for alpha and beta spin electrons in many cases. In general, at the HF level, the results can be rationalized in terms of orbital contributions. However, the definition of localization and delocalization indices is completely general, and they could be calculated at any level of theory, provided that the one- and two-electron densities are available.     

Theoretical study of one‐electron bonds in a series of high‐spin lithium–beryllium–hydrogen clusters: “Valence shell single‐electron repulsion” rule and electron localization function analysis

A series of high‐spin clusters containing Li, H, and Be in which the valence shell molecular orbitals (MOs) are occupied by a single electron has been characterized using ab initio and density functional theory (DFT) calculations. A first type (⁵Li₂, ⁿ⁺¹LiH_n+ (n = 2–5), ⁸Li₂H) possesses only one electron pair in the lowest MO, with bond energies of ～3 kcal/mol. In a second type, all the MOs are singly occupied, which results in highly excited species that nevertheless constitute a marked minimum on their potential energy surface (PES). Thus, it is possible to design a larger panel of structures (⁸LiBe, ⁷Li₂, ⁸Li, ⁴LiH⁺, ⁶BeH, ⁿ⁺³LiH (n = 3, 4), ⁿ⁺²LiH (n = 4–6), ⁸Li₂H, ⁹Li₂H, ²²Li₃Be₃ and ²²Li₆H), single‐electron equivalent to doublet “classical” molecules ranging from CO to C₆H₆. The geometrical structure is studied in relation to the valence shell single‐electron repulsion (VSEPR) theory and the electron localization function (ELF) is analyzed, revealing a striking similarity with the corresponding structure having paired electrons. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

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.     

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.     

On the original proof by reductio ad absurdum of the Hohenberg–Kohn theorem for many‐electron Coulomb systems

It is shown that, for isolated many‐electron Coulomb systems with Coulombic external potentials, the usual reductio ad absurdum proof of the Hohenberg–Kohn theorem is unsatisfactory since the to‐be‐refuted assumption made about the one‐electron densities and the assumption about the external potentials are not compatible with the Kato cusp condition. The theorem is, however, provable by more sophisticated means, and it is shown here that the Kato cusp condition actually leads to a satisfactory proof. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

A mechanism of the 1,3‐dipolar cycloaddition between the hydrogen nitryl HNO2 and acetylene HCCH: The electron localization function study on evolution of the chemical bonds

The reaction between the simplest nitro compound HNO₂ (hydrogen nitryl) and acetylene HCCH ‐ formally proceeding via 1,3‐dipolar cycloaddition ‐ has been studied by means of the B3LYP, MPW1K and MP2 methods. The energy barrier of 20.74 ÷ 32.91 kcal/mol is similar to ΔE_a of the NNO + HCCH process but is essentially larger than computed for the reactions of HCCH with fulminic acid (HCNO) and NNCH₂. Whole process is exothermic with the reaction energy: ?10.87 ÷ ?17.94 kcal/mol. An evolution of the chemical bonding has been analyzed by means of the Bonding Evolution Theory (BET) at the B3LYP/6‐31+G(d) and B3LYP/cc‐pVTZ levels. Two approximations of the reaction path have been considered, namely: the IRC and pseudo‐reaction paths. The reaction requires five steps and seven catastrophes of the fold and cusp type. A different effect of first fold catastrophe has been noticed. At the B3LYP/6‐31+G(d) level one of two nonbonding V_i=1,2(N) attractors is annihilated (F), meanwhile at B3LYP/cc‐pVTZ new V(N) attractor is created (F^?). The chemical bonds are not formed/broken in TS. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Electron localization function comparative study of ground state,triplet state,radical anion,and cation in model carbonyl and imine compounds

The modifications of bonding in carbonyl and imine compounds upon excitation, electron attachment, and ionization were studied within the framework of the electron localization function (ELF). The topological analysis of ELF allows a partition of the molecular space into regions having a clear chemical meaning: the basins. The electronic populations of the basins associated with bonding and nonbonding character, as well as the basin spin densities, were calculated at the MP2 level of the quantum mechanical calculation. Good agreement was found with the classical view in terms of mesomeric structures corresponding to the dominant localization of electrons contained in frontier molecular orbitals (MOs). The variations of the basins population were compared to the predictions of MO theory. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 897–910, 1999     

New insights on the bridge carbon-carbon bond in propellanes: a theoretical study based on the analysis of the electron localization function

The nature of the bonding between bridgehead carbon atoms (Ca, Ca') as well as the ring strain in a family of 10 propellanes formed by three-, four-, or five-member rings: [1.1.1] (I), [2.1.1] (II), [3.1.1] (III), [2.2.1] (IV), [3.2.1] (V), [2.2.2] (VI), [3.3.1] (VII), [3.2.2] (VIII), [3.3.2] (IX), and [3.3.3] (X) are studied by means of the electron localization function (ELF) at the DFT level (B3LYP/cc-pVTZ). The ELF analysis of smaller propellanes (I, II, and III) reveals the coexistence of two resonance forms: one with a nonbonding electron pair partially delocalized between Ca and Ca' atoms outside the cage (ionic) and the other with a bridge bond between the same atoms (covalent). The weights of each form are calculated according to the ELF-basin populations, yielding 94, 88, and 53% for the ionic structure of I, II, and III, respectively, while larger propellanes (IV-X) present only the covalent form. The question of the s-character of the bridge bond is addressed by dissecting the bridge-bond ELF basin into the molecular orbital contributions. Finally, sigma-aromaticity associated to surface electron delocalization has been analyzed by means of nucleus-independent chemical shift (NICS) calculations. The results point out that the stability of the fused ring structure of propellanes I, II, and III, can be assigned to the remarkable sigma-aromaticity of the involved three-member rings.     

Computerized implementation of higher‐order electron‐correlation methods and their linear‐scaling divide‐and‐conquer extensions

We have implemented a linear‐scaling divide‐and‐conquer (DC)‐based higher‐order coupled‐cluster (CC) and Møller–Plesset perturbation theories (MPPT) as well as their combinations automatically by means of the tensor contraction engine, which is a computerized symbolic algebra system. The DC‐based energy expressions of the standard CC and MPPT methods and the CC methods augmented with a perturbation correction were proposed for up to high excitation orders [e.g., CCSDTQ, MP4, and CCSD(2)_TQ]. The numerical assessment for hydrogen halide chains, polyene chains, and first coordination sphere (C1) model of photoactive yellow protein has revealed that the DC‐based correlation methods provide reliable correlation energies with significantly less computational cost than that of the conventional implementations. © 2017 Wiley Periodicals, Inc.     

Electron‐induced dissociation (EID) for structure characterization of glycerophosphatidylcholine: determination of double‐bond positions and localization of acyl chains

Glycerophospholipids are a highly abundant and diverse collection of biologically relevant lipids, and distinction between isomeric and isobaric species is a fundamental aspect for confident identification. The ability to confidently assign a unique structure to a glycerophospholipid of interest is dependent on determining the number and location of the points of unsaturation and assignment of acyl chain position. The use of high‐energy electrons (>20 eV) to induce gas‐phase dissociation of intact precursor ions results in diagnostic product ions for localizing double‐bond positions and determining acyl chain assignment. We describe a high‐resolution, tandem mass spectrometry method for structure characterization of glycerophospholipids using electron‐induced dissociation (EID). Furthermore, the inclusion of nomenclature to systematically assign bond cleavage sites with acyl chain position and double‐bond location enables a uniform platform for lipid identification. The EID methodology detailed here combines novel application of an electron‐based dissociation technique with high‐resolution mass spectrometry that facilitates a new experimental approach for lipid biomarker discovery and validation. Copyright © 2015 John Wiley & Sons, Ltd.     

Nature of the ring-closure process along the rearrangement of octa-1,3,5,7-tetraene to cycloocta-1,3,5-triene from the perspective of the electron localization function and catastrophe theory

We analyze the behavior of the energy profile of the ring‐closure process for the transformation of (3Z,5Z)‐octa‐1,3,5,7‐tetraene 5 to (1Z,3Z,5Z)‐cycloocta‐1,3,5‐triene 6 through a combination of electron localization function (ELF) and catastrophe theory (CT). From this analysis, concepts such as bond breaking/forming processes, formation/annihilation of lone pairs, and other electron pair rearrangements arise naturally through the reaction progress simply in terms of the different ways of pairing up the electrons. A relationship between the topology and the nature of the bond breaking/forming processes along this rearrangement is reported. The different domains of structural stability of the ELF occurring along the intrinsic reaction path have been identified. The reaction mechanism consists of six steps separated by fold and cusp catastrophes. The transition structure is observed in the third step, d(C1? C8) = 2.342 Å, where all bonds have topological signature of single bonds (C? C). The “new” C1? C8 single bond is not formed in transition state and respective catastrophe of the ELF field (cusp) is localized in the last step, d(C1? C8) ≈ 1.97 Å, where the two monosynaptic nonbonding basins V(C1) and V(C8) are joined into single disynaptic bonding basin V(C1,C8). The V(C1,C8) basin corresponds to classical picture of the C1? C8 bond in the Lewis formula. In cycloocta‐1,3,5‐triene 6 the single C1? C8 bond is characterized by relatively small basin population 1.72e, which is much smaller than other single bonds with 2.03 and 2.26e. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

A quantum‐chemical DFT study of the mechanism and regioselectivity of the 1,3‐dipolar cycloaddition reaction of nitrile oxide with electron‐rich ethylenes

The 1,3‐dipolar cycloaddition (13DC) reactions of nitrile‐oxide NO 1 with two ethylenes, enamine 2a and enamine 2b , were computationally studied using B3LYP/6‐31G(d) DFT methods. The two possible ortho and meta regioselective channels were characterized and analyzed. The moderate polarity of these 13DC reactions is related to the high nucleophilic character of both ethylenes, and the moderate electrophilic nature of the NO 1 , that accounts for the relatively low calculated activation energies. Analysis of different forms of energies along the different reaction channels indicates that the present 13DC reactions are completely ortho regioselective, accordingly to the experimental outcomes. Electron localization function analysis indicates that these 13DC reactions proceed via a nonconcerted (two‐stage) one‐step mechanism.     

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 ≤ Z_A ≤ 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 Z_A ≈ 1.2. Oneelectron and three‐electron strongest bonds occur respectively with low (ca. 0.7) and high (ca. 1.7) Z_A 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 Z_A and their occupancy number. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Collision‐induced dissociative chemical cross‐linking reagent for protein structure characterization: applied Edman chemistry in the gas phase

Chemical cross‐linking combined with a subsequent enzymatic digestion and mass spectrometric analysis of the created cross‐linked products presents an alternative approach to assess low‐resolution protein structures and to gain insight into protein interfaces. In this contribution, we report the design of an innovative cross‐linker based on Edman degradation chemistry, which leads to the formation of indicative mass shifted fragment ions and constant neutral losses (CNLs) in electrospray ionization (ESI)‐tandem‐mass spectrometry (MS/MS) product ion mass spectra, allowing an unambiguous identification of cross‐linked peptides. Moreover, the characteristic neutral loss reactions facilitate automated analysis by multiple reaction monitoring suited for high throughput studies with good sensitivity and selectivity. The functioning of the novel cross‐linker relies on the presence of a highly nucleophilic sulfur in a thiourea moiety, safeguarding for effective intramolecular attack leading to predictive and preferred cleavage of a glycyl‐prolyl amide bond. Our innovative analytical concept and the versatile applicability of the collision‐induced dissociative chemical cross‐linking reagent are exemplified for substance P, luteinizing hormone releasing hormone LHRH and lysozyme. The novel cross‐linker is expected to have a broad range of applications for probing protein tertiary structures and for investigating protein–protein interactions. Copyright © 2009 John Wiley & Sons, Ltd.     

The effect of the coordination orientation of N atoms on polymeric structures: synthesis and characterization of one‐ and two‐dimensional CuII coordination polymers based on 4‐amino‐3‐(pyridin‐2‐yl)‐5‐[(pyridin‐3‐ylmethyl)sulfanyl]‐1,2,4‐triazole

Three new one‐ (1D) and two‐dimensional (2D) Cu^II coordination polymers, namely poly[[bis{μ₂‐4‐amino‐3‐(pyridin‐2‐yl)‐5‐[(pyridin‐3‐ylmethyl)sulfanyl]‐1,2,4‐triazole}copper(II)] bis(methanesulfonate) tetrahydrate], {[Cu(C₁₃H₁₂N₅S)₂](CH₃SO₃)₂·4H₂O}_n ( 1 ), catena‐poly[[copper(II)‐bis{μ₂‐4‐amino‐3‐(pyridin‐2‐yl)‐5‐[(pyridin‐4‐ylmethyl)sulfanyl]‐1,2,4‐triazole}] dinitrate methanol disolvate], {[Cu(C₁₃H₁₂N₅S)₂](NO₃)₂·2CH₃OH}_n ( 2 ), and catena‐poly[[copper(II)‐bis{μ₂‐4‐amino‐3‐(pyridin‐2‐yl)‐5‐[(pyridin‐4‐ylmethyl)sulfanyl]‐1,2,4‐triazole}] bis(perchlorate) monohydrate], {[Cu(C₁₃H₁₂N₅S)₂](ClO₄)₂·H₂O}_n ( 3 ), were obtained from 4‐amino‐3‐(pyridin‐2‐yl)‐5‐[(pyridin‐3‐ylmethyl)sulfanyl]‐1,2,4‐triazole with pyridin‐3‐yl terminal groups and from 4‐amino‐3‐(pyridin‐2‐yl)‐5‐[(pyridin‐4‐ylmethyl)sulfanyl]‐1,2,4‐triazole with pyridin‐4‐yl terminal groups. Compound 1 displays a 2D net‐like structure. The 2D layers are further linked through hydrogen bonds between methanesulfonate anions and amino groups on the framework and guest H₂O molecules in the lattice to form a three‐dimensional (3D) structure. Compound 2 and 3 exhibit 1D chain structures, in which the complicated hydrogen‐bonding interactions play an important role in the formation of the 3D network. These experimental results indicate that the coordination orientation of the heteroatoms on the ligands has a great influence on the polymeric structures. Moreover, the selection of different counter‐anions, together with the inclusion of different guest solvent molecules, would also have a great effect on the hydrogen‐bonding systems in the crystal structures.