Electron localizability indicators ELI–D and ELIA for highly correlated wavefunctions of homonuclear dimers. I. Li2, Be2, B2, and C2

Electron localizability indicators based on the parallel‐spin electron pair density (ELI–D) and the antiparallel‐spin electron pair density (ELIA) are studied for the correlated ground‐state wavefunctions of Li₂, Be₂, B₂, and C₂ diatomic molecules. Different basis sets and reference spaces are used for the multireference configuration interaction method following the complete active space calculations to investigate the local effect of electron correlation on the extent of electron localizability in position space determined by the two functionals. The results are complemented by calculations of effective bond order, vibrational frequency, and Laplacian of the electron density at the bond midpoint. It turns out that for Li₂, B₂, and C₂ the reliable topology of ELI–D is obtained only at the correlated level of theory. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Electron localizability indicators ELI and ELIA: the case of highly correlated wavefunctions for the argon atom

Electron localizability indicators based on the same-spin electron pair density and the opposite-spin electron pair density are studied for correlated wavefunctions of the argon atom. Different basis sets and reference spaces are used for the multireference configuration interaction method following the complete active space calculations aiming at the understanding of the effect of local electron correlation when approaching the exact wavefunction. The populations of the three atomic shells of Ar atom in real space are calculated for each case.     

Tuning the Electronic Properties of the Dative N−B Bond with Associated O−B Interaction: Electron Localizability Indicator from X‐Ray Wavefunction Refinement

Despite the immense growth in interest in difluoroborate dyes, the nature of the interactions of the boron atom within the N‐BF₂‐O kernel is not yet fully understood. Herein, a set of real‐space bonding indicators is used to quantify the electronic characteristics of the dative N?B bond in difluoroborate derivatives. The atoms‐in‐molecules (AIM) partitioning scheme is complemented by the electron localizability indicator (ELI‐D) approach, and both were applied to experimental and theoretical electron‐density distributions (X‐ray constrained wavefunction fitting vs. DFT calculations). Additionally, Fermi orbital analysis was introduced for small DFT models to support and extend the findings for structures that contain BF₂.     

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     

Electron localizability indicator for correlated wavefunctions. I. Parallel-spin pairs

The electron localizability indicator (ELI) is based on a functional of the same-spin pair density. It reflects the correlation of the motion of same-spin electrons. In the Hartree–Fock approximation the ELI can be related to the electron localization function (ELF). For correlated wavefunctions the ELI formula differs from the one for the ELF.     

An extended-valence MC SCF procedure: determination of the dissociation energies of C2, N2, O2, and F2

A series of MC SCF calculations have been carried out on C₂, N₂, O₂, and F₂ with the goal of obtaining compact wavefunctions which recover a significant fraction of the electron correlation effects important for bond dissociation. The active orbital space is varied in size, with the largest spaces including the molecular orbitals derived from 2s, 2p, 3s, 3p and 4p atomic orbitals. Several basis sets ranging in size from 5s3p to 5s4p2d1f are investigated to determine the flexibility in the basis set needed with various choices of the active orbital space. The best extended-valence MC SCF (EVMC) dissociation energies are 0.2–0.5 eV less than the experimental values, indicating that further enlargement of the active orbital space is necessary to achieve 0.1 eV accuracy in the computed dissociation energies. The EVMC calculations reveal that, for the calculation of the dissociation energies, inclusion of non-valence orbitals is much more important for O₂ and F₂ than for C₂ and N₂. The EVMC results are compared with the predictions of full fourth-order perturbation theory, coupled cluster theory, and with the best available CI calculations.     

Electron localizability indicators from spinor wavefunctions

For the fully relativistic 4‐component many‐electron wavefunction six flavors of electron localizability indicators (ELI) have been proposed. Their counterparts, suitable for the application to the 2‐component wavefunctions, have been also derived. Six proposed indicators have been tested on Ar and Rn atoms and one of them, the ELI‐D for spatially antisymmetrized electron pairs, has been found to reveal atomic shell structures at quantitative level. Shell structures of all the atoms of periods 4–7 of the periodic table have been obtained using this indicator and compared with these obtained from the nonrelativistic limit calculations as well as from scalar‐relativistic (zero‐order regular approximation) calculations. © 2014 Wiley Periodicals, Inc.     

Quantum chemical calculation of S2O2−8, SO42− and SO4− by INDO/2 method

Electron density distribution on atomic bonds SO and OO in persulphate ion for two different -OO- bond lengths ?1.5 and 2.0Å using INDO/₂ method with parameters proposed by Pople on the BESM-6 computer have been calculated.The results of the calculations show that the electron density is lowest on -OO- bond, which is in accordance with experimental data. The calculations based on the assumption that d_-oo- » ∞ lead to the conclusion that the homolytic cleavage of -OO- bond in S₂O^2?₈ ion is more probable.     

Ab initio calculation of the lowest singlet and triplet states in CH2, CHF,CF2, and CHCH3

The lowest singlet and triplet states of the radicals CH₂, CHF, CF₂, and CHCH₃ have been investigated both in SCF and IEPA approximation (“independent electron pair approach” to account for electron correlation). The SCF calculations yield triplet ground states for CH₂, CHF, and CHCH₃, and a singlet ground state for CF₂. Electron correlation stabilizes the singlet state by about 14 kcal/mole with respect to the triplet for all four radicals leading to a singlet ground state also for CHF. The final triplet-singlet energy separations are 10, 6, ?11, ?47 kcal/mole for CH₂, CHCH₃, CHF, CF₂, respectively. Values for equilibrium bond angles, ionization potentials and bond energies are also given.     

Neutral tellurium rings in the coordination polymers [Ru(Te9)](InCl4)2, [Ru(Te8)]Cl2, and [Rh(Te6)]Cl3

Shiny black, air‐insensitive crystals of tellurium‐rich one‐dimensional coordination polymers were synthesized by melting a mixture of the elements with TeCl₄. The compounds [Ru(Te₉)](InCl₄)₂ and [Ru(Te₈)]Cl₂ crystallize in the monoclinic space group type C2/c, whereas [Rh(Te₆)]Cl₃ adopts the trigonal space group type R$\bar 3Shiny black, air-insensitive crystals of tellurium-rich one-dimensional coordination polymers were synthesized by melting a mixture of the elements with TeCl(4). The compounds [Ru(Te(9))](InCl(4))(2) and [Ru(Te(8))]Cl(2) crystallize in the monoclinic space group type C2/c, whereas [Rh(Te(6))]Cl(3) adopts the trigonal space group type R ?3c. In the crystal structures, linear, positively charged [M(m+) (Te(n)(±0))] (M=Ru, m=2; Rh, m=3) chains run parallel to the c axes. Each of the uncharged Te(n) molecules (n=6, 8, 9) coordinates two transition-metal atoms as a bridging bis-tridentate ligand. Because the coordinating tellurium atoms act as electron-pair donors, the 18-electron rule is fulfilled for the octahedrally coordinated transition-metal cations. Based on DFT calculations, the quantum theory of atoms in molecules (QTAIM) and the electron localizability indicator (ELI) provide insight into the principles of the polar donor bonding in these complexes. Comparison with optimized ring geometries reveals substantial tension in the coordinating tellurium molecules.     

Ab Initio and Quantum Chemical Topology studies on the isomerization of HONO to HNO2. Effect of the basis set in QCT

The article focus on the isomerization of nitrous acid HONO to hydrogen nitryl HNO₂. Density functional (B3LYP) and MP2 methods, and a wide variety of basis sets, have been chosen to investigate the mechanism of this reaction. The results clearly show that there are two possible paths: 1) Uncatalysed isomerisation, trans‐HONO → HNO₂, involving 1,2‐hydrogen shift and characterized by a large energetic barrier 49.7 ÷ 58.9 kcal/mol, 2) Catalysed double hydrogen transfer process, trans‐HONO + cis‐HONO → HNO₂ + cis‐HONO, which displays a significantly lower energetic barrier in a range of 11.6 ÷ 18.9 kcal/mol. Topological analysis of the Electron Localization Function (ELF) shows that the hydrogen transfer for both studied reactions takes place through the formation of a ‘dressed’ proton along the reaction path. 1 Use of a wide variety of basis sets demonstrates a clear basis set dependence on the ELF topology of HNO₂. Less saturated basis sets yield two lone pair basins, V₁(N), V₂(N), whereas more saturated ones (for example aug‐cc‐pVTZ and aug‐cc‐pVQZ) do not indicate a lone pair on the nitrogen atom. Topological analysis of the Electron Localizability Indication (ELI‐D) at the CASSCF (12,10) confirms these findings, showing the existence of the lone pair basins but with decreasing populations as the basis set becomes more saturated (0.35e for the cc‐pVDZ basis set to 0.06e for the aug‐cc‐pVTZ). This confirms that the choice of basis set not only can influence the value of the electron population at the particular atom, but can also lead to different ELF topology. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

H2O, H2S与双卤分子间相互作用的电子密度拓扑研究

运用量子化学微扰理论MP2和密度泛函B3LYP方法, 采用6-311＋＋G(d,p)基组, 对H₂O, H₂S与双卤分子XY (XY＝F₂, Cl₂, Br₂, ClF, BrF, BrCl)形成的卤键复合物进行构型全优化, 并计算得到了这些体系的分子间相互作用能. 利用电子密度拓扑分析方法对卤键复合物的拓扑性质进行了分析研究, 探讨了该类分子间卤键的作用本质. 结果表明, 形成卤键后, 作为电子受体的双卤分子X—Y键长增长, 振动频率减小. 复合物体系中的卤键介于共价键与离子键之间, 偏于静电作用成分为主.     

Crystal structure of [Co(NH3)5NO2]C2O4. Analysis of specific contacts and structural effects hindering inner-spheric nitro-nitrito isomerization

The structure of [Co(NH₃)₅NO₂]C₂O₄ is solved and refined (space group Immm, a=7.428(2), b=9.790(3), c=6.568(1) Å, V=477.6(2) ų, Z=2; R₁=0.0177, wR₂=0.0279 for F²>4σ(F²); R₁=0.1177, wR₂=0.0643 for all data; residual electron density from 0.125 to ?0.140 e/ų). Specific contacts in the structure are analyzed. Crystal chemical interpretation is suggested to explain the occurrence of photodecomposition rather than photochemical bond isomerization under the action of light in cobalt(III) nitropentammoniate oxalate crystals, in contrast to all previously investigated cobalt(III) nitropentammoniates.     

Quantum chemical topology: The electronic structure of the alkaline nitrites MONO (M = Li,Na, K) studied by means of topological analysis of the electron localization function

In the search of the protocovalent bonding, previously recognized in the nitrous acid (HONO), a nature of the chemical bonds in the alkaline nitrites MONO (M = Li, Na, K) has been studied by means of the topological analysis of the Electron Localization Function (ELF) and Electron Localizability Indicator (ELI‐D). Calculations carried out with the B3LYP and MP2(full) methods, in conjunction with the aug‐cc‐pVTZ and 6‐311++G(3df,3pd) basis sets, revealed the cis (C_2v, more stable) and trans (C_s) isomers as minima on PES. Alkaline nitrites consist of the alkali metal cation M^δ+ interacting, mainly via electrostatic forces, with the nitrite anion [ONO]^δ− (δ ≈ 1e). The covalent N O bonds are characterized by disynaptic basins V(N,O) with the basin populations: 1.58÷1.62e for cis‐M^δ+[ONO]^δ− but 1.39÷1.49e for single N O bond and 1.81÷1.87e for formally double NO bond in trans M^δ+[O NO]^δ−. The protocovalent nitrogen–oxygen bond has not been observed. The N O bonds are slightly polarized towards the nitrogen atom with the polarity index p_NO ≤ 0.12. Two different sets of the hybrid (Lewis) structures are compared leading to different pictures of the bonding. According to NBO data there is a delocalization between the single N O and double NO type bonds, meanwhile results of the ELF analysis emphasize an electron delocalization between the single N O and ionic O⁻N⁺ hybrids. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Anionic CH⋅⋅⋅X− Hydrogen Bonds: Origin of Their Strength,Geometry, and Other Properties

CF₃H as a proton donor was paired with a variety of anions, and its properties were assessed by MP2/aug‐cc‐pVDZ calculations. The binding energy of monoanions halide, NO₃^?, formate, acetate, HSO₄^?, and H₂PO₄^? lie in the 12–17 kcal mol^?1 range, although F^? is more strongly bound, by 26 kcal mol^?1. Dianions SO₄^2? and HPO₄^2? are bound by 27 kcal mol^?1, and trianion PO₄^3? by 45 kcal mol^?1. When two O atoms are available on the anion, the CH???O^? H‐bond (HB) is usually bifurcated, although asymmetrically. The CH bond is elongated and its stretching frequency redshifted in these ionic HBs, but the shift is reduced in the bifurcated structures. Slightly more than half of the binding energy is attributed to Coulombic attraction, with smaller contributions from induction and dispersion. The amount of charge transfer from the anions to the σ*(CH) orbital correlates with many of the other indicators of bond strength, such as binding energy, CH bond stretch, CH redshift, downfield NMR spectroscopic chemical shift of the bridging proton, and density at bond critical points.     

Localization function study of excitation processes in a set of small isoelectronic molecules

Electron localization function (ELF) theory is used to characterize changes that occur upon excitation from ground singlet to first excited triplet states in a series of isoelectronic 16‐electron molecules including H₂CCH₂, HNCH₂, H₂CO, HNNH, HNO, and O₂ (ground triplet to excited singlet). ELF allows one to visualize lone pair or nonbonding electrons, and in these cases the π→π* or n→π excitation processes involved lead to an effective 90° rotation of the electronic structure about one heavy atom center and consequent distortion towards pyramidal symmetry about both heavy atom centers. The heavy atom bond lengths change very little in those cases where effectively two‐center three‐electron bonds can be formed (HNNH, HNO, and O₂) while a significant lengthening occurs in those cases where hydrogen atoms prevent such interactions (H₂CCH₂, HNCH₂, and H₂CO). It is shown that both ELF basin populations and atoms‐in‐molecules (AIM) delocalization indices reflect expected bond orders for conventional single and double bonds provided one compares the ratio of the molecular quantities rather than their absolute magnitudes. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1702–1711, 2001     

Caracterisation Structurale de l′Oxyfluorotungstate de Cuivre CuWO3F2

Crystal Structure of CuWO₃F₂ The crystal structure of the copper(II) oxyfluoridetungstate CuWO₃F₂ has been determined from single crystal X-ray data. The symmetry is monoclinic (space group P2₁/m) with lattice parameters a = 5.223(1) Å, b = 9.599(4) Å, c = 3.670(1) Å, β = 106.26(1)° (Z = 2). The structure has been fixed by the heavy atom method and refined by least square calculations down to a R factor of 0.019. Oxygen-fluorine ordering has been determined on the network built up by corner sharing octahedra constituting infinite chains, by several methods: Raman spectroscopy, electrostatic energy calculations, and bond valence determinations. The structural formulation of the octahedra is (WO₂F₂O_2/2)^2?.     

Chemical Bonding and Electronic Localization in a GaI Amide

The electron density in a one‐coordinate [Ga^IN(SiMe₃)R] complex has been determined from ab initio calculations and multipole modeling of 90 K X‐ray data. The topologies of the Laplacian distribution and the ELI‐D match a situation having an sp³‐hybridized nitrogen with a tetrahedral arrangement of two single σ‐bonds (to carbon and silicon) and two lone pairs pointing towards gallium in a scissor‐grasping fashion. The analysis of the Laplacian distribution furthermore reveals a ligand‐induced charge concentration (LICC) in the outer core of gallium oriented directly towards the nitrogen atom, and thus in between the two lone pairs. These observations might suggest that the trigonal planar nitrogen geometry result from a dative Ga?N bond, in which the roles of the metal and the ligand have been reversed with respect to a “standard” metal–ligand interaction, that is, the metal is here electron‐donating. The ELI‐D reveals a diffuse and directional lone pair on gallium, suggesting that this complex could serve as a σ‐donor.     

Localized molecular orbital studies in momentum space. I. compton profiles of 1s core electrons and hydrocarbons

The calculations of momentum space properties for the polyatomic molecules CH₄, C₂H₄ and C₂H₆ using localized molecular orbitals of double zeta quality basis sets are presented. The LMO analysis shows that localized and canonical core electrons have different momentum space properties, and that in agreement with the experimental data of Eisenberger and Marra one can distinguish the momentum properties of the CC single and double bonds. The effect of environment on a bond is seen by comparing the CH bond in these three molecules.The concept of electron pair size is introduced as a quantitative guide for interpreting momentun space properties.