Use of ELF and AIM parameter ratios for bond order characterization of two‐, three‐, and four‐coordinate gallium hydrides

Calculations at the B3LYP/6‐311 + G(d,p)//B3LYP/6‐311 + G(d,p) level involving the electron localization function (ELF) and atoms‐in‐molecules (AIM) methods have been carried out for two‐, three‐, and four‐coordinate gallium hydrides present in Na and Li salts and as the isolated dianionic species, for some isoelectronic germanium compounds, and for several neutral gallium hydrides. Using the ratio of delocalization indices and bond basin populations referenced to reasonable standards, formal bond orders are derived. While chemically expected bond orders are found in most cases, the situation in the [HGaGaH]²⁻ species appears to lie intermediate between bonds of order 2 and 3, and that for neutral trans‐bent HGaGaH is found to be best described as a bond of order 1. In these cases the larger bond order predicted by ELF bond basin populations evidently results from overlap of the bond basin into the lone pair (nonbonding) region of the molecule. © 2003 Wiley Periodicals, Inc. Heteroatom Chem 14:175–185, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/hc.10120     

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     

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     

Electronic structure and stability of C86 fullerene Isolated‐Pentagon‐Rule isomers

All 19 Isolated‐Pentagon‐Rule isomers of fullerene C₈₆ were investigated by Density Functional Theory (DFT) methods with B3LYP functional at 6‐31G, 6‐31G*, and 6‐31+G* levels. Preliminary distribution of single, double, and delocalized pi‐bonds in molecules of these isomers of fullerene C₈₆ is fulfilled. Obtained results are perfectly supported by DFT quantum–chemical calculations of electronic and geometrical structures of these isomers. The main reason of instability of isomers 1, 3–15, 18, and 19 are phenalenyl‐radical substructures. Thus, there is a possibility to obtain them only as endohedral metallofullerenes or exohedral derivatives. Isomer 2 (C₂) is unstable due to higher local molecular strain. It is shown that empty C₈₆ may be produced and extracted only as isomers 16 (C_s) and 17 (C₂). © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Theoretical study of the Si2NO potential energy surface

The structures, spectroscopies, and stabilities of the doublet Si₂NO radical are explored at the density functional theory (DFT) and ab initio levels. Seventeen isomers are located, connected by 26 interconversion transition states. At the CCSD(T)/6‐311+G(2df)//QCISD/6‐311G(d)+ZPVE level, three low‐lying isomers are predicted, that is, one bent species SiNSiO 3 (5.1 kcal/mol) containing the important Si?N triple bonding and two four‐membered ring isomers including cyclic cSiNSiO 1 (0.0) with Si? Si cross‐bonding with C_2v symmetry and puckered cSiNSiO 1′ (11.9) with divalent carbene character. Three low‐lying isomers 1, 1′, and 3 have reasonable kinetic stabilities and might be observable either experimentally or astrophysically. The possible formation strategies of 1, 1′, and 3 in laboratory and in space are discussed in detail. The calculated vibrational frequencies and possible formation processes of 3 are consistent with recent experimental observations. In light of the fact that no cyclic nitrogen‐containing species have been detected in space, two cyclic isomers 1 and 1′ could be promising candidates. Furthermore, the bonding nature of three isomers 1, 1′, and 3 is analyzed. The calculated results are also compared with those of the analogue C₂NO radical. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

The valence isomers of (CH)8 and (SiH)8: An ab initio MO study

The 22 possible valence isomers of the (CH)₈ and (SiH)₈ systems have been studied by ab initio molecular orbital calculations at the MP2/6-31G*//6-31G* + ZPE level. Optimized geometries, relative energies, and, for some selected compounds, vibrational frequencies are reported. The systematic differences between the carbon and silicon compounds are analyzed. © 1994 by John Wiley & Sons, Inc.     

Substituent effect on intramolecular hydrogen bonding in 2‐hydroxybenzaldehyde

The effect of some substituents on intramolecular hydrogen bonding of 5‐X‐2‐hydroxybenzaldehyde (5‐X‐2‐HBA) has been studied by B3LYP and MP2 methods using 6‐311++G** and AUG‐cc‐PVTZ basis sets. The relationship between hydrogen bond energy E_HB and electron donation (or withdrawal) of substituents has been investigated. An approximately good linear relationship has been detected between Hammett coefficients and hydrogen bond formation energy (R² = 0.98). Herein, population analysis has been performed by atoms in molecules (AIM) and natural bond orbital (NBO) methods. The results of AIM and NBO analyses are in a good agreement with calculated energy values. Furthermore, correlation between ring aromaticity and hydrogen bonding has been investigated by nucleus‐independent chemical shift (NICS) at GIAO/B3LYP/6‐311++G** level of theory. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Electron delocalization and bond formation under the ELF framework

A first approach to the relationship between the electron localization function (ELF) and electronic delocalization upon bond formation is provided. We show from first principles the ability of ELF at the bond critical points to act as an index of the electron reorganization involved in chemical bonding. Simultaneously, this index, that we shall call ELF delocalization index (EDI), constitutes a good measure of electron delocalization. We will show how the core of ELF is proportional to the Wiberg index under the valence bond approach. This relationship will be exploited for some representative examples where EDI is able to identify the stages of bond formation. Furthermore, a maximum in EDI along this process has been found to correlate with the molecular equilibrium configuration, allowing for a formulation of a ??maximal localization principle?? for the stable structure of covalent compounds in terms of ELF.     

Isomerizations of CH3SO2: Quantum Chemistry and Topological Study

The structures, stabilities and the isomerization reactions of CH₃SO₂ isomers in a doublet electronic state have been studied at B3LYP/6‐311+ +G (d,p), MP2/6‐311++G (d,p) and CCSD(T)/6‐311++G (d,p) levels. The three different levels of calculation give the similar results: thirteen minimum isomers were located and they were connected by eleven transition states. Among the thirteen isomers, cis‐CH₃OSO, trans‐CH₃OSO and CH₃SO₂ are the most stable species, and they should be detected easily in experiment. This is well consistent with the experimental result. These isomers could isomerize to each other by chemical bond vibration, chemical bond rotation and atom migration. The non‐planar ring structure transition state (STS), which was found in this paper, extended the concept of ring STS to the non‐planar systems.     

Evaluation of the origin of conformational and tautomeric preferences in N‐formylformamide – A quantum chemical study

Quantum chemical study of N‐formylformamide (NFF) was carried out at various theoretical levels and the determinate equilibrium conformations were recomputed at the high level ab initio methods such as G2MP2, G2, G3, and complete basis set (CBS)‐QB3. The computational results reveal that the amide resonance and intramolecular hydrogen bonding are two superior factors in determining the most stable conformation of diamide (DA) and amide–imidic (AI) acid tautomers, respectively. The evaluation of hydrogen bond energies predicts that the hydrogen bond (HB( strength of NFF is weaker than the malonaldehyde (MA). But the results of atoms in molecules (AIM(, natural bond orbital (NBO), and geometrical parameters are given a different order, E_HB(NFF) > E_HB(MA). Although the bond average energies of tautomerization process emphasized on more stability of AI tautomer, but our theoretical calculations reveal that the DA conformers are more stable than the AI ones. The population analyses of equilibrium conformations by NBO method also predict that the origin of tautomeric preference is mainly because of the electron delocalization of amide functional group, especially LP(N)→ π*_C?O charge transfer. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

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     

Structure and stabilities of the isomers of SiB2H4

Ab initio quantum-mechanical methods at the HF/6–31G*, MP2/6–31G* and MP2/6–31G* levels are used to study the relative stabilities of the isomers of SiB₂H₄. Isomers obtained using the analogy between trivalent boron and divalent silicon are calculated to be more stable compared to isomers where carbon is replaced by the isovalent silicon. 2π aromaticity and the preference of silicon for lower valency control the relative stabilities of SiB₂H₄ isomers.     

Density Functional Theory Study on Hydrogen Bonding Interaction of Catechin-(H2O)n

Density functional theory B3LYP method with 6‐31G* basis set has been used to optimize the geometries of the catechin, water and catechin‐(H₂O)_n complexes. The vibrational frequencies have been studied at the same level to analyze these complexes. Six and eleven stable structures for the catechin‐H₂O and catechin‐(H₂O)₂ have been found, respectively. Theories of atoms in molecules (AIM) and natural bond orbital (NBO) have been utilized to investigate the hydrogen bonds involved in all the systems. The interaction energies of all the complexes corrected by basis set superposition error, are from ?13.27 to ?83.56 kJ/mol. All calculations also indicate that there are strong hydrogen‐bonding interactions in catechin‐water complexes. The strong hydrogen‐bonding contributes to the interaction energies dominantly. The O–H stretching motions in all the complexes are red‐shifted relative to that of the monomer.     

Theoretical (DFT, GIAO-NMR, NICS) study of carbocations (M+H)+, dications (M2+) and dianions (M2-) from dihydro-dicyclopenta[ef,kl]heptalene (dihydro-azupyrene), dihydro-dicyclohepta[ed,gh]pentalene, and related bridged [14]annulenes

The annulenium ions of protonation, the two-electron oxidation dications, and the two-electron reduction dianions derived from dihydro- and dimethyldihydro derivatives (cis and trans) of dicyclopenta[ef,kl]heptalene (azupyrene) (1) and dicyclohepta[ed,gh]pentalene (2), which are the nonalternant isomers of pyrene, were studied by density functional theory (DFT) at the B3LYP/6-31G(d), 6-31+G(d,p), or 6-31++G(d,p) levels. Charge delocalization modes in the energetically most favored annulenium ions, as well as in the singlet and triplet dications and dianions, were assessed based on gauge-including atomic orbital (GIAO) Deltadelta](13)C values and via changes in natural population analysis (NPA) charges. Relative aromaticity/antiaromaticity in the annulenes were gauged via nucleus-independent chemical shift (NICS) and DeltaNICS. Annulenium ions of monoprotonation, the dications, and dianions derived from bismethano- and propanediylidene [14]annulenes were also studied by DFT for comparison with the cis-dihydro isomers derived from . Computed GIAO NMR data and the optimized geometries were compared with the experimental data when available, and the optimized geometries were compared with the X-ray data if known. A basis-set dependency study of the computed GIAO chemical shifts was also undertaken. The present DFT work represents the first detailed comparative theoretical study of charged annulenes derived from the dihydro derivatives of and .     

Exploration on the structure,stability, and isomerization of planar CnB5 (n = 1−7) clusters

The structures, stabilities, nature of bonding, and potential energy surfaces of low‐energy isomers of planar C_nB₅ (n = 1?7) have been systematically explored at the CCSD(T)/6‐311+G(d)//B3LYP/6‐311+G(d) level. Incremental binding energy (IBE) and second order energy difference (Δ²E) analyses demonstrate that C_nB₅ clusters with even n have relatively higher stability. The nature of bonding in these clusters is discussed based on valence molecular orbital (VMO), and Mayer bond order (MBO). Hückel (4n + 2) rule and nucleus‐independent chemical shift (NICS) values suggest that the ground states of C₃B₅, C₄B₅, and C₇B₅ have π aromaticity. VMO, electron localization function (ELF), adaptive natural density partitioning (AdNDP), and NICS analyses reveal the double aromaticity of C₃B₅ cation. CB₅ and C₃B₅ are stable both thermodynamically and kinetically based on isomerization analysis. In addition, the simulated IR spectra are expected to be helpful for future experimental studies of these clusters.     

The three-center-four-electron (3c-4e) bond nature revisited. An atoms-in-molecules theory (AIM) and ELF study

Theoretical calculations (B3LYP/6–311+ +G**) were performed on a series of formally hypervalent compounds showing linear three-center geometries. The bonding nature was analyzed by the electron density, ρ(r), and electron-localization function (ELF) topologies, including calculations of the AIM charges and NMR chemical shifts (GIAO method). In addition, a quantitative analysis was also performed of the localization and delocalization indexes, obtained from the electron-pair density in conjunction with the definition of an atom in a molecule. Furthermore, the populations and fluctuations in the ELF basins were also evaluated. The compounds studied presented linear (1–5), T-shaped (6–9), and bipyramidal structures (10–15). Our results support the 3c-4e model for the linear (1–5) structures, but reveal for the T-shaped (6–9) structures only a small contribution from this model. In addition, there is no evidence to support the 3c-4e bond scheme for the bipyramidal compounds (10–15). Received: 1 June 2000 / Accepted: 4 October 2000 / Published online: 19 January 2001     

Molecular design of neutral intramolecular complexes bearing two silicon atoms anchored by a carbonyl oxygen atom: N,N'-bis(silylmethyl)propylene ureas

B3LYP and MP2 computations have been performed on a variety of Si,Si'-substituted N,N'-bis(silylmethyl)propylene ureas. According to electron-density atoms-in-molecules (AIM) and electron localization function (ELF) quantum-topological analyses, a transition from the unstable non-chelate forms of these compounds to mono- and bis-chelate forms results in the successive interaction of one and two tetracoordinate silicon atoms with the carbonyl oxygen and the formation, respectively, of one and two covalent, polar Si...O bonds. This previously unknown X-Si<--O-->Si-X type of bonding in isomers possessing an anchor structure may be classified as a five-center, six-electron (5c-6e) bond. The factors that favor the existence of Si,Si'-substituted N,N'-bis(silylmethyl)propylene ureas exclusively in the form of stable, bridged complexes (the size of equatorial ligands and the electronegativity of axial substituents at the silicon atom, change in the donor capability of the carbonyl group, and effect of the polar solvent) are discussed.