Nature of bonding in the sulfuryl group

The SO sulfuryl bond in a number of representative sulfoxides and sulfones has been studied at the B3LYP/6-311+G(d,p) level in the atoms-in-molecules (AIM) approach involving the AIM delocalization index and the Cioslowski-Mixon localized orbitals and associated covalent bond order. The sulfur-oxygen covalent bond is strongly polarized toward oxygen and the oxygen lone pairs provide significant backbonding to create short and strong SO bonds, similar in nature to those found in the analogous phosphoryl (PO) bond. Although the sulfoxides in general have larger delocalization indices than the sulfones, there is no correlation between these quantities and the bond dissociation energies.     

Accounting for the differences in the structures and relative energies of the highly homoatomic np pi-np pi (n > or = 3)-bonded S2I4 2+, the Se-I pi-bonded Se2I4 2+, and their higher-energy isomers by AIM, MO, NBO, and VB methodologies

The bonding in the highly homoatomic np pi-np pi (n > or = 3)-bonded S2I42+ (three sigma + two pi bonds), the Se-I pi-bonded Se2I42+ (four sigma + one pi bonds), and their higher-energy isomers have been studied using modern DFT and ab initio calculations and theoretical analysis methods: atoms in molecules (AIM), molecular orbital (MO), natural bond orbital (NBO), and valence bond (VB) analyses, giving their relative energies, theoretical bond orders, and atomic charges. The aim of this work was to seek theory-based answers to four main questions: (1) Are the previously proposed simple pi*-pi* bonding models valid for S2I42+ and Se2I42+? (2) What accounts for the difference in the structures of S2I42+ and Se2I42+? (3) Why are the classically bonded isolobal P2I4 and As2I4 structures not adopted? (4) Is the high experimentally observed S-S bond order supported by theoretical bond orders, and how does it relate to high bond orders between other heavier main group elements? The AIM analysis confirmed the high bond orders and established that the weak bonds observed in S2I42+ and Se2I42+ are real and the bonding in these cations is covalent in nature. The full MO analysis confirmed that S2I42+ contains three sigma and two pi bonds, that the positive charge is essentially equally distributed over all atoms, that the bonding between S2 and two I2+ units in S2I42+ is best described by two mutually perpendicular 4c2e pi*-pi* bonds, and that in Se2I42+, two SeI2+ moieties are joined by a 6c2e pi*-pi* bond, both in agreement with previously suggested models. The VB treatment provided a complementary approach to MO analysis and provided insight how the formation of the weak bonds affects the other bonds. The NBO analysis and the calculated AIM charges showed that the minimization of the electrostatic repulsion between EI2+ units (E = S, Se) and the delocalization of the positive charge are the main factors that explain why the nonclassical structures are favored for S2I42+ and Se2I42+. The difference in the structures of S2I42+ and Se2I42+ is related to the high strength of the S-S pi bond compared to the weak S-I sigma bond and the additional stabilization from increased delocalization of positive charge in the structure of S2I42+ compared to the structure of Se2I42+. The investigation of the E2X42+ series (E = S, Se, Te; X = Cl, Br, I) revealed that only S2I42+ adopts the highly np pi-np pi (n > or = 3)-bonded structure, while all other dications favor the pi-bonded Se2I42+ structure. Theoretical bond order calculations for S2I42+ confirm the previously presented experimentally based bond orders for S-S (2.1-2.3) and I-I (1.3-1.5) bonds. The S-S bond is determined to have the highest reported S-S bond order in an isolated compound and has a bond order that is either similar to or slightly less than the Si-Si bond order in the proposed triply bonded [(Me3Si)2CH]2(iPr)SiSi triple bond SiSi(iPr)[CH(SiMe3)2]2 depending on the definition of bond orders used.     

A General Procedure to Obtain Quantum Mechanical Charge and Bond Order Molecular Parameters

In an approach alternative to that of Mayer, a Hermitian operator is defined within the LCAO MO framework, which allows to obtain molecular charges and bond orders as expectation values of the first and second-order densities respectively. Such expectation values result to be nothing else than Mullikens atom and bond populations. Thus, Mulliken populations appear to be non arbitrary condensed electron density partitions, obtained according to quantum mechanical usual procedures for molecular one and two electron observables. The theoretical simplicity of the outlined procedure can be easily extended in order to obtain the expectation values for higher-order electronic chemical bonds.     

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     

A computationally efficient and reliable bond order measure

Bond order indexes are useful measures that connect quantum mechanical results with chemical understanding. One of these measures, the natural bond order index, based on the natural resonance theory procedure and part of the natural bond orbital analysis tools, has been proved to yield reliable results for many systems. The procedure's computational requirements, nevertheless, scales so highly with the number of functions in the basis set and the delocalization of the system, that the calculation of this bond order is limited to small or medium size molecules. We present in this work a bond order index, the first order perturbation theory bond order (fopBO), which is based on and strongly connected to the natural bond orbital analysis tools. We present the methodology for the calculation of the fopBO index and a number of test calculations that shows that it is as reliable as the natural bond orbital index, with the same weak sensitivity to variations among commonly used basis sets and, as opposed to the natural bond order index, suitable for the study of large systems, such as most of those of biological interest.     

Density and wave function analysis of actinide complexes: what can fuzzy atom, atoms-in-molecules, Mulliken, Lowdin, and natural population analysis tell us?

Recent advances in computational methods have made it possible to calculate the wave functions for a wide variety of simple actinide complexes. Equally important is the ability to analyze the information contained therein and produce a chemically meaningful understanding of the electronic structure. Yet the performance of the most common wave function analyses for the calculation of atomic charge and bond order has not been thoroughly investigated for actinide systems. This is particularly relevant because the calculation of charge and bond order even in transition metal complexes is known to be fraught with difficulty. Here we use Mulliken, Lowdin, natural population analysis, atoms-in-molecules (AIM), and fuzzy atom techniques to determine the charges and bond orders of UO(2)(2+), PuO(2)(2+), UO(2), UO(2)Cl(4)(2-), UO(2)(CO)(5)(2+), UO(2)(CO)(4)(2+), UO(2)(CN)(5)(3-), UO(2)(CN)(4)(2-), UO(2)(OH)(5)(3-), and UO(2)(OH)(4)(2-). This series exhibits a clear experimental and computational trend in bond lengths and vibrational frequencies. The results indicate that Mulliken and Lowdin populations and bond orders are unreliable for the actinyls. Natural population analysis performs well after modification of the partitioning of atomic orbitals to include the 6d in the valence space. The AIM topological partitioning is insensitive to the electron donating ability of the equatorial ligands and the relative atomic volume of the formally U(VI) center is counterintuitively larger than that of O(2-) in the UO(2)(2+) core. Lastly, the calibrated fuzzy atom method yields reasonable bond orders for the actinyls at significantly reduced computational cost relative to the AIM analysis.     

吡啶型氮快速热解中HCN和NH3生成机理研究

考虑煤中吡啶六元环与其他杂环的结合形式,对四种典型的吡啶型氮杂环结构及其热解中间产物中各键的Mayer键级进行了计算。通过对比Mayer键级的大小判断热解时最易发生断裂的键,进而对吡啶型氮热解时氮的逸出机理进行了分析。计算结果表明,吡啶型氮热解产生的含氮污染物主要是HCN;由于吡啶环与其他环结合方式的不同,氮的逸出过程也有差异。利用高频炉快速热解装置对吡啶和吖啶两种模型化合物进行了快速热解实验以验证计算结果。结果表明,吡啶和吖啶热解时虽有少量NH₃生成,但含氮污染物仍以HCN为主,实验结果可为计算所得的结论提供一定支持。
     

吡咯型氮快速热解中NH3和HCN生成机理研究

根据煤中吡咯五元环与其他杂环结合形式的不同,选择五种典型的吡咯型氮杂环结构作为考察对象,利用量子化学计算方法对吡咯型氮杂环及其热解中间产物中各键的Mayer键级进行了计算。通过对比Mayer键级的相对大小对分子结构中最易发生断裂的键进行判断,进而分析了吡咯型氮热解时NH₃和HCN的生成机理。通过计算结果表明,热解时吡咯型氮以-NH和-NH₂自由基的形式逸出,并主要转化为NH₃;氮的逸出过程因吡咯环与芳环结合方式的不同而存在差异。为验证计算结果,利用滴落式高频炉热解装置对吡咯和咔唑两种模型化合物进行了快速热解实验。结果表明,吡咯和咔唑热解时NH₃和HCN均有生成,NH₃是主要的含氮气体污染物。计算所得的结论在一定程度上得到了实验结果的支持。     

Interplay between hydrogen-bond formation and multicenter pi-electron delocalization: intramolecular hydrogen bonds

The specific case of intramolecular hydrogen bonds assisted by pi-electron delocalization is thoroughly investigated using multicenter delocalization analysis. The effect of the pi-electron delocalization on the intramolecular hydrogen-bond strength is determined by means of the relative molecular energies of "open" and "closed" structures, calculated at the B3LYP/6-311++G(d,p) level of theory. These relative energies are compared to variations in the multicenter electron delocalization indices and covalent hydrogen-bond indices, which are shown to correlate very well with the relative strength of the intramolecular hydrogen bonds studied. The multicenter electron delocalization indices and covalent bond indices have been computed using the quantum theory of atoms in molecules approach. The hydrogen bonds are formed with oxygen, nitrogen, or sulfur as acceptor atom, which are also the atoms considered to be bonded to the donor hydrogen. Malonaldehyde is taken as reference; the substitution of oxygen by other atoms at the acceptor and donor positions and the effect of the aromaticity have been studied. The results shown here match perfectly with the qualitative expectations derived from the resonance models. In addition, they provide a quantitative picture of the role played by the pi-electron delocalization on the relative strength of intramolecular hydrogen bonds.     

Interplay between hydrogen bond formation and multicenter pi-electron delocalization: intermolecular hydrogen bonds

The interplay between aromatic electron delocalization and intermolecular hydrogen bonding is thoroughly investigated using multicenter delocalization analysis. The effect on the hydrogen bond strength of aromatic electron delocalization within the acceptor and donor molecules is determined by means of the interaction energies between monomers, calculated at the B3LYP/6-311++G(d,p) level of theory. This magnitude is compared to variations of multicenter electron delocalization indices and covalent hydrogen bond indices, which are shown to correlate perfectly with the relative values of the interaction energies for the different complexes studied. The multicenter electron delocalization indices and covalent bond indices have been computed using the quantum theory of atoms in molecules approach. All the hydrogen bonds are formed with oxygen as the acceptor atom; however, the atom bonded to the donor hydrogen has been either oxygen or nitrogen. The water-water complex is taken as reference, where the donor and acceptor molecular environments are modified by substituting the hydrogens and the hydroxyl group by phenol, furan, and pyrrole aromatic rings. The results here shown match perfectly with the qualitative expectations derived from the resonance model.     

Electronic delocalization in N?C and N?N bonds

For a series of compounds with N? C or N? N bonds, the CNDO/S parameterized calculations for Q^π, the electronic charge density on the nitrogen atom, and π bond orders P^π provide evidence for the simultaneous dependence of the ¹⁵N chemical shift on both of these parameters. The multilinear regressions obtained produce high values for the regression coefficients. The results throw some light on the nitrogen lone pair delocalization mechanism.     

Real-space indicators for chemical bonding. Experimental and theoretical electron density studies of four deltahedral boranes

In an approach combining high-resolution X-ray diffraction at low temperatures with density functional theory calculations, two closo-borates, B(12)H(12)(2-) (1) and B(10)H(10)(2-) (2), and two arachno-boranes, B(10)H(12)L(2) [L = amine (3) or acetonitrile (4)], were analyzed by means of the atoms-in-molecules (AIM) theory and electron localizability indicator (ELI-D). The two-electron three-center (2e3c) bonds of the borane cages are investigated with the focus on real-space indicators for chemical bonding and electron delocalization. In compound 2, only two of the three expected bond critical points (bcp's) are found. However, a weakly populated ELI-D basin is found for this pair of adjacent B atoms and the delocalization index and the Source contributions are on the same order of magnitude as those for the other pairs. The opposite situation is found in the arachno-boranes, where no ELI-D basins are found for two types of B-B pairs, which, in turn, exhibit a bcp. However, again the delocalization index is on the same order of magnitude for this bonding interaction. The results show that an unambiguous real-space criterion for chemical bonding is not given yet for this class of compounds. The arachno-boranes carry a special B-B bond, which is the edge of the crown-shaped molecule. This bond is very long and extremely curved inward the B-B-B ring. Nevertheless, the corresponding bond ellipticity is quite small and the ELI-D value at the attractor position of the disynaptic valence basin is remarkably larger than those for all other B-B valence basins. Furthermore, the value of the ED is large in relation to the B-B bond length, so that only this bond type does not follow a linear relationship of the ED value at the bcp versus B-B bond distances, which is found for all other B-B bcp's. The results indicate that both 2e2c and 2e3c bonding play a distinct role in borane chemistry.     

单电子卤键复合体系H3C···Br-Y(Y=H, CN, NC, CCH, C2H3)的作用机制

对单电子溴键复合物H₃C···Br—Y(Y=H, CCH, CN, NC, C2H3)的结构与性质进行了理论研究. 在B3LYP/6-311++G**水平上计算了稳定构型并做了频率分析. BSSE矫正的相互作用能(E^BSSE)和NBO及AIM分析输入的波函数在MP2/6-311++G**水平下完成. 复合物H₃C···Br—Y中, CH₃(供电子体)自由基均提供一未成对电子与Br—Y中Br(受电子体)形成了单电子溴键, 此单电子溴键也具有“三电子”键的特征. 单电子溴键的形成导致甲基H的背向Y弯曲和Br—Y键的拉长及红移单电子溴键复合物的产生. 考察了电子受体中不同取代基, C(spⁿ)-Br杂化及溶剂的存在对复合物作用的影响, 将单电子氢键, 单电子卤键和单电子锂键的作用强度做了对比, 进一步对Popelier提出的氢键体系中的前三个重要拓扑指标在单电子溴键体系中的重现性进行了探讨.     

Theoretical study of the interaction mechanism of single-electron halogen bond complexes H3C⋯Br-Y (Y = H, CN, NC, CCH, C2H3)

The characteristics and structures of single-electron halogen bond complexes [H₃C?Br-Y (Y = H, CCH, CN, NC, C₂H₃)] have been investigated by theoretical calculation methods. The geometries were optimized and frequencies calculated at the B3LYP/6-311++G** level. The interaction energies were corrected for basis set superposition error (BSSE) and the wavefunctions obtained by the natural bond orbital (NBO) and atom in molecule (AIM) analyses at the MP2/6-311++G** level. For each H₃C?Br-Y complex, a single-electron Br bond is formed between the unpaired electron of the CH₃ (electron donor) radical and the Br atom of Br-Y (electron acceptor); this kind of single-electron bromine bond also possesses the character of a “three-electron bond”. Due to the formation of the single-electron Br bond, the C-H bonds of the CH₃ radical bend away from the Br-Y moiety and the Br-Y bond elongates, giving red-shifted single-electron Br bond complexes. The effects of substituents, hybridization of the carbon atom, and solvent on the properties of the complexes have been investigated. The strengths of single-electron hydrogen bonds, single-electron halogen bonds and single-electron lithium bonds have been compared. In addition, the single-electron halogen bond system is discussed in the light of the first three criteria for hydrogen bonding proposed by Popelier.     

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     

Topological analysis of the electronic charge density in the ethene protonation reaction catalyzed by acidic zeolite

In the present work, the distribution of the electronic charge density in the ethene protonation reaction by a zeolite acid site is studied within the framework of the density functional theory and the atoms in molecules (AIM) theory. The key electronic effects such as topological distribution of the charge density involved in the reaction are presented and discussed. The results are obtained at B3LYP/6-31G(**) level theory. Attention is focused on topological parameters such as electron density, its Laplacian, kinetic energy density, potential energy density, and electronic energy density at the bond critical points (BCP) in all bonds involved in the interaction zone, in the reactants, pi-complex, transition state, and alkoxy product. In addition, the topological atomic properties are determined on the selected atoms in the course of the reaction (average electron population, N(Omega), atomic net charge, q(Omega), atomic energy, E(Omega), atomic volume, v(Omega), and first moment of the atomic charge distribution, M(Omega)) and their changes are analyzed exhaustively. The topological study clearly shows that the ethene interaction with the acid site of the zeolite cluster, T5-OH, in the ethene adsorbed, is dominated by a strong O-H...pi interaction with some degree of covalence. AIM analysis based on DFT calculation for the transition state (TS) shows that the hydrogen atom from the acid site in the zeolitic fragment is connected to the carbon atom by a covalent bond with some contribution of electrostatic interaction and to the oxygen atom by closed shell interaction with some contribution of covalent character. The C-O bond formed in the alkoxy product can be defined as a weaker shared interaction. Our results show that in the transition state, the dominant interactions are partially electrostatic and partially covalent in nature, in which the covalent contribution increases as the concentration and accumulation of the charge density along the bond path between the nuclei linked increases.     

阿司匹林的热解机理及热动力学研究

在用热重法研究了阿司匹林的热稳定性实验的基础上,通过量子化学方法(ab initio DFT)计算了阿司匹林分子的键级,据此计算结果提出了阿司匹林的热解机理,按此机理得到的理论计算值与实验结果一致;运用Freeman-Carroll、Kissinger和Ozawa三种方法分别计算了阿司匹林的热解动力学参数:活化能(E)、反应级数(n)和指前因子(A),其热解动力学方程为: dα/dt=4.74×1011[exp(－(100.34±5.18)×103/RT)](1－α)2.8±0.3;用差示扫描量热法测定的该物质的熔点、摩尔熔化焓和摩尔熔化熵分别为(409.19 ± 0.22) K、(29.17 ± 0.41) kJ•mol-1和(71.09±1.06) J•mol-1•K-1.     

Three-center-two-electron and four-center-four-electron bonds. A study by electron charge density over the structure of methonium cations

We study the electronic density charge topology of CH(5)(+) species 1 (C(s)()), 2 (C(s)()), and 3 (C(2)(v)) at ab initio level using the theory of atoms in molecules developed by Bader. Despite the reports of previous studies concerning carbocationic species, the methane molecule is protonated at the carbon atom, which clearly shows its pentacoordination. In addition to the fact that hydrogen atoms in the methonium molecule behave in a very fluxional fashion and that the energy difference among the species 1, 2, and 3 are very low, is important to point out that two different topological situations can be defined on the basis of our study of the topology of the electronic charge density. Then, the species 1 and 2 present a three-center-two-electron (3c-2e) bond of singular characteristics as compared with other carbocationic species, but in the species 3, the absence of a 3c-2e bond is noteworthy. This structure can be characterized through the three bond critical points found, corresponding to saddle points on the path bonds between the C-H(2,3,5) that lie in the same plane. These nuclei define a four-center interaction where the electronic delocalization produced among the sigma(C-H) bonds provide a stabilization of the three C-H bonds involved in this interaction (the remaining two C-H bonds are similar to those belonging to the nonprotonated species). Our results show that bonding situations with a higher number of atom arrays are possible in protonated hydrocarbons.     

Bond orders and electron delocalization indices for S–N,S–C and S–S bonds in 1,2,3-dithiazole systems

A parametric QTAIM-based (topological) model of bond orders and a modification of the Pauling bond order model are proposed for N,S-containing heterocycles, in particular, for 1,2,3-dithiazoles and 1,2,3-dithiazolium systems, which are prone to the formation of stable radicals and therefore are promising compounds in photovoltaics. These models have been parameterized for covalent S–N, S–C and S–S bonds using the electron delocalization indices. A modified Pauling’s bond order model uses turning radii, that is, the distances within which the potential acting on an electron in a system still tends to return that electron to the atomic basin, and avoids the need to choose the hybridization state of bound atoms arbitrarily.     

Application de la Résonance Magnétique de l'Azote 15 à l'Etude de la Délocalisation Electronique dans les Anilines,Aminopyridines et Enamines

¹⁵N spectroscopy at natural abundance has been applied to the study of electronic delocalization in the N? C bond of a series of substituted anilines. The relationships which offer a good way for evaluating the extent of electronic delocalization from ¹⁵N chemical shift data in anilines have been extended to aminopyridines, aminopyrimidines and nucleosides. The results obtained for C? N bonds in the case of anilines and aliphatic enamines are consistent with those concerning amides and analogous compounds. The validity of ΔG^≠-δ¹⁵N relationships for predicting π delocalization is discussed in terms of the relative contribution of δ- or π-density and non-bonded atom interactions to the total barrier height.