Characterization of pericyclic reactions using multicenter electron delocalization analysis.

This work investigates the applicability of multicenter delocalization analysis to the characterization of pericyclic reactions. The results indicate that multicenter delocalization indices are a powerful tool for studying concerted processes, allowing the characterization of aromatic transition states with a significant increase in the electron delocalization. Moreover, an advantage over magnetic-based indices is that multicenter delocalization indices are not influenced by local electron currents but by the electron delocalization along the multiple (n) centers, and provide, in a quantitative sense, more reliable results. A thorough comparison with magnetic-based indices is carried out for the trimerization reaction of acetylene. Tracking the values of multicenter delocalization indices along the reaction path allows investigation of the nature of concerted mechanisms. Six-center electron delocalization displays a maximum at the transition state of the Diels-Alder reaction, whereas a similar maximum of four-center electron delocalization is slightly displaced to butadiene for the ring opening of cyclobutene. The profile of multicenter electron delocalization indices along the reaction path of [2+2] cycloaddition of ketene to ethene shows the presence of the two independent mechanisms that agree with the two HOMO/LUMO orbital interactions previously proposed to dominate this reaction.     

Electron delocalization patterns in models of distorted (D2d) mixed-valence cubanes

Low-symmetry distortions are present in cubanes such as Fe(4)S(4), but their effects on electron delocalization properties are not well-understood. Mixed-valence cubanes often exhibit experimentally measurable "pair delocalization" of a delocalizable electron. An important question is, what is the role of physical interactions (vibronic, electronic, exchange) and symmetry distortions in determining the electron delocalization pattern? Semiclassical models are used to explore the electron delocalization patterns of S=1/2 tetragonally (D(2d)) distorted mixed-valence cubanes comprising four metal centers with bridging ligands, a single delocalizable "excess" electron, and either closed-shell or open-shell ion cores. Phase diagrams show that distorted S=1/2 ground state cubanes with antiferromagnetic exchange (as found in nature) have delocalization patterns qualitatively similar to those of an S=1/2 model with no Heisenberg exchange, suggesting that exchange is not necessarily a dominant factor in determining electron delocalization properties. The open-shell model reveals two types of pair delocalization for the S=1/2 ground state, with differing dimer subunit spins for compressed and elongated geometries. Previous studies emphasize the importance of exchange interactions for pair delocalization. Here, it is shown that electron exchange is not always necessary for pair delocalization and that it can be achieved with relatively small tetragonal distortions from tetrahedral (T(d)) symmetry. The results contradict those of an earlier theoretical study of distorted Fe(4)S(4) clusters, which concluded that distortions of lower symmetry than D(2d) are necessary to induce a transition to pair delocalization.     

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 changes in pi-electron delocalization in the analogues of an ortho-hydroxy schiff base when the proton is replaced with Li+ or BeH+

Molecular geometries of ortho-hydroxy Schiff base in keto-enamine and enol-imine tautomeric forms, its anion, and their derivatives in which H+ was replaced with Li+ or BeH+ were optimized at the B3LYP/6-311+G level of theory. Isodesmic reactions for estimating delocalization due to H-bonding or cation chelating were calculated. Geometry-based aromaticity index HOMA and magnetism-based NICS1(zz) index were used to estimate pi-electron delocalization. Keto-enamine tautomer exhibits low aromaticity in the ring and a relatively high pi-electron delocalization in the quasi-ring. The reverse was found for enol-imine tautomer. The Li+ and BeH+ derivatives showed a relatively high pi-electron delocalization in the ring and in the quasi-ring. This may be interpreted by an extension of the electron delocalization path in the pi-electron system through low-lying unoccupied p-type orbitals of Li+ and BeH+ cations.     

The effects of conjugation path variation on electron delocalization in phenoxyl-based systems

A number of persistent 2,6-di-tert-butylphenoxyl based radicals were synthesized as models for unpaired spin delocalization as a function of conjugation pathway, and were investigated by ESR and UV-vis spectroscopy. Phenoxyl spin delocalizes significantly onto a para-phenyl ring, but further delocalization through a meta-vinyl or meta-carbonyl linkage is not detectable by ESR hyperfine coupling. UV- vis spectra do show a red shift of the longest wavelength transition for a carbonyl-type substituent by comparison to a vinyl substituent in the meta-position of a para-phenyl group. By comparison, a para-styryl substituent on the phenoxyl causes very large spin delocalization from the phenoxyl unit, with the largest hyperfine coupling being found on the ethenyl unit of the assemblage. This large delocalization accounts for the reactivity of radicals that incorporate such units.     

Analysis of Hückel's [4n + 2] rule through electronic delocalization measures

In the present work, we analyze the pi-electronic delocalization in a series of annulenes and their dications and dianions by using electron delocalization indices calculated in the framework of the quantum theory of atoms in molecules. The aim of our study is to discuss the Hückel's 4n + 2 rule from the viewpoint of pi-electronic delocalization. Our results show that there is an important increase of electronic delocalization (of about 1 e) when going from antiaromatic 4n pi systems to aromatic (4n + 2)pi systems. Less clear is the change in pi-electronic delocalization when we move from a (4n + 2)pi-aromatic to a 4n pi-antiaromatic species by adding or removing a pair of electrons.     

Chemical graph theory and n-center electron delocalization indices: a study on polycyclic aromatic hydrocarbons

Relations between aromaticity indices derived from chemical graph theory and those based on 6-center electron delocalization are investigated for a series of polybenzenoid hydrocarbons. Aromatic stabilization obtained by means of the effective scaled electron delocalization is highly correlated to the resonance energy, RE, obtained both from SCF MO calculations and conjugated ring circuits model. Local aromaticity of benzene rings is discussed using two different criteria, in one of them aromaticity is just given by the cyclic pi-electron conjugation of the ring, whereas terms involving more than one ring are also considered in the other one. Indices derived from chemical graph theory and those obtained from the 6-center electron delocalization give rise to the same local aromaticity. Moreover, 6-center electron delocalization provides more quantitative information.     

Poly-p-phenylene phosphine/polyaniline alternating copolymers: electronic delocalization through phosphorus

Phosphorus-containing poly(N-arylaniline)s and related polymer model compounds have been prepared. The spectroscopic and electronic properties of the materials were investigated via UV-vis-NIR spectroscopy and cyclic voltammetry. PPPP-PANI copolymers containing p-phenylene diamine units in the polymer backbone have electronic and spectroscopic properties characteristic of aromatic substituted p-phenylene diamines. Copolymers containing -(-C(6)H(4)-P-C(6)H(4)-P-C(6)H(4)-)- linkages between nitrogen centers show evidence for weak electronic delocalization along the polymer chain. The electrochemical and spectroscopic properties support strong electronic delocalization in copolymers containing -(-P-C(6)H(4)-N-C(6)H(4)-)- repeat units. The presence of a single diphenylphosphine bridge between nitrogen centers provides an efficient mode of electronic delocalization between nitrogen centers. PPPP oxide-PANI copolymers and related polymer model compounds were also prepared and investigated. The resemblance of PPPP oxide-PANI copolymers to isolated p-phenylene diamines or triarylamines suggests electronic isolation of the amine fragments in the polymer. The conversion of phosphorus(III) phosphines to phosphorus(V) phosphine oxides inhibits electronic delocalization through phosphorus, further supporting delocalization of the lone pair of electrons on phosphorus in PPPP-PANI copolymers. PPPP-PANI copolymers are a new type of pi-conjugated polymer with low oxidation potentials and electronic delocalization through phosphorus along the polymer chain.     

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.     

对取代苯Ph一X（X＝F，OH，NH_2）的价键理论研究

采用键表酉群方法对Ｃ６Ｈ５Ｆ、Ｃ６Ｈ５ＯＨ和Ｃ６Ｈ５ＮＨ２中的电子离域现象进行了计算和分析，讨论了取代苯的价键描述特性，并计算了取代基的π电子离域能．结果表明离子结构成分与离域能有直接关系，即离子成分越多，电子离域能越大．／６－３１Ｇ基组及“分子中的原子”方法将电荷密度分区积分得到各原子上的电荷集居数，并将此结果与取代苯的反应性能进行了比较。为在价键意义上分析和理解取代基对苯环电子结构及其反应性能的影响，本文对３个典型的取代苯Ｐｈ－Ｘ（Ｘ＝Ｆ，ＯＨ，ＮＨ２）进行了初步的价键计算和讨论．１计算方法及构型在键表酉群方法中［５］，体系的一个共振结构可用一个价键结构函数即键表ψ（ｋ）来描述，相应的体系总波函数Ψ可表示为Ｍ个正则键表的线性组合：式（１）便构成了键表相互作用（ＢＴＩ）计算方法［６］的基础．键表对体系的结构贡献定义为：原子轨道ｑ上的电荷集居数定义为：式中ｍｑ（ｋ）可取０、１或２，分别对应于键表ψ（ｋ）中原子轨道ｑ出现０、１或２次．为简比计算，我们将取代苯的σ骨架用ＨＦ分子轨道固定［７］，这样仅需考虑π电子及轨道．原子轨道积分及ＨＦ－ＳＣＦ计算采用Ｇａｕｓｓｉａｎ８０程序．联系人及第一作者：莫亦荣，男，２９     

High Charge Delocalization and Conjugation in Oligofuran Molecular Wires

The extent of charge delocalization and of conjugation in oligofurans and oligothiophenes was studied by using mixed valence systems comprising oligofurans and oligothiophenes capped at both ends by ferrocenyl redox units. Using electrochemical, spectral, and computational tools, we find strong charge delocalization in ferrocene‐capped oligofurans which was stronger than in the corresponding oligothiophene systems. Spectroscopic studies suggest that the electronic coupling integral (H_ab) is roughly 30–50 % greater for oligofuran‐bridged systems, indicating better energy matching between ferrocene units and oligofurans. The distance decay constant (damping factor), β, is similar for oligofurans (0.066 A^?1) and oligothiophenes (0.070 A^?1), which suggests a similar extent of delocalization in the bridge, despite the higher HOMO–LUMO gap in oligofurans. Computational studies indicate a slightly larger extent of delocalization in furan‐bridged systems compared with thiophene‐bridged systems, which is consistent with oligofurans being significantly more rigid and less aromatic than oligothiophenes. High charge delocalization in oligofurans, combined with the previously reported strong fluorescence, high mobility, and high rigidity of oligofuran‐based materials makes them attractive candidates for organic electronic applications.     

用分子片轨道逐步剔除法研究电子离域

估计分子中不同类型的电子离域作用（如p-π → d-π和p-π → σ~*）的相 对强弱对理解分子中化学键的本质有关键的作用。剔除某一分子片轨道（d-π或σ ~*）后分子体系能量的改变可用来计算电子离域到该轨道的离域能。由于轨道之间 的相互作用,使离域能的计算与轨道剔除的次序有关。为克服这种不确定性,可以 逐步轮流增加某一对特定轨道（d-π和σ~*）的库仑积分,以使这对轨道在分子波 函数中的比重逐步减少,即将这对轨道轮流逐步剔除。这样可将轨道间的相互影响 减小以至消除,从而得到各轨道的精确的离域能。以H_3PO中P-O键为例说明了轨道 逐步剔除方法的应用。     

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.     

Delocalized free electron densities in degraded polystyrene and polypropylene macroradicals: The source of different photooxidation rates

Electron structures of alkyl, alkoxy, and peroxy macroradicals for both polypropylene and polystyrene have been studied with quantum chemical methods. The polystyrene tertiary alkoxy macroradical has full delocalization of free spin on a neighboring aromatic ring. In addition, the spin is quite delocalized on polystyrene tertiary alkoxy macroradicals and also on both secondary and tertiary peroxy macroradicals. Such strong delocalization does not occur with polypropylene macroradicals, and it is proposed that the inactivation of polystyrene macroradicals caused by spin delocalization is the reason that polystyrene photodegradation rates are slower than those of polypropylene. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 1070–1076, 2003     

Pros and cons of σ -aromaticity

A discussion of σ-aromaticity requires a distinction between σ-conjugation, σ-electron delocalization, and σ-bond delocalization, all of which can be considered as prerequisites of σ-aromatic character. All molecules with three or more atoms encounter σ-conjugative interactions. Also, all σ-electrons are delocalized if the term delocalization is taken in its quantum theoretical meaning. However, σ-conjugation and σ-electron delocalization do not necessarily imply σ-bond delocalization. - One can distinguish between three different modes of σ-delocalization: ribbon delocalization in acyclic molecules and larger rings, surface delocalization in small rings, and volume delocalization in cage compounds. Surface delocalization of σ-electrons is found to lead to σ-bond delocalization. An example is cyclopropane. Bonding in cyclopropane can only be described in terms of nonclassical 2-electron 3-center and 4-electron 3-center bonds. Application of the criteria used to define π-aromaticity reveals that the properties of cyclopropane are in line with these criteria and that the term σ-aromaticity cannot be rejected on the grounds that aromaticity is restricted to π-electrons. The pros and cons of using the term σ-aromaticity in chemical discussions are presented.     

Mixed valent sites in biological electron transfer

Many of the active sites involved in electron transfer (ET) in biology have more than one metal and are mixed valent in at least one redox state. These include Cu(A), and the polynuclear Fe-S clusters which vary in their extent of delocalization. In this tutorial review the relative contributions to delocalization are evaluated using S K-edge X-ray absorption, magnetic circular dichroism and other spectroscopic methods. The role of intra-site delocalization in ET is considered.     

Fluorine-fluorine spin-spin coupling constants in aromatic compounds: correlations with the delocalization index and with the internuclear separation

This paper describes a new empirical approach for the evaluation of fluorine-fluorine spin-spin coupling constants (J(FF)) in aromatic compounds. The correlations between J(FF) and the delocalization index calculated within the framework of the theory of atoms in molecules (AIM) and with the fluorine-fluorine internuclear separation are investigated. Both the internuclear separation and the delocalization index are found to be highly correlated with J(FF). A regression model in which the experimental J(FF) coupling constant is fitted exponentially to the internuclear separation and linearly to the delocalization index yields a squared correlation coefficient as high as 0.96 for a data set consisting of 33 coupling constants spread over a range of 85 Hz.     

Comparison of the AIM delocalization index and the Mayer and fuzzy atom bond orders

In this paper the behavior of three well-known electron-sharing indexes, namely, the AIM delocalization index and the Mayer and fuzzy atom bond orders are studied at the Hartree-Fock level. A large number of five-membered ring molecules, containing several types of bonding, constitute the training set chosen for such purpose. A detailed analysis of the results obtained shows that the three indexes studied exhibit strong correlations, especially for homonuclear bonds. The correlation is somewhat poorer but still significant for polar bonds. In this case, the bond orders obtained with the Mayer and fuzzy atom approaches are normally closer to the formally predicted bond orders than those given by the AIM delocalization indexes, which are usually smaller than those expected from chemical intuition. In some particular cases, the use of diffuse functions in the calculation of Mayer bond orders leads to unrealistic results. In particular, noticeable trends are found for C-C bonds, encouraging the substitution of the delocalization index by the cheaper fuzzy atom or even the Mayer bond orders in the calculation of aromaticity indexes based on the delocalization index such as the para-delocalization index and the aromatic fluctuation index.     

Visualizing electron delocalization in contorted polycyclic aromatic hydrocarbons

Electron delocalization in contorted polycyclic aromatic hydrocarbon (PAH) molecules was examined through 3D isotropic magnetic shielding (IMS) contour maps built around the molecules using pseudo-van der Waals surfaces. The resulting maps of electron delocalization provided an intuitive, yet detailed and quantitative evaluation of the aromatic, non aromatic, and antiaromatic character of the local and global conjugated cyclic circuits distributed over the molecules. An attractive pictural feature of the 3D IMS contour maps is that they are reminiscent of the Clar π-sextet model of aromaticity. The difference in delocalization patterns between the two faces of the electron circuits in contorted PAHs was clearly visualized. For π-extended contorted PAHs, some splits of the π system resulted in recognizable patterns typical of smaller PAHs. The differences between the delocalization patterns of diastereomeric chiral PAHs could also be visualized. Mapping IMS on pseudo-van der Waals surfaces around contorted PAHs allowed visualization of their superimposed preferred circuits for electron delocalization and hence their local and global aromaticity patterns.

Electron delocalization in contorted polycyclic aromatic hydrocarbon (PAH) molecules was examined through 3D isotropic magnetic shielding (IMS) contour maps built around the molecules using pseudo-van der Waals surfaces.     

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.