Electronic structures and stabilities of GeC n and Ge2C n in Hückel theory

Some recent results about Ge _p C _n ⁺ ions (p=1, 2;n < 6) produced in laser microprobe mass analyser experiments (LAMMA) show very marked alternations in the emission intensities I(Ge _p C _n ⁺ ) as a function of then andp parities. I(Ge _p C _n ⁺ ) are maxima for evenn. Thus, intensity maxima occur when the total atom numberm of the aggregates is odd for GeC _n ⁺ (m=n+1) and even for Ge₂C _n ⁺ (m=n+2). As a result, GeC _n ⁺ ions seem to behave as C _m ⁺ ions, whereas the behaviour of Ge₂C _n ⁺ ions is quite similar to that of Ge _p ⁺ ions formed in SIMS or vaporization experiments on pure germanium. It is well known (correspondence rule) that the parity effect in the emissions corresponds to alternations in the ion stabilities. These results are analysed from a model built in Hückel approximation with hybridization. Forp=1, the clusters are assumed to be insp hybridization as for C _m ⁺ ions, hence with linear shapes, and forp=2, they would rather be insp ² orsp ³ hybridization as for Ge _p ⁺ ions. Relative stabilities and distributions of the energy levels of the aggregates are then calculated. The relative stabilities given for Ge _p C _n ⁺ by this model show maxima for evenn as in experiments, and we have thus a good agreement between our calculation results and the experimental data. Moreover, we found that Ge₂C _n ⁺ would rather be insp ³ hybridization, that is under three dimensional shapes.     

Perceiving molecular themes in the structures and bonding of intermetallic phases: the role of Hückel theory in an ab initio era

Qualitative molecular orbital theory is central to our understanding of the bonding and reactivity of molecules and materials across chemistry. Advances in computational technology and methodology, however, have made ab initio or density functional theory calculations a simpler alternative, offering reliable results on increasingly large systems in a reasonable time-scale without the need for concerns about the approximations and parameterization of semi-empirical one-electron based methods. In this perspective, we illustrate how the availability of higher-level computational results can augment, rather than supplant, the insights provided by approaches such as the simple and extended Hückel methods. We begin by describing a way to parameterize Hückel-type Hamiltonians against DFT results for intermetallic systems. The potential for chemical understanding embodied by such orbital-based models is then demonstrated with two schemes of bonding analysis that originated in them (but can be extended to DFT results): the μ(3)-acid/base model and the μ(2)-Hückel chemical pressure analysis, which translate the molecular concepts of acidity and electronic/steric competition, respectively, into the context of intermetallic chemistry.     

Extended Hückel theory applied to electrophilic substitution in imidazole

The σ-complex energies and total electron densities of the imidazole cation, neutral molecule, and anion have been calculated by the Extended Hückel Theory. Where the mechanism of electrophilic substitution is believed to involve a σ-complex, good agreement is obtained with the experimentally observed site of substitution.     

Steering Site-Selectivity in Transition Metal-Catalyzed C−H Bond Functionalization: the Challenge of Benzanilides

Selective C−H bond functionalization catalyzed by metal complexes have completely revolutionized the way in which chemical synthesis is conceived nowadays. Typically, the reactivity of a transition metal catalyst is the key to control the site-, regio- and/or stereo-selectivity of a C−H bond functionalization. Of particular interests are molecules that contain multiple C−H bonds prone to undergo C−H bond activations with very similar bond dissociation energies at different positions. This is the case of benzanilides, relevant chemical motifs that are found in many useful fine chemicals, in which two C−H sites are present in chemically different aromatic fragments. In the last years, it has been found that depending on the metal catalyst and the reaction conditions, the amide motif might behave as a directing group towards the metal-catalyzed C−H bond activation in the benzamide site or in the anilide site. The impact and the consequences of such subtle control of site-selectivity are herein reviewed with important applications in carbon-carbon and carbon-heteroatom bond forming processes. The mechanisms unraveling these unique transformations are discussed in order to provide a better understanding for future developments in the field of site-selective C−H bond functionalization with transition metal catalysts.     

Studies of the molecular-orbital theory of chemical reactivity—I : The significance of auxiliary inductive parameters in the Hückel M-O theory

Auxiliary inductive parameters have been incorporated in the Hückel MO theory primarily to obtain π-electron distributions that are compatible with chemical properties of compounds such as pyrrole. It is emphasized here that the widely accepted justification for the use of such parameters in terms of polarization of the σ-bonds around heteroatoms is not acceptable because the total electron distribution (π + σ) is even less compatible with chemical properties than is the π-distribution obtained without using such parameters.An alternative justification for the use of auxiliary coulomb parameters is now presented. They arise from the presence of abnormal core attraction terms in the vicinity of heteroatoms in the SCF molecular-orbital treatment of π-electron systems. The effect is limited essentially to the nearest neighbours of heteroatoms. It is present when the σ-electron charge densities are uniform, i.e. when σ-polarization is absent. The resultant total electron distribution is then compatible with chemical properties for compounds such as pyrrole.     

Extended Hückel theory—vi : Excited states and photochemistry of diazirines and diazomethanes

Approximate calculations are presented for the excited states of diazirine and diazomethane. The long wavelength transition in the former is assigned as allowed, B₁ ← A₁ π^* ← σ; in the latter as forbidden A₂ ← A₁, σ^* ← π. Tentative assignments are made for higher excited states. The change in molecular bonding upon excitation is consistent with the observed primary photochemical processes: dissociation to carbenes and N₂ in diazoalkanes, similar dissociation or rearrangement to diazomethanes in the diazirines. The latter isomerization is followed theoretically in some detail, and the role of geometrical changes in the various excited states of diazirine and diazomethane is examined.     

Electronic structures of C36 fulleride anions: C36− and C362−

Electronic structures for mono- and dianionic species of two promising C₃₆ fullerene isomers, 14 and 15, are investigated by means of the hybrid Hartree–Fock (HF)/density functional (DF) method. Structural deformations, charge distributions, and spin densities upon one- or two-electron reduction are explained in light of the lowest unoccupied molecular orbitals (LUMOs) of each neutral isomer. First electron affinities for the neutral isomers 14 and 15 are predicted to be 2.3 and 2.5 eV, respectively, facilitating n-type doping for C₃₆ solids. The degrees of local aromaticity of the isomers 14 and 15 tend to decrease with reduction in contrast with C₆₀.     

A theoretical study of CO adsorption on gold by Hückel theory and density functional theory calculations

It is crucial to understand the nature of CO adsorption on gold so as to elucidate the mechanism of low-temperature CO oxidation on nanogold catalysts. We performed theoretical analysis of CO adsorption on gold by using Hückel theory and density functional theory (DFT) calculations. Hückel theory indicates that CO adsorption on gold is dominated by the electron distribution at the Au atom, which is greatly affected by neighboring Au atoms, coadsorbed or doping species. The increase of σ-bonding electrons should weaken the CO adsorption, while the increase of π-electrons should strengthen the adsorption. DFT calculations proved this prediction quantitatively for various systems, including CO adsorption on a Au(100)-hex surface with locally varying subsurface configurations and CO coadsorption with acceptor or donor species.     

Algorithm for the calculation of the electronic structure of molecules by the expanded Hückel method

An algorithm is described for the calculation of quantum-chemical characteristics of molecules by the expanded Hückel method. The method for the calculation of the complete overlap matrix of Slater atomic orbitals of type ns, np, and nd was modified.     

Reaching Green: Heterocycle Synthesis by Transition Metal-Catalyzed C−H Functionalization in Sustainable Medium

Catalytic C−H functionalization has emerged as an efficient alternative to traditional coupling reactions. However, some of these reactions depend on environmentally harmful solvents, weakening the overall green nature of these methods. As organic processes consume large amount of solvents, the use of less harmful solvents enhance the sustainability of these reactions. Herein, we present an overview of transition metal-catalyzed C−H functionalization reactions for the synthesis of heterocycles in sustainable solvents based on CHEM21 solvent selection guide.     

Retaining Hückel Aromaticity in the Triplet Excited State of Azobenzene

The implication of the potential concept of aromaticity in the relaxed lowest triplet state of azobenzene, an efficient molecular switch, using elementary aromaticity indices based on magnetic, electronic, and geometric criteria has been discussed. Azobenzene exhibits a major Hückel aromatic character retained in the diradical lowest relaxed triplet state (T₁) by virtue of a twisted geometry with partial delocalization of unpaired electrons in the perpendicular p-orbitals of two nitrogen atoms to the corresponding phenyl rings. The computational analysis has been expanded further to stilbene and N-diphenylmethanimine for an extensive understanding of the effect of closed-shell Hückel aromaticity in double-bond-linked phenyl rings. Our analysis concluded that stilbene has Hückel aromatic character in the relaxed T₁ state and N-diphenylmethanimine has a considerable Hückel aromaticity in the phenyl ring near the carbon atom while a paramount Baird aromaticity in the phenyl ring near the nitrogen atom of the C=N double bond. The results reveal the application of excited-state aromaticity as a general tool for the design of molecular switches.     

Analytical derivation of the Hückel “4n + 2 rule”

The “4n + 2 rule” is derived analytically at the level of the simple Hückel theory for neutral even-membered chains, their double ions, as well as cations and anions of the odd-membered chains, by determining the first order energetic effect of the ring closure. The topological background of the “4n + 2 rule” is also briefly discussed.     

Rationalizing the AlI-Promoted Oxidative Addition of C−C Versus C−H Bonds in Arenes

The factors controlling the oxidative addition of C−C and C−H bonds in arenes mediated by Al^I have been computationally explored by means of Density Functional Theory calculations. To this end, we compared the processes involving benzene, naphthalene and anthracene which are promoted by a recently prepared anionic Al^I-carbenoid. It is found that this species exhibits a strong tendency to oxidatively activate C−H bonds over C−C bonds, with the notable exception of benzene, where the C−C bond activation is feasible but only under kinetic control reaction conditions. State-of-the-art computational methods based on the combination of the Activation Strain Model of reactivity and the Energy Decomposition Analysis have been used to rationalize the competition between both bond activation reactions as well as to quantitatively analyze in detail the ultimate factors controlling these transformations.     

Mechanisms of activation of C—H bonds in framework compounds: theory and experiment

On the basis of the data from experiments and from modern quantum-chemical calculations using framework hydrocarbons (adamantane, diamondoids, etc.) as models it was demonstrated that the mechanisms of activation of saturated hydrocarbons by various electron-deficient reagents (radicals, charged and neutral electrophiles) are universal.     

Density functional theory study of the structures,electronic states and stabilities of Al n Pt (n = 1–15) clusters

The binding energy, dissociation energy, ionization potentials, electron affinities, gap and stability of small Al _n Pt (n = 1–15) clusters, in comparison with pure aluminum clusters have been systematically investigated by means of density functional calculations at the B3LYP level. The growth patten for Al _n Pt clusters is that the Pt atom substituted the surface atom of the Al _{n + 1} clusters for n < 13. Starting from n = 13, the Pt atom completely falls into the center of the Al-frame. The Pt atom substituted the center atom of the Al _{n + 1} clusters to form the Pt-encapsulated Aln geometries for n > 13. We also find that the impurity Pt atom causes local structural distortion due to different atomic radii and different bonding characteristics. The clusters with total atom numbers of 2, 7, and 11 exhibit high stability.     

Nickel-catalyzed C−H arylation of benzoxazoles and oxazoles: Benchmarking the influence of electronic,steric and leaving group variations in phenolic electrophiles

Electronic, steric and leaving group effects for Ni-catalyzed direct arylations using C?O electrophiles were benchmarked. The scope of arylations with pivalates was general with respect to both the electronics on the electrophile and the azoles. Furthermore, the arylation of azoles with tosylates, mesylates and carbamates with varying electronics was explored, and showed electronic trends similar to those of the pivalate reactions. Finally, the relative rate of arylation of 5-methyl benzoxazole with two electronically-similar electrophiles bearing different leaving groups was established. The results from these studies implicate the following order of relative reactivity: mesylates>pivalates>carbamates.