On the sigma,pi-energy separation of the aromatic stabilization energy of cyclobutadiene

The separation of the aromatic stabilization energy (ASE) of cyclobutadiene (CBD) into a sigma- and a pi-component is reinvestigated. Eight different reactions are considered for this purpose. As expected, the total destabilization energies that result from these reactions depend only on the reference compound and not on the reaction itself. The heats of formation that can be obtained from the calculated reaction energies are in excellent agreement with the recently determined experimental value of 102.3 +/- 3.8 kcal mol(-1) (A. Fattahi, L. Liz, Z. Thian and S. R. Kass, Angew. Chem., Int. Ed., 2006, 45, 4984-4988). Evaluation of the angular strain in CBD from a newly considered reaction confirms earlier estimates and yields a strain energy of 34 +/- 3 kcal mol(-1). If referred to s-cis-butadiene this leads to an ASE of -37 +/- 4 kcal mol(-1) in close agreement with estimates provided by A. Fattahi, L. Liz, Z. Thian and S. R. Kass, Angew. Chem., Int. Ed., 2006, 45, 4984-4988; and by K. B. Wiberg, Chem. Rev., 2001, 101, 1317-1332. With s-trans-butadiene as reference we obtain -42 +/- 4 kcal mol(-1). This value is 8 to 10 kcal mol(-1) less destabilizing than recent estimates of A. A. Deniz, K. S. Peters and G. J. Snyder, Science, 1999, 286, 1119-1112; and Kovacevi?, D. Bari?, Z. B. Maksi?, T. Müller, J. Phys. Chem. A, 2004, 108, 9126-9133. Attempts to separate ASE(CBD) and E(strain)(CBD) into a sigma- and a pi-component do not lead to useful results. In contrast to ASE and E(strain) themselves, the sigma- and pi-components depend strongly on the applied reaction. A detailed analysis reveals that it is not possible to associate these components with only one of the molecules that participate in the reaction. The components depend on all of these molecules and therefore on the underlying reaction. Generally, components that result from a formal sigma,pi-energy separation of aromatic stabilization energies or strain energies cannot be considered as the sigma- and pi-components of these energies.     

Bond lengths and reorganization energies in fullerenes and their ions

A very simple tight binding method with bond-length-dependent couplings, similar to the Su-Schrieffer-Heeger model, is described and applied to fullerenes in different charge states. The bond lengths, calculated from the π bond orders, are in good agreement with results obtained by ab initio methods which include correlation, where comparisons can be made. The Jahn-Teller distortions are found to be small for the examples C₂₀, C₂₈-T_d, and C₆₀-I_h. Often many possible distortions are found, for example two different D_5d distortions for the C₂₀ spin triplet state. Bond reorganization energies (λ_b) for reduction and oxidation, which are measures for trapping efficiency and vibronic coupling, are obtained using a parabolic approximation of the energy surface. Received: 3 December 1996 / Accepted: 3 March 1997     

Remote aromatic stabilization in radical reactions

The rates of free radical reduction of a series of anthracene derivatives and 1-phenyl-4-bromodecane with tributyltin hydride are mediated by the remote aromatic substituent in an apparent through-space interaction. Density functional calculations suggest that this enhancement is not due to direct stabilization of the free radical intermediate, and is likely to be achieved through the interaction of the aromatic moiety with the polarized transition state leading to the intermediate.     

Comparative investigation on non-IPR C68 and IPR C78 fullerenes encaging Sc3N molecules

A computational study on the experimentally detected Sc(3)N@C(68) cluster is reported, involving quantum chemical analysis at the B3LYP/6-31G level. Extensive computations were carried out on the pure C(68) cage which does not conform with the isolated pentagon rule (IPR). The two maximally stable C(68) isomers were selected as initial Sc(3)N@C(68) cage structures. Full geometry optimization leads to a confirmation of an earlier assessment of the Sc(3)N@C(68) equilibrium geometry (Nature 2000, 408, 427), namely an eclipsed arrangement of Sc(3)N in the C(68) 6140 frame, where each Sc atom interacts with one pentagon pair. From a variety of theoretical procedures, a D(3h) structure is proposed for the free Sc(3)N molecule. Encapsulated into the C(68) enclosure, this unit is strongly stabilized with respect to rotation within the cage. The complexation energy of Sc(3)N@C(68) cage is found to be in the order of that determined for Sc(3)N@C(80) and exceeding the complexation energy of Sc(3)N@C(78). The cage-core interaction is investigated in terms of electron transfer from the encapsulated trimetallic cluster to the fullerene as well as hybridization between these two subsystems. The stabilization mechanism of Sc(3)N@C(68) is seen to be analogous to that operative in Sc(3)N@C(78). For both cages, C(68) and C(78), inclusion of Sc(3)N induces aromaticity of the cluster as a whole.     

Paradigms and paradoxes: O- and N-protonated amides, stabilization energy, and resonance energy

Protonation of amides most often occurs on oxygen, unless the amide bond is twisted out of planarity allowing the more favored nitrogen protonation to occur. Protonation of oxygen is believed to take place over that of nitrogen due to increased resonance stabilization of the O-protonated species. Resonance energies for O- and N-protonated dimethylacetamide are quantitated using quantum chemically calculated proton affinities for the two sites.     

On the aromatic stabilization of corannulene and coronene

The application of set of homodesmotic reactions allowed us to estimate the aromatic stabilization energy (ASE) of corannulene and coronene. Appropriate reactions have been applied to balance syn/anti mismatches in di-, tetra- and hexamethylene substituted derivatives. Based on many different polycyclic reference structures that compensate the effect of strain in the corannulene moiety the value of ASE comes to 44.5 kcal mol(-1). Planar corannulene is more stabilized by cyclic π-electron delocalization by ca. 10.7 kcal mol(-1), as compared with a bowl-shaped system. A similar approach for coronene leads to an ASE equal to 58.4 kcal mol(-1).     

An insight into the local aromaticities of polycyclic aromatic hydrocarbons and fullerenes

In this work we quantify the local aromaticity of six-membered rings in a series of planar and bowl-shaped polycyclic aromatic hydrocarbons (PAHs) and fullerenes. The evaluation of local aromaticity has been carried out through the use of structurally (HOMA) and magnetically (NICS) based measures, as well as by the use of a new electronically based indicator of aromaticity, the para delocalization index (PDI), which is defined as the average of all the Bader delocalization indices between para-related carbon atoms in six-membered rings. The series of PAHs selected includes C(10)H(8), C(12)H(8), C(14)H(8), C(20)H(10), C(26)H(12), and C(30)H(12), with benzene and C(60) taken as references. The change in the local aromaticity of the six-membered rings on going from benzene to C(60) is analyzed. Finally, we also compare the aromaticity of C(60) with that of C(70), open [5,6]- and closed [6,6]-C(60)NH systems, and C(60)F(18).     

The Raman spectrum and aromatic stabilization in a cyclic germylene

For the stable germylene, N,N'-di-tert-butyl-1,3-diaza-2-germacyclopent-4-en-2-ylidene, 2, the Raman line for the cyclic C=C stretching mode is strongly enhanced and shifted to longer wavelength, compared with that in reference compounds. The enhancement and frequency shift are even greater than those found for the corresponding stable silylene 1. These results, along with NMR evidence and theoretical calculations, suggest that the aromatic electron delocalization is even greater in the germylene than that in the silylene.     

Construction and utilisation of planar graphs of two series of IPR fullerenes through the use of threefold rotational symmetry

Threefold rotational symmetry has been used to develop an algorithm for the construction of planar graphs of IPR fullerenes and to factorize their characteristic polynomials. Two series of fullerenes of the formula C_60+12n and C_60+18n have thus been obtained. The algorithm has been shown to be useful for predicting the nature of variation of the point groups of the fullerenes with increased n, for counting the number of ¹³C nuclear magnetic resonance (NMR) signals (along with their relative intensities), and also for obtaining a large part of their eigenspectra. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Zigzags, railroads, and knots in fullerenes

Two connections between fullerene structures and alternating knots are established. Knots may appear in two ways: from zigzags, i.e., circuits (possibly self-intersecting) of edges running alternately left and right at successive vertices, and from railroads, i.e., circuits (possibly self-intersecting) of edge-sharing hexagonal faces, such that the shared edges occur in opposite pairs. A z-knot fullerene has only a single zigzag, doubly covering all edges: in the range investigated (n /= 38, all chiral, belonging to groups C(1), C(2), C(3), D(3), or D(5). An r-knot fullerene has a railroad corresponding to the projection of a nontrivial knot: examples are found for C(52) (trefoil), C(54) (figure-of-eight or Flemish knot), and, with isolated pentagons, at C(96), C(104), C(108), C(112), C(114). Statistics on the occurrence of z-knots and of z-vectors of various kinds, z-uniform, z-transitive, and z-balanced, are presented for trivalent polyhedra, general fullerenes, and isolated-pentagon fullerenes, along with examples with self-intersecting railroads and r-knots. In a subset of z-knot fullerenes, so-called minimal knots, the unique zigzag defines a specific Kekulé structure in which double bonds lie on lines of longitude and single bonds on lines of latitude of the approximate sphere defined by the polyhedron vertices.     

Steric strain versus hyperconjugative stabilization in ethane congeners

Rotation barriers in the group IVB ethane congeners H(3)X-YH(3) (X, Y = C, Si, Ge, Sn, Pb) have been systematically studied and deciphered using the ab initio valence bond theory in terms of the steric strain and hyperconjugation effect. Our results show that in all cases the rotation barriers are dominated by the steric repulsion whereas the hyperconjugative interaction between the X-H bond orbitals and the vicinal Y-H antibond orbitals (and vice versa) plays a secondary role, although indeed the hyperconjugation effect favors staggered structures. By the independent estimations of the hyperconjugative and steric interactions in the process of rotations, we found that the structural effect which mainly refers to the central X-Y bond relaxation makes a small contribution to the rotational barriers. Therefore, we conclude that both the rigid and fully relaxed rotations in the group IVB ethane congeners H(3)X-YH(3) observe the same mechanism which is governed by the conventional steric repulsion.     

CH bond dissociation energies,isolated stretching frequencies,and radical stabilization energy

An earlier correlation between isolated CH stretching frequencies, v, and experimental CH bond dissociation energies, in hydrocarbons, fluorocarbons, and CHO compounds, is updated. A stabilization energy, E, which reflects only the properties of the radical, is defined by the deviation of a point from the above correlation. E values for a variety of radicals are listed and discussed. In H? C? N and H? C? O compounds E is low or negligible, due to the low v found in these compounds. The conventional definition of E_S then represents a serious misnomer, which distracts attention from the probable source of discrepancies between experimental and ab initio values of DH°(C? H), namely, the parent molecules. Stereo electronic effects concerned with the breaking of CH bonds are predicted in a variety of situations. Some experimental determinations of DH°(C? H), viz., in C₂H₄, HCOOH, CH₃CHO, CH₃NH₂, are considered to be probably in error. Schemes for partitioning energies of atomization into ‘standard’ or ‘intrinsic’ bond energies are criticized.     

Bond dissociation energies and radical stabilization energies associated with model peptide-backbone radicals

Bond dissociation energies (BDEs) and radical stabilization energies (RSEs) have been calculated for a series of models that represent a glycine-containing peptide-backbone. High-level methods that have been used include W1, CBS-QB3, U-CBS-QB3, and G3X(MP2)-RAD. Simpler methods used include MP2, B3-LYP, BMK, and MPWB1K in association with the 6-311+G(3df,2p) basis set. We find that the high-level methods produce BDEs and RSEs that are in good agreement with one another. Of the simpler methods, RBMK and RMPWB1K achieve good accuracy for BDEs and RSEs for all the species that were examined. For monosubstituted carbon-centered radicals, we find that the stabilizing effect (as measured by RSEs) of carbonyl substituents (CX=O) ranges from 24.7 to 36.9 kJ mol(-1), with the largest stabilization occurring for the CH=O group. Amino groups (NHY) also stabilize a monosubstituted alpha-carbon radical, with the calculated RSEs ranging from 44.5 to 49.5 kJ mol(-1), the largest stabilization occurring for the NH2 group. In combination, NHY and CX=O substituents on a disubstituted carbon-centered radical produce a large stabilizing effect ranging from 82.0 to 125.8 kJ mol(-1). This translates to a captodative (synergistic) stabilization of 12.8 to 39.4 kJ mol(-1). For monosubstituted nitrogen-centered radicals, we find that the stabilizing effect of methyl and related (CH2Z) substituents ranges from 25.9 to 31.7 kJ mol(-1), the largest stabilization occurring for the CH3 group. Carbonyl substituents (CX=O) destabilize a nitrogen-centered radical relative to the corresponding closed-shell molecule, with the calculated RSEs ranging from -30.8 to -22.3 kJ mol(-1), the largest destabilization occurring for the CH=O group. In combination, CH2Z and CX=O substituents at a nitrogen radical center produce a destabilizing effect ranging from -19.0 to -0.2 kJ mol(-1). This translates to an additional destabilization associated with disubstitution of -18.6 to -7.8 kJ mol(-1).     

Distribution of mass and averaged internal energy of fullerenes produced in arc-discharge ion source

In this work, the decay rate of fullerene ion beams as well as its dependence on the flight time from standard plasma type ion source has been studied. We have performed direct measurements of the decay probability of each fullerene ion (n=44 to 70) using two energy analyzers. The experimental results are well accounted for in terms of the concept of evaporating ensemble for the behavior of fullerenes in the continuous arc-discharge ion source. The obtained individually different internal energy distributions for fullerenes from C ₄₄ ⁺ to C ₆₈ ⁺ are for the first time presented.     

Structure,strain, and reorganization energy of blue copper models in the protein

The copper coordination geometry in the blue copper proteins plastocyanin, nitrite reductase, cucumber basic protein, and azurin has been studied by combined density functional (B3LYP) and molecular mechanical methods. Compared to quantum chemical vacuum calculations, a significant improvement of the geometry is seen (toward the experimental structures) not only for the dihedral angles of the ligands but also for the bond lengths and angles around the copper ion. The flexible Cu–S_Met bond is well reproduced in the oxidized structures, whereas it is too long in some of the reduced complexes (too short in vacuum). The change in the geometry compared to the vacuum state costs 33–66 kJ/mol. If the covalent bonds between the ligands and the protein are broken, this energy decreases by ∼25 kJ/mol, which is an estimate of the covalent strain. This is similar to what is found for other proteins, so the blue copper proteins are not more strained than other metalloproteins. The inner‐sphere self‐exchange reorganization energy of all four proteins are ∼30 kJ/mol. This is 30–50 kJ/mol lower than in vacuum. The decrease is caused by dielectric and electrostatic effects in the protein, especially the hydrogen bond(s) to the cysteine copper ligands and not by covalent strain. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 335–347, 2001     

Bond length alternation and energy band gap of polyyne

The bond length alternation (BLA) and energy band gap of polyyne are investigated by various first-principles theories, including Hartree-Fock, MP2, hybrid, and nonhybrid density functional theories. Both solid-state calculations utilizing periodic boundary conditions on polymers and molecular quantum mechanical calculations on extra-long oligomers were performed with consistent results. By validation on similar linear conjugated polymers, polyacetylene and polydiacetylene, the combination of hybrid-DFT schemes, B3LYP//BHandHLYP or B3LYP//KMLYP, is shown to give the best predictions for both geometry and band gap of polyyne based on available experimental data. We conclude that the best estimate of the BLA of polyyne is about 0.13 A and that of the band gap is about 2.2 eV.     

Effect of support on the stabilization energy of Pt, Pd and Ru

Stabilization energies of Pt, Pd and Ru on oxide supports have been determined by the interacting bond method. Supports to ensure better dispersity of metals are suggested.

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