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Bond Lengths and Quadratic Force Field for Cubane

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Abstract

The molecular structure of pentacyclo[4.2.0.0(2,5).0(3,8).0(4,7)]octane (cubane) has been determined in the gas phase at a temperature of 77-degrees-C. Parameter values were obtained from four types of refinements: those based on electron-diffraction (ED) data alone, ED data with inclusion of a microwave (MW) rotational constant for cubane-d0 available from the literature, ED data with allowance for single-double multiple scattering (MS) effects, and the ED-MW data with allowance for MS effects. The results differ insignificantly. Bond lengths in terms of the distance types r-alpha-0 (geometrically consistent at 0 K) and r(g) (vibrationally averaged at the experimental temperature) are respectively as follows: C-H, 1.098 (6) and 1.114 (6) angstrom; C-C, 1.571 (2) and 1.573 (2) angstrom. Estimated equilibrium values are r(e)(C-H) = 1.0960 (130) and r(e)(C-C) = 1.5618 (40) angstrom. Some amplitudes of vibration are l(C-H) = 0.075 (10), l(C-C) = 0.062 (3), l(C.C) = 0.065 (4), l(C..C) = 0.072 (9); values are in angstroms with estimated 2-sigma uncertainties in parentheses. O(h) symmetry was assumed. A complete quadratic vibrational force field was also evaluated. The 32 independent force constants were fitted simultaneously to 156 observations consisting of 146 wavenumber fundamentals from eight isotopic species, 2 Coriolis constants, 1 centrifugal distortion constant, and 7 amplitudes of vibration. The values are in excellent agreement with recent ab initio results.

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... Concerning B 0 , different values derived from calculations or previous experimental results are summarized in Table 3. Cole et al., 22 Pine et al., 6 and Hirota et al. 23 published rotational constants obtained from gas phase spectroscopy, and Almenningen et al. 24 and Hedberg et al. 25 derived the GS rotational constants from electron diffraction measurements. The most accurate experimental determination of the rotational constant B 0 has been published by Hedberg et al. 25 It associates gas phase electron diffraction measurements with numerous experimental results and, in particular, with very accurate GS pure rotation spectroscopy of mono deuterated cubane. ...
... Concerning B 0 , different values derived from calculations or previous experimental results are summarized in Table 3. Cole et al., 22 Pine et al., 6 and Hirota et al. 23 published rotational constants obtained from gas phase spectroscopy, and Almenningen et al. 24 and Hedberg et al. 25 derived the GS rotational constants from electron diffraction measurements. The most accurate experimental determination of the rotational constant B 0 has been published by Hedberg et al. 25 It associates gas phase electron diffraction measurements with numerous experimental results and, in particular, with very accurate GS pure rotation spectroscopy of mono deuterated cubane. 23 Table 4. Effective Hamiltonian Parameters for the ν 12 and ν 11 Fundamental Bands a vibrational level order Ω(K,nC) ν 12 /cm −1 ν 11 /cm −1 "usual" notation 18 ...
... In the present work, the molecular structure optimized in our quantum chemistry calculations are in very good agreement with the experimental values from Hedberg et al. 25 Two geometrical parameters, C−C = 157.4 pm and C−H = 108.8 ...
Article
Carbon-cage molecules have generated a considerable interest from both experimental and theoretical point of views. We recently performed a high-resolution study of adamantane (C10H16), the smallest hydrocarbon cage belonging to the diamandoid family (O. Pirali et al., J Chem Phys 2012;136:024310). There exist another family of hydrocarbon cages with additional interesting chemical properties: the so-called Platonic hydrocarbons that comprise dodecahedrane (C20H20) and cubane (C8H8). Both possess C–C bond angles that deviate from the tetrahedral angle (109.8°) of the sp3 hybridized form of carbon. This generates a considerable strain in the molecule. We report a new wide-range high-resolution study of the infrared spectrum of cubane. The sample was synthesized in Bari upon decarboxylation of 1,4-cubanedicarboxylic acid thanks to the improved synthesis of literature. Several spectra have been recorded at the AILES beamline of the SOLEIL synchrotron facility. They cover the 600 to 3200 cm−1 region. Besides the three infrared-active fundamentals (ν10, ν11 and ν12), we could record many combination bands, all of them displaying a well-resolved octahedral rotational structure. We present here a preliminary analysis of some of the recorded bands, performed thanks the SPVIEW and XTDS software, based on the tensorial formalism developed in the Dijon group. A comparison with ab initio calculations, allowing to identify some combination bands, is also presented.
... Heat of formation [67] 144 kcal/mol Strain energy [68] 161.5 kcal/mol C-C bond lengths [63] 1.571 Å C-H bond lengths [63] 1.109 Å C 1 -C 4 distance [62] 2.72 Å Due to the unusual structure of cubane its physical properties are quite different from other hydrocarbons ( Table 3). The perfect cubic arrangement of the carbon atoms results in an octahedral point group O h , with a high density of 1.29 g/cm 3 . ...
... Heat of formation [67] 144 kcal/mol Strain energy [68] 161.5 kcal/mol C-C bond lengths [63] 1.571 Å C-H bond lengths [63] 1.109 Å C 1 -C 4 distance [62] 2.72 Å Due to the unusual structure of cubane its physical properties are quite different from other hydrocarbons ( Table 3). The perfect cubic arrangement of the carbon atoms results in an octahedral point group O h , with a high density of 1.29 g/cm 3 . ...
... The perfect cubic arrangement of the carbon atoms results in an octahedral point group O h , with a high density of 1.29 g/cm 3 . [62] The carbon-carbon distance of 1.571 Å is slightly longer than in unstrained alkanes (1.54 Å) and in cyclobutane (1.55 Å). [63] Further information can be deduced in comprehensive reviews [2,62,69] and book chapters, [70] each delivering a unique view onto chemistry`s platonic body par excellence. Figure 4. Bond length and internal C-C distance for the bridgehead carbons. ...
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Nonconjugated hydrocarbons, like bicyclo[1.1.1]pentane, bicyclo[2.2.2]octane, triptycene and cubane are a unique class of rigid linkers. Due to their similarity in size and shape they are useful mimics of classic benzene moieties in drugs, so-called bioisosteres. Moreover, they also fulfill an important role in material sciences as linear linkers, in order to arrange various functionalities in a defined spatial manner. In this review recent developments and usages of these special, rectilinear systems are discussed. Furthermore, we focus on covalently-linked, nonconjugated linear arrangements and discuss the physical and chemical properties and differences of individual linkers, as well as their application in material and medicinal sciences.
... In accordance with calculation by the DFT B3PW91/QZVP method, the carbon-carbon bond lengths in the cubane molecule are 156.1 pm, the carbon-hydrogen bonds are 108.7 pm, the bond angles are 90.0° and 125.2°, for CCC and CCH, respectively. These values are in very good agreement with the experimental values of these parameters found in [46,47] (157.1 pm, 108.2 pm, 90.0° and 125.0°, respectively). The noted good agreement allows us to assert that, using this method, it is possible to adequately describe the specificity of the dehydrogenation reaction of C8H8 to C8, including the molecular structures of intermediates and transient states TSn (so-called "activated complexes"). ...
... The indicated molecular structures are shown in Figure 4, some of their geometric parameters and negative frequency characteristic of the transient states TSn are presented in Table 3 In accordance with calculation by the DFT B3PW91/QZVP method, the carboncarbon bond lengths in the cubane molecule are 156.1 pm, the carbon-hydrogen bonds are 108.7 pm, the bond angles are 90.0 • and 125.2 • , for CCC and CCH, respectively. These values are in very good agreement with the experimental values of these parameters found in [46,47] (157.1 pm, 108.2 pm, 90.0 • and 125.0 • , respectively). The noted good agreement allows us to assert that, using this method, it is possible to adequately describe the specificity of the dehydrogenation reaction of C 8 H 8 to C 8 , including the molecular structures of intermediates and transient states TSn (so-called "activated complexes"). ...
Article
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Quantum-chemical calculation of most important parameters of molecular and electronic structures of octa-carbon C8 having cubic form (bond lengths, bond and torsion angles) using CCSD(T)/QZVP and DFT B3PW91/QZVP methods, has been carried out. NBO analysis data and HOMO/LUMO images for this compound are presented, too. Good agreement was found between the structural data obtained using the above two quantum-chemical methods and, also, with corresponding experimental data. Also, the standard thermodynamic parameters of formation of cubic C8 considered here, and namely standard enthalpy ΔfH0(298K), entropy Sf0(298K) and Gibbs’ energy ΔfG0(298K) of formation for this compound were calculated. By using this data, a theoretically possible variant of the synthesis of this compound by dehydrogenation of cubane C8H8 is considered, and the thermodynamic characteristics of each of the four stages of this process have been calculated. It is noted that each of the four stages of this process is characterized by a very high (about 500 kJ/mol) enthalpy of activation, as a result of that, for their realization within a sufficiently short time, the use of appropriate catalysts is necessary.
... Rights reserved. excellent agreement with the bond lengths determined from gas-phase electron diffraction [44] and using larger basis sets [12]. An early single-crystal x-ray diffraction analysis performed by Fleischer afforded a shorter bond length of 1.551(3) Å (CSD id CUBANE) [45] whereas a recent crystallographic study performed at low temperature (93 K) yielded average carbon-carbon distances of 1.5718(12) Å (CSD id CUBANE01) [46]. ...
... Hz is 3.0 Hz smaller than the value of 29.4 Hz estimated by Axenrod et al. [58] for a series of cubane derivatives. As far as this specific NMR parameter is concerned, a value of 37.49 Hz was obtained by Galasso [23] using the equation-of-motion (EOM) method and the experimental (gas-phase electron diffraction) structure determined by Hedberg et al. [44] while Krivdin [59] computed a value of 31.67 Hz using the second-order polarization propagation approach (SOPPA) and the geometry optimized at the B3LYP/6-311++G(2d,2p) level. From Table 3, we can see that all the persubstituted derivatives are characterized by slightly larger 1 J( 13 C 13 C) values than that of cubane. ...
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Using the quantum theory of atoms in molecules in combination with density functional theory, we investigate the charge densities of different cubane and hypercubane derivatives in which all the terminal hydrogen atoms of the title hydrocarbons are replaced by an equal number of substituents (F, Cl, Br, CH3, and NO2). The analysis of the charge densities of the bond, ring, and cage critical points indicates that these substituents have the ability to alter the charge density of the cubane skeleton, thereby enhancing the strain of its carbon–carbon bonds. Also, the change in the charge density as a function of the expansion and contraction of the cubane cage indicates that the persubstituted derivatives respond differently to the deformation of their carbon cages. A linear correlation between the one-bond nuclear spin–spin coupling constant ¹J(¹³C¹³C) and the charge densities calculated at the bond critical points suggests the possibility of employing this NMR parameter for studying the effects of substituents in cage hydrocarbons.
... With MM3, the structures of cyclobutane and related compounds were calculated fairly well, but the vibrational frequencies were not, especially, the CCC angle bending frequency. Also, two key compounds gave calculated structures that were not in very good agreement with the experimental data, cubane [9,10] and bicyclo[1.1.1]pentane [11]. ...
... A Ê , respectively. More recently, another investigation by gas phase electron diffraction [9,10] at 77 8C gave values of 1.573(2) and 1.114(6) A Ê . ...
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The MM4 force field has been extended to include cyclobutane and related molecules. Twenty-two compounds were examined. In addition to the structures, energy barriers, and heat of formation studies, the vibrational spectra of four molecules were examined and compared with the available data. Ab initio and density functional theory calculations were also carried out to help to resolve some experimental ambiguities. In general, the MM4 force field gives better results than did MM3.
... "…el desarrollo de los OGMs se ha dado en diferentes campos y disciplinas, y actualmente contamos con animales, plantas y microorganismos transgénicos…" Actualmente en México existen por lo menos 25 fármacos derivados de OGMs, además de importantes desarrollos como el de la insulina humana y la vacuna contra la hepatitis "B", por mencionar algunos (8). ...
... La longitud de la arista del cubano es de 1.5727 Å (Hedberg, 1991). Como para que te des una idea de lo pequeñísima que es esta molécula puedes tomar como referencia el modelo del cubo que construiste con tu cartón de leche, el cual será casi… ¡Veintidós y medio millones de veces más grande que el cubano! ...
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... 3,8 .0 4,7 ]octane, or more conveniently, cubane (1), and is the first of the five regular complex polyhedra to succumb to a considered chemical synthesis in 1964. 4 In the subsequent 50 years, the chemistry of this remarkable hydrocarbon and its many derivatives has been well developed and explored ( Figure 1). ...
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The fascination with elaborate molecular architectures that differ significantly from those ordinarily present in nature have motivated synthetic, physical organic, and theoretical chemists alike, to explore their distinct properties and to pursue novel applications. In addition, they noted that once the anion has been consumed, the amide can participate in an additional metalation, allowing for the access to doubly halogenated cubanes such as diiodocubecarboxamide. This was a significant discovery because the electron-withdrawing nature of cyano substituents on the cubane core with assistance from the amide moiety allows for a facile direct proton abstraction. It only requires a slight excess of base to give complete conversion. While the application of N,N-diisopropylcarboxamides were useful in the generation of lithiated cubane derivatives, in a variety of cases it was not advantageous to carry this functionality throughout the whole synthetic sequence.
... 8,9 Comparatively little attention has been paid to saturated hydrocarbons, in spite of the many advantages these groups lend in terms of solubility and toxicity. 10 Considering the geometry of cubane, it is noteworthy that the distance across the cube (the body diagonal) is 2.72 Å, which is almost equivalent to the distance across a benzene ring, i. e., 2.79 Å 11,12 which has led to renewed interest in it as an isostere in drug development. 13 Our interest in the cubane scaffold emerged from a search for rigid linking units which would inhibit electronic communication between bound electron transfer systems. ...
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Chapter
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Summary This document is part of Subvolume D ‘Molecules Containing Five or More Carbon Atoms’ of Volume 25 ‘Structure Data of Free Polyatomic Molecules’ of Landolt-Börnstein - Group II Molecules and Radicals. Substances contained in this document (element systems and chemical formulae) C8H8: Cubane.
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A calculation was carried out within the framework of self-consistent theory of finite perturbations SCPT INDO for coupling constants 13C-13C, and estimation was performed of orbital hybridization of carbon-carbon bonds in 30 carcass carbocycles: polyhedranes, prismanes, tricycloalkanes, and cubanes. We established that all the compounds studied to a certain degree possessed abnormally low s-character of the carbon-carbon bonds that decreased with growing dihedral angle and bond length.
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Disproving a textbook example for a very long C-C-bond: The reported 1.643 Angstrom central bond length in propellane 5-cyano-1,3-dehydroadamantane was structurally re-determined and "only" amounts to 1.584 Angstrom. While this value is well reproduced with ab initio methods, common density functional theory approaches perform less well. By comparison of a series of CCSD(T)/cc-pVTZ optimized [n.n.n]propellanes, the DFT and ab initio geometries are only consistent for non-inverted carbons (n>2). Large deviations from experimental geometries were also found for other molecules with atypical elec-tron density distributions, e. g., cubane, bicyclo[2.2.0]hexane, bicyclo[2.1.0]- and bicyclo[1.1.1]pentane, thereby presenting challenging structures for some common DFT implementations.
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Using density functional theory we design a molecular analog of the four-dimensional hypercube or tesseract which we called hypercubane. The title hydrocarbon (C40H24) is O-h-symmetric like cubane and is characterized by a double-shell architecture. The perfluorinated analog of hypercubane also is stable with a positive value of the electron affinity. Removal of the C-8 core from hypercubane yields a hollowed O-h-symmetric hydrocarbon with enough room to host a single atom/ion guest. The resonances of the NMR-active C-13 and H-1 nuclei have been computed so as to assist the spectroscopic identification of the predicted molecules.
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The electronic and structural properties of molecular and solid cubane have been studied by first-principles, self-consistent field total energy calculations. Calculated molecular properties such as equilibrium geometry and electronic and vibrational spectra are found to be in good agreement with experimental data. Structural parameters and the energetics of both the low-temperature, orientationally ordered and high-temperature, orientationally disordered or plastic phases of solid cubane are determined. The valence band of solid cubane is derived from the molecular states; the energy gap between the lowest unoccupied and highest occupied molecular orbital bands is rather large due to the saturated carbon atoms. The effect of alkali-metal-atom doping on the electronic energy bands is investigated. It is found that the metallic band of doped cubane is derived from the undoped solid cubane's lowest conduction band with a significant contribution from the alkali-metal atom.
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Results of calculations of thermodynamic properties (heat capacities, standard entropies, and enthalpies of formation) of some cage hydrocarbons of the general formula CnHn in the ideal-gas state are presented: tetrahedrane C4H4, triprismane C6H6, cubane C8H8, pentaprismane C10H10, hexaprismane C12H12, truncated tetrahedrane C12H12, heptaprismane C14H14, octaprismane C16H16, dodecahedrane C20H20, truncated octahedrane C24H24, and truncated cubane C24H24.
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The performance of various Density Functional Theory (DFT) functionals and additional frequency scaling for predicting cubane vibrational harmonic frequencies is evaluated. All studied DFT functionals give more accurate frequencies (i.e., in better agreement with experimental values) not only than Hartree-Fock calculations (as expected) but also better than performed localized MP2 (LMP2) calculations. This accuracy can be additionally enhanced by frequency scaling. The B3LYP, B3PW91 and SVWN functionals are best suited for evaluation of vibrational frequencies of cubane. However, SVWN functional performs more poorly than other DFT functionals in reproducing cubane geometry.
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Successful isolation and characterization of higher diamondoids has revitalized the interest in this compound [1]. Diamondoids represent a group of hydrocarbon molecules with a structure similar to part of a typical diamond structure. In fact, one can successively construct different diamondoids by excising from the diamond crystal lattice and saturating dangling carbon bonds with hydrogen atoms. Recent molecular simulation studies [2] reveal more details about this compound and suggest some possible applications in nanotechnology. Adamantane has important pharmaceutical applications. Adamantane and cyclopentane are also known as “plastic crystals” [3]. The theoretical challenge to simulate those diamondoids mainly comes from the system size. For instance, the smallest one, called adamantane (from αδααχ, the Greek word for diamond) is a tricyclodecane C10H16 (see Figure 10.1). Within the Hartree-Fock approximation and multiple-configuration interaction with a limited basis set, adamantane can be easily handled by much state-of-art software such as Molpro, Gaussian, and GAMES. In this respect, theoretical computations are much easier than those in transition metal oxide compounds and clusters where the electron correlation plays an important role. However, when the system size becomes larger, which is most like those in real experiments, a theoretical investigation becomes rather difficult, especially if one is interested in studying the properties at the first-principles level.
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Die Untersuchung von Verbindungen, die in der Natur nicht vorkommen, hat viel zum Verständnis der Bindungsverhältnisse und der Reaktivität in der Organischen Chemie beigetragen. Oft erhielt man im Laufe dieser Untersuchungen Substanzen, die man für undenkbar gehalten hatte. Das Cuban, ein Meilenstein in der Welt „unmöglicher” Verbindungen, zeigt eine reichhaltige Chemie voller unerwarteter Aspekte. Die vor kurzem begonnene Renaissance der Cubanchemie, die durch mögliche Anwendungen von Cubanverbindungen – beispielsweise als sehr energiereiche Treibstoffe – ausgelöst wurde, hat zu vielen neuen Erkenntnissen geführt. So wurde z. B. die erste Methode zur systematischen Substitution gespannter gesättigter Verbindungen und ein neuer Reaktionstyp der Metallierung von Arenen, der ortho-Magnesiierung, entwickelt. Reaktive Zwischenprodukte mit außergewöhnlichen Bindungs-parametern wurden charakterisiert: 1(9)-Homocuben, das Olefin mit der stärksten Verdrillung; Cuben, das Olefin, mit der stärksten Pyramidalisierung; das Cubyl-Kation, das einmal als das am wenigsten wahrscheinliche Kation gegolten hatte; das Cubylmethylradikal, ein gesättigtes Radikal, das sich innerhalb von Picosekunden umlagert, und viele andere außerge-wöhnliche Verbindungen. Sicherlich werden zukünftige Arbeiten auf dem Cubangebiet mindestens genauso viele – wahrscheinlich sogar mehr – Ergebnisse hervorbringen und zu einem tieferen Verständnis der Chemie beitragen.
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The outer valence ionization potentials, low-lying electronically excited states and nuclear spin-spin coupling constants of cubane have been investigated at ab initio level by using the outer valence Green function, random phase approximation and equations of motions approaches, respectively, which incorporate the main portion of the electron correlation effects. The theoretical results give an overall picture of these spectroscopic observables, which bear peculiar aspects stemming from the unique electronic structure of the cubic cage.
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It is relatively easy to predict the structural properties of a solid made of spherical molecules. However this is not the case for a solid composed of cubic molecules such as solid cubane. The cubic structure of the cubane molecule gives rise to many unusual solid state properties. Here we present a brief review of our X-ray and neutron scattering studies along with our model calculations of the structure and lattice dynamics of solid cubane. The low-temperature phase (below the transition temperature of 394 K) is rhombohedral with α = 72.69 ° and a = 5.20 Å. Surprisingly, the crystal structure of cubane in the orientationally-disordered phase is not cubic, but instead remains rhombohedral with α = 103.3 °, far from the fcc value of 60 °. The jump in lattice constant at this transition is 0.05 Å, which corresponds to a 5.4% volume expansion, among the largest ever observed. Neutron inelastic scattering measurements indicate that the librons lie higher in energy than do the phonons, but that they soften rapidly with increasing temperature. Remarkably, model calculations predict the correct low and hightemperature crystal structures, and reveal cubane to be a text-book example of a system with anisotropic large-amplitude collective motions in the disordered phase.
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Mean-square amplitudes of vibration were calculated using ab initio and density functional methods for benzene and cubane. Both 6-31G∗ and 6-311G∗∗ basis sets were employed. It was found that significant improvements were achieved when electron correlation was introduced, even if only at the local density functional level. The mean-square amplitudes calculated were not effected by the basis set used for benzene and slightly improved for the highly strained cubane molecule when the larger basis set was used. An attempt was also made to improve the calculated mean-square amplitudes by making use of scale factors found in the literature, which were developed to improve the calculated frequencies. It was found that only the SCF mean-square amplitudes were significantly improved.
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We have performed density functional calculations on the recently discovered energetic molecule, octanitrocubane C8(NO2)8. We predict a strongly exothermic dissociation energy and calculate the ionization potentials, electron affinities and vibrational spectra. We predict that the isolated molecule exhibits a symmetry which is higher than that found in the solid. The vibrational density of states shows strong Raman activity at low frequencies and strong IR intensities at high frequencies. We identify a low-energy anharmonic mode which is consistent with the experimentally assumed free torsional rotations of the NO2 groups about their respective C–N axes.
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In this paper, we show that first-principle calculations using a van der Waals density functional (vdW-DF) [M. Dion, H. Rydberg, E. Schroder, D. C. Langreth, and B. I. Lundqvist, Phys. Rev. Lett. 92, 246401 (2004)] permit the determination of molecular crystal structure within density functional theory (DFT). We study the crystal structures of hexamine and the platonic hydrocarbons (cubane and dodecahedrane). The calculated lattice parameters and cohesion energy agree well with experiments. Further, we examine the asymptotic accounts of the van der Waals forces by comparing full vdW-DF with asymptotic atom-based pair potentials extracted from vdW-DF. The character of the binding differs in the two cases, with vdW-DF giving a significant enhancement at intermediate and relevant binding separations. We analyze consequences of this result for methods such as DFT-D and question DFT-D's transferability over the full range of separations.
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A harmonic field for cubane is developed by means of the following experimental data from literature: vibrational frequencies for C8H8, sym-C8H6D2, sym-C8H2D6 and C8D8, in addition to three Coriolis constants of C8H8. As a part of this analysis a new iteration method was developed for simultaneous fitting of vibrational frequencies and first-order Coriolis constants of a three-dimensional symmetry block. The force constants were used to calculate the vibrational frequencies of all the twenty existing partially deuterated cubanes, in addition to the unsub-stituted (C8H8) and perdeuterated (C8D8) molecules. Also the first-order Coriolis constants, mean amplitudes of Vibration and perpendicular amplitude correction coefficients for selected cubane molecules are reported.
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A gaseous electron‐diffraction investigation of SOF4 has led to the discovery of four models in excellent agreement with experiment, all with molecular symmetry C2υ corresponding to replacement of an equatorial fluorine atom of a trigonal bipyramid with oxygen. The models differ largely in the relative magnitudes of the F(eq)⋅⋅⋅F(eq) and F(eq)⋅⋅⋅O distances and the F(ax)⋅⋅⋅F(eq) and F(ax)⋅⋅⋅O distances. The favored model has the following distance (ra), angle, and root‐mean‐square amplitude (la) values (parenthesized errors are 2σ): S☒O=1.403 Å (0.0032), S☒F(eq) = 1.552 Å (0.0043), S☒F(ax) = 1.575 Å (0.0038), F(eq)⋅⋅⋅F(eq) = 2.545 Å (0.0259), F(ax)⋅⋅⋅O = 2.121 Å (0.0073), F(eq)⋅⋅⋅O = 2.621 Å (0.0139), F(ax)⋅⋅⋅F(eq) = 2.204 Å (0.0050), F(ax)⋅⋅⋅ = 3.150 Å (0.0076), ∠F(eq)SF(eq) = 110.17°(1.82), ∠F(ax)SO = 90.65°(0.42), ∠F(ax)SF(eq) = 89.63°(0.24), ∠F(eq)SO = 124.91°(0.92), lS = O = 0.0367Å(0.0050),lS�F(eq) = lS�F(ax) = 0.0540Å(0.0029),lF(eq)...F(eq) = 0.0468Å(0.0124),lF(ax)...O = 0.0431Å(0.0055),lF(eq)...O = 0.0758Å(0.0192),lF(ax)...F(eq) = 0.0962Å(0.0074),andlF(ax)...F(ax) = 0.0611Å(0.0122).
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The electron-diffraction data of gaseous cubane are consistent with Oh symmetry and the two geometrical parameters have been determined: τα(CC) = 157.5(1) pm and τα(CH) = 110.0(6) pm. Root-mean-square amplitudes of vibration have been determined from the electron diiffraction data and they compare well with values calculated from a symmetry force field fitted to experimental frequencies. Contribution to the intensity from multiple scattering has been shown to be small but significant. The CC bond is much longer than in cyclobutane.
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A 1975 treatment of single-double multiple scattering of electrons by randomly oriented vapor-phase molecules is put on a firmer footing and extended to higher order. It is shown how to include effects of intramolecular Fresnel diffraction, as an electron scattered by one atom propagates to the next, without ever explicitly evaluating the scattered wave function in the target. Theoretically derived estimates are made of the limitations of the approach at various levels of approximation. Numerical calculations are compared as a function of energy and scattering angle with newly available high quality calculations by Kohl and Arvedson (KA). In the expected range of applicability — roughly, 10 keV and higher − the present approach yields results that are satisfactory and (unlike those of KA) inexpensive enough for use in routine electron diffraction analyses.
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Carboxylic acid esters derived from N-hydroxypyridine-2-thione undergo efficient radical chain decarboxylation to the corresponding nor-alkane on treatment with either tri-n-butylstannane or t-butylmercaptan; in the absence of these hydrogen atom donors a smooth decarboxylative rearrangement giving noralkyl 2-pyridyl sulphides is observed.
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The geometry, complete harmonic force field, and dipole moment derivatives of cubane, C8H8, have been calculated at the Hartree-Fock level using a 4–21 Gaussian basis set. The infrared and Raman spectra of cubane and four deuterated derivatives were calculated and compared with previously observed spectra. A set of five scale factors for the calculated force constants was then derived by least-squares fitting of the fundamental vibrational frequencies calculated from the scaled force field to the frequencies obtained by direct experimental measurement. The resulting scaled quantum-mechanical (SQM) force field, containing 73 unique elements, is believed to give an accurate representation of the harmonic vibrational potential of cubane. In most cases, the spectral assignments previously made from purely empirical considerations were confirmed, but a few corrections are proposed. The only major alteration is for an A2u mode revised to appear at 1030 cm−1 in the undeuterated molecule. Coriolis constants and approximate infrared intensities are also calculated.
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The equilibrium geometry and vibrational frequencies of cubane have been studied with accurate ab initio SCF calculations. The calculations confirm the cubic symmetry of the molecule, and the computed bond distances RCC = 1.570 Å, RCH = 1.081 Å compare well with experiment. Intensities and depolarization ratios have also been calculated for the Raman-active fundamentals. The orbital energies are discussed in relation to the photoelectron spectrum.
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The reactive properties of cubane, homocubane, and bishomocubane have been studied by means of their calculated electrostatic potentials and bond paths. These were computed by using ab initio SCF-MO STO-5G wave functions, based on optimized structures Significant negative potentials are associated with the strained C-C bonds. A quantitative measure of their strain is obtained from their bond paths and the defined "bond deviation index". The rotation of C-H bonds away from the adjoining C-C bonds which increases the strain around the carbon, enlarges and strengthens the corresponding negative regions and focuses them upon carbon sites. An interesting feature of such rotations is that they also strengthen negative regions opposite to the site of the C-H rotation. The strained, cubane-like portion of homocubane, especially the bonds of the type C4-C8 (II) is predicted to be the single most reactive region (toward electrophiles) in these molecules, followed by cubane itself. These conclusions are fully consistent with the experimentally observed behavior of cubane and homocubane in undergoing rearrangements catalyzed by transition-metal ions. The present study demonstrates again, however, that there is no simple universal correlation between the degree of strain in a bond and its electrostatic potential.
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Incoherent scattering factors for all spherically symmetric free atoms have been computed from numerical SCF Hartree—Fock wavefunctions. The complete Waller—Hartree theory with all exchange terms has been used.
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Vibrational spectra are reported for cubane, cubane-d1, sym-cubane-d2, sym-cubane-d6, and cubane-d8. Infrared spectra are from 400 to 3600 cm-1 for CS2 and CCl4 solutions, and for a solid deposited from the vapor at ∼100 K. Raman spectra are for the same solutions and for the polycrystalline solid at room temperature. Vibrational assignments have been made for all the fundamentals of all five compounds, 120 modes in all. The fortuitous crystal structure of cubane and cubane-d8 was an important aid. Of the 18 fundamentals of cubane, only one or two are not certain. The spectra show almost no effect of the severe bond angle strain. Also there are no low molecular modes; the lowest for cubane is 617 cm-1.
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The use of ab initio molecular orbital calculations to predict accurate geometries and heats of formation has been studied for cyclohexane, cubane, adamantane, and dodecahedrane at the SCF level with use of the basis sets STO-3G, 4-31G, and 6-31G*. Good agreement with experiment is obtained for geometries in all cases. In the 6-31G* basis set, heats of formation of cyclohexane, adamantane, and cubane are in error by 0.5, 2.1, and 9.9 kcal/mol, respectively; for dodecahedrane, the heat of formation is predicted to be -5.0 kcal/mol. This work has been somewhat hampered by the unreliability of experimental thermochemical data.
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Confirmation of the octahedral symmetry and improved bond length measurements are obtained from high-resolution tunable laser spectra of the three infrared-active fundamental vibrations of cubane in the vapor phase. The C-H stretching band (ν10) was recorded with a difference-frequency laser and is found to be severely perturbed by a second-order Coriolis resonance with another nearby (nominally inactive) C-H stretch. The C-H bend (ν11) and the C-C stretch (ν12), which were studied with diode lasers, are relatively unperturbed, revealing the symmetry from the nuclear spin weight intensities of the ro-vibrational clusters and the bond lengths from an analysis of the rotational fine structure. The data also provided the f1u-block ζ constants, which have been used, together with vibrational fundamentals from an earlier solid-state study of cubane and its isotopic derivatives, to determine a quadratic force field for the molecule which results in some minor reassignments of the modes.
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A theoretical analysis of properties of eight alkanes, four cycloalkanes, seven bicycloalkanes, four propellanes and cubane, tetrahedrane, and spiropentane is presented, based on properties of charge distributions derived from 6-31G* wave functions. Molecular structures are assigned, and a bridgehead bond is found to be present in each of the propellanes. The shortcomings of using density deformation maps or selected sets of orbitals to assign a molecular structure are discussed. Bonds are characterized in terms of a bond order, a bond ellipticity, and the differing extents to which charge is locally concentrated and depleted as determined by the Laplacian of rho. Bond orders range from 0.7 to 1.3 in the propellanes. Ellipticities of bonds in three-membered rings - a measure of the tendency for charge density to be preferentially accumulated in a given plane - are found to exceed that for the double bond in ethylene. This property and the Laplacian of rho are used to account for the relative reactivities and structural stabilities of molecules containing small rings. The difference between the bond angle and the corresponding angle formed by bond paths provides a measure of the degree of relaxation of the charge density away from the geometrical constraints imposed by the nuclear framework. The bond path angle is found to exceed the geometrical angle by 23° in spiropentane, 21° in tetrahedrane, 19° in cyclopropane, and -1.5° in cyclohexane. The lowest energy transition densities in the propellanes are used to describe the charge reorganizations accompanying the most facile of the nuclear motions in these molecules.
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A new molecular mechanics force field (called MM3) for the treatment of aliphatic hydrocarbons has been developed and is presented here. This force field will enable one to calculate the structures and energies, including heats of formation, conformational energies, and rotational barriers, for hydrocarbons more accurately than was possible with earlier force fields. In addition to simple molecules, a great many highly strained molecules have been studied, and the results are almost always of experimental accuracy.
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Extensive SCF calculations are reported for the structures of cubane, cubene, and the cubyl radical. An estimate is provided for the energy required for scission of a C-H bond in cubane and a β C-H bond in the cubyl radical. The energetics of both of these reactions are used to understand the geometry of the cubyl radical.
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A spectroscopic method has been developed to observe rotational spectra of molecules in the millimeter- and submillimeter-wave regions. Advantages and disadvantages of the method are discussed and compared to those of Stark-modulation and Fourier-transform spectroscopy in the centimeter-wave region. As examples of the method's applicability, the results for cubane-d and cis and trans cyclobutane-1,2-d2 are presented. The transitions of J = 14 ← 13 up to 26 ← 25 are observed for cubane-d, yielding the rotational and centrifugal distortion constants B0 = 3220.720 08 (85) and DJO = 0.000 180 99 (93) MHz; values in parentheses represent three standard deviations. Trans cyclobutane-1,2-d2 is found to exist in an equatorial-equatorial and an axial-axial conformation, with only the b-dipole component being nonvanishing, as expected from previous results on the structure of cyclobutane. The observed spectra lead to the rotational constants A = 9 794.3831 (58), B = 9 758.3272(56), and C = 5 782.6540(73) and A = 9 738.242 (15), B = 9 693.452(14), and C = 6 048.564 (14) MHz, for the two forms, respectively; values in parentheses again represent three standard deviations. Cis cyclobutane-1,2-d2 is expected to exist in two equivalent forms, axial-equatorial and equatorial-axial. The observed spectrum exhibits the effect of puckering. Preliminary values of the rotational constants are A = 9 938.757 (47), B = 9 577.008(47), and C = 5 913.212(41) MHz.