A MNDO study of carbon clusters with specifically fitted parameters

Summary A MNDO method with new parameters for carbon clusters is presented. The parameters in the new sets are specifically tuned to fit the properties of small carbon clusters, C₂, C₃, C₅ and C₇–C₁₀, and buckminsterfullerene, C₆₀. The validity of these MNDO parameters is verified by experimental data. The calculated (with new parameters) IR spectra of C₆₀ and the heat of formation, geometry and IR spectra of C₇₀ agree satisfactorily with observed data. Heats of formation of other fullerenes, from C₂₀ to C₈₄, and C₆₀O are evaluated. The resulting heats of formation of the isomers of C₇₆ and C₈₄ are reliable and their relative stability is in excellent agreement with other reports. The predicted IR spectra of several fullerenes, C₂₄(C_6v ), C₂₈(T _d ), C₃₂(D₃), C₃₆(D_6h ), C₅₀(C_5h ) and C₈₀(D_5d ) are provided to aid assignments of experimental spectra.     

Theoretical studies of C60/C70 fullerene derivatives: C60O and C70O

A semiempirical (AM1) calculation on the structures and stabilities of isomers of the fullerene derivatives C₆₀O and C₇₀O is carried out. The ozonolysis reaction mechanism and the thermodynamics of the compounds are studied. The two isomers of C₆₀O (56 bond and 66 bond) formed by an oxygen atom bridging across a C-C bond have an epoxide-like or an annulene-like structure. According to the ozonolysis reaction mechanism and kinetic factor analysis, the possible products of this ozonolysis reaction are C₆₀O with oxygen bridging over the 66 bond (C_2v) as an epoxide-like isomer and that with oxygen bridging over the 56 bond (C_s) as an annulene-like isomer. Further, the sixteen isomers of C₇₀O (both epoxide-like and annulene-like structures) have been studied with respect to the same reaction mechanism. The most possible product in this ozonolysis reaction contains oxygen bridging across in the upper part (66 bond in C₇₀O-2 or C₇₀O-4) as an epoxide-like structure. The other possible product is C₇₀O-8 (annulene-like structure), in which oxygen bridges across an broken equatorial CC bond in C₇₀ (D_5h). The vibrational frequency analysis and the electronic structure of the selected C₆₀O and C₇₀O isomers are generated for experimental characterisation. The experimental results indicate that C₆₀O and C₇₀O may decompose into the odd number fullerenes C₅₉ and C₆₉. We therefore studied the structures of C₅₉ and C₆₉ also.     

Theoretical identification of the lowest-energy structure of (SiC)12 heterocluster: Segregation of C and Si in planar and cage structures

The structures and relative stabilities of various plane and cage isomers of (SiC)₁₂ cluster have been systematically computed using density functional theory at the level of BLYP. A number of starting configurations were generated from the low-energy isomers of C₂₄ cluster via replacing 12 C atoms by Si atoms, which are D_6h planar structure, and the D_6d, D_2h, O_h, and D_4h symmetrical fullerene cages. The heterofullerene cage obeying six isolated squares rules are not the most preferred structural motif for (SiC)₁₂ cluster. The structural candidates with fully alternating Si–C arrangement are energetically unfavorable. Instead, the (SiC)₁₂ cluster tend to adopt plane, bowl, saddle, and highly distorted cage structures. In all cases, segregation of C atoms is a common feature.     

Effect of the bridging ligands on the CO stretching force constants of the compounds Co2(CO)6(μ-Y)2 and Fe2(CO)6(μ-X)2 (where Y = CO,P, As,CR and X = S,SR, Se,PRR′, Br,I)

The molecular structures of (C₅H₅)₂V and (C₅H₅)₂Cr have been determined by gas phase electron diffraction. The best agreement between calculated and experimental curves is obtained for models with eclipsed C₅H₅ rings (symmetry D_5h), but models with staggered rings (symmetry D_5d) cannot be definitely ruled out. The MC and CC bond distances are 2.169(4) and 1.431(2) Å respectively in (C₅H₅)₂Cr, and 2.280(5) and 1.434(3) Å respectively in (C₅H₅)₂V. The CH bonds in (C₅H₅)₂Cr are bent 2.9(1.1)° out of the plane of the carbon atoms towards the metal atom.The molecular structures of the known di-π-cyclopentadienyl compounds of the first row transition elements are compared in the light of what is known about their electronic structures.     

The Exohedral Diels–Alder Reactivity of the Titanium Carbide Endohedral Metallofullerene Ti2C2@D3h‐C78: Comparison with D3h‐C78 and M3N@D3h‐C78 (M=Sc and Y) Reactivity

The chemical functionalization of endohedral (metallo)fullerenes has become a main focus of research in the last few years. It has been found that the reactivity of endohedral (metallo)fullerenes may be quite different from that of the empty fullerenes. Encapsulated species have an enormous influence on the thermodynamics, kinetics, and regiochemistry of the exohedral addition reactions undergone by these species. A detailed understanding of the changes in chemical reactivity due to incarceration of atoms or clusters of atoms is essential to assist the synthesis of new functionalized endohedral fullerenes with specific properties. Herein, we report the study of the Diels–Alder cycloaddition between 1,3‐butadiene and all nonequivalent bonds of the Ti₂C₂@D_3h‐C₇₈ metallic carbide endohedral metallofullerene (EMF) at the BP86/TZP//BP86/DZP level of theory. The results obtained are compared with those found by some of us at the same level of theory for the D_3h‐C₇₈ free cage and the M₃N@D_3h‐C₇₈ (M=Sc and Y) metallic nitride EMFs. It is found that the free cage is more reactive than the Ti₂C₂@D_3h‐C₇₈ EMF and this, in turn, has a higher reactivity than M₃N@D_3h‐C₇₈. The results indicate that, for Ti₂C₂@D_3h‐C₇₈, the corannulene‐type [5, 6] bonds c and f , and the type B [6, 6] bond 3 are those thermodynamically and kinetically preferred. In contrast, the D_3h‐C₇₈ free cage has a preference for addition to the [6, 6] 1 and 6 bonds and the [5, 6] b bond, whereas M₃N@D_3h‐C₇₈ favors additions to the [6, 6] 6 (M=Sc) and [5, 6] d (M=Y) bonds. The reasons for the regioselectivity found in Ti₂C₂@D_3h‐C₇₈ are discussed.     

Electronic structure of C40 possible structures

C₄₀ is a fullerene with a conformation that has been proposed as T_d, D_2d, D_4h and D_5d symmetry groups. The correct structure has not been determined because it has not been possible to isolate the molecule, but there have been several studies of minor fullerenes that include it. In this work we present a theoretical study at the gaussian 94 HF/3-21G level that gives answers about the principal differences between the mentioned structures and the possible thermodynamic stability of each one. Furthermore, we include a similar study on the new D_2h structure that we propose.     

Symmetry of Kekulé structures

The symmetry of Kekulé structures for aromatic hydrocarbons is studied by group theory. The general problem of deducing the distribution over irreducible representations (Λ_Kek) or characters of the representation based on the Kekulé structures (χ_Kek) has not been solved. A partial solution is given for two classes of molecules, namely (a) the “straight chain” aromatics (polyacenes): naphthalene, anthracene, naphthacene, etc., and (b) the “zig-zag chain” aromatics: phenanthrene, chrysene, picene, etc. As a part of this solution the number of Kekulé structures (K) in the two cases was found to be (a) K = Q + 1 and (b) K = F_Q+1, respectively. Here Q is the number of benzene rings in the molecule in question, and F_i denotes the i-th member of the Fibonacci series. Symmetrical structures (Λ_Kek) or characters (χ_Kek) are given for a number of additional molecules as examples: benzene (D_6h), tetraphene (C_s), benzo[c] phenanthrene (C_2v), pyrene (D_2h), triphenylene (D_3h), perylene (D_2h), pentaphene (C_2v), dibenzophenanthrene (C_2v), heptaphene (C_2v) and coronene (D_6h). Here the appropriate symmetry groups are given in parentheses.     

The molecular structure of gaseous tetrafluoro-p-benzoquinone and tetramethyl-p-benzoquinone as determined by electron diffraction

The molecular structures of gaseous tetrafluoro-p-benzoquinone (p-fluoranil) and tetramethyl-p-benzoquinone (duroquinone) have been investigated by electron diffraction. Except for the methyl group hydrogen atoms, the molecules are planar to within experimental error, but small deviations from planarity are completely compatible with the data. Values for the geometrical parameters (r_adistances and r_α with parenthesized uncertainties of 2σ including estimated uncertainty in the electron wavelength and correlation effects, are as follows. Tetrafluoro-p-benzoquinone: D_2h symmetry (assumed); r(C0) = 1.211(6) Å, r(CC) = 1.339(12) Å, r(C-C) = 1.489(5') Å, r(C-F) = 1.323(5) Å, ∠C-C-C = 116.8(7)° and ∠C-C-F = 116.1(7)°. Tetramethyl-p-benzoquinone: C_2h symmetry (assumed);r(C-H) = 1.102(18) Å, r(CO) = 1.229(8) Å, r(CC) = 1.352(8) Å, r(C_sp2-C_sp2) = 1.491(11) Å, r(C_sp2-C_sp3) = 1.504(12) A, ∠C-CO-C = 120.8(8)°. ∠C-C-CH₃ = 116.1(8)°, ∠C-C-H = 110.5(34)° and α₁ = α₂ (methyl torsion = 30° (assumed).     

Unusual pentagon and hexagon geometry of three isomers (no 1, 20, and 23) of fullerene C84

Three isomers 23 (D_2d), 1 (D₂), and 20 (T_d) of fullerene C₈₄ have been investigated by PM3, HF/6‐31G*, and DFT methods with B3LYP functional at the 6‐31G and 6‐31G* levels. In this article we reveal for the first time that some distortion of hexagon (pentagon), measured as its maximal dihedral angles, caused by local molecular strains may serve as a new criterion of stability of fullerenes with closed shell. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Ab initio study of cyclic siloxanes (H2SiO)n: n = 3, 4, 5

The geometry optimizations for several conformations of tri-, tetra-, and pentacyclosiloxane (H₂SiO)_n (n = 3, 4, and 5) were carried out, and the relative stabilities were compared at the Hartree-Fock (HF) and second order perturbation theory (MP2) levels of theory using the 6–31G* and 6–311G(d, p) basis sets. At the highest levels of theory, the only minimum for n = 4 (D₄) occurs at the highly symmetric D_4h structure. In contrast, several, nearly isoenergetic, minima are found on the D₅ surface. These have C₁, C₂, C_s, and D_5h symmetries. While the C₁ structure has the lowest MP2/6–311G(d, p) energy, this species is predicted to be highly fluxional, and the distribution of isomers is dependent on temperature. © 1996 by John Wiley & Sons, Inc.     

New Trifluoromethylated Derivatives of Metal Nitride Clusterfullerenes: Sc3N@Ih‐C80(CF3)14 and Sc3N@D5h‐C80(CF3)16

Trifluoromethylated derivatives of Sc₃N@I_h‐C₈₀ and Sc₃N@D_5h‐C₈₀ were synthesized by the reaction with CF₃I at 440 °C. HPLC separation of the mixture of Sc₃N@D_5h‐C₈₀(CF₃)_n derivatives resulted in isolation and X‐ray structure determination of Sc₃N@D_5h‐C₈₀(CF₃)₁₆, which represents a precursor of the known Sc₃N@D_5h‐C₈₀(CF₃)₁₈. Among the CF₃ derivatives of Sc₃N@I_h‐C₈₀, two new isomers of Sc₃N@I_h‐C₈₀(CF₃)₁₄ ( Sc‐14‐VI and Sc‐14‐VII ) were isolated by HPLC, and their molecular structures were determined by X‐ray diffraction, thus enabling a comprehensive comparison of altogether seven isomers. Two types of addition patterns with different orientations of the Sc₃N cluster relative to the I_h‐C₈₀ fullerene cage were established. In particular, Sc‐14‐VII represents a direct precursor of the known Sc₃N@I_h‐C₈₀(CF₃)₁₆‐ II . All molecular structures exhibit an ordered position of a Sc₃N cluster inside the fullerene C₈₀ cage.     

Synthesis and Isolation of the Titanium–Scandium Endohedral Fullerenes—Sc2TiC@Ih‐C80, Sc2TiC@D5h‐C80 and Sc2TiC2@Ih‐C80: Metal Size Tuning of the TiIV/TiIII Redox Potentials

The formation of endohedral metallofullerenes (EMFs) in an electric arc is reported for the mixed‐metal Sc–Ti system utilizing methane as a reactive gas. Comparison of these results with those from the Sc/CH₄ and Ti/CH₄ systems as well as syntheses without methane revealed a strong mutual influence of all key components on the product distribution. Whereas a methane atmosphere alone suppresses the formation of empty cage fullerenes, the Ti/CH₄ system forms mainly empty cage fullerenes. In contrast, the main fullerene products in the Sc/CH₄ system are Sc₄C₂@C₈₀ (the most abundant EMF from this synthesis), Sc₃C₂@C₈₀, isomers of Sc₂C₂@C₈₂, and the family Sc₂C_{2 n} (2 n=74, 76, 82, 86, 90, etc.), as well as Sc₃CH@C₈₀. The Sc–Ti/CH₄ system produces the mixed‐metal Sc₂TiC@C_{2 n} (2 n=68, 78, 80) and Sc₂TiC₂@C_{2 n} (2 n=80) clusterfullerene families. The molecular structures of the new, transition‐metal‐containing endohedral fullerenes, Sc₂TiC@I_h‐C₈₀, Sc₂TiC@D_5h‐C₈₀, and Sc₂TiC₂@I_h‐C₈₀, were characterized by NMR spectroscopy. The structure of Sc₂TiC@I_h‐C₈₀ was also determined by single‐crystal X‐ray diffraction, which demonstrated the presence of a short Ti=C double bond. Both Sc₂TiC‐ and Sc₂TiC₂‐containing clusterfullerenes have Ti‐localized LUMOs. Encapsulation of the redox‐active Ti ion inside the fullerene cage enables analysis of the cluster–cage strain in the endohedral fullerenes through electrochemical measurements.     

Some aspects of the symmetry and topology of possible carbon allotrope structures

Elemental carbon has recently been shown to form molecular polyhedral allotropes known as fullerenes in addition to the familiar graphite and diamond known since antiquity. Such fullerenes contain polyhedral carbon cages in which all vertices have degree 3 and all faces are either pentagons or hexagons. All known fullerenes are found to satisfy the isolated pentagon rule (IPR) in which all pentagonal faces are completely surrounded by hexagons so that no two pentagonal faces share an edge. The smallest fullerene structures satisfying the IPR are the known truncated icosahedral C₆₀ of I _h symmetry and ellipsoidal C₇₀ of D _5h symmetry. The multiple IPR isomers of families of larger fullerenes such as C₇₆, C₇₈, C₈₂ and C₈₄ can be classified into families related by the so-called pyracylene transformation based on the motion of two carbon atoms in a pyracylene unit containing two linked pentagons separated by two hexagons. Larger fullerenes with 3ν vertices can be generated from smaller fullerenes with ν vertices through a so‐called leapfrog transformation consisting of omnicapping followed by dualization. The energy levels of the bonding molecular orbitals of fullerenes having icosahedral symmetry and 60n ² carbon atoms can be approximated by spherical harmonics. If fullerenes are regarded as constructed from carbon networks of positive curvature, the corresponding carbon allotropes constructed from carbon networks of negative curvature are the polymeric schwarzites. The negative curvature in schwarzites is introduced through heptagons or octagons of carbon atoms and the schwarzites are constructed by placing such carbon networks on minimal surfaces with negative Gaussian curvature, particularly the so-called P and D surfaces with local cubic symmetry. The smallest unit cell of a viable schwarzite structure having only hexagons and heptagons contains 168 carbon atoms and is constructed by applying a leapfrog transformation to a genus 3 figure containing 24 heptagons and 56 vertices described by the German mathematician Klein in the 19th century analogous to the construction of the C₆₀ fullerene truncated icosahedron by applying a leapfrog transformation to the regular dodecahedron. Although this C₁₆₈ schwarzite unit cell has local O _h point group symmetry based on the cubic lattice of the D or P surface, its larger permutational symmetry group is the PSL(2,7) group of order 168 analogous to the icosahedral pure rotation group, I, of order 60 of the C₆₀ fullerene considered as the isomorphous PSL(2,5) group. The schwarzites, which are still unknown experimentally, are predicted to be unusually low density forms of elemental carbon because of the pores generated by the infinite periodicity in three dimensions of the underlying minimal surfaces. This revised version was published online in July 2006 with corrections to the Cover Date.     

Expanding the Number of Stable Isomeric Structures of the C80 Cage: A New Fullerene Dy3N@C80

The production, isolation, and spectroscopic characterization of a new Dy₃N@C₈₀ cluster fullerene that exhibits three isomers ( 1 – 3 ) is reported for the first time. In addition, the third isomer ( 3 ) forms a completely new C₈₀ cage structure that has not been reported in any endohedral fullerenes so far. The isomeric structures of the Dy₃N@C₈₀ cluster fullerene were analyzed by studying HPLC retention behavior, laser desorption time‐of‐flight (LD‐TOF) mass spectrometry, and UV‐Vis‐NIR and FTIR spectroscopy. The three isomers of Dy₃N@C₈₀ were all large band‐gap (1.51, 1.33, and 1.31 eV for 1 – 3 , respectively) materials, and could be classified as very stable fullerenes. According to results of FTIR spectroscopy, the Dy₃N@C₈₀ (I) ( 1 ) was assigned to the fullerene cage C₈₀:7 (I_h), whereas Dy₃N@C₈₀ (II) ( 2 ) had the cage structure of C₈₀:6 (D_5h). The most probable cage structure of Dy₃N@C₈₀ (III) ( 3 ) was proposed to be C₈₀:1 (D_5d). The significant differences between Dy₃N@C₈₀ and other reported M₃N@C₈₀ (M=Sc, Y, Gd, Tb, Ho, Er, Tm) cluster fullerenes are discussed in detail, and the strong influence of the metal on the nitride cluster fullerene formation is concluded.     

Vibration spectra and NMR spectra of octahedral (Oh and O) fullerenes

On analyzing the topological structures of the three big types of octahedral fullerenes: (1) C_n(O_h, n=24h²; h=1, 2,…); (2) C_n(O_h, n=8h²; h=1, 2,…), and (3) C_n(O, n=8(h²+hk+k²); h>k, h, k=1, 2,…), we have obtained theoretically the infrared and Raman active modes by means of the derived formulas for the decomposition of their nuclear motions into irreducible representations and the NMR spectra by using the distribution functions for all of the octahedral (O_h and O) fullerenes, respectively. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 72: 199–205, 1999     

A study of electronic structures of some C9H9- carboanions

The electronic structures of five C₉H₉^-, carboanions have been studied by ab initio STO-3G calculations, and some general conclusions on related C₉H₉^- and C₉H₉⁺ structures are presented. Large antibonding interactions in one occupied MO make barbaral-9-yl anion (2) unstable as its cationic counterpart (8). The proposed D_9h-symmetrical cation and D_3h-symmetrical anion (3) do not exist due to Jahn-Teller distortions. A study of the MO correlations confirms that the two tetracyclic anions with C_2v symmetry (5 and 6) are the results of the Jahn-Teller distortions of 3. Anion 5 is identified as the proper intermediate of the Cope rearrangement of anion 2.     

The molecular structure of gaseous tetrachloro-p-benzoquinone and tetrachloro-o-benzoquinone by electron diffraction

The structures of tetrachloro-p-benzoquinone and tetrachloro-o-benzoquinone (p- and o-chloranil) have been investigated by gas electron diffraction. The ring distances are slightly larger and the carbonyl bonds slightly smaller than in the corresponding unsubstituted quinones. The molecules are planar to within experimental error, but small deviations from planarity such as those found for the para compound in the crystal are completely compatible with the data. Values for the geometrical parameters (r_a distances and bond angles) and for some of the more important amplitudes (l) with parenthesized uncertainties of 2σ including estimated systematic error and correlation effects are as follows. Tetrachloro-p-benzoquinone: D_2h symmetry (assumed); r(CO) = 1.216 Å(4), r(CC) = 1.353 Å(6), r(C-C) = 1.492 Å(3), r(C-Cl) = 1.701 Å(3), ∠C-C-C = 117.1° (7), ∠CC-C1 = 122.7° (2), l(CO)= 0.037 Å(5), l(CC) = l(C-C) - 0.008 Å(assumed) = 0.049 Å(7), and l(C-Cl) = 0.054 Å(3). Tetrachloro-o-benzoquinone: C_2v symmetry (assumed); r(CO) = 1.205 Å(5), r(CC) = 1.354 Å(9), r(C_cl-C_cl) = 1.478 Å(28), r(Co-C_cl) = 1.483 Å(24), r(C_o-C_o) = 1.526 Å(2), r(C-Cl)= 1.705 Å(3), <C_o-CO = 121.0° (22), ∠C-C-C = 117.2° (9), ∠C_co, ClC-Cl = 118.9° (22), ∠C_ccl, ClC-Cl = 122.2°(12), l(CO) = 0.039 Å(5), and l(C_cl-C_cl) = l(C_o-C_cl) = l( Co-Co) = l(CC) + 0.060 Å(equalities assumed) = 0.055 Å(9). Vibrational'shortenings (shrinkages) of a few of the long non-bond distances have also been measured.