Theoretical study of fullerene derivatives: C28H4 and C28X4 cluster molecules

Based on the basic theory of C₂₈ cluster molecule proven by H. W. Kroto and the research findings of C₂₈'s derivative such as Ti@C₂₈* and Mg@C₂₈, proven by T. Guo, B. I. Dunlap, O. D. Haberlen, and others, we examine the two series fullerene derivatives, C₂₈H₄ and C₂₈X₄ cluster molecules, which are formed by the skeleton of C₂₈ cluster molecule. In this work, we not only prove that C₂₈ cluster molecule belongs to the T_d symmetry structure and its ground state is ⁵A₂ open-shell with four unpaired electrons, but also find that C₂₈ can easily react with single valence electron atoms, like hydrogen atom and halogen atoms, to be formed to stable fullerene derivatives, C₂₈H₄ and C₂₈X₄ cluster molecules (X=F, Cl, Br, I). The PM3 semiempirical molecular orbital method from G94W and Hyperchem program packages were applied very well in these fullerene derivatives. According to the results presented herein, we obtain the structures of geometrical optimization, ionization potential energy gap, heat of formation, atomization energy, and vibration frequency data of the C₂₈H₄ and C₂₈X₄ cluster molecules. The above calculation data confirm that these unknown fullerene derivatives are stable molecules; the stable behavior resembles the 1,3,5,7-tetrahaloadamantane molecules. It is quite possible that they can be synthesized experimentally in the near future. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 67: 187–197, 1998     

Theoretical study of two C50H40 isomers with three dodecahedrane cages sharing two pentagons

Structures, energies, and vibrational frequencies have been calculated for two C₅₀H₄₀ isomers with three dodecahedrane cages sharing two pentagons at the B3LYP/6‐31G* level of theory. Thus, two C₅₀H₄₀ isomers have the form of coplanar tri‐dodecahedrane‐cage molecules. The symmetry of one isomer is D_5d and that of another is C_2V. Heats of formation and vertical ionization energies for two C₅₀H₄₀ isomers have been estimated in this study. Heats of formation as well as vibrational analysis indicate that two C₅₀H₄₀ isomers enjoy sufficient stability to allow for its experimental preparation. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Conformational study of C24 cyclic polyyne clusters

Polyynes were first synthesized before the year 1900, and isolated and characterized after 2000. Cyclic polyynes are of particular interest since possess a high order of symmetry. Furthermore, some studies reported special mechanical properties of the condensed polyyne bulks. The optimal size of polyynes to form rings has been previously investigated and was found to be 24 with a stable cluster of crossing four C₂₄ cyclic polyynes. We investigated in this study the conformation of clusters of polyynes (nC₂₄) by the pattern previously identified to stabilize the cluster. Clusters of 4C₂₄, 10C₂₄, 22C₂₄, 46C₂₄, and 94C₂₄ were designed and subjected to energy minimization. The main finding is the preservation of the symmetry for the nC₂₄ cluster with the increase of its size. The study revealed that 4C₂₄, 10C₂₄, and 22C₂₄ preserve a high symmetry and the calculations suggest an excellent increasing of the cluster stability with the increase of the number of polyyne rings. A 22C₂₄ derived cluster namely 28C₂₄ was found as the one likely to limit the growth of the polyyne clusters.     

Density functional study of tricyclo[3,3,1,13,7]decane and tricyclo[3,3,1,13,7]decsilane and their halogen derivatives

The B3LYP/3‐21G* ab initio molecular orbital method from the Gaussian 94 computer program package was applied to study tricyclo[3,3,1,1^3,7]decane and tricyclo[3,3,1,1^3,7]decsilane molecules and their halogen derivatives (1,3,5,7‐tetrahalotricyclo[3,3,1,1^3,7]decane and 1,3,5,7‐tetrahalotricyclo[3,3,1,1^3,7]decsilane, C₁₀H₁₂X₄, and Si₁₀H₁₂X₄). The optimized structures of these compounds were obtained. Ionization potentials, HOMO and LUMO energies, energy gaps, heats of formation, atomization energies, and vibration frequencies were calculated. These calculations indicate that these molecules are stable and have T_d symmetry. Tricyclo[3,3,1,1^3,7]decsilane and its halogen derivatives (Si₁₀H₁₂X₄) are found to have higher conductivity than that of tricyclo[3,3,1,1^3,7]decane and its halogen derivatives (C₁₀H₁₂X₄). 1,3,5,7‐Tetraflourotricyclo[3,3,1,1^3,7]decane (C₁₀H₁₂F₄) and 1,3,5,7‐tetraflourotricyclo[3,3,1,1^3,7]decsilane (Si₁₀H₁₂F₄) were found to be the easiest compounds to form and the most difficult to dissociate of all 1,3,5,7‐tetrahalotricyclo[3,3,1,1^3,7]decane and 1,3,5,7‐tetrahalotricyclo[3,3,1,1^3,7]decsilane compounds, respectively. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 72: 189–198, 1999     

Aromaticity of All Possible C26N2 Isomers

The aromaticity of all possible heterofullerenes C₂₆N₂ and C₂₈ based on T_d symmetry has been studied by means of the topological resonance energy and percentage topological resonance energy methods. The relationship between the aromaticity of the C₂₆N₂ isomers and the sites where nitrogen atoms dope at the C₂₈ cage has been discussed. The calculation results show that the most stable isomer of C₂₆N₂ derivatives is formed by nitrogen atoms doping at the two tetrahedral vertices. C₂₆N₂ isomers are more stable than C₂₈, but the C₂₆N₂^2? isomers are less stable than C₂₈ ^4?4. The effect of nitrogen substitution on C₂₈ stability was investigated by the topological charge stabilization rule.     

Stabilization Studies on Divalent Five‐Membered Rings C4H4C,C4H4Si,C4H4Ge,C4H4Sn,and C4H4Pb

Energy differences, ΔX_S‐t (X = E, H and G) (ΔX_S‐t = X_(singlet)‐X_(triplet)) between singlet (s) and triplet (t) states are calculated at B3LYP/6‐311++G (3df,2p). The DFT calculations show that the triplet state of C₄H₄C is a ground state with planar conformer respect to its corresponding nonplanar singlet state. Both singlet and triplet states of C₄H₄M (M = Si, Ge, Sn and Pb) have a planar conformer with the singlet ground state. Four isodesmic reactions are presented for determining the stability energies, SE. NICS calculations are carried out for C₄H₄M to determine the aromatic character.     

Stabilities,electronic properties of exohedral fluorine and trifluoromethyl derivatives for Td C28 fullerene C28F4–n(CF3)n (n = 0,1,2,3,4)

ABSTRACT: Stability and electronic property calculations are performed systematically based on density functional theory at the B3LYP/6‐31G(d) level for T_d C₂₈ fullerene and exohedral fluorine and trifluoromethyl derivatives C₂₈F_4–n(CF₃)_n (n = 0,1,2,3,4). All the exohedral derivatives that are on the potential energy surfaces are kinetically stable with large HOMO‐LUMO gaps. Further investigations show that binding energies of C₂₈F_4–n(CF₃)_n (n = 0,1,2,3,4) molecules are positive, suggesting they are thermodynamically stable. An analysis of the π‐orbital axis vector indicates the high strain in T_d C₂₈ cage could be greatly released by fluorine and trifluoromethyl decorations. Mulliken charge analysis reveals that adding different electron groups to the T_d C₂₈ cage can cause remarkably different charge populations. In addition, from the ionization potential and electron affinity investigations, the C₂₈F_4–n(CF₃)_n (n = 0,1,2,3,4) molecules manifest weak redox properties. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Sc2O@Td(19151)‐C76: Hindered Cluster Motion inside a Tetrahedral Carbon Cage Probed by Crystallographic and Computational Studies

A new cluster fullerene, Sc₂O@T_d(19151)‐C₇₆, has been isolated and characterized by mass spectrometry, UV/Vis/NIR absorption, ⁴⁵Sc NMR spectroscopy, cyclic voltammetry, and single‐crystal X‐ray diffraction. The crystallographic analysis unambiguously assigned the cage structure as T_d(19151)‐C₇₆, which is the first tetrahedral fullerene cage characterized by single‐crystal X‐ray diffraction. This study also demonstrated that the Sc₂O cluster has a much smaller Sc?O?Sc angle than that of Sc₂O@C_s(6)‐C₈₂ and the Sc₂O unit is fully ordered inside the T_d(19151)‐C₇₆ cage. Computational studies further revealed that the cluster motion of the Sc₂O is more restrained in the T_d(19151)‐C₇₆ cage than that in the C_s(6)‐C₈₂ cage. These results suggest that cage size affects not only the shapes but also the cluster motion inside fullerene cages.     

Simulation of the structure of some silicon carbide clusters by the MNDO method

Simulations of the geometric and electronic structure of C₄₄, C₄₅, Si₄₅, C₄₀Si₅, and C₄₄Si clusters were performed by the MNDO method. The geometries of the filled clusters, calculated by the MM2 method, were used as initial approximations. It was found that the filled clusters C₄₅ and C₄₄Si are transformed into endohedral clusters X@C₄₄ (X-C or Si, respectively) after energy optimization. The highest occupied energy level of the HOMO of the filled tetrahedral cluster Si₄₅ ofT symmetry is triply degenerate and is only occupied by four electrons. The structure of Si₄₅ ²⁻ dianion ofT symmetry was calculated. Two filled structures for the C₄₀Si₅ cluster were found. The coordination numbers of the central Si atom in these structures are 4 and 3, respectively. Translated fromIzvestiya Akademii Nauk, Seriya Khimicheskaya, No. 1, pp. 54–56, January, 1997.     

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.     

Crystal structures of four δ‐keto esters and a Cambridge Structural Database analysis of cyano–halogen interactions

The revived interest in halogen bonding as a tool in pharmaceutical cocrystals and drug design has indicated that cyano–halogen interactions could play an important role. The crystal structures of four closely related δ‐keto esters, which differ only in the substitution at a single C atom (by H, OMe, Cl and Br), are compared, namely ethyl 2‐cyano‐5‐oxo‐5‐phenyl‐3‐(piperidin‐1‐yl)pent‐2‐enoate, C₁₉H₂₂N₂O₃, (1), ethyl 2‐cyano‐5‐(4‐methoxyphenyl)‐5‐oxo‐3‐(piperidin‐1‐yl)pent‐2‐enoate, C₂₀H₂₄N₂O₄, (2), ethyl 5‐(4‐chlorophenyl)‐2‐cyano‐5‐oxo‐3‐(piperidin‐1‐yl)pent‐2‐enoate, C₁₉H₂₁ClN₂O₃, (3), and the previously published ethyl 5‐(4‐bromophenyl)‐2‐cyano‐5‐oxo‐3‐(piperidin‐1‐yl)pent‐2‐enoate, C₁₉H₂₁BrN₂O₃, (4) [Maurya, Vasudev & Gupta (2013). RSC Adv. 3 , 12955–12962]. The molecular conformations are very similar, while there are differences in the molecular assemblies. Intermolecular C—H...O hydrogen bonds are found to be the primary interactions in the crystal packing and are present in all four structures. The halogenated derivatives have additional aromatic–aromatic interactions and cyano–halogen interactions, further stabilizing the molecular packing. A database analysis of cyano–halogen interactions using the Cambridge Structural Database [CSD; Groom & Allen (2014). Angew. Chem. Int. Ed. 53 , 662–671] revealed that about 13% of the organic molecular crystals containing both cyano and halogen groups have cyano–halogen interactions in their packing. Three geometric parameters for the C—X...N[triple‐bond]C interaction (X = F, Cl, Br or I), viz. the N...X distance and the C—X...N and C—N...X angles, were analysed. The results indicate that all the short cyano–halogen contacts in the CSD can be classified as halogen bonds, which are directional noncovalent interactions.     

Two different modes of halogen bonding in two 4‐nitroimidazole derivatives

In the crystal structures of the two imidazole derivatives 5‐chloro‐1,2‐dimethyl‐4‐nitro‐1H‐imidazole, C₅H₆ClN₃O₂, (I), and 2‐chloro‐1‐methyl‐4‐nitro‐1H‐imidazole, C₄H₄ClN₃O₂, (II), C—Cl...O halogen bonds are the principal specific interactions responsible for the crystal packing. Two different halogen‐bond modes are observed: in (I), there is one very short and directional C—Cl...O contact [Cl...O = 2.899 (1) Å], while in (II), the C—Cl group approaches two different O atoms from two different molecules, and the contacts are longer [3.285 (2) and 3.498 (2) Å] and less directional. In (I), relatively short C—H...O hydrogen bonds provide the secondary interactions for building the crystal structure; in (II), the C—H...O contacts are longer but there is a relatively short π–π contact between molecules related by a centre of symmetry. The molecule of (I) is almost planar, the plane of the nitro group making a dihedral angle of 6.97 (7)° with the mean plane of the imidazole ring. The molecule of (II) has crystallographically imposed mirror symmetry and the nitro group lies in the mirror plane.     

Algebraic expressions of irreducible bases for molecules C20H20, C80, and C240

Using the symmetrized boson representation technique, concise algebraic expressions of the irreducible bases symmetry adapted to the group chain I_h⊃C₅ for the fullerene molecules C₂₀H₂₀, C₈₀, and C₂₄₀ are derived for the most general cases and those for any specific case can be derived from them easily without a projection procedure. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 73: 283–297, 1999     

Structural stability and energetics of C,Si, and Ge microclusters: empirical many-body potential energy function calculation

The structural stability and energetics of carbon, silicon, and germanium microclusters containing 3?7 atoms have been investigated by using a recently developed empirical many-body potential energy function (PEF), which comprises two- and three-body atomic interactions. The PEF satisfies both bulk cohesive energy per atom and bulk stability exactly. It has been found that the most stable C_3?4 microclusters are linear withD _∞h symmetry but C_5?7 microclusters are planar withD _nh symmetry. Silicon and germanium microclusters show similar structural stability. TheX _n (X=Si, Ge;n=3?7) microclusters are found to be most stable in the following forms:X ₃ is triangular withD _3h symmetry,X ₄ is tetragonal withT _d symmetry,X ₅ is square pyramidal withD _4h symmetry,X ₆ is bipyramidal square withO _h symmetry, and finallyX ₇ is square pyramidal having two atoms underneath withD _2h symmetry.     

Hydrogen uptake capacity of C2H4Sc and its ions: A density functional study

We report the gravimetric hydrogen uptake capacity of C₂H₄Sc complex and isoelectronic ions using Density Functional Theory. We predict that C₂H₄Sc⁺ can bind maximum seven hydrogen molecules in dihydrogen form giving gravimetric uptake capacity of 16.2 wt %, larger by about 2 and 4 wt % than the neutral and anion, respectively. We also found that the interaction of hydrogen molecules with C₂H₄Sc⁺ ion is characteristically different than that with neutral and anion. Vibrational spectroscopic study reveals that C₂H₄Sc and isoelectronic ions are quantum mechanically stable with their characteristic change in respective identified mode. The large gravimetric H₂ uptake capacity of C₂H₄Sc⁺ is well above the target specified by Department of Energy (DOE) by 2015. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Approximate symmetry characteristics using fuzzy-subset theory study for chiral transitions of allene-1,3,-dihalides

Based on our study of the application of fuzzy-subset theory to the characterization of imperfect symmetry in some stable molecular systems and simple dynamic molecular systems, we analyze the internal rotation process of allene-1,3- dihalides. Allene-1,3-dihalides (CHX=C=CHY, where X and Y may be the same or different halogen atoms) are optically chiral nonplanar molecules. The two end-groups may internally rotate about the near straight linear C=C=C axis, and the molecule may change its chirality. The internal rotation process may pass through two different planar transition state (TS): cis-TS and trans-TS, which belong to C_2v and C_2h point groups (as X and Y to be same), respectively. The intrinsic reaction coordinate (IRC) corresponding to the two TS processes is denoted as cis-IRC and trans-IRC. However, for the whole IRC reaction process, only their subgroup C₂ well-defined symmetry remains. Other symmetry transformations in C_2v and C_2h point groups can only be examined in terms of imperfect symmetry, although there appear certain reaction reversal joint point group G(R_cC_2v) and G(R_tC_2h) well-defined symmetry in the dynamics through the IRC processes. If X and Y are different, the stable molecule has no conventional nontrivial point group symmetry. The internal rotation processes may pass through two different planar TS’s (cis-and trans-TS). The TS will still be a planar molecule belonging to C_S point group with the molecule plane as its symmetry plane. Other states in the IRC may belong to certain reaction reversal joint point groups, G(RM)_C and G(RM)_T. We have thus examined the approximate symmetry of MO’s related to C₂ point group. Moreover, we have also analyzed the membership functions, representation components, and their relationships shown in the MO fuzzy main representation correlation diagrams.     

Low-temperature Heat Capacities and Thermodynamic Properties of the Solid State Complexes(C2H10N2)MCl4(s)(M=Cu and Cd)

The tetrachlorocuprate(II) ethylenediammonium and tetrachlorocadmate(II) ethylenediammonium were synthesized. Chemical analysis, elemental analysis, and X‐ray crystallography were applied to characterize the compositions and crystal structures of the two complexes. The lattice potential energies and the radiuses of the anions of two complexes were calculated to be U_POT[(C₂H₁₀N₂)CuCl₄]=1810.19 kJ·mol^?1, U_POT[(C₂H₁₀N₂)CdCl₄]=1784.39 kJ·mol^?1, r[(CuCl₄)^2?]=0.308 nm, and r[(CdCl₄)^2?]=0.321 nm from the data of the crystal structure, respectively. Low‐temperature heat capacities of the two complexes were measured by a precision automatic adiabatic calorimeter with the small sample over the temperature range from 78 to 400 K, respectively. Two polynomial equations of heat capacities against the temperatures were fitted by least square method: C_p,_m[(C₂H₁₀N₂)CuCl₄, s] =213.553+118.578X?5.816X²+4.392X³+0.276X⁴ and C_p,_m[(C₂H₁₀N₂)CdCl₄, s] =190.927+98.501X?7.931X²+0.657X³+3.834X⁴, in which X= (T?239)/161. Based on the fitted polynomial equations, the smoothed heat capacities and thermodynamic functions of the two complexes relative to the standard reference temperature 298.15 K were calculated at intervals of 5 K.     

[Mn12O12(O2CMe)12(NO3)4(H2O)4]: facile synthesis of a new type of Mn12 complex

The title dodecanuclear Mn complex, namely dodeca‐μ₂‐acetato‐κ²⁴O:O′‐tetraaquatetra‐μ₂‐nitrato‐κ⁸O:O′‐tetra‐μ₄‐oxido‐octa‐μ₃‐oxido‐tetramanganese(IV)octamanganese(III) nitromethane tetrasolvate, [Mn₁₂(CH₃COO)₁₂(NO₃)₄O₁₂(H₂O)₄]·4CH₃NO₂, was synthesized by the reaction of Mn²⁺ and Ce⁴⁺ sources in nitromethane with an excess of acetic acid. This compound is distinct from the previously known single‐molecule magnet [Mn₁₂O₁₂(O₂CMe)₁₆(H₂O)₄], synthesized by Lis [Acta Cryst. (1980), B 36 , 2042–2044]. It is the first Mn₁₂‐type molecule containing nitrate ligands to be directly synthesized without the use of a preformed cluster. Additionally, this molecule is distinct from all other known Mn₁₂ complexes due to intermolecular hydrogen bonds between the nitrate and water ligands, which give rise to a three‐dimensional network. The complex is compared to other known Mn₁₂ molecules in terms of its structural parameters and symmetry.     

First-principles investigation of structural,electronic, and optical properties of transition metal-doped C40 CrSi2

Although CrSi₂ silicide is an attractive advanced functional material, the improvement of electronic and optical properties is still a challenge for its applications. Here, we apply the first-principles calculations to investigate the influence of transition metals (TMs) on the electronic and optical properties of C40 CrSi₂ silicide. Five possible TMs, Ti, V, Pd, Ag, and Pt, are considered in detail. The calculated results show that the additive metals Ti, V, Pd, and Pt are thermodynamically stable in C40 CrSi₂ because the calculated impurity formation energy of TM-doped C40 CrSi₂ is lower than zero. In particular, the V dopant is more thermodynamically stable than that of the other TMs. The calculated electronic structure shows that the band gap of C40 CrSi₂ is 0.391 eV, which is in good agreement with the other results. In particular, the additive TMs improve the electronic properties of C40 CrSi₂ due to the role of the d-state of TMs. Naturally, the additive TMs result in band migration (Cr-3d state and Si-3p state) from the valence band to the conduction band. Interestingly, the additive TMs lead to a red shift for optical adsorption of C40 CrSi₂ silicide.     

Simultaneous Delamination and Rutile Formation on the Surface of Ti3C2Tx MXene for Copper Adsorption

In this work, we studied the formation of the rutile phase of titanium dioxide (TiO₂) on delaminated MXene (d‐Ti₃C₂T_x) flakes by the reaction of Ti₃C₂T_x with amino acids in water. Three types of amino acids with varied side‐chain polarity were used to delaminate Ti₃C₂T_x. d‐Ti₃C₂T_x flakes formed stable colloidal solutions due to the negative surface charges of chemisorbed amino acids on the d‐Ti₃C₂T_x. Rutile formed on d‐Ti₃C₂T_x at room temperature upon the intercalation of aromatic amino acids and subsequent sonication of the solution, while flakes intercalated with aliphatic amino acids did not oxidize. X‐Ray diffraction (XRD), transmission electron microscopy (TEM) and Raman spectroscopy revealed the nanosize rutile formation on the surface of Ti₃C₂T_x flakes. The XPS results indicated the surface functionalization of histidine on d‐Ti₃C₂T_x flakes. As‐synthesized histidine functionalized rutile TiO₂@d‐Ti₃C₂T_x hybrid was used for adsorption of Cu²⁺ ions from aqueous solution with a maximum uptake of 95 mg g^?1.