Ih Point Group Research Articles

Au30Si12: A DFT study of the pentakis icosidodechedron

A stable hollow cage containing 30 gold atoms and 12 silicon atoms, Au30Si12, has been studied using density functional theory and compared with the icosahedral Au42. The results show that the Au42 cage is an icosahedron structure which is composed of 20 trigonal-planar faces, and it has 12 vertexes. The Au30Si12 is pentakis icosidodechedron structure constructed by 80 triangular faces and it has 42 vertexes. This Au30Si12 molecular cluster also is Ih point group symmetry. The doped Si atoms make the Au30Si12 clusters more compact and enhance the stability of gold fullerence. The p-d hybridizations between Si and Au atoms play a significant role in forming the cagelike structure. The HOMO-LUMO gap is only 0.18eV, suggesting its chemical activities. Therefore, the hollow space within Au30Si12 can be used to accommodate foreign atoms and emphasizes the benefit of studying endohedral fullerenes and may have potential applications in semiconductor and microelectronic industry.

Influence of Antipodally Coupled Iodine and Carbon Atoms on the Cage Structure of 9,12-I2-closo-1,2-C2B10H10: An Electron Diffraction and Computational Study.

Because of the comparable electron scattering abilities of carbon and boron, the electron diffraction structure of the C2v-symmetric molecule closo-1,2-C2B10H12 (1), one of the building blocks of boron cluster chemistry, is not as accurate as it could be. On that basis, we have prepared the known diiodo derivative of 1, 9,12-I2-closo-1,2-C2B10H10 (2), which has the same point-group symmetry as 1 but in which the presence of iodine atoms, with their much stronger ability to scatter electrons, ensures much better structural characterization of the C2B10 icosahedral core. Furthermore, the influence on the C2B10 geometry in 2 of the antipodally positioned iodine substituents with respect to both carbon atoms has been examined using the concerted application of gas electron diffraction and quantum chemical calculations at the MP2 and density functional theory (DFT) levels. The experimental and computed molecular geometries are in good overall agreement. Molecular dynamics simulations used to obtain vibrational parameters, which are needed for analyzing the electron diffraction data, have been performed for the first time for this class of compound. According to DFT calculations at the ZORA-SO/BP86 level, the (11)B chemical shifts of the boron atoms to which the iodine substituents are bonded are dominated by spin-orbit coupling. Magnetically induced currents within 2 have been calculated and compared to those for [B12H12](2-), the latter adopting a regular icosahedral structure with Ih point-group symmetry. Similar total current strengths are found but with a certain anisotropy, suggesting that spherical aromaticity is present; electron delocalization in the plane of the hetero atoms in 2 is slightly hindered compared to that for [B12H12](2-), presumably because of the departure from ideal icosahedral symmetry.

Algorithms for computer detection of symmetry elements in molecular systems

Simple procedures for the location of proper and improper rotations and reflexion planes are presented. The search is performed with a molecule divided into subsets of symmetrically equivalent atoms (SEA) which are analyzed separately as if they were a single molecule. This approach is advantageous in many aspects. For instance, in those molecules that are symmetric rotors, the number of atoms and the inertia tensor of the SEA provide one straight way to find proper rotations of any order. The algorithms are invariant to the molecular orientation and their computational cost is low, because the main information required to find symmetry elements is interatomic distances and the principal moments of the SEA. For example, our Fortran implementation, running on a single processor, took only a few seconds to locate all 120 symmetry operations of the large and highly symmetrical fullerene C720, belonging to the Ih point group. Finally, we show how the interatomic distances matrix of a slightly unsymmetrical molecule is used to symmetrize its geometry.

C60+ and B80+: A Comparative Study of the Jahn-Teller Effect

The ground state wave function of the neutral icosahedral C60 and B80 belong to the totally symmetric representation, where the HOMOs are fivefold degenerate and form the basis of the Hu representation of the Ih point group. Hence both C60+, and B80+ are prone to a molecular distortion of the Jahn-Teller type. Density Functional Theory calculation is applied and revealed that a minimum energy configuration in D5d point group is obtained for C60+; whereas a slight S6 distortion of a D3d nuclear configuration is obtained for B80+. Thus the vibronic coupling between the 2Hu electronic states of both systems with the degenerate normal modes in the Ih point group are analysed and presented here in a comparative point of view. Moreover, a simple and efficient procedure, which is fully non-empirical, based on the harmonic approximation, is presented in order to calculate the Jahn-Teller parameters and the first order vibronic coupling coefficient.

Density functional theory study of the multimode Jahn‐Teller problem in the fullerene anion

AbstractThe fullerene anion, C60−, within the Ih point group, is a spherical molecule subject to the T ⊗ h Jahn–Teller (JT) distortion. The descent in symmetry goes to the three epikernel subgroups, namely D5d, D3d, and D2h. The last one completely removes the electronic degeneracy, whereas D5d and D3d structures are subject to further JT distortion, leading to C2h minimum energy structure. The multideterminantal density functional theory approach was applied to calculate the JT parameters for all seven different structures of lower symmetry. The multimode problem in this system was addressed using the intrinsic distortion path method, in which the JT distortion is expressed as a linear combination of all totally symmetric normal modes in the particular low symmetry minimum energy conformation. Results obtained by both methods are consistent and give direct insight into the coupling of electronic distribution and nuclear movements in C. © 2012 Wiley Periodicals, Inc.

Enumeration of a class of IPR hetero-fullerenes

Hetero-fullerenes are fullerenes in which some of the carbon atoms are replaced by other atoms. This paper uses the P?lya theorem to count the number of their possible positional isomers and chiral isomers. To do this, the computer algebra system GAP was applied to compute this number for a class of IPR hetero-fullerenes with Ih point group symmetry. These fullerenes were constructed by means of the leapfrog principle.

Enumeration of a class of IPR hetero-fullerenes

Hetero-fullerenes are fullerenes in which some of the carbon atoms are replaced by other atoms. This paper uses the Pólya theorem to count the number of their possible positional isomers and chiral isomers. To do this, the computer algebra system GAP was applied to compute this number for a class of IPR hetero-fullerenes with Ih point group symmetry. These fullerenes were constructed by means of the leapfrog principle.

Optimization of bimetallic Cu–Au and Ag–Au clusters by using a modified adaptive immune optimization algorithm

A modified adaptive immune optimization algorithm (AIOA) is designed for optimization of Cu-Au and Ag-Au bimetallic clusters with Gupta potential. Compared with homoatom clusters, there are homotopic isomers in bimetallic cluster, so atom exchange operation is presented in the modified AIOA. The efficiency of the algorithm is tested by optimization of Cu(n)Au(38-n) (0 < or = n < or = 38). Results show that all the structures with the putative global minimal energies are successfully located. In the optimization of Ag(n)Au(55-n) (0 < or = n < or = 55) bimetallic clusters, all the structures with the reported minimal energies are obtained, and 36 structures with even lower potential energies are found. On the other hand, with the optimized structures of Cu(n)Au(55-n), it is shown that all 55-atom Cu-Au bimetallic clusters are Mackay icosahedra except for Au55, which is a face-centered cubic (fcc)-like structure; Cu55, Cu12Au43, and Cu1Au54 have two-shell Mackay icosahedral geometries with Ih point group symmetry.

The Chirality of Icosahedral Fullerenes: a Comparison of the Tripling (leapfrog), Quadrupling (chamfering), and Septupling (capra) Transformations

Fullerene polyhedra of icosahedral symmetry have the midpoints of their 12 pentagonal faces at the vertices of a macroicosahedron and can be characterized by the patterns of their hexagonal faces on the (triangular) macrofaces of this macroicosahedron. The numbers of the vertices in fullerene polyhedra of icosahedral symmetry satisfy the Goldberg equation v=20(h2+hk+k2), where h and k are two integers and 0 <h≥ k≥ 0 and define a two-dimensional Goldberg vector G = (h, k). The known tripling (leapfrog), quadrupling (chamfering), and septupling (capra) transformations correspond to the Goldberg vectors (1, 1), (2, 0), and (2, 1), respectively. The tripling and quadrupling transformations applied to the regular dodecahedron generate achiral fullerene polyhedra with the full Ih point group. However, the septupling transformation destroys the reflection operations of the underlying icosahedron to generate chiral fullerene polyhedra having only the I icosahedral rotational point group. Generalization of the quadrupling transformation leads to the fundamental homologous series of achiral fullerene polyhedra having 20 n2 vertices and Goldberg vectors (n, 0). A related homologous series of likewise achiral fullerene polyhedra having 60 n2 vertices and Goldberg vectors (n, n) is obtained by applying the tripling transformation to regular dodecahedral C20 to give truncated icosahedral C60 followed by the generalized operations (as in the case of quadrupling) for obtaining homologous series of fullerenes. Generalization of the septupling (capra) transformation leads to a homologous series of chiral C20m fullerenes with the I point group and Goldberg vectors G=(h, 1) where m=h2+h+1.

Application of the Correlation Method to Vibrational Spectra of C60 and Other Fullerenes: Predicting the Number of IR- and Raman-Active Bands

The C60 molecule (Buckyball/soccer ball) exhibits only 4 IR and 10 Raman bands although it possesses 174 (3 x 60 - 6) normal vibrations. This striking reduction in the number of observed bands is evidently due to the molecule's extremely high symmetry (Ih point group). First, the 120 symmetry elements of its truncated icosahedral structure are identified and the local (site) symmetry of the carbon atoms (Cc) is determined. Use of molecular models greatly facilitates the process in determining the local and molecular symmetries. Then the correlation method is used to derive a table that classifies the 174 normal vibrations into the respective symmetry species of the Ih point group. In this method, symmetry properties of atomic displacements in terms of the local point group (Cc) are correlated with those in terms of the molecular point group (Ih). After the normal vibrations are classified into respective symmetry species, the numbers of IR- and Raman-active vibrations can be determined by the symmetry selection rules for IR and Raman spectra. The vibrational spectra of C60 and C70 (rugby ball) are analyzed by the above procedure, and the results obtained for C28, C32, C50, and dodecahedrane are provided.

Resonance Raman Scattering from Solutions of C60

The resonance Raman (RR) spectrum of C60 has been studied in benzene and carbon disulfide using eight excitation wavelengths between 406.7 and 647.1 nm. Raman excitation profile calculations have been performed on the five most intense RR bands; the Hg(1), Ag(1), Gg(4), Hg(7), and Ag(2) vibrational modes. Two main scattering mechanisms predominate, Herzberg−Teller (HT) B-term scattering and nonadiabatic D-term scattering. This is the first observation of rare D-term scattering in a system without a metal. The requirement of a Jahn−Teller distortion of the excited state, produced upon population of the degenerate T1u LUMO, is essentially negated by solvent distortion of the symmetry of C60. While the Ih point group is a good descriptor for the 10 fundamental Raman modes of C60, the slight reduction in the high symmetry of the molecule, due to solvent and 13C effects, activates at least 6 of the remaining 36 Raman-silent modes. At resonance with the HOMO−LUMO transition of C60, or its vibronic sideband, the...

Unit Subduced Cycle Indices with and without Chirality Fittingness for Ih Group. An Application to Systematic Enumeration of Dodecahedrane Derivatives

Abstract Subduction of the coset representations of Ih point group produces tables of unit subduced cycle indices (USCIs) with and without chirality fittingness (CF). These indices are applied to the enumeration of dodecahedrane derivatives with respect to their molecular formulas as well as to their symmetries. The USCIs are effective to the enumeration of such derivatives as having only achiral substituents on the vertices of a dodecahedrane skeleton. On the other hand, the USCI–CFs are used for enumerating dodecahedrane derivatives with achiral and chiral substituents. Substitutions on the edges of the dodecahedrane skeleton are also discussed in terms of the present USCI approach.