Ih symmetry

It should be pointed out again that these layers would, of course, contain identical numbers of atoms if the triangular faces had not been rotated and, thus, the Ih-symmetry had been preserved[7]. The reason for preferring the arrangement with 1-symmetry (which can still be called icosahedral) is that it leads to higher coordination of the atoms at the borders between the triangular faces. 

Note that each of the C2 axes not only is coincident with a B-F bond but also is the line of intersection of the horizontal plane with one of the vertical planes. It is generally true that the intersection of a vertical plane of symmetry with a horizontal plane generates a C2 axis. The list of symmetry elements that we have found for the BF3 molecule includes one C3 axis, three vertical planes (horizontal plane (ah). A molecule possessing these symmetry elements, such as BF3, S03, C03 , and N03 , is said to have l)ih symmetry. In the cases of H20, C1F3, H2CO, and NH3, the symmetry elements included only a C axis and n vertical planes. These molecules belong to the general symmetry type known as C . Molecules that have a Cn axis and also have n C2 axes perpendicular to the C axis are known as Dn molecules. 

By observing the number and relative intensity of 13C resonances it is possible to identify to which point group an adduct belongs. For C60, with Ih symmetry, all 60 carbon atoms are equivalent, giving rise to a single sharp line at 143.3 ppm in C6D6. Complex formation causes a reduction in symmetry, and the fullerene carbon atoms become in-... 

Scuseria, G. E. Odom, G. K. 1992 Exo-fluoririated C60F60 has Ih symmetry. Chem. Phys. Lett. 195 531-533. 

The three-dimensional equi-charge density surface of the La2 C80 molecule is shown in Fig. 13. The equi-density level is 1.7 el A3. The obtained MEM charge density reveals six- and five-membered rings consistent with Ih symmetry of the C80 cage. Figures 13a and 13b represent the top views along the SI0 and C2 axis of... 

Having determined that it is very likely that six electrons are transferred to the C80 molecule - in agreement with the 13C NMR data which suggest Ih symmetry for the carbon cage [6] - it is now interesting to consider the valence band photoemission spectrum of the endohedral to see if the consequences of this high symmetry are visible in the energy distribution of the n-MO s of the system. 

On the other hand the Ih symmetry imposes no constraint on the lengths of the 6-6 and 6-5 bonds, other than that all 6-6 bonds must be identical and all 6-5 bonds must be identical. There are thus just two geometric degrees of freedom, and both can be represented by stretching force constants just as in planar hydrocarbons. 

Although it has been generally believed that molecules would never be found in icosahedral (Ih) symmetry (31, 32), we now know that such is not the case. There are at least three molecules possessing icosahedral symmetry. These are the borohydride anion (33) dodecahedrane, C20H20 (34), and the... 

Since the discovery of the soccer-ball-like, 60-carbon buckminsterfullerene, scientists have been fascinated by this molecule. The molecule possesses a truncated icosahedral structure, of Ih symmetry, and is depicted in Fig. 4-37. 

The Ih symmetry of the 60-atoms molecule allows 2Ag and SH modes to be Raman active and 4T modes to be IR active. The four IR active modes are at 1430, 1185, 580 and 528 cm , respectively. The most important Raman modes are at 1469 (tangential bond alternation or pinch mode, Ag), 495 (radial breathing mode, T ) and 271 (squashing mode, Hg) cm , respectively. In the low temperatur phase degenerate modes split from a crystal field and Davidov interaction. Good reviews on the group theoretical analysis and on the line positions are given in (Dresselhaus et al., 1992 Matus and Kuzmany, 1993). 

Tan, Y.Z., Liao, Z.J., Qian, Z.Z. etal. (2008) Two Ih-symmetry-breaking Ceo isomers stabilized by chlorination. Nature Materials, 7, 790-794. 

Eor example, to operate the GT Calculator for the case of structures of Ih symmetry, select Ih.xls and open this spreadsheet in the usual manner, either by pressing the ENTER button on your keyboard or with your mouse. The initial screen display will be as in the first diagram in Eigure 1.2 and it is necessary to choose the enable macros option in order to activate the functionality of the calculator. After a short graphic display, which can be cancelled with the ESC button, the standard logo screen for the calculator files is displayed with the centre text used to distinguish the different point groups. 

Proceeding in this way we have found that the most stable of all 1812 distinct C60 fullerene structures does indeed have icosahedral (Ih) symmetry, with no adjacent pentagonal faces, and corresponds to the face spiral shown in fig. 2. (In ofiier words Hiickel theory really does predict that the fullerene Qo is icosahedral. ) The most stable C50 fullerene has D3 symmetry, with no more than two adjacent pentagonal... 

Since Ceo has Ih symmetry with fivefold degenerate HOMO levels and threefold degenerate ti LUMO levels, the Jahn-Teller effect occurs in the anionic or cationic states. For example, as the electronic state of Cgg has T u symmetry, two Ug and eight hg vibrational modes couple to the T u state. In the case of C o> l e electronic state has Hu symmetry and the vibrational modes that couple to the Hu electronic state are two ag, six gg and eight hg modes [14]. To understand the Jahn-Teller effect in Ceo ions, the vibronic coupling constants have been estimated using experimental and theoretical methods [20]. 

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