Au Chin Tang

Hückel treatment of carbon species with icosahedral symmetry

A new method which is based on the use of the ‘patch’ concept and the matrices of non-equivalent irreducible representations has been proposed for the Huckel treatment of the fullerenes with Ih symmetry. This method has been used to calculate the eigenvalues of C240, C540, C960, C1500, C2160, and C2940, and the calculated results indicate that all these fullerenes should stable.

Stability rules of icosahedral (Ih or I) fullerenes

Abstract According to the number of carbon atoms, the icosahedral (I h or I) fullerenes can be classified into two types: the first with n = 60 N , and the second with n = 60 N ′ + 20, where N and N ′ are non-negative integers determined by group properties. By means of our proposed method for Huckel chemistry calculation, we have calculated the electronic structures for 66 molecules of the first type and 87 molecules of the second type. From the calculated results, some general rules on stability and chemical reactivity have been found.

Electronic structures of octahedral fullerenes

Abstract The topological property of octahedral fullerenes is discussed. The eigenvalues of these molecules including giant octahedral fullerenes are calculated using a Huckel approximation based on a representative patch and the matrices of irreducible representations. From the calculated results we conclude that these molecules all have n /2 bonding molecular orbitals and are stable in the ground states.

Electronic structures and stability rules of tetrahedral fullerenes

Abstract According to the topologies of tetrahedral (T, T d and T h ) fullerenes, we have calculated the electronic structures of these molecules by means of our proposed method for Huckel chemistry calculation. According to the number of carbon atoms, the tetrahedral fullerenes are divided into three classes: Class 1 with n = 12 N , Class 2 with n = 12 N + 4 and Class 3 with n = 12 N + 8, where n is the number of carbon atoms and N is a non-negative integer determined by group properties. From the calculated results, we have found: the molecules of Class 1 are closed-shell, those of Class 2 are open shell and those of Class 3 are open shell or pseudo-closed shell.

Group theoretical applications to icosahedral fullerenes

Abstract Two problems have been studied. First, by using the structural properties of representative patch chosen for an icosahedral fullerene, the whole set of irreducible representations (IR) have been obtained for the π molecular orbitals of the fullerene. Secondly, on starting with the π electronic energy levels of fullerenes C n (I H , n = 60 k 2 ) and C n (I h n = 20 k 2 ) calculated using the Huckel approximation, their parities have been determined with the aid of a table in which the decomposition of the spherical harmonics into the IR of the I h group have been listed.

Ab initio and DFT studies of the weakly bound nitrogen molecule complexes (N2)n (n=3–6)

Abstract A theoretical research on the low-energy structures, binding energies, and Raman spectra of the (N 2 ) n ( n =3–6) complexes has been systematically explored. Similar to the water trimer, the energetically lowest-lying structure of the nitrogen molecule trimer is a C 3h -symmetric cyclic structure. However, different from the water tetramer and pentamer being simple ring structures, the lowest-lying structures of the tetramer and the pentamer are pyramidal structures with C 3 and C 4 symmetry. Additionally, the hexamer prefers the C i -symmetric bipyramidal structure rather than the prism structure that is the most stable of the water hexamer. Moreover, the binding energy and the Raman spectrum for each complex are also predicted.

Electronic structures of dihedral (D5h, D5d, D6h, D6d) fullerenes

Abstract By means of our proposed method for Huckel theory calculation, we have calculated the electronic structures of dihedral (D 5h , D 5d , D 6h , D 6d ) fullerences, which are generated from icosahedral C 20 , C 60 , C 80 , C 180 , C 240 and C 540 , respectively. From the calculated results of 1224 fullerence molecules, certain rules on the stability and chemical reactivity have been drawn for such types of dihedral fullerenes.

Symmetries of closed-shell icosahedral fullerenes

Abstract Based on our Huckel calculated results for icosahedral fullereness the molecules C n with n = 60 N are closed shell, where N has to satisfy the group requirements. By using the representative patch, we obtain the symmetries of π molecular orbitals for the icosahedral fullerenes. With the aid of the relationship between C 60 N and C 20 N , the symmetries of π bonding molecular orbitals are also offered.

Frontier electronic energy levels of icosahedral fullerenes

Abstract In this Letter, we have calculated the electronic structures of 161 icosahedral fullerenes of which the frontier electronic energy levels have been examined in detail. On the analysis of the electronic energy levels, their corelation rules have been obtained. By use of the corelation rules, we can predict the frontier electronic energy levels of all the icosahedral fullerenes and discuss their electronic spectra in a more convenient way.

THEORETICAL STUDIES ON CARBON TUBULES

Abstract A simple method has been proposed for calculating the band structures of carbon tubules on the tight-binding orbital approximation. Both the open and capped carbon tubules have been discussed, and the capped carbon tubules might be generated from any fullerene C n of I h symmetry with n = 60 k 2 or n = 20 k 2 where k is any positive integer.