Ying-Nan Chiu

The structures of fullerene C40 and its derivatives

Abstract In this paper, the three possible fullerene isomers of C40 and their derivatives are investigated employing ab initio methods with using 3 Gauss type orbitals instead of one Slater type orbital (STO-3G). Of the three structures, two have D5d symmetry [D5d(I) and D5d(II)], the other has Td symmetry. Through the full optimized calculation, the predicted order of stability for isomers is found to be D5d(I) > Td > D5d(II). Energies and properties of the negative ion and positive ions of different kinds of C40 are calculated. Generally, the stability of negative ions is better than positive ions. The hydrogenated C40 has also been studied. It can be concluded that the most active center for adding hydrogen is the vertex of three adjacent pentagons.

Theoretical study of metallofullerenes M@C32

Abstract 14 systems of metal atoms, embedded inside the C 32 cage, have been calculated and analyzed using the ab initio quantum chemistry Gamess program. We study their electronic structure, compare their stability. The metal atom with even electrons interjected inside the C 32 cage is more stable than the metal atom with odd electrons. Ti@C 32 system is the most stable in the 14 metallofullerenes.

Theoretical study for exohydrogenates of small fullerenes C28∼C40

Abstract In this article the structure and electronic properties of small fullerene structures C28, C32, C36, C40, and 24 exohydrogenates of them, were studied by employing the quantum-chemistry ab initio method. Calculations show that the stability order of addition hydrogen to carbon cage for carbon site is: Download : Download full-size image We suggest that this implies the vertex of triplet pentagons of the small carbon cage is an activation site for addition. This article also discussed geometrical and electronic factors in influence of hydrogenates stability.

One-dimensional Schrödinger equation in the harmonic oscillator basis with various potentials

Abstract A FORTRAN 77 program has been written for computing the one-dimensional Schrodinger equation in the harmonic oscillator basis. It runs on the personal computer PC-486. Seven different kinds of vibrational operator functions have been considered. The program can be readily modified by users for different purposes. The polynomial potential function is discussed in much detail and comparisons have been made. Some test-run inputs and outputs have also been given.

On the closed form of Wigner rotation matrix elements

The closed forms of some rotation matrix elementsdm′ mj (π/2) are presented. The closed forms of summation involved two binomials and some special hypergeometric functions are also obtained. The MAPLE V program which calculates dm′ mj(β), dm,. (π/2) and the help file are given in appendix.

Special geminals and Schlegel diagrams of molecular structures of fullerenes and metallofullerenes

Abstract Geminals in fullerenes and metallofullerenes have been discussed. Schlegel diagrams have been used to demonstrate the location of geminals in the molecules. The following molecular systems have been studied: C42H28→C42 (C2v, D2h), C30H18→C30 (C2v, D5h), C4H4 (D4h), C4H6, C28 (Td), Ti@C28 (Td), Sc3@C82 (C3v), and SC@C20 (D5) with free π radicals from electrons of 3+3, 4 and 5+5 carbons with Λ=0,±1, Λ=0,±1,2, Λ=0,±1,±2 and Λ=0,±1,±2,3 out of the geminals of 4⇒1,2,3,4⇒12,23,24,13,14,34.

On the summations involving Wigner rotation matrix elements

Two new methods to evaluate the sums over magnetic quantum numbers, together with Wigner rotation matrix elements, are formulated. The first is the coupling method which makes use of the coupling of Wigner rotation matrix elements. This method gives rise to a closed form for any kind of summation that involves a product of two Wigner rotation matrix elements. The second method is the equivalent operator method, for which a closed form is also obtained and easily implemented on the computer. A few examples are presented, and possible extensions are indicated. The formulae obtained are useful for the study of the angular distribution of the photofragments of diatomic and symmetric-top molecules caused by electric-dipole, electric-quadrupole and two-photon radiative transitions.

A model Hamiltonian for the YBa2Cu3O7–8 superconductor

Abstract A model Hamiltonian has been presented based on the tight-binding approximation. The critical temperature of superconductivity T c is not related to the reduced mass of the positive and negative ions. Therefore, there is no isotopic effect according to this model.

The harmonic oscillator tensor approach to the eigenspectra of multiple-well molecular potentials II. Periodic potentials

Abstract We display the matrix elements for the vibrational operators qk sin(ωkq), qk cos(ωkq), qk sinh(ωkq) and qk cosh(ωkq) k = 0, 1, 2, 3, … derived using an irreducible tensor technique in the basis of the non-degenerate harmonic oscillator wave functions. We give an example of a variational eigenvalue calculation, using matrix elements calculated in this manner, of an arbitrary periodical and non-periodical potentials expanded in fourier series.

Young operator methods for fermion systems

SummaryAlternative methods to the standard Young technique for the construction of Fermion wave functions in the spin orbital formalism are presented and shown to be equivalent to the standard technique. To develop these methods: (i) the starting or primitive function is factored into spin and spatial parts, (ii) the conjugacy feature required to satisfy the antisymmetry principle is exploited, (iii) the necessary commutation relations with the Fermion antisymmetrizer are shown to hold and (iv) the one-to-one correspondence between the independent picture of the Young tableaux and the independent Slater determinants is used. This last feature has the advantage of reducing all three methods to rapid efficient graphical procedures. Each method is analyzed to consider the amount of labor involved to carry it out. Several examples of the methods are given for constructing both electronic wave functions and spin functions.