Tai-ichi Shibuya

Two icosahedral structures for the C60 cluster

Abstract Two icosahedral structures, a truncated icosahedron and a truncated dodecahedron, have been examined for the C 60 cluster. Optimized geometries by INDO calculations are: in the former, 1.449 A (for pentagonal edges) and 1.397 A; in the latter, 1.41 A (for triangular edges) and 1.345 A. At these geometries, HOMO-LUMO gaps are 9.23 and 8.86 eV, respectively.

A dielectric model for the solvent effect on the intensity of light absorption

A new dielectric model is proposed for the solvent effect on the absorption intensity. The ratio of the apparent oscillator strength f″ of a solute molecule measured in a solution of refractive index n to the oscillator strength f of the solute molecule is given by f″/f=[s(n2−1)+1]2/n, where s is a ‘‘shape’’ parameter of the cavity in which the solute molecule is supposed to lie. The parameter s is identified with the depolarization factor of a dielectric in the same shape as the cavity, for the direction of the transition moment. The proposed linear relation between (nf″)1/2 and n2−1 is demonstrated for the π → π* transition of β‐carotene and for the n→ π* transition of pyrazine. For the allowed π → π* transitions of long linear polyenes, the s value is approximately 0, leading to the relation f″/f=1/n. The proposed formula also reduces to the well‐known Chako formula f″/f=(n2+2)2/(9n) for the spherical cavity whose s value is 1/3. The theory predicts that 1/n≤f″/f≤n3. It is shown that the proposed formu...

The refractive-index correction to the radiative rate constant

Abstract It is widely accepted that the refractive-index correction factor for the radiative rate constant is n2, where n is the refractive index of the solution. This letter points out that the factor varies between n and n5, depending upon the shape of the solute molecule and the direction of the transition moment.

Linear relationship between the bond lengths and the Pauling bond orders in fullerene molecules

Abstract The Pauling bond orders are calculated for the fullerene molecules, C 60 and C 70 , and are correlated to the bond lengths. It is concluded that there is a good linear relationship between them.

Ionization energies, electron affinities, and absorption spectrum of fullerene C60 calculated with the semiempirical HAM/3 and CNDO/S methods

Abstract Ionization energies (PES), excitation energies (UV) and electron affinities (EA) of fullerene C 60 have been calculated with the semiempirical HAM/3 method. The first few ionization energies calculated with HAM/3 show errors as great as 1.4 eV. The HAM/3-CI method has reproduced the observed UV spectrum fairly well. The HAM/3-Δe method has given fairly good energies for the forbidden lowest singlet and triplet transitions but rather poor results for the allowed transitions. The correlation between calculated PES, UV and EA values is discussed. A method to estimate accurate electron affinity is proposed. The CNDO/S method, on the other hand, has given good values for some of the ionization energies and electron affinities.

Equations‐of‐motion method for the spin–orbit coupling of aromatic molecules: Application to the phosphorescence lifetime of benzene

A phosphorescence theory for aromatic molecules is formulated in terms of the equations‐of‐motion method. The theory is applied to the INDO/S calculations on the lowest triplet radiative lifetime of benzene. All the calculations are performed within the spin‐same‐orbit interaction approximation. The random‐phase approximations are found to give better results than the Tamm–Dancoff approximation (or the singly excited CI). The importance of the spin‐other‐orbit interactions contributing to the phosphorescence lifetime is discussed from the formula derived in an Appendix.

Phase of essential single and essential double bonds in HOMO/LUMO of benzenoid hydrocarbons

There are certain bonds that are necessarily single/double in all the Kekule structures of a given benzenoid hydrocarbon (molecular graph); such a single/double bond is called essential or fixed in valence bond theory. We conclude by use of perturbation molecular orbital theory that the bond phase, i.e. the sign either plus for bonding or minus for antibonding, of essential single/double bonds, respectively, is negative/positive in HOMO of benzenoid hydrocarbons; the bond phase of essential single/double bonds alters in HOMO and LUMO.

Study of chemically stable/unstable isomers of the fullerene hydrides, C60H2 and C60H4, by use of a generalized Pauling bond order method

Abstract A new index, defined as a generalization of the Pauling bond order, i.e. a ratio between the number of Kekule structures in an isomer of the hydride derivatives C 60 H 2 and C 60 H 4 to that in the fullerene C 60 molecule, is proposed. This index is shown to be useful for predicting the chemical stability/instability of the hydride isomers.

Two-Electron Excited States of Fullerene-C60: Analysis by the CNDO/S-SDCI Calculations

ABSTRACT Possible existence of the low-lying two-electron excited states of fullerene-C60 is investigated by the singly- and doubly-excited CI calculations in the semi-empirical CNDO/S approximation.

The third-order polarizability γ of C60: The role of low-lying two-electron excited singlet states Ag and Hg

The third-order polarizability γ of the C60 molecule has been calculated for the third harmonic generation at several incident frequencies using two different schemes of the sum-over-state (SOS) method, and the contribution of the low-lying singlet excited states as the second intermediate states has been analyzed. The group-theoretical analysis of the SOS expression clarifies that the 1Ag and 1Hg states are the only states that contribute to the γ as the second intermediate states. For the numerical analysis, the electronic states previously obtained in the semiempirical CNDO/S approximation with the singly and doubly excited configuration interaction method are used. It is found that the inclusion of the doubly excited configurations is essential in evaluating the γ. Those excited 1Ag and 1Hg states which make significant positive contributions to the γ are practically the doubly excited states. In order to secure error-free SOS calculations, equivalent but independent calculations have been also carrie...