The results of first principles calculations on H-silsesquioxanes (i.e., (HSiO 3/2 ) n with n ) 4, 6, 8, 10, 12, 14, and 16) are reported here. Double numeric basis sets and local and nonlocal density approximations to density functional theory are employed for calculations. It is shown that use of the nonlocal density approximation is required for the reliable prediction of the most stable isomer for silsesquioxanes. Furthermore, a progression of the preferred building unit with the increase in size of the T cage is revealed. The smaller T cages prefer four-and five-member rings while the larger cages are found to prefer four-and six-member rings. Analysis of the energy of the hydrolysis reaction, binding energy, and fragmentation paths finds the relative stability of the silsesquioxane cages containing four-, five-, and six-member rings in agreement with experimental observations. For the (HSiO 3/2 ) 16 cage, the calculated results predict the stability of the D 2d -6 4 5 0 4 6 configuration over the D 4d -6 0 5 8 4 2 configuration in contradiction to suggestions based on 29 Si NMR measurements. We find a consistent picture for the highest occupied molecular orbitals (HOMOs) of all silsesquioxanes considered showing them to be composed of (lone-pair) oxygen p-type atomic orbitals. On the other hand, the lowest unoccupied molecular orbitals (LUMOs) show size dependence in their composition which appears to cause the presence of a state in the HOMO-LUMO gap for higher silsesquioxane cages. Density of states plots and analysis of molecular orbitals reveal this state to be due to the terminal hydrogens bonded to silicon atoms.

We report the results of density functional theory calculations on chromium oxide clusters responding to the formula Cr m O n (m ) 1-2, n ) 1-3). Double numeric basis sets supplemented by polarization functions have been used in both local and nonlocal spin density approximations. Geometry optimizations of different spin states have been performed at the unrestricted spin level for the selected initial configurations. We have found that the covalent polarized Cr-O bonds dominate the chemical description of the CrO n series, while for the Cr 2 O n series the presence of the Cr-Cr bond reduces the metal to oxygen charge transfer, yielding much softer clusters, as reflected by the smaller HOMO-LUMO gaps. The stability of all the isomers has been checked by computing their harmonic vibrational frequencies and the energetics of different fragmentation paths. The calculations reveal that the linear isomers are not true minima and that the oxygen-rich clusters are preferred over the metal-rich clusters. Overall, our results show good agreement with the available experimental data in terms of geometrical parameters, vibrational frequencies, atomization energies, and fragmentations for the CrO n clusters. For the Cr 2 O series, our computed values are discussed in connection with recent infrared spectroscopy measurements and with available data in analogous metal oxide clusters.

We report the frequency dependence of linear and nonlinear optical susceptibilities of H-silsesquioxanes of various cage sizes and conformations using the INDO/CI method coupled with the SOS method. The average dynamic refractive index of silsesquioxanes is found to decrease as the cage size increases, and its variation is very small for the different conformations of the same cage size at the same incident wavelength. The calculated second-order susceptibilities show that small cages have a larger magnitude which is comparable to that of crystalline R-quartz. It is suggested here that H-silsesquioxanes of a smaller cage size can be a good candidate materials for nonlinear optical applications having low absorption, wide transparency and adequate susceptibility in ultraviolet or vacuum ultraviolet region of the spectrum.