The crystal growth process in colloidal nanocrystal systems is usually associated with the Ostwald-ripening mechanism. Here, we report on experimental evidence indicating that another crystal growth process took place in a colloidal nanocrystal system at room temperature. This crystal growth process is based on grain rotation among neighboring grains, resulting in a coherent grain–grain interface, which, by eliminating common boundaries, causes neighboring grains to coalesce, thereby forming a single larger nanocrystal. This phenomenon was observed in SnO2 nanocrystals (particle size ranging from 10 to 30 Å).

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Except for the case of van der Waals interactions, homopolar bonds are covalent and therefore a concentration of the electron density is expected at the bond midpoint. Many experimental and theoretical studies have reported standard deformation density maps and molecular density minus spherical atoms densities, which show a depletion of electron density between formally covalently bonded atoms. For example, electron deficits are found in the theoretical map of the FF bond in F2, in the experimental map of the NN bond in carbonohydrazide, and in the experimental and theoretical maps of the OO bond in 1,2,7,8‐tetraaza‐4,5,10,11‐tetraoxatricyclo[6.4.1.1]tetradecane. Other partitioning schemes, such as subtraction of valence state atoms rather than spherical atoms from the total density, have been proposed to interpret these unexpected features. In the present work we examine these electronically depleted covalent bonds on the basis of the topological analysis of the electron localization function (ELF) of theoretically calculated electron densities. The attractors of ELF determine basins that are either core or valence basins. The valence basins are characterized by the number of core basins with which they share a common boundary, and this number is called the synaptic order. Disynaptic valence basins have been found for the FF bond in F2, for the NN bond in carbonohydrazide and for the OO bond in 1,2,7,8‐tetraaza‐4,5,10,11‐ tetraoxatricyclo[6.4.1.1]tetradecane. In the case of F2, polarization functions increase the V(F, F′) basin population, whereas accounting for the Coulomb correlation lowers this basin population. The results calculated for F2 are compared with those obtained for other diatomic molecules, such as N2 and O2, and the ELF picture of the bond compared with the molecular orbital analysis. In the case of carbonohydrazyde, the V(N, N′) basin population is the lowest among all the populations of the disynaptic valence basins present in the molecule, in good agreement with the experimental observations. Analogous results are obtained for the V(O, O′) basin population in 1,2,7,8‐tetraaza‐4,5,10,11‐ tetraoxatricyclo[6.4.1.1]tetradecane. Population fluctuation analysis indicates a strong delocalization of the electron density toward lone pairs and adjacent bonds. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1517–1526, 1999

A theoretical study on geometrical, thermodynamic and electronic properties of V x O y + and V x Oy (x = 2−4, y = 2−10) systems in different electronic states has been carried out. Analytical gradient techniques with a hybrid spin unrestricted and spin restricted Hartree−Fock density functional method (B3LYP) have been used. An analysis of potential energy surfaces at ground and some excited states renders the most stable structures an their corresponding vibrational frequencies. The reaction energies of the possible decomposition channels are reported and the results indicate that the formation of larger clusters is energetically favorable from the smaller VO+ (3∑), VO (4∑), VO2 (2A1), VO3 (2A‘),V2O4 (3A‘ ‘) and V2O5 (1A‘) systems and O2 (3∑g). A comparative discussion of the bonding in these species has been carried out on the basis of the topological analysis of the electron localization function. Numerical results are analyzed and confronted with available experimental data.

Calculations based on density functional theory at Becke’s three-parameter exchange functional combined with the Lee–Yang–Parr correlation functional (B3LYP) level and periodic slab models have been done to obtain: (i) the surface energy per unit area of different stoichiometric SnO2 surfaces, and (ii) by using a simple Wulff construction equation-type, the thermodynamic stability associated to the formation of nanoribbons from these surfaces has been obtained. In agreement with previous theoretical studies, the (110) face is the thermodynamically most stable surface. The present theoretical results and high-resolution transmission electron microscopy data reveal that the nanoribbons preferentially grow along the [101] crystal direction.