We provide a simple explanation for X-H bond contraction and the associated blue shift and decrease of intensity in IR spectrum of the so-called improper hydrogen bonds. This explanation organizes hydrogen bonds (HBs) with a seemingly random relationship between the X-H bond length (and IR frequency and its intensity) to its interaction energy. The factors which affect the X-H bond in all X-H...Y HBs can be divided into two parts: (a) The electron affinity of X causes a net gain of electron density at the X-H bond region in the presence of Y and encourages an X-H bond contraction. (b) The well understood attractive interaction between the positive H and electron rich Y forces an X-H bond elongation. For electron rich, highly polar X-H bonds (proper HB donors) the latter almost always dominates and results in X-H bond elongation, whereas for less polar, electron poor X-H bonds (pro-improper HB donors) the effect of the former is noticeable if Y is not a very strong HB acceptor. Although both the above factors increase with increasing HB acceptor ability of Y, the shortening effect dominates over a range of Ys for suitable pro-improper X-Hs resulting in a surprising trend of decreasing X-H bond length with increasing HB acceptor ability. The observed frequency and intensity variations follow naturally. The possibility of HBs which do not show any IR frequency change in the X-H stretching mode also directly follows from this explanation.

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A generally applicable electron-counting rule-the mno rule-that integrates macropolyhedral boranes, metallaboranes, and metallocenes and any combination thereof is presented. According to this rule, m + n + o number of electron pairs are necessary for a macropolyhedral system to be stable. Here, m is the number of polyhedra, n is the number of vertices, and o is the number of single-vertex-sharing condensations. For nido and arachno arrangements, one and two additional pairs of electrons are required. Wade's n + 1 rule is a special case of the mno rule, where m = 1 and o = 0. B20H16, for example has m = 2 and n = 20, leading to 22 electron pairs. Ferrocene, with two nido polyhedral fragments, has m = 2, n = 11, and o = 1, making the total 2 + 11 + 1 + 2 = 16. The generality of the mno rule is demonstrated by applying it to a variety of known macropolyhedral boranes and heteroboranes. We also enumerate the various pathways for condensation by taking icosahedral B12 as the model. The origin of the mno rule is explored by using fragment molecular orbitals. This clearly shows that the number of skeletal bonding molecular orbitals of two polyhedral fragments remains unaltered during exohedral interactions. This is true even when a single vertex is shared, provided the common vertex is large enough to avoid nonbonding interactions of adjacent vertices on either side. But the presence of more than one common vertex results in the sharing of surface orbitals thereby, reducing the electronic requirements.

First-principles electronic structure calculations show that boron clusters B98, B99, B100, B101, and B102 based on icosahedral-B12 stuffed fullerenes are more stable than the fullerenelike boron clusters. These more stable structures are envisaged as an icosahedral B12 each vertex of which is connected to the apex of a pentagonal pyramid (B6) via radial 2c-2e sigma bonds. The resulting B84 (B(12)@B(12)@B(60)) retains the same symmetry as C60, and the B(n) (n=84-116) clusters are generated around it. We further project the possibility of producing such B12 based giant clusters.