By comparing data on a variety of examples, an empirical correlation for the photoelastic response of simple metal oxides is discovered and used to predict new families of zero-stress optic glasses. The birefringence induced by uniaxial stress on glass is found to correlate well with the ratio of the metal oxygen bond metallicity to the metal coordination number; the metallicity itself is quantified through the metal oxygen bond length. This correlation was obtained by consideration of the stress optic response of a number of oxide crystals, obtained both from the literature when possible and also from first principles calculations. The correlation obtained provides a simple rule for choosing the composition of oxide glass so as to minimize the stress optic response; this rule is shown to agree with known data on lead oxide glasses and to predict the existence of previously unknown lead-free, zero-stress optic glasses. These glasses were then synthesized, tested, and shown to give the predicted response.

The interaction of BeX(2) (X = H, F) with water molecules has been analyzed at the B3LYP/6-311+G(3df,2p)//B3LYP/6-311+G(d,p) level of theory. The formation of strong beryllium bonds between water molecules and the BeX(2) derivative triggers significant electron density redistribution within the whole system, resulting in significant changes in the proton donor and proton acceptor capacity of the water molecules involved. Hence, significant cooperative and anti-cooperative effects are present, explaining why there is no case in which the global minimum corresponds to a tetracoordinated beryllium atom. In fact, the most stable clusters can be viewed as the result of the attachment of BeX(2) to the water trimer and the water dimer, respectively, and not as the result of the solvation of the BeX(2) molecule. We have also shown that the decomposition of the interaction energy into atomic components is a reliable quantitative tool to describe all the closed-shell interactions present in the clusters investigated herein, namely hydrogen bonds, beryllium bonds and dihydrogen bonds. Indeed, we have shown that the changes in the atomic energy components are correlated with the changes in the strength of these interactions, and they provide a quantitative measure of cooperative effects directly in terms of energies.

The mutual interaction between beryllium bonds and halogen bonds within H2Be···FCl···Base complexes, where Base includes a wide set of N- and O-containing Lewis bases, has been studied at the M06-2X/6-31+G(d,p) level of theory. The reliability of this theoretical model was assessed by comparison with ab initio CCSD/aug-cc-pVTZ reference calculations. Cooperative effects were investigated within the framework of the atoms in molecules theory (AIM) by analyzing the topology of the electron density and the changes in the atomic energy components. The decomposition of the total stabilization energy into atomic components is found to be a very reliable tool to describe halogen bond interactions. Both the topological analysis of the electron density and the changes in the atomic energy components of the binding energy show the existence of strong cooperative effects between beryllium and halogen bonds, which are in some cases very intense. In general, there is a correlation between the intrinsic basicity of the Lewis base participating in the halogen bond and the resulting cooperativity in the sense that the stronger the base, the larger the cooperative effects.

Atomic energies are used to visualize the local stabilizing and destabilizing energy changes in water clusters. Small clusters, (H(2)O)(n), from n = 2-5, at MP2/aug-cc-pVTZ geometries are evaluated using energies defined by the quantum theory of atoms in molecules (QTAIM). The atomic energies reproduce MP2 total energies to within 0.005 kcal mol(-1). Oxygen atoms are stabilized for all systems and hydrogen atoms are destabilized. The increased stability of the water clusters due to hydrogen bond cooperativity is demonstrated at an atomic level. Variations in atomic energies within the clusters are correlated to the geometry of the waters and reveal variations in the hydrogen bond strengths. The method of visualization of the energy changes applied here is especially suited for application to large biomolecules.

Atomic energies are used to describe local stability in eight low-lying water hexamers: prism, cage, boat 1, boat 2, bag, chair, book 1, and book 2. The energies are evaluated using the quantum theory of atoms in molecules (QTAIM) at MP2/aug-cc-pVTZ geometries. It is found that the simple, stabilizing cooperativity observed in linear hydrogen-bonded water systems is diminished as clusters move from nearly planar to three-dimensional structures. The prism, cage, and bag clusters can have local water stabilities differing up to 5 kcal mol(-1) as a result of mixed cooperative and anticooperative interactions. At the atomic level, in many cases a water may have a largely stabilized oxygen atom but the net water stability will be diminished due to strong destabilization of the water's hydrogen atoms. Analysis of bond critical point (BCP) electron densities shows that the reduced cooperativity results in a decrease in hydrogen bond strength and an increase in covalent bond strength, most evident in the prism. The chair, with the greatest cooperativity, has the largest average electron density at the BCP per hydrogen bond, whereas the cage has the largest total value for BCP density at all hydrogen bonds. The cage also has the second largest value (after the prism) for covalent bond critical point densities and an oxygen-oxygen BCP which may factor into the experimentally observed stability of the structure.