Connected bond networks

The recent development of internal coordinate quantum Monte Carlo has made it possible to directly compare classical and quantum calculations for many body systems. Classical molecular dynamics simulations of many body systems may sometimes overestimate vibrational motion due to the leakage of zero point energy. The problem appears to become less severe for more highly connected bond networks and more highly constrained systems. This suggests that current designs of some nanomachine components may be more workable than MD simulations suggest. Further study of classical-quantum correspondence in many body systems is necessary to resolve these concerns. 

The polyethylene system, a loosely connected bond network, was chosen as a worst possible case in order to illustrate the limitations of classical MD simulation. Systems with external constraints (such as nearby chains in a crystal) or cyclical bond networks would be expected to exhibit significantly restricted motion. In fact, classical simulations of carbon nanotubes, which have a two-dimensional bond network, showed a sizeable but significantly smaller disagreement with quantum results. 

Stimulated by these observations, Odelius et al. [73] performed molecular dynamic (MD) simulations of water adsorption at the surface of muscovite mica. They found that at monolayer coverage, water forms a fully connected two-dimensional hydrogen-bonded network in epitaxy with the mica lattice, which is stable at room temperature. A model of the calculated structure is shown in Figure 26. The icelike monolayer (actually a warped molecular bilayer) corresponds to what we have called phase-I. The model is in line with the observed hexagonal shape of the boundaries between phase-I and phase-II. Another result of the MD simulations is that no free OH bonds stick out of the surface and that on average the dipole moment of the water molecules points downward toward the surface, giving a ferroelectric character to the water bilayer. 

It has been found by Will (2004) from X-ray scattering measurements that valence electrons concentrate along the lines connecting the boron atoms, confirming that the boron layer is a covalently bonded network. The titanium layers are metallic. However, the layers are not characteristic of either pure Ti, or pure B, so the bonding is quite complex. 

Let us first seek to give a more rigorous and operational ab initio characterization of such units. The important physical idea underlying the above definitions is that of the connecting covalent bonds that link the nuclei. One can therefore recognize that a molecular unit is equivalently defined by the covalent-bond network that contiguously links the nuclei included in the unit. We can re-state the definition of a molecular unit in a way that emphasizes the electronic origin of molecular connectivity. 

Strong intermolecular interactions between active SCO mononuclear building blocks stem from the presence of efficient hydrogen-bonding networks or 7i-7i stacking interactions and have led to abrupt spin transitions [1], sometimes with associated hysteresis [2-4]. Despite the important efforts made by crystal engineers in establishing reliable connections between molecular and supramolecular structures on the basis of intermolecular interactions, the control of such forces is, however, difficult and becomes even more complicated when uncoordinated counter-ions and/or solvent molecules are present in the crystal lattice. 

In contrast to the TREN template, 75 with the NTA template preferred the h-cis configuration . This could be caused either due to the inverse directionality of the hydroxamate group, or, more plausibly, because the tripeptide is connected through the amino end, leading to opposite orientation of the hydrogen-bonding network. ... 

As pointed out above, the bond flux depends on the connectivity of the compound, that is, on the bond graph. This means that the length of a bond depends not only on its immediate environment, but also on the structure of the whole crystal or molecule of which the bond is part. Thus anions such as PO, which ideally are perfect tetrahedra, will often be distorted when they appear in crystals. However, this distortion can normally be predicted via the network equations provided the graph of the bond network is known. 

The graph of the bond network is simple and contains all the necessary chemistry. It is fully defined by the atomic valences and the connections between... 

Fig. 2.61. Homo- and heteronuclear shift correlations for the determination of the bonding network (the connectivities ).

The hydrogen-bonded network picture of Rahman and Stillinger (1973, 1974) is the most favored model. Stillinger (1980) also described water as a macroscopically connected (three dimensional) random... 

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