Boundaries Through Bonds

Much like the RISM method, the LD approach is intermediate between a continuum model and an explicit model. In the limit of an infinite dipole density, the uniform continuum model is recovered, but with a density equivalent to, say, the density of water molecules in liquid water, some character of the explicit solvent is present as well, since the magnitude of the dipoles and their polarizability are chosen to mimic the particular solvent (Papazyan and Warshel 1997). Since the QM/MM interaction in this case is purely electrostatic, other non-bonded interaction terms must be included in order to compute, say, solvation free energies. When the same surface-tension approach as that used in many continuum models is adopted (Section 11.3.2), the resulting solvation free energies are as accurate as those from pure continuum models (Florian and Warshel 1997). Unlike atomistic models, however, the use of a fixed grid does not permit any real information about solvent structure to be obtained, and indeed the fixed grid introduces issues of how best to place the solute into the grid, where to draw the solute boundary, etc. These latter limitations have curtailed the application of the LD model. 

All of the QM/MM models discussed this far, much like continuum models, envision partitioning a chemical system into (at least) two distinct regions, where the boundary between these regions is everywhere characterized by a very low level of electron density. That is, no atoms on one side of the boundary are bonded to atoms on the other side. As a result, the //qm/mm term in the Hamiltonian of Eq. (13.1) is restricted to non-bonded interactions. 

The situation is vastly more complicated when the boundary between the QM and MM regions passes across one or more chemical bonds. Somehow, the dangling valences from the two separate regions must be joined in a chemically (and computationally) sensible fashion. Developmental work is ongoing in this area this section will focus on the current most widely used procedures. 

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QM/MM boundary through space in such a way that the sterically bulky groups fall on the MM side and the interesting part of the molecule falls on the QM side. Finally, to avoid the question of how to deal with a cut bond, one may assume that the electronic structure of the QM region will be of similar quality with either the non-polar, bulky group as a cap, or with simply hydrogen atoms as caps. With such a philosophy, the energy of the system as a whole may be expressed as a linear combination of model compounds of different size and at different levels of theory. In simplest form... 

The basic idea of the QM/MM methods [32, 33] is to partition the system into an inner quantum zone, in which the interesting chemistry happens, and an outer classical force field region. While this division is physically sensible, it can be quite tricky to handle the boundary between the two domains. If there is no covalent bond linking the QM and MM regions, the partitioning is simpler. If the boundary cuts through chemical bonds, however, the partitioning is more difficult. Several approaches have... 

Figure 3. Structural representation of the computational models A-F. Models B, D, and E are combined QM/MM models where the regions enclosed in the dotted polygons represent the QM region. The regions outside the polygons are treated by a molecular mechanics force field. For the electronic structure calculation of the QM region, the covalent bonds that traverse the QM/MM boundary (the dotted polygon), have been capped with hydrogen atoms. In model A the atoms labelled 1 through 4 are the atoms that have been fixed in the calculations of models A through E.

Moisture acts as a debonding agent through one of or a combination of the following mechanisms 1) attack of the metallic surface to form a weak, hydrated oxide interface, 2) moisture assisted chemical bond breakdown, or 3) attack of the adhesive. (2 ) A primary drawback to good durability of metal/adhesive bonds in wet environments is the ever present substrate surface oxide. Under normal circumstances, the oxide layer can be altered, but not entirely removed. Since both metal oxides and water are relatively polar, water will preferentially adsorb onto the oxide surface, and so create a weak boundary layer at the adhesive/metal interface. For the purposes of this work, the detrimental effects of moisture upon the adhesive itself will be neglected. The nitrile rubber modified adhesive used here contains few hydrolyzable ester linkages and therefore will be considered to remain essentially stable. 

Highly ramified macromolecule in which essentially each constitutional unit is connected to each other constitutional unit and to the macroscopic phase boundary by many permanent paths through the macromolecule, the number of such paths increasing with the average number of intervening bonds the paths must on the average be co-extensive with... 

By comparison, all bonds other than Sn - C in the tin hydroxides are quite strong. In ClsSnOH the bond energies are 125 kcalmor 95 kcal mol and 87 kcal mol for the 0 - H, Sn - 0, and Sn - Cl bonds, respectively. Thus, it appears likely that the hydroxide ligand is quite stable and could survive transit through the thermal boundary layer in a CVD reactor and form tin oxide. 

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