Combined models, mixing basic combinations

In this section we focused our attention to a rationalization of the factors determining the stereoselectivity through ab initio mixed quantum/classical (QM/MM) Car-Parrinello molecular dynamic simulations. We have used the same basic computational approach used in Section 3 to explore the potential energy surface of the reaction. Since the catalyst system, 1, is relatively large, we have used the combined QM/MM model system B as shown in Figure 3 and described in subsections 2.1 and 3.1. 

In contrast to the four tetrahedrally oriented elliptic orbits of the Sommer-feld model, the new theory leads to only three, mutually orthogonal orbitals, at variance with the known structure of methane. A further new theory that developed to overcome this problem is known as the theory of orbital hybridization. In order to simulate the carbon atom s basicity of four an additional orbital is clearly required. The only possible candidate is the 2s orbital, but because it lies at a much lower energy and has no angular momentum to match, it cannot possibly mix with the eigenfunctions on an equal footing. The precise manoeuvre to overcome this dilemma is never fully disclosed and appears to rely on the process of chemical resonance, invented by Pauling to address this, and other, problems. With resonance, it is assumed that, linear combinations of an s and three p eigenfunctions produce a set of hybrid orbitals with the required tetrahedral properties. 

To estimate isotopic discrimination at the ecosystem, local or regional scales, an estimate of the exchange flux, or the 6 C value of NEE, at the relevant scale is required. Such estimates are obtained by sampling air in and above plant canopies, or in the and above the atmospheric boundary layer (ABL). A simple and powerful approach employs a two-member mixing model as first proposed by Keeling (1958, 1961). The equation used in the Keeling approach is derived from the basic assumption that the atmospheric concentration of a substance in an ecosystem reflects the combination of some background amount of the substance that is already present in the atmosphere and some amount of substance that is added or removed by a source or sink in the ecosystem ... 

More commonly, Kr has been combined with other dating tracers, in particular with tritium. This tracer combination is particulary useful because the two isotopes have similar half-lives but experienced completely different input histories (Fig. 6). The basic idea in the interpretation of H- Kr data, which can be generalised to all multi-tracer approaches, is to calculate the expected concentrations of and Kr for different mean ground-water residence times and/or different models of mixing in the aquifer, and to compare the measured concentrations with the model predictions (Loosli 1992 Loosli et al. 2000). This approach has been used successfully to derive mean residence times and to quantify admixing of old, tracer-free ground water, which is identified by concentrations of and Kr below those predicted by the models (Purtschert 1997 Mattie 1999). 

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