Partial enumeration

Partial enumeration perform a full enumeration of parts of the solution. 

Once the reactant pools have been filtered, the next step in product-based designs is usually to enumerate the full virtual library. This can be a very time-consuming step and hence a useful precursor can be to enumerate carefully chosen subsets that will give an indication of the success or otherwise of the full virtual experiment. Thus, in a two component reaction it can be useful to take the first reactant in the first pool and combine it with all the reactants in the second pool (to generate 1 x nB products). This should then be followed by the enumeration of one reactant in the second pool with all reactants in the first pool to give nA x 1 products. If either of these two partial enumeration steps fail, then the full enumeration will also fail. Thus, troublesome reactants can be identified early. 

Had they attempted to enumerate the particular powers or means, not necessary or proper for carrying the general powers into execution, the task would have been no less chimerical and would have been liable to this further objection that every defect in the enumeration, would have been equivalent to a positive grant of authority. If to avoid this consequence they had attempted a partial enumeration of the exceptions, and described the residue by the general terms, not necessary or proper It must have happened... 

Partially enumerate CSLN see Note 5) on variation site XI running program dbexplode using command Une ... 

Mean Field Theory for Non-Gaussian Chain Architectures 5.3.2.1 Partial Enumeration Schemes... 

In the case of general chain architectures, however, the mean fleld problem of a single chain in an external fleld cannot be cast in the form of a modified diflusion equation, and the density that a single chain creates in the external field and the concomitant single-chain partition function have to be estimated by partial enumeration [30-34], This methodology has been successfully applied to study the packing of short hydrocarbon chains in the hydrophobic interior of lipid bilayers [31,32,34] and polymer brushes [33] and to quantitatively compare the results of Monte Carlo simulations to the predictions of the mean field theory without adjustable parameters [30], The latter application is illustrated in Figure 5.2. 

This procedure, however, is impractical because the generation of the representative set of single-chain conformations in the external field via importance sampling is computationally more expensive than partial enumeration and one would have to perform a computer simulation in each iteration cycle of the self-consistent adjustment of fields and densities. 

Fig. 38. Temperature dependence of the interfacial tension of the pure polymer for chain length N = 10. Circles correspond to MC results and the solid line to the SCF ealculations. The line with diamonds shows the the result of a density functional calculation, which uses the TPTl-equation of state, decomposes the interaction free energy functional into a repulsive short-ranged and an attractive long-ranged contribution, and employs a partial enumeration scheme to take due account of the chain conformations on all length scales [154]. The dashed line shows the result of density functional calculations which do not use the decomposition of the free energy functional, but employ the same equation of state and chain model [99]. The inset compares the free energy densities / = F/VkgT of the SCF calculations and the accurate TPTl equation of state. Adapted from [99,154]...

---