Solution structure generation algorithm

When the number of solution structures generated by algorithm SSG is exceedingly large, however, their optimization can be indeed time-consuming. In practice, only a... 

Subsequent to the generation of the maximum structure, the combinatorially feasible network structures are exhaustively recovered as the solution-structures by resorting to algorithm SSG. Each solution-structure signifies a combinatorially feasible network of pathways linking the raw materials to the products. Nevertheless, not all the solution-structures are necessarily feasible due to the violation of the mass balances in or around... 

All of the algorithms described in this article have been based on an assembly of structural fragments. Recently, a new approach of 3D structure elucidation from infrared spectra by counterpropagation neural networks has been reported. Although the output structure depends on the training data set, the mechanism is quite different from the conventional method. This method is probably useful in cases where the solution space is restricted. The complementary use of both methods may open the door to new fields enhanced by structure generation. 

Fig. 12 (a) The molecular fragment (thick lines), comprising half the TDMM molecule, used in the direct-space genetic algorithm stmcture solution calculation from powder XRD data. The arrows indicate the variable torsion angles. The central carbon atom is located on a twofold rotation axis (as indicated), and the other half of the molecule (faint lines) is generated by this symmetry operation, (b) The final refined crystal structure of TDMM, with hydrogen atoms omitted for clarity... 

We have also examined here the use of approximate solutions of the coupled perturbed Hartree-Fock equations for estimating the Hessian matrix. This Hessian appears to be more accurate than any updated Hessian we have been able to generate during the normal course of an optimization (usually the structure has optimized to within the specified tolerance before the Hessian is very accurate). For semi-empirical methods the use of this approximation in a Newton-like algorithm for minima appears optimal as demonstrated in Table 17. In ab-initio methods searching for minima, the BFGS procedure we describe is the best compromise. 

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