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Cycloheptane.world File ReferenceA cycloalkane with a 7 carbon loop. More... Go to the source code of this file. Detailed Description
IntroductionCycloheptane is a cycloalkane with the molecular formula C7H14. Cycloheptane is used as a nonpolar solvent for the chemical industry and as an intermediate in the manufacture of chemicals and pharmaceutical drugs. The purpose of this benchmark is to show how, using CUIK, one can compute the set of cycloheptane conformations that are compatible with its rigid-geometry model. This model assumes that all bond lengths and angles are kept fixed, and only the torsion angles can vary. Conformations that satisfy such constraints are among the most stable ones. In the robotics language, this is equivalent to finding the possible configurations of a 7R loop: the links are the carbon atoms, and the revolutes are the free torsions around each C-C bond. Given that the loop involves more than six bodies (atoms), it is mobile with one degree of freedom. As we will see, though, the loop can be assembled in two different ways, corresponding to the chair and boat (mobile) conformations of this molecule. The same benchmark is used in [Crippen 1992] to illustrate the performance of the linear-embedding technique on this problem and our results are in agreement with Crippen's. It is worth mentioning that, while our technique is complete (it guarantees all solutions are found) Crippen's method relies on an initial grid sampling, and hence may fail to find all solutions if the grid is not fine enough. Note that the definition we provide allows to reconstruct the position of all cyclohexane atoms (even the hydrogens rigidily attached to the carbons). If we are only interested in the loop of carbons a simpler formulation is possible: a unitary vector along each CC bond, a fixed dot product (i.e., fixed angle) between those vectors and a sum of all vertors set to 0. References
Definition in file Cycloheptane.world. |