Cycloheptane.world File Reference

Detailed Description

[Introduction] [Process] [Statistics] [Results] [References]

Introduction

Cycloheptane 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.

Process

This example is treated following this steps (from the main CuikSuite folder):

• Generate the equations: Execute
  • bin/cuikequations examples/Cycloalkanes/Cycloheptane
• Solve the positional analysis problem: Execute
  • bin/cuik examples/Cycloalkanes/Cycloheptane
• Sort the solutions:
  • bin/cuiksort examples/Cycloalkanes/Cycloheptane
• Animate the solutions (the chair and boat components):
  • scripts/cuikplayer examples/Cycloalkanes/Cycloheptane.world examples/Cycloalkanes/Cycloheptane_1
  • scripts/cuikplayer examples/Cycloalkanes/Cycloheptane.world examples/Cycloalkanes/Cycloheptane_2
• Plot and visualize the configuration space (you will see the two one-dimensional solution sets):
  • bin/cuikplot3d examples/Cycloalkanes/Cycloheptane 11 21 33 0 c7.gcl
  • geomview c7.gcl

Statistics

Characteristics of the problems:

Nr. of loops	1
Nr. of links	7
Nr. of joints	7
Nr. of equations (in the simplified system)	13
Nr. of variables (in the simplified system)	14

Here you have the statistics about the execution (on an Intel Core i7 at 2.9 Ghz).

Nr. of empty boxes	494
Nr. of solution boxes	377
Solver time (s)	60

Results

The following figure shows the output boxes returned by the algorithm on the cycloheptane loop. The problem with SIGMA set to 0.75, 0,25, and 0.05. The initial stages (i.e., the ones with larger SIGMA are shown in transparency).

References

• D. Crippen, "Exploring the Conformational Space of Cycloalkanes by Linearized Embedding", Journal of Computational Chemistry, vol. 13, no. 3, pp. 351-361, 1992.

Definition in file Cycloheptane.world.