
doi: 10.1002/jcc.21828
pmid: 21618558
AbstractSymmetry is one of the most fundamental properties of nature and is used to understand and investigate physical properties. Classically, symmetry is treated as a binary qualitative property, although other physical properties are quantitative. Using the continuous symmetry measure (CSM) methodology one can quantify symmetry and correlate it quantitatively to physical, chemical, and biological properties. The exact analytical procedures for calculating the CSM are computationally expensive and the calculation time grows rapidly as the structure contains more atoms. In this article, we present a new method for calculating the CSM and the related continuous chirality measure (CCM) for large systems. The new method is much faster than the full analytical procedures and it reduces the calculation time dependency fromN! toN2, whereNis the number of atoms in the structure. We evaluate the cost of the applied approximations, estimate the error of the method, and show that deviations from the analytical solutions are within an error of 2%, and in many cases even less. The method is applicable at the moment for the cyclic symmetry point groups—Ci,Cs,Cn, andSn, and therefore it can be used also for chirality measures, which are the minimal of theSnmeasures. We demonstrate the application of the method for large structures across chemistry: proteins, macromolecules, nanotubes, and large unit cells of crystals. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011
Nanotubes, Molecular Structure, Macromolecular Substances, Proteins, Stereoisomerism, Algorithms
Nanotubes, Molecular Structure, Macromolecular Substances, Proteins, Stereoisomerism, Algorithms
| selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | 30 | |
| popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network. | Top 10% | |
| influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | Top 10% | |
| impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network. | Top 10% |
