TY - JOUR
T1 - Improved algorithms for symmetry analysis
T2 - structure preserving permutations
AU - Alon, Gil
AU - Tuvi-Arad, Inbal
N1 - Publisher Copyright:
© 2017, Springer International Publishing AG.
PY - 2018/1/1
Y1 - 2018/1/1
N2 - We propose an improved algorithm for calculating Avnir’s continuous symmetry and chirality measures of molecules. These measures evaluate the deviation of a given structure from symmetry by calculating the distance between the structure and its nearest symmetric counterpart. Our new algorithm utilizes structural properties of the given molecule to increase the accuracy of the calculation and dramatically reduce the running time by up to tens orders of magnitude. Consequently, a wide variety of molecules of medium size with ca. 100 atoms and even more can be analyzed within seconds. Numerical evidence of the algorithm’s efficiency is presented for several families of molecules such as helicenes, porphyrins, dendrimers building blocks, fullerene and more. The ease and efficiency of the calculation make the continuous symmetry and chirality measures promising descriptors for integration in quantitative structure–activity relationship tools, as well as chemical databases and molecular visualization software.
AB - We propose an improved algorithm for calculating Avnir’s continuous symmetry and chirality measures of molecules. These measures evaluate the deviation of a given structure from symmetry by calculating the distance between the structure and its nearest symmetric counterpart. Our new algorithm utilizes structural properties of the given molecule to increase the accuracy of the calculation and dramatically reduce the running time by up to tens orders of magnitude. Consequently, a wide variety of molecules of medium size with ca. 100 atoms and even more can be analyzed within seconds. Numerical evidence of the algorithm’s efficiency is presented for several families of molecules such as helicenes, porphyrins, dendrimers building blocks, fullerene and more. The ease and efficiency of the calculation make the continuous symmetry and chirality measures promising descriptors for integration in quantitative structure–activity relationship tools, as well as chemical databases and molecular visualization software.
KW - Chirality
KW - Continuous symmetry measures
KW - Graph automorphism
KW - Permutations
KW - QSAR descriptors
UR - http://www.scopus.com/inward/record.url?scp=85027491559&partnerID=8YFLogxK
U2 - 10.1007/s10910-017-0788-y
DO - 10.1007/s10910-017-0788-y
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AN - SCOPUS:85027491559
SN - 0259-9791
VL - 56
SP - 193
EP - 212
JO - Journal of Mathematical Chemistry
JF - Journal of Mathematical Chemistry
IS - 1
ER -