Prevalence and Significance of Approximate Symmetry in Organic <i>Pc</i> Structures

Brock, Carolyn Pratt

doi:10.1002/hlca.202200170

Cited by 2 publications

(3 citation statements)

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“…All but two of the SG #3 and #5 structures fit the categories used in previous studies of SGs #1 1 and #7. 2 Table 2 shows that approximate symmetry in SG #5, Z* > 1 structures is very common but not as common as in SG #1 and #7 structures.…”

Section: ■ Results and Discussionmentioning

confidence: 99%

“…Previous work − , has highlighted the importance of layers in molecular crystals. Of the 570 SG #5 structures considered, 338 have H bonds or short N···I contacts; in 209 of the 338, those bonds are all located within identifiable layers.…”

Section: Discussionmentioning

confidence: 99%

“…The frequent occurrence of approximate periodic symmetry in molecular crystals has been documented for Z′ > 1 structures (those with more than one crystallographically independent formula unit) in space groups (SGs) #1 (P1) 1 and #7 (Pc, Pn, Pa), 2 and for Z′ > 4 structures in all space groups. 3 Approximate symmetry has also been shown to be common in P1, Z′ = Z = 1 structures of molecules that can have approximate inversion symmetry.…”

Section: ■ Introductionmentioning

confidence: 99%

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Approximate Symmetry in Low-Symmetry Space Groups: P2 and C2

Brock

2024

Crystal Growth & Design

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This project determined the frequency of approximate periodic symmetry in well-determined (R ≤ 0.050) organic crystal structures refined in space groups (SGs) #3 (P2) and #5 (C2, A2, I2). The survey considered structures with Z′ > 1 (Z′ is the number of crystallographically independent molecules) and Z′ = 1 = 2( 1 / 2 ) (two molecules, each on a 2-fold axis). The reasons that group #3 occurs rarely (20 structures) have been analyzed. Of the 570 SG #5 structures examined, 13 (2%) should have been refined in a higher symmetry group, leaving 557 reliable structures. The frequency of approximate symmetry in SG #5 is high (73%) but is somewhat lower than that in SG #1 (P1; 86%) and in SG #7 (Pc, Pn, Pa; 83%). As was found for SG #1, many of the enantiopure substances (95 of 471) mimic centrosymmetric packing; in another 17, the achiral parts of the molecule are segregated in layers described by non-Sohncke symmetry. Molecular layers well described by a layer group occur considerably less frequently than in SGs #1 and 7, but in SG #5, there are more structures in which symmetric layers are related by a good 2 x axis perpendicular to the layer normal but with x not close to either 0 or 1. A guide to identifying and documenting approximate periodic symmetry has been deposited.

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Section: ■ Results and Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: ■ Introductionmentioning

confidence: 99%

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Approximate Symmetry in Low-Symmetry Space Groups: P2 and C2

Brock

2024

Crystal Growth & Design

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Continuous symmetry and chirality measures: approximate algorithms for large molecular structures

Alon,

Ben-Haim,

Tuvi-Arad

2023

J Cheminform

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Quantifying imperfect symmetry of molecules can help explore the sources, roles and extent of structural distortion. Based on the established methodology of continuous symmetry and chirality measures, we develop a set of three-dimensional molecular descriptors to estimate distortion of large structures. These three-dimensional geometrical descriptors quantify the gap between the desirable symmetry (or chirality) and the actual one. They are global parameters of the molecular geometry, intuitively defined, and have the ability to detect even minute structural changes of a given molecule across chemistry, including organic, inorganic, and biochemical systems. Application of these methods to large structures is challenging due to countless permutations that are involved in the symmetry operations and have to be accounted for. Our approach focuses on iteratively finding the approximate direction of the symmetry element in the three-dimensional space, and the relevant permutation. Major algorithmic improvements over previous versions are described, showing increased accuracy, reliability and structure preservation. The new algorithms are tested for three sets of molecular structures including pillar[5]arene complexes with Li+, C100 fullerenes, and large unit cells of metal organic frameworks. These developments complement our recent algorithms for calculating continuous symmetry and chirality measures for small molecules as well as protein homomers, and simplify the usage of the full set of measures for various research goals, in molecular modeling, QSAR and cheminformatics.

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Prevalence and Significance of Approximate Symmetry in Organic Pc Structures

Cited by 2 publications

References 32 publications

Approximate Symmetry in Low-Symmetry Space Groups: P2 and C2

Approximate Symmetry in Low-Symmetry Space Groups: P2 and C2

Continuous symmetry and chirality measures: approximate algorithms for large molecular structures

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