Distribution of molecular pairs in Z′ = 2 structures

Abstract

The positions of pairs of independent molecules in Z 0 = 2 structures have been surveyed for six of the most populated space groups for that class of structure. These results have been compared with the Z 0 = 1 situation to reveal whether there are any fundamental differences in the construction of the asymmetric units in these cases. The results indicate that, broadly speaking, the packing of the molecular pairs in Z 0 = 2 structures resembles that of single molecules in structures with Z 0 = 1; this similarity may be chiefly attributed to the constraints imposed by the symmetry operators of the space group. However, there are key differences, which are particularly marked in the space groups with higher symmetry, that indicate that the asymmetric units in Z 0 = 1 and Z 0 = 2 structures are not directly comparable. In those cases where the positions of the pair centroids in Z 0 = 2 structures are similar to the positions of molecular centroids for Z 0 = 1 structures, it follows that the molecular centroids in Z 0 = 2 structures must follow a different distribution. A different pattern is produced if the independent molecules in Z 0 = 2 structures behave like the individual molecules in Z 0 = 1 structures. These two scenarios combine to form the observed distributions of pair centroid positions.

cis-Bis(dimethyl sulfide)dinitratoplatinum(II) at 295 and 150 K

“…The centres of pseudosymmetry, viz. ( 1 2 , 1 2 , 3 4 ) and ( 1 2 , 0, 3 4 ), are as far away as possible from the space group operators, 2 1 , n and 1, in accordance with the ®ndings of Collins (2006) for molecular pairs in Z H =2 structures. Each column is surrounded by six other columns in a pseudo-honeycomb rod-like packing (O'Keeffe & Andersson, 1977) stabilized by CÐHÁ Á ÁO (HÁ Á ÁO = 2.47±2.69 A Ê and CÐHÁ Á ÁO = 117±161 ) and CÐ HÁ Á ÁS (HÁ Á ÁS = 2.96 A Ê and CÐHÁ Á ÁS = 149 ) interactions and SÁ Á ÁO contacts [3.228 (5) and 3.255 (4) A Ê ] (Fig.…”

High-Pressure Structure and Properties of N,N-Dimethylformamide (DMF)

“…There are two symmetry-independent molecules ( Z ′ = 2), and we also intended to investigate the effect of pressure on Z ′. In most crystals of organic compounds Z ′ = 1 (currently about 81% of all structures deposited in the Crystallographic Structural Database), − and several reasons for the occurrence of larger Z ′ values have been considered. − High temperature usually leads to phase transitions that reduce Z ′, − although reverse changes are also known. − The effects of pressure on various properties of crystals are often inverse to those of temperature; hence the rule of inverse effects of pressure and temperature was formulated . However, there are many exceptions to the inverse p / T effects rule.…”

Can the Formation of Pharmaceutical Cocrystals Be Computationally Predicted? 2. Crystal Structure Prediction

“…Such algorithms can also promote our understanding of the formation of molecular salts, 7,8 solvates, 9 and hydrates 10,11 and can also be used to rationalize crystallization with more than one chemically identical molecule in the asymmetric unit (Z′ g 2). [12][13][14][15][16][17][18] The most widely used approach for predicting organic crystal structures is to minimize the lattice energy of a large number of systematically or randomly generated candidate structures. 6,[19][20][21][22] In this approach, the experimentally observed structure is assumed to correspond to the most stable packing arrangement.…”

“…Hence, the development of algorithms to predict the structure and thermodynamic stability of single and multicomponent crystals can assist the screening for cocrystals, by showing which, if any, arrangements of the two molecules are thermodynamically plausible. Such algorithms can also promote our understanding of the formation of molecular salts, , solvates, and hydrates , and can also be used to rationalize crystallization with more than one chemically identical molecule in the asymmetric unit ( Z ′ ≥ 2). − …”