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The total number of atoms in B12, B80, and B180 cannot be described by one general formula since the number of atoms shared by the DRs varies from one cage to another.
The observed success or failure of fragment merging appears generally ordered with the average distance between the common atoms shared by the two parent fragments.
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Thus, the silicon-to-oxygen ratio varies according to the extent to which the oxygen atoms are shared by silicon atoms as the tetrahedrons are linked together.
Hydrogens may be either connected to skeletal atoms or shared by a group of skeletal atoms (such groups may also share negative charge).
Note in Fig. 1b that the black atoms belong only to one DR, in contrast, the white atoms are shared by two crossing DRs. However, for B300and all larger fullerenes the number of shared atoms is constant and the total number of atoms in the cage can be obtained using a simple formulaN(n) = N(B180) + 120(n − 3), where withn(n ≥ 4) we label the fullerenes starting from the smallest cage.
Ab initio cluster calculations performed at the B3LYP/6-31G** B3LYP/6-31G**ry exclevel coffiguratheoryith O atoms bondexcludedree Si atoms and proved that the most probable is the configuration withe an O atomsis shared bondedee Al atoms.
Because none of the oxygen atoms is shared by other tetrahedrons, the chemical formula contains a multiple of SiO4, as in zircon, topaz, or olivine.
For a polypeptide chain, the peptide unit as defined by the IUPAC nomenclature (rather than the conventional residue) is assigned to be the smallest fragment that contains the atoms −CαIRICO NHCαI+1H– in the conventional residues I and I + 1, where each Cα atom is shared by two adjacent peptide units.
The essential structural feature of a zeolite is a three-dimensional tetrahedral framework in which each oxygen atom is shared by two tetrahedra.
Note that the black atoms are not shared by the DRs but each white atom is shared by two of them.
Since one ligand atom can belong to more than one fragment in this definition, the patterns of the interactions in larger parts of molecules, i.e. those derived from binding motifs, can be considered by focusing on the consensus of the fragment interactions through atoms that are shared by more than one fragment.
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