3,4-Bis-O-propargyl-1,2:5,6-di-O-isopropylidene-d-mannitol: a study of multiple weak hydrogen bonds in the solid state

Primary weak hydrogen bonds in each of three independent molecules in 3,4-bis-O-propargyl-1,2:5,6-di-O-isopropylidene-d-mannitol are elucidated by single-crystal X-ray diffraction and their importance in molecular conformation and crystal packing determined. Parallel searches of the Cambridge Structural Database using motifs based on donor and acceptor propargyl D—H⋯A contacts reveal distance and angle dependencies that are especially sensitive to acceptor type, so, together, these findings will be beneficial in applications for the molecule and its congeners as anion binders and precursors for the synthesis of macrocycles.


Figure 3
Inter-and intrastrand contacts between like molecules of strands A, B and C, as seen from directly above the mean planes of the A, B and C sheets, with unit cells indicated, as well as closeup views with labels and distance measurements included.
completeness. The values for D1, D2 and ANG for all matching contacts found in the CSD were recorded and the results displayed as scatterplots against 'Identity Number' in Fig. S3 and discussed more fully in Section 3.4.3.

Results and discussion
3.1. Molecules in the unit cell The asymmetric unit comprises three independent molecules (represented as A-green, B-blue and C-red), each with the mannitol 2R,3R,4R,5R configuration [ Fig. 1(b), randomly selected molecule A] and differing only in the conformation of the molecule. This establishes asymmetry in each molecule. Hence, in future, and for ease of reference, the terms 'head' and 'tail' sections will be used for each molecule, based on lower and higher crystallographic element numbers, respectively [ Fig. 1(c)].
3.1.1. Conformations of molecules A-C. Based on torsion angles (Table 2), there are marginal differences in the conformation about the central mannitol core (Entries 1-3), with molecule A the most notable. Marginal differences are also observed in torsions associated with the orientation of the dioxolanyl groups relative to the core (Table 2, Entries 4-15), but most notably in molecule A and to the largest extent in the tail portion of the molecules. In contrast, puckering of the dioxolanyl group, as reflected in the C1/14-O3/10-C3/16-C6/10 torsion angles (Table 2, Entries 16-21), was most varied in the head section, and to the most significant extent (moderately) in molecule C; configurations in the tails of molecules A-C were highly consistent. The propargyloxy substituents potentially have three sources of conformational freedom. Marginal differences are observed in the torsions associated with their attachment to the mannitol core in both head and tail sections (Table 2, Entries 22-27), but most noticeably in molecule A. From this point, the orientation of the propargyl groups in comparison with the mannitol core are relatively conserved in the heads and tails of all three molecules (Table 2, Entries 28-33). However, significant differences are then observed in the orientations of the terminal acetylenic groups in the head and tail sections relative to the mannitol fragment ( More detailed analysis reveals that, in the crystal, the three independent species (A-green, B-blue and C-red) align in strands, each with matching identical molecules A, B and C.  The unit cell of compound 1 viewed down the crystallographic b axis after rotating by 135 about the vertical axis, showing molecules A (green), B (blue) and C (red) with selected atom labels of close contacts as defined automatically within the limits of van der Waals radius À0.05 to 0.30 Å , within the crystal lattice, and an enlarged inset with details of the linear and orthogonal contacts involving C9B-H9B and C2C-H2CB with additional enforced distance measurements to C2C indicated. Note that the C9C-H9CÁ Á ÁO2A contact was not detected under the conditions set for close contacts.
interactions. The differences in each case appear to arise because of subtle differences in the conformations of each molecule. Such individual strands all occur through C13-H13Á Á ÁO6 contacts and are represented and viewed along the a axis in Fig. 2(a) and along the c axis in Fig. 2(b). Thus, the contacts for molecules A (green) and B (blue) occur in a unidirectional sense along the b axis, with identical symmetry codes, namely (x + 1, y, z), while strands of molecules C (red) are oriented perpendicular, along the a axis [consider Figs. 2(a) and 2(b)], through a different symmetry code, (x, y À 1, z). As is also evident, particularly in Fig. 2(b) and the positions of atoms C5 and C9, the molecules in strands A and B are flipped relative to each other by approximately 180 about the length of the two strands. This feature permits near coincidence of the C13-H13Á Á ÁO6 alignments, with unidirectionality of the overall strands, while accommodating the steric demands of the remaining portions of the molecules.
3.2.2. Homogeneous molecular strands and sheets. 3.2.2.1. Intrastrand contacts between like molecules. Significant advances have been made towards estimating the H-atom positions of small organic molecules from X-ray crystallographic data (Jayatilaka & Dittrich, 2008;Capelli et al., 2014;Woiń ska et al., 2016). These have achieved results that are within the accuracy of neutron diffraction. However, a very limited number of examples have been described. As a consequence, contact data for short intra-and interstrand interactions between like molecules of each type have been summarized in Table 3 using parameters that have become accepted more widely as good indicators of strength and efficiency in the field for weak hydrogen bonds (Desiraju, 2005). The values include the accurately measured DÁ Á ÁA distance (D, Å ), the estimated D-H bond length using the previously utilized predicted position of the H atom for each type of weak acid species [CH (acetylenic) = 0.95 Å , CH (methine at sp 3 carbon) = 1.00 Å , CH 2 (methylene) = 0.99 Å and CH 3 (methyl) = 0.98 Å ], without any additional normalization, and the resulting HÁ Á ÁA distance (Å ). Common to each of the strands are the aforementioned intrastrand tail-totail C13-H13Á Á ÁO6 contacts (Table 3; Entries 1, 4 and 12). All three achieve short DÁ Á ÁA distances with near-linear D-HÁ Á ÁA contact angles (A 158.3, B 164.7 and C 167.8 ).
Observed values are consistent with acetylenic groups with pK a (Me 2 SO) $ 24.9 (Pedireddi & Desiraju, 1992). These intrastrand associations stand alone for molecule A, but are reinforced within the strands from molecule B by additional more distant C13-H13BÁ Á ÁC14B, C13-H13BÁ Á ÁC17B and C17B-H17DÁ Á ÁH13B contacts (Table 3, Entries 5-7), and within those from molecule C by an equally distant head-tohead C4C-H4CBÁ Á ÁC9C contact (Table 3, Entry 13) (see also Fig. 3). Those involving molecule B are exceptionally weak, as assessed by DÁ Á ÁA distance measurements. They stem from additional engagement by the C13B-H13B group as a donor in a trifurcated contact with quaternary atom C14B and its neighbouring bonded methyl C17B and H17D atoms. The additional intrastrand contact involving molecules C is remarkable because it occurs between highly remote groups that ordinarily are weak donors and acceptors.
A consequence of these analyses is that, despite the orthogonal alignment of strands of molecules C relative to those of molecules A and B, the two-dimensional array of short contacts between like molecules in compound 1 is found to result in the formation of homogenous sheets of each molecular type.
3.2.3. Cross-strand/cross-sheet interactions. Separate molecular interactions occur between, rather than within, the sheets of molecules A-C. The nonconforming orientation of the C strand compared with the A and B strands, in particular, led us to examine even more closely this aspect of the supramolecular structure. In addition, the intermolecular interactions involving the propargylic C9-H9 acetylene donor functional groups in the head moieties were of interest. Contact data for these cross-strand/cross-sheet contacts (contacts between donors and acceptors from different molecular types A-C), almost all of which are ostensibly stronger C-HÁ Á ÁO contacts, are summarized in Table 4. Contact angle (, ), as well as distance measurements, are given for added depth of analyses. Values for intrastrand acetylenic C13-H13Á Á ÁO6 contacts are included for comparison (Table 4, Entries 1-3). As with the earlier analyses, it is acknowledged that the resulting data are derived from a single-crystal X-ray crystallographic study and not a comprehensive crystallographic database search. However, the observations and conclusions drawn from them are based on comparisons from well debated past literature.
Cross-strand acetylenic C9-H9 donor interactions occur from molecules A, B and C (Table 4, Entries 4-6). Superficially, those from molecules A (green) and B (blue) engage in unique finger-like intrusions, that are almost perpendicular to the axis of the parent strand, into separate strands of molecules C (red) [Fig. 2(b)], yet each one of the three contacts is different in detail. Readers will find Fig. 4 helpful in providing a pictorial view of the short contacts within the unit cell, as expressed in Table 4.
3.2.3.1. Cross-strand interactions from the standpoint of donor elements. Interstrand interactions are grouped in Table 4 according to notional donor acid strength, as defined by calculated D-H bond lengths, which are based on donoratom electronegativity. This classification does not correlate directly with the understood mark of contact strength, namely, DÁ Á ÁA distance, even when contact angle () is considered. The interactions in Table 4 are therefore discussed in this order, but within the context of three interaction types: singlet, pivot and couplet (see Fig. 5).
Molecules A (green) provide a modest cross-strand C9A-H9A acetylenic donor interaction with the tail dioxolanyl O6C atom in addition to the strong intrastrand, C13C-H13C donor contact with the same acceptor (Table 4, Entries 3 and 4). Because the acceptor O6C serves as a fulcrum in bringing together adjacent A and C molecules, the contact is called here a 'pivot' interaction [ Fig. 5(a)]. The short-to-medium C9A-H9AÁ Á ÁO6C contact distance [D = 3.376 (4) Å ] is consistent with a slightly weaker acid than the acetylenic C13-H13 groups (Pedireddi & Desiraju, 1992). Its contact angle (140.8 ) ( Table 4, Entry 4) is far from the near linear alignment of its partner (167.8 ; Table 4, Entry 3) but within the range of other contacts from weak acids where interactions have been attributed to electrostatics (Desiraju, 1990;Pedireddi & Desiraju, 1992). However, in this pivot case, where both donors are of the same chemical type, the different DÁ Á ÁA distances is most likely a reflection of the different contact angles, with the linear contact being more dominant.
In a separate pivot interaction [Fig. 5(e)], molecules C (red) demonstrate a somewhat longer [D = 3.541 (2) Å ] acetylenic donor contact (C9C-H9CÁ Á ÁO2A; Table 4, Entry 6), identified only by a directed measurement (therefore not visible in Fig. 4) with the head dioxolanyl group of an A molecule. The interaction is associated with another nonlinear contact angle (146.6 ), but in this case made with a near linear contact (169.1 ) with its pivot donor partner C4C-H4CB (Table 4, Entry 17). The donor in this portion of the pivot is derived from a dioxolanyl methyl group, which would normally be a much less acidic proton source than a terminal acetylene group (compare the estimated D-H bond lengths of 0.98 versus 0.95 Å ). The observed DÁ Á ÁA distances for the two interactions are indicative of the anticipated donor strengths, but closer in magnitude than one might expect. One explanation for their similarity is the acute angle of the first, which would diminish the donor effectiveness from pK a , and linearity of the latter, which would enhance effectiveness from pK a for the methyl H atoms that are already the most acidic of those attached to sp 3 C atoms in compound 1.
These contacts, together, contribute to another type of cooperative set of contacts, called here a 'couplet', that include in this example the non-acetylenic dioxolanyl methine C16B-H16BÁ Á ÁO1C contact [ Table 4 Table 4 Short-contact donor (D) acetylenic (Entries 1-8) and non-acetylenic (Entries 9-18) HÁ Á Áacceptor (A) interactions, initially defined automatically within the limits of van der Waals radius À0.05 to 0.30 Å , and measured in Angstroms (Å ), for molecules A-C in the crystal lattice of compound 1, as well as D-HÁ Á ÁA contact angles (, ), where A = oxygen (O) in most cases, and relevant carbon (C) and hydrogen (H) close contacts in other cases, with relevant head and tail denominations for participating groups, useful for indicating the nature of their alignment. Major types of oxygen-acceptor-centred short interstrand contacts in the X-ray crystal structure of compound 1, with key atomic labels and bond angles, as recorded by Mercury (Version 2020.3.0; Macrae et al., 2020), for molecules A (green), B (blue) and C (red).
somewhat longer than for the only other methine contact, C6C-H6CÁ Á ÁO5A (Entry 15), for which the contact angle is smaller. However, it is nearly identical to those of the pivot partners around O2A (Table 4, Entries 6 and 17), wherein contact angles are unequal. It is also very similar to those of methyl donor contacts C5B-H5BÁ Á ÁO3A and C18A-H18BÁ Á ÁO5C (Entries 18 and 19) with more linear contact angles. The medium-to-large DÁ Á ÁA distance in the case of C16B-H16BÁ Á ÁO1C is possibly the result of it being part of a reasonably large couplet of atoms, and its contact angle the result of confinement of the donor C16B-H16B bond as part of the tail dioxolanyl ring system in molecule B. Three non-acetylenic donor types of C-HÁ Á ÁO close contacts are recognisable within the distance range initially defined, and all are cross-strand (see Fig. 3). Those recorded as Entries 11-14 in Table 4 are considered in the first category because they involve similarly weakly acidic D-H participants (note the longer estimated D-H distances for Entries 9-14 compared with those for the acetylenic donor examples in Entries 1-8). They proceed from the methylene groups at atoms C7 and C11 in the head and tail propargyloxy substituents, respectively, but their interactions are in turn each different.
Molecules A and B make reciprocal head-group methylene contacts with the dioxolanyl O1 acceptor from the partner molecule. Notably, the donor from molecule B (Entry 12) makes a 'singlet' contact with O1A [ Fig. 5(g)], that is, a contact without the involvement of any other partner. The singlet C7B-H7BAÁ Á ÁO1B contact is closer [D = 3.261 (2) Å ] and more linear (165.8 ) than the C7A-H7AAÁ Á ÁO1B contact from molecule A [Entry 11; D = 3.393 (2) Å , = 142.5 ], which is part of another symmetrical seven-membered couplet [Fig. 5(c)] with the donor methyl C5B-H5BAÁ Á ÁO3A interaction [Entry 18, D = 3.525 (3) Å , = 160.0 ]. The smaller ring size of this tight couplet appears to impart a more acute angle to the C7A-H7AAÁ Á ÁO1B contact and thereby must reduce the DÁ Á ÁA distance. In contrast, only C11C-H11E participates as donor from the equivalent methylene group of molecule C, but the same donor makes contact with two quite different acceptors, namely, dioxolanyl O2B and C3B, with very different DÁ Á ÁA distances. However, these acceptors reside at adjacent positions in the same molecule B (Table 3, Entries 13 and 14), and largely for this reason the contact is defined here as a 'singlet' interaction [Fig. 5(f)]. As expected, because the acceptor O2B has two frontier orbitals, each with lone pairs of electrons, contact with O2B is much shorter and more linear [Entry 13, D = 3.372 (3) Å , = 176.9 ] with respect to the predicted C11C-H11E bond than it is with the adjacent methine C3B acceptor [Entry 14, D = 3.687 (4) Å , = 146.7 ], with no free bonding electron pairs. The fact that atom H11E is bifurcated probably accounts for the slightly longer C11CÁ Á ÁO2B contact compared with the C7BÁ Á ÁO1A contact, but with a distance that is tempered by the near perfect alignment of the former.
The second type of non-acetylenic donor close contacts exhibit methine donor contributions from C6C-H6C and C16B-H16B, respectively (Table 4, Entries 15 and 16). Contacts occur with interstrand dioxolanyl oxygen partners, but with only moderate DÁ Á ÁA distances (D) and contact bond angles (). Both C atoms are derived from the mannitol skeleton, the first bearing a propargyloxy substituent and the other an oxygen substituent that is part of the tail dioxolanyl group. It is possibly significant that none of molecules A-C exhibit close contacts involving donor C-H bonds from either of the symmetry-equivalent atoms C10 and C3, respectively, of these positions. However, it is worth recalling that C3B does participate in a contact with donor C11C-H11E (Table 4, Entry 14), but only as a weak acceptor, and then with limited efficiency. Donor C16B-H16B was also mentioned earlier as a close contact with O1C within the first couplet complex [Fig. 5(d)], with C9B-H9BÁ Á ÁO3C. The remaining methine donor contact, C6C-H6CÁ Á ÁO5A (Table 4, Entry 15), participates in an unsymmetrical nine-membered couplet with a tail-tail methyl donor contact, C18B-H18BÁ Á ÁO5C [ Table 4, Entry 19; Fig. 5(b)]. Perhaps because of its slightly different methine donor character, the C6C-H6CÁ Á ÁO5A contact has a measurably shorter DÁ Á ÁA distance [D = 3.457 (2) Table 4, Entries 15 and 16). Equally, the difference in DÁ Á ÁA contact distances might arise from the smaller contact angle for C6C-H6CÁ Á ÁO5A brought about by constraints of its smaller ring couplet than those of the larger one involving C16B-H16BÁ Á ÁO1C. Finally, the three remaining non-acetylenic donor contacts emanate from a C-H bond in one of the slightly more acidic, axial or equatorial geminal methyl groups attached to the dioxolanyl groups (Table 4, Entries 17-19). The three donors interact either head-head or tail-tail with a dioxolanyl O-atom acceptor and have comparable DÁ Á ÁA distances (D) with near-linear contact angles (). All three contacts have been discussed above within the context of other interactions (Table 4, Entries 6, 15, and 16).
Between them, this complex array of contacts affords stability to the observed alternating layered sheets of A (green)-C (red)-B (blue) molecules (Fig. 6). The arrangement leaves no interdigitation of propargyl groups between layers of molecules of type A (green) and B (blue). However, there are alternative AÁ Á ÁB reciprocal C-HÁ Á ÁO contacts (Table 4, Entries 11-12 and 18), of which the head-to-head propargylic C7B-H7BÁ Á ÁO1A contact and nonpropargylic C5B-H5BAÁ Á ÁO3A contact are most important.
With this improved understanding of contacts from the perspective of C-H donors, a brief study was made of the geometry about the most important cross-strand contact acceptors in compound 1, the relevant dioxolanyl and propargyloxy ether O atoms.
3.2.3.2. Cross-strand interactions from the standpoint of O-atom acceptors. Data derived from measurements of individual bond and contact angles associated with covalently bound O atoms and their close intermolecular donor C-H contacts are summarized in Table 5. This process was initiated on the questionable premise that acceptor interactions would take place through O-atom lone pairs of electrons (Taylor & Kennard, 1982, 1984Steiner & Desiraju, 1998) and with the intention of providing better insight into the geometry at the acceptor sites.

research papers
The method used acknowledges that the O atoms in molecule 1 are all ethers and should have an electron-pair geometry that is approximately tetrahedral with coordinate angles of 109.5 . Accordingly, the sum of the triplet of bond and contact angles surrounding each relevant acceptor O atom has been calculated and the geometry arbitrarily assessed as 'pyramidal' (trigonal pyramidal) or 'planar', depending on whether the angle sum is less or more, respectively, than 344 , midway between the ideal for tetrahedral (328.5 ) and planar (360 ). In this study, close donor-acceptor (DÁ Á ÁA) contacts are limited to those shorter than the sum of the van der Waals radii minus 0.01 Å . Under these conditions, atoms O2C, O3B, O4A-O4C and O5B showed no close contacts. In Table 5, the values of the DÁ Á ÁA distance (D, Å ) and contact angle (, ) of each observed C-HÁ Á ÁO short contact are repeated from Table 4 and the contact types from Fig. 5 are added, all for reference purposes and as an aid to interpretation.
Surprisingly, only six of the 14 contacts with O atoms can be classified as pyramidal in their geometry. While all these are associated with dioxolanyl O atoms, not all the dioxolanyl O-atom contacts can be classified in this way. As partly discussed in the context of donors, in two of the six cases, dioxolanyl atoms O6C (tail) and O2A (head) each makes pivot contacts with two C-H donors (Table 4, Entries 3/4 and 6/17, respectively). This gives the interactions a degree of complexity, but with some hope of understanding differences in the geometry at the fulcrum, which is their O atom. In the first case [ Table 5, Entries 3 and 4; Fig. 5(a)], two of the angular components used to evaluate the pyramidal or planar geometry about O6C are nearly identical, but the C15C-O6AÁ Á ÁD angle differs markedly, i.e. 135.4 (1) when D = C13C and 99.2 (1) when D = C9A. The rendition of these contacts in Fig. 5(a) gives insight into the competition by donors C13C-H13C and C9A-H9A for access to O6C. It also gives an understanding as to how the closer more linear contact resulting from the former might have arisen through an overall planar geometry with O6C, with a splaying of the C15C-O6AÁ Á ÁC13C angle, and a slightly weaker more apical contact at O6C through an acute angular interaction (probably electrostatic) by C9A-H9A. In the second pivot example [ Table 5, Entries 9 and 10; Fig. 5(e)], a similar interplay appears to be involved, but the less acidic donor partner, C4C-H4CB, exerts a closer than expected near-linear contact with acceptor O2A at an angle sum [341.5 (2) ] that is close to being defined as that for a planar contact. As a result, the C1A-O2AÁ Á ÁC4C and C3A-O2AÁ Á ÁC9C component angles are increased and the C9C-H9CÁ Á ÁO2A contact weakened concomitantly with a decrease in the observed contact angle to 146.6 .
Analyses of observed geometries around each of the Oatom acceptors in the three sets of couplet interactions reported in Table 5 (2) Å ] takes place through an acute D-HÁ Á ÁA angle (135.6 ) and planar though angularly distorted interaction with O5A. This result occurs despite the more linear (168.1 ) contact of the normally more acidic methyl donor C18A-H18B with its couplet partner O5C. Analysis of the seven-membered couplet [ Table 5, Entries 7 and 13; Fig. 5(c)] provides a similarly satisfying explanation for angular distortions around the O1B and O3A acceptors and indicates a more convincing dominance of one contact, the C7A-H7AAÁ Á ÁO1B interaction, over the other.
The situation in the 11-membered couplet [ Table 5, Entries 8 and 14; Fig. 5(d)] is more complex because of the participation of the orthogonal donor arrangement of the bifurcated H2C atom, but it is clear that equally explicable distortions of contributing angles around key acceptor components O1C, C9B and O3C do take place as a result of the couplet arrangement of the two partner components. Equally, tolerated distortions around the O2B and O1A acceptor O atoms in the two singlet cases [ Table 5, Entries 11 and 12; Figs. 5(f) and 5(g)] are explicable for the simple reasons of neighbouring-atom participation and crystallographic dislocation of participants.

Crystal packing
A review of the crystallographic data to this point highlights a number of noteworthy features about compound 1. The three independent molecules A-C that make up the unit cell differ subtly in conformation, but significantly at two of their ether sites. They each assemble into unique linear strands of like molecules, primarily through C13-H13Á Á ÁO6 contacts, but supported by intramolecular and intrastrand interactions. Furthermore, the assemblies are unidirectional, with the strands of A and B aligned in close proximity, head-to-tail, along the crystallographic a axis and those of C aligned orthogonal along the b axis. Additional interstrand interactions between like molecules establish a two-dimensional sheet array of like parallel strands. However, a network of donor-acceptor contacts occur between strands/sheets of unlike molecular type.
3.3.1. Molecular strand and sheet planes. Initial examination of the crystal packing reveals a repeat layering of the three molecular types in the order A (green)-B (blue)-C (red), when viewed along the a and b axes (Fig. 7). Analysis of the mean planes of each molecule across three separate strands confirms their parallel arrangement, which is most convincing in Fig. 7(a). Such layering is consistent with the establishment of sheets (Section 3.2.2.2).
Further analysis of the mean planes of the A, B and C molecules in their respective strands across a span of five molecules in each strand reveals tilts of 6.28, 12.51 and 23.52 , respectively, from the mean planes of the sheets of each molecular type, which are themselves separated unequally by  Table 5 Analysis of the geometry of close intermolecular contacts, as defined as shorter than the sum of the van der Waals radii minus 0.01 Å , through measurement of triplet component angles at each of the key O-atom acceptor atoms a in molecules A-C of compound 1, the arithmetic sum of the individual angles and resulting assignment of configuration, and duplicate records of relevant DÁ Á ÁA distances (Å ) and C-HÁ Á ÁO contact angles, ( ), with the contact type.  (Fig. 8).
In Fig. 7, the C13-H13-bearing propargyl group in each molecule is highlighted by encircling the group. Collectively the orientations of the encircled groups reinforce their orthogonality in the A and B strands relative to those in the C strands. The intrusion of the equivalent C9-H9-bearing propargyl groups from molecules A and B into the strands of molecule C and reciprocal angular intrusion of the group from molecule C only into strands of molecule A is noticeable in Fig. 7(a), and accounts for the minor differences in inter-sheet spacings. This leaves very little interaction between molecules A and B, as is evident in Fig. 7(b) and as was discussed in Section 3.2.3.1. Minor void spaces are visible, especially in Fig. 7(b), but these are too small for any molecular inclusions.

CSD searches based on Mercury Crystal Packing
Features and ConQuest search motifs involving donor and acceptor acetylenic contacts observed in compound 1.
3.4.1. Background. In the preceding diffraction studies of compound 1, intra-and intermolecular contacts were observed in which acetylenic components of the two propargyl groups participated in various situations as C-H donors and as C-H acceptors. Two principal searches of the Cambridge Structural Database (CSD; Groom et al., 2016) were carried out in order to ascertain the prevalence of these interactions and their scope in crystal engineering. These comprised firstly a Mercury-based study using highly constrained contact motifs derived from its Crystal Packing Feature (PFF) (Fig. S1) using measurements taken directly from compound 1 (Fig. S2). The second study utilized the ConQuest search tool and more loosely defined motifs (CSM) (Fig. S3) that, while artificial in their construct, were again based on general interpretations of the observed contacts (Fig. S2). The outcomes of these searches are discussed separately.

Analysis of Mercury Crystal Packing Feature (PFF)
search results. As a general observation from the results summarized in Fig. 9 and Table S2, the propargylic group gave more positive matches when it participated as a donor through its terminal acetylenic proton than when the group served as a proton acceptor (Fig. 9). An analysis of findings from each contact type is described in detail in the supporting information, and summarized in the following sections.
3.4.2.1. Propargyl group as donor. There were considerable differences when the propargyl group served as a donor. Searches C and D were the more populous in terms of positive and negative results, while search B was extremely variable, especially with respect to negative results. Searches were dependent upon DÁ Á ÁA distances, with the observed shorter distances of stand-alone strand-forming contacts in group A being less common than equivalent interstrand contact distances or distances involving shared contacts with adjacent acceptor atoms. This dependence showed strong variation with the nature of the acceptor atom and with the number and extent of prescription, including Cyclicity, in the atoms/groups associated with the acceptor atom.
3.4.2.2. Propargyl group as acceptor. Despite many fewer positive results from motifs E-J than from motifs A-D, the number of negative results from searches remained in excess of 70 in cases E-I3, and there was less scope than in the A-D cases for varying attached groups to either D or A atoms. Cases G1.1 and H1.1 provided situations with equivalent D and A types where minor differences in numbers of positive results (1 versus 3, respectively, perfectly counterbalanced by the differences in negative results, 75 versus 73) were observed. It was not possible to determine if these resulted intrinsically from very slightly higher DÁ Á ÁA contact distances, or ultimately by the significantly different D-HÁ Á ÁA bond angles brought about by intermolecular intrastrand (G1.1) compared with interstrand (H1.1) contacts ( Fig. 3 and Table 4).  Crystal packing diagrams for compound 1, showing the distinct layering of independent molecules A (green), B (blue) and C (red), as viewed in (a) along the a axis and in (b) along the b axis; the propargylic group in the 'tail' moiety of each molecule is circled in its respective colour to highlight the orthogonal directionality of the C (red) compared with the A (green) and B (blue) groups. Void spaces observed in the space-filling models are illustrated in cartoon form by dark-grey shapes with relative sizes drawn approximately to scale. This situation was helped marginally when the E1.1, F1.1 and F2.1 interactions were considered as a whole (Fig S1 and  Table 3). The E1.1 and F2.1 features showed a similarity not evident in F1.1; the bond to the distal C atom to which their donor methyl groups are attached is nearly unidirectional to the axis of the methyl C atom to acetylenic C atom trajectory, while in F1.1 it is at an acute angle (Fig. S1). Despite this observation, individual analyses showed that the more accurately measureable DÁ Á ÁA distances increased in the order F2.1 E1.1 << F1.1, which was not the same as the order of the HÁ Á ÁA distances (F2.1 F1.1 << E1.1) or the D-HÁ Á ÁA angles (E1.1 < F2.1 << F1.1). On the other hand, for E1.1 there were no positive results but 71 negative results, and for F1.1 and F2.1, both recorded 76 results, with four and three, respectively, recorded as positive.
It was concluded from the lack of direct correlation between any of these trends, including intrastand and interstrand interactions, and the observed number of positive results, that the E1.1, F1.1 and F2.1 features are equally common to those in G, H and I, in the solid state. Again, the DÁ Á ÁA distances encountered in the crystal structure of compound 1 must impose tight limitations that are not commonly met in structures within the CSD.
3.4.2.3. Analysis of structure codes for negative search results. Analysis of the breakdown of structure codes from each search (Table S2) showed relatively good coherence in the structure codes in the negative results for categories A1, A2 and C-I, but not for B1.1-B1.3. This outcome appears to mark a change from cyclic to acyclic O-atom acceptors. A similar lack of coherence was observed, albeit to a less dramatic extent because of fewer overall search results, for PFF J1.2-J1.4. Here it was noted that the donor H atom was part of a cyclic methylene group rather than from an exocyclic methyl group. Such factors were therefore important in interpreting the negative search results.
3.4.2.4. Analysis of structure codes for positive search results. As for positive results, there was a degree of coherence between structure codes within each of the search PFFs A1.1-A1.4, A2.1-A2.4, B1.1-B1.3 and C1.1-C1.4. The differences that were observed were readily attributable to variations in the attachments to the common acceptor atom in each set. In contrast, there was no overall coherence in the codes in the positive results between the first three categories, i.e. A1, A2 and B1 (Table S2). Initial thoughts of donor type or DÁ Á ÁA distance as the cause were ruled out. Instead, a much more subtle feature appeared to be at play, namely, a different type of O-atom acceptor (Fig. S2), the influence of which was not as evident in the negative results. The similarities in positive result structure codes between A2, C and D results could then be explained by HÁ Á ÁC interactions in PFF C and D that were strongly influenced by the presence of the corresponding dioxolanyl-derived O-CH 2 attachment to the formal quaternary C-atom acceptors. Mean planes of molecules A (green), B (blue) and C (red), as viewed slightly offset along the crystallographic b axis and recorded (a) in pale shades for individual molecular strands showing nonparallel but like planes for A and B, which are orthogonal to the angular plane of C strands, and (b) in dark shades for mean planes over five strands of each type, showing parallel but unequally spaced layers, which are repeated in the same order throughout.

Analysis of loosely constrained
values versus the CSD Index Numbers, with their respective search structure motifs (Fig. S3), revealed different cluster patterns in the distances, and to some degree contact angles, of each category, but no direct correlations, particularly between cases of multiple independent contacts within the one structure.
3.4.3.2. Contact distances and distance differences versus contact angles. Far more useful patterns emerged when scatterplots were constructed of D1 and D2 distances versus D-HÁ Á ÁA (ANG) contact angles for the most populous donor acetylenic contacts to O (CSM1_R1) and C (CSM1_R4) acceptor atoms on the one hand, and acceptor acetylenic contacts at terminal C atoms (CSM1_R5) and C atoms adjacent to the terminal C atoms (CSM1_R6) by sp 3 C-H donors on the other [ Fig. 10(a)].
All searches gave noticeable differences between D1 and D2 that became larger with increasing contact angles [upper portions of each plot in Fig. 10(b)]. Initial observations were codified by additionally recording scatterplots of D2-D1 values against contact angles for each contact motif [lower portions of each plot in Fig. 10(b)]. These showed a nonlinear progression of larger D2-D1 values with increasing contact angle. However, calculated trend lines for each set of the D1 and D2 distance curves unmasked stark differences for each search category in the contributions of D1 and D2. For example, at the two extremes, the CSM1_R1 interactions involved a relatively constant D2 (DÁ Á ÁA) distance and decreasing D1 (HÁ Á ÁA) distances, while those of the CSM1_R4 and CSM1_R6 interactions showed the opposite, with relatively constant D1 and decreasing D2 distances. In CSM1_R5, the D2 (DÁ Á ÁA) distances increased marginally, while the D1 (HÁ Á ÁA) distances decreased noticeably, with increasing D-HÁ Á ÁA angle, indicating that both parameters contributed. Neither absolute magnitudes of D1 and D2 in each search category, which fell in the order CSM1_R1 < CSM1_R4 < CSM1_R5 ' CSM1_R6, nor reported contact angles, which fell within four different ranges, could account for these observations. Instead, it was concluded that the type of acceptor atom (O versus C and terminal versus nonterminal acetylenic C) was probably responsible.
Relevant to the present study, an overlay of the corresponding measured data for representatives of contacts from the three crystallographic molecules A-C from compound 1 showed perfect superposition, with marker points [Fig. 10(c)] in red that were dispersed within the normal scatter across the full angular range of the data from the CDS searches.
To our knowledge, the type of comparisons just described have not been reported previously. They support the notion that acetylenic groups, particularly those originating in propargylic substituents, can participate in a wide range of weak but highly influential donor and acceptor interactions that are important in establishing crystal packing. These contacts can be mediated over a large range of contact angles, even within crystals of the one compound. It is valuable to recognize the high consistency of the correlations participated in by the terminal acetylenic component of the propargyl group, both as donor and as acceptor. As a corollary, rare departures from this norm can be an indication of additional powerful influences that might be present.

Summary and conclusion
A comprehensive single-crystal X-ray crystallographic analysis of 3,4-bis-O-propargyl-1,2:5,6-di-O-isopropylidene-d-mannitol, 1, has revealed the presence of three independent molecules A-C in the unit cell, each differing in conformation. The molecules form a close-packed layered structure aligned in the a and b axes, with each layer comprising a well-ordered homogeneous array of like molecules. Tail-to-tail acetylenic C13-H13 donor and dioxolanyl O6 acceptor contacts are associated with strand-like substructures in each layer. Multiple, much weaker, interstrand contacts are associated with the packing of parallel strands in each sheet. Strands derived from molecules A and B align co-operatively with minimal contact, along the crystallographic a axis, while those from C align orthogonally along the b axis. A thorough systematic analysis of intra-and intermolecular interactions, including an examination of the geometric parameters associated with the observed close contacts, and consideration of the crystallographic planes, allows identification of the key interactions and provides strong support for the current understanding of weak hydrogen bonds and their description as a continuum of van der Waals contacts and electrostatic interactions. The evidence supports the notion that contact strength is best assessed in a D-HÁ Á ÁA system from the DÁ Á ÁA distance (D, Å ), with a considerable flexibility in the D-HÁ Á ÁA contact angle and the geometry about the acceptor, at least when A is oxygen or carbon.
Two secondary studies of the Cambridge Structural Database (CSD) using Mercury Crystal Packing Features (PFF) and ConQuest structural motifs, based on features identified in the crystals of compound 1 involving the propargyl group, add further insight into the value of 1 as a model for the study of weak interactions in the solid state. They give mathematical credence to the close correlation that exists in these D-HÁ Á ÁA systems between the difference in distance between DÁ Á ÁA and HÁ Á ÁA, and the D-HÁ Á ÁA angle, but point to different contributions that the DÁ Á ÁA and HÁ Á ÁA parameters can have in this correlation, depending upon the particular structural motif involved.
Overall, the studies described here provide new insight into factors involved in weak acetylenic HÁ Á ÁA interactions and might well prove useful in guiding the design of chemoselective applications of such functional groups, especially where these are propagated in or close to the solid state. Data collection: APEX3 (Bruker, 2016); cell refinement: SAINT (Bruker, 2016); data reduction: SAINT (Bruker, 2016); program(s) used to solve structure: SHELXT (Sheldrick, 2015a); program(s) used to refine structure: SHELXL (Sheldrick, 2015b); molecular graphics: OLEX2 (Dolomanov et al., 2009); software used to prepare material for publication: OLEX2 (Dolomanov et al., 2009).  (17) Special details Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes. Refinement. A colourless block-like crystal of 1 with the dimensions 0.19 × 0.21 × 0.24 mm, selected under a polarizing microscope (Leica M165Z), was picked up on a MicroMount (MiTeGen, USA) consisting of a thin polymer tip with a wicking aperture. The X-ray diffraction measurements were carried out on a Bruker kappa-II CCD diffractometer at 150 K using IµS Incoatec Microfocus Source with Mo-Kα radiation (λ = 0.710723 Å). The single crystal, mounted on the goniometer using a cryo loop for intensity measurements, was coated with immersion oil type NVH and then quickly transferred to the cold nitrogen stream generated by an Oxford Cryostream 700 series. Symmetry-related absorption corrections using the program SADABS (Bruker, 2016) were applied and the data were corrected for Lorentz and polarisation effects using Bruker APEX3 software (Bruker, 2016). The structure was solved by program SHELXT (Sheldrick, 2015a) (with intrinsic phasing) and the full-matrix least-square refinements were carried out using SHELXL (Sheldrick, 2015b) through the OLEX2 (Dolomanov, 2009) software platform. Details of the experimental crystallographic data collected for compound 1 are summarized in Table 1. The non-hydrogen atoms were refined anisotropically. The H atoms were not located in the difference Fourier map. Instead, the H atoms were placed geometrically and constrained according to their environment using different AFIX commands available in SHELXL (Sheldrick, 2015b) operating via the OLEX2 (Dolomanov, 2009)  0.0317 (7) 0.0284 (7) 0.0229 (7) 0.0074 (6) −0.0044 (6) −0.0058 (6)  O4B 0.0285 (7) 0.0328 (7) 0.0248 (7) 0.0034 (6) −0.0034 (6) −0.0127 (6)  O5B 0.0290 (7) 0.0242 (7) 0.0412 (9)