Constructor Graphs as Useful Tools for the Classification of Hydrogen Bonded Solids : The Case Study of the Cationic ( Dimethylphosphoryl ) methanaminium ( dpma H + ) Tecton

The structural chemistry of a series of dpmaH (dpmaH = (dimethylphosphoryl)methanaminium) salts has been investigated using constructor graph representations to visualize structural dependencies, covering the majority of known dpmaH salts. It is shown that the structurally related α-aminomethylphosphinic acid can be integrated in the systematology of the dpmaH salts. Those dpmaH salts with counter anions that are weak hydrogen bond acceptors (ClO4 ́, SnCl62 ́, IrCl62 ́,I ́) tend to form head-to-tail hydrogen bonded moieties purely consisting of dpmaH+ cations as the primarily structural motif. In structures with weak to very weak hydrogen bonds between the dpmaH+ cations and the counter anions, the anions fill the gaps in the structures. In salts with medium to strong hydrogen bond acceptor counter ions (Cl ́, NO3 ́, PdCl42 ́), the predominant structural motif is a double head-to-tail hydrogen bonded (dpmaH)2 dimer. These dimeric units form further NH ̈  ̈  ̈ X hydrogen bonds to neighboring counter anions X, which results in one-dimensional and two-dimensional architectures.

Above all, the dpmaH + cation is an excellent tecton to construct hydrogen bonded architectures.In terms of the concepts of Crystal Engineering, the dpmaH + is a building block with a threefold hydrogen donor functionality at one end (the NH 3 group) and a hydrogen-bond acceptor functionality at the oxygen atom of the phosphoryl moiety at the other end (Scheme 1, left part).dpmaH + can thus be abstracted by a block-shaped informative icon (Scheme 1, right part) which reduces the functionality of the tecton to the striking symbols of a blue plus sign (indicating the NH 3 group) and a red dot (indicating the oxygen atom), which enables a general und uniform description of simple and especially complicated structures e.g., for dpmaH + salts.Coding of individual hydrogen bonding motifs by graph sets classification and notation has been widely used in the literature [9][10][11].The main disadvantage of classical graph sets in the context of a broader comparison of chemically varied compounds is that similar connectivities may not be displayed in the corresponding graph set descriptors.A system less frequently used which is more favorable to classify larger sections of hydrogen bonded structures and to compare related structures is based on so-called constructor graphs [10,11].In this methodology, each molecule is substituted by a dot and hydrogen bonds are symbolized by arrows pointing from the donor to the acceptor group.Infrequent use of constructor graphs may be related to the fact that the advantage of the abstraction of multifunctional molecules to dots is not intuitively comprehensible whereas the individual graph sets coding similar hydrogen-bond motifs are very handy for the description of one isolated structure or structure type.Further developments in this area concerns automated analysis and interpretation of hydrogen bonded networks [12].The present contribution is meant to exemplarily show the ability of constructor graphs to classify extended hydrogen bonded structures.Furthermore, the usage of informative icons instead of simple dots in these constructor graphs is suggested, which should be more intuitive.Modified constructor graphs illustrated by such informative icons will be used throughout this contribution.Hopefully, a broader use of constructor graphs may support activities to systematize structurally and hierarchically related hydrogen bonded solids.

Results and Discussion
The hydrogen-bond functionality of dpmaH + predestines this cation for the formation of head-to-tail connected dimers, chains or higher dimensional polymers.Most dpmaH + salts containing weakly hydrogen bond accepting counter anions have the tendency to form (dpmaH + ) n polymers.Salts with stronger hydrogen bond accepting counter anions mainly comprise (dpmaH + ) 2 of dimers which are further connected by the counter anions.

Salt Structures Based on Head-to-Tail Connected Hydrogen Bonded Polymers: (dpmaH + ) n
Hexahalogenometallate dianions of tetravalent metals like tin [13], iridium [14] and platinum [15] and some other perhalogenometallates are well known to be weak hydrogen bond acceptors, showing a tendency to bifurcated hydrogen bonds [16].The synthesis of the (dpmaH) 2 [MCl 6 ] with M = Sn, Ir gave structures that show a highly symmetrical arrangement of the [MCl 6 ] 2á nions in a monoclinic unit cell (Figure 1).The substructure formed by the anions seems to be a common feature of many hexahalogenidometallate salts, ranging from K 3 [IrCl 6 ] [17] to analogous alkylammonium salts [13][14][15]18].Hydrogen bonded (dpmaH + ) n polymers form the one-dimensional cationic substructure.This polymeric chain is formed by a head-to-tail connection of dpmaH + units, which is an ubiquitous motif throughout structural chemistry.A prominent example would be dicarboxylic acids [19], which are well documented neutral compounds forming such a hydrogen bonding scheme.However, a few cationic chains are also documented in combination with weakly coordinating anions [20][21][22].Starting from linear zig-zag arrangements, it is obvious that the formation of a ring motif should be possible.
In  The next, more complex motif can be obtained by connecting two adjacent hydrogen bonded parallel chains.Figure 3a shows the corresponding strand (cationic substructure) of the structure of the dpmaH[ClO 4 ] salt [24].To realize an optimal interaction between the neighboring chains, they are shifted against each other by one half of the repetition unit.Consequently, hydrogen bonded ring motifs with the graph set descriptor R 2 3 (9) characterize the connections between parallel chains.A more complex cationic, one-dimensional strand-type motif with the general formula dpmaHX¨dpma (X = [ ClO 4 ] ´ [24], I ´ [25]) is closely related to the double chain structure discussed before (Figure 3b).In this more complex case, the dpmaH + cation (icon as introduced before) and one neutral dpma molecule (brick-shaped icon composed of a black circle and a red dot) can formally combined to give a new tecton which is indicated by a red colored circle in Figure 3b.This new assembly generally has the same functionality as the "pure" dpmaH + tecton alone.Each dpmaHX¨dpma unit is head-to-tail connected to two adjacent ones.In addition, this primary chain structure is connected to another parallel chain in the same way as in the prototype structure of dpmaH[ClO 4 ] (Figure 3a).The structural similarity between them can be easily summarized by the two constructor graphs shown in Figure 3a  A neutral chain-type structure similar to that present in the structures of the dpmaHX¨dpma salts can be obtained by combination of the dpmaH + cation with an HSO 4 ´anion.The HSO 4 ´anion is a typical tecton which is predestined to do a head-to-tail connection.In this case, the implementation of a brick-shaped icon composed of a black circle and a red minus sign for the HSO 4 ´anion is useful (Figure 3c).In the structure of dpmaH[HSO 4 ] [26], we find the desired head-to-tail connected ion pairs (Figure 3c; highlighted by a red colored circle) which are connected to the neighboring ones in the same manner as in the structure of dpmaHX¨dpma.This similarity can easily be visualized by the three corresponding constructor graphs in Figure 3. Within the {dpmaH} + [HSO 4 ] ´ion pair, the HSO 4 ánion is a medium-strong hydrogen bond donor and at the same time a hydrogen bond acceptor.Therefore, the HSO 4 ´anion in this structure forms a hydrogen bonding scheme which is identical to that of neutral dpma molecule in dpmaHX¨dpma.For this structure, the individual graph set descriptors for the ring motifs (R 4  4 ( 12) and R 2 2 ( 9)) again do not fit with those of the structurally related structures of dpmaHX¨dpma and dpmaH[ClO 4 ].
As an intermediate conclusion, two things should be mentioned: • A comparison of the chain-type and strand-type structures discussed before has been simplified by the use of the modified constructor graphs.• The intuitive dissection of these complex hydrogen bonded structures into subunits (tectons) that look like as they were taken from a "chemical toolbox", unquestionable supports the understanding of the individual structures and should support the prediction of structural features.
The next systematic step towards a higher dimensional framework would be the construction of layered structure consisting of parallel chains.For steric reasons, this motif is not possible for the dpmaH + tecton.Furthermore, it would be very unusual for a phosphoryl group to accept more than two hydrogen bonds.A systematic search for a related tecton shows that the zwitterionic α-aminomethylphosphinic acid (H 3 N-CH 2 PO 2 Me) [27] exactly forms the predicted layered structure.This alternative tecton can be easily generated from the dpmaH + tecton by the exchange of a methyl group with an oxido group.This modification of the basic tecton generates one more hydrogen-bond acceptor atom at the formal negatively charged part of the zwitterionic α-aminomethylphosphinic acid molecule.An informative icon with a plus and a minus sign is showing the zwitterionic character of the α-aminomethylphosphinic acid (Figure 4).In the structure of α-aminomethylphosphinic acid, each of the three hydrogen atoms of the aminium group forms an unbifurcated hydrogen bond to a symmetry related molecule.The formation of a three-dimensional hydrogen bonded connection of α-aminomethylphosphinic acid tectons or of closely related molecules seems to be possible, in general, but to the best of the author's knowledge, such a structure has not been determined to date.

Salts Based on Hydrogen Bonded (dpmaH + ) 2 Dimers
For salts containg dpmaH + and counter anions, which are good or excellent hydrogen-bond acceptors, a very different structural chemistry can be observed.The predominant motif in these structures are head-to-tail connected (dpmaH + ) 2 units (Figure 5).Two out of six hydrogen atoms of the two aminium groups are used for the formation of the dimer.The four other hydrogen atoms are generally available for the formation of hydrogen bonds to the counter anions.
In the structure of dpmaHCl [28], such (dpmaH + ) 2 dicationic units are present.Each dicationic dimer donates four NH¨¨¨Cl hydrogen bonds, and each chloride anion accepts two of them to form a chain structure (Figure 5).The constructor graph for this structure illustrates the structural similarity to dpmaH[ClO 4 ]¨dpma (Figure 3b), which also consist of head-to-tail connected basic units.In the structures of dpmaH[ClO 4 ]¨dpma, the oxygen atom of the phosphoryl group accepts two hydrogen bonds to realize chain propagation.In the structure of dpmaHCl, there is no need to form such a bifurcated hydrogen bond at the phosphoryl group because of the presence of chloride anion, an excellent hydrogen bond acceptor.An alternative arrangement for a dpmaHX salt with a cation to anion ratio of 1:1 has been reported for dpmaH [NO 3 ] [29].This two-dimensionally connected structure can be understood as the next stage of aggregation (Figure 6a).Again, each dimeric ((dpmaH + ) 2 unit is connected to four anions and each nitrate anion is connected to two dicationic moieties.Two of the three oxygen atoms of each nitrate anion form hydrogen bonds.The reason for additional structural complexity must be associated with the nitrate counter anion, which obviously causes a larger distance of the (dpmaH + ) 2 dimers.Similar hydrogen bonded networks are well known for (H 2 NR 2 ) 2 [MCl 6 ] (R = alkyl, M = Sn, Ir, Pt [13][14][15]18]) and ((CH 3 ) 2 NH 2 ) 4 [MCl 6 ]Cl (M = Ru, W [30,31]) which can be discussed as an inverse structure type, as the dialkylaminium cations form two hydrogen bonds whereas there are four for each halogenometallate anions.
Finally, the (dpmaH) 2 [PdCl 4 ] salt [32] should be discussed.In this structure, each (dpmaH + ) 2 dimer and each [PdCl 4 ] 2´i ons form two hydrogen bonded connections to adjacent counter ions (Figure 6b).The chain structure generated by this connection can be understood as a structural motif already known from dpmaH[NO 3 ] (Figure 6a; blue-shaded area).This is a nice proof of the potential of this system in terms of crystal engineering.The "toolbox" for salts with strong hydrogen-bond acceptors contains dimeric (dpmaH + ) 2 units that tends to donate four hydrogen bonds, whereas the counter anions are only twofold connected.

Limitations
The use of constructor graphs, especially those with the informative icons, become cumbersome for more complex three-dimensional structures.There are similar limitations of use if there are several crystallographically independent building units and individual hydrogen bonding schemes for each of them.

Conclusions
In this contribution, it has been shown that the majority of dpmaH + salts are closely structurally related.Their structural and hierarchical dependencies can easily be visualized by so-called constructor graphs.In contrast to the use of classical constructor graphs which consist of dots and arrows [10,33,34], informative icons and colored arrows are used here for the analysis and comparison of the hydrogen bonded architectures.As abstraction is ubiquitous used in chemistry, biochemistry and related fields, this modification of a mathematical tool towards a chemist-friendly design should broaden the usability of this method.Moreover, the potential of constructor graphs is illustrated by the integration of the structurally related α-aminomethylphosphinic acid into the structure systematology of simple dpmaH + salts.

Scheme 1 .
Scheme 1. Hydrogen bonding functionality of the dpmaH + tecton (left part) and the corresponding icon useable in constructor graphs (right part).

Figure 2 .
Figure 2. (a) Showing the primary structural motif of a four-membered, hydrogen bonded ring (N-H¨¨¨I hydrogen bonds to the adjacent iodide counter anions are omitted); (b) modified constructor graph of the tetrameric (dpmaH + ) 4 ring unit.

Figure 3 .
Figure 3. (a) part of the hydrogen bonded chain structure and modified constructor graph of dpmaH[ClO 4 ]; (b) hydrogen bonded strands in the structure of dpmaHX¨dpma (X = [ClO 4 ] ´[24], I ´[25]) and its modified constructor graph (the dpma molecule is shown as brick-shaped icon composed of a black circle and a red dot; red colored circle indicates a composite tecton); (c) hydrogen bonded strands constructed from head-to-tail connected {dpmaH} + [HSO 4 ] ´ion pairs [26] and the corresponding modified constructor graph (brick-shaped icon composed of a black circle and a red minus sign is shown for the HSO 4 ´anion; red colored circle indicates a composite tecton).
and b, but not by the associated individual graph set descriptors of the hydrogen bonded rings (R 2 2 (10); R 3 4 (11); R 4 6 (15)) in the structure of dpmaHX¨dpma and those in the structure of dpmaH[ClO 4 ].

Figure 5 .
Figure 5. Hydrogen bonded structure of dpmaHCl containing (dpmaH + ) 2 dimers and chloride counter anions; a modified constructor graph for a section of the chain is shown.

Figure 6 .
Figure 6.(a) the hydrogen bonded layered structure of dpmaH[NO 3 ] and the corresponding constructor graph is shown; (b) the hydrogen bonded chain structure of (dpmaH) 2 [PdCl 4 ] and the corresponding modified constructor graph is shown.