Ring-Laddering and Ring-Stacking - American Chemical Society

Jan 5, 2005 - ABSTRACT: The ring-laddering and ring-stacking concepts of structural inorganic chemistry, having been shown previously to be useful for...
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Ring-Laddering and Ring-Stacking: Unifying Concepts in the Structural Chemistry of Organic Ammonium Halides Andrew D. Bond*

CRYSTAL GROWTH & DESIGN 2005 VOL. 5, NO. 2 755-771

University of Southern Denmark, Department of Chemistry, Campusvej 55, 5230 Odense M, Denmark Received July 21, 2004;

Revised Manuscript Received September 9, 2004

ABSTRACT: The ring-laddering and ring-stacking concepts of structural inorganic chemistry, having been shown previously to be useful for rationalizing the crystal structures of organic secondary ammonium halides, are shown also to be applicable to describe the structural chemistry of tertiary and primary ammonium halides. General examination of the directional preferences of N+‚‚‚X- contacts in the crystal structures of 196 tertiary ammonium halides (R3NH+X-) and 59 primary ammonium halides (RNH3+X-) confirms that the shortest contacts in each structure are N+-H‚‚‚X- hydrogen bonds that are close to linear. The next shortest N+‚‚‚X- contacts display preferred directions of approach toward the centers of the faces of the pseudo-tetrahedral R3NH+ and RNH3+ moieties. Association of R3NH+X- ion pairs according to these preferences leads frequently to the formation of dimers, ladders, and 2D nets in crystal structures of tertiary ammonium halides. Similar association of R3NH+X- ion pairs leads frequently to the formation of ladders, 2D nets, cubanes, and extended stacks in crystal structures of primary ammonium halides. The observed structural motifs, in particular the distribution of N+(-H)‚‚‚X- distances, are influenced by interactions between the R groups of the organic moieties, both within and between motifs. 1. Introduction The ring-laddering and ring-stacking concepts, developed by Snaith and co-workers in the mid-1980s,1 are widely applied to rationalize the structural chemistry of a variety of main-group and transition-element complexes.2 Discrete {M+X-} ion pairs are envisaged to form dimeric or trimeric rings which may associate in either a lateral manner to form oligomeric or polymeric ladders,3 or in a perpendicular manner to form cubanes,4 hexamers,5 or extended stacks (Scheme 1).6 Association is driven primarily by electrostatic forces, leading to higher coordination numbers for M+ and X-, thereby maximizing Coulombic energy. The tendency for association in either a laddering or stacking manner is controlled primarily by the steric constraints imposed by the groups that comprise the anionic moiety: where X- is an organic anion containing groups that project above and below the plane of the dimeric or trimeric rings, lateral association is encouraged, for example, in the lithium amides [R2NLi]n, and where X- contains flat groups that lie largely in the plane of the dimeric or trimeric rings, stacking association is preferred, for example, in the lithium imides [(R2CdN)Li]n. In many cases, the nature of X- is such that any further association is inhibited and discrete dimers and trimers are observed.7 The laddered, stacked, and discrete motifs may be viewed as successively smaller fragments of infinite [M+X-]∞ lattices, prevented from further association by the influence of the organic moieties. In addition to a certain predictive capability, the ringladdering and ring-stacking concepts may be applied to rationalize bond distances within complexes such as alkali-metal amides and imides in terms of 2-center or * Dr. Andrew D. Bond, University of Southern Denmark, Department of Chemistry, Campusvej 55, 5230 Odense M, Denmark. Tel: +45 6550 2545. Fax: +45 6615 8780. E-mail: [email protected].

Scheme 1. Schematic Representation of the Ring-Stacking and Ring-Laddering Concepts for {M+X-} Ion Pairsa

a Stacking of trimeric {M+X-} rings is also common in inorganic 3 complexes (not represented here).

3-center interactions, depending on whether the orbitals on N (considered as sp3 hybrids in the amides or sp2 hybrids in the imides) are oriented directly toward one M+ cation or point between two M+ cations.2 A recent examination of the structural chemistry of secondary ammonium halides, R2NH2+X-, has demonstrated that ring-laddering and ring-stacking concepts may also be applied in the organic solid state.8 The N+‚‚‚X- contacts in R2NH2+X- crystal structures display several preferred directions of approach with respect to the organic moiety (Figure 1). The two shortest N+‚‚‚Xcontacts (3.0-3.2 and 3.2-3.4 Å for X ) Cl, Br) in each structure are hydrogen bonds, lying approximately along the directions of the N+-H bond vectors. The next shortest contacts (3.2-3.5 and 3.2-3.9 Å for X ) Cl, Br) lie close to the H-N+-H plane, along the direction

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Figure 1. Preferred directions for the third-shortest (i.e., nonhydrogen-bonded) N+‚‚‚X- contacts in secondary ammonium halides, R2NH2+X- (X ) Cl or Br), forming two N+-H‚‚‚Xhydrogen bonds. Both hydrogen bonds and each of the preferred directions lie in the plane of the NH2 unit (the plane of the page).

of the bisector of the H-N+-H angle. Slightly longer contacts (4.0-4.2 and 4.0-4.4 Å for X ) Cl, Br) are also observed close to the H-N+-H plane, along the direction of an axis extending to the rear of one N+-H bond. Considering the R2NH2+ moiety as a pseudo-tetrahedral unit, these regions correspond respectively to approach toward the middle of the H‚‚‚H edge and toward the center of one R2H face. The longer N+‚‚‚X- contacts observed in the latter region are consistent with a more hindered approach resulting from the steric bulk of the R groups. Both of these preferred approaches are coplanar with the H-N+-H group, so that association of R2NH2+X- commonly occurs in a lateral manner to form extended polymeric ladders (Figure 2). Since there are two preferred approaches, two distinct types of ladders may be classified, distinguished from each other by the distribution of N+‚‚‚X- distances: Type 1 ladders (Figure 2a) contain two short N+-H‚‚‚X- hydrogen bonds that form the ladder arms and one longer N+‚‚‚Xcontact lying along the bisector of the H-N+-H angle that forms the ladder rungs; Type 2 ladders (Figure 2b) contain two short N+-H‚‚‚X- hydrogen bonds that form the ladder rungs and one section of the ladder arms, and one significantly longer N+‚‚‚X- contact toward the backside of one N+-H bond that forms the second section of the ladder arms. The N+‚‚‚X- distance distribution within the two types of ladders is dependent on the arrangement of the N+‚‚‚H bond vectors within the ladder motifs, which is in turn dependent on the alignment of the organic moieties with respect to the ladders. This is governed by interactions between organic moieties, both within and between ladders. The ring-laddering concept imparts some degree of order to the observed structures that is not obtained by a more conventional analysis of the hydrogen bonds alone: although the two types of ladders appear to form quite different hydrogen-bond motifssa cis,cis arrangement in the first case and a trans,trans arrangement in the secondsthey are quite clearly related by the ringladdering concept. Ring-stacking is also observed in secondary ammonium halides, forming discrete cubanes in one example,11 and extended stacks in several others.12 Stacking association is considerably less prevalent than laddering association, which may be attributed to the projection of the R groups of secondary ammonium moieties above and below the plane of the H-N+-H unit. The fact that ring-stacking is observed at all in the secondary ammonium halides when it is

Figure 2. Representative ladder motifs in secondary ammonium halides. (a) Type 1 ladder in PEFCUY,9 in which the third-shortest N+‚‚‚X- contact lies along the bisector of the H-N+-H angle and the hydrogen-bond motif (shaded) forms a cis,cis arrangement. (b) Type 2 ladder in BUHCIQ,10 in which the third-shortest N+‚‚‚X- contact lies to the backside of one N+-H bond and the hydrogen-bond motif forms a trans,trans arrangement.

not common in lithium amides, for example, reflects the fact that the N+‚‚‚X- distances in R2NH2+X- crystal structures are generally much longer than N‚‚‚Li distances in [R2NLi]n, thereby relaxing the steric constraints. In the initial study,8 secondary ammonium halides, R2NH2+X-, were considered since these resemble most closely amide complexes of monovalent metal cations, [R2NLi]n, for which the ring-laddering and ring-stacking concepts were first devised. In this report, it is shown that comparable motifs also exist in the solid-state structures of primary and tertiary ammonium halides, RNH3+X- and R3NH+X-. On first sight, this is perhaps somewhat surprising since the differing number of N+-H hydrogen-bond donors would be expected to lead to vastly different arrangements in each case. It is shown that ring-laddering and ring-stacking provide unifying concepts for description of the structural chemistry of primary, secondary, and tertiary organic ammonium halides. 2. Experimental Section Tertiary Ammonium Halides, R3NH+X-. A survey of the Cambridge Structural Database (CSD, version 5.25 plus January 2004 update, 306872 structures)13 using the search fragment C3NH with one intermolecular H‚‚‚X (X ) F, Cl, Br, I) contact specified in the range 1-4 Å located 730 structures, comprising 4 fluorides, 554 chlorides, 161 bromides, and 11

Ring-Laddering and Ring-Stacking

Figure 3. Spherical polar coordinate description of the geometry of the N+‚‚‚X- contacts in (a) tertiary ammonium halides and (b) primary ammonium halides (see text for full description). iodides. Duplicate entries were removed, and the structures were examined manually to remove also those molecules containing more than one ammonium center and those structures in which other donors and acceptors participate in the hydrogen-bond network. For the latter purpose, structures were omitted in all cases where the N+-H group of the ammonium center forms hydrogen bonds to any atom other than X- and in most cases where any other hydrogen-bond donor forms a hydrogen bond to X-. Manual filtering was preferred to automated removal of structures with other short H‚‚‚X- contacts to ensure correct treatment in cases where other hydrogen bonds are present but do not interfere with the N+-H‚‚‚X- system. Following this filtering, 168 chlorides, 28 bromides, and 4 iodides remained. For each of these structures, the local environment of N+ was examined and the two shortest N+‚‚‚X- vectors were retained, regardless of magnitude. Distance cutoffs were not applied at this stage to reflect the long-range nature of electrostatic forces and to ensure that the inherent directionality of the N+‚‚‚X- contacts was not obscured. Where more than two N+‚‚‚X- contacts of comparable magnitude were present, all were retained. The coordinates of the relevant atoms were orthogonalized using XP14 and geometry calculations were performed within EXCEL.15 The geometry of the N+‚‚‚X- contacts is described with respect to a plane perpendicular to the N+-H bond vector (Figure 3a). To avoid as far as possible any deficiencies in the location of the H atomsand thereby uncertainty in the definition of the reference planesits position was recalculated within XP14 prior to calculation of the geometric parameters. The N+‚‚‚X- contacts are described by spherical polar coordinates in which the polar angle θ is the angle between the N+‚‚‚X- vector and the reference plane. This is given in the range -90 e θ e 90°, with positive values denoting approach from the same side of the plane as the N+-H bond and negative values denoting approach from the opposite side of the plane. The angle (90 - θ)° is therefore equivalent to the H-N+‚‚‚X- angle. The azimuthal angle φ is defined as the inplane angle between the projections of the N+‚‚‚X- vector and the shortest N+-C bond. The angle is given in the range 0 e φ e 180°, so that there is no distinction between different directions of rotation. In this description, the N+-H bond vector of the ammonium moiety lies at θ ) 90° (with φ undefined) and the N+-C bond vectors lie close to θ ≈ -20°, φ ≈ 0, 120°. A full list of the 200 R3NH+X- structures with associated φ and θ values is available as Supporting Information.

Crystal Growth & Design, Vol. 5, No. 2, 2005 757 Primary Ammonium Halides, RNH3+X-. A survey of the CSD using the search fragment C-NH3 with three intermolecular H‚‚‚X contacts specified in the range 1-4 Å located 495 structures, comprising 4 fluorides, 405 chlorides, 69 bromides, and 17 iodides. The entries were filtered in the manner described previously to leave 41 chlorides, 13 bromides, and 5 iodides. For each of these structures, the local environment of N+ was examined and the four shortest N+‚‚‚Xvectors were retained, regardless of magnitude. Where more than four N+‚‚‚X- vectors of comparable magnitude were present, all were retained. The geometry of the N+‚‚‚Xcontacts is described with respect to a plane perpendicular to the C-N+ bond vector (Figure 3b), thus avoiding as far as possible the high degree of uncertainty associated with the positions of the H atoms of the RNH3+ group. The polar angle θ is the angle between the N+‚‚‚X- vector and the reference plane, given in the range -90 e θ e 90°, with positive values denoting approach from the same side of the plane as the C-N+ bond and negative values denoting approach from the opposite side. In this case, the angle (90 - θ)° is equivalent to the C-N+‚‚‚X- angle. The azimuthal angle φ is that between the N+‚‚‚X- vectors projected into the reference plane. The zero of φ is defined in each case as the projection of the shortest N+‚‚‚X- vector, and the angles are given as positive values in the range 0 e φ e 180°, so that there is again no distinction between different directions of rotation. In this description, the N+-H bond vectors of the ammonium moiety lie close to θ ≈ -20°, φ ≈ 0, 120° (the φ value of 0 assuming that the shortest N+‚‚‚X- contact forms part of a linear hydrogen bond). A full list of the 59 RNH3+X- structures with associated φ and θ values is available as Supporting Information.

3. Results and Discussion Tertiary Ammonium Halides, R3NH+X-. Figure 4a shows scatterplots of the φ and θ parameters for all N+‚‚‚X- contacts from the tertiary ammonium chlorides and bromides; for the fluorides and iodides, there are too few structures for meaningful discussion and these are not considered further. The shortest N+‚‚‚X- contacts in each structure (2.936-3.671 Å for X ) Cl, 3.112-3.389 Å for X ) Br) lie in the θ range ca. 6090°, predominantly toward 90°. Thus, the shortest contacts correspond unsurprisingly to N+-H‚‚‚X- hydrogen bonds that are close to linear. At this θ value, φ has little significance and spans the entire range from 0 to 180°. For this discussion, it is the second-shortest contacts that are of greatest interest. Figure 4b shows polar plots of θ versus the magnitude of the N+‚‚‚Xvector for the second-shortest contact in each structure. Considering initially the chlorides, it is clear that the shortest of these contacts (ca. 3.8-4.4 Å) are clustered in the region -90 e θ e -60° (denoted Region 1). A second less-pronounced cluster is observed at -10 e θ e 30° (Region 2), containing slightly longer contacts (predominantly 4 Å and above, with two somewhat shorter contacts also present). As the N+‚‚‚Cl- distance increases above ca. 4.2 Å, the distribution broadens and the directional preferences of the contacts become more diffuse. On the basis of this observed directionality, the subsequent discussion is focused principally on structures in which the second-shortest N+‚‚‚Cl- contact has magnitude less than 4.2 Å. This value for the distance cutoff is perhaps slightly conservative, but is chosen partly to aid brevity and partly for consistency with the previous discussion of the secondary ammonium halides, for which the same cutoff was applied.8 For the bromides, of which there are far fewer examples, the pattern resembles closely that of the chlorides, and a

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Figure 4. Distribution of the two shortest N+‚‚‚X- contacts in the crystal structures of the tertiary ammonium chlorides (left) and bromides (right): (a) all identified contacts (up to the longest of ca. 6.4 and 5.9 Å, X ) Cl, Br), with the shortest contact in each structure denoted by an open circle and the second-shortest contact by a filled circle; (b) polar plot of θ versus the N+‚‚‚Xseparation for the second-shortest contacts only. The shaded regions denote conservative estimates for broadening of the directionality and set the distance cutoffs for subsequent discussion. For both the chlorides and the bromides, the very short contacts at θ ≈ 30° form one component of a bifurcated hydrogen bond (PADFEF and VALJOH; see text); (c) second-shortest contacts only with N+‚‚‚X- distances less than 4.2 Å for the chlorides and 4.4 Å for the bromides.

distance cutoff of 4.4 Å is appropriate, again consistent with that employed previously for the secondary ammonium halides.8 Figure 4c shows scatterplots of the φ and θ parameters for only the second-shortest contacts with magnitudes less than the specified distance cutoffs. For both the chlorides and the bromides, it is clear that these contacts lie within several distinct regions. The contacts with -90 e θ e -60° (Region 1) correspond to approach of X- along an axis extending to the backside of the N+-H bond, i.e., toward the center of the R3 face of the pseudo-tetrahedral R3NH+ unit. At this value of θ, the φ parameter has little significance and spans the entire range from 0 to 180°. For the contacts with -10 e θ e 30° (Region 2), φ lies in two distinct regions, centered at 60 and 180°. These correspond to approach close to the plane perpendicular to the N+-H bond, bisecting one C-N+-C bond angle, i.e., approximately along an axis extending to the backside of one N+-C bond. Thus, Region 2 contacts correspond to approach of X- ap-

proximately toward the center of one R2H face of the pseudo-tetrahedral R3NH+ unit. The fact that the N+‚‚‚X- contacts observed in Region 2 are longer than those in Region 1 cannot simply be attributed to the steric influence of R3NH+ since Region 1 approach toward the center of the R3 face would be expected to offer greater steric hindrance than Region 2 approach toward an R2H face. Clearly, relating the closeness of approach to the steric influence of the R3NH+X- unit requires that the mutual influence of all X- anions also be taken into account. Structural Motifs in R3NH+X-. One-hundred-four R3NH+X- structures (86 chlorides, 18 bromides) were identified in which the second-shortest N+‚‚‚X- contacts (encompassing both Regions 1 and 2) lie within the specified distance limits. Selected structures are listed in Table 1, with the full list available as Supporting Information. In most cases, additional N+‚‚‚X- contacts are also evident that lie within the specified preferred regions of approach and these are included in Table 1.

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Table 1. Selected R3NH+X- Structures in Which the Second-Shortest N+‚‚‚X- Contact Lies within the Specified Distance Limitsa d (Å)

θ (°)

φ (°)

d (Å)

Cl Br Br Cl

2.996 3.159 3.236 3.113

85.4 73.6 66.0 58.0

32.3 171.7 159.8 85.7

4.151 4.332 3.678 4.107

2.4 1.3 27.4 4.5

173.3 177.2 61.2 174.3

Chains CMHBOB EDEQUZ FIYDEW HUXRIB MEADOB01

Br Cl Br Cl Br

SECQUM VALJUN ZICGOH

Cl Br Cl

3.261 3.040 3.174 3.119 3.152 3.123 3.097 3.196 3.034 3.033

62.9 87.8 80.9 85.8 88.2 81.8 80.1 77.7 89.1 88.0

88.8 96.0 35.0 82.7 60.3 118.1 113.0 60.0 163.9 163.8

4.187 3.954 4.150 3.918 4.322 4.266 3.963 4.041 3.943 3.946

-86.0 -87.9 -81.3 -81.4 -65.3 -65.4 -79.9 -81.3 -85.6 -85.9

21.2 141.8 124.1 75.4 137.6 112.8 53.6 35.3 108.5 138.0

Type 1 Ladders BMPYNP EDERAG ELCPHB10 KUNNAI HMHXZB01 PADFEF POLCEY SUKNOB SUKPUJ

Cl Cl Br Br Cl Cl Cl Cl Cl

VALJIB VEFXOT VODWUG YOVYUD ZIDBET

Discrete Dimers HIJDEJ MOATPB10 VALJOH ZIXDAL

θ (°)

φ (°)

d (Å)

θ (°)

φ (°)

Br Cl Cl Cl Cl

Ladder rung 4.103 16.5 64.4 4.286 -5.5 59.5 4.271 13.5 53.0 4.407 4.5 65.2 4.224 -7.4 67.1 3.360 34.2 54.9 4.386 -7.4 55.7 4.130 6.9 64.2 4.711 2.6 77.0 4.361 7.6 1.0 4.134 11.5 173.8 4.151 20.8 66.8 3.894 16.7 52.3 4.665 -2.8 37.5 4.652 -7.6 77.7

Ladder arm 1 3.009 78.2 127.3 3.069 82.8 2.7 3.249 85.1 69.0 3.187 86.5 11.8 3.050 86.2 112.3 2.984 63.9 148.5 2.991 77.3 67.9 3.073 85.2 91.9 3.106 76.7 115.8 3.069 80.1 27.6 3.235 60.5 63.2 3.075 72.3 125.1 3.067 80.8 150.8 3.017 83.6 166.0 3.102 86.7 156.2

Ladder arm 2 4.423 -69.2 0.7 4.077 -84.7 45.0 4.151 -84.7 3.7 4.167 -80.8 171.9 3.878 -86.9 176.7 4.258 -28.6 65.7 4.048 -67.7 56.2 4.293 -65.8 74.0 3.942 -85.9 48.1 3.980 -71.7 131.9 4.610 -68.3 123.7 4.443 -73.4 90.2 4.323 -51.2 54.5 3.971 -86.3 13.6 4.088 -74.9 177.2

Type 2 Ladders FADBUH FADCAO FUHGIY HADBET LEBHAB SAVYIX SEKTAD

Cl Br Cl Br Cl Cl Cl

Ladder rung 3.034 77.8 177.2 3.212 75.7 177.4 3.006 71.9 63.7 3.199 84.5 32.6 2.992 82.3 59.9 3.013 84.0 74.8 3.013 88.7 180.0

Ladder arm 1 4.151 13.2 56.4 4.253 15.1 59.5 3.998 27.7 177.7 4.274 6.6 179.7 4.001 13.5 178.9 4.156 -7.0 59.9 4.000 11.7 60.3

Ladder arm 2 4.210 -4.4 172.6 4.339 -4.8 174.6 4.291 -13.1 56.1 4.464 7.3 71.5 4.001 13.5 59.0 4.162 4.8 176.8 4.000 11.7 60.3

2D nets AETHPY

Cl

COSFOF COSFUL FIMNIY

Cl Br Cl

MHPSPE PEDDUX PEDFEJ POLCIC RAVXER PROCLB PROMZC01 SITJAG

Cl Cl Cl Cl Cl Cl Cl Cl

3.029 3.007 3.035 3.200 2.992 3.027 3.108 3.671 3.037 3.042 3.043 3.058 2.936 3.048

84.8 86.9 85.5 80.5 84.6 86.4 69.5 77.8 72.4 81.1 88.7 72.6 81.9 71.1

168.5 145.5 30.4 59.0 152.1 115.8 0.3 23.4 179.0 20.6 180.0 177.1 153.7 62.7

4.004 3.875 3.924 4.068 3.965 4.036 4.216 3.697 3.960 4.011 4.033 4.203 4.104 3.869

-87.0 -81.1 -85.5 -84.2 -85.2 -79.6 -7.8 -7.5 -85.9 -85.0 -87.1 -80.0 13.7 -85.7

139.1 172.0 70.4 65.8 165.8 170.9 66.9 68.2 18.7 142.8 180.0 70.5 67.5 83.3

4.272 4.446 4.298 4.467 4.446 4.266 4.247 4.162 4.250 4.220 4.161 4.269 4.168 4.212

-5.8 2.3 -8.5 -12.5 -7.2 -3.6 -3.4 -7.2 2.1 5.1 2.5 12.1 -70.8 1.8

170.4 169.5 58.0 61.5 169.3 57.2 68.2 106.3 53.2 62.0 59.0 51.6 133.5 179.7

Higher-order motifs MABZAL10

Br

74.5 166.4 168.4 33.2

4.263 5.578 4.229 4.032

8.6 -6.6 -1.0 13.6

72.5 9.4 67.0 176.1

-84.4

87.8

Cl

89.0 -6.4 83.2 77.6

4.300

POLDEZ

3.126 4.694 3.004 3.030

4.326 4.092

-7.4 5.0

170.9 61.9

d (Å)

θ (°)

φ (°)

4.684 4.491 4.632 4.514 4.843 4.292 4.535 4.492 4.903 4.383 4.161 5.951 7.498 5.266

5.4 -0.4 4.5 5.0 4.6 6.9 -61.7 -81.7 14.2 2.3 2.5 1.7 1.2 3.2

34.5 58.5 167.6 176.0 27.8 173.5 3.7 140.6 132.4 62.4 59.0 127.6 123.7 20.4

4.258

6.1

116.8

a In each case, the shortest contact is an N+-H‚‚‚X- hydrogen bond. For the remaining contacts, those within Region 1 are shown in bold text and those within Region 2 are in normal text. 3D rotatable images in PDB format are available for each structure (See Supporting Information). Literature citations are given in ref 16.

Discussion of the third- and fourth-shortest contacts is not limited to any particular distance cutoff, but rather each contact is considered in terms of its role in forming the observed structure motif. Among the structures listed in Table 1, all of the motifs derived from ring laddering that were described previously for the secondary ammonium halides are present. Stacking associa-

tion is rather more rare, but is also evident. In the following discussion, the motifs are described in terms of increasing dimensionality. Ion Pairs, Discrete Dimers, and Chains. Where there are no significant directional N+‚‚‚X- contacts other than the N+-H‚‚‚X- hydrogen bonds, the structural motifs may be classified as discrete ion pairs.

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Figure 5. One-dimensional chains formed via N+-H‚‚‚Xhydrogen bonds and Region 1 contacts in (a) SECQUM, containing linear N+‚‚‚X-‚‚‚N+ links, and (b) HUXRIB, containing bent N+‚‚‚X-‚‚‚N+ links.

These are in fact rather rare. Although 92 of the 196 chloride and bromide structures exhibit no further N+‚‚‚X- contacts within the conservative distance limits, almost all of these structures contain slightly longer contacts that are close to the preferred regions of approach, mostly with magnitude less than 5 Å.17 Figure 4b shows that the directionality of these contacts becomes less well defined at greater N+‚‚‚X- distances, but nonetheless the structures clearly resemble one of the motifs to be discussed. Among the very few examples that might genuinely be referred to as discrete ion pairs are QIRSAL,18 YIHJAA01,19 and ZIKMAH.20 Where the second-longest N+‚‚‚X- contact lies in Region 1 and there are no other significant directional N+‚‚‚X- contacts, the structures comprise one-dimensional chains (Figure 5). Representative examples of such chains are found in the chlorides HUXRIB and SECQUM, and in the bromides CMHBOB and MEADOB01. Since the Region 1 N+‚‚‚X- contact is in general close to collinear with the N+-H‚‚‚X- hydrogen bond, the principal variation within these motifs lies in the N+‚‚‚X-‚‚‚N+ angle. In the structures identified, examples are found in which this angle lies in the range ca. 115-180°. Where the second-longest N+‚‚‚X- contact lies in Region 2 and there are no other significant directional N+‚‚‚X- contacts, discrete dimers are formed. Representative examples include HIJDEJ (Figure 6a), MOATPB10 (Figure 6b), and ZIXDAL. In most of the dimers, the N+-H‚‚‚X- hydrogen bond is short and close to linear and the second N+‚‚‚X- contact has θ ≈ 0 and is much longer. Thus, there is a clear distinction between one hydrogen-bonded contact and one nonhydrogen-bonded (electrostatic) contact lying approximately perpendicular to it. In several cases, the hydrogen bond might reasonably be described as bifurcated, most notably in the bromide VALJOH, in which the second-shortest contact is only 3.678 Å (Figure 6c).21 Most dimers adopt a transoid conformation (i.e., equivalent R groups of the R3NH+ moieties lie on opposite sides of the plane containing the N+(-H)‚‚‚X- interactions), commonly across crystallographic centers of symmetry.

Figure 6. Discrete dimers in the crystal structures of (a) HIJDEJ, (b) MOATPB10, and (c) VALJOH. In (a) there is a clear distinction between a hydrogen-bonded and non-hydrogenbonded contact, while in (c) the hydrogen bond appears bifurcated. MOATPB10 (b) is a rare example of a cisoid dimer.

One example of a cisoid dimer also exists in the bromide MOATPB10 (Figure 6b). Type 1 Ladders. From the perspective of ringladdering and ring-stacking, dimers are obvious precursors to more extended motifs,22 and further association in a laddering manner is indeed observed in numerous structures. Two distinct types of ladders exist. The first (denoted Type 1) includes ladder arms that are formed via N+-H‚‚‚X- hydrogen bonds and Region 1 contacts (Figure 7a) so that the N+-H bonds lie within the ladder arms. The ladder rungs are formed via Region 2 contacts and the motifs are essentially planar. Since Region 1 contacts are in general shorter than Region 2 contacts, the N+‚‚‚X- distance distribution in Type 1 ladders is most often identical to that in archetypal ringladdered systems such as the lithium amides:2 short and intermediate distances alternate along the ladder arms, while longer contacts comprise the ladder rungs. Examples also exist in which the longest contacts form one section of the ladder arms and intermediate contacts form the ladder rungs (e.g., BMPYNP, SUKNOB, VALJIB). In most Type 1 ladders, the N+-H bonds lie exactly within the ladder arms so that there is a clear distinction between short hydrogen-bonded N+‚‚‚Xcontacts and longer electrostatic contacts lying approximately perpendicular to them. In one chloride, PADFEF, the N+-H bond points between two Cl-

Ring-Laddering and Ring-Stacking

Figure 7. Type 1 ladders in (a) POLCEY, (b) PADFEF, and (c) EDERAG. In (a) there is a clear distinction between hydrogen-bonded and non-hydrogen-bonded contacts, while in (b) the hydrogen bonds are bifurcated. In (c) the ladders are polar and no distinction can be made between intra- and interdimer contacts.

anions, forming bifurcated N+-H‚‚‚Cl- hydrogen bonds (Figure 7b), so that the ladder rungs form the intermediate N+‚‚‚Cl- distances and the ladder geometry is somewhat distorted.23 There is one further distinction within the Type 1 ladders: in the majority, the N+-H bonds within the ladder arms point in opposite directions so that (pseudo)centrosymmetric dimers are formed and a clear distinction can be envisaged between intradimer and interdimer contacts (e.g., Figure 7a). In others, all N+-H bonds within the ladder arms point in the same direction so that the ladders are polar and there is no distinction between intra- and interdimer

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contacts (e.g., Figure 7c). In most of these latter cases, the ladders are formed about crystallographic 21 screw axes. In each of the ladders described, the underlying manner of association of the R3NH+X- ion pairs and the resulting spatial distribution of the N+ and X- centers is comparable: planar infinite ladders are formed. The different distributions of the N+‚‚‚X- distances arise as a result of different orientations of the R3NH+ moiety with respect to the ladder motif. The principal variation lies in the orientation of the N+-H bond vector within the plane of the ladders: the N+-H bond may lie exactly in one ladder arm or form a bifurcated interaction across the ladder. This is reflected statistically by elongation in the direction of θ for the clusters in the scatterplots of Figure 4c. In many Type 1 ladders, the ammonium moiety itself is predominantly “flat”, with the bulk of the molecule lying largely in a plane perpendicular to the N+-H bond. This is illustrated most clearly in EDERAG (Figure 7c). The organic moieties are often interdigitated (across centers or pseudo-centers of symmetry) between adjacent ladders, in a manner similar to that described previously for the secondary ammonium halides.8 Such an arrangement is compatible with the N+-H bond vector lying exactly within the ladder arms. The unusual bifurcated hydrogen-bond geometry in PADFEF (giving the contact lying furthest to the right of the cluster at φ ≈ 60° in Figure 4b) appears to be driven largely by the fact that the organic moiety bears flat ring-based substituents, but the N+-H bond vector forms an angle of ca. 45° to the plane of these rings (Figure 7b). The rings of adjacent ammonium moieties in each ladder arm adopt interdigitated arrangements similar to those in EDERAG, but this causes the N+-H bond vector to lie at an angle to the ladder arms rather than within them. This gives rise to the bifurcated hydrogen-bond arrangement and the somewhat distorted ladder geometry. In this example, the N+‚‚‚X- distance distribution within the ladder is most clearly governed by the relative arrangements of the organic moieties, influenced by interactions between ladders. Type 2 Ladders. In a second distinct class of ladder (denoted Type 2), N+-H‚‚‚X- hydrogen bonds form the ladder rungs while the ladder arms comprise two Region 2 contacts lying at ca. 120° to each other (Figure 8a). Thus, Type 2 ladders adopt a “sawtooth” rather than a planar conformation. In all cases, a Newman-type projection along the N+-H bond vector that comprises the ladder rungs shows that the three N+-C bonds of the tertiary ammonium moiety are staggered with respect to the N+‚‚‚X- contacts of the ladder arms (Figure 8b), i.e., Region 2 contacts lie only at φ ≈ 60 and 180°. The ammonium moieties that form Type 2 ladders display one common feature: the bulk of the molecule lies to the backside of the N+-H bond vector (above the plane depicted in Figure 3a) so that the ammonium moiety presents a largely unhindered face toward the ladder motif (see Figure 8a). Where the ammonium moieties bear flat ring-based substitutents, interdigitation between ladders (often across centers or pseudo-centers of symmetry) is again common (e.g., LEBHAB, SAVYIX,24 and SEKTAD).

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Figure 8. (a) Type 2 “sawtooth” ladder in LEBHAB. The bulk of the organic moiety lies to the outside of the ladder arms; (b) Newman-type projection along the N+-H vector in SAVYIX showing the staggered orientation of the tertiary ammonium moiety with respect to the N+‚‚‚X- contacts that comprise the ladder arms.

Two-Dimensional Motifs (2D Nets). In many cases, association in a lateral manner occurs in two directions to form 2D nets. In every example identified, the R3NH+ moiety consists either of two methyl groups and a more bulky substituent attached to N via a -(CH2)nalkyl link (e.g., COSFOF, FIMNIY, SITJAG) or an N-methylated ring-based system such as N-methylpiperidine (e.g., MHPSPE, PEDDUX, RAVXER). In all of the structures, the nets contain (pseudo)centrosymmetric dimers formed via one N+-H‚‚‚X- hydrogen bond and one Region 2 contact. These dimers are aligned either in a parallel manner so that all of the N+-H bond vectors lie approximately parallel, or in a perpendicular manner so that adjacent dimers are rotated ca. 90° with respect to each other. There is no obvious correlation between the two types of R3NH+ moiety identified above and the two types of 2D arrangement. Representative examples of the first arrangement are found in POLCIC (Figure 9a), RAVXER, and PROMZC01. The motifs in POLCIC and RAVXER may be classified as 44 nets,25 resembling most closely Type 2 ladders associated further via Region 1 contacts. Since Region 1 contacts are collinear with the N+-H bond vectors, these nets are indistinguishable from Type 2 ladders when viewed in projection along the N+-H bonds (Figure 9a). In both POLCIC and RAVXER, one methyl subtituent of the R3NH+ moiety lies exclusively to the inside of the sawtooth arrangement while the bulkier substituents lie exclusively to the outside. In PROMZC01 (Figure 9b), one Region 2 contact is significantly elongated (ca. 7.5 Å) so that the motif resembles more closely a 4.82 net rather than a 44 net. Elongation of this N+‚‚‚X- contact appears to be attributable to interactions between organic moieties in adjacent 2D nets: the R groups of adjacent nets interdigitate approximately along the direction of the elongated contact, forming edge-to-face arrangements between phenyl rings that impose the long N+‚‚‚X- distance. It appears also that optimization of these interactions serves to flatten the 2D net so that one of the methyl substituents lies almost within the plane of the N+(-H)‚‚‚X- contacts (the elongated N+‚‚‚Xcontact has φ ≈ 120°; Figure 9b). Although the fourth N+‚‚‚X- contact in this case is exceptionally long and lies toward the outside of the directional preferences

Figure 9. Projections onto the plane and perpendicular to the plane of the 2D net motifs. (a) 44 net in POLCIC in which dimers are aligned in a parallel manner and the net displays a sawtooth conformation in projection along the N+-H bonds; (b) 4.82 net in PROMZC01 in which one N+‚‚‚X- contact of each N+ center is elongated and the net is flattened; (c) 44 net in MHPSPE in which adjacent R groups form cisoid and transoid arrangements with their neighbors along the directions parallel to the N+‚‚‚X- contacts; (d) 44 net in SITJAG in which adjacent R groups form cisoid and transoid arrangements with their neighbors along the directions 45° to the N+‚‚‚X- contacts.

described, the relationship between the 4.82 net in PROMZC01 and the 44 nets of POLCIC and RAVXER is clear. The remainder of the 2D nets listed in Table 1 comprise (pseudo)centrosymmetric dimers lying at ca. 90° to each other. This arrangement gives rise to 44 nets that are slightly less regular in their appearance (Figure 9c). In all cases, the R groups of the organic moieties form cisoid arrangements with their neighbors along

Ring-Laddering and Ring-Stacking

Figure 10. (a) Stacked Type 1 ladders (highlighted) in MABZAL10; (b) Type 2 ladders (highlighted) in POLDEZ, associated in a unique perpendicular manner.

one direction and transoid arrangements in the perpendicular direction. One subtle distinction exists in the conformations, namely, that the aforementioned perpendicular directions can lie either parallel to the N+(-H)‚‚‚X- contacts of the 44 net (e.g., MHPSPE, PEDDUX, and PEDFEJ; Figure 9c) or at ca. 45° to them (e.g., COSFOF, FIMNIY, and SITJAG; Figure 9d). Again, adoption of either arrangement is not obviously correlated with the molecular structure of the R3NH+ moiety and must be attributed in a general sense to optimization of the interactions between organic moieties, both within and between 2D nets. Higher-Order Motifs. Two examples were identified among the tertiary ammonium halides in which the order of the structural motif may be considered to be higher than that of a 2D net. In the bromide MABZAL10, Type 1 ladders exist which associate further in a stacking manner via Region 2 contacts (Figure 10a). The planes through adjacent ladders within the stack are not parallel, but form an angle of ca. 95° with respect to each other, presumably driven to some extent by the tendency for Region 2 contacts to lie at ca. 120° to each other. An alternative classification of the MABZAL10 structure as stacked 44 nets seems less appropriate since the 44 nets of such a description contain all N+-H bond vectors aligned in a parallel manner, an arrangement that is not observed in any other (discrete) 44 net. The distinction between the two descriptions of the structure is somewhat arbitrary; both involve laddering and stacking association of [R3NH+X-]2 rings. In the final example, POLDEZ, Type 2 ladders exist that are associated further via Region 2 contacts. The manner of this association is unique in that the ladders are turned approximately perpendicular to each other and association occurs through only one of two crystal-

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lographically distinct N atoms (Figure 10b). The Type 2 ladders and the organic moieties themselves actually resemble very closely those in LEBHAB (Figure 8a); the unique arrangement in POLDEZ must be attributed to the distinct packing requirements of the oxime ether and nitrile substituents present in that case. Primary Ammonium Halides, RNH3+X-. Figure 11a shows scatterplots of the φ and θ parameters for all N+‚‚‚X- contacts from the primary ammonium chlorides and bromides; for the fluorides and iodides, there are again too few structures for meaningful discussion and these are not considered further. The shortest N+‚‚‚X- contacts in this case have φ ) 0 by definition, with -40 e θ e 0° for the chlorides and -30 e θ e 0° for the bromides. The second- and thirdshortest contacts in both samples are clustered within the region 90 e φ e 140°, -45 e θ e 0°, corresponding in each case to N+-H‚‚‚X- hydrogen bonds. Thus, again unsurprisingly, three hydrogen bonds are formed in every structure, distributed in an approximate 3-fold arrangement about the NH3+ group, so that the hydrogen-bonding capacity of the RNH3+ moiety is utilized in full. As might be expected, the spread of the thirdshortest contacts (denoted by open circles in Figure 11a) is slightly broader than that of the second-shortest contacts (denoted by an open square). For the primary ammonium halides, it is the fourthshortest contacts that are of greatest interest. In this case, the relatively small sample size precludes any meaningful statistical examination of appropriate distance cutoffs and the 4.2 (X ) Cl) and 4.4 (X ) Br) Å limits are applied without further derivation. Figure 11b shows scatterplots of the φ and θ parameters for only the fourth-shortest contacts with magnitudes less than these specified distance limits. It is clear from the plot of the chlorides that the shortest contacts occupy several distinct regions of space. For the bromides, of which there are fewer examples, clustering is necessarily less distinct, but a similar pattern appears to be emerging. The shortest contacts (3.304 Å for the chloride ZZZIZM01 and 3.412 Å for the bromide ETAMBR) lie at φ ≈ 180, θ ≈ -80° (denoted Region 1) and correspond to approach of X- toward the center of the H3 face of the pseudotetrahedral RNH3+ group, i.e., along the direction of an axis extending outward from the N+-C bond. At this value of θ, φ has little significance. Slightly longer contacts (3.534-4.090 and 3.436-3.621 Å for X ) Cl, Br) lie in the region θ ≈ 0-30° (denoted Region 2), with the majority lying in the range φ ≈ 60-80° and one in each sample lying at φ ≈ 180°. These contacts correspond to approach of X- toward the center of one RH2 face of the RNH3+ pseudo-tetrahedron. Thus, the distributions for the primary ammonium halides are essentially identical to those for the tertiary ammonium halides. The fact that the distributions are identical for the tertiary and primary samples does not indicate identical arrangements of X- about the N+ center; Figure 4 refers to the second-shortest N+‚‚‚X- contact in R3NH+Xwhile Figure 11 refers to the fourth-shortest N+‚‚‚Xcontact in RNH3+X-. In both R3NH+X- and RNH3+X-, the “first coordination sphere” of the N+ center approximates a pseudo-tetrahedral arrangement. In R3NH+X-, this comprises three R groups and one N+-

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Figure 11. Distribution of the four shortest N+‚‚‚X- contacts in the crystal structures of the primary ammonium chlorides (left) and bromides (right): (a) all identified contacts (up to the longest of ca. 6.8 and 6.3 Å, X ) Cl, Br), with the shortest contact in each structure denoted by a shaded diamond (constrained by definition to lie at φ ) 0), the second-shortest contact by an open square, the third-shortest contact by an open circle, and the fourth-shortest contact by a filled circle; (b) fourth-shortest contacts only with N+‚‚‚X- distances less than 4.2 Å for the chlorides and 4.4 Å for the bromides.

H‚‚‚X- hydrogen bond, while in RNH3+X- it comprises one R group and three N+-H‚‚‚X- hydrogen bonds. It is the preferred directions for further N+‚‚‚X- contacts that are comparable: there is a clear preference in both cases for X- to cap one or more faces of the pseudotetrahedron.26 Hydrogen-Bonded Motifs in RNH3+X- without Further Association. Unlike the secondary and tertiary cases, three N+-H‚‚‚X- hydrogen bonds in the primary ammonium halides are sufficient alone to form ring-laddered and ring-stacked motifs. Selected hydrogenbonded structures are listed in Table 2. Among these, the ladder motif is most prevalent. There are no examples of discrete dimers or ion pairs, i.e., the hydrogen-bonding capacity of the RNH3+ moiety is always utilized in full. Ladders. The RNH3+X- hydrogen-bonded ladders resemble most closely Type 2 ladders of the tertiary ammonium halides: one N+-H‚‚‚X- hydrogen bond forms the ladder rungs and two others make up the ladder arms, forming X-‚‚‚N+‚‚‚X- angles of ca. 110° on account of the tetrahedral disposition of the N+-H bonds (Figure 12a). In all but one case, the ladder conformation is fully transoid, i.e., equivalent R groups of all adjacent ammonium moieties lie on opposite sides of the ladder plane. The N+‚‚‚X- distance distribution in most cases also resembles that of the Type 2 R3NH+X- ladders, the ladder rungs being significantly shorter than the N+‚‚‚X- contacts within the ladder arms. Exceptions to this are FINVAZ and HVALAC, in which the ladder rungs form intermediate contacts, and JACRAH and KAZPUW, in which the ladder rungs form the longest contacts. The chloride FINVAZ is the single

example of an RNH3+X- ladder with a cisoid-transoid conformation. The R group of the ammonium moiety in this case is a bulky adamantane unit, which lies exclusively to the outside of the sinusoidal ladder (Figure 12b). A similar conformation was described previously8 for the secondary ammonium halide CACVIM,28 which bears one methyl group and one bulky 2,4-di(tBu)-phenyl moiety. In HVALAC, JACRAH, and KAZPUW, the N+‚‚‚X- distance distribution appears to be influenced by the presence of additional Region 1 contacts formed to electronegative atoms bound to the R-C of the ammonium moiety (Figure 12c). In HVALAC and KAZPUW this is the oxygen atom of a carbonyl group, while in JACRAH it is a bromine substituent bound to a phenyl ring. These contacts clearly influence the magnitude of the N+‚‚‚N+ distances across the ladder (shortening them compared to most cases where the interactions are absent), thereby influencing the N+‚‚‚X- distance distribution.29 Cubanes. Three examples of discrete [RNH3+X-]4 cubanes were identified, all of which are chlorides.30 From the N+(-H)‚‚‚Cl- distance distributions, it is not possible to distinguish between “intradimer” and “interdimer” contacts, so that it is not possible to define a “ring-stacking” direction such as that usually described for archetypal ring-stacked systems such as the alkalimetal imides.2 The N+‚‚‚X- distances around each N+ center within the cubane motif have been shown previously to be influenced by the orientation of the ammonium moiety with respect to the cubane.30 In each of the three cases identified here, all four ammonium moieties within each particular structure adopt comparable orientations so that the N+‚‚‚X- distances are

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Table 2. Selected RNH3+X- Structures Displaying Ring-Laddered and Ring-Stacked Motifs Comprising Hydrogen Bonds Alonea d (Å)

θ (°)

Cl Cl Cl Cl Cl Cl Cl Cl Br Br Cl Cl Cl Cl Br

3.167 3.087 3.096 3.123 3.172 3.115 3.162 3.196 3.299 3.241 3.193 3.137 3.120 3.078 3.294

Ladder rung -30.0 -9.2 -8.3 -14.0 -18.8 -24.5 -25.6 -19.7 -35.2 -27.4 -4.6 -42.0 -14.3 -35.0 -21.4

Cubanes CUGBUB KEQNID

Cl Cl

YIQKIS

Cl

3.162 3.129 3.122 3.134 3.130 3.165

2D nets EDUGUF FINVED OTOLUC PUDKUU UFAJAM UFAJEQ VEDCOW

Cl Cl Cl Cl Cl Br Cl

3.147 3.162 3.181 3.155 3.136 3.299 3.122

Ladders AGENOP BAJPIL BAJPOR BAJPUX FINVAZ HABXAK HALMEM HVALAC JACRAH JACREL01 KAZPUW KEQMUO QAFRIY RUWGAR TAJROL

φ (°)

d (Å)

θ (°)

0 0 0 0 110.3 0 0 109.1 123.1 0 112.6 0 0 0 0

3.237 3.163 3.174 3.179 3.163 3.152 3.192 3.108 3.268 3.294 3.148 3.345 3.142 3.217 3.294

Ladder arm 1 -16.1 -30.3 -29.7 -19.4 -18.7 -3.9 -24.3 -28.7 -13.2 -5.3 -18.6 -17.7 -17.9 6.4 -26.1

-27.7 -26.7 -38.5 -27.3 -29.1 -25.4

0 0 0 0 0 0

3.163 3.149 3.129 3.150 3.156 3.168

-17.1 -17.7 -12.4 -6.7 -18.4 -20.0 -0.1

0 0 0 0 0 0 0

3.166 3.170 3.184 3.201 3.169 3.319 3.143

φ (°)

d (Å)

θ (°)

φ (°)

103.3 113.6 112.7 114.8 0 94.5 101.0 0 0 93.3 0 102.6 101.4 87.0 102.0

3.289 3.233 3.218 3.244 3.219 3.247 3.240 3.225 3.275 3.294 3.166 3.359 3.240 3.311 3.308

Ladder arm 2 -18.3 2.6 2.1 -2.0 -19.6 -35.8 -27.2 -3.4 -30.9 -5.3 -30.6 -14.0 -41.2 -41.1 -24.2

103.5 103.2 103.9 107.1 139.4 110.1 114.1 135.5 118.2 93.3 131.8 104.6 108.7 126.5 112.6

-33.1 -38.0 -25.3 -36.6 -36.2 -22.3

103.3 113.9 115.4 114.4 116.9 117.5

3.192 3.199 3.225 3.183 3.206 3.203

-36.1 -35.8 -35.4 -35.4 -35.4 -39.2

121.6 111.9 134.2 113.0 112.4 113.6

-21.2 -19.2 -22.3 -10.4 -21.1 -22.7 -1.6

110.9 120.0 125.0 136.9 111.0 108.9 104.3

3.192 3.178 3.201 3.202 3.183 3.326 3.223

-6.0 -13.7 -17.5 -32.7 -10.6 -13.4 -30.6

127.3 118.9 124.5 92.7 128.1 130.1 111.7

a 3D rotatable images in PDB format are available for each structure (See Supporting Information). Literature citations are given in ref 27.

comparable around each N+ center. To date, there have been no reported examples of hydrogen-bonded cubanes among the primary ammonium bromides. This cannot simply be attributed to unfavorable steric factors within the cubanes themselves since N+-H‚‚‚Br- contacts are longer than N+-H‚‚‚Cl-. It is perhaps noteworthy in this context that the cubane arrangement gives rise to (relatively long) Region 1 contacts across the body diagonal of the cube that must contribute some stabilizing Coulombic interaction to the motif. These may provide at least part of the explanation for the absence (to date) of bromide cubanes: it is possible that the Region 1 contacts in the bromides are sufficiently long (and therefore sufficiently less stabilizing) that the adoption of alternative arrangements becomes energetically favored.31 Of course, the primary bromide sample is very small at present, and it may simply be that [RNH3+Br-]4 cubanes await discovery. 2D Nets. On account of the 3-fold distribution of the N+-H‚‚‚X- hydrogen bonds formed about RNH3+ moieties, the 2D networks made up from hydrogen bonds alone may be classified as 63 nets.25 In all cases identified, the R groups of the organic moieties form cisoid arrangements with their neighbors along one direction and transoid arrangements in the direction ca. 120° to it. Within the examples listed in Table 2, several conformations exist. In the first (exemplified by EDUGUF, OTOLUC, UFAJAM, and UFAJEQ), the 3-fold coordination sphere of X- is approximately planar so that the six-membered rings of the 63 net form an “envelope” arrangement in which all N+ centers and two of the X- anions lie in a common plane and the third X- anion lies out of this plane (Figure 14a). Viewed

along the direction of the N+‚‚‚N+ vectors, a “sawtooth” arrangement is observed, although not exactly comparable to the sawtooth ladders described previously on account of the approximately linear N+‚‚‚X-‚‚‚N+ angle. In a second conformation (exemplified by FINVED and PUDKUU), the coordination geometry of X- is pyramidal and the six-membered rings form a boat arrangement (Figure 14b). When viewed along one set of N+H‚‚‚X- hydrogen-bond vectors, these nets clearly resemble the cisoid-transoid conformation of the sinusoidal ladder FINVAZ (Figure 12b). In a third conformation, observed in VEDCOW, the six-membered rings of the 63 net form a chair arrangement (Figure 14c). This also gives rise to an undulating net, in this case viewed most clearly in projection along the N+‚‚‚N+ vectors. Further Association via Region 1 Contacts. Nine RNH3+X- structures (six chlorides, three bromides) were identified in which the fourth-shortest N+‚‚‚Xcontact lies within the specified distance limits (Table 3). In two of these, the isostructural ethylammonium chloride (ZZZIZM01) and ethylammonium bromide (ETAMBR), the N+‚‚‚X- contact lies within Region 1. The structures contain typical transoid hydrogenbonded ladders that are stacked in an offset manner (rather than one directly on top of the other) via Region 1 contacts (Figure 15). The distinction between this arrangement and the “crinkled” 44 nets observed in R3NH+X- structures such as POLCIC and RAVXER is slight, but the stacked ladder description seems most appropriate in this case since, unlike the R3NH+Xstructures, the ladder planes in ETAMBR and ZZZIZM01 are parallel and the X-‚‚‚N+‚‚‚X- angles are ca. 90°. This structural arrangement also accommodates relatively

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Figure 12. (a) Hydrogen-bonded transoid ladder in HABXAK; (b) cisoid-transoid conformation in the sinusoidal ladder FINVAZ; (c) additional N+‚‚‚Oδ- Region 1 contacts in the ladder KAZPUW.

Figure 13. Hydrogen-bonded cubane in CUGBUB. Long Region 1 N+‚‚‚Cl- contacts are formed across the cubane body diagonals.

short Region 2 contacts (4.550 and 4.615 Å for X ) Cl, Br). If these contacts are taken into account, the structure might be considered to be a rather distorted manifestation of stacked 44 nets. At first sight, it is somewhat surprising that so few structures were identified in which short Region 1 contacts exist. Since these contacts approach the least hindered face of the pseudo-tetrahedral RNH3+ moiety, they give rise to the shortest N+‚‚‚X- distances and thereby the largest Coulombic energy. On this basis, they would be expected to be most prevalent. The apparent anomaly is clarified by examining the structures in a more general sense: many of the structures

Bond

Figure 14. Hydrogen-bonded 63 nets: (a) UFAJAM, in which the six-membered rings form an “envelope” arrangement; (b) FINVED, in which the six-membered rings form a boat arrangement. In projection along the N+‚‚‚X-‚‚‚N+ vectors, the conformation clearly resembles the sinusoidal ladder FINVAZ; (c) VEDCOW, in which the six-membered rings form a chair arrangement.

do in fact possess short Region 1 contacts, but they are more commonly formed to other electronegative atoms within the ammonium moiety rather than to X-. An example of this has already been described for the hydrogen-bonded ladder KAZPUW (Figure 12c). Association in this manner appears to be especially common in halo-substituted anilines such as CURGOL,33 EDUGUF, and JACRIP.34 In the first two of these cases, the contacts are formed within and between 2D hydrogen-bonded nets, while in the latter case they bridge across a hydrogen-bonded ladder in a manner similar to that in KAZPUW. Further Association via Region 2 Contacts. Seven structures (five chlorides, two bromides) were identified within the specified distance limits in which the fourth-shortest N+‚‚‚X- contacts lie in Region 2. These structures epitomize the ring-laddering and ringstacking concepts: they comprise five examples of 44 nets (DEAMMC02, DODAMB, DOMBOW01, HECBEW, ZZZLWK02) and two examples of extended stacks (ADOLIO and WOWXOV). Each of the 44 nets display a conformation comparable to POLCIC (Figure 9a): the R groups of adjacent ammonium moieties form cisoid arrangements with their four neighbors that lie along the directions of the N+‚‚‚X- vectors, and transoid arrangements with their neighbors lying along the diagonals of the 44 net. In projection along the N+‚‚‚Xvectors, these nets are comparable to Type 2 R3NH+Xladders (Figure 16). The organic moieties in these examples comprise either n-alkyl chains or small aromatic groups. Thus, they present minimal steric hin-

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Crystal Growth & Design, Vol. 5, No. 2, 2005 767

Table 3. Primary Ammonium Halide Structures in Which the Fourth-Shortest N+‚‚‚X- Contact Lies within the Specified Distance Cutoffsa d (Å)

θ (°)

φ (°)

d (Å)

θ (°)

φ (°)

d (Å)

θ (°)

φ (°)

d (Å)

θ (°)

φ (°)

Br Cl

3.372 3.197

-11.7 -10.4

0 0

3.377 3.215

-9.3 -8.7

110.1 109.2

3.377 3.215

-9.3 -8.7

110.1 109.2

3.412 3.304

-82.2 -80.8

180.0 180.0

Region 2 ADOLIO DEAMMC02 DODAMB DOMBOW01 HECBEW WOWXOV

Cl Cl Br Br Cl Cl

ZZZLWK02

Cl

3.134 3.092 3.278 3.294 3.144 3.150 3.149 3.131

-22.7 -12.9 -16.0 -12.3 -17.9 -21.8 -42.5 -25.5

0 0 0 0 0 0 0 0

3.151 3.159 3.341 3.312 3.200 3.182 3.182 3.132

-26.8 -21.4 -26.8 -19.7 -19.2 -47.6 -32.7 -17.6

116.1 106.9 156.1 97.7 91.1 126.2 135.6 105.9

3.224 3.214 3.377 3.331 3.212 3.212 3.199 3.135

-40.2 -26.2 -19.0 -18.6 -37.1 -23.9 -15.6 -13.9

113.0 146.8 103.0 102.2 163.7 108.5 112.5 148.2

4.090 4.025 3.621 3.436 3.534 3.853 3.837 4.060

29.9 18.4 7.8 0.8 8.4 23.5 24.0 16.0

67.0 79.0 82.2 175.4 76.4 179.3 59.8 69.7

Region 1 ETAMBR ZZZIZM01

In each case, the three shortest contacts are N+-H‚‚‚X- hydrogen bonds. 3D rotatable images in PDB format are available for each structure (See Supporting Information). Literature citations are given in ref 32. a

Figure 15. Stacked hydrogen-bonded ladders (highlighted) in ethylammonium bromide, ETAMBR. Ethylammonium chloride (ZZZIZM01) is isostructural.

Figure 16. 44 net in DOMBOW01. In projection along the N+‚‚‚X- vectors, the net is comparable to Type 2 R3NH+Xladders.

drance to lateral association in the plane of the net. Crucially, the ammonium moieties also present minimal steric hindrance to interdigitation of adjacent nets; they permit effective interdigitation of the organic moieties without requiring expansion of the N+‚‚‚X- contacts. This situation contrasts with that described for the 4.82 net in the tertiary chloride PROMZC01, for example. The 44, 63, and 4.82 nets described throughout are fundamentally comparable: the 63 and 4.82 nets may be viewed simply as 44 nets in which one or more of the Region 2 contacts are elongated. This perspective facilitates a global view of the 2D nets in the primary, secondary, and tertiary ammonium halides. On the basis of Coulombic interactions alone, the regular 44 net must be the most stable of these arrangements since it contains the greatest number of short N+‚‚‚X- contacts.35 If no other forces were in operation, 44 nets would be expected for all of the 2D motifs. The observa-

tion of 63 and 4.82 nets results from the influence of other interactions within the solids, namely, those between the organic moieties, coupled with the driving force for primary ammonium moieties to form three linear N+-H‚‚‚X- hydrogen bonds. Observation of the regular 44 nets described in this section demonstratess perhaps somewhat unexpectedlysthat the latter tendency is by no means dominant. The fact that 63 nets are rather more common than regular 44 nets in RNH3+X- illustrates primarily that formation of the latter is rarely compatible with efficient interaction between the R groups of the organic moieties. In the final two examples listed in Table 3, ADOLIO and WOWVOX, stacking association is observed. In WOWXOV,36 extended stacks are formed about crystallographic 21 screw axes, with each RNH3+ moiety forming three N+-H‚‚‚X- hydrogen bonds and one Region 2 contact (Figure 17a). The N+‚‚‚X- distances are distributed so that discrete hydrogen-bonded cubanes can be envisaged, associated further via Region 2 contacts. The organic moieties are predominantly flat, but with their planes turned approximately perpendicular to the planes of the stacked dimers. In ADOLIO, similar stacks are formed about crystallographic 42 screw axes (Figure 17b). The organic moieties are again predominantly flat, in this case lying in the plane of the stacked dimers (cf. lithium imides, for example). The distribution of the N+-H‚‚‚X- hydrogen bonds and the Region 2 contacts does not suggest discrete hydrogenbonded cubanes. In fact, a more insightful analogy can be made if the motif is considered to comprise two ladders stacked one on top of the other. The ladders in such a description are in essence identical to Type 2 ladders of the secondary ammonium halides:8 they are planar with two N+-H bonds of the RNH3+ moiety lying approximately within the plane, one forming the ladder rungs and the second forming one section of the ladder arms. The remaining section of the ladder arms is formed by a significantly longer (electrostatic) N+‚‚‚Xcontact (i.e., the Region 2 contact), lying along an axis extending to the backside of one N+-H bond. With the RNH3+ moiety in ADOLIO, a third N+-H bond projects close to perpendicular to the plane of these ladders, allowing them to stack one on top of the other via N+H‚‚‚X- hydrogen bonds. The distinction between the various descriptions of the motifs again is perhaps somewhat arbitrary; the key feature is the clear relationship between the motifs formed in the secondary and

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Bond

Figure 18. Associated Type 2 ladders in (a) GEWWIO and (b) MESCAL. In GEWWIO, the ladder planes lie approximately perpendicular to the plane of the 2D motif and the arrangement resembles stacked 63 nets. In MESCAL, the ladder planes lie parallel to the 2D motif and bifurcated Region 2 contacts (dotted lines) exist between ladders. Figure 17. Extended stacks in (a) ADOLIO and (b) WOWXOV. In ADOLIO, the motifs may be considered to contain ladders (highlighted), comparable to Type 2 ladders in secondary ammonium halides,8 associated further via N+-H‚‚‚Xhydrogen bonds. In WOWXOV, the motifs may be considered to comprise cubanes (highlighted) associated further via Region 2 contacts.

primary ammonium halides, and their description within the framework of ring-laddering and ring-stacking. It is noteworthyseven within the confines of the limited sample sizessthat stacking association is observed more frequently in the primary ammonium halides than in the tertiary sample. Structures Containing N+‚‚‚X- Contacts Outside of the Imposed Distance Limits. Further examination of the structures beyond the imposed distance limits reveals numerous additional examples of comparable structure motifs. Among the most notable examples, CISGOA forms an extended stack motif that appears to comprise a 3-connected N+-H‚‚‚X- hydrogen-bond network.37 In the manner described for the 2D nets, the cross-hexagon contacts (4.68 Å) may be considered to be extended Region 2 contacts, and this motif is therefore comparable to that in ADOLIO. The comparison is made particularly clear by viewing the structures in projection along their extended axes (the crystallographic c axis in both cases): both display a 4-fold square arrangement of the organic moieties (although with different symmetries in the projections). Two other structures, GEWWIO38 and MESCAL,39 contain archetypal Type 2 ladders that align to form extended 2D motifs. In GEWWIO, the planes through the ladders lie approximately perpendicular to the plane of the 2D motif so that the ladders associate in a stacking manner via additional Region 2 contacts (4.544 Å). The manner of the stacking is such that the sawtooth ladders are aligned “peak-to-peak” rather than “peak-to-trough”,

Figure 19. 44 nets in the structure of the quaternary ammonium halide cocrystal GIXGAV.

giving rise to a 2D arrangement that resembles stacked 63 nets (Figure 18a). In MESCAL, the planes through the ladders lie parallel to the 2D arrangement so that the ladders associate in a lateral manner, similar to the arrangement in the 44 nets DEAMMC02, DODAMB, etc. The association in MESCAL is rather curious, however, since the N+ centers lie halfway between two Cl- anions of the adjacent ladder, forming what might be best described as bifurcated Region 2 contacts (Figure 18b). This arrangement is conceptually comparable to the formation of bifurcated hydrogen bonds, and must be driven by the distinct packing requirements of the 3,4,5trimethoxyphenyl groups of the RNH3+ moieties. A Note Regarding Quaternary Ammonium Halides. Quaternary ammonium halides present a slightly more complex situation since in the absence of any N+H‚‚‚X- hydrogen bonds there is no immediate constraint on any of the N+‚‚‚X- vectors, all of the N+‚‚‚Xdistances are relatively long, and it is often rather more difficult to trace them in a rational manner through the structures. As a result, the usefulness of ring-laddering

Ring-Laddering and Ring-Stacking

and ring-stacking concepts in the quaternary ammonium halides is relatively less than that in their primary, secondary, and tertiary counterparts. A CSD survey performed in the manner similar to those described previously yielded 10 structures after filtering: ACHOLC01, BELXAR, BUXTOD, BZEPIP10, CIKBIH, GIXGAV, KAYMIG, KAYTIN, POBPOL, and XEDWAE.40 Although the distance distributions are not formally derived here, it is clear from a cursory inspection of the structures that the preferred approaches of X- anions are again those that serve to cap the faces of the R4N+ tetrahedra. The shortest N+‚‚‚X- contacts lie in the approximate range 3.9-4.1 Å, comparable in magnitude to the non-hydrogen-bonded contacts described for the primary, secondary, and tertiary systems. In several of the structures, it is possible to envisage ladders or 44 nets, most clearly in the cocrystal GIXGAV, in which the presence of a second organic moiety introduces clear boundaries within the extended arrangement of N+‚‚‚X- contacts (Figure 19). 4. Conclusions This study, together with the previous report concerning the structural chemistry of the secondary ammonium halides,8 demonstrates that comparable motifs exist in the crystal structures of primary, secondary, and tertiary organic ammonium halides. This observation is perhaps slightly surprising, since conventional analysis based on N+-H‚‚‚X- hydrogen bonds alone would suggest vastly different structures for each class of compound. It is shown that the ring-laddering and ringstacking conceptsspreviously more familiar in inorganic structural chemistrysprovide a unified framework within which to rationalize the observed structures. Several notes of caution are appropriate: the ringladdering and ring-stacking concepts are applicable for ionic materials, where maximization of Coulombic energy plays a major role in determining the solid-state structures. The ionic structures of the ammonium halides are by no means typical of organic crystals and it is not suggested that ring-laddering and ring-stacking will find widespread utility for describing organic crystals in general. In addition, this study makes no attempt toward structure prediction: even within the framework of ring-laddering and ring-stacking, there is no immediately obvious predictive correlation between the structure of the ammonium moiety and the resulting motif within its crystal structure. The motifs formed, in particular, the distribution of N+(-H)‚‚‚X- distances, are very clearly influenced by interactions between R groups of the organic moieties, both within and between the motifs themselves. It is recognized that this crucial point is treated here in a very nonspecific manner. Perhaps the most significant conclusion of the study is a reiteration of the fact that the driving forces responsible for formation of the motifs described are comparable in the organic solid state and in certain inorganic complexes for which the bonding is predominantly ionic (e.g., lithium amides and imides, main-group amides such as those of Ge and Sn, etc.). Thus, the relative plentitude of structural information available in the organic solid state might be applied to assist in rationalizing motifs observed in inorganic complexes, perhaps even to suggest routes to new target complexes.

Crystal Growth & Design, Vol. 5, No. 2, 2005 769

Preparation of new inorganic compounds guided by information derived from organic crystal structures is an intriguing prospect. Acknowledgment. I am grateful to the Danish Natural Science Research Council (SNF) for funding and to Dr. Dominic S. Wright (University of Cambridge, U.K.) for encouraging my interest in this topic. Supporting Information Available: Complete lists of CSD reference codes and associated φ and θ parameters for all structures identified. Electronic representations (PDB format) of all structure motifs referred to specifically in the text. This material is available free of charge via the Internet at http://pubs.acs.org.

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Bond (17) It is recognized that these longer N+‚‚‚X- contacts are significant. It is problematic to impose cutoffs solely in terms of distance or even directionality; each contact should be assessed in the context of the structure as a whole. The 4.2 and 4.4 Å cutoffs are applied principally to aid brevity in the discussion. (18) Newman, A. H.; Robarge, M. J.; Howard, I. M.; Wittkopp, S. L.; George, C.; Kopajtic, T.; Izenwasser, S.; Katz, J. L. J. Med. Chem. 2001, 44, 633 (QIRSAL). (19) Chnag, A.-C.; Takemori, A. E.; Ojala, W. H.; Gleason, W. B.; Portoghese, P. S. J. Med. Chem. 1994, 37, 4490 (YIHJAA01). (20) Bolte, M. Acta Crystallogr. Sect. C 1995, 51, 2587 (ZIKMAH). (21) The second component of the bifurcated hydrogen bond in VALJOH is the very short contact (3.678 Å) within Region 2 that can be seen for the bromide sample in Figure 4b. (22) For inorganic systems, Downard and Chivers (ref 2) have distinguished primary laddering units (PLUs) which are most often (although not exclusively) dimeric in nature. PLUs are considered to associate to form higher-order motifs via secondary laddering. Although these concepts are not considered in detail in this report, they are clearly applicable here and may find future utility in organic systems of this type. (23) The second component of the bifurcated hydrogen bond in PADFEF is the very short contact (3.360 Å) within Region 2 that can be seen for the chloride sample in Figure 4b. (24) The CSD notes that the crystal structure of SAVYIX is reported in the original literature (see ref 16) in space group P2, but corrects this to P21. Like most interdigitated Type 2 ladders, there is in fact a center of symmetry between ladderssthe true space group appears to be P21/m. (25) The notation is that of Wells: np describes p polygons of n edges meeting at each vertex of the two-dimensional net. In the commonly used “vertex symbol” notation, the 44 net would be denoted [4.4.4.4]. The 4.82 and 63 nets referred to subsequently would be [4.8.8] and [6.6.6], respectively: see O’Keefe, M.; Eddaoudi, M.; Li, H.; Reineke, T.; Yaghi, O. M. J. Solid State Chem. 2000, 152, 3. (26) In this respect, the tertiary and primary ammonium halides display only partial similarity with their secondary counterparts. The first coordination sphere in R2NH2+X- comprises a pseudo-tetrahedral arrangement of two R groups and two N+-H‚‚‚X- hydrogen bonds. Further N+‚‚‚Xcontacts of ca. 4 Å and greater (see Figure 1) serve to cap the faces of this unit in a manner comparable to that seen here. The shortest contacts in R2NH2+X-, however, serve to bridge the H‚‚‚H edge of the R2NH2+ moiety. There is no comparable edge-bridging approach in R3NH+X- or RNH3+X-. (27) Kazuta, Y.; Tsujita, R.; Uchino, S.; Kamiyama, N.; Mochizuki, D.; Yamashita, K.; Ohmori, Y.; Yamashita, A.; Yamamoto, T.; Kohsaka, S.; Matsuda, A.; Shuto, S. J. Chem. Soc., Perkin Trans. 1 2002, 1199 (AGENOP); Brosz, C. S.; Calabrese, J. C.; Kettner, C. A.; Teleha, C. A. Tetrahedron Asym. 1997, 8, 1435 (BAJPIL, BAJPOR, BAJPUX); Belanger-Gariepy, F.; Brisse, F.; Harvey, P. D.; Butler, I. S.; Gilson, D. F. R. Acta Crystallogr. Sect. C 1987, 43, 756 (FINVAZ); Jaeger, M.; Steglich, W.; Polborn, K. Private Communication to the CCDC, 2003 (HABXAK); Goeta, A. E.; Punte, G.; Rivero, B. E. Acta Crystallogr. Sect. C 1993, 49, 1996 (HALMEM); Usher, J. J.; English, R. B. Acta Crystallogr. Sect. B 1978, 34, 2012 (HVALAC); Lopez-Dupla, E.; Jones, P. G.; Vancea, F. Z. Naturforsch. B 2003, 58, 191 (JACRAH); Jones, P. G.; Lozano, V. Acta Crystallogr. Sect. E 2003, 59, o1092 (JACREL01); Alcock, N. W.; Crout, D. H. G.; Gregorio, M. V. M.; Lee, E.; Pike, G.; Samuel, C. J. Phytochemistry 1989, 28, 1835 (KAZPUW); Froimowitz, M.; Wu, K.-M.; Rodrigo, J.; George, C. J. Comput.-Aided Mol. Des. 2000, 14, 135 (KEQMUO, KEQNID); Sutton, L. R.; Blake, A. J.; Cooke, P. A.; Gould, R. O.; Parsons, S.; Schroder, M. Synlett 1999, 921 (QAFRIY); Blaton, N. M.; Peeters, O. M.; De Ranter, C. J. Acta Crystallogr. Sect. C 1997, 53, 1952 (RUWGAR); Klebe, G.; Krishnan, V. G.; Weiss, A.; Fuess, H. Eur. Cryst. Meeting 1983, 8, 245 (TAJROL); Knupp, G.; Frahm, A. W.; Kirfel, A.; Frohlich, T.; Will, G. Acta Crystallogr. Sect. C 1985, 41, 468 (CUGBUB); Walther, D.; Heubach, K.; Bottcher, L.; Schreer,

Ring-Laddering and Ring-Stacking

(28) (29)

(30)

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(32)

(33) (34) (35)

H.; Gorls, H. Z. Anorg. Allg. Chem. 2002, 628, 20 (YIQKIS); Trueblood, K. N. Acta Crystallogr. Sect. C 1987, 43, 711 (FINVED); Cameron, T. S.; Duffin, M.; Singh, E. B. Cryst. Struct. Commun. 1976, 5, 927 (OTOLUC); Galindo, A.; Orea, L.; Gnecco, F. D.; Enriquez, R. G.; Toscano, R. A.; Reynolds, W. F. Tetrahedron Asym. 1997, 8, 2877 (PUDKUU); Gray, L.; Jones, P. G. Z. Naturforsch. B 2002, 57, 61 (EDUGUF, UFAJAM, UFAJEQ); Gorbitz, C. H. Acta Chem. Scand. 1989, 43, 871 (VEDCOW). Riviere, F.; Ito, S.; Yoshifuji, M. Tetrahedron. Lett. 2002, 43, 119 (CACVIM). This arrangement may be compared to covalent “crosslinking”, which is observed in inorganic complexes. See for example: Hellmann, K. W.; Bergner, A.; Gade, L. H.; Scowen, I. J.; McPartlin, M. J. Organomet. Chem. 1999, 573, 156 (GUCJOD); Clegg, W.; Horsburgh, L.; Mulvey, R. E.; Ross, M. J.; Rowlings, R. B.; Wilson, V. Polyhedron 1998, 17, 1923 (VAQLEE). A fourth example exists in the crystal structure of 2,6-di(iPr)aniline hydrochloride, not yet present in Version 5.25 of the CSD or in the January 2004 update: Bond, A. D.; Doyle, E. L. Chem. Commun. 2003, 2324. The net electrostatic energy of the cubane motif is related to the reciprocal of the length of the cube edge (i.e., E ∝ r-1). Thus, the electrostatic energy for [RNH3+X-]4 decreases in the order X ) Cl > Br > I. Jellinek, F. Acta Crystallogr. 1958, 11, 626 (ETAMBR); Kaduk, J. A. Private Communication to the CCDC, 1996 (ZZZIZM01); Paulus, E. F.; Burgard, A.; Lang, H.-J.; Gerlach, U. Z. Kristallogr. New Cryst. Struct. 2001, 216, 663 (ADOLIO); Pinto, A. V. A.; Vencato, I.; Gallardo, H. A.; Mascarenhas, Y. P. Mol. Cryst. Liq. Cryst. 1987, 149, 29 (DEAMMC02, ZZZLWK02); Lunden, B.-M. Acta Crystallogr. Sect. B 1974, 30, 1756 (DODAMB); Klebe, G.; Krishnan, V. G.; Weiss, A.; Fuess, H. Eur. Cryst. Meeting 1983, 8, 245 (DOMBOW01); Barnes, J. C.; Paton, J. D.; Rae, D.; Cairns, J.; Redpath, J. Acta Crystallogr. Sect. C 1994, 50, 728 (HECBEW); Buchler, J.; Maichle-Mossmer, C.; Kovar, K.A. Z. Naturforsch. B 2000, 55, 1124 (WOWXOV). Ploug-Sørensen, G.; Andersen, E. K. Acta Crystallogr. Sect C. 1985, 41, 613 (CURGOL). Lopez-Dupla, E.; Jones, P. G.; Vancea, F. Z. Naturforsch B. 2003, 58, 191 (JACRIP). Although the 44 net contains the shortest attractive N+‚‚‚Xcontacts, of course it also contains the shortest repulsive

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(36)

(37)

(38)

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N+‚‚‚N+ and X-‚‚‚X- contacts. Evaluation of the net electrostatic energy for idealized planar netssin the manner for which Madelung constants are derived for extended ionic solidssconfirms the assertion that the magnitude of the net electrostatic energy decreases in the order 44 > 4‚82 > 63. Identification of the stacked cube motif in WOWXOV (ref 30) reveals a crystallographic error: atoms N2 (a primary ammonium group) and C20 (a methyl group), belonging to one of two independent molecules in the asymmetric unit, are interchanged. The ammonium and methyl groups in question are bound to the same chiral carbon so that the published structure appears to contain two different enantiomers within space group P21212! McDonald, I. A.; Lacoste, J. M.; Bey, P.; Wagner, J.; Zreika, M.; Palfreyman, M. G. J. Am. Chem. Soc. 1984, 106, 3354 (CISGOA). Flores-Parra, A.; Suarez-Moreno, P.; Sanchez-Ruiz, S. A.; Tlahuextl, M.; Jaen-Gaspar, J.; Tlahuext, H.; Salas-Coranado, R.; Cruz, A.; Noth, H.; Contreras, R. Tetrahedron Asym. 1998, 9, 1661 (GEWWIO). Tsoucaris, D.; de Rango, C.; Tsoucaris, G.; Zelwer, C.; Parthasarathy, R.; Cole, F. E. Cryst. Struct. Commun. 1973, 2, 193 (MESCAL). Frydenvang, K.; Jensen, B. Acta Crystallogr. Sect. B 1996, 52, 184 (ACHOLC01); Barefield, E. K.; Carrier, A. M.; Sepelak, D. J.; Van Derveer, D. G. Organometallics 1982, 1, 103 (BELXAR); Gieren, A.; Kokkinidis, M. Z. Naturforsch. C 1982, 37, 282 (BUXTOD); Carruthers, J. R.; Fedeli, W.; Mazza, F.; Vaciago, A. J. Chem. Soc., Perkin Trans. 2 1973, 1558 (BZEPIP10); Mueller, R. H.; Thompson, M. E.; DiPardo, R. M. J. Org. Chem. 1984, 49, 2217 (CIKBIH); Grebe, J.; Geiseler, G.; Harms, K.; Dehnicke, K. Z. Naturforsch. B 1999, 54, 77 (GIXGAV); Brown, D. S.; Burns, C. A.; Heaney, H.; Papageorgiou, G.; Wilkins, R. F. Acta Crystallogr. Sect. C 1990, 46, 64 (KAYMIG); Krug, V.; Muller, U. Acta Crystallogr. Sect. C 1989, 45, 2022 (KAYTIN); van der Schaaf, P. A.; Sutter, J.-P.; Grellier, M.; van Mier, G. P. M.; Spek, A. L.; van Koten, G.; Pfeffer, M. J. Am. Chem. Soc. 1994, 116, 5134 (POBPOL); Glaser, R.; Novoselsky, A.; Shiftan, D.; Drouin, M. J. Org. Chem. 2000, 65, 6345 (XEDWAE).

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