Understanding the Role Structural Changes Play in the Formation of Strong and Weak Hydrogen Bonds in Tetramethylalkyldiammonium Dithiocyanate Salts David J. Wolstenholme,*,† Jan J. Weigand,‡ Elinor M. Cameron,† and T. Stanley Cameron†
CRYSTAL GROWTH & DESIGN 2009 VOL. 9, NO. 1 282–290
Department of Chemistry, Dalhousie UniVersity, Halifax, NoVa Scotia, Canada, B3H 4J3, and Institut fu¨r Anorganische and Analytische Chemie, Westfa¨lische Wilhelms-UniVersita¨t Mu¨nster, Corrensstrasse 28/30, D-48149 Mu¨nster, Germany ReceiVed May 2, 2008; ReVised Manuscript ReceiVed September 29, 2008
ABSTRACT: Structural analyses for a series of tetramethylalkyldiammonium dithiocyanate salts have been carried out on lowtemperature and high-resolution X-ray diffraction data. This series of organic salts contains both strong and weak hydrogen bonds which vary depending on the number of methylene groups bridging the two ammonium portions of the molecules. The S-N · · · H angles associated with the strong N-H · · · N hydrogen bonds in this series progressively decrease as the length of the alkyl bridge increases (ethylene > propylene > butylene). This results in less linear interaction between the N-H donor groups and the lone pair of the N acceptor atoms. The N,N,N′,N′-tetramethylpropylenediammonium and N,N,N′,N′-tetramethylbutylenediammonium dithiocyanate salts also produce weak C-H · · · N hydrogen bonds. The C-H · · · N and N-H · · · N interactions in this series undergo bifurcation, while one set of C-H · · · N and N-H · · · N hydrogen bonds in the propylene salt appears to experience a cooperative effect. A comparison of the topological properties of the electron density has shown a number of similarities and differences in the electronic nature of the strong and weak interactions in all three salts. This has all led to a better understanding of the electronic nature of these interactions and how they logically distribute themselves in the crystalline state. Introduction The design and understanding of new materials with desirable physical and chemical properties is of paramount importance in solid state chemistry. One way that this can be achieved is by generating a desired packing motif within a crystalline framework.1,2 The manipulation of strong and weak intermolecular interactions represents a common method of facilitating a particular arrangement of molecules in the crystalline state. Hydrogen bonds (both strong and weak) represent an important class of intermolecular interactions used in the formation and stabilization of molecular and ionic crystals.1-6 The investigation of intermolecular interactions through experimental charge density studies has provided a means of understanding these interactions based on their electron densities rather than being limited to geometrical features alone.7-15 The theory of atoms in molecules (AIM) extracts information on chemical bonding from the experimental or theoretical topology of the electron density.16 This theory states that the nuclei of two bonded atoms are linked by a line, commonly referred to as a bond path (BP), in which the electron density is a maximum with respect to any neighboring line. A rational BP can be considered as a universal indicator of chemical bonding regardless of its nature.16 A bond critical point (BCP) represents a saddle point in the electron density, at which the electron density is a minimum along the BP and a maximum in the two directions perpendicular to the tangent of the BP. This special point on the interatomic surface can be considered as the gateway between two bonded atoms. The BCP possesses several important topological features used in the characterization of chemical interactions (the accumulation of electron density, Fb(r), and the Laplacian of the electron density, 32Fb(r)). In general, closed-shell interactions (i.e., hydrogen * To whom the correspondence should be addressed. D. W. phone, +1-(902)494-3759, e-mail.
[email protected]. † Dalhousie University. ‡ Westfa¨lische Wilhelms-Universita¨t Mu¨nster.
bonds) possess Fb(r) < 0.5 e Å-3 and positive 32Fb(r) values. The positive 32Fb(r) values indicate that a local charge depletion is occurring at the BCP for these interactions. In open-shell interactions (i.e., covalent bonds), the 32Fb(r) values are negative, indicating that a local charge concentration is occurring at the BCP. The investigation of hydrogen bonds involving cationic donors and anionic acceptors (X+-H · · · Y-, X/Y ) N, O, S, etc...) has received a considerable amount of attention in a variety of different fields of science.1-4 However, experimental charge density studies involving these types of interactions are relatively scarce in the literature.17-22 Recently, a series of symN-methyl substituted ethylenediammonium dithiocyanate salts were shown to produce intricate strong and weak hydrogen bonding networks that varied depending on the N-H · · · SCN(donor/acceptor) ratio.21,22 This provided a means of studying the progression of both classes of hydrogen bonds upon varying the number of available N-H donor groups. However, the effect of lengthening the alkyl bridge between the two ammonium portions of the molecules has yet to be investigated. The present study involves a detailed structural analysis of the strong and weak interactions present in a series of tetramethylalkyldiammonium dithiocyanate salts (Scheme 1). These salts possess a variety of different structural features which have an effect on the formation of both the strong and weak hydrogen bonds and their relative distributions. The variations in the strong and weak hydrogen bonds occur exclusively as a result of the lengthening of the alkyl bridge between the two ammonium cations, since the ionic charge is consistent throughout the series. The structural analysis is followed by a comparison of the topological properties of the electron density for the salts in this series. The similarities and differences associated with the electronic nature of the hydrogen bonding and other intermolecular interactions in the title compounds have been thoroughly analyzed. Thus, this study provides a better under-
10.1021/cg800452w CCC: $40.75 2009 American Chemical Society Published on Web 12/08/2008
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Crystal Growth & Design, Vol. 9, No. 1, 2009 283
Scheme 1. Structural Diagrams of the Tetramethylalkyldiammonium Dithiocyanate Salts
Table 1. Experimental X-ray Data
compound formula refinement crystal size (mm) formula weight space group temperature (K) a (Å) b (Å) c (Å) R (deg) β (deg) γ (deg) V (Å3) Z Dc (g/cm) F(000) µ (mm-1) no. of observed reflections no. of reflections (multipole) Rint R(F)spherical R(F)multipole Rw(F)multipole GOFspherical GOFmultipole collection range (sin θ)/λ
salt II,
salt III,
N2C7H20, 2(SCN) multipole 0.22 × 0.11 × 0.10 248.43 P212121 (No. 19) 123 7.5086(1) 11.3385(3) 16.1484(6) 90.0 90.0 90.0 1374.80(7) 4 1.200 536 0.366 64300
N2C8H22, 2(SCN) multipole 0.16 × 0.12 × 0.11 262.44 P21/c (No. 14) 123 8.7211(8) 7.2486(8) 12.1118(17) 90.0 105.612(5) 90.0 737.41(15) 2 1.182 284 0.345 44366
5743
3957
2.60% 3.53% 2.04% 2.42% 1.485 1.199 -17 e h e 20; -26 e k e 26; -33 e l e 42 1.303
2.80% 6.54% 2.55% 2.18% 1.073 1.097 -21 e h e 21; -16 e k e 17; -24 e l e 28 1.303
standing of the role that small structural changes can play in the formation of strong and weak hydrogen bonds in ionic crystals. Experimental Section23 Synthesis and Crystallization Details for Salts II and III. The synthesis of salts II and III involved the appropriate pure amine (∼1-2 mL, 1 mmol), (CH3)2HN(CH2)nNH(CH3)2 [n ) 3 (salt II) or 4 (salt III)] being treated with dilute H2SO4 (1 M) until the resulting solutions were slightly acidic, as indicated by a faint pink color on pH paper. The solution were then treated with Ba(SCN)2 solution until no BaSO4 precipitate was formed. The solutions were then filtered to remove the BaSO4 and left to crystallize under a desiccant. High quality crystals were then obtained from a recrystallization in ethyl alcohol. The synthesis and crystallization of salt I were carried out using a similar procedure.21 Single Crystal Data Collection and Processing. A colorless needleshaped crystal for both salts II and III was mounted on the end of a “MicroMount”. A Micromount is essentially a tube of polyimide (used in Kapton tape) cut away to provide a nib-like shape with a loop at the top where the crystal is mounted. The high-resolution, single-crystal X-ray diffraction data were collected on a Rigaku RAPID diffractometer using a sealed Mo KR radiation source. The details for each of the
X-ray diffraction experiments are given in Table 1. Both compounds were collected at a temperature of 123 ( 1 K, to maximum 2θ values of 144.42 (II) and 144.30° (III). The data for compound II were collected with 4 scans, resulting in a total of 114 images with an exposure rate of 35.0 [min/5.0°], and slices of ω between 50-170°, 20-185°, 52.5-172.5°, and 22.5-187.5° in increments of 5° [χ ) 0°, 54°, and φ ) 0°, 180°]. A total of 82 images were collected for compound III, in which a series of data sweeps were performed using ω scans from 40-70°, 76.25-151.25°, 46-98°, 20-170°, 42.5-72.5°, and 78-153° in increments of 5° [χ ) 0°, 54°, and φ ) 0°, 90°, 180°], with an exposure rate of 30.0 [min/5.0°]. These strategies provided high-resolution, large redundancy, and reasonable completeness in the data sets. The data collections were processed with d*TREK as incorporated in the CrystalClear software package.24 The structures were then solved by direct methods and expanded through Fourier techniques using the CrystalStructure software package.25 The thermal ellipsoid plots for these compounds were all generated using the ORTEP-3 program.26 Multipole Refinement. The electron distributions for salts II and III were obtained from multipole expansions, incorporating the HansenCoppens model.27 The scattering factors used throughout the multipole refinement were those derived by Su, Coppens, and Macchi for all atoms.28,29 The least-squares refinements involved the minimization of the ∑w(|F0| - K|Fc|)2 function for all reflections with I > 3σ(I). The multipole refinements for salts II and III were carried out with a (sin θ)/λ limit of 1.0, since the reflections greater than this cutoff were very weak and fell into the realm of the background. The multipole expansion was applied up to the hexadecapole level [lmax ) 4] for all the nonhydrogen atoms and up to the dipole [lmax ) 1] level for all hydrogen atoms. Separate κ and κ′ parameters were employed for each chemically unique heavy atom until a reasonable model was achieved. The expansion/contraction parameters for the hydrogen atoms were left fixed at the default XDLSM value of 1.2. The representation of the core electrons for sulfur atoms has previously been shown to produce deficiencies when the default nl and ξ values are used in multipole refinements.30 The nl and ξ parameters were therefore chosen based on a previous theoretical study, in order to produce the best R-factors and residual features [nl ) 2,2,4,6,8 and ξ ) 3.6].30 The sulfur atoms were also refined using third-order coefficients of a Gram-Charlier expansion, which has been shown to provide accurate representations of the thermal motion surrounding S atoms.31 The addition of these coefficients significantly improved the residual features of the electron density for these salts. The C-H and N-H bond lengths were set to the reported neutron diffraction distances of similar compounds [C-H ) 1.059 Å, N-H ) 1.03 Å].32 A high-order ((sin θ)/λ g 0.7) refinement of the heavy atoms was carried out to obtain initial positional and thermal parameters for the heavy atoms. This was followed by a low-order ((sin θ)/λ e 0.7) refinement of the hydrogen atoms to obtain initial positional and isotropic thermal parameters for these light atoms. The following strategy was then cycled through until convergence was achieved. (a) Pv, (b) Plm, (c) κ and κ′ for all heavy atoms, (d) Pv and Plm, and (e) positional and thermal parameters for all heavy atoms. The difference mean square displacement amplitudes (DMSDA) for all bonds were found to be within the Hirshfeld limits. An accurate scale factor has been applied to the multipole refinement of salts II and III as shown by the normal distribution plots (Supporting Information, Figure S1).33 The high qualities of the final models are highlighted in the residual maps for all the ions of interest (Supporting Information, Figure S2). The XDPROP module was used to determine the topological properties of the electron density at the BCP for all the interactions of interest. The topological plots relating to the electron density were produced using the XDGRAPH option in XD2006.34
Results and Discussion23 The salts of compounds I,21 II, and III form colorless crystals in the space groups, P1j (No. 2), P212121 (No. 16), and P21/c (No. 14), respectively. This illustrates the flexible nature of these ion pairs in forming a variety of different packing motifs. Figure 1 shows ORTEP views of the three salts, indicating the atom labeling for their asymmetric units. The salts of compounds I and III consist of half an ion pair (half the dication and one thiocyanate anion) in their respective asymmetric units, with
284 Crystal Growth & Design, Vol. 9, No. 1, 2009
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Figure 1. ORTEP view of (a) salt I, (b) salt II, and (c) salt III at 123 K with 50% ellipsoids.
Figure 2. Crystal packing diagrams for salts (a) I, (b) II, and (c) III, viewed in the bc plane.
the remainder being generated via inversion centers located directly in the middle of the alkyl bridges. The asymmetric unit for salt II consists of one complete N,N,N′,N′-tetramethylpropylenediammonium dithiocyanate salt. In order for consistency in the description of these three salts, they will each be described with respect to complete neutral ion pairs. Structural Details and Crystal Packing. The tetramethylalkyldiammonium dithiocyanate salts investigated in this study each possess significant structural differences, which results in the formation of diverse hydrogen bonding networks. This series of tetramethylalkyldiammonium dications progressively provides longer alkyl bridges between the two ammonium portions of the molecules (ethylene f propylene f butylene), while maintaining the same number of N-H donor groups and the same overall ionic charges. Hence, the variations in the strong and weak hydrogen bonds result solely from the lengthening of the alkyl bridge. When the operations of the inversion centers are taken into account, the two ammonium portions of salts I21 and III arrange themselves in a trans orientation, resulting in both N-H donor groups facing in opposite directions.35 However, the uneven number of methylene groups in salt II results in the formation of a “cavity” between the two ammonium portions of the dication, which allows both N-H donor groups to face in the same direction. The crystal packing for salts I-III produces different arrangements of the diammonium dications and the thiocyanate anions (Figure 2). The orientations of these ion pairs in these
crystal lattices are primarily determined by the strong and weak interion interactions between symmetry related units. The 35 unique interion interactions found in these three salts can be separated into five distinct types: N-H · · · N, C-H · · · N, C-H · · · S, C-H · · · Cπ, and C-H δ+ · · · δ+ H-C. The packing of salt I results in each thiocyanate anion forming one N-H · · · N, one C-H · · · N, and one C-H · · · Cπ interaction, along with four C-H · · · S interactions.21 The crystalline geometry for salt II results in two unique thiocyanate anions, which each form one N-H · · · N, two C-H · · · N, four C-H · · · S, and one C-H · · · Cπ interactions (Figure 3a). In addition, the second thiocyanate anion (S2-C2-N2) orients itself so that an additional C-H · · · N interaction is formed. Finally, the crystal lattice for salt III results in each thiocyanate anion forming one N-H · · · N, three C-H · · · N, five C-H · · · S, and one C-H · · · Cπ interaction (Figure 3b). The tetramethylbutylenediammonium dication also forms one unique intramolecular C-H δ+ · · · δ+ H-C interaction. Progression of the Strong and Weak Hydrogen Bonds. A recent study of the progression of strong N-H · · · N hydrogen bonds in a series of diammonium dithiocyanate salts has shown that these interactions form linear then bifurcated N-H · · · N hydrogen bonds upon varying the N-H · · · SCN- ratios (the 2:1 and 3:1 ratios result in N-H · · · N bifurcation).22 However, in the present series of diammonium dithiocyanate salts, the N-H · · · SCN- ratio is consistently 1.1 which provides only one classical N-H donor group per thiocyanate anion. The lengthening of the alkyl bridge thus has no effect on N-H · · · N
Formation of Strong and Weak Hydrogen Bonds
Crystal Growth & Design, Vol. 9, No. 1, 2009 285
Figure 3. Illustrative plots of the BP character for all the strong and weak interactions present in (a) salt II and (b) salt III. The BPs and BCPs are represented by dashed lines and solid dots, respectively. The symmetry operations for these interactions are the same as those given in Table 3.
hydrogen bonds being formed (they remain nearly linear in all three salts). On the other hand, the weak C-H · · · N and C-H · · · S hydrogen bonds formed are significantly different upon varying the number of methylene groups in the alkyl bridge. In salt I, the nitrogen end of the thiocyanate anions produce no C-H · · · N hydrogen bonds, while the S atoms form two C-H · · · S hydrogen bonds.21 However, the thiocyanate anions in salts II and III each form one weak C-H · · · N hydrogen bond. These weak hydrogen bonds form solely from methylene groups of the extended alkyl bridges. The remaining C-H · · · N interactions in these two salts are best described as van der Waals in nature. The C-H · · · S hydrogen bonds in salt II involve a methylene group of the bridging region and an N-methyl group, while the C-H · · · S hydrogen bonds in salt III involve only N-methyl groups of the dication. These observations appear to indicate that there is a degree of order in the formation of these weak interactions. The C-H · · · N hydrogen bonds preferentially form to the methylene groups while the C-H · · · S hydrogen bonds use whichever donor alkyl group is available. The crystalline geometry of salt III also allows for the formation of a unique intramolecular H-H bond, which closes a six-membered ring [H2a-C2-C3-N2-C4-H4b]. This type of intramolecular H-H bond is similar to those found in polycyclic aromatic hydrocarbons containing a fjord region.13 It is noteworthy, that the thiocyanate anions in all three salts consistently form a single weak C-H · · · Cπ interaction. The use of statistical and quantum-mechanical methods has shown that thiocyanate anions preferentially form hydrogen bonds with consistent geometries at the nitrogen [θN ) S-N · · · H ) 180°] and sulfur [θS ) N-S · · · H ) 105°] ends of these anions.36,37 The involvement of these acceptor atoms in multiple hydrogen bonds can result in deviations from these preferred angles. The strong and weak hydrogen bonds in this series each possess consistent θN and θS angles as shown in Table 2. The strong N-H · · · N hydrogen bonds progressively form interactions that are less collinear between the N-H donor groups and the axis of the thiocyanate anions (θN) with salt I > salt II > salt III. In salts II and III, the smaller θN values are consistent with multiple hydrogen bonding to the N acceptor atoms of the anions. In fact, the θN values associated with the N-H · · · N and C-H · · · N hydrogen bonds in these two salts are very similar to those of the bifurcated N-H · · · N hydrogen
bonds in N,N′-dimethylethylenediammonium dithiocyanate salts [θN ) 131.18° and 147.47°].22 However, the strong bifurcated N-H · · · N hydrogen bonds in N,N′-dimethylethylenediammonium dithiocyanate form at nearly right angles to each other [H1 · · · N1 · · · H3 ) 81.16°].22 Here the N-H · · · N and C-H · · · N bifurcated hydrogen bonds form at a much more acute angle to each other [H · · · N · · · H ) 58.57°, 64.17° (salt II) and 61.07° (salt III)]. This can possibly be attributed to the weaker nature of the C-H · · · N hydrogen bonds in these salts, compared with the strong N-H · · · N hydrogen bonds in the N,N′-dimethylethylenediammonium dithiocyanate salts. The C-H · · · S hydrogen bonds in the three salts of interest possess θS angles [θS ) 125.75°, 136.01° (salt I), 81.75°, 108.70° (salt II), and 139.46° (salt III)] in which the H donor atoms can be considered as approaching the lone pair of the S acceptor atom from approximately the preferred 105° angle. In these three salts, the weak C-H · · · Cπ interactions appear to consistently form a rational geometry, with the C-H donor groups of the dication forming perpendicular to the C-N π system of the anions [θπ ∼ 90°]. In general, the strong and weak hydrogen bonds in this series tend to form nearly linear interactions between the donor groups and the acceptor atoms (X-H · · · Y, X ) N and C, Y ) N and S). Topological Comparison of the Electron Densities. The topological properties of the electron density for the strong and weak interactions in salts I-III provide significant insight into the electronic similarities and differences between these interactions. The details for all the topological parameters used to characterize these interactions are given in Table 3. The location of a consistent BP and BCP establishes the existence of all the interactions, as shown in Figure 3. The interaction lengths, Rij, for the N-H · · · N and C-H · · · S hydrogen bonds, along with the C-H · · · N, C-H · · · S, and C-H · · · C π van der Waals interactions are relatively similar in all three salts. However, the Rij values associated with the C-H · · · N hydrogen bonds in salt II and III are considerably shorter than the C-H · · · N van der Waals interactions. The Rij values for these three hydrogen bonds are consistent with those of the C-H · · · N hydrogen bonds found in the N,N,N,N′,N′,N′-hexamethylethylenediammonium dithiocyanate structure, which exclusively forms weak interactions.22
286 Crystal Growth & Design, Vol. 9, No. 1, 2009
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Table 2. Geometrical Parameters for all the Inter-Ion Interactions in Salts I-IIIa
interaction
internuclear distance d (Å)
θN (deg)
1.7602
167.45
2.8116
133.40
θS (deg)
θH (deg)
Salt I N1 · · · H2-N2 -1 + x, +y, +z N1 · · · H2b-C2 3 - x, -y, 1 - z S1 · · · H2b-C2 +x, 1 + y, +z S1 · · · H3b-C3 2 - x, -y, -z S1 · · · H3c-C3 +x, 1 + y, +z S1 · · · H4b-C4 +x, 1 + y, +z C1 · · · H4c-C4 2 - x, -y, 1 - z
163.71 116.17
3.0597
127.36
137.75
2.8400
125.75
172.62
2.7958
136.01
153.05
2.9508
168.81
145.57
θπ ) 76.18
140.91
2.7957
θπ ) 99.77
1.8019
155.31
166.79
1.7568
151.82
161.11
2.4052
139.61
145.73
2.8427
102.48
138.74
2.4681
121.98
143.12
2.6603
104.63
163.78
2.8559
69.80
133.65
Salt II N1 · · · H2-N4 +x, +y, +z N2 · · · H1-N3 +x, +y, +z N1 · · · H4b-C4 +x, +y, +z N1 · · · H7c-C7 +x, +y, +z N2 · · · H5b-C5 +x, +y, +z N2 · · · H8c-C8 -x, 3/2 + y, -1/2 - z N2 · · · H9c-C9 +x, +y, +z S1 · · · H3b-C3 -x, 3/2 + y, 1/2 -z S1 · · · H6b-C6 1 /2 - x, 2 - y, 1/2 + z S1 · · · H6c-C6 -x, 1/2 + y, 1/2 - z S1 · · · H7a-C7 1 /2 - x, 2 - y, 1/2 + z S2 · · · H7a-C7 -x, -1/2 + y, 1/2 - z S2 · · · H8a-C8 -1/2 + x, 3/2 - y, 1 - z S2 · · · H9a-C9 -1 + x, +y, +z S2 · · · H9b-C9 -1/2 + x, 3/2 - y, 1 - z C1 · · · H6a-C6 1 - x, 1/2 + y, 1/2 - z C2 · · · H3a-C3 1 - x, -1/2 + y, 1/2 - z
2.7030
81.75
157.55
2.8847
135.77
152.20
2.9280
139.49
160.97
2.9321
104.33
152.65
3.0039
112.87
109.82
2.8009
120.14
166.50
2.8493
108.70
163.76
3.0088
106.75
153.44
2.6712
θπ ) 88.08
θπ ) 91.12
169.52
2.7840
θπ ) 88.80
θπ ) 89.28
135.53
1.7583 2.6250
148.95 122.24
168.58 147.41
2.6664
85.82
155.46
2.7059
110.35
161.20
Salt III N1 · · · H1-N2 1 - x, -1/2 + y, 1/2 - z N1 · · · H2b-C2 -1 + x, 1/2 - y, 1/2 + z N1 · · · H3a-C3 1 - x, -y, -z N1 · · · H5b-C5 -1 + x, +y, +z S1 · · · H2a-C2 1 - x, 1 - y, -z S1 · · · H4a-C4 1 - x, -y, -z S1 · · · H4b-C4 1 - x, 1 - y, -z S1 · · · H4c-C4 +x, +y, +z S1 · · · H5a-C5 +x, +y, +z C1 · · · H3b-C3 -1 + x, +y, +z C2-H2a · · · H4b-C4 +x, +y, +z a
2.9843
96.10
146.33
2.9901
94.11
149.03
2.7734
139.46
169.86
2.8486
144.86
159.61
2.9766
113.55
154.60
θπ ) 86.22
177.82
2.6031 2.1652
θN ) S-N · · · H, θS ) N-S · · · H, θH ) C-H · · · N/S, and θπ ) N/S-C · · · H.
θπ ) 91.77
106.15/113.92
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Crystal Growth & Design, Vol. 9, No. 1, 2009 287
Table 3. Topological Properties of the Electron Density at BCPs for all the Inter-Ion Interactionsa interaction
type of interaction Fb(r) (e Å-3) 32Fb(r) (e Å-5) Rij (Å) ∆rH + ∆rA (Å) ∆rH - ∆rA (Å) bond energies (kJ/mol)
Salt I N1 · · · H2-N2 -1 + x, +y, +z N1 · · · H2b-C2 3 - x, -y, 1 - z S1 · · · H2b-C2 +x, 1 + y, +z S1 · · · H3b-C3 2 - x, -y, -z S1 · · · H3c-C3 +x, 1 + y, +z S1 · · · H4b-C4 +x, 1 + y, +z C1 · · · H4c-C4 2 - x, -y, 1 - z
HB
0.271
3.850
1.761
1.039
0.154
-51.72
VDW
0.034
0.492
2.832
-0.032
-0.021
-3.35
VDW
0.034
0.423
3.070
-0.130
0.201
-3.04
HB
0.034
0.647
2.842
0.098
0.333
-5.06
HB
0.033
0.556
2.887
0.053
0.260
-3.59
VDW
0.037
0.493
2.961
-0.021
0.229
-3.53
VDW
0.041
0.553
2.799
0.251
-0.095
-4.04
HB
0.269
3.576
1.804
0.946
0.090
-51.30
HB
0.356
3.606
1.760
0.990
0.097
-72.31
HB
0.078
1.084
2.417
0.333
0.064
-9.38
VDW
0.032
0.457
2.860
-0.110
0.092
-3.08
HB
0.066
0.946
2.498
0.252
0.067
-7.67
VDW
0.038
0.562
2.665
0.085
0.094
-3.89
VDW
0.044
0.641
2.869
-0.119
0.267
-4.63
HB
0.062
0.779
2.733
0.267
0.080
-6.57
VDW
0.048
0.584
2.892
0.108
0.134
-4.63
VDW
0.044
0.528
2.934
0.067
0.116
-4.11
VDW
0.040
0.543
2.940
0.061
0.187
-3.93
VDW
0.050
0.578
3.068
-0.068
-0.001
-4.75
VDW
0.047
0.721
2.807
0.193
0.236
-5.19
HB
0.055
0.662
2.854
0.146
0.128
-5.49
VDW
0.038
0.468
3.014
-0.014
0.112
-3.47
VDW
0.041
0.597
2.728
0.322
-0.007
-4.24
VDW
0.039
0.488
2.847
0.203
-0.124
-3.62
N1 · · · H1-N2 1-x,-1/2+y,1/2-z
HB
0.275
3.909
1.761
0.989
0.261
-54.13
N1 · · · H2b-C2 -1 + x, 1/2 - y, 1/2 + z N1 · · · H3a-C3 1 - x, -y, -z N1 · · · H5b-C5 -1 + x, +y, +z S1 · · · H2a-C2 1 - x, 1 - y, -z S1 · · · H4a-C4 1 - x, -y, -z S1 · · · H4b-C4 1 - x, 1 - y, -z S1 · · · H4c-C4 +x, +y, +z S1 · · · H5a-C5 +x, +y, +z C1 · · · H3b-C3 -1 + x, +y, +z C2-H2a · · · H4b-C4 +x, +y, +z
HB
0.050
0.684
2.627
0.123
0.036
-5.23
VDW
0.031
0.516
2.684
0.066
0.162
-3.30
VDW
0.022
0.395
2.758
-0.008
0.251
-2.33
VDW
0.033
0.455
2.994
0.006
0.131
-3.13
VDW
0.039
0.506
3.026
-0.026
0.169
-3.70
HB
0.044
0.622
2.777
0.223
0.220
-4.54
VDW
0.030
0.555
2.898
0.102
0.262
-3.43
VDW
0.041
0.399
3.003
-0.003
0.204
-3.34
VDW
0.039
0.521
2.661
0.389
0.009
-3.77
H-H
0.065
0.903
2.145
0.255
0.015
-7.39
Salt II N1 · · · H2-N4 +x, +y, +z N2 · · · H1-N3 +x, +y, +z N1 · · · H4b-C4 +x, +y, +z N1 · · · H7c-C7 +x, +y, +z N2 · · · H5b-C5 +x, +y, +z N2 · · · H8c-C8 -x, 3/2 + y, -1/2 - z N2 · · · H9c-C9 +x, +y, +z S1 · · · H3b-C3 -x, 3/2 + y, 1/2 - z S1 · · · H6b-C6 1 /2 - x, 2 - y, 1/2 + z S1 · · · H6c-C6 -x, 1/2 + y, 1/2 - z S1 · · · H7a-C7 1 /2 - x, 2 - y, 1/2 + z S2 · · · H7a-C7 -x, -1/2 + y, 1/2 - z S2 · · · H8a-C8 -1/2 + x, 3/2 - y, 1 - z S2 · · · H9a-C9 -1 + x, +y, +z S2 · · · H9b-C9 -1/2 + x, 3/2 - y, 1 - z C1 · · · H6a-C6 1 - x, 1/2 + y, 1/2 - z C2 · · · H3a-C3 1 - x, -1/2 + y, 1/2 - z Salt III
a
VDW, HB, and H-H represent van der Waals interaction, hydrogen bond, and H-H bond, respectively.
288 Crystal Growth & Design, Vol. 9, No. 1, 2009
Figure 4. Static deformation map for the N4-H2 · · · N1 and C4-H4b · · · N1 bifurcated hydrogen bonds plotted in the H2 · · · N1 · · · H4b plane of salt II. The positive and negative accumulations of electron density are represented by red and blue contours, respectively. All contours increase in increments of 0.05 e Å-3. The dashed line represents the zero contour line, separating the positive and negative electron densities.
The amount of electron density accumulated in a strong or weak interaction can be measured by the Fb(r) parameter, which is also highly correlated with the bond order for these interactions.16,38 The Fb(r) value for one of the N-H · · · N hydrogen bonds in salt II is significantly larger than that of the N-H · · · N hydrogen bonds in salt I, while the remaining N-H · · · N interaction accumulates approximately the same amount of electron density. This is of interest, since both the N-H · · · N hydrogen bonds in salt II form interactions that are less collinear between the N-H donor groups and the lone pair of the N atoms [θN ) 167.45° (salt I) and 151.82°, 155.31° (salt II)]. This may possibly be the result of a cooperative effect between the strong N3-H1 · · · N2 and weak C5-H5b · · · N2 hydrogen bonds found in salt II. In a cooperative effect, the interactions are either strengthened or weakened by the presence of the other interaction. This type of relationship has been shown to be a common feature for bifurcated strong and weak hydrogen bonds.39 The only unique N-H · · · N hydrogen bond in salt III accumulates approximately the same amount of electron density as its counterpart in salt I. The three C-H · · · N hydrogen bonds (II and III) and the H-H bond in salt III accumulate the greatest amount of electron density for any of the weak interactions in these three salts, with the exception of the C7-H7a · · · S2 interaction (salt II). These values fall into the same region as those of other weak hydrogen bonds and H-H bonds reported in the literature.11,12,22 The static deformation map for the bifurcated N4-H2 · · · N1 and C4-H4b · · · N1 hydrogen bonds in salt II highlights the accumulation of electron density in these interactions (Figure 4). This static map shows features similar to those of the bifurcated N-H · · · N hydrogen bonds found in the crystals of the sym-N-methyl substituted ethylenediammonium dithiocyanate salts.22 In addition, this static map highlights the more linear relationship between the N atom lone pair and the N4-H2 donor group compared to the C4-H4b donor group. It is also noteworthy that the C3-H3b · · · S1 hydrogen bond in salt II accumulates significantly more electron density than the hydrogen bonds found in salts I and III. This hydrogen bond forms a less collinear interaction between the C-H donor group and the S acceptor atom compared with the C-H · · · S hydrogen bonds found in salts I and III.
Wolstenholme et al.
Figure 5. Laplacian [32Fb(r)] distribution for the N4-H2 · · · N1 and C4-H4b · · · N1 bifurcated hydrogen bonds in salt II. The contours are drawn at logarithmic intervals in -32Fb(r). The solid blue and red lines represent the positive and negative contours, respectively. The arrows point to the regions of local charge depletion in these interactions probability for all non-hydrogen atoms.
The Laplacian of the electron density at the BCP, 32Fb(r), represents the sum of the eigenvalues (curvatures) of the Hessian matrix, which allows this parameter to measure the local charge concentration or depletion along any interaction of interest.16 The 32Fb(r) values for all the strong and weak interactions in the three salts of interest are positive, indicating that they are closed-shell interactions. The nature of these closed-shell interactions is illustrated in the Laplacian map of Figure 5. The local charge depletion experienced by the N-H · · · N hydrogen bonds and all of the van der Waals interactions are relatively similar in all three diammonium salts. However, the 32Fb(r) values for the weak C-H · · · N and C-H · · · S hydrogen bonds in salt II are somewhat larger than their counterparts in salt I and III. The H-H bond in salt III experiences a similar amount of charge depletion as the weak C-H · · · N hydrogen bonds in salt II. It is also noteworthy that the weak van der Waals interactions possess Fb(r) and 32Fb(r) values consistent with weak hydrogen bonds, indicating that a certain degree of hydrogen bonding character is present in these interactions. The mutual penetration of the donor and acceptor atoms by the BCP is generally an excellent measure of hydrogen bonding character.40 This parameter can be obtained by comparing the non-bonding radii of the donor and acceptor atoms with their corresponding bonding radii (∆rA + ∆rB). The non-bonding radius can be taken as the appropriate gas-phase van der Waals nonbonding radius [C ) 1.85 Å, N ) 1.55 Å, S ) 1.80 Å, and H ) 1.20 Å].41,42 The bonding radius is taken as the distance from the nucleus of either the donor or acceptor atoms to the respective BCP. The degree of mutual penetration in salts I-III is always greater for hydrogen bonds compared to van der Waals interactions. Hence, the amount of mutual penetration appears to mirror the strength of these interactions. Similar to the previous topological parameters, the mutual penetration values for the various classes of interactions are relatively equal in all three salts. The only differences occur between the weak hydrogen bonds and the van der Waals interactions. In this instance, the weak hydrogen bonds experience substantially more penetration for both the donor and acceptor atoms compared to the van der Waals interactions. The C-H · · · N and C-H · · · S van der Waals interactions which experience mutual penetration [two C-H · · · N and six C-H · · · S] possess acceptor atoms that are not penetrated by the BCP. This has previously
Formation of Strong and Weak Hydrogen Bonds
been shown to occur as a result of broad minima in the electron density surrounding the BCP of such interactions.22 This causes a greater than normal amount of uncertainty in the actual position of the BCP, since it can feasibly shift to either side of its observed location (within the error associated with the electron density). Such a shift would result in significant changes to the calculated penetrations of both the donor and acceptor atoms. Thus, these weak interactions can be considered as belonging to a transition region from van der Waals to hydrogen bonding in nature. Similar to the other topological properties, the mutual penetration of the H atoms in the H-H bond of salt III falls in the same range as the weak hydrogen bonds. Finally, the weak C-H · · · Cπ interactions possess somewhat large ∆rA + ∆rB values. However, these interactions are best described as van der Waals in nature, since the C atoms experience significantly more penetration than their corresponding H atoms (∆rA - ∆rB). The C3-H3b · · · C1 interaction in salt III represents an exception, where the H3b atom is penetrated to a greater extent than the C1 atom. The strength of intermolecular interactions has previously been shown to be accurately estimated experimentally through the use of the relationship between potential energy densities [bond energy ) 1/2V(r)] and the overall bond energies.43 In general, the strength of the strong and weak interactions in these three salts decrease in the following order. N-H · · · NHB > C-H δ+ · · · δ+H-CH-H > C-H · · · NHB > C-H · · · SHB > C-H · · · N, C-H · · · S, and C-H · · · Cπ van der Waals interactions. This pattern clearly follows the normally observed hierarchy for strong and weak interactions, where stronger interactions involve the better hydrogen bond donor and acceptor atoms. The bifurcated N-H · · · N and C-H · · · N interactions in salt I and III experience little to no cooperative effect, since the C-H · · · N interaction is not strong enough to influence the electronic nature of the stronger N-H · · · N hydrogen bond. However, the N3-H1 · · · N2 and C5-H5b · · · N2 hydrogen bonds in salt II appear to have direct influence on each others’ overall bond energies. In this instance, the N3-H1 · · · N2 hydrogen bond significantly increases in strength compared to the remaining N-H · · · N interactions, while the C5-H5b · · · N2 hydrogen bond experiences a slight decrease in strength compared to the other weak C-H · · · N hydrogen bond in salt II. The remaining, N-H · · · N and C-H · · · N bifurcated hydrogen bonds in salt II and III appear to possess similar energies to the bifurcated interactions in salt I. Conclusions The structural analysis for this series of tetramethylalkyldiammonium dithiocyanate salts has led to a better understanding of underlying trends leading to the formation of both strong and weak interactions in the solid state. The N-H · · · N hydrogen bonds have been shown to form progressively less collinear interactions between the N-H donor groups and the lone pair of the N acceptor atoms upon lengthening the alkyl bridge region of the dications. The N-H · · · N hydrogen bond and C-H · · · N van der Waals bifurcation in salt I is replaced by N-H · · · N and C-H · · · N hydrogen bond bifurcation in salt II and III. The N3-H1 · · · N2 and C5-H5b · · · N2 bifurcated hydrogen bonds in salt II appear to undergo a cooperative effect, in which one interaction strengthens and the other slightly weakens. A topological comparison of the electron densities for these three salts has shown many similarities and differences in the electronic features of their strong and weak interactions. The bifurcated interactions in salt II possess topological features similar to those of other strongly bifurcated systems. This has
Crystal Growth & Design, Vol. 9, No. 1, 2009 289
all led to significant new insight into the role structural changes play in the formation of strong and weak interactions in ionic diammonium crystals. This study has also shown the effects of structural changes on the topology of the electron density for these types of interactions. Acknowledgment. We would like to thank the Natural Science and Engineering Research Council of Canada and the Alexander von Humboldt Foundation (Feodor Lynen Return Fellowship for J.J.W.) for financial support. We would also like to thank Dr. K. N. Robertson for insightful discussion. Supporting Information Available: Cif files containing the crystallograpic data including final experimental atomic coordinates, multipole populations, and statistical plots, and figures showing Laplacian maps, and residual maps. This material is available free of charge via the Internet at http://pubs.acs.org.
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CG800452W
