Experimental and Theoretical Charge Density Studies of 8

Article pubs.acs.org/JPCA

Experimental and Theoretical Charge Density Studies of 8-Hydroxyquinoline Cocrystallized with Salicylic Acid Thanh Ha Nguyen,† Paul W. Groundwater,† James A. Platts,‡ and David E. Hibbs*,† †

Faculty of Pharmacy, University of Sydney, NSW 2006, Australia School of Chemistry, Main Building, Cardiff University, Park Place, Cardiff CF10 3AT, United Kingdom

‡

S Supporting Information *

ABSTRACT: The experimental electron density distribution (EDD) in 8-hydroxyquinoline cocrystallized with salicylic acid, 1, has been determined from a multipole refinement of highresolution X-ray diffraction data collected at 100 K. The experimental EDD is compared with theoretical densities resulting from high-level ab initio and BHandH calculations using Atoms in Molecules theory. 1 crystallizes in the triclinic crystal system, and the asymmetric unit consists of a neutral salicylic acid molecule, a salicylate anion, and an 8-hydroxyquinolinium cation exhibiting a number of inter- and intramolecular hydrogen bonds and π−π interactions. Topological analysis reveals that π−π interactions are of the “closed-shell” type, characterized by rather low and flat charge density. In general, the agreement of the topological values (ρbcp and ∇2ρbcp) between experiment and theory is good, with mean differences of 0.010 e Å−3 and 0.036 e Å−5, respectively. The energetics of the π−π interactions have been estimated, and excellent agreement is observed between the relative energy and the strength of π-stacking derived from the Espinosa approach, with an average difference of only 4.4 kJ mol−1.

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INTRODUCTION The π−π interaction in aromatic systems has been studied extensively in the past two decades as it is of pivotal importance in the fields of chemistry and biology.1−9 These attractive interactions control such diverse phenomena as the intercalation of drugs in DNA,10 the packing of aromatic molecules in crystals,7 the tertiary structures of proteins,11 and complexation in host−guest systems.12 Despite the many theoretical1,5−7,13−16,18,19 and experimental4,17−23 studies addressing the importance of π−π interactions in biological systems, obtaining a clear picture of their strength and geometrical preference remains a challenge for both experiment and theory due to the general weakness of the interaction and the shallowness of potential energy surfaces. This has provided the drive to create simple chemical models containing relatively few atoms, which have, by design, specific weak interactions, making them ideal for detailed investigation.17 An increased understanding of aromatic π−π interactions in simple π-stacked systems may facilitate deeper understanding of these interactions in the complex biological environment. In this study, the experimental electron density distribution (EDD) of salicylic acid cocrystallized with 8-hydroxyquinoline (1) is reported and compared with theoretical results. The structure of complex 1 (Figure 1) has previously been determined24 and was shown to contain a number of aromatic π−π interactions and both intra- and intermolecular hydrogen bonding. Despite the fact that π−π interactions have been recognized in numerous charge density studies, no detailed investigation into the intermolecular electronic structure and © 2012 American Chemical Society

bond properties (such as topological properties and integrated atomic charges) associated with π−π interaction has been published to date. The main emphasis of the current study, therefore, is to examine the intermolecular features of the π−π interaction based on the theoretical and experimental topological properties. The experimental EDD of a molecular system obtained from high-resolution X-ray diffraction experiments forms a unique physical chemical method, which allows detailed information about the nature of intra- and intermolecular charge interaction in the solid state to be obtained. Bader’s Atoms in Molecules (AIM)25 approach provides an excellent tool for interpretation of both X-ray-determined and theoretical charge densities. Analysis of the charge density is based on the topological properties of the density ρ(r), where the topological analysis is based on those bond critical points (BCPs) where the gradient of the density, ∇ρ, vanishes. Properties evaluated at such points characterize the bonding interactions present and have been widely used to study intermolecular interactions. The application of AIM not only allows the network of intermolecular contacts to be established but also permits an estimation of their energy through the correlation between the energy and the electron density at the BCP.26 Although the energy density estimation was originally intended for hydrogen bonding and has not been properly tested for weaker, less directional Received: November 9, 2011 Revised: February 2, 2012 Published: February 13, 2012 3420

dx.doi.org/10.1021/jp2108076 | J. Phys. Chem. A 2012, 116, 3420−3427

The Journal of Physical Chemistry A

Article

Figure 1. ORTEP drawing of complex 1. Thermal ellipsoids show 50% probability surfaces.

interactions, Overgaard et al.27 recently estimated the strength of π−π interactions using this approach. In addition to the electron density approach to estimating the energetics of the π−π interaction, Waller et al.28 recently showed that Becke’s hybrid BHandH functional,29 combined with a medium-sized basis set augmented with polarization and diffuse functions, for example, 6-311++G(d,p), is able to reproduce qualitatively the ab initio potential energy surfaces of π−π stacked species, such as the parallel-displaced benzene dimer. They showed that BHandH generally agrees with MP2 and/or CCSD(T) results for a range of π-stacked complexes, including dimers of monosubstituted benzenes and DNA and RNA bases, to within ±2 kJ mol−1. This paper extends the use of the BHandH method to estimate the π-stacking energy in 1 and also presents a detailed analysis of the experimental charge densities of π−π interactions. The comparison of the theoretical and experimental charge density study of the cocrystallized π-system (1) offers unique insight into the nature of aromatic π−π interactions, which extend beyond the typical comparison of the simple geometry considerations of π−π interactions.

medium-angle data, while 2650 frames were measured at the high angle. The diffraction data were integrated using SAINT+,30 and the unit cell parameters for 1 at 100 K were refined from 22595 reflections in the triclinic space group P1 with Z = 2, F(000) = 440, and μ = 0.110 mm−1 (Table 1). Table 1. IAM Refinement of 1 1 formula molecular mass crystal size (mm3) temperature (K) crystal system space group a (Å) b (Å) c (Å) α (o) β (o) γ (o) volume (Å3) Z refinement method no. of reflections collected no. unique Rint no. reflections used data/parameter ratio ρc (gcm−1) F(000) μ (mm−1) sin θ/λmax θ range for data collection (°) index ranges

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EXPERIMENTAL SECTION Crystal Preparation. All chemicals were purchased from Sigma-Aldrich and used without further purification. 8-Hydroxyquinoline (1 equiv) and salicylic acid (1 equiv) were each dissolved in benzene and mixed to give a yellow precipitate. The solid was then recrystallized from ethanol to give yellow square crystals (1) by slow evaporation at room temperature. X-ray Data Collection and Reduction. The single-crystal X-ray diffraction experiments were carried out at the University of Sydney using a Bruker SMART1000 CCD-based diffractometer with an X-ray wavelength of 0.7107 Å (Mo Kα) and at an experimental temperature of 100 K. The yellow single crystal of 1 (0.25 × 0.20 × 0.20 mm) was mounted on the tip of a thin glass fiber with a minimum amount of Paratone N oil and inserted in the cold N2 stream of an Oxford Cryosystem instrument. X-ray diffraction data were collected using 0.3° Δω scans, maintaining the crystal-to-detector distance at 4.95 cm. Reciprocal space was covered by positioning the detector arm at three different setting angles in 2θ, −30, −60, and −100°, with corresponding exposure times of 10, 50, and 80 s/frame. A total of 2600 frames were collected for each of the low- and

residual density (e Å−3) final R1, wR2 goodness of fit Multipole Refinement refined on Nobs/Nvar. Rw(F), Rw(F2) > 2σ(F) R(F), R(F2), all data goodness of fit 3421

C9H8NO ·C7H5O3−·C7H6O3 421.39 0.25 × 0.20 × 0.20 100 triclinic P1 9.877 (1) 10.122 (1) 10.477 (1) 85.681 (3) 87.482 (3) 72.299 (3) 994.72 2 full-matrix least-squares 57490 22595 0.0183 16529 46.4 1.407 440.0 0.105 1.25 Å−1 1.97−62.27° −13 =< h =< 13, −13 =< k =< 13, −13 =< l =< 14 0.330, −0.313 e Å−3 0.0432, 0.1161 1.024 +

Fo2 18.3983 0.0290, 0.0429 0.0484, 0.0454 3.3268



Article

Charge Density Refinement. The structure of 1 was solved using direct method SHELXS-97,31 and full-matrix leastsquares refinement on F2 was carried out using SHELXL-97.31 All non-hydrogen atoms were refined anisotropically. Bond lengths to hydrogen atoms were fixed at neutron positions as obtained from average neutron diffraction values.32 The structure from IAM was imported into the multipole refinement program XD,33 which is based on the pseudoatomic description of the aspherical electron density suggested by Hansen and Coppens.34

with mean differences of 0.005 Å and 0.2°. In general, the bond lengths and angles between the optimized structure and both X-ray structural investigations do not differ significantly and hence merit little discussion; full details are reported in the Supporting Information. The crystal structure of 1 exhibits a number of inter- and intramolecular hydrogen bonds, as detailed in Table 2. Only the Table 2. Hydrogen Bond Geometries in Complex 1

3

ρj(rj) = Pcρc + κ′ Pv ρv (κ′r) 3

+ κ″

Intramolecular O(3)···H(4A)−O(4) O(3′)···H(4′)−O(4′) Intermolecular O(3′)a···H(1)−N(1) O(1)···H(4′)a−O(4′)a O(2)···H(8)−C(8) O(2)···H(2′)−O(2′)a C(3)−H(3)···πb

l max m = 1

∑ ∑

PlmR l(κ″rj)dlmp(θj , ϕj)

l = 0 m =−l

The expression for the pseudoatom density includes the usual spherical core, a term to describe the spherical component of the valence density, plus a deformation term describing the asphericity of the valence density. The radial functions {Rl(rj)} are modulated by angular functions {dlmp(θj,ϕj)}, defined by axes centered on each atom. A number of radial functions may be used, the most common being Slater-type functions.35 The starting point for the multipole refinement is the highorder spherical atom refinement. The bond lengths to the hydrogen atoms in the O−H, N−H, and C−H bonds were fixed at 0.967, 1.009, and 1.083 Å, respectively, with the heavyatom hydrogen vectors taken from the IAM refinement; the multipole refinement was carried out using the least-squares part of the XD program package,33 and only reflections with I > 2σ(I) were included. The scale factor and temperature factor were refined, separately. Subsequently, the multipoles were added in a stepwise manner, ultimately reaching the octapole level for O, N, and C (lmax = 3), while the hydrogen atoms were treated with one monopole and the aspherical density was modeled by a single-bond-directed dipole (lmax = 1). Each heavy atom was assigned a κ′, with a single κ″ refined for each atom type, and hydrogen atoms had a fixed κ′ of 1.2.36 The refinements were continued until convergence, and the Hirshfeld “rigid bond” test37 was applied. The crystallographic statistics are summarized in Table 1, and the molecular constituents in 1 are shown in Figure 1 with 50% probability thermal ellipsoids. More details of charge density refinements can be found in the Supporting Information. Theoretical Calculations. All calculations were performed with Gaussian0338 at the BHandH/6-311++G** and MP2/ 6-31G(0.25d) levels of theory, using the experimentally determined geometries. Gas-phase DFT optimization results in proton transfer from 8-hydroxyquinolinium to salicylate, resulting in three neutral compounds in the unit cell, and therefore was not considered further. Experimental topological analysis of electron densities was performed using the program XDPROP.33 The EXTREME39 and AIM200040 packages were used for the topological analysis of the theoretical wave functions. Integrated atomic properties were calculated from the experimental and theoretical densities using the programs TOPXD41 and AIM2000, respectively.

a

d1−2/Å

d1−3/Å

angle/o

1.656(8) 1.752(1)

2.649(8) 2.622(1)

151.7 147.9

1.806(2) 2.393(3) 2.186(2) 1.551(2) 2.740(2)

2.794(2) 2.975(2) 3.181(2) 2.510(2) −

165.4 118.2 151.7 170.5 −

x, y, 1 + z. b−1 + x, 1 + y, z.

intramolecular hydrogen bonds in each of the salicyl moieties (between the phenolic OH and carboxy group) are observed. Jebamony et al.24 found an additional intramolecular N−H···O interaction in the 8-hydroxyquinolinium cation. The geometry of the intramolecular H-bonds are also slightly different; that in the salicylic anion, O(3)···H(4A)−O(4), is more planar, has an O−H−O angle closer to 180°, and has a shorter distance dO···H compared to that in the salicylic acid, O(3′)···H(4′)−O(4′). 1 also contains several intermolecular hydrogen bonds, whose geometrical details are also included in Table 2. The intermolecular O(2)···H(2′)−O(2′) H-bond is the shortest of all in 1, with a distance of d(O(2)···H(2′) = 1.551 Å and an almost linear O···H−O angle of 170.5°. In this case, the oxygen atom O(2) acts as an acceptor in a bifurcated hydrogen bond, forming contacts to both H(8) and H(2′). The hydrogen bond formed with hydroxyquinolinium N−H as a donor, O(3′)···H(1)−N(1), is also relatively short and linear, whereas O(2)···H(8)−C(8) displays a similar angular geometry to the intramolecular O(3)···H(4A)−O(4) hydrogen bond with an angle of 151.7° but a much longer O···H distance. Finally, the contact between salicylic acid and salicylate, O(1)···H(4′) − O(4′), is very long and nonlinear. Besides the intra- and intermolecular hydrogen bonds, 1 also contains a C−H···π interaction (see Figure 2). The hydrogen atom H(3) of the 8-hydroxyquinolinium cation is located above the aromatic ring of the salicylicate anion, adopting an edge-toface structure, lying 2.340 Å above the mean-square plane of the ring with an average H···C distance of 2.740 Å. This is a significantly closer contact to the aromatic ring than that observed by Hibbs et al.,42 who reported a C−H···π interaction with an average distance to the six carbons of 2.89 Å and lying 2.570 Å above the mean-square plane of a nearby aromatic ring. Hirshfeld’s “rigid bond” test37 was applied during the multipole refinement for intramolecular bonds not involving H atoms. The maximum difference of mean-square displacement amplitudes was 10 × 10−4 Å2 for the bond C(13)−C(14), indicating that the atomic thermal vibrations are properly accounted for. The EDD in 1 is illustrated (Figure 3) by the static deformation density in the molecular plane of (a) the 8-hydroxyquinolinium cation, (b) the salicylic acid, and (c) the salicylate anion.

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RESULTS AND DISCUSSION The asymmetric unit consists of a neutral salicylic acid molecule, a salicylate anion, and an 8-hydroxyquinolinium cation (Figure 1). The structural details of complex 1 are in excellent agreement with that reported by Jebamony et al.24 3422



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On the basis of the theory of AIM,25 a topological analysis of the total electron density was performed (described by the refined multipoles). BCPs were located for all covalent bonds in 1, with electron density properties at these points providing no surprises. Full details of this analysis, showing both experimental and theoretical (BHandH) data, is reported as Supporting Information. The experimental ρbcp and ∇2ρbcp values at BCPs of C−C bonds are well reproduced by theory, with mean differences of 0.105 e Å−3 and 2.734 e Å−5, respectively. However, the value for ∇2ρbcp in C−O bonds differs significantly between the experiment and theory, with the largest deviation being 27.3 e Å−5. This feature has been observed before44,45 and is attributed to the large curvature of the density in the region of the BCP, such that small shifts in location of BCPs give rise to large changes in ∇2ρbcp. Electron density data can be used to probe in more detail the range of hydrogen bonds in 1, as shown in Table 3. Each interaction identified on the basis of structural data gives rise to a BCP in the experimental electron density. Interestingly, experimentally, the C−H···π interaction is classified as a (3,+1) ring CP based on the curvature of ρ(r), whereas theory predicts this to be a (3,−1) BCP. It should be noted that the electron density at this region is very low; therefore, the experimental classification of the C−H···π interaction could be artificial. In Table 3, the experimental electron density at the (3,+1) CP and the Laplacian value in the C(3)−H(3)···π interaction are given as average values. Both the experimental and theoretical topological values (ρbcp and ∇2ρbcp) are relatively low and positive, respectively, indicating closed-shell electrostatic interactions typical of H-bonding.25 In general, the theory gives a higher value of ρbcp while at the same time giving a lower value of ∇2ρbcp compared to that from the experiment. The largest deviation of the latter values between the theory and experiment exists in the intermolecular O(3′)−H(1)−N(1) hydrogen bond and the intramolecular O(3′)−H(4A)−O(4) hydrogen bond, where the differences are 0.108 e Å−3 and 1.108 e Å−5, respectively. Using the semiempirical relationship between energy densities and topological indices, proposed by Abramov,26 the potential and total energy density of the hydrogen bondings were calculated as shown in Table 5. Furthermore, the shorter intramolecular contact is ∼70% stronger than the longer one. In addition, Espinosa et al.46 have established a correlation

Figure 2. Structure of C−H···π interactions.

These plots show significant bonding electron density in all of the bonds, as well as two well-defined lone pairs on both of the oxygen atoms [O(2) and O(3)] in the plane of the salicylate anion. In addition, the 8-hydroxyquinolinium cation and the salicylic acid also show lone pairs on the oxygen atom O(1) and O(2′), respectively. Closer examination reveals that the electron density cloud corresponding to the lone pair electrons of the conjugated carboxylic oxygen atom O(3) is more shifted toward H(4A) than that of the carboxylic acid oxygen atom O(3′) toward H(4′) (Figure 3b and c, respectively). Figure 4 depicts the ∇2ρ distribution in the plane of (a) the 8hydroxyquinolinium cation, (b) salicylic acid, and (c) the salicylic anion. The observed lack of shared valence shells in the polar C−O bonds [C(1)−O(1), C(12′)−O(4′), and C(12)− O(4)] has been encountered in the experimental EDD studies of complexes with C−O bonds.43 Nevertheless, the topological analysis does demonstrate the significant covalent character of these polar bonds. The Laplacian distribution clearly reveals the valence shell charge concentration (VSCC) on all oxygen atoms.

Figure 3. Static experimental deformation density map in the molecular plane of (a) the 8-hydroxyquinolinium cation, (b) the salicylate anion, and (c) the salicylic acid. 3423



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Figure 4. Experimental ∇2ρ distribution in the molecular plane of (a) the 8-hydroxyquinolinium cation, (b) the salicylate anion, and (c) the salicylic acid.

Table 3. Experimental and Theoretical (in parentheses) Topological Analysis of the Hydrogen Bonds bond Intramolecular O(3)···H(4A)−O(4) O(3′)···H(4′)−O(4′) Intermolecular O(2)···H(8)−C(8) O(3′)a···H(1)−N(1) O(1)···H(4′)a−O(4′)a O(2)···H(2′)−O(2′)a C(3)−H(3)···πb

ρ/e Å−3

∇2ρ/e Å−5

G

V

H

EHB/kJ mol−1

0.30(8) 0.18(6)

(0.36) (0.27)

5.30(3) 4.37(6)

(3.60) (3.25)

0.36 0.25

−0.34 −0.20

0.01 0.05

66.1 38.9

0.06(6) 0.10(8) 0.06(5) 0.46(5) 0.02(4)

(0.10) (0.20) (0.05) (0.43) (0.06)c

1.48(6) 3.81(3) 1.06(4) 5.08(8) 0.62(3)

(1.31) (2.91) (0.91) (4.01) (0.69)c

0.08 0.20 0.06 0.46 0.03

−0.05 −0.12 −0.04 −0.57 −0.02

0.03 0.07 0.02 0.11 0.01

9.7 23.3 7.8 110.9 3.9

x, y, 1 + z. b−1 + x, 1 + y, z. cThe values of ρbcp and ∇2ρbcp correspond to only the H(3)···C(16) interaction obtained from theoretical (BHandH) calculation. a

between hydrogen bond energies and potential energy densities. Using this relationship, the hydrogen bond energies EHB were estimated and are given in Table 3. The values of V(r) and EHB support the view suggested by the geometry (shorter H···O distance) and topology (higher density at the BCP) that the intermolecular O(2)···H(2′)−O(2′) is the strongest hydrogen bond in 1, followed by the intramolecular O(3′)−H(4A)−O(4). The calculation shows that the six hydrogen bonds fall into three distinct groups, following the classification of Hibbert and Emsley.47 Two hydrogen bonds, both involving the salicylate anion, fall into the class of strong interactions, with EHB > 60 kJ mol−1. A further two, both with O(3′) as the hydrogen-bond acceptor, can be classified of moderate strength, with 40 > EHB > 20 kJ mol−1, and a final two are classified as weak H-bonds with EHB < 10 kJ mol−1. This analysis also confirms that the edge-to-face interaction C−H···π is the weakest intermolecular interaction present in 1. Hibbs et al.42,48−50 have previously studied the concept of directionality between hydrogen bonding and lone pair geometries using experimental EDD data. They proposed that the hydrogen bond directionality can be quantified as the angle O−LP−H, where LP is the oxygen lone pair and H is the hydrogen involved in the hydrogen bond. (For definition of the angles see Scheme 1.) We have applied this approach to the interactions in 1, with lone pair positions located as local maxima in the Laplacian function, −∇2ρ(r).25 The CO···H angles are 102.5 and

Scheme 1. Schematic Drawing of the Lone Pair Position on O(3)

101.3° for the intramolecular O(3)···H(4A)−O(4) and O(3′)···H(4′)−O(4′) H-bonds, respectively, which are almost exactly coincident with the lone pair directions on the acceptor atoms, 104.5 and 100.1° (see Table 4). A similar pattern is Table 4. Comparison of the Hydrogen Bond and Lone Pair Geometry hydrogen bond

ϕ

O(3)···H(4A)−O(4) O(3′)···H(4′)−O(4′) O(2)···H(8)−C(8) O(3′)a···H(1)−N(1) O(1)···H(4′)a−O(4′)a O(2)···H(2′)−O(2′)a

102.5 101.3 126.9 156.7 154.2 118.1

φ1 104.5 100.1 111.3 103.6 109.1

(104.8) (105.2) (108.7) (108.4) (107.1) (105.8)

a

x, y, 1 + z, and values in parentheses are from single-point calculations at the BHandH/6-311++G** level. 3424



Article

Table 5. Topological Analysis of π−π Interactionsa

found for the strongest intermolecular H-bond, O(2)···H(2′)− O(2′), with a difference in the C−O···H and C−O···LP angles of 9.0°. However, the difference between C−O···H and C− O···LP angles is far greater in the weaker intermolecular hydrogen bonds, with a difference as great as 50.6° in the O(1)···H(4′)−O(4′) hydrogen bond. To gain a deeper insight into the nature of π−π interactions, we performed topological analysis of such interactions present in the crystal structure of 1. As mentioned previously, the crystal structure of 1 exhibits π−π interaction between the aromatic rings. Two different geometries of π−π interaction were found in crystal 1 (Figure 5); trimer 1 is a sandwich

ρ/e A−3 Trimer 1 N(1)···C(11′)b N(1)···C(12′)b O(1)···C(10′)b C(1)···C(10′)b C(1)···C(11′)b C(1)···C(16′)b C(4)···C(15′)b C(5)···C(14′)b C(5)···C(15′)b C(6)···C(14′)b C(7)···C(13′)b C(8)···O(4′)b C(8)···C(13′)b C(9)···C(11′)b C(9)···C(12′)b C(9)···C(13′)b C(11′)···C(13′)b C(11′)···C(14′)b C(12′)···C(13′)b C(12′)···C(14′)b C(12′)···C(15′)b C(13′)···C(11′)b C(13′)···C(12′)b C(13′)···C(13′)b C(13′)···C(14′)b C(13′)···C(15′)b C(14′)···C(11′)b C(14′)···C(12′)b C(14′) ···C(13′)b C(15′)···C(12′)b C(15′)···C(13′)b Dimer 1 O(1)···C(4)c N(1)···C(2)c N(1)···C(3)c C(1)···C(5)c C(1)···C(9)c C(2)···N(1)c C(2)···C(5)c C(2)···C(9)c C(3)···N(1)c C(3)···C(9)c C(4)···O(1)c C(5)···C(1)c C(5)···C(2)c C(9)···C(1)c C(9)···C(2)c C(9)···C(3)c

Figure 5. Structure of π-stacking models.

between three aromatic compounds, consisting of one 8-hydroxyquinolinium cation and two salicylic acid molecules, whereas dimer 1 is an antiparallel face-to-face orientation of two 8-hydroxyquinolinium cations. In all cases, the interplanar distance is within the range of 3.4−4.0 Å, as expected of π−π interactions. Details of these π−π interactions were elaborated by location of BCPs between the aromatic rings in both the theoretical and experimental EDD. Three types of BCPs and associated bond paths in trimer 1 and dimer 1 were observed, (1) C···C, (2) O···C, and (3) N···C, with details of properties at these points reported in Table 5. Both experimental and theoretical values for all such interactions have positive ∇2ρbcp, classifying them as closed-shell interactions. BCPs are located approximately midway between the stacked rings. Topological parameters of BCPs for π−π interactions in 1 are listed in Table 5, showing both the experimental and the theoretical values. No significant differences between values calculated with MP2 and DFT are found (average deviations in ρbcp and ∇2ρbcp of 0.021 e Å−3 and 0.080 e Å−5, respectively); therefore, only the former are reported. Overall, experiment and theory are in broad agreement, with low values of ρbcp and small, positive ∇2ρbcp. Theoretical data typically yields slightly higher values of ρbcp and more positive values of ∇2ρbcp compared to those from experiment, although this trend is not consistently observed for all BCPs. An intriguing aspect of the data presented in Table 5 is that less than half of the BCPs found in the experimental density are present in the theoretical data. In both experimental and theoretical data, at least one C-atom is found to link with several atoms in the stacked partner, giving rise to multiple BCPs. For instance, in trimer 1, C(9) of the 8-hydroxyquinolinium cation is linked with C(11′), C(12′), and C(13′) of the salicylic acid, giving rise to three different BCPs with electron densities of 0.017, 0.031, and 0.028 e Å−3 (internuclear distances of 3.473, 3.585, and 3.858 Å) respectively. This type of “mult” linkage is predominantly observed in the experimental

∇2ρ/e A−5

XD

MP2

XD

MP2

0.02 0.03 0.04 0.03 − 0.02 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.03 0.02 0.01 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02

(0.03) (0.04)

0.34 0.39 0.72 0.72 − 0.40 0.33 0.19 0.21 0.21 0.17 0.19 0.15 0.21 0.36 0.35 0.20 0.24 0.29 0.28 0.34 0.33 0.24 0.28 0.28 0.33 0.29 0.29 0.34 0.33 0.33

(0.40) (0.76)

0.02 0.02 0.02 0.03 0.02 0.02 0.03 0.02 0.02 0.02 0.02 0.03 0.03 0.02 0.02 0.02

(0.03) (0.04) (0.02)

(0.02) (0.04) (0.03) (0.01) (0.02)

(0.02) (0.03)

(0.03) (0.04)

(0.03) (0.03)

(0.04)

(0.03)

0.32 0.34 0.36 0.36 0.34 0.34 0.35 0.33 0.36 0.35 0.32 0.36 0.35 0.34 0.33 0.35

(0.51) (0.45) (0.25)

(0.20) (0.45) (0.39) (0.26) (0.30)

(0.30) (0.32)

(0.37) (0.39)

(0.38) (0.37)

(0.39)

(0.38)

a

Standard uncertainties have been omitted from the table for clarity. They are closely scattered around 0.02 e Å−3 (ρbcp) and 0.05 e Å−5 (∇2ρbcp). b−x, 2 − y, 1 − z. c−1 − x, 2 − y, 2 − z.

model, whereas in the theoretical model, only C9 and C13 in trimer 1 are linked to more than one C-atom, while in dimer 1, only C···C interactions are observed. The angle A−BCP−B in these interactions is slightly more linear in the experimental than that in the theoretical data, which is not surprising as the molecules in the crystal are organized in a more packed 3425



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much fewer BCPs located in the theoretical data. For dimer 1, the Abramov/Espinosa approach gives an estimate much lower than the dispersive π−π contribution estimated from HF and MP2 data but is in excellent agreement with the binding of a neutral model. Waller’s approach, based on theoretical density, also agrees well with the neutral model binding energy, whereas this method with experimental density is in better agreement with the MP2-HF data. Collectively, the data in Table 6 support use of the Abramov/Espinosa approach for the estimation of interaction energies, which is highly encouraging given that the approach was originally intended for the welldefined hydrogen bonding and not for the weaker, less directional π−π interactions. While the overall trend in energy values is certainly clear from both experimental and theoretical approaches and given that the values of standard uncertainties on the experimental energies are surprisingly small (as they are derived from extremely low values of the density), they introduce some doubt as to the validity of the energy values obtained. It remains important, however, to evaluate the applicability of this approach on other π-stacking systems before it can be considered routine.

arrangement, where each individual molecule is affected by the others, creating a specific molecular array, whereas the gasphase calculations lack this crystal field effect (environmental effect). Gas-phase DFT calculations using crystallographic atomic coordinates of trimer 1 and dimer 1 were employed to evaluate the relative binding energies using MP2/6-311++G** with counterpoise correction for the basis set superposition error.51 For the parallel-displaced sandwich trimer 1, this results in a binding energy of −65.3 kJ mol−1. On the other hand, in dimer 1, the binding energy is calculated to be strongly repulsive at 200.1 kJ mol−1, which is unsurprising as dimer 1 consists of two 8-hydroxyquinolinium cations that should experience electrostatic repulsion. The HF binding energy is estimated to be 257.6 kJ mol−1, even more repulsive than the MP2 value, such that we can estimate the dispersive π−π contribution as the difference between the HF and MP2 at −57.5 kJ mol−1. To further check this point, the binding energy of a neutral model system, constructed by deprotonation of each nitrogen to yield a dimer of 8-hydroxyquinoline, was calculated to be −24.2 kJ mol−1. Previous studies have shown that the energy density distribution is a sensitive tool for description of weak interactions52,53 because the relative total binding energy offers limited chemical insight. Hence, the strength of the π-stacking interactions in trimer 1 and dimer 1 was estimated by two different approaches, (1) the formula derived by Waller et al.28 and (2) the combined development by Abramov26 and Espinosa et al.46 Both approaches estimate the energy of πstacking using the topological properties (ρbcp and ∇2ρbcp) of the electron density. Although the approach developed by Espinosa54,55 was originally intended for hydrogen bonding and has not been properly tested for weaker, less directional interactions, Overgaard et al.27 recently estimated the strength of π−π interactions using this approach. More recently, Waller et al.28 have constructed a similar method for π-stacking. They found that the sum of electron density (∑ ρπ) is linearly correlated with the binding energy with r2 = 0.950 and a standard deviation of 2.0 kJ mol−1. Approach (2) was only applied to the experimental EDD, while approach (1) was applied to both experimental and theoretical (MP2/6-311++G**) EDD. Table 6 summarizes these attempts to estimate stacking energies directly from the density.

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CONCLUSIONS The experimental electron density distribution (EDD) of the cocrystal 1 was modeled using the multipole model, and the interatomic interactions were analyzed using the atoms-inmolecules approach. The topological analysis of the experimental electron density and a comparison with high-level theoretical calculations allow us to investigate in detailed the bond properties and electronic structures of π−π interactions. The asymmetric unit consists of a neutral salicylic acid molecule, a salicylic anion, and an 8-hydroxyquinolinium cation. The crystal structure of 1 exhibits a number of inter- and intramolecular hydrogen bonds; furthermore, the neutral salicylic acid molecule and 8-hydroxyquinolinium cation are connected by three types of intermolecular C···C, O···C, and N···C contacts, corresponding to π−π interactions. The topological analysis reveals that all three linkages are of the “closed-shell” type; however, the π−π interaction is characterized by a rather low and flat charge density. The presence of critical points in the experimental topology that were absent in the theoretical analysis certainly seems to suggest some inadequacy of the multipole model for describing weak/ long-range interactions such as the π−π interactions that we have investigated here. The energy of the π−π interactions has been estimated, and reasonable agreement was observed between the relative energy and the strength of π-stacking derived from the Espinosa approach, with a difference of only 6.8 and 2.0 kJ mol−1 in dimer 1 and trimer 1, respectively.

Table 6. Experimental and Theoretical Binding Energy (kJ mol−1) trimer 1 dimer 1

supermoleculara

approach (1)b

approach (2)

−65.3 −57.5c/−24.2d

−78.8 (−38.5) −47.8 (−24.6)

−60.3 −31.1

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a

MP2/6-31++G** with counterpoise correction. bValue from experimental EDD, with the theoretical value in parentheses. cTaken as the difference between the HF and MP2 binding energies. dBinding energy of a neutral model system. Values are in kJ mol−1Standard uncertainties for the experimental binding energies (1) are 5 and 7 kJ mol−1, respectively.

ASSOCIATED CONTENT

S Supporting Information *

Tables of experimental bond lengths and angles and details of the intramolecular topological analysis. This material is available free of charge via the Internet at http://pubs.acs.org.

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For trimer 1, both approaches based on experimental EDD are in reasonable agreement with the directly calculated supermolecular binding energy and with that from Abramov/ Espinosa (20 slightly closer to the direct value. Use of the method of Waller et al. from theoretical EDD results in a much lower binding energy, perhaps unsurprisingly because there are

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest. 3426



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Article

(36) Howard, S. T.; Hibbs, D. E., Unpublished results. (37) Hirshfeld, F. Acta Crystallogr., Sect. A 1976, 32, 239−244. (38) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J. A. J.; Stratmann, R. E.; Burant, J. C. et al. Gaussian 03; Gaussian, Inc.: Pittsburgh, PA, 2003. (39) http://www.chemistry.mcmaster.ca/bader/aim. (40) Biegler-König, F.; Schönbohm, J.; Bayles, D. J. Comput. Chem. 2002, 23 (15), 1489−1494. (41) Volkov, A.; Gatti, C.; Abramov, Y.; Coppens, P. Acta Crystallogr., Sect. A 2000, 56, 252−258. (42) Hibbs, D. E.; Hanrahan, J. R.; Hursthouse, M. B.; Knight, D. W.; Overgaard, J.; Turner, P.; Piltz, R. O.; Waller, M. P. Org. Biomol. Chem. 2003, 1, 1034−1040. (43) Birkedal, H. Ph.D Thesis, University of Lausanne, Switzerland, 2000. (44) Koritsanszky, T.; Buschmann, J.; Lentz, D.; Luger, P.; Perpetuo, G.; Rottger, M. Chem.Eur. J. 1999, 5, 3413−3420. (45) Flaig, R.; Koritsanszky, T.; Zobel, D.; Luger, P. J. Am. Chem. Soc. 1998, 120, 2227−2238. (46) Espinosa, E.; Molins, E.; Lecomte, C. Chem. Phys. Lett. 1998, 285, 170−173. (47) Hibbert, F.; Emsley, J. Adv. Phys. Org. Chem. 1990, 26, 255−279. (48) Overgaard, J.; Waller, M. P.; Hibbs, D. E. J. Phys. Chem. A 2003, 107, 11201−11208. (49) Hambley, T. W.; Hibbs, D. E.; Turner, P.; Howard, S. T.; Hursthouse, M. B. J. Chem. Soc., Perkin Trans. 2 2002, 235−239. (50) Hibbs, D. E.; Overgaard, J.; Piltz, R. O. Org. Biomol. Chem. 2003, 1, 1191−1198. (51) Boys, S. F.; Bernardi, F. Mol. Phys. 1970, 19, 553−556. (52) Cremer, D.; Kraka, E. Angew. Chem., Int. Ed. 1984, 23, 627−628. (53) Cremer, D.; Kraka, E. Croat. Chem. Acta 1984, 57, 1259−1281. (54) Espinosa, E.; Alkorta, I.; Elguero, J.; Molins, E. J. Chem. Phys. 2002, 117, 5529−5542. (55) Espinosa, E.; Lecomte, C.; Molins, E. Chem. Phys. Lett. 1999, 300, 745−748.

ACKNOWLEDGMENTS D.E.H. would like to thank the Australian Research Council for funding. T.H.N. thanks the Faculty of Pharmacy, The University of Sydney, for a Ph.D. scholarship.

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REFERENCES

(1) Blundell, T.; Singh, J.; Thornton, J.; Burley, S. K.; Petsko, G. A. Science 1986, 234, 1005−1005. (2) Brijesh, K. M.; Sathyamurthy, N. J. Phys. Chem. B 2005, 109, 6−8. (3) Chipot, C.; Jaffe, R.; Maigret, B.; Pearlman, D. A.; Kollman, P. A. J. Am. Chem. Soc. 1996, 118, 11217−11224. (4) Claessens, C. G.; Stoddart, J. F. J. Phys. Org. Chem. 1997, 10, 254−272. (5) Hobza, P.; Selzle, H. L.; Schlag, E. W. Chem. Rev. 1994, 94, 1767−1785. (6) Hobza, P.; Sponer, J. J. Am. Chem. Soc. 2002, 124, 11802−11808. (7) Hunter, C. A.; Sanders, J. K. M. J. Am. Chem. Soc. 1990, 112, 5525−5534. (8) McGaughey, G. B.; Gagne, M.; Rappe, A. K. J. Biol. Chem. 1998, 273, 15458−15463. (9) Muehldorf, A. V.; Vanengen, D.; Warner, J. C.; Hamilton, A. D. J. Am. Chem. Soc. 1988, 110, 6561−6562. (10) Lerman, L. S. J. Mol. Biol. 1961, 3, 18−30. (11) Burley, S. K.; Petsko, G. A. Science 1985, 229, 23−28. (12) Hunter, C. A. Chem. Soc. Rev. 1994, 23, 101−109. (13) Daabkowska, I.; Jurecka, P.; Hobza, P. J. Chem. Phys. 2005, 122. (14) Elstner, M.; Hobza, P.; Frauenheim, T.; Suhai, S.; Kaxiras, E. J. Chem. Phys. 2001, 114, 5149−5155. (15) Evans, D. J.; Watts, R. O. Mol. Phys. 1975, 29, 777−785. (16) Jorgensen, W. L.; Severance, D. L. J. Am. Chem. Soc. 1990, 112, 4768−4774. (17) Emseis, P.; Failes, T. W.; Hibbs, D. E.; Leverett, P.; Williams, P. A. Polyhedron 2004, 23, 1749−1767. (18) Hamilton, A. D. Abstr. Pap. Am. Chem. Soc. 1990, 199, 150. (19) Mignon, P.; Loverix, S.; Geerlings, P. Chem. Phys. Lett. 2005, 401, 40−46. (20) Henson, B. F.; Hartland, G. V.; Venturo, V. A.; Felker, P. M. J. Chem. Phys. 1992, 97, 2189−2208. (21) Krause, H.; Ernstberger, B.; Neusser, H. J. Chem. Phys. Lett. 1991, 184, 411−417. (22) Narten, A. H. J. Chem. Phys. 1968, 48, 1630−1634. (23) Scherzer, W.; Selzle, H. L.; Schlag, E. W. Chem. Phys. Lett. 1992, 195, 11−15. (24) Jebamony, J. R.; Muthiah, P. T. Acta Crystallogr., Sect. C 1998, 54, 539−540. (25) Bader, R. F. W. Atoms in molecules: a quantum theory; Clarendon Press: Oxford, U.K., New York, 1990. (26) Abramov, Y. A. Acta Crystallogr., Sect. A 1997, 53, 264−272. (27) Overgaard, J.; Waller, M. P.; Piltz, R.; Platts, J. A.; Emseis, P.; Leverett, P.; Williams, P. A.; Hibbs, D. E. J. Phys. Chem. A 2007, 111, 10123−10133. (28) Waller, M. P.; Robertazzi, A.; Platts, J. A.; Hibbs, D. E.; Williams, P. A. J. Comput. Chem. 2006, 27, 491−504. (29) Becke, A. D. J. Chem. Phys. 1993, 98, 1372−1377. (30) SMART, SAINT and XPREP. Area detector control, data integration and reduction software; Bruker Analytical X-ray Instruments Inc.: Madison, WI, 1995. (31) Sheldrick, G. M. Acta Crystallogr., Sect. A 2008, A64, 112−122. (32) Brown, G. M.; Levy, H. A. Acta Crystallogr., Sect. B 1973, 29, 790−797. (33) Koritsanszky, T.; Howard, S. T.; Richter, T.; Mallinson, P. R.; Su, Z.; Hansen, N. K. XD. A Computer Program Package for Multipole Refinement and Analysis of Charge Densities from X-ray Diffraction Data; Free University of Berlin: Berlin, Germany, 1998. (34) Hansen, N. K.; Coppens, P. Acta Crystallogr., Sect. A 1978, 34, 909−921. (35) Hehre, W. J.; Stewart, R. F.; Pople, J. A. J. Chem. Phys. 1969, 51, 2657−2664. 3427


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