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Inter- and Intramolecular Interactions in Crystalline 2-nitrobenzoic Acid – an Experimental and Theoretical QTAIM Analysis Vladimir V Zhurov, and A. Alan Pinkerton J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.5b10027 • Publication Date (Web): 30 Nov 2015 Downloaded from http://pubs.acs.org on December 2, 2015

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The Journal of Physical Chemistry

Inter- and Intramolecular Interactions in Crystalline 2-Nitrobenzoic Acid – an Experimental and Theoretical QTAIM Analysis Vladimir V. Zhurov and A. Alan Pinkerton* University of Toledo, Toledo, OH 43606, USA ABSTRACT We have quantified the inter- and intramolecular interactions in crystalline 2-nitrobenzoic acid from QTAIM analysis of the topology of the electron density distribution obtained from both a low temperature (20K) X-ray diffraction experiment and from theoretical calculations. The covalent bonds have been characterized by the properties at their (3,-1) bond critical points; in particular the nature of the aromatic/nitro group C – N bond is discussed. All non-covalent bonds of the type O⋯H (both strong and weak), C⋯C, O⋯O, and O⋯C have also been characterized. Intermolecular interactions may be roughly divided into three types, the formation of a classical carboxylic acid hydrogen bonded dimer, an unusual ribbon of O⋯O interactions parallel to a, and a number of predominantly O⋯H interactions perpendicular to a. Integrated atomic charges (in particular for the acidic hydrogen, ~+0.6) and the derived molecular dipole moment are reported.

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1. INTRODUCTION Whereas much of chemistry relies on the understanding of intramolecular structure and bonding, the field of crystal engineering relies on the prediction of the strength and directionality of intermolecular interactions.1 As evidenced by the vast literature describing the importance of hydrogen bonding in determining structural motifs,2 one could be forgiven for believing that this is the only intermolecular interaction of importance. However, it is becoming increasingly clear that the arrangement of molecules in crystalline solids is also influenced by other types of noncovalent interactions.3,4 Although these individual interactions may not be as strong as hydrogen bonds, the sum of their contributions to the lattice energy may well be quite substantial. In order to obtain an appreciation of the importance of such non-covalent bonds, we may quantify their individual interaction energies using the Quantum Theory of Atoms in Molecules (QTAIM) approach,5 which relies on the topological analysis of the total electron density distribution. Although originally proposed for analyzing theoretical electron densities,5 the application of this analysis to experimental densities has since been substantiated. Every pair of interacting atoms is linked by a bond path, a path of maximum electron density, with a corresponding bond critical point at the position of minimum electron density along the path. For intermolecular, closed shell interactions, the dissociation energy may be estimated from the potential energy density at the bond critical point.6 This energy density may be obtained from the electron density (ρ(r)), and its first and second derivatives (∇ρ(r) and ∇2ρ(r)).7,8,9,10 The necessary values for ρ(r), ∇ρ(r) and ∇2ρ(r) may be obtained either from accurate low temperature X-ray diffraction data or from theoretical calculations with periodic boundary conditions.11 In the present paper, we report and analyze the electron density distribution in 2-nitrobenzoic acid crystals. The interatomic distances reported for the known structure12,13,14,15 indicated that in


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addition to quantifying an example of a classical carboxylic acid hydrogen bonded dimer, a remarkable variety of interactions between different types of atoms should exist, as well as a weak intramolecular interaction between the carboxylate and nitro groups. Whereas in most aromatic nitro compounds the nitro groups are close to coplanar with the benzene ring,16 the nitro group in 2-nitrobenzoic acid is twisted approximately 50° out of the aromatic plane.12,13,14,15 This provides an opportunity to examine more closely the N – C bond in this class of compound. 2-Nitrobenzoic acid is a strong carboxylic acid (pKa = 2.1717), hence the determination of the charge on the acidic hydrogen and its comparison with other organic acids is also of interest. 2. EXPERIMENTAL SECTION 2.1 Data Collection and Reduction. A colorless, single crystal of 2-nitrobenzoic acid (0.33x0.27x0.20 mm) grown by slow evaporation from a single drop of a 1:2 water/methanol solution on a paraffin film was mounted in oil on a capillary with a thin nylon loop. The crystal was cooled to 20K using an open flow, liquid helium device. 18,19 Intensity data were collected using a Rigaku diffractometer comprised of an ULTRAX-18 rotating anode (Mo-Kα, graphite monochromator) generator operating at 50 kV and 300 mA, and a RAPID cylindrical image plate detector.20 Intensity data were collected using 180 s, 6° omega oscillations with 3° of overlap in six runs of 59 images each covering 180°. The starting goniometer angles for the runs were set to = 0° ( = 0, 180°), = 40° ( = 0, 90, 180, 270°) thus ensuring adequate data completeness and redundancy. Reflection indexing was carried out using HKL2000,21 and the integrated intensities were determined using VIIPP applying background and reflection profiles averaged


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over the complete data set as previously described. 4,20,22 Scaling and merging of the data was carried out with the program SORTAV. 23,24 2.2 Electron density model refinement. The structure was initially re-solved and refined using the SHELXTL program suite.25 The resulting independent atom model was then used as the starting point for refinement of the electron density using the Hansen-Coppens multipole formalism26 implemented in the program XD2006. 27 In the multipole model, the total electron density in the crystal is respresented as a superposition of individual aspherical atoms, whose electron density is calculated according to: 4

l

ρ (r ) = Pc ρ c (r ) + Pv κ s3 ρ v (κ s r ) + ∑ κ l3 Rl (κ l r ) ∑ Plm ± y lm ± (r/r ) l =0

m =0

where ρc and ρv are spherical core and valence densities normalized to one electron. In the last term, which accounts for the aspherical deformation, Rl are normalized Slater-type radial functions, and ylm± are density normalized real spherical harmonics. The parameters κs and κl allow contraction/expansion of the spherical and aspherical valence parts respectively. Refinement was based on F2 over all merged data with I/ (I) > 3 using the VM databank. In the initial cycles of refinement a variety of chemical and symmetry constraints were applied. These were gradually released and the final model only constrained 0 - 4 to common values by atom type (C, N, O), s and 0 - 4 for hydrogen being set to 1.2. Thus, all multipoles up to hexadecapoles were refined for C, N and O atoms, and all dipoles and quadrupoles for hydrogens. The resulting geometrical model was used to optimize the wavefunctions and hydrogen atom positions (all other atoms remaining fixed) using the Crystal09 software. 28,29 New covalent bond lengths to hydrogen were calculated after optimization and a new refinement against the experimental data was performed with the C – H and O – H bond lengths constrained


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to the theoretical values. After that, the refined anisotropic atomic displacement parameters (ADPs) for C, N and O atoms and isotropic ADPs for hydrogen atoms were used as input for the SHADE software.30 The anisotropic ADPs for hydrogen atoms calculated in the SHADE package were then used as a starting point for their refinement against the experimental data using a rigid XD2006 distance constraint for C - H atom pairs. The anisotropic refinement for H(1) was unstable and this atom was hence refined isotropically. The final experimental model included positional parameters and anisotropic ADPs for all atoms (except H(1)), a single Pv term for each atom, and multipoles of orders 1-4 for non-hydrogen atoms and 1-2 for hydrogen atoms. The electroneutrality constraint was maintained throughout the refinements. A crystallographic summary is reported in Table 1, and full details have been deposited. The quality of the data and refinement model was confirmed with a normal probability plot, and a scale factor plot with respect to resolution. The corresponding plots have been deposited. Table 1. Crystallographic data for 2-nitrobenzoic acid Chemical formula

C7H5NO4

Space group

P1

a (Å)

4.9472 (2)

b (Å)

7.4767 (3)

c (Å)

10.3691 (3)

α (°)

68.856 (3)

(°)

86.708 (2)

γ (°)

70.864 (3)

Volume (Å3), Z

337.15(2), 2


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T (K)

20.0(1)

Wavelength λ (Å)

0.71073

Crystal size (mm)

0.33 x 0.27 x 0.20

(sin θ/ λ)max (Å-1)

1.30

Reflections integrated

62471

Rint/average data multiplicity

0.015/5.8

Completeness: d > 0.75 Å, all data (%)

100, 86.4

Independent reflections

10723

Observed reflections (I > 3)

9250

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Spherical atom refinement R1, wR2, GOF

0.0254, 0.0809, 1.104

ρmin/max e Å-3

-0.35/0.67

Multipole refinement R1, wR2, GOF

0.0140, 0.0160, 1.341

Weighting scheme: a, ba

0.002, 0.002

ρmin/max e Å-3 all data, sinθ/λ < 1.0 Å-1

-0.219/0.190, -0.103/0.112

a

= 1⁄ + + , = 0.3333"#$ + 0.6667'()'

2.3 Theoretical calculations. A density functional theory (DFT) calculation with periodic boundary conditions was carried out with the CRYSTAL09 package28,29 using the BLYP functional (we were not able to reach convergence with the hybrid B3LYP functional). The (8s)(411sp)-(1d1d) and (6s)-(311sp)-(1d1d) basis sets31 were chosen for oxygen and carbon atoms respectively, and the more common 6-311G** basis for nitrogen and hydrogen atoms. As described above, the calculations were performed twice. The first time, the wavefunctions and hydrogen atom positions were optimized and the results used to constrain the bond distances to hydrogen during re-refinement against the experimental structure factors as discussed above. The


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second time the crystal geometry remained unchanged from the final refinement based on the experimental data. This last result was then used for further calculations. Topological analysis of the resulting electron density distribution was carried out with TOPOND. 32 Static theoretical structure factors were calculated corresponding to the same (sinθ/λ)max as for the experimental data set, and used as a basis for a similar multipole refinement with the scale factor fixed to unity, all ADP’s fixed to zero and zero anomalous scattering. As previously shown,4 including two monopole terms, Pv and P00, for C and O atoms in the refinement improves the fit in the core region especially for the refinement against theoretical structure factors. We were able to do this in the present case for all non-hydrogen atoms except nitrogen, which was unstable in the refinement. Also for this atom only multipoles up to the octapole level were used. For hydrogen atoms the P00 term was not used. Except for N, the nonhydrogen atoms were refined up to the 4th order of multipoles, and for hydrogens all 1st and 2nd order multipoles were refined. The kappa sets were the same for the same atom type, while within each set the appropriate s and 0 - 4 were refined independantly. All kappas for hydrogen atoms were constrained to 1.2 as in the experimental refinement. 3. RESULTS As previously reported,12,13,14,15 2-nitrobenzoic acid crystallizes in space group P1 with two molecules per unit cell. The molecules form classic, centrosymmetric hydrogen bonded dimers. A plot of such a dimer from the final refinement is shown in Fig. 1. The crystal packing is dominated by a series of O⋯O intermolecular interactions parallel to a, supplemented by a number of predominantly CH⋯O interactions perpendicular to a.


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In order to characterize the intra- and intermolecular bonding, we have calculated the total electron density as well as its derivatives from the refined multipole parameters.33,34 In the following we will discuss the covalent bonding properties, in particular the C – N bond, the atomic charges with respect to the pKa, and the nature and strength of the intermolecular interactions. The discussion will be mainly based on the parameters obtained from the experimental data as the agreement with theory is typically very good.

Figure 1. 2-Nitrobenzoic acid, 95% probability ellipsoids,35 hydrogen bonded dimer showing intermolecular bond paths (blue) and their critical points as yellow spheres,33,34 and dihedral angles of the substituents with respect to the aromatic ring. 3.1 Covalent bonds Static deformation maps in the plane of the aromatic ring and in the plane of the nitro group (Figure 2) clearly show the charge concentrations associated with covalent bonds and lone pairs (similar results from theory have been deposited). The topology of the total electron density was analyzed using the program WinXPRO.33,34 All of the bond critical points have been characterized, and derived values are reported in Table 2, where the values of the properties are organized with three lines per atom: i) results from the experimental multipole values, ii) the


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same values obtained by refining against theoretical structure factors, and iii) the results from pure theory.

Figure 2. Static deformation map a) in the plane of the aromatic ring, b) in the plane of the nitro group. Contours 0.10 e Å-3. The properties of the (3,-1) bond critical points for all of the aromatic bonds, the N = O multiple bonds, and the bonds associated with the carboxylic acid group are typical for the various bond types. Their strength can be inferred via determination of the topological bond order, ntopo, obtained from the electron density and its Laplacian,36,37,38,39 and the complete set of bond orders is included in Table 2.

+,"-" = + ./ + 0.1 + . + 23# All aromatic C-C bonds have ntopo = 1.27 – 1.37, and the lack of conjugation of the carboxylate to the aromatic ring is confirmed by ntopo = 0.98 for C(1) – C(7).


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Table 2. Properties of the covalent bond critical points for 2-nitrobenzoic acid; first line from the multipole fit to experimental data, second line from the multipole fit to theoretical structure factors, third line directly from theory Bond

C(1) - C(2)

C(1) - C(6)

C(2) - C(3)

C(3) - C(4)

C(4) - C(5)

C(5) - C(6)

C(1) - C(7)

C(2) - N(1)

N(1) - O(3)

N(1) - O(4)

C(7) - O(1)

C(7) - O(2)

O(1) - H(1)

C(3) - H(3)

ρ(r), eÅ-3 ∇2ρ(r), eÅ-5 Rij, Å d1, Å 2.096 2.027 2.031 2.094 2.036 2.045 2.151 2.090 2.099 2.101 2.040 2.051 2.140 2.065 2.078 2.114 2.048 2.065 1.839 1.779 1.795 1.785 1.728 1.755 3.364 3.237 3.313 3.327 3.195 3.266 2.373 2.237 2.220 2.938 2.711 2.720 2.089 1.991 2.018 1.904 1.865

-17.77 -16.72 -18.24 -18.01 -16.86 -18.53 -19.26 -18.02 -19.45 -17.92 -16.95 -18.82 -18.25 -17.48 -19.30 -17.36 -17.05 -18.99 -14.75 -13.11 -14.89 -14.94 -10.75 -15.74 -12.07 -12.14 -22.65 -12.74 -11.60 -21.59 -28.95 -21.55 -18.97 -38.29 -22.23 -18.70 -34.57 -27.21 -43.74 -20.35 -19.36

1.400 1.400 1.400 1.398 1.398 1.398 1.386 1.386 1.386 1.398 1.398 1.398 1.393 1.393 1.393 1.396 1.396 1.396 1.486 1.486 1.486 1.470 1.470 1.470 1.223 1.223 1.223 1.229 1.229 1.229 1.315 1.315 1.315 1.230 1.230 1.230 1.021 1.021 1.021 1.086 1.086

0.686 0.686 0.686 0.713 0.711 0.711 0.720 0.719 0.717 0.703 0.705 0.706 0.691 0.697 0.697 0.697 0.693 0.692 0.719 0.716 0.723 0.597 0.622 0.595 0.593 0.587 0.574 0.597 0.591 0.579 0.510 0.497 0.475 0.467 0.444 0.435 0.791 0.783 0.813 0.723 0.714

d 2, Å

g, au

ν, au

h, au

ε

ntopo

0.715 0.715 0.715 0.686 0.687 0.688 0.667 0.668 0.670 0.695 0.693 0.692 0.702 0.696 0.696 0.700 0.703 0.704 0.767 0.771 0.763 0.873 0.848 0.876 0.630 0.636 0.649 0.633 0.639 0.650 0.806 0.818 0.841 0.763 0.786 0.795 0.230 0.238 0.208 0.363 0.372

0.2859 0.2711 0.2620 0.2837 0.2732 0.2643 0.2939 0.2825 0.2754 0.2868 0.2738 0.2645 0.2973 0.2780 0.2698 0.2949 0.2756 0.2676 0.2268 0.2206 0.2129 0.2097 0.2221 0.1953 0.8163 0.7602 0.7207 0.7954 0.7453 0.7073 0.3027 0.3067 0.3190 0.4533 0.4742 0.5020 0.1677 0.1871 0.0814 0.2078 0.2029

-0.7563 -0.7156 -0.7132 -0.7542 -0.7213 -0.7209 -0.7876 -0.7519 -0.7525 -0.7595 -0.7234 -0.7242 -0.7838 -0.7374 -0.7399 -0.7700 -0.7281 -0.7323 -0.6065 -0.5772 -0.5803 -0.5745 -0.5558 -0.5538 -1.7578 -1.6463 -1.6765 -1.7229 -1.6110 -1.6387 -0.9056 -0.8370 -0.8348 -1.3037 -1.1790 -1.1980 -0.6940 -0.6566 -0.6165 -0.6267 -0.6065

-0.4703 -0.4445 -0.4512 -0.4705 -0.4481 -0.4566 -0.4937 -0.4694 -0.4771 -0.4727 -0.4496 -0.4597 -0.4866 -0.4594 -0.4701 -0.4751 -0.4525 -0.4646 -0.3798 -0.3566 -0.3674 -0.3648 -0.3336 -0.3585 -0.9415 -0.8861 -0.9557 -0.9275 -0.8657 -0.9313 -0.6029 -0.5303 -0.5158 -0.8505 -0.7048 -0.6960 -0.5263 -0.4694 -0.5351 -0.4189 -0.4037

0.217 0.209 0.210 0.198 0.188 0.182 0.208 0.209 0.211 0.168 0.171 0.165 0.185 0.176 0.169 0.148 0.176 0.170 0.119 0.112 0.118 0.067 0.092 0.091 0.064 0.110 0.117 0.068 0.109 0.114 0.123 0.086 0.085 0.081 0.053 0.114 0.034 0.014 0.012 0.036 0.016

1.29 1.35 1.24 1.27 1.37 1.24 1.30 1.40 1.28 1.29 1.37 1.22 1.34 1.38 1.24 1.37 1.38 1.24 0.98 1.09 0.97 0.74 0.74 0.71 1.89 1.78 1.63 1.85 1.76 1.61 1.17 1.15 1.07 1.56 1.40 1.28 0.21 0.12 0.60 0.94 0.96


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C(4) - H(4)

C(5) - H(5)

C(6) - H(6)

1.903 1.894 1.875 1.916 1.890 1.864 1.903 1.882 1.874 1.910

-22.89 -20.55 -19.57 -23.09 -19.83 -19.11 -22.75 -20.77 -19.51 -22.94

1.086 1.085 1.085 1.085 1.086 1.086 1.086 1.085 1.085 1.085

0.711 0.719 0.712 0.710 0.715 0.710 0.707 0.726 0.710 0.708

0.375 0.366 0.373 0.375 0.371 0.376 0.379 0.359 0.375 0.377

0.1899 0.2032 0.2045 0.1926 0.2071 0.2041 0.1909 0.1981 0.2046 0.1916

-0.6172 -0.6196 -0.6119 -0.6248 -0.6199 -0.6065 -0.6177 -0.6116 -0.6116 -0.6212

-0.4274 -0.4164 -0.4074 -0.4321 -0.4128 -0.4024 -0.4269 -0.4135 -0.4070 -0.4296

0.011 0.051 0.016 0.009 0.048 0.018 0.011 0.038 0.016 0.012

0.89 0.94 0.97 0.89 0.96 0.97 0.90 0.91 0.97 0.89

There is continuing discussion of the nature of the C – N bond in nitroaromatic compounds. In the vast majority of such compounds, the nitro group is close to coplanar with the aromatic ring.16 A simple interpretation of this would suggest a π-contribution to the C – N bond, and theoretical calculations over the years have attempted to confirm this with little success.40,41,42,43,44 Among the many thousands of nitroaromatic compounds whose structures have been determined, there is a small but significant number where the nitrogroup is twisted out of the aromatic plane. It was previously suggested that the presence/absence of π-bonding would imply that the C – N bond should be longer for non-planar structures. In an earlier study, Holden and Dickensen45 examined 104 compounds and found no correlation between the C – N bond length and the dihedral angle between the nitro-group and the aromatic ring. We have confirmed this result based on the many thousand structures currently available,16 and have plotted the correlation in Figure 3. This implies a negligible 4 component to this bond.


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2 1.8 1.6 C - N (Å Å

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1.4 1.2 1 0.8 0.6 0

20

40

60

80

100

Dihedral Angle (°°

Figure 3. Plot showing lack of correlation between C – N bond length and the dihedral angle for nitro-aromatic compounds. However, information on the nature of this bond should be encoded in the electron density distribution. Hence, in Table 3 we have compared the topology of the C - N bond in this nonplanar example with the few other similar studies available in the literature.46,47,48,49,50,51,52,53 Despite the scatter of the values, the low value of the ellipticity (ε = λ1/λ2 – 1) of the electron density at the bond critical point observed in the present case compared with the more substantial values for all smaller dihedral angles suggests that there may well be a modest 4-component to this bond for the majority of “coplanar” nitroaromatics that is lost on severe out-of-plane twisting. If this is indeed the case, then the lack of correlation of C – N bond length with the dihedral angle must be due to cancellation of the energy gain from the 4-interaction by the steric repulsion of the oxygen atoms by the substituents on the ortho-carbon atoms. We note that although the topological bond orders36,37,38,39 for most bonds (Table 2) are close to expectations, the value for the C – N bond is significantly below unity (0.74). There are few values in the literature for comparison. In 2,6-dinitrophenol the values are 0.83 (τ = 3.7°) and


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0.77 (τ = 13.6°), whereas the values for the three nitro-groups in 1,3,4-trinitro-7,8-diazapentalene are close to unity (0.92, 0.94, 0.99) corresponding to torsion angles with respect to the aromatic diazapentalene plane of 12.7, 28.5 and 22.8°.54 Table 3. Comparison of C – N bond characteristics in nitroaromatic compounds. Compound 2-nitrobenzoic acid α-4-nitrophenol -4-nitrophenol 4-methyl-5-nitroaniline 1-(2-hydroxy-5-nitrophenyl)ethanone Dimethyl-3-(4-nitrophenyl)aziridine-2,2-dicarboxylate Dimethyl-3-(4-nitrophenyl)oxirane-2,2-dicarboxylate Dimethyl-2-(4-nitrobenzylidene)malonate 2,4,6-trinitroaniline

2,6-dinitrophenol 4-nitrobenzoic acid 3,3’-dinitrobenzophenone I 3,3’-dinitrobenzophenone II

R, Å 1.470 1.452 1.447 1.463 1.456 1.470 1.470 1.461 1.453 1.452 1.460 1.450 1.466 1.472 1.471 1.465 1.467

ρ, eÅ-3 1.79 1.78 1.91 1.72 1.89 1.89 1.83 1.77 1.80 1.80 1.82 1.87 1.79 1.76 1.83 1.87 1.93

ε 0.07 0.29 0.20 0.22 0.16 0.18 na na 0.27 0.20 0.20 0.12 0.12 0.13 0.06 0.10 0.10

τ, ° 52.7 1.9 8.2 6.5 4.3 1.5 4.6 12.7 13.9 4.7 26.4 3.7 13.6 15.1 2.5 7.5 14.8

Ref. 46 46 47 48 49,50 49 49 51

52 53 53 53

3.2 Non-covalent interactions Characterization of the non-covalent, weak interactions obtained from the topological analysis of the total electron density is reported in Table 4. The kinetic (gb) and potential (νb) energy densities at the bond critical points were calculated from the electron density and its derivatives for all interactions using the DFT formulas and the local virial theorem.10 It has been previously suggested6 that the energy of weak, closed shell interactions may be estimated as Eint = -νb/2, and these values are included in Table 4. This empirical relationship was originally determined for hydrogen bonds, but it has been extrapolated to give reasonable values for all closed shell, weak interactions.54 However, we reiterate that this is based on an empirical relationship and note that


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its application still remains controversial.55,56,57,58,59 We continue to use this methodology here as a better tool for understanding these interactions has yet to be proposed. Bond paths and virial paths for all non-covalent interactions have been found, and the characteristics of their (3,-1) critical points are reported in Table 4. All may be classified as closed shell interactions. There is one intramolecular non-covalent interaction between the carbonyl oxygen and the neighboring nitro group. The bond path may terminate at either the nitro oxygen or nitrogen depending on the model, perhaps indicating that the interaction is better described as between oxygen and the N – O bonding density. The energy of the interaction (11.3 kJ/mol) is of the same order as observed between neighboring oxygen atoms in phthalic acid (9.4 kJ/mol),60 but weaker than that reported for the phenolic oxygen/nitro interaction in 2,6-dinitrophenol (19.2 kJ/mol).52 The molecules form classical centrosymmetric cyclic carboxylic acid hydrogen bonded dimers (Figure 1).61 The O ··· H bond is fairly short 1.754 Å and has an estimated interaction

energy 65.1 kJ/mol that is within the normal range for carboxylic acid dimers 50.8 – 73.8 kJ/mol).60,62,63,64,65,66,67,68 Table 4. Properties of the non-covalent bond critical points in 2-nitrobenzoic acid, first line from the multipole fit to experimental data, second line from the multipole fit to theoretical structure factors, third line directly from theory. Bond ρ(r), eÅ-3 ∇2ρ(r), eÅ-5 Non-covalent bonds - intramolecular O(2) - N(1) 0.088 1.29 O(2) - O(3) 0.078 1.28 O(2) - N(1) 0.081 1.30 Non-covalent bonds - intermolecular 0.333 2.99 K O(2) - H(1 ) 0.380 2.78 0.378 3.01 0.063 0.75 O(1) - H(6j) 0.058 0.76

Rij, Å

d 1, Å

d 2, Å

g, au

2.802 2.840 2.802

1.408 1.416 1.425

1.418 1.457 1.436

0.0110 0.0105 0.0108

-0.0086 -0.0078 -0.0081

0.0024 0.0027 0.0027

11.3 10.3 10.6

1.623 1.623 1.623 2.454 2.454

1.102 1.082 1.105 1.452 1.456

0.523 0.542 0.520 1.004 0.999

0.0397 0.0430 0.0444 0.0064 0.0063

-0.0485 -0.0571 -0.0575 -0.0049 -0.0047

-0.0087 -0.0141 -0.0131 0.0014 0.0016

63.6 75.0 75.5 6.5 6.2


ν, au

h, au

Eint, kJ/mol

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0.061 0.72 2.454 1.460 0.994 0.0061 -0.0047 0.0014 6.2 0.025 0.35 3.327 1.668 1.671 0.0027 -0.0017 0.0010 2.3 d O(1) - O(2 ) 0.022 0.34 3.327 1.657 1.683 0.0025 -0.0016 0.0009 2.1 0.027 0.36 3.327 1.640 1.691 0.0028 -0.0018 0.0010 2.4 0.019 0.24 3.140 1.746 1.539 0.0018 -0.0012 0.0007 1.5 O(2) - H(4g) 0.019 0.27 3.140 1.731 1.426 0.0020 -0.0013 0.0008 1.7 0.020 0.27 3.140 1.735 1.458 0.0020 -0.0013 0.0007 1.7 0.049 0.60 2.480 1.488 1.008 0.0049 -0.0036 0.0013 4.8 O(2) - H(5i) 0.054 0.67 2.480 1.457 1.024 0.0056 -0.0042 0.0014 5.5 0.054 0.67 2.480 1.478 1.002 0.0056 -0.0042 0.0014 5.5 0.018 0.27 3.404 1.702 1.702 0.0020 -0.0012 0.0008 1.6 l O(2) - O(2 ) 0.018 0.27 3.404 1.702 1.702 0.0020 -0.0012 0.0008 1.6 0.020 0.29 3.404 1.702 1.702 0.0022 -0.0014 0.0008 1.8 0.053 0.71 2.377 1.448 0.951 0.0058 -0.0043 0.0016 5.6 O(3) - H(4g) 0.062 0.82 2.377 1.411 0.966 0.0068 -0.0052 0.0017 6.8 0.061 0.82 2.377 1.411 0.967 0.0068 -0.0051 0.0017 6.7 0.046 0.69 2.990 1.511 1.480 0.0055 -0.0038 0.0017 5.0 O(3) - O(4d) 0.043 0.68 2.990 1.517 1.475 0.0054 -0.0036 0.0017 4.8 0.040 0.70 2.990 1.539 1.452 0.0054 -0.0036 0.0018 4.7 0.032 0.44 3.222 1.611 1.611 0.0034 -0.0023 0.0011 3.0 a O(3) - O(3 ) 0.030 0.45 3.222 1.611 1.611 0.0034 -0.0022 0.0012 2.9 0.034 0.46 3.222 1.611 1.611 0.0036 -0.0024 0.0012 3.2 0.060 0.79 3.006 1.503 1.503 0.0066 -0.0049 0.0016 6.5 O(4) - O(4c) 0.049 0.81 3.006 1.503 1.503 0.0064 -0.0044 0.0020 5.7 0.054 0.80 3.006 1.503 1.503 0.0064 -0.0046 0.0018 6.0 0.050 0.71 2.594 1.505 1.090 0.0057 -0.0041 0.0016 5.4 O(4) - H(3c) 0.049 0.70 2.594 1.506 1.091 0.0057 -0.0040 0.0016 5.3 0.054 0.65 2.594 1.525 1.075 0.0054 -0.0041 0.0013 5.4 0.044 0.62 2.651 1.516 1.156 0.0049 -0.0035 0.0015 4.5 O(4) - H(4i) 0.041 0.62 2.651 1.523 1.146 0.0048 -0.0033 0.0016 4.3 0.047 0.58 2.651 1.539 1.131 0.0047 -0.0035 0.0013 4.6 0.030 0.53 2.757 1.600 1.184 0.0040 -0.0025 0.0015 3.3 O(4) - H(5i) 0.034 0.54 2.757 1.583 1.192 0.0042 -0.0027 0.0014 3.6 0.034 0.51 2.757 1.582 1.186 0.0039 -0.0026 0.0013 3.4 0.032 0.35 3.405 1.862 1.605 0.0028 -0.0020 0.0008 2.6 C(2) - O(3a) 0.030 0.35 3.405 1.841 1.602 0.0027 -0.0019 0.0009 2.5 0.027 0.34 3.405 1.816 1.612 0.0026 -0.0017 0.0009 2.3 0.037 0.41 2.975 1.706 1.291 0.0033 -0.0024 0.0009 3.1 C(3) - H(4f) 0.031 0.42 2.975 1.745 1.279 0.0032 -0.0022 0.0011 2.8 0.034 0.39 2.975 1.739 1.274 0.0031 -0.0022 0.0009 2.9 0.036 0.32 3.440 1.723 1.717 0.0027 -0.0020 0.0006 2.7 C(3) - C(6b) 0.032 0.30 3.440 1.723 1.717 0.0024 -0.0018 0.0006 2.3 0.034 0.31 3.440 1.721 1.719 0.0026 -0.0019 0.0007 2.5 a –x -y -z, b 1+x y z, c 1-x -y -z, d -1+x y z, e x 1+y z, f -x 1-y -z,g x -1+y z, h -x -y 1-z, i 1+x –1+y z, j -1-x -y 1-z, j 1-x –y 1-z, k –x -1-y 1-z, l 1-x -1-y 1-z


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A striking feature of the packing of these dimers is provided by two series of O ··· O interactions parallel to the a axis Figure 4. The first is due to the alignment of the carboxylate groups with an O ··· O separation of 3.327 Å, and an estimated interaction energy of 2.3 kJ/mol. The second is an unusual interaction between neighboring nitro groups favored by the twisting of the nitro group out of the aromatic plane. The O ··· O interactions form a ribbon parallel to a with separations of 2.990, 3.006 and 3.222 Å, and with corresponding estimated interaction energies of 5.0, 6.5 and 3.0 kJ/mol. The interactions responsible for lattice binding perpendicular to the a axis are largely of the CH ··· O type as shown in Figure 5. The estimated interaction energies range from 1.5 to 6.5 kJ/mol ave. 4.5 kJ/mol. The energies of all the identified intermolecular interactions sum to 47.0 kJ/mol per asymmetric unit, which can be compared to 63.6 kJ/mol for the strong hydrogen bond in the dimer.

Figure 4. Bond paths (blue lines) for O ··· O interactions parallel to a. Oxygen atoms are red,

nitrogen blue, carbon black, hydrogen green, and bond critical points are yellow.


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Figure 5. Bond paths (blue lines) for intermolecular interactions predominantly perpendicular to a. Colors as in Fig. 4. Integrated properties The atomic charges derived from the integration of the electron density over the atomic basins and their volumes (delimited by zero flux surfaces) are reported in Table 5, and the agreement between experiment and theory is again very good. The values for the C, N and O atoms are not remarkable, the oxygens carrying significant negative charge and the carbons being close to neutral with the exception of the carboxylate carbon. The modest positive charges of the hydrogen atoms on the aromatic ring reflect the electron withdrawing effect of the substituents. The significant positive charge of 0.649 on the acidic hydrogen H(1) is similar to the few other reported values for carboxylic acids.53,60,64Although it is tempting to relate the charge on an acidic hydrogen atom to the pKa this may be inappropriate. For example, Meldrum’s acid has a pKa < 5.0, but the integrated charge of the acidic hydrogen (CH) is 0.105, the main contributor to the acidity being the conjugated structure of the anion.69 However, for a series of closely related acids, one might expect a significant correlation between the pKa and the charge on hydrogen. Indeed, Hollingsworth et al.70 computationally demonstrated such a correlation for a


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Page 18 of 30

series of substituted benzoic acids. We note that our current results are in accord with their theoretical study, extending the pKa range to 2.17,17 and the integrated charge to 0.607 (charge here taken from theory to be as comparable as possible with the Hollingsworth study). A relevant plot has been deposited (Figure S8). Intuitively, pKa should be related to the strength of the O-H bond. Although the topological bond order (0.21) of the O – H bond in the present case is low suggesting a high acidity, this bond may well be weakened in the crystal by the strong OH··· O hydrogen bond. Table 5. Integrated atomic charges and volumes for 2-nitrobenzoic acid from experiment, theoretical structure factors, and theory.

atom O(1) O(2) O(3) O(4) N(1) C(1) C(2) C(3) C(4) C(5) C(6) C(7) H(1) H(3) H(4) H(5) H(6) Total

Experiment Ω Å3 qe 16.15 -1.131 16.43 -1.012 16.87 -0.458 14.48 -0.445 6.65 0.388 9.84 0.017 9.33 0.231 11.39 -0.035 13.15 -0.031 12.77 -0.104 11.28 -0.064 5.20 1.403 1.30 0.649 6.60 0.130 5.50 0.146 5.78 0.128 5.64 0.172 168.34 -0.017

Theoretical structure factors Ω Å3 qe 15.58 -0.989 16.26 -1.023 16.70 -0.429 14.55 -0.430 6.47 0.415 9.70 0.026 9.46 0.160 11.15 0.004 12.82 -0.009 12.32 -0.015 10.98 -0.011 5.50 1.337 1.67 0.587 6.92 0.104 5.98 0.100 6.19 0.088 6.07 0.089 168.31 0.005

Theory (TOPOND32) Ω Å3 qe 15.88 -1.062 16.45 -1.090 16.99 -0.450 14.82 -0.467 6.46 0.437 9.57 0.031 9.13 0.237 11.10 0.013 12.72 -0.002 12.21 -0.009 11.02 -0.008 5.28 1.421 1.74 0.607 6.87 0.097 5.98 0.092 6.12 0.074 6.11 0.082 168.45 0.003

Vol/2 = 168.58 Å3


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A significant enhancement of the molecular dipole moment (expt., theory) derived from either the atomic multipole parameters (7.13, 6.32 D) or from the integrated atomic charges and dipole moments (8.05, 7.95 D) is observed compared to the experimental values of 3.82 or 4.07 D reported in benzene or dioxane solution.71 Conclusion. We have carried out a charge density analysis from a low temperature (20K) X-ray diffraction experiment coupled with theoretical calculations using periodic boundary conditions for crystalline 2-nitrobenzoic acid. The intra- and intermolecular bonding interactions along with the integrated charge density properties were characterized via a QTAIM analysis. The interaction energy for the hydrogen-bonded dimer is typical for carboxylic acid dimers. From a comparison of the topological bond properties of the rotated C – N bond with those of other “coplanar” nitro-aromatics, additional understanding of the role of 4- bonding in this bond has been provided. The crystal packing of the hydrogen bonded dimers is dominated by O ··· O interactions parallel to the a direction, and by CH⋯O hydrogen bonds perpendicular to a. ASSOCIATED CONTENT Supporting Information. Crystallographic information file (CIF) including full multipole refinement for 2-nitrobenzoic acid, residual Fourier maps, deformation density maps, normal probability plot and scale factor plot, plot of pKa vs q(H), comparison of refined hydrogen ADP’s and SHADE calculations. This material is available free of charge via the internet at http://pubs.acs.org AUTHOR INFORMATION Corresponding Author Email: [email protected]


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Author Contributions The manuscript was written through equal contributions of all authors. All authors have given approval to the final version of the manuscript Funding Sources This work was supported by the National Science Foundation (grant NSF-CHE-1213329). ACKNOWLEDGMENT We thank Dr. C. Gatti for providing a preliminary Windows version of TOPOND.

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SYNOPSIS Quantification of intra- and intermolecular interactions in 2-nitrobenzoic acid crystals from topological analysis of the electron density obtained from 20K X-ray diffraction data and theoretical calculations.


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