Experimental and Theoretical Charge Density Studies of

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Experimental and Theoretical Charge Density Studies of Tetrafluorophthalonitrile and Tetrafluoroisophthalonitrile David E. Hibbs,*,† Jacob Overgaard,† James A. Platts,‡ Mark P. Waller,† and Michael B. Hursthouse§ School of Chemistry, UniVersity of Sydney, NSW 2006, Sydney, Australia, Department of Chemistry, Cardiff UniVersity, CF10 3TB Cardiff, United Kingdom, and Department of Chemistry, UniVersity of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom ReceiVed: December 3, 2003

The experimental electron density distributions (EDD) in tetrafluorophthalonitrile and tetrafluoroisophthalonitrile have been determined from a multipole refinement with use of accurate X-ray diffraction data collected at 100 K. As hydrogen atoms pose a serious challenge to a successful X-ray based EDD determination due to their diminishing diffraction power, the absence of any such atoms in the studied complexes is an important advantage. The experimental EDD is compared with theoretical densities resulting from high-level ab initio and DFT calculations using the atoms in molecules theory. Topological analysis of the electron density was used to compare the two different isomers and to estimate the similarity of identical functional groups in different crystalline environments. Comparison with theoretical results reveals subtle differences in C-F bonds. The experimental molecular electrostatic potential satisfactorily explains the observed differences in the patterns of weak intermolecular interactions.

Introduction The field of experimental charge density studies is ever expanding in terms of molecular size and the capability to handle heavier atoms, now successfully dealing with second-row transition-metal complexes.1 However, the light element fluorine, particularly in its covalently bonded form and not as a ligand, continues to cause problems which are sometimes ascribed to its extreme electronegativity. For this reason, a number of recent publications have focused on the polar C-F bond.2 Similarly, covalently bonded fluorine is known to be problematic for many standard theoretical techniques, especially in electron-rich molecules such as F2 or FOOF.3 Another current challenge to experimental charge density studies is the accurate description of two crystallographically different molecules within the asymmetric unit. Only a few studies on such systems have been published,4 despite the fact that they represent 8% of all 272 066 published crystal structures in version 5.24 of the CSD.5 Thus, such structures are significantly underrepresented in the EDD field, and the effects of differing crystallographic environments on electron densities are relatively understudied. One reason for the paucity of such studies is the requirement of sufficient accurate data, which has only recently become available due to improvements in experimental facilities, such as CCD-based area detectors and cooling devices.6 We have therefore carried out a combined experimental and theoretical study of the charge density distributions in two perfluorinated isomers of phthalonitrile previously characterized structurally by Britton, namely tetrafluoroisophthalonitrile7 * Address correspondence to this author. E-mail: d.hibbs@chem. usyd.edu.au. Phone: +61-2-9036-9122. † University of Sydney. ‡ Cardiff University. § University of Southampton.

(tfipn, 1) and tetrafluorophthalonitrile8 (tfpn, 2), both shown in Figure 1. The analysis of the EDD employs Bader’s method of atoms in molecules (AIM).9 As well as the methodological aspects discussed above, these molecules show a number of intriguing chemical features that warrant study in their own right. Not least among these is the lack of any hydrogen atoms, which not only eases their study via X-ray diffraction, but also ensures a complete lack of hydrogen bonding in the crystalline lattice. These molecules therefore make ideal subjects for the study of other interactions such as π‚‚‚π, F‚‚‚F, and F‚‚‚π. These nonclassical interactions are of great importance in the fields of molecular recognition and crystal engineering,10 and a study of the associated electron densities in the absence of H-bonding should be particularly revealing. Also, this study of a series of related molecules allows us to examine the effects of changing the chemical or crystallographic environment of individual groups on their electron density distributions. This information is directly relevant to attempts to transfer electron densities of atoms and/or fragments between molecules.11 Such methods build up large molecules from electron densities or multipole populations of smaller fragments, and clearly depend on the transferability of fragments. One aim of the current work is therefore to examine how the properties of fragments such as C-F and C-CN vary across the environments considered here. Experimental Section Single-Crystal X-ray Data Collection. Crystals of 1 and 2 were grown from ethanol by slow evaporation. High-resolution low-temperature X-ray diffraction data were collected with an Enraf-Nonius FAST area detector diffractometer. Cell constants were obtained from the least-squares refinement of 50 reflections located between 5.3 and 90.7° 2θ (1), and 5.1 and 90.46° (2).

10.1021/jp037700l CCC: $27.50 © 2004 American Chemical Society Published on Web 02/25/2004

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Figure 1. ORTEP drawings of molecule A in 1 (left) and 2 (right). Thermal ellipsoids show 50% probability surfaces.

Two reciprocal space data shells were collected, with one shell providing data between +3.0 and -52° 2θ, and a second for data between -37 and -110° 2θ. Data were collected at 100(2) K with ω-scan increments of 0.20°, with the orientation matrix continually recalculated every 250 reflections. The intensities of 15 standard reflections collected in the overlap region did not change significantly during either data collection therefore no scaling correction was applied. The data collection resulted in a total of 45 136 (1) and 18992 (2) reflections, which were integrated and corrected for Lorentz and polarization effects with the program ABSMAD.12 Due to the combination of small crystal sizes and vanishing absorption coefficients, no absorption correction was performed. The set of intensities was averaged and merged with SORTAV.13 Ab Initio Calculations. All monomer calculations were performed with GAUSSIAN9814 at the B3LYP/6-311++G** level of theory.15 Such DFT calculations have been shown to reproduce accurate experimental molecular charge distributions, but are known to describe weak van der Waals interactions rather poorly. Therefore, dimer energies and electron densities were evaluated at the MP2/cc-pVDZ level,16 using the experimentally determined geometries reported here. This level of theoretical treatment has been shown to be adequate for treatment of van der Waals interactions.17 Potential energy surface scans for a dimer of 2 were performed by varying the distance between the closest F‚‚‚F contact in the structure, namely F(3)‚‚‚F(4)′. All other inter- and intramolecular geometrical parameters were fixed at their crystallographic values. Binding energies of the dimers were corrected with the standard counterpoise method.18 The AIMPAC suite of programs19 was used for the topological analysis of the theoretical wave functions. Calculations were performed on a Silicon Graphics ORIGIN2400 computer [reference: http://www.ac3.com.au/sgi-origin-2400.htm] and on the UKCCF’s central Columbus facility. Structural and Multipole Refinements. Refinement procedures adopted for compounds 1 and 2 were very similar. Their molecular structures were solved from direct methods with the program SHELXS.20 Initially, positional and anisotropic atomic displacement parameters (ADP) were refined for all atoms in a conventional independent atom model (IAM) least-squares refinement with the program SHELXL-97. To model the aspherical electron density, the final parameters from these refinements were imported into the program package XD.21 This program implements the Hansen-Coppens multipole formal-

ism22 to describe the static aspherical electron density in the crystal using a superposition of pseudoatomic charge densities:

Fatomic(r) ) PcoreFcore(r) + PvalFval(r)κ3 + lmax

l

Rl(κ′r)κ′ ∑ Plm( dlm((θ,φ) ∑ l)0 m)0 3

(1)

The first and second term of eq 1 gives the spherical core and valence densities, respectively, described with HartreeFock densities. The aspherical part of the atomic density is given in the third term. Rl are Slater-type radial functions, while κ and κ′ are dimensionless expansion-contraction parameters. The angular dependency is described using the real spherical harmonic functions dlm((θ,φ). The ξ values used in the radial functions were 5.108, 3.839, and 3.176 bohr-1 for F, N, and C, respectively, with the nl-values 2, 2, and 3 for l ) 1, 2, and 3. No hexadecapoles (l ) 4) were used in the refinements. High-order refinements (sin(θ)/λ > 0.7 Å-1) were performed initially to give more accurate positional and thermal parameters. These were then fixed in the initial refinements of the multipole populations. Hereafter, a strategy was adopted that included a stepwise increase in the flexibility of the model. Two sets of chemical constraints were imposed from the outset: (a) noncrystallographic mirror planes confined the electron density to be symmetrical with respect to the molecular planes; (b) mirror symmetry was imposed in a plane perpendicular to the molecules (including the atoms F(2)-C(2)-C(5)-F(5) in 1 and bisecting the two bonds C(2)-C(11) and C(4)-C(5) in 2) and atoms were pairwise identical. When the maximum level of multipole expansion was reached, the structural parameters were refined in a separate cycle. In addition to the chemical constraints mentioned above, the number of refined multipoles was significantly reduced by imposing certain local noncrystallographic symmetries on the atomic EDD. The EDD of all atoms were constrained to obey mm2 symmetry, with the rotation axis lying along the bond to the ring substituent. Compound 2 crystallizes in the acentric space group P212121, and the structure factor phases are thus not restricted to values of 0 or π as they are for centrosymmetric crystals. Previous studies have shown that this uncertainty may lead to large correlation effects between multipoles and structural parameters.23 To remedy this, the above-mentioned chemical constraints were introduced in the least-squares refinement. However, the uncertainty may also influence the ADPs, thus it is

Tetrafluorophthalonitrile and Tetrafluoroisophthalonitrile TABLE 1: Crystallographic Details empirical formula formula wt/g mol-1 cryst system space group Z, Z′ temp (K) A (Å) B (Å) C (Å) V (Å3) Fcalcd (g cm-3) F(000) µ (mm-1) cryst size (mm) λ (Å) sin(θ)/λmax (Å-1) limiting indices (h, k, l) no. of collected reflns no. of symmetryindependent reflns av multiplicity reflns with I > 1σ(I) Rint R(F); R(F2) Rw(F2) S no. of variables Nref/Nv

1

2

C8F4N2 200.10 orthorhombic Pbca 16, 2 100 10.411 13.338 21.948 3047.74 1.744 1568 0.177 0.25 × 0.25 × 0.20 0.71073 1.00 -20, 16; -26, 26; -42, 42 45136 5306

C8F4N2 200.10 orthorhombic P212121 4, 1 100 5.655 10.644 12.350 743.37 1.788 392 0.181 0.30 × 0.25 × 0.25 0.71073 1.00 -11,1 1; -21, 20; -22, 24 18992 2065

6.2 5294 0.030 0.031; 0.038 0.045 0.58 157 34

5.8 2060 0.031 0.031; 0.034 0.033 0.93 89 23

imperative to ensure that the atomic motion is not biased. An excellent way to warrant this is by applying the Hirshfeld rigidbond test.24 In both refinements, this test clearly fulfils the requirement that the difference of mean-square displacements (MSDs) between bonded atoms must be less than 10 × 10-4 Å2 (average values for all bonds are 3.9 × 10-4 Å2 for 1 and 4.3 × 10-4 Å2 for 2). However, another effect of the phase uncertainty can be increased standard uncertainties on refined parameters and it was observed that simultaneous refinement of multipoles with positional and thermal parameters resulted in large esds on the multipoles. Thus, the refinements were done in separate cycles. All refinements were carried out on F2. Crystallographic details are shown in Table 1, and the final residual maps are shown in Figure 2. Results and Discussion Structural Details. The experimental bond distances in 1 and 2 are given in Table 2, along with the DFT(B3LYP)optimized geometries of the corresponding monomers (full geometrical details are deposited as Supporting Information).

J. Phys. Chem. B, Vol. 108, No. 11, 2004 3665 TABLE 2: Experimental and Theoretical Bond Distances in 1 and 2 1

2

bond

exp(A)

exp(B)

opt

bond

exp

opt

C(2)-F(2) C(4)-F(4) C(5)-F(5) C(6)-F(6) N(1)-C(11) N(2)-C(22) C(1)-C(11) C(3)-C(22) C(2)-C(1) C(2)-C(3) C(3)-C(4) C(4)-C(5) C(5)-C(6) C(6)-C(1)

1.323(1) 1.327(1) 1.331(1) 1.327(1) 1.157(1) 1.155(1) 1.429(1) 1.424(1) 1.388(1) 1.396(1) 1.397(1) 1.382(1) 1.388(1) 1.398(1)

1.323(1) 1.327(1) 1.339(1) 1.329(1) 1.161(1) 1.162(1) 1.425(1) 1.426(1) 1.395(1) 1.389(1) 1.398(1) 1.390(1) 1.386(1) 1.392(1)

1.328 1.325 1.330 1.325 1.154 1.154 1.424 1.424 1.397 1.398 1.402 1.389 1.389 1.402

C(3)-F(3) C(4)-F(4) C(5)-F(5) C(6)-F(6) N(1)-C(11) N(2)-C(22) C(1)-C(11) C(2)-C(22) C(1)-C(2) C(2)-C(3) C(3)-C(4) C(4)-C(5) C(5)-C(6) C(6)-C(1)

1.322(1) 1.327(1) 1.327(1) 1.330(1) 1.160(1) 1.164(1) 1.425(1) 1.425(1) 1.412(1) 1.386(1) 1.391(1) 1.387(1) 1.391(1) 1.386(1)

1.329 1.327 1.327 1.329 1.154 1.154 1.425 1.425 1.417 1.394 1.392 1.389 1.392 1.394

It is interesting to compare the two different molecules in the asymmetric unit of 1. In both molecules the C(5)-F(5) bond appears longer than the other C-F bonds, in agreement with theory. In the C-C bonds in the aromatic rings in 1, the experiment does not exhibit four long and two short bonds as predicted by theory. Instead, molecule A shows three longer bonds and molecule B only two. The two different molecules do, however, agree that the C(3)-C(4) and C(6)-C(1) bonds are long, while the C(4)-C(5) and C(5)-C(6) bonds are short. In 2, the C(3)-F(3) bond is significantly shorter than the other three C-F bonds in contrast to the results of the theoretical calculations. The substitution pattern in 2 creates five almost equidistant C-C bonds in the aromatic ring, which is shown both by experiment and theory. The sixth bond, C(1)-C(2), is much longer and has only slight double bond character. The Electron Density. A complete list of all refined multipoles is given in the Supporting Information. The main purpose of the current study is to compare the EDD in similar, yet different molecules. The first step in this process is the examination of the different models, which is conveniently done by the graphical representation of the static deformation density in the molecular planes, see Figure 3. The static deformation density map of molecule B of 1 is undistinguishable from the one shown in Figure 3 and is therefore omitted. The major features, such as the magnitude and appearance of the excess bond density, are comparable in all similar bonds except for the C-F bonds. In the C(4)-F(4) and C(5)-F(5) bonds in 2 (compared to the other C-F bonds) more electron density seems to be accumulated on the F atom in the region facing the bonded C-atom. Also the distributions of the negative deformation density on the F-atoms are

Figure 2. Residual density in the molecular planes of molecule B of 1 (left) and 2 (right). Contours are shown at (0.1 e Å-1. Solid lines show positive contours, dashed lines negative contours.

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Figure 3. Static experimental deformation density maps in the molecular planes of molecule A in 1 (left) and 2 (right). Contours as in Figure 2, zero contours shown as dotted lines.

Figure 4. Experimental negative Laplacian distribution maps in the molecular planes of molecule A in 1 (left) and 2 (right). Solid lines show positive contours, dashed lines show negative contours, both at the following values: 2, 4, 8 × 10n e Å-5, n ) (3, (2, (1, 0.

dissimilar. In 1, the negative contours around F appear more circular, whereas they have a slightly more complex shape in 2. The overall impression is that the F-atoms lack any preferred directionality of its lone pairs. However, it is common in charge density analysis that the deformation density method may be biased by the use of a reference model, the IAM model. Thus, the 2D-Laplacian distribution will reveal more accurately the features of the EDD, as shown in Figure 4. The most conspicuous feature is the apparent closed-shell nature of the C-F bonds, which support the observed lack of excess bonding density in these bonds in Figure 3. These features are further supported by the corresponding theoretical maps, shown in Figure 5. The observed lack of shared valence shells in the C-F bonds is interesting. A similar feature has recently been encountered in the experimental EDD studies of complexes with C-O bonds; however, in these cases a contradiction was observed between theory and experiment.25 The excellent agreement observed here between theory and experiment suggests that the depletion of electronic charge in the interatomic region of the C-F bonds is enhanced compared to that of the C-O bonds, and not unexpectedly so due to the greater electronegativity of F. Nevertheless, the topological analysis (see next section) will demonstrate significant covalent character of these bonds.

The Laplacian distribution also reveals a more pronounced localization of the fluorine lone pairs in the theoretical map, compared to their experimental counterparts. Considering the latter, only on the sides of F(3) and F(6) in 2 can the valence shell charge concentrations (VSCC) be recognized. However, all F-atoms have discernible indications of lone pairs on their sides, perpendicular to the C-F bonding directions. Topological Analysis. Tables 3 and 4 list the results of the topological analysis of 1 and 2, respectively. These tables quantify the above-mentioned discrepancy between theory and experiment in the C-F bonds. Despite the fact that the variation in the position of the bcps is within 0.02 Å for all bonds, the experimental values of ∇2Fbcp are all negative while theory gives positive values. According to the rules of the theory of atoms in molecules such characteristics suggest predominantly covalent character in the experimental description of the C-F bonds but ionic in the theoretical model. A breakdown of ∇2Fbcp into the three curvatures comprising it (λ1-3) shows that this difference is essentially due to the curvature along the bond direction only. In the experiment, with the exception of F(2B)-C(2B) in 1, the values of λ3 in the C-F bonds are close to the values of λ1-2. However, theory results in a significantly steeper curve along the bond path (higher λ3), while the values of λ1-2 are nearly identical in theory and experiment.

Tetrafluorophthalonitrile and Tetrafluoroisophthalonitrile

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Figure 5. Theoretical negative Laplacian distribution maps in the molecular planes of molecule A in 1 (left) and 2 (right). Contours and labels as in Figure 4.

TABLE 3: Topological Analysis of 1a bond F(2)-C(2) F(4)-C(4) F(5)-C(5) F(6)-C(6) N(1)-C(11) N(2)-C(22) C(11)-C(1) C(22)-C(3) C(1)-C(2) C(2)-C(3) C(3)-C(4) C(4)-C(5) C(5)-C(6) C(6)-C(1)

a

A B T A B T A B T A B T A B T A B T A B T A B T A B T A B T A B T A B T A B T A B T

Fbcp/e Å-3

∇2Fbcp/e Å-5



d1-2/Å

d1-bcp/Å

d2-bcp/Å

-λ1/e Å-5

-λ2/e Å-5

λ3/e Å-5

1.92(4) 1.72(5) 1.83 1.93(4) 1.92(4) 1.83 1.91(5) 2.07(5) 1.81 1.93(4) 1.92(4) 1.83 3.13(4) 3.09(4) 3.23 3.14(4) 3.08(4) 3.23 1.84(3) 1.88(3) 1.90 1.85(3) 1.88(3) 1.90 2.06(2) 2.09(3) 2.09 2.04(3) 2.10(3) 2.09 2.08(2) 2.13(3) 2.07 2.24(2) 2.16(3) 2.16 2.22(3) 2.17(3) 2.16 2.08(3) 2.14(3) 2.07

-14.1(2) -1.9(3) 3.6 -12.5(2) -9.8(2) 4.0 -14.8(2) -24.9(2) 3.9 -12.5(2) -10.4(1) 4.0 0.6(3) -5.4(3) -5.4 1.0(3) -5.7(3) -5.4 -17.2(1) -15.0(1) -18.4 -17.7(1) -15.0(1) -18.4 -19.31(7) -20.27(8) -20.73 -18.76(8) -20.73(9) -20.72 -20.02(6) -21.32(7) -20.37 -24.16(7) -22.90(8) -22.22 -23.61(8) -23.23(9) -22.22 -19.93(8) -21.83(7) -20.37

0.16 0.19 0.03 0.06 0.01 0.03 0.01 0.06 0.03 0.06 0.01 0.03 0.01 0.10 0.03 0.01 0.10 0.03 0.11 0.08 0.09 0.11 0.08 0.09 0.23 0.29 0.30 0.23 0.29 0.30 0.21 0.23 0.29 0.16 0.36 0.37 0.16 0.36 0.37 0.21 0.23 0.29

1.323 1.323 1.327 1.327 1.327 1.326 1.331 1.339 1.331 1.327 1.330 1.325 1.157 1.161 1.154 1.155 1.162 1.154 1.429 1.425 1.424 1.424 1.426 1.424 1.388 1.395 1.398 1.396 1.390 1.398 1.397 1.399 1.402 1.382 1.390 1.389 1.388 1.387 1.389 1.398 1.392 1.402

0.866 0.881 0.884 0.870 0.884 0.882 0.868 0.869 0.885 0.871 0.885 0.882 0.757 0.759 0.743 0.756 0.760 0.743 0.810 0.738 0.747 0.810 0.739 0.747 0.691 0.720 0.678 0.701 0.672 0.719 0.683 0.707 0.678 0.674 0.692 0.701 0.711 0.696 0.688 0.714 0.688 0.678

0.458 0.442 0.444 0.457 0.443 0.443 0.463 0.470 0.446 0.456 0.445 0.443 0.400 0.402 0.410 0.399 0.402 0.410 0.620 0.687 0.677 0.614 0.687 0.677 0.698 0.676 0.719 0.695 0.717 0.678 0.714 0.692 0.724 0.708 0.698 0.688 0.677 0.691 0.701 0.684 0.704 0.724

15.68 12.49 13.16 14.47 14.89 13.18 14.24 17.94 12.62 14.48 14.79 13.18 24.78 27.65 24.59 24.93 27.59 24.59 12.62 12.61 13.51 12.74 12.60 13.52 14.87 15.73 16.22 14.68 15.90 16.22 15.20 16.11 15.97 16.91 17.41 17.48 16.72 17.53 17.48 15.16 16.29 15.97

13.57 10.54 12.78 13.68 14.78 12.83 14.08 16.85 12.22 13.70 14.67 12.83 24.45 25.23 23.95 24.60 25.17 23.94 11.34 11.63 12.44 11.44 11.62 12.44 12.05 12.21 12.44 11.90 12.33 12.44 12.56 13.07 12.35 14.52 12.81 12.76 14.36 12.91 12.76 12.53 13.22 12.35

15.10 21.12 29.57 15.61 19.89 29.98 13.55 9.92 28.72 15.70 19.12 30.00 49.81 47.45 43.16 50.54 47.09 43.14 6.77 9.2 7.57 6.52 9.21 7.58 7.61 7.67 7.94 7.81 7.5 7.94 7.73 7.86 7.95 7.27 7.33 8.01 7.47 7.21 8.02 7.76 7.68 7.95

For each bond, A(B) indicates experimental results for molecule A(B) and T is the theoretical results from the optimized DFT calculation.

This is illustrated in Figure 6. The behavior of F(r) along the bond is almost identical for theory and experiment within 0.2 Å of the bcp. However, considering instead ∇2F(r), the differences that do exist become more pronounced. The figure

shows that on the C-side (left) of the bcp, Fteo(r) decreases slightly faster than Fexp(r). On the F-side (right) of the bcp, the situation is reversed, as Fexp(r) increases sooner and faster than Fteo(r). The result is that the value of ∇2Fteo(r) is still positive

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TABLE 4: Topological Analysis of 2a bond F(3)-C(3) F(4)-C(4) F(5)-C(5) F(6)-C(6) N(1)-C(11) N(2)-C(22) C(11)-C(1) C(22)-C(2) C(1)-C(2) C(2)-C(3) C(3)-C(4) C(4)-C(5) C(5)-C(6) C(6)-C(1) a

E T E T E T E T E T E T E T E T E T E T E T E T E T E T

Fbcp/e Å-3

∇2Fbcp/e Å-5



d1-2/Å

d1-bcp/Å

d2-bcp/Å

-λ1/e Å-5

-λ2/e Å-5

λ3/e Å-5

2.03(5) 1.81 1.88(5) 1.82 1.88(5) 1.82 2.01(5) 1.81 3.38(7) 3.23 3.36(7) 3.23 1.86(3) 1.90 1.86(3) 1.90 1.99(2) 1.97 2.31(3) 2.10 2.11(3) 2.14 2.02(2) 2.15 2.11(3) 2.14 2.31(3) 2.10

-21.3(3) 3.8 -6.5(3) 4.1 -6.5(3) 4.1 -21.4(3) 3.7 -20.1(5) -5.4 -21.0(5) -5.4 -15.3(1) -18.6 -15.3(1) -18.6 -16.37(6) -18.5 -24.47(8) -21.0 -19.70(8) -22.0 -17.00(6) -22.1 -19.76(8) -22.0 -24.48(6) -21.0

0.00 0.00 0.05 0.00 0.05 0.00 0.00 0.00 0.08 0.03 0.08 0.03 0.17 0.08 0.17 0.08 0.25 0.24 0.16 0.31 0.24 0.36 0.21 0.37 0.24 0.36 0.16 0.31

1.323 1.329 1.327 1.327 1.327 1.327 1.330 1.329 1.161 1.154 1.164 1.154 1.425 1.425 1.425 1.425 1.413 1.417 1.387 1.394 1.391 1.392 1.387 1.389 1.391 1.392 1.386 1.394

0.845 0.884 0.879 0.883 0.879 0.883 0.843 0.885 0.752 0.744 0.754 0.744 0.783 0.748 0.783 0.748 0.706 0.709 0.721 0.677 0.718 0.693 0.694 0.695 0.673 0.700 0.666 0.717

0.478 0.445 0.448 0.444 0.448 0.444 0.488 0.445 0.409 0.410 0.410 0.410 0.642 0.677 0.642 0.677 0.707 0.709 0.666 0.717 0.674 0.700 0.694 0.695 0.717 0.693 0.721 0.677

16.71 12.70 13.68 12.75 13.69 12.76 16.40 12.68 30.24 24.63 29.94 24.63 13.18 13.59 13.19 13.59 14.86 14.69 18.44 16.35 16.31 17.34 14.68 17.42 16.33 17.34 18.44 16.36

16.66 12.67 13.06 12.71 13.07 12.73 16.32 12.65 28.00 23.96 27.70 23.97 11.25 12.56 11.26 12.56 11.88 11.83 15.83 12.49 13.12 12.77 12.14 12.74 13.14 12.77 15.84 12.49

12.02 29.15 20.23 29.58 20.30 29.62 11.35 29.07 38.14 43.17 36.65 43.17 9.15 7.60 9.15 7.60 10.37 8.07 9.80 7.89 9.73 8.07 9.82 8.02 9.71 8.07 9.79 7.89

Experimental values are given in the first line (E) and theoretical results from optimized DFT calculation are given in the second line (T).

Figure 6. The behavior of F(r) (left) and ∇2F(r) (right) along the C(4)-F(4) bond in 2. The position of the bcps is indicated by the vertical lines.

at the bcp, while ∇2Fexp(r) has become negative. However, the more rapid increase in Fexp(r) after the bcp is responsible for the increase in ∇2Fexp(r) to significantly positive values. This view reinforces our recent findings26 that subtle differences in ∇2F(r) profiles in polar bonds can lead to significant differences at critical points, and hence that care must be taken in simple assignment of covalent/electrostatic character from bcp properties alone in such bonds. The experimental topologies of the C-N bonds present some differences between 1 and 2. In 1, Fexp(r) is close to 3.1 e Å-3 while Fexp(r) for these bonds is 3.4 e Å-3 in 2. Also ∇2Fbcp(r) deviates: ∇2Fbcp(r) is significantly negative (-20 e Å-5) in 2 but close to zero in 1 (0 to -5 e Å-5). In this case, the reason is even smaller deviations in the behavior of F(r). The topological analysis of C-C bonds in the aromatic ring is well reproduced by theory. In particular, the two shorter bonds (C(4)-C(5) and C(5)-C(6)) appear slightly stronger (larger Fbcp(r) and more negative ∇2Fbcp(r)). The topological analysis compares well with literature values from studies of other F-containing complexes.2 On certain counts, however, the present analysis seems to compare significantly better with theory than has been the case in the literature. For instance, the experiment and theory in both 1

and 2 agree very well on the position of the bcp as they also result in very similar ellipticities. It is remarkable that all published studies so far on C-F bonding find a highly significant discrepancy in the value of ∇2Fbcp(r) between experiment and theory. As we have suggested here, the origin of this disparity may be subtle differences in the EDD. The results in Tables 3 and 4 also allow us to examine the extent to which density properties are transferable between molecules and crystalline environments. Taking C-F bonds first, molecule A of 1 shows remarkable consistency, with average values of Fbcp(r) and ∇2Fbcp(r) of 1.932 ( 0.010 and -13.48 ( 1.16, but molecule B shows a much greater spread with averages of 1.908 ( 0.144 and -11.75 ( 9.58, the larger variations mainly due to the high values found for C(5)-F(5). The average values for 2 are similar to 1A at 1.950 ( 0.081 and -13.93 ( 8.57, but this masks considerable differences between the bonds to F(3) and F(6), which are much stronger than those to F(4) and F(5). In contrast, values for aromatic C-C bonds show much less variation across the three molecules considered here, with averages of Fbcp(r) ranging from 2.138 to 2.155 e Å-3. Thus it seems that care must be taken in assuming density properties are conserved in chemically similar

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J. Phys. Chem. B, Vol. 108, No. 11, 2004 3669

TABLE 5: Atomic Chargesa 1a atom F(2) F(4) F(5) F(6) N(1) N(2) C(11) C(22) C(1) C(2) C(3) C(4) C(5) C(6) dipole moment

E T E T E T E T E T E T E T E T E T E T E T E T E T E T E T

1b

2

q(Ω)

q(Pv)

q(Ω)

q(Pv)

-0.72 -0.60 -0.71 -0.59 -0.72 -0.58 -0.71 -0.59 -1.15 -1.04 -1.16 -1.04 0.96 0.89 0.96 0.89 0.20 0.12 0.72 0.60 0.21 0.12 0.72 0.60 0.70 0.60 0.72 0.61 1.0(4) 2.5

-0.06(2)

-0.74 -0.60 -0.67 -0.59 -0.85 -0.58 -0.66 -0.59 -1.24 -1.04 -1.24 -1.04 1.19 0.89 1.19 0.89 -0.04 0.12 0.76 0.60 -0.04 0.12 0.82 0.61 0.70 0.60 0.81 0.61 1.7(4) 2.5

-0.14(2)

F(3)

0.01(2)

F(4)

-0.14(2)

F(5)

0.01(2)

F(6)

-0.08(6)

N(1)

-0.08(6)

N(2)

-0.04(2) -0.06(2) -0.04(2) 0.01(6) 0.01(6) -0.10(7) -0.10(7) 0.05(6) 0.08(5) 0.05(6) 0.07(5) 0.07(5) 0.07(5)

atom

0.11(7)

C(11)

0.11(7)

C(22)

-0.08(6)

C(1)

0.11(5)

C(2)

0.08(6)

C(3)

0.11(5)

C(4)

0.02(5)

C(5)

0.11(5)

C(6)

q(Ω) -0.59 -0.59 -0.58 -0.58 -0.59 -0.58 -0.58 -0.59 -1.19 -1.03 -1.17 -1.03 0.91 0.88 0.90 0.88 0.05 0.12 0.06 0.12 0.78 0.60 0.63 0.61 0.63 0.61 0.76 0.60 6.2(4) 4.2

q(Pv) 0.03(2) 0.01(2) 0.01(2) 0.03(2) 0.12(6) 0.12(6) -0.34(7) -0.34(7) 0.02(3) 0.02(3) 0.12(3) 0.04(2) 0.04(2) 0.12(3)

a The first line for each atom gives experimental values (E), the second line the theoretical results (T) from the optimized DFT calculation. The molecular dipole moment is given in units of debye.

groups, or even between identical molecules in different crystalline interactions. Atomic Charges. Several attempts have been made in recent years to enable the derivation of atomic charges from experimental charge densities.27 Table 5 lists the results from the integration of the EDD within the atomic basins in 1 and 2. Also shown are the refined monopoles, which can provide an alternative estimate of atomic charge using the following relation: q ) N - Pv, where N is the number of valence electrons for the neutral atom.28 It is worth pointing out that the same flexibility was used in the refinements of both complexes. For that reason, the significant differences between 1 and 2 are surprising. In 2, the fluorine charges are remarkably constant around -0.58 e, and they are equally constant (close to -0.71 e) in molecule A of 1. In accord with the critical point data noted above, molecule B does show significant deviations in atomic charges. Although the average charge on F of -0.73 e is similar to that in molecule A, individual values cover a range of almost 0.2 e, with F(5) being the most negative. The nitrogens are all highly negative while the C atoms in the cyano group are highly positive. As expected, the C atoms bonded to fluorine are significantly more positive than the ones substituted with a CN group. Table 5 also stores the theoretical atomic charges from an integration of the atomic basins. The values show an excellent correspondence with the experimental charges for the F atoms in 2. For the remaining atoms, the correspondence is slightly less impressive. The theoretical dipole moment for a monomer of 2 is as expected less than the experimental dipole moment for the molecule in the crystal and supports the finding of dipole moment enhancement.29 Electrostatic Potential. One of the most useful applications of experimental charge densities is the derivation of the

Figure 7. The MEP on the isodensity surface of molecule A of 1 (left) and 2 (right). For 1 the MEP range is -37.5 to +37.5 kJ mol-1; for 2 the range is -97.2 to +97.2 kJ mol-1. The color scheme ranges from blue (negative) via green to red (positive).

molecular electrostatic potential (MEP).30 The MEP can be used as a highly sensitive measure to predict the strength of intermolecular interactions and due to complementarity give novel insight into electronic receptor environments in drugreceptor interactions.31 It can also be used as a tool to further highlight the influence of isomerism, as is the case for the pair 1 and 2. Figure 7 shows the MEP on the isodensity surface of 0.007 e Å-3. It is clear that the two molecules appear significantly different from their environments. In both cases, the two CN groups are highly electronegative, but in 1 they are well separated and represent rather shallow minima. In 2, on the other hand, these negative regions merge to form a much larger, deeper minimum. Electropositive regions are also rather different: in 2 a large region of positive MEP is found opposite the CN groups (a clear illustration of the significant molecular dipole moment in

3670 J. Phys. Chem. B, Vol. 108, No. 11, 2004

Hibbs et al.

Figure 8. (a, top) Intermolecular interactions involving molecules A (left) and B (right) of 1. The orange balls represent the bond critical points listed in Table 6a. (b, bottom) Intermolecular interactions involving the unique molecule in 2. The orange balls represent the bond critical points listed in Table 6b. The bond path of bcp8 is shown as a black line.

2 of 6.2(4) D), the F atoms becoming more electropositive the further they are from the CN groups. The situation in 1 is more complex, with two fluorines, F(4) and F(6), electropositive and the remaining two, F(2) and F(5), essentially neutral. Unlike in 2, proximity to the CN groups does not appear to be the deciding factor in determining the MEP of the F atoms, since F(2) lies between the CN’s but is neutral. Instead, it appears that resonance effects play a major factor here, as both electropositive F’s are ortho to one CN group and para to another. It is also readily apparent that the aromatic rings are quite different. In 1 the entire ring is electropositive while the potential over the ring in 2 is very close to neutral. These differences lead us to expect significant differences in the intermolecular interactions of these isomers. This will be examined in the following section. Intermolecular Interactions. The absence of hydrogen atoms in the complexes necessitates the presence of other types of attractive intermolecular interactions to create the crystalline

phase. To investigate the nature and strengths of these interactions, we have identified the different types by searching bcps in the experimental EDD (Table 6a,b). To supplement this, a number of molecular dimers have been studied, using theoretical methods and the relevant topological analyses included in Table 6. The positions of the intermolecular bcps are indicated in Figure 8. Overall, as indicated in Table 6, three types of interactions are found: (1) F-F, (2) F-π, and (3) N-π, where the π-system in type 2 can be either (a) a CtN bond or (b) the aromatic ring system, while the N-π interaction involves only the aromatic ring system. It is observed that the N-π type of interactions have slightly higher concentration of density at the bcp (Fbcp ∼ 0.06 e Å-3) despite being longer than the other types of interactions (d(N-C) > 3.1 Å, d(F-F) > 2.9 Å). The two F-π interactions of type 2a in 2 (bcp 5 and 6, see Figure 8b) are perhaps more appropriately characterized as π-π interactions, as the C-F-bcp angles are 79°. Figure 8b also includes the

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J. Phys. Chem. B, Vol. 108, No. 11, 2004 3671

TABLE 6: Topology in the Intermolecular Interactions in 1 (a) and 2 (b)a type

bcp no.

1 1

1 2

2a 2b 2b 3 3

3 4 5 6 7

3 3 3 3

8 9 10 11

1

1

1 1 2a 2a 2a

2 3 4 5 6

2a

7

2b 3 3

8 9 10

bondb

Fbcp

∇2Fbcp



F(6A)-F(4A)i F(2A)-F(5B)ii theoryc F(5A)-N(1A)iii F(5A)-C(2A)iv F(4A)-C(2B)v N(1A)-C(4A)vi N(2A)-C(2B)vii theoryc N(1B)-C(4B)viii N(2B)-C(5A)ix N(1B)-C(2A)x N(2B)-C(6B)xi

0.04 0.05 0.036 0.05 0.06 0.04 0.06 0.07 0.060 0.06 0.06 0.05 0.06

(a) topology in 1 0.7 0.03 0.8 0.10 0.82 0.06 0.7 0.08 0.8 0.33 0.6 0.24 0.7 1.52 0.8 0.81 0.71 1.81 0.7 3.11 0.7 0.44 0.6 0.68 0.7 0.95

F(4)-F(3)xii theoryc F(5)-F(3)xiii F(3)-F(3)xii F(5)-C(22)xii F(5)-C(11)xiv F(4)-C(22)xiv theoryc F(3)-N(2)xii theoryc F(6)-C(3)xv N(1)-C(2)xvi N(2)-C(5)xvii

0.04 0.04 0.03 0.02 0.05 0.05 0.05 0.036 0.03 0.022 0.05 0.07 0.06

(b) topology in 2 0.8 0.01 0.83 0.01 0.5 0.53 0.4 0.41 0.6 0.40 0.6 2.36 0.6 2.31 0.60 0.83 0.4 0.51 0.36 0.46 0.7 0.88 0.8 1.92 0.7 0.97

d1-2

d1-bcp

-λ1

-λ2

λ3

2.899 2.862 2.862 3.010 2.951 3.136 3.073 3.094 3.094 3.300 3.088 3.245 3.174

1.456 1.435 1.457 1.447 1.413 1.465 1.512 1.483 1.551 1.543 1.538 1.567 1.533

-0.13 -0.16 -0.15 -0.13 -0.13 -0.10 -0.14 -0.16 -0.16 -0.13 -0.12 -0.10 -0.14

-0.13 -0.14 -0.14 -0.12 -0.10 -0.08 -0.05 -0.09 -0.06 -0.03 -0.08 -0.06 -0.07

0.99 1.14 1.11 0.96 1.06 0.77 0.93 1.04 0.92 0.85 0.88 0.75 0.87

2.862 2.862 3.063 3.198 3.093 3.198 3.187 3.187 3.420 3.420 3.103 3.177 3.338

1.435 1.450 1.516 1.599 1.432 1.534 1.529 1.527 1.552 1.579 1.439 1.488 1.514

-0.14 -0.15 -0.08 -0.05 -0.12 -0.09 -0.09 -0.09 -0.06 -0.06 -0.12 -0.15 -0.13

-0.13 -0.15 -0.05 -0.04 -0.09 -0.03 -0.03 -0.05 -0.04 -0.04 -0.06 -0.05 -0.07

1.06 1.13 0.65 0.45 0.84 0.70 0.72 0.73 0.48 0.47 0.82 0.99 0.89

Units are e Å-3 (Fbcp), e Å-5 (∇2Fbcp and λ1-3), and Å (d1-2, d1-bcp, and d2-bcp). b Superscript notations: (i) -x, 0.5 + y, 0.5 - z; (ii) -1.5 + x, y, 0.5 - z; (iii) -x, -0.5 + y, 0.5 - z; (iv) 0.5 + x, y, 0.5 - z; (v) -0.5 + x, y, 0.5 - z; (vi) -0.5 - x, 0.5 + y, z; (vii) -1 + x, 0.5 - y, 0.5 + z; (viii) -0.5 + x, 0.5 - y, z; (ix) 1 - x, -0.5 + y, 0.5 - z; (x) 0.5 - x, 1 - y, -0.5 + z; (xi) 1.5 - x, -0.5 + y, z. (xii) 0.5 + x, -0.5 - y, 1 - z; (xiii) 0.5 - x, -y, -0.5 + z; (xiv) 1 + x, y, z; (xv) -x, 0.5 + y, 0.5 - z; (xvi) -0.5 + x, 0.5 - y, 1 - z; (xvii) -0.5 - x, - y, 0.5 + z. c Theoretical results are from single-point MP2 calculation with experimental atomic coordinates. a

bond path for the F(6)-C(3) interaction (bcp 8). This line represents the other interactions of type 2b (F-π), where it is the π-electron system, rather than the C atom, that interacts with F. In all cases, theoretically predicted electron density properties are in close agreement with experimental values, confirming the suitability of the MP2 method for studying these weak interactions. Comparing the MEP shown in Figure 7 with these intermolecular interactions reveals a significant correlation between the degree of complementarity in the MEP and the strength of the interaction (measured by Fbcp). The highest values of Fbcp are as mentioned in the N-π interactions. These interactions represent regions with opposing signs of the MEP. However, weaker interactions do not follow this trend: for instance, both 1A and 2 contain distinct F-F contacts, despite the fact that all F’s are seen to be either neutral or electropositive in Figure 7, which may account for the relative weakness of such bonds. It has been suggested that F-F interactions in some situations should in fact destabilize the molecular crystal;32 however, we do observe the existence of bcps in these interactions which implies that they contribute positively, however little, to the assembly of the crystal. It should be noted that interactions of type 3 (N-π) are more abundant in 1 than in 2 (Table 6), which relates well to the larger difference in MEP in 1 between the electronegative cyano group and the electropositive central ring (Figure 7). It has been shown that in cases such as hydrogen bonds, where values of electron density in the interatomic regions are low, energy densities can be estimated from the values of Fbcp and ∇2Fbcp.33 The resulting energy density has also been successfully correlated to theoretical values of the bond energiesshence it is possible to get experimental estimates of intermolecular bond energies from the multipole description of

the electron density.34 For 1, the sum of all intermolecular bond energies is 62 kJ mol-1 while for 2 this sum equals 42.8 kJ mol-1. This is in excellent agreement with lattice energies from the XDINTER program,35 which predicts values of 62.7(17) kJ mol-1 for 1 and 36.9(22) kJ mol-1 for 2. Theoretical dimer calculations also allow us to explore the energies associated with the observed intermolecular interactions. We find that, in general, there is very little difference in dimer binding energies between similar contacts in 1 and 2. Dimers of both 1 and 2 that contain F-F and N-π contacts are stabilized by 4.61 and 3.09 kJ mol-1, respectively, after BSSE correction. These rather weak binding energies concur with our previous findings for F-F interactions,17 but contrast with those for dimers containing F-π and N-π contacts, for which stabilization energies of 13.05 and 15.43 kJ mol-1 are found for 1 and 2. Finally, the observation that F-F contact distances are consistently found at 2.86 Å prompted us to study the dependence of the dimer stabilization energy with regard to F-F distance. Figure 9 shows the (BSSE uncorrected) potential energy surface for this contact, which reveals a clear minimum in the region 2.7-2.8 Å, and the classic shape of a LennardJones or Buckingham potential. However, the PES is also very shallow, such that it requires less than 1 kJ mol-1 to perturb the dimer from its minimum energy structure at 2.75 Å to the X-ray value of 2.86 Å. Thus it appears that the very high degree of consistency seen in F-F distances here is not due to any unexpected features of the associated potential energy surfaces. Conclusions The experimental and theoretical charge densities of two hydrogen-free perfluorinated isomers of phthalonitrile have been

3672 J. Phys. Chem. B, Vol. 108, No. 11, 2004

Figure 9. Potential energy surface for the dimer of 2 with respect to F-F distance.

obtained. Comparisons of the density distributions of the two crystallographically different molecules of 1 with use of Bader’s topological approach indicates that the concept of transferability of multipole parameters requires that sufficient consideration is being given to the differences in intermolecular interactions. The detailed analysis of the theoretical and experimental electron density in the polar C-F bond shows that the observed differences originate in slightly deviating radial distribution that has a profound effect on the topological resultssa clear indication of the inadequacy of the bcp as the sole point of interest for bond nature determination. The energetics of the weak interactions has been estimated and an excellent agreement is observed between the lattice energy and the sum of individual intermolecular interactions. Significantly, the proportion of weak interactions of type 3 (N-π) is significantly higher in 1, in agreement with the larger differences in the electrostatic potentials of the cyano group and the aromatic ring in 1 compared to 2, underpinning the importance of the electrostatic potential to establish long-range interactions, as recognized in drug design. Acknowledgment. We would like to thank the Australian Research Council for funding this work and the Australian Centre for Advanced Computing and Communications and the UK Computational Chemistry Facility for generous allocations of computational resources. J.O. would like to thank the Danish Research Council for financial support. D.E.H. thanks Cardiff University’s Visiting Fellowship scheme, and the Royal Society of Chemistry for a Journals grant. Supporting Information Available: Tables of refined parameters and local coordinate systems (CIF file). This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Pillet, S.; Wu, G.; Kulsomphob, V.; Harvey, B. G.; Ernst, R. D.; Coppens, P. J. Am. Chem. Soc. 2003, 125, 1937-1949. (2) Bach, A.; Lentz, D.; Luger, P. J. Phys. Chem. A 2001, 105, 74057412. Bach, A.; Lentz, D.; Luger, P.; Messerschmidt, M.; Olesch, C.; Patzschke, M. Angew. Chem., Int. Ed. 2002, 41, 296-299. Buschmann, J.; Koritsanszky, T.; Lentz, D.; Luger, P.; Nickelt, N.; Willemsen, S. Z. Kristallogr. 2000, 215, 487-494. Larsen, S.; Flensburg, C.; Bengaard, H. S.; Sørensen, H. O. Acta Crystallogr. Sect. A 1999, S55, 38. Lentz, D.; Patschke, M.; Bach, A.; Scheins, S.; Luger, P. Org. Biomol. Chem. 2003, 1, 409-414. (3) Lucchese, R. R.; Schaefer, H. F., III; Rodwell, W. R.; Radom, L. J. Chem. Phys. 1978, 68, 2507-2508. Kraka, E.; He, Y.; Cremer, D. J. Phys. Chem. A 2001, 105, 3269-3276. (4) Zhurova, E. A.; Martin, A.; Pinkerton, A. A. J. Am. Chem. Soc. 2002, 124, 8741-8750. Overgaard, J.; Schiøtt, B.; Larsen, F. K.; Iversen, B. B. Chem. Eur. J. 2001, 7, 3756-3767. Pichon-Pesme, V.; Lecomte, C.

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