Article pubs.acs.org/JPCA
Experimental and Theoretical Electron Density Determination for Two Norbornene Derivatives: Topological Analysis Provides Insights on Reactivity Christopher G. Gianopoulos,† Bartosz Zarychta,†,‡ Simone Cenedese,† Vladimir V. Zhurov,† and A. Alan Pinkerton*,† †
Department of Chemistry, School of Green Chemistry and Engineering, The University of Toledo, Toledo, Ohio 43606-3390, United States ‡ Department of Chemistry, Opole University, ul. Oleska 48, 45-052 Opole, Poland S Supporting Information *
ABSTRACT: The electron density distribution of two substituted norbornene derivatives (cis-5-norbornene-endo2,3-dicarboxylic anhydride (1) and 7-oxabicylo[2.2.1]hept-5ene-exo-2,3-dicarboxylic anhydride (2) has been determined from low-temperature (20 K) X-ray diffraction data and from DFT calculations with periodic boundary conditions. Topological analysis of the electron density is discussed with respect to exo-selective additions, the partial retro-Diels−Alder (rDA) character of the ground state, and intermolecular interaction energies.
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INTRODUCTION The exo selective addition to the CC bond of norbornene derivatives is well-known1−3 and has been attributed to groundstate properties such as sterics,1 torsional strain4 and orbital perturbation.5 Theoretical calculations have further suggested that the selectivity is due to energetics of the transition state, which are influenced by torsional strain.6 Structural studies have established that the olefin hydrogen atoms are bent toward the endo face, facilitating exo attack as a result of steric interactions.7 This structural aspect also affects the transition state of addition reactions as the reorganization energy of the olefinic substituents is less in the case of attack at the exo face. The angle that characterizes the out-of-plane bending is denoted χ (Figure 1) and is typically small, around 0.5−2.0°, but can be as large as 25° in sterically strained systems (Figure 2).
selectivity in addition reactions to sterically hindered norbornenes is not as striking as the exo selectivity observed in unhindered substrates. For example, the hydroboration− oxidation of norbornene is >99% exo selective whereas the same reaction with 7,7-dimethylnorbornene results in 22% exo and 78% endo products.1 In light of these results, it seems that the striking exo selectivity in such addition reactions is likely due to a complicated interplay of these aforementioned factors. Norbornene derivatives have also attracted attention due to unusual properties observed in their NMR spectra, such as abnormally large 1JCC coupling constants.9 Here again several explanations have been proposed to account for the interesting electronic properties of norbornenes such as hyperconjugative effects10 and partial retro-Diels−Alder (rDA) character.9 In this context, we have been involved in examining what can be gleaned from structural studies with respect to the interesting properties of norbornene derivatives11 and herein expand upon our previous contribution with analysis of the experimentally and theoretically derived ground-state electron density of two norbornene derivatives. There is also significant current interest in the phenomena of molecular recognition and crystal packing, which are driven by noncovalent intermolecular interactions. Among these interactions, strong E···H (E = O, N) hydrogen bonds are generally recognized as the most energetically important. However, C···H and H···H interactions are also relevant and can be as strong as
Figure 1. Out-of-plane bending angle denoted χ.
Theoretical results have further suggested that the π faces are asymmetric with the HOMO rotated in the direction of the hydrogen atoms.5 It is worth noting at this point that endo attack is favorable in the case of norbornene derivatives that are substituted with bulky groups at the methylene bridge due to steric effects that block the exo face. Nevertheless, the endo © 2016 American Chemical Society
Received: April 13, 2016 Revised: May 26, 2016 Published: May 27, 2016 4059
DOI: 10.1021/acs.jpca.6b03787 J. Phys. Chem. A 2016, 120, 4059−4070
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The Journal of Physical Chemistry A
Figure 2. Histogram of χ angles in structurally characterized norbornene derivatives (CSD8). The upper trace is a magnification of the region for χ > 2°.
Rigaku diffractometer equipped with an ULTRAX-18 rotating anode (Mo, graphite monochromator) generator operating at 50 kV and 300 mA and a RAPID II cylindrical image plate detector.18 For both compounds, diffraction images were collected using 5° omega oscillations with 2.5° overlap combined in runs covering 180° each. Eight runs were collected for compound 1 and six for compound 2 to provide adequate data completeness and redundancy. The starting goniometer angles for the six runs were set to χ = 0° (φ = 0, 180°), χ = 40° (φ = 0, 90, 180, 270°) for both crystals. Two additional runs were collected for 1 with χ = 20° (φ = 60, 120°). The exposure time was 120 s per frame for 1 and 90 s per frame for 2. Indexing was carried out with HKL2000,19 and integrated intensities were determined using VIIPP applying background and reflection profiles averaged over the complete data set as previously described.12,18,20 Scaling and merging of the data was carried out with the program SORTAV.21,22 Electron Density Model Refinement. The structures were initially resolved and refined by a full-matrix least-squares method using the SHELXTL program suite.23 All hydrogen atoms were located from difference Fourier syntheses. The atomic displacement parameters were freely refined, anisotropically for non-hydrogen atoms and isotopically for H atoms. The absolute configuration was determined using the unmerged data sets. Because of the low redundancy of high-order data, the Friedel pairs were merged and f ″ anomalous scattering coefficients were set to zero in further refinements for compound 1. For compound 2, Friedel pairs were not merged as the redundancy of the high-order data was deemed sufficient. Thermal ellipsoid plots and the atom numbering are shown in Figure 3, and a summary of crystallographic results in Table 1. The crystal structures resulting from the spherical atom modeling were used as a starting point for the refinement of the electron density using the Hansen−Coppens multipole atom
weak E···H hydrogen bonds. Recently, we have demonstrated the usefulness of experimental electron density studies, in conjunction with the Quantum Theory of Atoms In Molecules (QTAIM), for quantifying the strength of such weak interactions in crystals.12−15 As an extension of our previous work, herein we report the characterization of the electron density distribution of two substituted norbornene derivatives, cis-5-norbornene-endo-2,3dicarboxylic anhydride (1) and 7-oxabicylo[2.2.1]hept-5-eneexo-2,3-dicarboxylic anhydride (2) from high-resolution X-ray diffraction experiments, as well as from theoretical calculations with periodic boundary conditions, and discuss their implications on studying the aforementioned properties of norbornene compounds.
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EXPERIMENTAL SECTION Data Collection and Reduction. The single crystals of 1 were grown by vacuum sublimation and those of 2 were grown from acetone by slow evaporation. The crystal of 1 chosen for data collection was measured as 0.15 × 0.24 × 0.32 mm and the crystal of 2 as 0.14 × 0.29 × 0.33 mm. The crystals were mounted on glass capillaries with a cryo-oil composed of a mineral and paratone oil mixture. During the data collection they were maintained at 20 K in a stream of helium using an open flow device.16,17 X-ray intensity data were collected on a 4060
DOI: 10.1021/acs.jpca.6b03787 J. Phys. Chem. A 2016, 120, 4059−4070
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Figure 3. Molecular structure and numbering scheme for 1 and 2. Thermal ellipsoids are drawn at 99% probability.
Table 1. Crystallographic Data 1 chemical formula space group a (Å) b (Å) c (Å) volume (Å3), Z T (K) wavelength λ (Å) crystal size (mm) (sin θ/λ)max (Å−1) no. of reflns integrated Rint/average data multiplicity completeness: sin θ/λ < 1.00 Å−1, all data (%) no. of ind reflns no. of obsd reflns (I > 3σ) spherical atom refinement R1[F, I > 2σ(I)], wR2(F2), GOF Δρmin/max (e Å−3) multipole refinement R1[F, I > 3σ(I)], wR2(F2), GOF weighting scheme: a, ba Δρmin/max (e Å−3) all data, sin θ/λ < 1.0 Å−1 a
2
C9H8O3 P212121 5.87150(10) 9.4021(2) 13.3312(2) 735.94(2), 4 20.0 K 0.710 73 0.32 × 0.24 × 0.15 1.30 89 016 0.0209/12.3 99.3, 97.0 7215 7017
C8H6O4 P212121 5.30180(10) 6.92650(10) 18.6795(5) 685.97(2), 4 20.0 K 0.710 73 0.33 × 0.29 × 0.14 1.30 112 666 0.0171/10.1 95.8, 88.0 11103 10519
0.0226, 0.0680, 1.063 −0.28/0.54
0.0202, 0.0621, 1.082 −0.238/0.498
0.0119, 0.0116, 1.162 0.002, 0.002 −0.123/0.154, −0.058/0.059
0.0109, 0.0107, 1.233 0.001, 0.001 −0.167/0.145, −0.075/0.064
w2 = 1/{σ2(F2) + (ap)2 + bp}, p = 0.3333Fobs2 + 0.6667Fcalc.
formalism24 implemented in the program XD2006.25 It allows modeling of the nonspherical part of the atomic electron density using atom-centered multipole functions:
applied at the initial stage of refinement. These were gradually released. At the first stage, the bond lengths for the hydrogen atoms were restrained to standard neutron distances. After convergence of the multipole model, partial geometry optimization of hydrogen atom positions was accomplished with the CRYSTAL0926,27 program suite. Further multipole refinement was done with hydrogen bond lengths constrained to values obtained from the optimization. At the final stage, the ADPs of the H atoms were obtained from the SHADE program28 and then refined using rigid constraints with the parent atoms in XD2006. The ADPs of all other atoms were refined anisotropically at all times. The κ0 − κ4 were kept constrained to the same value for each atom type in the final model. The κ coefficients of hydrogen atoms were set to 1.2 and not further refined. All multipoles up to hexadecapoles were refined for C and O atoms. Three dipoles for hydrogen atoms were refined in the case of 2, and quadrupoles were
ρ(r) = Pcρc (r ) + Pvκs 3ρv (κsr ) 4
+
l
∑ κl 3Rl(κlr) ∑ Plm±ylm±(r/r) l=0
m=0
where Pc and Pv account for the spherical core and valence populations respectively, the ylm± represent real angular spherical harmonic functions of order m,l, the Rl are normalized Slater-type radial functions, and the Plm± are the mth multipole populations of order l. The coefficients κs and κl describe the contraction−expansion for the spherical and multipolar valence densities, respectively. The refinement was done on structure factors F over the merged data using reflections with I/σ(I) > 3 and employing the VM databank. Various constraints were 4061
DOI: 10.1021/acs.jpca.6b03787 J. Phys. Chem. A 2016, 120, 4059−4070
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Figure 4. Experimental static deformation maps for 1 and 2 in O1−O2−O3 and C1−C4−C6 planes. Contours are at ±0.05 e/Å3. Red solid contours denote positive charge density, blue dashed contours denote electron depletion.
Figure 5. Experimental static deformation density distribution in the perpendicular plane bisecting the C(5)C(6) bond. The origin of the cross indicates the position of the bond. Horizontal line is the projection of the C1C4C5C6 plane. Contours are at ±0.05 e/Å3. Red solid contours denote positive charge density, blue dashed contours denote electron depletion.
−0.12, +0.15; 2 −0.17, +0.15 for all data). Thus, the electron density is well modeled by the multipole expansion, as further confirmed by the low R values (Table 1) and the deposited scale factor and normal probability plots (Figure S2). For both compounds the final total electron density was positive everywhere. The topology of the total electron density was analyzed, in particular to characterize all of the bond critical points, using the program WinXPRO.29,30 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 local virial theorem and the DFT formulas. All critical points have been checked for the existence of a virial path in the negative potential energy density. CPs not mirrored by a virial path have been rejected. All derived values are reported in Tables S1−S4.
additionally refined for hydrogen atoms in the case of 1. The electroneutrality constraint was maintained during the refinements. In the calculations for both compounds, the resolution up to sin θ/λ = 1.3 Å−1 was used for the refinement of the scale factor, xyz, Uij, valence and multipolar populations, κs and κl. The parameters were refined in blocks multiple times one group after another. In the final step all parameters were refined together until convergence. A crystallographic summary is reported in Table 1. Plots of the molecules from the final refinements along with the atom numbering scheme are shown in Figure 3. The total electron density, as well as its derivatives, were calculated from the refined multipole parameters. Static deformation maps are shown in Figures 4 and 5. The residual Fourier maps in the mean planes of both molecules have been deposited (Figure S1). The maps are featureless with residual densities in the range ±0.1 e·Å−3 (1 4062
DOI: 10.1021/acs.jpca.6b03787 J. Phys. Chem. A 2016, 120, 4059−4070
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The Journal of Physical Chemistry A Theoretical Calculations. Density functional theory (DFT) calculations with periodic boundary conditions were carried out with the CRYSTAL09 package26,27 for 1 and 2 using the B3LYP hybrid functional. The basis set for hydrogen atoms was taken from the common 6-311G** compilation; however, the (8s)-(411sp)-(1d1d) and (6s)-(311sp)-(1d1d) basis sets31 were chosen for oxygen and carbon atoms, respectively. Computational details have been deposited (Tables S5−S7). The calculations have been done in two stages. As mentioned above, the results of multipole refinement with hydrogen bond lengths constrained to typical values were first used as a starting geometry for C−H bond distances optimization. Only C−H geometry optimization was performed at that time, the unit cell and atomic coordinates for the heavy atoms were fixed to those obtained from the multipole refinement of the experimental data. At the second stage, the geometry obtained from the final multipolar model refinement with hydrogen bonds constrained to previously optimized lengths was used as the starting point to calculate wave functions again. The obtained wave functions were then employed to generate static theoretical structure factors for further multipolar refinement and topological analysis of the theoretical multipolar density. The resulting electron density distribution was also analyzed with the program TOPOND32 directly from wave functions. The theoretical structure factors were calculated corresponding to the same (sin θ/λ) resolution as for the experimental data set. The multipole refinement over calculated structure factors was done with the scale factor fixed to unity, all ADP’s fixed to zero and frozen atomic coordinates. Unlike the experimental refinement, the κ0 − κ4 were allowed to refine separately within a single atom type. Also, two monopole terms, Pv and P00, were refined for all atoms except hydrogens to model the core contraction. As shown before,12 this significantly improves the fit for theoretical structure factors. The topological analysis of the resulting electron density was carried out as for the experimental results. In the case of 3, a similar DFT calculation was carried out on the basis of the published neutron structure,7 and a multipole refinement carried out as above on the basis of theoretical structure factors.
theory. This distortion results in the H(5) and H(6) hydrogen atoms being bent in the direction of the endo face. The pyramidalization at the olefin carbons, measured by the χ angle (out-of-plane bending), for 3 amounts to χ = 7.4(2)° (χ5 = 7.3(2)° and χ6 = 7.5(2)°, where χ5 and χ6 correspond to out-ofplane bending of H(5) and H(6) and χ is their average). For 1, the χ angle is 3.6(2)° (with χ5 = 4.2(2)° and χ6 = 3.1(2)°), whereas for 2, the χ angle is 6.5(2)° (with χ5 = 7.7(2)° and χ6 = 5.2(2)°). Although the resulting angle for 2 is in close agreement with the result from the neutron diffraction study on 3, the angle for 1 is significantly smaller. This may result from steric interactions with the maleic anhydride substituent on the endo face of 1. Molecular Properties. Compared to the structural parameters obtained in routine diffraction studies, chargedensity analysis, particularly the topology of the total electron density and the atomic properties derived from it using QTAIM, offers much greater insight into the potential factors which afford norbornene derivatives their unusual properties.40 Atomic charges obtained from integration of the electron density of the volume elements delimited by zero flux surfaces are reported in Tables 2 and 3. The agreement between theory Table 2. Integrated Volumes Ω and Atomic Charges q for 1 from Experiment (Exp), Theoretical Structure Factors (Theo-F), and Theory (Theo) Exp
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RESULTS AND DISCUSSION The structure of 1 was previously reported from X-ray diffraction measurements made at 173 K33 and 130 K,34 whereas the structure of 2 was previously determined at room temperature35,36 and at 130 Ka.37 Both compounds crystallize in the space group P212121 with four molecules per unit cell, in agreement with the previous reports. Furthermore, the geometries of 1 and 2 are in good agreement with the earlier results (Crystallographic Information File is deposited). The results of preliminary charge density experiments at 100 K on 1 and 2 have been previously published.38 However, the current experiments, conducted at 20 K and refined using the multipolar model, have improved on the precision of the previous measurements. The structures and atom numbering are shown in Figure 3. As addition reactions are known to exhibit high selectivity for the exo faces of norbornene derivatives, the ethylene bridge region is of particular interest.4,7,39 A neutron diffraction study performed on cis-5-norbornene-exo-2,3-dicarboxylic anhydride, 3, at 15 K7 unequivocally confirmed the slight pyramidalization of the C(5) and C(6) carbon atoms in norbornene derivatives in the solid state, which had previously been predicted by
atom
Ω, Å3
O(1) O(2) O(3) C(1) C(2) C(3) C(4) C(5) C(6) C(7) C(8) C(9) H(1) H(2) H(3) H(4) H(5) H(6) H(7a) H(7b) total
16.195 18.634 19.546 8.347 7.411 7.576 8.274 11.337 12.201 8.738 5.420 5.328 6.209 6.651 5.918 6.752 7.445 7.295 7.579 6.923 183.779
Theo-F q, e
Ω, Å3
Theo q, e
−0.98 15.920 −0.93 −1.15 18.759 −1.12 −1.18 19.253 −1.11 0.03 8.103 0.02 0.03 7.277 0.04 −0.05 7.332 0.02 0.06 8.165 0.03 −0.07 11.088 −0.07 −0.15 11.799 −0.07 0.01 8.593 0.01 1.40 5.518 1.33 1.44 5.405 1.35 0.08 6.334 0.06 0.10 6.731 0.08 0.11 6.334 0.09 0.10 7.209 0.05 0.07 7.618 0.07 0.09 7.469 0.08 0.02 7.690 0.03 0.03 6.993 0.04 0.00 183.591 0.01 Vol/4 = 183.985 [Å3]
Ω, Å3
q, e
15.985 19.020 19.184 8.142 7.330 7.384 8.181 11.471 12.145 8.563 5.222 5.176 6.223 6.642 6.374 7.134 7.485 7.431 7.674 6.874 183.641
−0.99 −1.13 −1.11 0.03 0.01 0.01 0.03 −0.07 −0.07 0.02 1.42 1.42 0.06 0.07 0.08 0.04 0.06 0.07 0.02 0.03 0.01
and experiment is very good, and the results are similar for 1 and 2. A graphical comparison has been deposited (Figure S3). All oxygens carry significant negative charges; however, the O(b) bridging atom in 2 is slightly less negative. As expected, carbonyl carbon atoms are highly positive and all hydrogen atoms bear slight positive charges. The bridgehead carbon atoms connected with the O(b) atom in 2 are slightly more positive in comparison to the other carbons, which are essentially neutral. Selected experimental static deformation density (DD) maps, the difference between the total electron density and neutral 4063
DOI: 10.1021/acs.jpca.6b03787 J. Phys. Chem. A 2016, 120, 4059−4070
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The Journal of Physical Chemistry A Table 3. Integrated Volumes Ω and Atomic Charges q for 2 from Experiment (Exp), Theoretical Structure Factors (Theo-F), and Theory (Theo) Exp atom
Ω, Å
O(b) O(1) O(2) O(3) C(1) C(2) C(3) C(4) C(5) C(6) C(8) C(9) H(1) H(2) H(3) H(4) H(5) H(6) total
12.986 13.852 19.924 19.836 7.651 7.996 8.104 7.780 12.759 12.343 5.301 5.466 5.635 6.269 6.449 5.600 6.348 6.745 171.045
3
Theo-F q, e −0.83 −1.03 −1.21 −1.16 0.30 −0.09 −0.04 0.28 −0.20 −0.15 1.48 1.45 0.21 0.19 0.18 0.25 0.23 0.15 0.01 Vol/4
Ω, Å
3
13.217 13.996 20.171 20.230 7.062 7.364 7.573 7.043 12.084 11.498 5.701 5.581 5.806 6.532 7.037 6.112 7.341 6.812 171.161 = 171.492
responsible for directing the selectivity. The deformation density in the plane perpendicular to the C(5)C(6) double bond going through the bridge atom (Figure 5, hydrogen atoms are located on the left of each diagram), is notably elongated in the direction perpendicular to the olefin plane for both 1 and 2 due to the π contribution to the bond. However, there does not appear to be significant polarization of the experimental DD favoring either the exo or endo face for 1 or 2. Thus, it appears rather unlikely that the asymmetry of the π-face is a major contributor to the exo selectivity of addition reactions to norbornenes. The electrostatic environment around the C(5)C(6) bond was also investigated for any possible asymmetry, which could influence reactivity (Figure 6). The usefulness of the electrostatic potential (ESP) is that it provides an opportunity to understand the specificity of molecular recognition and binding properties, and sites of nucleophilic or electrophilic attack. Accordingly, electrostatic effects are believed to be the primary driving force for some facially selective addition reactions to ketones, although the absence of such an electrostatic effect has been noted for addition reactions to olefins.41 Although the ESP is indeed negative over the exo-face of the double bond in 2, this may be partially due to the influence of the bridging oxygen. The situation is less clear for 1 where there is a small minimum on the exo-face, but the oxygen atoms from the anhydride moiety dominate the ESP over the endo-face. To avoid the complications due to the presence of the electronegative oxygen atoms, we have carried out a theoretical study on 3 on the basis of the reported neutron structure at 15 K,7 followed by a multipole refinement based on theoretical structure factors. As shown in Figure 6.3, the exo- and endofaces are now clearly differentiated. Thus, we conclude that there is indeed a contribution of the ground-state charge distribution to the exo/endo selectivity in this class of compounds. The characteristics of the (3,−1) critical points of all covalent bonds are summarized in Table 4. The experimentally derived
Theo q, e
−0.86 −0.92 −1.08 −1.08 0.36 0.04 0.04 0.37 −0.07 −0.02 1.30 1.29 0.11 0.10 0.10 0.11 0.10 0.10 0.01 [Å3]
Ω, Å
q, e
13.437 13.866 20.101 20.016 7.062 7.526 7.839 7.167 12.065 11.878 5.290 5.362 5.906 6.688 6.875 6.004 7.302 6.915 171.299
−0.97 −1.00 −1.11 −1.11 0.43 0.01 0.01 0.42 −0.05 −0.05 1.43 1.43 0.10 0.09 0.09 0.11 0.08 0.09 0.00
3
spherical atoms, of 1 and 2 are depicted in Figure 4. The experimental and theoretical DD maps are in good agreement for both compounds, and the corresponding maps derived from theory have been deposited (Figure S4). All covalent bonds are well-defined by a concentration of electron density, as well as the lone pairs associated with all oxygens. As previously mentioned, the selectivity of addition reactions to norbornene derivatives has intrigued researchers for many years. It has been suggested previously that asymmetry of the electron density distribution at the CC double bond is
Figure 6. Experimental electrostatic potential in the perpendicular plane bisecting the molecules through the C(5)C(6) bond and bridge atom together with electrostatic potential projected onto the visible half of the molecular (ρ(r) = 0.001 au) surface. Red color denotes positive electrostatic potential; blue color denotes negative electrostatic potential. Picture 3 is for theoretical calculations of 3. Pictures were created with MoProViewer software.42 4064
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Table 4. Summary of Topological Characteristics of the Electron Density at the Covalent Bond Critical Points for 1 and 2a 1 atom 1
atom 2
O(1)
C(8)
O(1)
C(9)
O(2)
C(8)
O(3)
C(9)
C(1)
C(2)
C(1)
C(6)
C(1)
C(7)
C(1)
H(1)
C(2)
C(3)
C(2)
C(8)
C(2)
H(2)
C(3)
C(4)
C(3)
C(9)
C(3)
H(3)
C(4)
C(5)
C(4)
C(7)
C(4)
H(4)
C(5)
C(6)
C(5)
H(5)
C(6)
H(6)
−3
ρ(r), e·Å 2.010 1.913 1.903 1.923 1.837 1.842 3.016 2.908 2.922 3.058 2.957 2.963 1.500 1.452 1.464 1.682 1.656 1.667 1.568 1.569 1.586 1.864 1.905 1.937 1.653 1.613 1.626 1.805 1.774 1.768 1.848 1.849 1.896 1.507 1.472 1.485 1.800 1.767 1.761 1.877 1.873 1.903 1.677 1.644 1.667 1.604 1.564 1.586 1.889 1.883 1.917 2.324 2.279 2.274 1.888 1.878 1.917 1.853 1.876
∇ ρ(r), e·Å 2
−19.77 −15.73 −16.22 −19.31 −13.73 −15.33 −28.30 −19.59 −16.53 −23.69 −19.50 −15.66 −9.35 −8.17 −9.45 −11.83 −11.17 −12.72 −10.67 −9.88 −11.45 −19.68 −20.73 −23.67 −11.58 −10.82 −12.00 −15.73 −14.16 −14.87 −20.16 −19.45 −22.60 −9.04 −8.40 −9.69 −14.26 −13.89 −14.75 −20.51 −20.23 −22.75 −12.16 −10.89 −12.63 −10.75 −9.78 −11.30 −21.45 −20.17 −23.18 −22.51 −21.39 −22.36 −20.23 −19.70 −23.33 −18.99 −19.86
2 −5
Rij, Å
ε
ntopo
atom 1
atom 2
1.383
0.08 0.06 0.01 0.09 0.06 0.01 0.08 0.06 0.12 0.10 0.06 0.12 0.00 0.02 0.01 0.04 0.06 0.04 0.05 0.01 0.01 0.02 0.01 0.01 0.02 0.02 0.02 0.07 0.06 0.06 0.01 0.01 0.01 0.02 0.02 0.01 0.04 0.04 0.05 0.02 0.01 0.01 0.03 0.05 0.04 0.02 0.02 0.01 0.03 0.01 0.00 0.28 0.28 0.33 0.01 0.02 0.02 0.01 0.03
0.962 0.920 0.903 0.881 0.862 0.866 1.453 1.426 1.296 1.419 1.427 1.303 0.908 0.910 0.869 1.047 1.069 0.968 0.935 1.006 0.920 0.958 0.976 0.905 1.016 1.014 0.957 0.985 1.081 0.967 0.930 0.964 0.907 0.948 0.930 0.889 1.095 1.086 0.964 0.953 0.962 0.905 1.015 1.067 0.982 0.995 1.004 0.942 0.931 0.971 0.905 1.595 1.663 1.473 0.968 0.978 0.901 0.969 0.971
O(b)
C(1)
O(b)
C(4)
O(1)
C(8)
O(1)
C(9)
O(2)
C(8)
O(3)
C(9)
C(1)
C(2)
C(1)
C(6)
C(2)
C(3)
C(2)
C(8)
C(3)
C(4)
C(3)
C(9)
C(4)
C(5)
C(5)
C(6)
C(1)
H(1)
C(2)
H(2)
C(3)
H(3)
C(4)
H(4)
C(5)
H(5)
C(6)
H(6)
1.397
1.201
1.195
1.574
1.519
1.545
1.082
1.539
1.501
1.088
1.571
1.503
1.087
1.520
1.547
1.085
1.345
1.079
1.079
4065
−3
ρ(r), e·Å 1.778 1.698 1.707 1.755 1.699 1.701 1.958 1.896 1.876 1.918 1.892 1.863 3.031 3.005 2.963 3.060 3.002 2.963 1.556 1.510 1.512 1.734 1.685 1.701 1.618 1.575 1.606 1.759 1.756 1.748 1.545 1.511 1.505 1.766 1.731 1.741 1.720 1.692 1.701 2.347 2.282 2.288 1.807 1.943 1.944 1.753 1.861 1.869 1.740 1.885 1.903 1.795 1.905 1.910 1.752 1.858 1.903 1.775 1.882
∇ ρ(r), e·Å−5
Rij, Å
ε
ntopo
−14.64 −8.16 −13.23 −12.32 −7.98 −13.16 −20.40 −13.72 −15.74 −18.97 −12.87 −15.59 −21.00 −26.57 −15.78 −24.47 −26.31 −15.62 −11.21 −9.24 −10.19 −14.04 −11.19 −13.33 −11.33 −9.26 −11.62 −14.99 −13.21 −14.53 −10.92 −9.26 −10.05 −15.14 −12.45 −14.31 −13.67 −11.45 −13.37 −24.03 −19.61 −22.56 −20.00 −22.63 −24.20 −17.82 −19.88 −22.15 −17.89 −20.53 −22.87 −20.38 −21.95 −23.33 −17.80 −19.07 −23.13 −17.21 −20.00
1.438
0.07 0.06 0.05 0.06 0.09 0.05 0.06 0.04 0.01 0.06 0.08 0.01 0.07 0.06 0.12 0.07 0.07 0.13 0.06 0.05 0.03 0.09 0.06 0.06 0.03 0.04 0.03 0.07 0.06 0.07 0.06 0.05 0.03 0.05 0.06 0.06 0.06 0.06 0.05 0.26 0.27 0.32 0.04 0.04 0.03 0.00 0.01 0.01 0.00 0.01 0.01 0.03 0.03 0.02 0.04 0.01 0.02 0.03 0.01
0.813 0.748 0.823 0.809 0.754 0.815 0.947 0.872 0.887 0.932 0.871 0.878 1.374 1.543 1.310 1.411 1.556 1.309 0.902 0.923 0.863 1.012 1.091 0.957 1.016 1.053 0.961 1.013 1.080 0.954 0.902 0.930 0.867 1.013 1.088 0.962 1.018 1.095 0.949 1.598 1.722 1.494 0.853 0.948 0.877 0.883 0.969 0.892 0.874 0.968 0.900 0.837 0.934 0.878 0.882 0.981 0.891 0.929 0.971
2
1.439
1.388
1.392
1.196
1.195
1.569
1.517
1.543
1.505
1.573
1.509
1.517
1.340
1.090
1.095
1.087
1.099
1.083
1.079
DOI: 10.1021/acs.jpca.6b03787 J. Phys. Chem. A 2016, 120, 4059−4070
Article
The Journal of Physical Chemistry A Table 4. continued 1 atom 1
atom 2
C(7)
H(7a)
C(7)
H(7b)
−3
ρ(r), e·Å 1.917 1.850 1.843 1.890 1.887 1.862 1.896
∇ ρ(r), e·Å 2
2 −5
−23.38 −19.49 −18.85 −22.41 −20.90 −19.57 −22.53
Rij, Å 1.089
1.090
ε
ntopo
0.02 0.02 0.01 0.00 0.02 0.01 0.00
0.899 0.961 0.977 0.915 0.956 0.972 0.916
atom 1
atom 2
−3
ρ(r), e·Å 1.917
∇ ρ(r), e·Å−5 2
−23.57
Rij, Å
ε
ntopo
0.02
0.889
First line is from the multipole fit to experimental data, second line from the multipole fit to theoretical structure factors, and third line directly from theory. Rij is the bond length, ρ and ∇2ρ denote the total electron density and its Laplacian, ε is the ellipticity, and ntopo is the topological bond order. Complete details of the topological properties are given in Tables S1 and S3. a
bond order and covalent bond strength can be inferred from the estimated topological bond order (ntopo),43 which is derived from the electron density (ρ), and its principal curvatures (λ1, λ2, λ3) at the bond critical points. ntopo = a + bλ3 + c(λ1 + λ 2) + dρ
The coefficients a, b, c, d were obtained from theoretical calculations in accordance with the description of bond orders as defined by Cioslowski and Mixon.44−47 The complete set of bond orders and related topological parameters are listed in Tables S1 and S3. Graphical comparison of the electron density at the bond critical points and of the topological bond order have been deposited (Figures S5, S6). The bond orders for CO bonds are indicative of a strong π-component, as expected (compound 1, O(2)C(8)/ O(3)C(9), exp 1.453/1.419, theory 1.296/1.303; compound 2, O(2)C(8)/O(3)C(9), exp 1.374/1.411, theory 1.310/ 1.309) and are in good agreement with the values obtained for carbonyl groups in other molecules.15 All other CO bonds in both molecules demonstrate ntopo values close to unity (exp 0.809−0.962; theory 0.815−0.903), indicating polarized single bonds lacking in any π contribution from the oxygen lone pair in the bonding. Similar values are observed in both molecules for all CC (exp 0.902−1.095; theory 0.863−0.982) and C H single bonds. As expected, ntopo is considerably larger for the C(5)C(6) bond and there is good agreement for both molecules (1, exp 1.595, theory 1.473; 2, exp 1.598, theory 1.494). The topological bond orders are also of interest to address the question of partial retro-Diels−Alder character in 1 and 2. Previous structural studies have been employed in support of the manifestation of partial retro-Diels−Alder in norbornene derivatives on the basis of bond lengths. Such a phenomenon also ought to be reflected in the topological bond order, which is independent of bond distance. The expected trend is indeed observed in the values of ntopo in the case of 1 and 2 (Figure 7). In other words, the bonds which would break in an rDA reaction have the smallest bond orders of all C−C bonds. Furthermore, the C(1)−C(6), C(4)−C(5), and C(2)−C(3) bonds in 1, which should have partial double bond character (assuming that there is incipient rDA character) have larger bond order values than those of bonds to the methylene carbon (which do not change formal bond order in an rDA reaction). The situation is similar in the case of 2. Here again the bonds that would break in an rDA reaction have the smallest bond orders of all C−C bonds. Comparison of the bond orders is less intuitive in this case as the bridging C−O bonds possess the lowest bond orders in 2. This is not unexpected, however, as
Figure 7. Bond distances for 1 and 2 (Å, top and bottom left, respectively) and topological bond orders over a depiction of bonds formed and broken in the rDA reaction (expt, red; theoretical structure factors, blue; theory, purple).
the large difference in electronegativity between carbon and oxygen results in a polarized bond with slight ionic character and a lower bond order than homonuclear bonds. At first glance, it seems unsurprising that there is little difference in the magnitude of the bond orders for the C−C bonds when 1 and 2 are compared. This is of note, however, as the rDA reaction is more facile in the case of the furan adduct 2 than cyclopentadiene derivative 1 and might be expected to be reflected in the bond orders, assuming that the ease with which a molecule undergoes the rDA reaction depends on the electronic properties of the ground state. On the basis of the topological bond orders, it seems that the ground-state electronics are not related to the ease of undergoing the rDA reaction. It is perhaps worth noting that a lack of correlation of bond distance to the propensity to undergo an rDA reaction was already noted by White and co-workers when comparing furan and cyclopentadiene derived norbornene compounds.37 In this context, it would be interesting to evaluate this problem from another vantage point such as the electronic properties of the transition state; however, this is beyond the scope of the work presented herein. Thus, we may only propose that the topological bond orders derived from both the experimental 4066
DOI: 10.1021/acs.jpca.6b03787 J. Phys. Chem. A 2016, 120, 4059−4070
Article
The Journal of Physical Chemistry A
Table 5. Summary of Topological Characteristics of the Electron Density at Intermolecular Bond Critical Points for 1 and 2a 1 atom 1
atom 2 a
O(1)
O(2)
O(1)
H(2)b
O(2)
H(3)c
O(2)
H(7a)d
O(2)
H(7b)c
O(3)
H(1)e
O(3)
H(4)f
O(3)
H(5)g
O(3)
H(7b)h
C(5)
H(1)i
C(6)
H(2)i
C(7)
H(6)j
H(2)
H(7a)d
H(4)
H(5)g
ρ(r), e·Å−3 0.050 0.044 0.040 0.031 0.029 0.027 0.078 0.069 0.067 0.037 0.030 0.027 0.040 0.033 0.034 0.061 0.059 0.061 0.059 0.057 0.061 0.042 0.039 0.040 0.033 0.039 0.041 0.051 0.049 0.054 0.029 0.030 0.033 0.033 0.036 0.040 0.031 0.034 0.034 0.026 0.027 0.027
2
∇2ρ(r), e·Å−5 0.66 0.64 0.67 0.35 0.37 0.36 0.81 0.86 0.84 0.32 0.31 0.34 0.40 0.41 0.39 0.80 0.80 0.75 0.72 0.78 0.75 0.56 0.56 0.53 0.61 0.59 0.55 0.56 0.59 0.55 0.31 0.30 0.27 0.39 0.48 0.48 0.34 0.39 0.36 0.31 0.33 0.31
Rij, Å 3.109
2.828
2.425
2.865
2.784
2.492
2.470
2.674
2.685
2.680
3.046
2.768
2.436
2.519
De, kJ/mol 5.1 4.6 3.8 2.5 2.5 2.0 8.1 7.5 5.5 2.7 2.3 1.9 3.3 2.9 2.3 6.6 6.4 4.8 6.1 6.2 4.8 4.2 3.9 3.1 3.8 4.0 3.2 4.7 4.8 3.6 2.3 2.3 2.3 2.9 3.4 2.9 2.5 2.9 2.2 2.1 2.2 1.8
atom 1
atom 2
ρ(r), e·Å−3
∇2ρ(r), e·Å−5
Rij, Å
De, kJ/mol
0.057 0.071 0.067 0.067 0.056 0.061 0.035 0.026 0.027 0.056 0.045 0.047 0.043 0.031 0.034 0.077 0.068 0.067 0.030 0.029 0.027 0.051 0.036 0.040 0.075 0.077 0.074 0.044 0.035 0.034 0.036 0.045 0.040 0.041 0.035 0.040
0.870 0.74 0.82 0.840 0.87 0.84 0.420 0.37 0.39 0.640 0.63 0.63 0.540 0.53 0.48 0.980 1.01 1.01 0.380 0.30 0.34 0.560 0.55 0.51 1.020 0.92 0.96 0.520 0.53 0.53 0.610 0.49 0.55 0.410 0.37 0.39
2.397
6.6 7.1 7.2 7.3 6.5 6.8 3.1 2.4 2.5 5.5 4.6 4.8 4.1 3.3 3.3 8.8 8.2 8.1 2.6 2.2 2.3 4.7 3.7 3.8 8.8 8.6 8.5 4.1 3.6 3.5 4.0 4.0 4.0 3.3 2.9 3.2
a
O(b)
H(4)
O(b)
H(5)b
O(1)
H(2)b
O(1)
H(2)c
O(1)
H(3)b
O(2)
H(1)d
O(2)
H(2)b
O(2)
H(3)c
O(3)
H(1)e
O(3)
H(4)f
O(3)
H(6)g
C(6)
H(5)h
2.527
2.900
2.735
2.720
2.436
2.836
2.742
2.341
2.771
2.563
2.874
a First line is from the multipole fit to experimental data, second line from the multipole fit to theoretical structure factors, and third line directly from theory. Rij is the bond length, ρ and ∇2ρ denote the total electron density and its Laplacian, and De is the estimated dissociation energy. Symmetry operators for atom 2 for 1 are 0.5 + x, 0.5 − y, −za; −0.5 + x, 0.5 − y, −zb; −1 + x, y, zc; 1 − x, 0.5 + y, −0.5 − zd; 0.5 − x, −y, 0.5 + ze; −0.5 + x, −0.5 − y, −zf; 0.5 + x, −0.5 − yg; −z, 1.5 − x, −y, 0.5 + zh; 1 − x, −0.5 + y, −0.5 − zi; 1 + x, y, zj. Symmetry operators for atom 2 for 2 are 2 − x, −0.5 + y, 0.5 − za, 1 + x, y, zb, 0.5 + x, 1.5 − y, −zc, 0.5 + x, 0.5 − y, −zd, 1 − x, x, 1 + y, ze, 2 − x, 0.5 + y, 0.5 − zf, 1 + x, 1 + y, zg, −z, 1 − x, −0.5 + y, 0.5 − zh.
and theoretical electron density support the presence of retroDiels−Alder character in the ground state of norbornene derivatives 1 and 2. Interatomic Interactions. The crystal structure of 1 is characterized by 14 stabilizing intermolecular interactions characterized by their respective bond paths as summarized in Table 5. In total there are eight O···H, three C···H, two H··· H, and one O···O interaction. Although these are primarily weak interactions (
