Mapping of N−C Bond Formation from a Series of Crystalline Peri‐Substituted Naphthalenes by Charge Density and Solid‐State NMR Methodologies

Abstract A combination of charge density studies and solid state nuclear magnetic resonance (NMR) 1 J NC coupling measurements supported by periodic density functional theory (DFT) calculations is used to characterise the transition from an n–π* interaction to bond formation between a nucleophilic nitrogen atom and an electrophilic sp 2 carbon atom in a series of crystalline peri‐substituted naphthalenes. As the N⋅⋅⋅C distance reduces there is a sharp decrease in the Laplacian derived from increasing charge density between the two groups at ca. N⋅⋅⋅C = 1.8 Å, with the periodic DFT calculations predicting, and heteronuclear spin‐echo NMR measurements confirming, the 1 J NC couplings of ≈3–6 Hz for long C−N bonds (1.60–1.65 Å), and 1 J NC couplings of <1 Hz for N⋅⋅⋅C >2.1 Å.

General. The solution NMR characterisation was completed using a JEOL ECLIPSE 400 spectrometer operating at 1 H, 13 C and 15 N Larmor frequencies of 400, 100.6 and 40.6 MHz respectively, or an 11.7 T Bruker Avance HD NMR spectrometer, operating at 1 H, 13 C and 15 N Larmor frequencies of 500.1, 125.9 and 50.8 MHz respectively, using CDCl3 as solvent and tetramethylsilane (TMS) as standard (δiso = 0 ppm) unless otherwise stated. The 15 N NMR spectra in solution are measured relative to nitromethane. The IR spectra were recorded on a Perkin Elmer Spectrum 100 FT-IR Spectrometer using Attenuated Total Reflection sampling unless otherwise stated, and are reported in cm 1 . Mass spectra were recorded at the EPSRC Mass Spectrometry Centre at the University of Swansea on an LTQ Orbitrap spectrometer or NTU using an Agilent 6890N Network GC System equipped with a 5975 Inert XL Mass Selective Detector. Flash chromatography was performed on 40-63 silica gel (Merck).

Single Crystal X-ray Diffraction and Charge Density Measurements.
Topological analysis of charge density distributions using Bader's Atom in Molecules approach (AIM) [S3] is well established and now used to explore weaker types of bonding and interactions, for example, hydrogen bonding, halogen bonding, O···O and O···Br interactions and also systems containing anions and receptors [S4] . To probe the development of N-C bonding between the peri-groups in 1-6, a charge density determination and analysis has been carried out on a high-quality single crystal of each substance. Highly redundant high-resolution X-ray data (sin/ >1.0 Å -1 ) of 2 and 4 were carefully collected on a Nonius KappaCCD area-detector diffractometer located at the window of Nonius FR591 rotating-anode X-ray generator, equipped with a molybdenum target (MoK = 0.71073 Å) and Roper CCD camera, [S5] whereas for 1 and 5 X-ray intensities were collected on a Rigaku AFC12 goniometer equipped with an enhanced sensitivity (HG) Saturn724+ detector mounted at the window of an FR-E+ SuperBright (Mo Kα, λ = 0.71073 Å) rotating anode generator with HF Varimax optics (100µm focus), [S6] and processed with the CrystalClear [S7] software package. Crystals were cooled using an Oxford Cryosystems Cobra system. X-ray diffraction data from 3 were collected on Bruker Nonius X8 Apex diffractometer equipped with a Kryoflex cooling device and a data collection strategy for the high-resolution data set was determined using COSMATIC and COSMO. [S8] Diffraction data for 6 were collected in Experimental Hutch 1 (EH1) on the I19 beamline at the Diamond Light Source, which is equipped with a Crystal Logic 4-circle kappa geometry diffractometer and a Rigaku Saturn 724+ CCD detector. The sample was cooled to and maintained at 100 K using an Oxford Cryosystems Cryostream Plus device and diffractometer control and data processing were carried out using the CrystalClear software. [S7] The data integrations for 1-2 and 4-5 were performed with EvalCCD [S9] and SORTAV [S10] was used to apply a Gaussian absorption correction and to average and merge the sets of intensities.
The crystal structures were all solved by direct methods and the hydrogen atoms located on carbon atoms were placed at calculated positions. Least squares independent atom refinement (IAM) was carried out with the SHELX-2014 [S11] software package. All the non-hydrogen atoms were refined with anisotropic displacement parameters, whereas all hydrogen atoms were refined using a riding model on their parent atoms with isotropic displacement parameters based on the equivalent isotropic displacement parameter (Uiso(H) = 1.2 Ueq(aromatic) and Uiso(H) = 1.5 Ueq(CH3) ) of the parent atom.    Figure S2: Molecular structures of 1-5, (a)-(e) and the two independent molecules of 6, (f) and (g), with anisotropic displacement parameters for non-hydrogen atoms at the 50% level and anisotropic displacement parameters for non-hydrogen atoms were estimated using the SHADE3 server. [S12] Multipolar refinement.
Modelling the electron density distribution in each crystal structure using the experimental X-ray diffraction data was performed using the multipole refinement model advocated by Hansen and Coppens [S13] . The electron density is described using the formula shown in Equation 1, where ρc(r) and ρv(r) are the spherical core and valence electron densities, the summation in the third term accounts for the valence electron deformations and the dlm± are density-normalised real spherical harmonics expressed in polar coordinates. The isolated atom valence density and the Slater type radial functions R1 are modified by the scaling factors (κ and κ') to account for the radial expansion or contraction of the valence shell. (1) The IAM model served as an initial point for the further aspherical atom refinement, using the Hansen-Coppens formalism [S13] as implemented in the XD2016 program. [S14] The multipole refinement was carried out in a stepwise manner. Initially, only the scale factor was refined on all data. Next, accurate positional and displacement parameters for all non-hydrogen atoms were obtained from the high order refinement (sin/ > 0.7 Å -1 ) whereas positional and isotropic displacement for hydrogen atoms were refined using low-angle data (sin/ < 0.7 Å -1 ). Due to the unavailability of neutron data all C-H distances were fixed to averaged distances from neutron studies [S15] .
The anisotropic displacement parameters for each hydrogen atom in the crystal structure were then determined using the SHADE3 (Simple Hydrogen Anisotropic Displacement Estimator) server. [S12] These were imported into the multipole model and fixed throughout the subsequent refinement steps. Next, multipole populations were introduced, and the complexity of the model was gradually increased. For all carbon atoms, the atomic populations were refined up to octapolar level (l=3), whereas all heteroatoms (N and O) were refined as hexadecapole (l=3) with a single expansion/contraction  parameter. All hydrogen atoms were represented by the bond directed dipole (l=1). Chemically and symmetry-related atoms were constrained to share the same expansion/contraction (/') parameters. Throughout multipole refinement the expansion/contraction (/') parameters of all hydrogen atoms were fixed to default values  =1.2 and ' = 1.2. The multipole refinement was performed in blocks until satisfactory convergence was achieved. To reduce the number of parameters several chemical constraints for similar atoms were applied at the initial stages of multipole refinement. These constraints were gradually released, and the final model was chemically unconstrained. The electron neutrality condition was imposed on the molecule for the entire refinement. Final multipole refinement led to a featureless residual density map for all refined crystal structures.
The Gaussian distributions of the residual electron densities (see fractal dimension distribution plots [S16] (Fig. S3)) suggest that the remaining residual densities are consistent with noise and that the electron density has been fitted appropriately. The resulting agreement factors for the six data sets are summarised in Table S1. Final structural information containing atomic coordinates, displacement parameters, multipole populations are presented in Tables S3-S14

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Theoretical quantum mechanics studies.
To validate the electronic models of molecules 1-6 calculated from experimental data with XDPROP [S14] and also to obtain electronic properties for two molecules for which high-resolution X-ray data were unavailable, Senkirkine S1 and Clivorine S2, DFT computational studies were performed with Gaussian09 software package, [S17] using B3LYP functionals [S18] and the 6-311++G** basis set. The resulting wave functions for models based on molecular geometries (not optimised) from single crystal diffraction studies were analysed in terms of electronic distribution and properties using AIMAll and AIM2000. [S19] The properties of the topological analysis of electron density distribution at bond critical points (BCPs) are in good agreement with those derived from experimental models for 1-6.

Fractal Distribution Plots and Residual Density Maps:
1, the dibenzoyl derivative.

Static deformation charge density distribution maps and - 2 ρ(r) maps.
For each crystal structure, the first static deformation charge density distribution map and the Laplacian (- 2 ρ(r)) map are plotted in the plane of naphthalene ring after multipole refinement. The second set of maps are plotted in the plane of the two peri atoms, N1, and C11 and the ring carbon attached to the N atom, C1, to show clearly the situation along the vector between the two peri atoms.

QTAIM Calculations.
The QTAIM properties for the N---C interaction/bond of 1-6 and S1 and S2 were calculated at the (B3LYP/6-311+G(d,p) level in Gaussian [S17] and analysed with AIMA11. [S19] A comparison of the experimental and calculated charge density and Laplacians at the N···C BCP are shown in Table S16. A plot of calculated Laplacian v N---C separation is shown in Figure S27. A plot of the energy density at the BCP against N---C separation is given in Figure S28.  Figure S27. Plot of calculated Laplacian for 1-6, S1 and S2 against Me2N---C separation (black dots), with experimental values for 1-6 added (red crosses).

Solid State NMR.
All solid state NMR (SS-NMR) experiments were performed on an 11.7 T Bruker Avance III NMR spectrometer, operating at 1 H, 13 C and 15 N Larmor frequencies of 500.1, 125.8 and 50.7 MHz respectively. A Bruker 3.2 mm tripleresonance magic angle spinning (MAS) probe was used to facilitate spinning frequencies of 11 kHz. The determined 13 C and 15 N π/2 pulses of 5.0 µs were utilised, which represent a nutation frequency (ν1) equal to 50 kHz. Ramped cross polarisation was employed to all 13 C and 15 N spectra, with a contact time of 1.0 ms. A 1 H π/2 pulse of 2.5 µs (100 kHz) and a recycle delay of 16 seconds were employed to allow the probe's coil to cool down after SPINAL-64 heteronuclear decoupling (ν1( 1 H) = 120 kHz). A minimum of 800 transients were recorded for each spectrum.
The 15 N chemical shifts were referenced indirectly to neat liquid nitromethane (CH3NO2, 0 ppm) by using the secondary reference of powdered [ 15 N]histidine (δiso = −333.1, −204.3 and −191.0 ppm). To convert to the chemical shift scale employed by protein NMR (NH3 (l), −50 o C) it is necessary to add 379.5 ppm to the given scale. The 13 C chemical shifts were referenced to the primary reference of neat tetramethylsilane (l, TMS, Si(CH3)4, 0 ppm). [S20] The 13 C-15 N 1 J-coupling measurements were performed as previously described by Hung and co-workers using the sequence given in Figure S30. [S21] Here, an initial CPMAS to 15 N was completed, before an identical π refocussing pulse on both 15 N and 13 C channels during a varying τ period was utilised. Tau (τ) was incremented from 0 to 300 ms. A total of 32-64 scans were collected per increment, with 60 increments, and a recycle delay of 16 scans giving a total experiment time of ~18 hours. All experiments where completed from the perspective of the 15 N nuclei, which is coupled to 99 % 13 C. We have previously shown it is possible to measure 1 J-couplings from a 13 C which is coupled to quadrupolar nuclei ( 1 J 13 C 17 O). [S24] However, larger scalar couplings are typically required to isolate the 1 J terms from the quadrupolar effects. Figure S30: Cross polarisation heteronuclear spin-echo experiment utilised in the 13 C-15 N 1 J coupling measurements.
All spectra were made using DMFit [S22] , and the CASTEP derived MAS NMR parameters were simulated with SIMPSON [S23] with the experimental parameters discussed above. The SIMPSON simulation package was also used to derive the 1 JNC couplings, as this package does not incorporate T2, then these outputs were multiplied by the homonuclear echo determined T2' (exp(-τ/T2 ' )). The output of these simulations with varying 1 JNC values and for two different T2' values are given in Figure S31. We have previously discussed this methodology in further detail. [S24] Figure S31: (a) The Simpson simulated 15 N-13 C heteronuclear spin-echo intensities showing the 1 JNC cosine modulations over a 0.5 to 6 Hz range (these follow a cos(πJNCτ) function, no T2' contributions). The weighting of these cosine oscillations with T2' (exp(-τ/T2 ' )) values of (b) 400 and (c) 100 ms. These simulations show that for small 1 J-couplings that T2' causes the cosine modulated exponential decays to converge. This is not an issue for 15 N, which has narrow native linewidths and couplings and can be overcome by using faster MAS for other nuclei.

Density Functional Theory for Solid State NMR Studies.
All density functional theory (DFT) calculations used the CASTEP 16.1 code which employs Kohn-Sham DFT methodology using periodic plane-waves under the ultrasoft pseudopotential approximation. [S25] The generalized gradient approximation for the exchange-correlation energy was employed using the Perdew-Burke-Ernzerhof (PBE) functional. [S26] The pseudopotentials were generated 'on-the-fly' using the standard Materials Studio pseudoatom definitions (Accelrys, San Diego CA, USA).
The calculation was converged with respect to basis-set size and Brillouin zone k-point sampling to at least an accuracy of 0.4 mH (~2 x10 -6 % of total energy) per atom for each of the systems under investigation. To confirm this level of energy convergence was sufficient to produce accurate ionic forces, energy minimization with respect to their ionic positions was repeated with increasing plane wave cut off energy and density of k points within the Monkhorst-Pack Brillouin zone grid. This level of convergence was achieved using plane-wave cutoff energy of 1400 eV for the systems, and by invoking k-point Monkhorst-Pack grids of 2 × 3 × 2. [S27] To calculate isotropic chemical shifts were determined using the following references; σref = 170 ppm for 13 C and −153 ppm for 15 N.
Cross Polarisation 13 C and 15 N Solid State NMR Figure S32: The proton ( 1 H-> 13 C) cross polarised, and 120 kHz 1 H decoupled, 13 C and 15 N solid state NMR of the doubly isotopically labelled structures (a) 2, (b) 3, (c) 4 and (d) 6 (for which there are two crystallographically independent molecules). * represents the location of the spinning sidebands. The 15 N MAS NMR of (b) shows some broadening to one side of the resonance. A bond between peri substituents is not formed, which allows for a small degree of rotation about the N-C(ring) bond at room temperature. This rotation and the variation in potential overlap between the nitrogen lone pair and aromatic π system will lead to a distribution of environments, which could ead to broadening. Alternatively, there could be some disorder in the orientation of this group between different regions of the crystal.
The powder 13 C and 15 N solid state NMR of the labelled samples were achieved using a proton ( 1 H) crosspolarization (CP) magic angle spinning (MAS) experiment before proton decoupled acquisition. Hence, the data presented is no longer quantitative due to CP being directly affected by internuclear 1 H -13 C/ 15 N distances and this lack of quantitation is enhanced by the isotopic labelling of the peri environments with 13 C and 15 N. The 13 C CPMAS NMR spectra of compounds 2 and 3 ( Figure S32) both show a single distinct environment at 188.6 and 168.4 ppm respectively, these are consistent with the two polar groups (CH=O and CH=C(CN)2), respectively.
Conversely, the formation of the bond between the 13 C and 15 N labelled sites (ring closed structure) produces a more shielded environment giving a shielded shift of 94.7 ppm for compound 4. Compound 6 displays isotropic