Symmetry of three-center, four-electron bonds†‡

Three-center, four-electron bonds provide unusually strong interactions; however, their nature remains ununderstood. Investigations of the strength, symmetry and the covalent versus electrostatic character of three-center hydrogen bonds have vastly contributed to the understanding of chemical bonding, whereas the assessments of the analogous three-center halogen, chalcogen, tetrel and metallic 
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Created by potrace 1.16, written by Peter Selinger 2001-2019
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 -type long bonding are still lagging behind. Herein, we disclose the X-ray crystallographic, NMR spectroscopic and computational investigation of three-center, four-electron [D–X–D]+ bonding for a variety of cations (X+ = H+, Li+, Na+, F+, Cl+, Br+, I+, Ag+ and Au+) using a benchmark bidentate model system. Formation of a three-center bond, [D–X–D]+ is accompanied by an at least 30% shortening of the D–X bonds. We introduce a numerical index that correlates symmetry to the ionic size and the electron affinity of the central cation, X+. Providing an improved understanding of the fundamental factors determining bond symmetry on a comprehensive level is expected to facilitate future developments and applications of secondary bonding and hypervalent chemistry.


Preparation of complexes
(1,2-Bis(pyridin-2-ylethynyl)benzene)proton complex, 1-H: The proton complex of the clamp was prepared by mixing (1,2-Bis(pyridin-2-ylethynyl)benzene (8 mg, 0.029 mmol) and AuBr 3 ×(H 2 O) x (12 mg, 0.029 mmol) in methanol (2 mL). As a result of the bottle with AuBr 3 being old and wet, the proton complex was formed, instead of gold coordination. The complex was dried under reduced pressure, before crystals for x-ray analysis were made by dissolving the complex in dichloromethane, followed by diffusion of n-pentane into the solution of the complex, CCDC ID: 1989941. Previously reported spectroscopic data for 1-H with BF 4 as counterion 8 : 1  [(1,2-Bis(pyridin-2-ylethynyl)benzene)lithium(I)] tetrakis(pentafluorophenyl)borate, 1-Li : (1,2-Bis(pyridin-2-ylethynyl)benzene (1 equiv.) and lithium tetrakis(pentafluorophenyl)borate ethyl etherate (1 equiv.) were dried and dissolved in dichloromethane under an nitrogen atmosphere. Single crystal for x-ray analysis were attempted grown by slow diffusion of n-pentane into a solution of the complex in dichloromethane at room temperature, however no suitable crystals were obtained. 1  [(1,2-Bis(pyridin-2-ylethynyl)benzene)sodium(I)] tetrakis [3,5-bis(trifluoromethyl)phenyl]borate, 1-Na : (1,2-Bis(pyridin-2-ylethynyl)benzene (1 equiv.) and LiBArF (1 equiv.) were dried and dissolved in dichloromethane under an nitrogen atmosphere. Single crystal for x-ray analysis were grown by slow diffusion of n-pentane into a solution of the complex in dichloromethane under a nitrogen atmosphere at room temperature. For 1-H, the additional scattering (particularly from the electron-rich AuBr 4 counter-ion) of the twin gives a small systematic error (approximately 1-3%) in the structure factors, which yields increased noise and false peaks in the electron density map. This small but significant error is highly challenging to treat as the signal of the minor twin is too weak to integrate separately. Although the twin law for 1-H was identified (see Figure S1), its signal could not be separated from that of the main component, neither during data reduction nor refinement. Due to the nature of the disorder, the false peaks appear in a region of the crystal structure where hydrogen placement is a key issue ( Figure S1). Such small peaks of apparent electron density could easily be misinterpreted as a proton, or possibly a lithium ion. It should be emphasized that hydrogens cannot be precisely located by X-ray diffraction in structures that contain heavy atoms, such as gold, using standard independent atom model (IAM) refinements, due to the very weak scattering power of hydrogen, and the delocalized electron cloud. While there are recent examples of precise hydrogen position determination using Hirschfeldt atom refinement (HAR) 36 and early quantum crystallography examples, 37 these methods rely on accurate basis sets (HAR), or are under development (QCr). Thus, neutron diffraction remains currently the most reliable method for precisely locating hydrogens in coordination complexes involving heavy atoms.  3. IPE Measurements -13 C NMR Chemical Shifts and Their Temperature Dependence 3.1. General Information IPE NMR experiments of 2:1 mixtures of mono-deuterated/non-deuterated Ag + , Au + , Na + and Li + complexes were recorded on a 500 MHz Bruker Avance Neo spectrometer equipped with TCI cryogenic probe. The experiments were run with 13 C detection at 126 MHz using broadband 1 H and inverse-gated 2 H decoupling. 1 H and 13 C NMR spectra of mixtures were recorded for CD 2 Cl 2 (δ H 5.32, δ C 54.00) in the temperature interval 35 C to -10 or -35 C, depending on the solubility of the complex. Upon cooling, the temperature was allowed to stabilize for at least 15 min. The data was then zero-filled to 262144 (256K) points using the software MestreNova V14.1. Figure S2. The 13 C{ 1 H, 2 H} spectrum of 1-Ag/1-Ag-d acquired at 25 o C in CD 2 Cl 2 at 126 MHz. Table S2. The 13 C NMR Chemical Shifts of 1-Ag/1-Ag-d given in ppm.   S7   Table S3. The temperature dependence of the isotope shifts observed for 1-Ag/1-Ag-d given in ppm.

Computations
To corroborate the experimental findings, density functional theory (DFT) calculations were performed . The equilibrium geometries were obtained  with the B3LYP exchange and correlation functional 29-32 in conjunction with Dunning's cc-pVTZ correlation consistent basis set 33 on all carbon  and hydrogen atoms and the aug-cc-pVTZ basis set 34,35 on the nitrogen atoms as well as the coordinating ions. The MDF 28 Stuttgart/Cologne  effective core potential was used for iodine 36 and silver, 37 while the MDF60 was instead adopted for gold. 37 Correspondingly, modified aug-cc-pVTZ-PP basis sets were used for these three ions. 38-40 Solvent effects were taken into account by the polarizable continuum model (PCM) 41,42  using the integral equation formalism variant, with CH 2 Cl 2 as a solvent ( = 8.93) to mirror the experimental setup. The effects of dispersion interactions were considered through the Grimme D3 empirical dispersion correction. 43 The DFT-optimized structures were subsequently used in the calculation of 15 N NMR chemical shifts. Prediction of NMR chemical shifts was obtained using the Gauge-independent atomic orbital (GIAO) method. 44 Natural population analysis (NPA) and natural bond orbital (NBO) analysis were carried out on all systems using the NBO 3.1 program. 45 All calculations were performed using the Gaussian 09 program package, revision d01, setting the integration grid to ultrafine.. 46 This particular choice of computational parameters is supported by previous investigations on analogous systems, all in agreement with the experimental findings. 20-23

Predicted 13 C NMR Chemical Shifts
For all systems considered, the 13 C NMR shifts were calculated using the GIAO method. The results are reported in Table S10.

Bonding character
To investigate the [NXN] + bonding character we have performed a natural bond orbitals analysis on the 1-X complexes. For systems 1-Cl, 1-Br, 1-I, 1-Ag and 1-Au, two valid sets of natural bond orbitals (NBOs) were found. For all symmetric complexes, the automatic search of the NBO 3.1 program identifies two partially occupied nitrogen lone pairs and a partially occupied atomic orbital on the central ion: the p z orbital for the halogens, the s orbital for the metals and both the 2s and 2p z orbitals for lithium and sodium. In Table S11 we summarize the important information of the analysis. For 1-H and 1-F, the NBO analysis confirms the covalent bond formed by hydrogen and fluorine to one of the pyridines. For 1-Li and 1-Na, the partial atomic charges suggest that the alkali metals essentially remain cations and thus only interact electrostatically with the nitrogen lone pairs. This interpretation is supported by the corresponding small ΔE PT2 value of the second-order perturbation of the Fock matrix. For 1-Cl, 1-Br, 1-I, there is a clear trend: the lighter the halogen, the more electron density is donated by the nitrogen lone pairs to the halonium ion. This can be seen from the partial atomic charges, as well as from the ΔE PT2 value. Larger electron donation to X and larger second-order couplings mean a stronger covalent character of the 3c4e bond. For the transition metal complexes we observe the same behavior. More electron density donated to the metal corresponds to a stronger covalent character of the bond, agreeing with the ΔE PT2 values. Note that the percentage of Lewis-explained density increases with heavier X (even more than the "empty" clamp), but this is ascribed the total number of electrons being larger for heavier elements. Indeed, by looking at the amount of non-Lewis electrons, we notice that the empty clamp has the least of all. Note that almost all of the non-Lewis electron density occupies π* antibonding orbitals localized over the pyridines and the benzene rings and correspond to the resonance structures of the rings. Table S11. Natural population and orbital analysis. The first three columns correspond to the atomic partial charges obtained by the natural population analysis. The fourth column corresponds to the amount of electron density (in %) that populates natural bond orbitals describing the natural Lewis structure. The fifth column corresponds to the amount of electron density (in number of electrons) that could not be placed in NBOs describing the natural Lewis structure. The last column corresponds to the second-order perturbation of the Fock matrix between the nitrogen lone pair and the accepting, partially occupied NBO of the central ion. [a] Total contribution for the interaction between one lone pair of nitrogen and both the 2s (3s) and 2p z (3p z ) orbitals of lithium (sodium).

Complex
In Figures S10-S18 we report the natural bond orbitals localized around the [NXN] + bond from the "lone pair" set plotted for an isosurface value of 0.05 au, unless otherwise stated. Note that for the halogens, the accepting orbital is the p z atomic orbital, while for the metals is the s atomic orbital. Figure S10. "Lone pair" NBOs for 1-H. Note that this set of NBOs does not find a bonding orbital between the nitrogen and the hydrogen, but rather the third orbital is considered a pure nitrogen lone pair, donating to the hydrogen 1s orbital displayed in the first image. Figure S11. "Lone pair" NBOs for 1-Li. Note that usually only three orbitals are involved, but because the interaction is so weak and the 2s and 2p z orbitals are almost equal in energy, they both receive approximately the same amount of electron density from the nitrogen lone pairs. Figure S12. "Lone pair" NBOs for 1-Na. Note that usually only three orbitals are involved, but because the interaction is so weak and the 3s and 3p z orbitals are similar in energy, they both receive approximately the same amount of electron density from the nitrogen lone pairs. S16 Figure S13. "Lone pair" NBOs for 1-F. Figure S14. "Lone pair" NBOs for 1-Cl. Figure S15. "Lone pair" NBOs for 1-Br.   For all symmetric systems other than 1-Li and 1-Na, a second set of NBOs reflecting the Pimentel-Rundle 3c4e-bond picture was identified. This second set was obtained by activating the three-center bond search in the NBO program with the "3CBOND" keyword as well as specifying the S17 expected Natural Lewis structure (that is, all two-center and three-center bonds as well as all lone pairs) for the various systems. Note that the nonbonding orbital is considered by the program as "non-Lewis", which is consistent with a three-center, two-electron bond, however, within the three-center, four-electron context, the non-bonding orbital should contribute to the Lewis structure. Thus, the values reported in Table S12 for the electron density percentage in the Lewis structure and the amount of electron density that could not be placed by the NBO set count the nonbonding orbital as being part of the Natural Lewis structure. The relevant information and a comparison with the "lone pair" set is reported on Table S12. For 1-Cl, 1-Br, 1-I, 1-Ag and 1-Au, the 3c4e-bond picture accounts for more electron density than the lone pair one. In case of 1-Li and 1-Na, no such set of orbitals could be found: further highlighting the weak electrostatic character of the interaction between the alkali metals and the clamp. Note that the natural population analysis does not depend on the natural bond orbitals and is thus the same for both sets. The "disadvantage" of the 3c4e bond with respect to the lone pair set is the loss of relevance of the second-order perturbation of the Fock matrix. Within the 3c4e NBO basis, the interaction between the nitrogens and the central ion is captured by the explicit formation of the 3c4e orbitals, rather than a coupling between the separate lone pairs and the accepting central atomic orbital. Table S12. Natural population and orbital analysis. We report the electron density percentage in the Lewis structure and the amount of electron density that could not be placed for both sets. [a] Even though 1-Li and 1-Na are symmetric, no reasonable NBO set with three-center orbitals was found.

Complex
In Figures S19-S23 we report the 3c4e NBOs for the complexes 1-Cl, 1-Br, 1-I, 1-Ag and 1-Au plotted with a cutoff of 0.05 au. One can note that for the metals, the s atomic orbital forms the 3c4e NBOs, rather than the p z in the case of the halogens. This is particularly emphasized for 1-Ag, for which a less tight cutoff has been used in order to highlight the constructive overlap with the nitrogen lone pairs. Figure S19. "3c4e" NBOs for 1-Cl. Figure S20. "3c4e" NBOs for 1-Br. Figure S21. "3c4e" NBOs for 1-I. Figure S22. "3c4e" NBOs for 1-Ag. The second picture is the same as the first one, just with a less tight cutoff of 0.03 instead of 0.05, to emphasize that the 3c4e bonding orbital is formed using the s atomic orbital rather than the p atomic orbital as it is for the halogens. This can also be seen from the orbitals phases. Figure S23. "3c4e" NBOs for 1-Au.

Computational details on the calculation of ΔE sym , ΔE stretch , ΔE SB and ΔE PB
To obtain a more quantitative estimation of the energy involved in the 3c4e bond, estimates of the energy required to move the coordinating ion from an asymmetric to a asymmetric position within the clamp, as well as approximate primary and secondary bond energies for the related 2-X systems have been reported in the main text. This data is reported on Table 6 of the main text and refers to the reactions reported in Figure 7. First, for all ions studied, an estimate of the "optimal" N-X covalent bond distance is calculated by optimizing the geometry of a N-X-pyridinium ionic system, labeled in the following as pyr-X. The values found in this way are reported in the d N1-X column of Table 6 in the main text. Note that for pyr-Li and pyr-Na, no minimum of the potential energy surface corresponding to a covalently bonded system was identified. Furthermore, for the proton and the fluoronium ion, the values corresponding to the optimized 1-H and 1-F structures are used to obtain all energies discussed here and reported on Table 6 of the main text.
ΔE stretch , corresponding to Figure 7d of the main text, was calculated by computing the electronic energy difference between the pyr-X systems at the "symmetric" N-X bond distance and the optimal one. This value corresponds to the amount of energy required to pull X from its optimal covalent bond distance to the symmetric one found in the 1-X complexes.
In a similar way, ΔE sym , corresponding to Figure 7a of the main text, quantifies the energy gain/loss in pulling X from the covalent N-X bond distance to the symmetric one within the clamp, i.e. for the 1-X complexes. Note that in this case, the energy difference is taken between the optimized structure of the 1-X complexes and the optimized structure of the complexes where the N-X bond distance was kept frozen at the optimal covalent length during optimization, that we shall call 1-X'. This value is negative for all symmetric 1-X systems, whereas is positive for 1-H and 1-F, which prefer an asymmetric geometry.
ΔE SB (Figure 7b) and ΔE PB (Figure 7c) were obtain in the same way. First, the optimized geometries obtained for 1-X and 1-X' are taken, and the backbone connecting the pyridines is cut out. Two hydrogen atoms are used to saturate the dangling bonds and their bond distance is relaxed while keeping the remaining part of the (now) bis(pyridine)-X system frozen. At this point, the interaction energy between the two fragments is computed in the usual way: E complex -E pyr-X -E pyr . The ΔE PB values refer to the optimal starting structure, 1-X, while ΔE SB values refer to the asymmetric starting structures, 1-X' (which are equal to the optimal one in the case of the proton and the fluoronium ion). All interaction energies reported in Table 6 are corrected for basis set superposition error by the counterpoise scheme, estimated without accounting the solvent effect due to technical limitation of the software.

Potential energy surfaces
The potential energy surfaces reported on Figure 8 of the main text correspond to relaxed surface scan starting from the symmetric geometry and decreasing the N-X bond distance in step of 0.05 Å at a time. At each step, the shortened N-X bond is kept frozen during relaxation of the structure. Note that it was not possible to obtain the same amount of data points for all systems, as constraining the N-X bond to too short distances resulted in convergence issues of the geometry optimization.