Quantification of Noncovalent Interactions in Azide–Pnictogen, –Chalcogen, and –Halogen Contacts

Abstract The noncovalent interactions between azides and oxygen‐containing moieties are investigated through a computational study based on experimental findings. The targeted synthesis of organic compounds with close intramolecular azide–oxygen contacts yielded six new representatives, for which X‐ray structures were determined. Two of those compounds were investigated with respect to their potential conformations in the gas phase and a possible significantly shorter azide–oxygen contact. Furthermore, a set of 44 high‐quality, gas‐phase computational model systems with intermolecular azide–pnictogen (N, P, As, Sb), –chalcogen (O, S, Se, Te), and –halogen (F, Cl, Br, I) contacts are compiled and investigated through semiempirical quantum mechanical methods, density functional approximations, and wave function theory. A local energy decomposition (LED) analysis is applied to study the nature of the noncovalent interaction. The special role of electrostatic and London dispersion interactions is discussed in detail. London dispersion is identified as a dominant factor of the azide–donor interaction with mean London dispersion energy‐interaction energy ratios of 1.3. Electrostatic contributions enhance the azide–donor coordination motif. The association energies range from −1.00 to −5.5 kcal mol−1.


Introduction
Noncovalent interactions play av ery important role in biological, physical, and chemicals ciences. [1][2][3][4][5] They are crucial for crystalp acking, for the self-assembly of large molecules in solution,a nd for biological pattern recognition, to name just a few examples. [6][7][8] In addition to highly electrostatic interactions (e.g.,i on-ion,i on-dipole, dipole-dipole), the most prominent type is hydrogen bonding, but chalcogen-chalcogen [9][10][11][12] and halogen-halogen interactions, [13][14][15] or combinationst hereof, have also received significant attention duringt he last few decades.F urthermore, moietiest hat only consist of p-systems often stronglyi nteract with each other through so-called p-p stacking interactions, [16,17] and even between purely sp 3 -hybridized hydrocarbon moieties one encounters weakly attractive forcest hat are mainlyb ased on London dispersion. [18] All of thesei nteractionsh ave been successfully employed in crystale ngineering and supramolecular assembly of compounds, [19][20][21][22][23][24][25][26][27][28] and to facilitatec atalysis. [29][30][31][32][33][34][35] During our solidstate studies of some compounds containing flexible azide moieties and oxygen atoms, we noticedt hat mono-andd ivalent oxygen functionalities often displayed ac lose intramolecular contact with the central nitrogena tom (N2) of the azide moiety.I nm any of these cases, numerous other conformations would have been possible, but, nonetheless, the molecular conformation with the closest contact between N2 and O seemst ob ep referred. Twor epresentative exampleso fm olecules that show close azide-oxygen contacts in the solid state are depicted in Figure1. [36] In 2017, ac lose intermolecularc ontact between azide moieties and the oxygen of cucurbit [6]uril was discovered by Keinan and co-workers, but not investigated in detail. [37] To investigate whether these interactionsl ed to a significant energy gain, we compiled al arger set of structures involving intermolecular contacts (Figure2). Structures deposited in the Cambridge Crystallographic Data Centre (CCDC) [38] were evaluated with respect to pnictogen-, chalcogen-, and halogen (henceforth denoteda sP CH)-azide contacts. These contactsi nclude, for example, divalento xygen moieties, as in ethers or esters, or monovalent oxygen,a sf ound in carbonyls, phosphine oxides, and sulfoxides. Figure 3d epictsd ata obtained for azide interacting moieties. It is observed that many of these contacts are much shortert han the sum of the van der Waals radii [39] (3.07 for nitrogen···oxygen,b lue dashed line in Figure 3). For the N3ÀN2···X angle (for ad efinition, see Figure 4), there is as trong accumulation of data points between 85 and 1308.S omeo ft hese might have to be interpreted with care because not every structure has been individually evaluated.
Furthermore,i ns ome cases, the close contacts may have other causes than attractive oxygen-azide interactions. However,t he strength and the nature of these interactions have not yet been investigated. Herein, we close this gap using quantum chemical computations, which indicate the preferred arrangements and respective interactione nergies of PCHs interacting with azides.

Computational investigations
The intermolecular interactions between organic azide and PCH-containing moieties in 44 model systems( 10 pnictogen,  24 chalcogen, and 10 halogen;F igure 2) werei nvestigated with respect to structuralp arameters and interaction energies. As chematic representation of the investigated orientations is depicted in Figure 4.

Structural properties
For all 44 azide adducts, the structuralf eatureso fg as-phase local minimum structures (SCS-MP2 [40,41] /def2-QZVPP [42] )w ere analyzed ( Table 1). The model systems, which were chosen to resemble observeds olid-state interaction motifs, mostly show distances close to or only slightly below the sum of the van der Waals radii of the central nitrogen atom (N2; approx. 3.07 for O···N) and the interacting moiety.I nt he solid-state structures, al arge number of very short oxygen-nitrogen dis-tancesa re observed. Nevertheless, the slight shortening, relative to the sum of van der Waals radii, hints at ar elevant attractivei nteraction between the central nitrogen (N2) and the chalcogenide moiety.T he predominant orientation of the PCH moietya tN 3 ÀN2···X angles of around 80-908 underlines the role of the central nitrogen as an interacting atom. For some cases involving ap ossible interaction with heavier elements, such as Sb or I, distortions of the N3ÀN2···X angles result from slight shifts of the Xa tom away from the azide moiety;t his may result from the increaseds ize and/or electronic properties of the corresponding moieties. The slight bending of the azide moiety( q(N1-N2-N3) mean = 174.18)i sa lmost unaffected by the interacting partner.T he C-N1-N2-X dihedrala ngle indicates the planarity of the coordinationp attern. All investigated systems display an in-plane orientation with the azide moiety.

Association and interaction energies
The gas-phase association energies for azide-donorp airs 1-44, with respect to the relaxedd issociated monomer geometries (interaction energies are calculated with respect to the unrelaxed fragments), were calculated at the W2-F12,W 1-F12, [43] and DLPNO-CCSD(T) [44,45] /VeryTightPNO [46] levels extrapolated to the complete basis set (CBS) limit (Figure5). Deformation energiesu pon coordination are mainlys mall, on average,r epresenting only < 3% of the association energies, with am aximum value of À9.3 %f or phosphabenzene (7). For complexes including heavier elements, for which the W2-F12 or W1-F12 approaches are not applicable, DLPNO-CCSD(T)/CBS association energies were calculated. This alternative approach proveds atisfactorily accurate to reproducet he highly accurate association energies calculated at the W2-F12/W1-F12 level with very small statistical deviations (meana bsolute deviation (MAD) = 0.14 kcal mol À1 )i na greement with recent benchmark studies. [47,48] The calculated association energies range from À1.00 to À8.00 kcal mol À1 and severalt rends are observed. First, chalcogenidec ompounds seem to yield larger association energies compared with those of pnictogens andh alogens. This is specifically the case for chalcogen atoms involved in highly polar bonds, as in pnictogen-chalcogenides.I ns ystems 17, 18,a nd 19,f or example, the increasing electronegativity difference between the oxygen atom and centralp nictogen upon descending Group 15 is well reflected by the increasing association energies, indicating the important role of electrostatic interactions. For less polar bound atoms, this trend is not as pronounced and, in some cases, even reversed, for example, for furan (23)a nd thiophene ( 30). Nevertheless, comparable electronegativity trends are observed for the pnictogens,a lthought oas maller extent (e.g.,a ldimine 1 compared with phosphaalkene 5). If heavier fourth and fifth row elements are involved, the association energies become systematically larger,e ven thought he electronegativity difference decreases or is even reversed. This indicates that, in addition to electrostatic interactions, dispersion interactions can play ad ominant role in determining the association energies. Furthermore, the correlation of secondary pnictogen-pnictogen or pnictogenchalcogen interactions with electronegativity can influence the observedt rends. Overall,d ecomposition of the interaction energies indicates that ab alance of electrostatic interactions and London dispersion determines the strength of the PCH-azide interaction. Sophisticated wave functiont heory (WFT)-based methods are routinelya pplicable only to quite small systems (W2/W1-F12: < 30 atoms;D LPNO-CCSD(T) with tight threshold settings and large basis set: < 150 atoms) because of the high computational cost. Systemso fm ore realistic size often include severalh undreds or even thousands of atoms.T herefore, we assessedt he reproduction of the association energy by common density functional approximations( DFAs) (applicable for < 500 atoms) and tight-binding-based semiempirical quantum mechanical (SQM)m ethods of the GFNn-xTB method family [49] (applicable for < 5000 atoms;T able2). It was found that the range-separated hybrid functional wB97X-V [50] (MD = 0.13, MAD = 0.15 kcal mol À1 )b est reproduces the coupled-cluster (CC) based association energies. Furthermore, all other tested D4-corrected [51,52] hybrid functionals perform reasonably well. The application of more costly double-hybridm ethods does not improve the results. Generally,aslight underestimation of the association energy,w ith respecttothe CC reference values, is observed. Efficient small basis set composite DFT methods, such as B97-3c [53] and, specifically,P BEh-3c, [54] yield comparably good results to the methods applying al arge quadruple-z basis set. The SQM methods show ap oorer performance, but both GFN1- [55] and GFN2-xTB [56] yield at least reasonable association energies. Furthermore, the capability of severalD FT-a nd WFT-based methodst or eproduce the unre-laxed dissociation curve (W2-F12//SCS-MP2/def2-QZVPPl evel) of the azide-donora dduct was assessed ( Figure 6). Almost all tested methods yield as atisfactory reproduction of the minimum distance, with ac onsistently very slight overestimation of the X···N2 distance. The depth and shape of the dissociation potentiali sg enerally reproduced well, with deviations below 0.5 kcal mol À1 .N evertheless,t he error has to be seen in the context of the generally small interaction and association energies. Overall, the range-separated hybrid functional wB97X-V reproduces the reference dissociation curves best. Surprisingly, the low-costs mall basis set composite method PBEh-3co utperforms mosto ft he other methods,w ith respectt ot he potentiald epth and position of the equilibrium distance, even thought he interaction energy at increased distances is underestimated.

Interaction energy decompositiona nalysis
Generally,v ariousc omponentsc an be postulated for the interactions with the azide, principally 1) donor-acceptor interactions (orbital relaxation);2 )electrostatic interactions;3 )electron correlation, including specifically long-range correlation effects, such as Londond ispersion, and4 )Pauli exchange repulsion.E nergy decomposition schemesc an help to quantify these components, and thus, helpt ou nderstand the nature of the interactions. Specifically,c anonical energy decomposition analysis( EDA), [57] symmetry-adapted perturbation theory (SAPT), [58] and the DLPNO-CCSD(T)-based local energy decomposition( LED) [59,60] have proved to yield reasonable insights. [61] Therefore, we applied LED to all complex equilibrium geometries and to three representative model systems, 1, 11,a nd 35, as af unctiono ft he X···N2 distance ( Figure 6). The LED scheme decomposes the interaction energyi nto contributions including the electronic preparation energy at the Hartree-Fock (HF) level (E HF-elprep ), which represents the repulsive part of the exchange interaction and can be conceptionally referred to as "Pauli repulsion". Other major components are the attractive exchange energy, E exch ;e lectrostatic interactions, E elstat ;a nd London dispersion interactions, E disp ,h enceforth namedd ispersion for simplicity.M inor contributions are represented by the perturbative triple correction to the interaction energy, E (T) ,a nd E non-disp ,w hich mainly represents ac orrection to errors in the permanent electrostatic interactions originating from HF overestimation of dipole moments.A nother decomposition into unrelaxed ("frozen state")a nd relaxed ("SCF state") energy contributionsi sa lso possible, allowing the quantification of an orbital relaxation energy contribution, E orb-relax ,w hich may be, to some extent,c omparable to the orbitalr elaxation term of Morokuma-type EDA schemes and includes charge-transfer (CT), polarization,a nd induction effects. [62] The frozen-state energy contributions are indicated by the suffix "0". The total decompositionoft he interaction energy is given by Equation (1): The total dispersion energy term, E disp ,i sc alculated by summing the CCSD dispersion energy part;t he weak-pair contribu- tions;a nd the scaled intermolecular triple correction, E (T) ,g iven by Equation (2). The correction factor, g,i st he ratio of the strong-pair dispersion contribution and the total intermolecular strong-pair contribution.
The third term of Equation (2) is an estimate of the perturbative triple contribution to the intermoleculard ispersione nergy. The remainingp art of the triple contribution is incorporated in the E non-disp contribution (for furtherd etailso ft he energy decomposition, see the Supporting Information). For all investigated systems, the LED scheme identifies exchange, London dispersion, and electrostatic interactions as the dominant attractive componentso ft he interaction energy,w hereas orbital relaxation effects seem to play am inor role. In the following, we investigate the role of these three attractive contributions in some detail. On inspecting the molecular electrostatic potentials (ESPs; Figure 7), ac lear correlation of the structural features and the electrostatic properties of the interacting atoms can be recognized. The ESPs show the expected electron-poor region at the centraln itrogen atom (N2) of the azide moiety. Thus, the electrostatic interactions of electron-rich regionso f the interacting molecule should be improved with increased electron density differenceb etween N2 and X. This is in line with the observed structuralp roperties of an angular fixation and shortenedd istances in the case of strong differences in the ESP regions of the interacting moieties.

Hydrogen-bonding andorbital interactions
In some structures, secondary hydrogen bonds (HBs) contribute to the overall interaction energy.T oq ualitatively estimate this contribution,an atural bond orbital [63] (NBO) based approach was applied, as recommended by Weinhold and Glendening, [64] at the PBE0-D4/def2-QZVPP level of theory.I nt his context,asecond-order perturbation theory (SOPT) estimate of the stabilization energy ( P E 2 ðÞ n!s * ;HB ), resulting from CT from the lone pair (LP), n, at N1 of the azide moiety into the antibondingo rbital, s XÀH *,o ft he HB donor,i sa pplied. [65,66] CT is mostly proposed ast he dominant attractive energyc ontribution in hydrogen bonding. [67] Nevertheless, this attractive component has to be offset against the stericrepulsion component ( P E rep s!n;HB ), involving the corresponding bonding, s XÀH ,o rbital, and is estimated from NBO analysis. [68,69] The resulting hydrogen-bondings trength estimate (E NBO HB )i sc alculated from Equation (3).
Notably,f urther much smaller,a ttractive components, such as the London dispersion, are not included in this estimate; thus, for very weak hydrogen-bonding contacts, repulsivee stimates are expected. This is mostly the case if the corresponding N1···HÀXa ngle deviates strongly from the optimum 1808 region, [70] which is the case for most of the presented model systems( cf. Figures 8a nd 9a, f(N1···H-X) mean = 1368,T able 1). The angle dependence of the HB strength estimates for 11 is depictedi nF igure 9b.Aclear relationship between CT and steric repulsion estimates with N1···HÀXi so bserved. Furthermore,t he attractive nature of the oxygen···azide contact is verified by the total interaction energy increase with larger f, even though hydrogen bonding is enhanced and approaching linearity.E xcept for the strongly hydrogen-bonded formic acid adduct (E NBO = À6.19 kcal mol À1 ), NBOa nalysis yields mainly slightly repulsive HB estimates for almost all other model systems ( Figure 8). Overall, this reveals only am inor role of hydrogen bondingi nt he investigated model systems, which is in agreement with the observed small angles, f,a nd the comparably large N1···H distances. Nevertheless,d ue to other weakly attractive components,s uch as the London dispersion, the secondarilyh ydrogen-bonded adducts are slightly preferred on the potential-energy surface( PES) in the intermolecular case. Thus, to investigate true local minima on the PES, this secondary effect was accepted for the models ystems. Deviations from local minimum structures may result in artificially less attractive or even slightly repulsive adduct struc-tures, even thought he general nature of the azide-X interaction is clearly attractive. Therefore, ap erfect transfer of the crystal-structure motifs into the gas phasei sn ot possible. Compared with the chalcogen-azide interaction, other interactions, such as chalcogen-chalcogen, have as ignificant Lewislike donor-acceptor bonding character,a nd thus, ag reater influence of orbital relaxation effects is observed. For the azidedonor interaction, this is not generally the case. The LED analysis consistently yields minor orbital relaxation contributions for all 44 systems (Figure10). This is attributable to the nature of the frontier molecular orbitalsi nvolved ( Figure 11). The LUMO of the azide moiety is delocalized over the whole azide function and the orbital contribution at the N2 atom competes with the occupied HOMO-1, which represents the LP at N1, which is generally involved in secondary hydrogen bonding. Thus, the overall donor-acceptor interaction cannot benefit from X!N2 donation. This picture may change upon orientation changes to some interaction partners with double-bond moieties. For the latter,i ft he orientation changes from an inplane to an orthogonal structure, the azide can become an electron-donating moiety and as mall n!p * contribution is observed (cf. systems 12, 14,a nd 26). Comparable behaviori s observed for systemst hat allow for n!s * (XÀC/H) donation, such as 5.H ere, as mall CT contribution of À0.38 kcal mol À1 for n!s * (PÀH) is observed. These secondary interactions (pnictogen-pnictogen and pnictogen-chalcogen,s ee Ta bleS13 in the Supporting Information) explain somec omparably large interaction energieso bserved for systemss uch as 10,w hich involves an n!s * (SbÀC) CT contributiono fÀ0.72 kcal mol À1 ,o r 19,w ith ac ontribution of À1.58 kcal mol À1 .T hese observations are qualitatively in line with larger orbitalr elaxation terms in the LED analysesf or the corresponding systems. Considering these contributions, the correspondings ystems end up in a comparable interaction energy range to that of systems lacking such secondary interactions.

Londondispersion interactions
Another important attractive component of the interaction energy is the Londond ispersion. The extent of its influence, as estimated from LED analysis,i ss hown in Figures 10 and 12. Prior studies indicated that the DFT-D4 dispersion correction for as omewhatr epulsive DFA, such as B3LYP (with almost no indirect,i ntrinsic reproductiono fL ondon dispersion effects), correlatedw ell with the LED dispersion energy and could be appliedf or al ow-cost estimate of the dispersion interaction energy. [71] To verify this estimate, we analyzed the correlation of the B3LYP-D4 [72,73] correction and the LED dispersion interaction energy for all 44 systems (Figure 13). On average, 80 %o f the LED dispersion energy is coveredb yt he D4 correctiont o B3LYP;o nly for 15 is this value underestimated at 63 %. As caling of the B3LYP-D4 correction by af actor of 1.25 yields 100 % reproduction, on average, for the investigated systems. Nevertheless, this estimate should be used with caution because the quality may vary for more exotic systems. The DE disp /DE tot ratio can be further utilized to identify whether the interaction is dominated by the London dispersion. Av alue of > 1i ndicates an interaction dominated by the London dispersion (cf. 1.92 for the methane dimer [59] ). For all systems, except 15,t his ratio is close to or above 1.00, with am aximum of 1.65 for 26 and a mean value of 1.30 (for individual data, see the Supporting Information). Furthermore, the N2···X distance dependence of the LED dispersion energy and the D4 dispersion correction for four representative DFAs (PBE, [74] PBE0, [75] BLYP, [76][77][78] B3LYP) was investigated ( Figure 12) for 5 and 13,a se xamples. Both repulsive DFA( BLYP,B 3LYP) D4 corrections correlate very well with the LED dispersion energy in the dissociative regions. Specifically,a tt he equilibrium distance, the correctionsm atch the LED estimate well. For less repulsive functionals, such as PBE and PBE0, the D4 corrections are much smaller.B ecause B3LYP reproduces the associationa nd interaction energies much better than those with BLYP,t he former is recommended for an estimate of the dispersion interaction energy.

Conformational studies
To estimate the transferability of the observed structural motif preference from the solid to gasp hase, example conformational studies were conducted by starting from the molecular solid-state structureso fA and B (Figure 1). For both structures, ac onformer ensemble wasg enerated fully automatically by applying the CREST [79,80] program at the GFN2-xTB level. The obtained conformers werer eranked according to Gibbs free energy at the DLPNO-CCSD(T)/CBS//SCS-MP2/def2-TZVPP level and analyzed for the presence of an azide-donor contact ( Figure 14). Although for both compounds, according to the  Gibbs free energy,m ore favorable gas-phase conformers were found, only for A is the low free energy conformer region dominatedb ys tructures with short azide-donor contacts. Here, the lowest conformer shows proximity of the donor moiety to the azide, but, because the distance is long, it was classified as an onmotif structure.F or B,t he lowest conformers do not show pronounced azide-donorc ontacts. Here, the first conformer with this motif is approximately 1.3 kcal mol À1 higheri n free energy than that of the lowest. Thus,w ec onclude that the structural features only partly originate from azide-donor interactions presenti nt he gas phase, indicating ap ossible role of solid-state effects, such as crystal packing. Crystale ffects may be large enough to favor an azide-donor arrangement, even though the attractive interaction mayn ot be large enough to fix this structural motif in the gas phase or in solution. Furthermore, structurals train and steric repulsion effects are influenced by the bridging moiety between the azide and donor. LED analysiso fasimplified intermolecularm odel of A optimized with ac onstraint on the O···N2 distance and essential dihedrala ngles reveals an interaction energy of À1.79 kcal mol À1 ,w hich is on the same scale as that of comparable models ystems (e.g., 24;F igure 15).

Conclusion
The structural motif of an azide moiety in close contact with an electron-rich donor moiety is observed in surprisingly many solid-state structures.T ou nderstandt he interaction between the azide and the partner molecule or moiety,w ec reated4 4 intermolecular model systems to investigate computationally the nature of the interaction in the gas phase. Furthermore, several new organic compounds were synthesized,w ith the aim of systematicallyc reating as tructural motif that was found empirically in the CCDC. Overall, the calculated (W2-F12/W1- F12/DLPNO-CCSD(T)/CBS) association energies for side-on azide-X complexes varied between À1.00 and À5.50 kcal mol À1 (formic acid (15)e xcluded). The LED analysiso ft he interaction identifies electrostatic and London dispersion interactions as the dominating attractive contributionst ot he interaction energy.I ft he electrostatic contribution is large enough to overcomel ess favorable steric motifs,a nd secondaryh ydrogen bondingi sn ot dominant, the X···N2 interaction motif is preserved. In this motif, little or no Lewis-like donor-acceptor bondingi so bserved, which is reflected by the comparably small orbital relaxation contributions to the interaction energies. This flexibility of the interaction components furthere xplains the large varietyo fs tructuralp atterns found in many solid-state structures.Acomparison of D4 London dispersion corrections to the LED resultsi ndicates good comparability of both energy contributions for the investigated systems, in accordancew ith previous studies. Conformational studies on the newly synthesized compounds indicate that other intermolecular crystal (packing) effects may play an importantr ole in stabilizing this weak azide interaction. Overall, considering the com-  plexity of further decomposings ingle contributions to the interaction energy into specific parts of the molecular systems, the unbiased azide-X interaction is estimated to be 1.5 to 3.0 kcal mol À1 .W ea re convinced that these stabilizing interactions are of importance,n ot only for the arrangement of azide moieties in supramolecular assembliesa nd crystal engineering (e.g.,c lick chemistry in the solid state), [81][82][83][84][85] but are also the basis for conformational bias in azido-functionalizedn ucleic acids, peptides,p roteins, and carbohydrates. Future investigations will revealw hether azido-based interactions have as imilar potential to facilitatec atalysis, as hasb een extensively and successfully explored for halogen and chalcogen bonding.