NO3− anions can act as Lewis acid in the solid state

Identifying electron donating and accepting moieties is crucial to understanding molecular aggregation, which is of pivotal significance to biology. Anions such as NO3− are typical electron donors. However, computations predict that the charge distribution of NO3− is anisotropic and minimal on nitrogen. Here we show that when the nitrate's charge is sufficiently dampened by resonating over a larger area, a Lewis acidic site emerges on nitrogen that can interact favourably with electron rich partners. Surveys of the Cambridge Structural Database and Protein Data Bank reveal geometric preferences of some oxygen and sulfur containing entities around a nitrate anion that are consistent with this ‘π-hole bonding' geometry. Computations reveal donor–acceptor orbital interactions that confirm the counterintuitive Lewis π–acidity of nitrate.

M olecular recognition phenomena are of pivotal significance in biology and define the field of supramolecular chemistry [1][2][3][4] . Well-known intermolecular forces include hydrogen and halogen bonding. Both have recently been contextualized as instances of 's-hole bonding' [5][6][7] . A s-hole can be seen as a region of electropositive potential on a molecule that is roughly located on the unpopulated s* antibonding orbital of a covalent bond. Typical examples of such s-holes can be found along the O-H/C-Br vectors in phenol or bromobenzene 8 . In analogy, a p-hole can be seen as a region of electropositive potential on a molecule that is roughly located on an unpopulated p* antibonding orbital of a p bond, for example, on carbonyls or p-acidic aromatics like hexafluorobenzene [8][9][10][11] .
It is known that p-holes in nitro-compounds such as nitrobenzene (Fig. 1a) can be directional in the solid state 8,12 .
The magnitude of such p-holes can be enhanced when the negative charge is diluted over a larger area, for example, if the O-atoms interact with water or NaCl (Fig. 1b,c). We wondered to what extend this rationale applies to nitrate anions and if perhaps this anion might function as a p-hole to enable so-called (pseudo)anti-electrostatic interactions 13,14 . This seems counterintuitive, yet the charge distribution in naked NO 3 À is anisotropic and reminiscent of a p-hole (Fig. 1d) 15 . Dampening the charge with water further exposes the p-hole (Fig. 1e), and the potential even becomes positive at þ 25 kcal mol À 1 in charge-neutral [LiNO 3 Á 2H 2 O] (Fig. 1f). We found that such an exposed p-hole on NO 3 À can form complexes with electron rich partners with calculated energies of up to -31.6 kcal mol À 1 . Statistical evaluations of the Cambridge Structural Database (CSD) and the Protein Data Bank (PDB) indeed reveal some geometric preferences consistent with this 'p-hole bonding' geometry. Several examples lifted from these databases are highlighted, where the Lewis acidity of NO 3 À seems evident.

Results
Computational models. To further evaluate a possible p-hole on NO 3 À computationally, we designed trisurea based receptors that fully surround a nitrate anion with hydrogen bond donors (Fig. 2a, related [2 þ 2] macrocycles are known) 16,17 . This might mimic nitrate anions in crystal structures, which are typically enclosed by several (charge assisted) hydrogen bonds and/or charge compensated by coordination to a metal ion. In the anionic complexes 2 (Fig. 2b), the p-hole region represents a relative electron depletion and is positive at þ 25 kcal mol À 1 in the anionic species 2c.
Next, we computed some complexes of 2 with electron rich partners and found that complexes [2c Á Á Á NCCH 3 ] À and [2c Á Á Á Cl] 2gave interaction energies of À 7.7 and À 31.6 kcal mol À 1 , respectively (see Supplementary Note 1 and  Supplementary Tables 1 and 3, for details). These values are in the range of weak to strong hydrogen bonding 18 . An 'atomsin-molecules' (AIM) analysis 19 revealed a single-bond critical point between the nitrate N-atom and N/Cl of the interacting partner (see Supplementary Figs 1

and 2).
Database analyses. Encouraged by these computational predictions we wondered if there might be any experimental evidence for p-hole bonding with NO 3 À within the crystal structures deposited in the CSD 20 and the Brookhaven PDB 21 . More in particular we were interested in ascertaining any possible directional behaviour 22 of this interaction. We limited our inquiries to uncoordinated nitrate anions to simplify our analysis. Also, if uncoordinated nitrate can act as Lewis acid, it is likely that coordinated nitrate will do so as well (and likely even more so). Initial data sets were retrieved by limiting the À O 3 N Á Á Á El.R. distance to 5 Å (El.R. ¼ 'electron rich atom'). The data are thus confined within a sphere with 5 Å radius but will-due to symmetry-be represented as contained within a 5 Å high and 10 Å wide hemisphere. The interacting entities considered here are H 2 O, O ¼ X (X ¼ any atom for the CSD data and only C for the PDB data) and S (CSD)/S-C (PDB).  Geometries were optimized with DFT/ BLYP/6-31G* and MEPs and energetic values (in kcal mol À 1 ) generated at the B3LYP/6-31G* level of theory. The colour codes of the MEPs represent more negative (red) to more positive (blue) potentials in between: À 80 and À 18 (2a); À 72 and À 1 (2b); À 80 and þ 35 (2c).   Fig. 4, bottom) consists of two isostructural chains (A and B) that are stuck together surrounding a central nitrate ligand. The NO 3 À anion is H-bonded to two arginine residues (Arg-54) with N Á Á Á N distances of about 3 Å. In addition, the carbonyl O-atoms of two glycine residues (Gly-51) appear to interact with the nitrate ligand's p-hole. Indeed, the interatomic N Á Á Á O distances (2.70 and 2.81 Å) are well within the van der Waals benchmark for N þ O (3.07 Å).
The AIM analyses of these four examples revealed a clear bond critical point between the nitrate's N-atom and the interacting electron donor for both EVIKEA and 3EZH ( Supplementary  Fig. 6). A natural bond orbital analysis (with a focus on second order perturbation) 30 for each example revealed electron donation from a lone pair of electrons (LP) into an unoccupied orbital of the nitrate anion (for example, 0.35 kcal mol À 1 for the LP(C ¼ O)-p*(NO 3 À ) in 3EZH, see Supplementary Note 2 for details). This confirms that the NO 3 À anion can act as a Lewis acid in these examples.

Discussion
The above computations, database analyses and examples clearly point out that a genuine p-hole might persist on a nitrate anion and that NO 3 À may thus act as a Lewis acid to form formally (pseudo)anti-electrostatic interactions in the solid state. One naturally wonders what other anions might be capable of displaying such behaviour (using other atoms than hydrogen). It occurred to us that nitrate actually has a rather unique set of properties that set it apart from other common anions in this respect: NO 3 À is fairly polarized and further polarizable, not so charge-dense and nitrate is flat, rendering the p-hole sterically accessible (see Supplementary Note 3 for a discussion of possible candidates). As nitrate anions are very common in chemistry and biology, we anticipate that our finding may serve as a (retrospective) guide to interpret chemical data where nitrate anions are involved; for example, orthonitrate formation 31,32 , cases where NO 3 À anions may be a structural determinant (as in 3EZH), or in transport phenomena involving this ubiquitous anion 33,34 .

Methods
Computations. The energies of all complexes included in this study were computed at the BP86-D3/def2-TZVP level of theory. The calculations have been performed by using the programme TURBOMOLE version 7.0 (ref. 35). For the calculations we have used the BP86 functional with the latest available correction for dispersion (D3) 36 . The optimization of the molecular geometries has been performed imposing the C 3 v symmetry point group. The Bader's 'Atoms in molecules' theory has been used to study the interactions discussed herein by means of the AIMall calculation package 37 .
Queries used to retrieve data from the CSD and PDB. The CSD (version 5.37 (November 2015 including two updates) was inspected using ConQuest (version 1.18) on the 3rd of April 2016. The PDB was inspected with the online Query Sketcher of Relibase version 3.2.1 on the 2nd of March 2016. For the CSD search, a subset of data was first created containing uncoordinated nitrate anions (9,439 crystallographic information files). All searches of the CSD were limited to high quality structure (Rr0.1) and powder structures and structures containing errors were omitted. The N-O bonds were set to 'any type'. All covalent bond distances and selected triatomic angles were collected to reconstruct the average models (one for the PDB data and one for the CSD data) used for accessing directionality (see below). The interatomic distance between the interacting atom (O in O ¼ C or OH 2 ; S in S, SC or SCC; or F, Cl, Br, I, At, O, S, Se, Te, N, P or As in El.R. ('electron rich') and the nitrate's N-atom (e, highlighted in red in Fig. 5) was set as r5 Å so that the data was confined within a 10 Å diameter sphere centred on N. In the PDB study the NO 3 central unit was marked as a ligand and the interacting atom(s) were marked as part of a protein, or in the case of water the interacting O was specified as water.
Deriving XYZ coordinates and r. The interatomic distances between the interacting atom and O1 and O3, as well as the O1-O3 distance were also collected (set to r8 Å in the PDB search and left unspecified for the CSD search). The triangle formed by O1-N-O3 was chosen as the base, and the interacting atom as the tip of a tetrahedron (see Fig. 5) so that Cartesian Coordinates {X, Y, Z} of all the atoms could be derived as follows: the N-atom was taken as the centre {0, 0, 0}, O1 as {0, c, 0}, O3 as {x, y, 0} and the interacting atom at {l, m, n}. Distances a-f were measured, from which y, x, m, l and n can be derived using equations (1)(2)(3)(4)(5), respectively.
Thus, the distance between the interacting atom and the plane defined by O1-N-O3 is n, that is, the Z-value. With this and the N Á Á Á interacting atom distance (e) the parallel displacement parameter (r) could be derived according to equation (6): With this procedure the sign of n (that is, the Z-axis) is always positive, meaning that data in one half of the sphere were reflected to the other half of the sphere to obtain the data within a 5 Å high and 10 Å wide hemisphere. To obtain all {X, Y, Z} coordinates of the average models, it was assumed that O2 was coplanar with O1-N-O3. The averages of relevant distances and angles were then used together with the rules of sine and cosine to obtain the {X, Y, Z} coordinates. The relative standard deviations of the parameters used were typically below 5%. A numerical overview of the data retrieved is shown in Supplementary Table 2.  Rendering 4D plots and analysis of directionality. 4D density plots were generated by first binning the data (using a custom build Excel spreadsheet, available on request) in 405 volumes {X [9 Â 10 / 9 Å], Y [9 Â 10 / 9 Å], Z [5 Â 5 / 5 Å]}. The percentage of the total that each volume contains was computed by dividing the number of data in a certain volume by the total amount of data. This density information was projected onto the centre of each volume using Origin Pro 8. The size and colour of the spheres in the resulting plots are a visual representation of the density of data, whereby red and larger is denser, empty and small is less dense. The average {X, Y, Z} coordinates of the atoms of nitrates found within the CSD or the PDB, together with the standard van der Waals radii for N (1.55 Å) and O (1.52 Å) were used to generate a model as a single body 'part' file (.ipt) using Autodesk Inventor Professional 2016 (by using mm instead of Å). Similarly, a hemisphere was created with a radius of 5 mm. Derived from this hemisphere were bodies where the volume above the base with basal radius (representative for r) was trimmed, that is, 'cylindrically trimmed hemispheres'. The NO 3 model, the hemisphere and the cylindrically trimmed hemispheres were collected in an assembly file (.iam), properly alighted, as is illustrated in Fig. 6 with (cylindrically trimmed) hemispheres of 1, 2, 3, 4 and 5 mm basal radius.
Using the 'Analyse Interference' option in Autodesk Inventor Professional 2016 the interfering volumes between the model and the cylindrically trimmed hemispheres could be determines. The volume difference between two such interfering volumes of incremental r-values, say r a and r b , thus represent the volume that the model occupies in between two values of r, that is, V model . Similarly, the interfering volume between two cylindrically trimmed hemispheres could be derived as a function of r, from which the volume in between two r-values as found within the hemisphere could be derived, that is, V no model . The actual free volume in between two r-values that a 'host' can occupy, that is, V r free , is thus given V no model À V model . The total freely accessible volume, V total free , is naturally given the volume of the hemisphere minus the volume of the model in the hemisphere. The random (or volume) distribution as a function of r, that is, D r chance , is thus given by: The actual distribution of the data, D r data , is naturally given by: Thus, the chance corrected distribution of data, P(r) is given by: For an accidental distribution, P should be unity across all r-values; a P value greater than unity is thus evidence of positive clustering (suggesting a favourable interaction), while P values smaller than unity reflect a depletion of data (suggesting an unfavourable interaction).
Data availability. All the data that support the findings of this work are available from the corresponding authors upon reasonable request.