On the ability of pnicogen atoms to engage in both σ and π-hole complexes. Heterodimers of ZF2C6H5 (Z = P, As, Sb, Bi) and NH3

When bound to a pair of F atoms and a phenyl ring, a pyramidal pnicogen (Z) atom can form a pnicogen bond wherein an NH3 base lies opposite one F atom. In addition to this σ-hole complex, the ZF2C6H5 molecule can distort in such a way that the NH3 approaches on the opposite side to the lone pair on Z, where there is a so-called π-hole. The interaction energies of these π-hole dimers are roughly 30 kcal/mol, much larger than the equivalent quantities for the σ-hole complexes, which are only 4–13 kcal/mol. On the other hand, this large interaction energy is countered by the considerable deformation energy required for the Lewis acid to adopt the geometry necessary to form the π-hole complex. The overall energetics of the complexation reaction are thus more exothermic for the σ-hole dimers than for the π-hole dimers.


Introduction
Recent years have witnessed a dramatic growth in interest in noncovalent interactions. New insights have been gleaned from a palette of computational tools based on quantum chemistry. While any single noncovalent interaction is weak in comparison to a covalent bond, such interactions nonetheless exert a powerful impact on numerous processes linked to biochemistry or crystal engineering, nanoparticle self-assembly, drug binding, and biomolecular folding processes [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. After decades of scientific attention devoted to the hydrogen bond [4,8,[15][16][17][18][19][20], a number of different but related noncovalent interactions have enjoyed the limelight more recently. Many of these bonds derive from the σ-hole concept, wherein-even though it does not carry a partial positive charge-an electronegative atom can nonetheless attract a nucleophile via an anisotropic electronic distribution which provides a positive electrostatic potential in a constricted region lying opposite a covalent bond [21][22][23][24][25][26][27][28]. The σ-hole area may be treated as an acidic binding site that attracts an incoming nucleophile, which may take the form of a lone pair, an anion, or even a π-electron system. In addition to the electrostatic attraction, noncovalent bonds benefit from electron transfer from a Lewis base to a σ* antibonding orbital of the acid [29][30][31][32][33], which also contributes to the directionality of the σ-hole bond [34][35][36].
The pnicogen bond is a case in point. It has been reasonably widely examined [34,[61][62][63][64][65][66][67][68][69][70][71][72][73][74], but little has been determined in terms of competing configurations of a given pair of molecules. For example, the complexes PH 2 R···BrCl (R = H, F, OH, OCH 3 , CH 3 ) were studied at the MP2 level [74], focusing on two possible σ-hole arrangements: halogen-bonded vs pnicogen-bonded. The halogen bonds were calculated to be stronger and driven primarily by electrostatics, while the weaker pnicogen bonds relied mostly on dispersion. With respect to π-electron donors, Zhu and coworkers observed a reversal in that pnicogen bonds were stronger than halogen bonds in complexes between PH 2 Cl and substituted benzene [68]. The strongest σ-hole bonding in PH 2 R complexes with formaldehyde [75] was found to occur when R = NO 2 , followed by R = F and R = Cl. Pnicogen bonds exhibit cooperativity with H-bonds, as noted in complexes of π-electron systems such as benzene with PCl 3 [65]. There have been some studies of π-hole pnicogen bonds, but those studies focused on the hypervalent PO 2 Cl molecule [76], PO 2 R [77], or the (H 2 C=PH 2 ) + ion [78], none of which can contain a σ-hole. π-Hole pnicogen bonds have been identified in unconventional bonding situations such as NNO [79], but these are quite weak and there is no competing σ-hole interaction.
Although there has been little examination of σ-hole versus π-hole bonding in pnicogen bonds, there has been some study of this question for the related tetrel bond wherein TF 4 (T = Si, Ge, Sn) molecules were paired with pyridine derivatives [80]. The approach of the Lewis base prompted large-scale geometry distortion in TF 4 , changing its shape from tetrahedral to trigonal bipyramidal. This transformation led to the formation of two types of dimers with σ-hole and π-hole characteristics. While the latter were more stable with regard to interaction energies (surpassing 50 kcal/mol), the accompanying deformation of the monomer geometry was so high in these configurations that the overall energetics favored the σ-hole complexes. The ability of tetrel atoms to engage in both σ-hole and π-hole interactions was recently examined [81], and it was learned that π-complexes can be stronger than their σ analogues, although different molecules were used for each class of interaction. Aerogen bonds are capable of forming both σhole and π-hole interactions, and recent calculations [82] suggest that it is the latter that are the stronger. In another somewhat related study, σ-hole pnicogen bonds were compared with a π-hole tetrel bond [83].
The ability of TF 4 molecules to undergo [80] a geometrical transformation so as to form either a σ-hole or π-hole tetrel bond inspired us to wonder if something of this sort is also possible for pnicogen atoms. If such is the case, then there are a number of obvious and important questions. Would σ-hole or π-hole complexes be more stable, and how much deformation energy might be required for each to form? It would be interesting to determine the underlying sources of the stability of each to see what differences there might be. Do both sorts of bonds require the same proportions of electrostatic, polarization, and dispersion energy contributions? How do the quantitative aspects of the σand π-holes of the properly distorted monomer differ from each other, and do their magnitudes correlate with the strength of the interaction with a base? It would be interesting to determine whether both sorts of bonds undergo the same systematic trends as the pnicogen atom grows larger, i.e., P → As → Sb → Bi. The present communication details the results of calculations intended to answer these questions.

Systems and computational methods
The proper selection of electron donors and acceptor is crucial to deriving a systematic understanding of the nature of the bonding. In the Lewis acid, sufficiently potent electronwithdrawing substituents must be attached to the pnicogen atom to ensure the presence of regions of positive potential that can attract a base. The entire molecule must be flexible enough that geometrical deformations to accommodate both sorts of bonding are feasible. For the Lewis acid, then, the set of molecules ZF 2 C 6 H 5 (Z = P, As, Sb, Bi) was selected. The F atoms act as electron-withdrawing agents, and the phenyl ring can rotate as needed. NH 3 was chosen as the Lewis base due to its small size, which minimizes complicating secondary interactions, as well as its easily available lone pair of electrons.
The geometries of dimeric complexes between ZF 2 C 6 H 5 (Z = P, As, Sb, Bi) and NH 3 were optimized at the MP2 level in conjunction with the aug-cc-pVDZ basis set [84,85]. Optimization was also carried out at the BLYP-D3/ Def2TZVPP level of theory. Energies were additionally computed at the CCSD(T)/aug-cc-pVDZ level (using MP2generated minima) for the purposes of comparison and validation [86][87][88][89][90][91][92]. For accurate electronic descriptions of the heavy Sb and Bi atoms, the aug-cc-pVDZ-PP basis set with pseudopotentials taken from the EMSL library was employed [93]. Structures were verified as true minima by checking that all vibrational frequencies were positive. Computations were performed via the Gaussian 09 software package [94]. Molecular electrostatic potential (MEP) analysis was applied to identify and quantify all MEP extrema using the WFA-SAS and MultiWFN programs [95][96][97]. Interaction energies were calculated as the difference in energy between the complex and the sum of monomers (with the same geometries as they adopt within the complex). Binding energies were computed relative to the monomers in their isolated optimized structures. Both quantities were corrected for basis set superposition error (BSSE) using the counterpoise protocol [98]. The electron density topology was analyzed using AIMAll software [99]. Energy decomposition analysis (EDA) was performed at the BLYP-D3/ZORA/TZ2P level using DFT-optimized geometries with the aid of ADF software [100][101][102]. In order to analyze interorbital connections and charge flow between the monomers, the natural bond orbital (NBO) procedure (using GenNBO 6.0) was utilized using the wavefunction generated at the DFT level [103]. The CSD (Cambridge Structural Database) [104] was searched for pertinent experimental crystal structures similar to those described in this manuscript.

Monomer characteristics
The isolated ZF 2 C 6 H 5 (Z = P, As, Sb, Bi) monomers were fully optimized at the MP2/aug-cc-pVDZ and BLYP-D3/ Def2TZVPP levels. The equilibrium geometries of these monomers calculated at the MP2 level are similar; they all have a highly pyramidal Z atom close to the C s point group. This general structure is presented as conformer A in Fig. 1. Despite appearing to be in close proximity, AIM analysis does not find any bond critical point between the F and ring H atoms when Z = P, As, or Bi. In the case of BiF 2 C 6 H 5 , however, one of the F atoms is nearly coplanar with the aromatic ring, with a dihedral angle φ(F-Bi-C-C) = 11.3°(see Table S1 in the BElectronic supplementary material,^ESM), and AIM finds a BCP between this F and the nearby ring H atom. On the other hand, this interaction is rather weak, with an electron density at the BCP of only 0.0095 au.
Unlike MP2, the DFT functional identified two separate stable conformers of ZF 2 C 6 H 5 . In addition to the A geometry discussed above, the B conformer rotates the ZF 2 group such that both F atoms lie below the phenyl ring, and the Z lone pair points above this ring, belonging to the C s point group. Structure B is slightly less stable than A, by 1.04, 0.70, and 0.58 kcal/mol for Z = P, As, and Sb, respectively; these differences are even smaller in terms of ΔG. DFT, like MP2, does not identify a B geometry for BiF 2 C 6 H 5 .
The molecular electrostatic potential surrounding the A geometry of PF 2 C 6 H 5 is displayed in Fig. 2; similar diagrams are obtained for the other ZF 2 C 6 H 5 systems. The most intense σ-holes lie opposite the F atoms, along extensions of the P-F bonds. The value of V s,max on this surface increases with the size of the Z atom from 19.4 kcal/mol for Z = P to 52.6 kcal/ mol for Z = Bi, as may be seen in the first column of Table 1. There is a second, but weaker, σ-hole opposite the C-P bond, with smaller V s,max values listed in the last column of Table 1. The calculated V s,min for the isolated ammonia molecule that acts as a Lewis base is −37.7 kcal/mol.

σ-Hole and π-hole dimer interactions
When each ZF 2 C 6 H 5 molecule was paired with NH 3 , two types of dimer geometries were identified. As illustrated in the top half of Fig. 3, in the first case the NH 3 approaches Z along the direction of one of the two Z-F σ-holes. Another dimer structure is related to the B monomer geometry, wherein the NH 3 lies roughly perpendicular to the C-Z covalent bond, in between the two Z-F bonds. These two structures are designated σ-hole and π-hole complexes, respectively.
The geometric details of these two types of dimers are listed in Table 2. F1 refers to the F atom that lies directly opposite the NH 3 N atom in the σ-hole structure, and F2 refers to the other F atom. The angle θ(F1-Z···N) in the σ-hole geometries ranges between 155°and 166°, and is more linear for the smaller Z atoms. The intermolecular distances R(Z···N) are surprisingly insensitive to the nature of the Z atom, and are longest for P and shortest for As. In contrast, this same distance is highly dependent upon Z for the π-hole complexes, elongating from 1.932 Å for P to 2.343 Å for Bi. This pattern fits the simple idea of a progressively larger Z atom along this series. Note also that the N atom lies on the same side of the phenyl plane as the two F atoms, with the angles θ(F-Z-N) all less than 80°. The bond lengths r(Z-F1) for the F lying . The Z-F bond lengths are considerably longer in the π-hole complexes. The substituents around the central Z atom constitute a pyramidal structure. Its deviation from planarity can be quantified as the sum of the three angles θ(X-Z-Y), where X and Y refer to the substituent atoms (C or F). This sum would be equal to 360°for a fully planar structure, so deviations from this sum can be considered as a measure of the nonplanarity, i.e., the Bpyramidality.^As shown in the last column of Table 2, this angle sum is quite small for the σ-hole complexes, less than 290°. The deviation from planarity gets larger as the Z atom grows in size. On the other hand, the uncomplexed monomers are also quite nonplanar, as may be seen in the last column of Table S1. The increase in nonplanarity caused by complexation, i.e., the difference in ∑θ(Z) between the monomer and complex, is between 4°and 7°. The angle sum is much closer to 360°for the π-hole complexes. This change from the monomer amounts to a 40-50°loss of pyramidal character, i.e., a flattening of the pyramid at the central Z atom. This alteration has important repercussions for the energetics of this process, as elaborated below.
The interaction energies of the various heterodimers obtained at three different levels of theory are presented in Table 3. The most striking trend in these values is that the interactions involved in the π-hole complexes are much stronger than those for the σ-hole complexes. E int lies in the range 24-34 kcal/mol for these structures-much larger than the 4-13 kcal/mol range for the σ-hole geometries. Taking the CCSD(T)/aug-cc-pVDZ values as a benchmark, the MP2 quantities for the π-hole dimers are slightly inflated, whereas those calculated at the BLYP-D3/Def2TZVPP level are significantly underestimated. The three levels provide much more uniform data for the σ-hole geometries. With regard to the former structures, E int tends to drop slowly as the Z atom becomes larger; the opposite pattern emerges for the σ-hole dimers, where NH 3 is bound more than three times more strongly for Z = Bi than for P. AIM analysis of these complexes helps us to understand these energetic trends. The relevant molecular graphs are displayed in Fig. S1 of the ESM, where all structures are shown to contain a bond critical point between the pnicogen and the N atom of the base. The relevant characteristics of this critical point are listed in Table 4, along with any secondary critical points between the two molecules. All of the data support the stronger binding of the π-hole dimers as compared to the σ-hole dimers. For example, ρ is between 2 and 5 times larger for the former than the latter, and ∇ 2 ρ is much larger as well. H is much more negative for the π-hole dimers than for the σ-hole dimers, again consistent with the stronger binding in the former. Less consistent are the values within each series. ρ only grows slowly with increasing Z size for the σ-hole set, while the interaction energy grows much more quickly. While the π-hole E int is insensitive to the identity of Z, there is a clear tendency for ρ to decrease as the size of Z increases. It can also be observed that additional NH···F H-bonds are indicated by AIM, which add to the larger interaction energies for the π- Fig. 2 MEPs of the isolated PF 2 C 6 H 5 σ-hole donor molecule, computed on the 0.001 au isodensity surface at the MP2/ aug-cc-pVDZ level. Color ranges, in kcal/mol, are: red greater than 15, yellow between 8 and 15, green between 0 and 8, blue below 0 kcal/mol  Table 2 Structural parameters (distances in Å, angles in degrees) in complexes of ZF 2 C 6 H 5 with NH 3 , as evaluated at the MP2/aug-cc-pVDZ level NBO evaluation of the charge transfer from orbitals of the base to those of the Lewis acid provides an alternative perspective on the nature of the bonding. The second and sixth columns of Table 5 present the total charge transferred from the N lone pair to any of the orbitals of the Lewis base for σ-hole-bonded and π-hole-bonded complexes, respectively. In other columns of the table, this total charge transferred is split into that transferred to LV orbitals of the Z atom, defined by NBO as onecenter unfilled nonbonded valence orbitals of Z, and that transferred to the σ*(Z-C) antibonding orbital involving the phenyl C, respectively. Another two columns of the table refer to CT the total charge transferred, i.e., the total natural charge on all atoms of each subunit. The NBO data tend to mimic the interaction energies in Table 3 to some extent. As an illustration of this, the relationship between CT and interaction energy is presented in Fig. S2 of the ESM. The much stronger binding of the π-hole complexes is reflected in the interorbital and total charge transfer. Also reproduced is the diminishing π-hole bond strength with larger Z. With the exception of Z = Bi, the σ-hole data show a trend for increasing energy as Z gets larger.
Decomposition of the interaction energy into its constituent parts provides further insights into the nature of these dimers. The data in Table 6 illustrate that roughly 60% of the interactions in both σ-hole and π-hole complexes are based on electrostatic attraction. This percentage increases a little as the Z atom grows heavier. Orbital interactions account for a larger share of the interaction energy in the π-hole dimers (35-46%) as compared to their σ-hole analogues (only 30-32%). This distinction is consistent with the larger NBO charge transfer values. The σ-hole geometries make up the difference with a larger fraction of dispersion energy, which makes virtually no contribution to the π-hole structure. However, there is quite a distinction between the σ-hole and π-hole dimers in that the overall quantities are much larger for the latter structures. A large part of this increase is due to their much shorter intermolecular distances, as detailed in Table 2.

Monomer deformations
The above analyses considered the interactions between the two subunits after each has altered its internal geometry to that which it adopts within the context of the dimer. This atomic rearrangement requires a certain amount of energy. The deformation energies required for this transformation are reported in Table 7. These values show that it is the Lewis acid ZF 2 C 6 H 5 which undergoes the major transformation, as the NH 3 requires less than 1 kcal/mol. The deformation energy of the Lewis acid is also quite small for the σ-hole dimers-on the order of 1 kcal/mol or less. However, the deformation energies of the π-hole structures are dramatically different; they are all greater than 15 kcal/mol. This quantity is smallest for BiF 2 C 6 H 5 , but it climbs rapidly as Z shrinks, reaching over 43 kcal/mol for Z = P.
As described earlier, a major aspect of the internal rearrangement of each Lewis acid is a change in the pyramidization of the Z atom. This deformation results in an intensification of the positive region of the MEP surrounding the Z atom. The V s,max in each properly deformed Lewis acid is displayed in the last column of Table 7, along with the increase relative to the undistorted monomer in parentheses. One can see that this increase is relatively modest for the σhole geometries in the upper part of the table-only about 10% or less. However, the much weaker pyramidization of the Z atom in the π-hole dimers is accompanied by substantial enhancement of V s,max . This enhancement is as much as nearly  50% in the case of Z = P. The much more intense holes in the π-hole cases are largely responsible for their much larger interaction energies as compared to the σ-hole cases. However, an apparent anomaly is also present, but only for π-hole-bonded complexes. The π-holes in the deformed Lewis acids become progressively more intense as the Z atom grows larger, but at the same time there is no corresponding increase in the interaction energy. In fact, the latter quantity steadily decreases as Z grows larger. The electrostatic component of the interaction energy from Table 6 also diminishes in the sequence P → Bi, in contrast to the rising pattern of V s,max seen in Table 7. This contrary behavior is an indication that the value of the MEP of a particular point in the vicinity of a molecule does not always correlate with the actual electrostatic element of an intermolecular interaction. It should also be emphasized that this lack of correlation can be explained as the consequence of the large contribution of the orbital interaction component.
When considering the overall complexation reaction, all species (monomers and dimer alike) are typically considered to be in their optimized geometries. This reaction, or binding, energy must therefore incorporate any deformation energies of each species. The binding energies E b obtained when the deformation energies are appropriately combined with the interaction energies are presented in Table 8. Comparison with Table 3 shows that the energetics of the σ-hole complexes barely change, since their deformation energies are small. The large deformation energies of the π-hole dimers, on the other hand, lead to dramatic changes. E b is quite a bit less exothermic than E int , even to the point of becoming endothermic for the smaller Z atoms. Another notable reversal is that it is the σ-hole rather than the π-hole complexes that are more stable. This preference is quite large, 14 kcal/mol for Z = P, but it then diminishes for larger Z atoms, dropping to only 1 or 2 kcal/mol for Bi. The trend in the binding energies also changes to a trend noted earlier for the interaction energies. Whereas the latter quantity is insensitive to the nature of the Z atom for the π-hole complexes, the binding energies display strongly increasing exothermicity as Z transitions from P to Bi.

Vibrational analysis
Certain features of the vibrational spectrum can shed light on the fundamental nature of molecular interactions. Selected vibrational frequencies and intensities of the monomers and their complexes are displayed in Table 9. The first two rows of this table document progressively redshifted symmetric and antisymmetric Z-F stretching frequencies as Z grows larger, along with slowly reducing intensities. With respect to the σhole complexes, the N···Z stretching frequency shifts to the blue as Z becomes larger, consistent with the strengthening interaction energy. The interaction becomes slightly weaker in Table 5 NBO values of the sum of E(2) for LP(N) donation to the Lewis acid, along with the charge donated to selected ZF 2 C 6 H 5 orbitals (Z = P, As, Sb, Bi) and the total charge transferred (CT, in me) from ammonia to ZF 2 C 6 H 5 , as calculated at the BLYP-D3/def2-TVZPP level  the π-hole dimers, which is also consistent with the redshifting Z···N stretching frequency. The much higher interaction energies of the π-hole complexes are reflected in the considerably greater Z···N stretching frequencies.
In fact, there are very strong correlations between these intermolecular stretching frequencies and other aspects of the binding. The correlation with the interaction energy exhibited in Fig. 4a for both the σ-hole and π-hole complexes suggests a linear relationship. This correlation is especially good for the σ-hole structures, with R 2 = 0.946. The correlation is even better with the intensities of the σ-holes and π-holes, with R 2 reaching 0.999 for the σ-holes. However, it is perhaps surprising to note a negative slope for the π-holes in Fig. 4b, which links a more intense π-hole to a reduced ν(N···Z). This opposite behavior was also noted above for the relationship of V s,max to the full electrostatic component.
The formation of σ-hole complexes is expected to result in the transfer of electron density into the σ*(Z-F1) antibonding orbital. This shift will lengthen this bond, as already noted above, and will weaken the bond and thereby shift the stretching frequency to the red. A comparison of the frequency ν a (ZF 2 ) of each monomer with ν(Z-F1) in the corresponding σ-dimer confirms this expectation, with a redshift of about 40 cm −1 . This change in frequency is accompanied by band intensification, with I increasing by a factor of 1.5 for all Z except Bi. For the π-geometries, we can compare the ν a (ZF 2 ) values for the dimer and monomer. This frequency shifts heavily to the red by 126-227 cm −1 , with the greatest shifts occurring for the smallest Z atoms.

Discussion and conclusions
The Z atom in ZF 2 C 6 H 5 is not the only site that can attract a base such as NH 3 . There are positive regions of the MEP that surround the aryl H atoms as well, as may be seen in Fig. 2. Table S2 in the ESM shows that V s,max lies in the vicinity of +20 kcal/mol for these H atoms. It is no surprise, then, that there are a number of secondary minima on the potential energy surfaces of these heterodimers that contain a CH···N Hbond. These structures are depicted in Table S3 of the ESM, along with selected geometric parameters and interaction energies. The latter are all between 2 and 3 kcal/mol, very much smaller than those of the primary σ-hole and π-hole complexes that are the focus of this work. Even the complexes which combine a CH···N H-bond with NH···F interactions in the last row of Table S3 of the ESM are still much more weakly bound than the primary structures.
In any computational elucidation of bimolecular complexes, there is always the issue of experimental confirmation. A survey of the CSD (Cambridge Structural Database) [104] provides experimental evidence of the existence of both σand π-types of tetracoordinate pnicogen complexes. The first two examples collected in Table S4 of the ESM [107][108][109][110] clearly indicate the ability of a pnicogen atom, in this case As,  to bind a Lewis base through a σ-hole that lies directly opposite a F atom. Three examples of π-systems are also provided, including systems incorporating As and Bi. The large deformation energies noted here for the π-hole complexes are not without precedent. A recent study of hypervalent pnicogen and other bonds [111] noted a rearrangement from a trigonal bipyramidal ZF 5 monomer to a square-pyramidal complex, which was associated with a large deformation energy. This sort of deformation occurs not only in ZF 5 but also in TF 4 [112] (T = tetrel atom), which would not be considered hypervalent. These distortion energies in tetrel bonds can control the preferred equilibrium geometry [80] and tend to lessen as the size of the central tetrel atom increases [113], consonant with the findings here for pnicogen bonds. Similar distortions were observed [81] in both TR 4 (σ) and TR 2 =CH 2 (π) tetrel-bonding molecules.
In conclusion, ZF 2 C 6 H 5 molecules containing a pair of F atoms and a phenyl ring surrounding a pnicogen atom Z form a fairly strong complex with an NH 3 molecule. For each Z, there are two possible geometric arrangements, depending upon the positions of the two F atoms. When one F is located above the aromatic ring plane and the other below it, the base positions itself directly opposite one of the two F atoms in a σhole arrangement. If both F atoms lie on the same side of the ring and almost in the same plane, the NH 3 is located directly above the Z atom, perpendicular to the ring plane, in a π-hole  Fig. 4 Linear relationships between ν(N···Z) and a E int and b V s,max orientation. The interaction energies in the latter system are considerably larger than those in the former, on the order of 30 kcal/mol. However, at the same time, the π-hole dimers require a good deal more deformation of the ZF 2 C 6 H 5 monomer, meaning that the overall dimerization process is more exothermic for the σ-hole structures. This overall preference for the σ-hole is most substantial for the smaller Z atoms, nearly disappearing for Z = Bi.