Introduction

Noncovalent bonding has gained a great deal of attention of late as research has shifted to a family of interactions that share many facets with the well studied H-bond (HB). [1][2][3][4][5][6] The halogen bond (XB) is a prime example where the bridging H of the HB is replaced by any of the halogen group of the periodic table. [7][8][9][10][11][12][13][14][15][16] Like the HB, there is an attractive charge transfer component that shifts density from a lone pair of the nucleophile to the σ*(RX) antibonding orbital, where X refers to a halogen rather than a H atom. One distinction between the two sorts of bonds arises within the context of the electrostatic component. The central H is characterized by an overall partial positive charge that attracts the negative region connected with the basic atom's lone pair. Due to its higher electronegativity, the analogous X contains an overall negative charge. However, this net charge is far from uniformly distributed around the X center. Indeed, the presence of the RÀX covalent bond within the Lewis acid pulls electron density away from the extension of the bond axis, leaving a deficit in this area. This reduced density, commonly referred to as a σ-hole, leads to a positive region of the electrostatic potential along the pole of this bond axis, surrounded by an equator of negative potential. It is this σhole which provides a strong electrostatic component to a XB, comparable in magnitude to that of the closely related HB.

In its typical monovalent bonding situation, the X atom contains a single such σ-hole so is limited to one XB. The chalcogen family presents a different scenario. Its most common covalent bonding environment is a divalent one, with each chalcogen (Y) atom attached to two R groups, disposed very roughly at 110°from one another around Y. Each of the two YÀR bonds can produce a σ-hole on Y, again lying approximately along the extension of the RÀY bond axis. And each σ-hole can in turn bind to a nucleophile in what is called a chalcogen bond (ChB), in very close analogy to a XB. The ChB has engendered a quickly growing literature, [17][18][19][20][21][22][23][24][25][26] as it is involved in a wide range of chemical phenomena. These bonds participate in supramolecular semiconductors, [27] transfer hydrogenation catalysis, [28] enantioseparation in liquid-phase chromatography, [29] and as a driver of cycloaddition reaction which controls stereoselectivity. [30] They can lead to otherwise unfavorable conformations [31] or influence cis/trans isomerization, and help form container assemblies that persist in water. [32] Some of these many applications have been reviewed recently. [33,34] Continuing research has revealed the occurrence of these bonds in biomolecules such as proteins and nucleic acids [21,[35][36][37][38][39] or SAM riboswitches. [36] The ChB runs a full spectrum of bond strength [40] with Te being particularly strong, [41] and reveals itself in a number of ways including solid state NMR. [42,43] A good deal of our present understanding of the ChB is contained in a number of recent review articles [24,[44][45][46][47][48] to which an interested reader is referred.

Years of research into the ChB have provided a growing understanding of the factors that control its strength. As the chalcogen atom grows larger, it becomes both more polarizable and electropositive. Both of these factors lead to a deeper σhole and thus to a stronger ChB. Electron-withdrawing substituents such as NO 2 or CN placed on the central chalcogen atom will have a similar effect. The combination of a heavy chalcogen atom, decorated by strongly electron-withdrawing groups, can make for strong ChBs, well in excess of 10 kcal/mol, which can effectively compete with other noncovalent interactions such as H-bonds. And this strength is further magnified by charge assistance, which arises if the Lewis acid is positively charged, and/or the base is an anion.

It stands to reason that each of the two σ-holes on the Y atom in a R 1 YR 2 unit will be intensified by the electronwithdrawing capacity of the two R groups. What is less obvious is which of these two holes will be deeper if R 1 and R 2 are different. As a second question, will the deeper of these two holes necessarily result in a stronger ChB? There are contributors to the total ChB energy in addition to the simple Coulombic interaction of a σ-hole with a nucleophile's negative region that can influence this question. For example, the base lone pair can transfer charge to both the σ*(R 1 Y) and σ*(R 2 Y) antibonding orbitals, regardless of which R group it lies opposite. There are also issues of dispersive attractions and steric repulsions with the nearer of the two R groups which will influence its stability.

As another matter, the ChB differs from the XB in one important way. The σ-hole of a RX molecule lies symmetrically and directly opposite the R group, surrounded by the three X lone pairs. But the Y atom of R 1 YR 2 contains two lone pairs, unsymmetrically positioned around either RY axis. This arrangement "pushes" the σ-hole away from the R 1 Y bond extension to some extent toward the other R 2 Y bond. How does this deviation of the σ-hole from the RY bond axis affect the ultimate disposition of the base within the ChB? And what is the effect of any repositioning of the base relative to the σ-hole on the competition between the two holes for a base?

A third question concerns the ability of both σ-holes to maintain a ChB at the same time. As a base is added to one of the two σ-holes, electron density is transferred to the Lewis acid. This additional density will tend to diminish the positive charge on the remaining σ-hole, presumably lessening its ability to attract a second base. A central question concerns how much each ChB will weaken the other in this anticooperative arrangement. As a corollary, will the weakening of the second σ-hole be such that a second ChB is not tenable?

The work described below applies DFT quantum calculations to answer these questions. A series of simple R 1 YR 2 molecules is constructed in which R 1 =F, and R 2 is a different halogen Br or I, or conversely, an electron-donating tert-butyl (tBu) group. The bulkiness of the latter brings the matter of steric repulsions into focus. Placing the chalcogen atom within the context of a ring imposes a certain degree of rigidity into the system. The chalcogenazole (YNC 3 H 3 ) set of systems also adds the wrinkle of aromaticity which involves one of the two Y lone pairs in a different Y sp 2 hybridization than sp 3 of R 1 YR 2 . The two σ-holes in these aromatic systems lie opposite N and C atoms of the ring, of quite different electronegativity. Indeed, this sort of system is of particular relevance as aromatic systems containing a chalcogen atom have been the subject of a good deal of experimental and theoretical scrutiny with regard to their ability to engage in ChBs. [49][50][51][52][53][54][55][56][57][58] As a further issue, the electron-donating ability of tBu was brought into the conversation by adding it to the neighboring C atom in another subset of systems. In each case, S, Se, and Te was considered as the central chalcogen atom so as to obtain a full picture. NH 3 was taken as the universal base, due in part to its moderate nucleophilic strength. This base has been used in numerous other studies of chalcogen and related bonding interactions, so will facilitate comparisons with the existing literature. As another important consideration, the small size of this unit ought to minimize any secondary interactions, and thereby retain focus on the ChBs of interest.

Computational Details

Quantum chemical calculations were performed via the Gaussian 16 [59] set of codes, applying density functional theory (DFT) in the framework of the M06-2X functional, [60] along with the polarized aug-cc-pVDZ basis set. The aug-cc-pVDZ-PP pseudopotential was applied to Te so as to account for certain relativistic effects. There is ample confirmation in the literature of the reliability of this approach. [61][62][63][64][65][66][67][68] The interaction energy E int of each dyad was calculated as the difference between the energy of the complex and the sum of the energies of the Lewis acid and NH 3 base, each in the context of the geometry they adopt within the dimer. The individual interaction energy of each ChB within the triad considered the two subunits to be one NH 3 and the combined Lewis acid-NH 3 dyad, again with all geometries in the context of the triad. Basis set superposition error was corrected by the counterpoise protocol. [69] The Multiwfn program [70] located and quantified the relevant maxima of the molecular electrostatic potential (MEP) residing on the ρ = 0.001 au isodensity surface of each monomer. Bond paths were identified by the QTAIM formalism, and the density at the bond critical point evaluated by AIMAll software. [71] Charge transfers between individual orbitals and their associated second-order energies, were derived by Natural Bond Orbital (NBO) theory [72,73] by way of the NBO3 program incorporated into Gaussian.

Results

Electrostatic Potentials of Monomers

As an initial step in understanding the relevant ChBs, it is instructive to first elucidate the depth and positions of the relevant σ-holes. One can achieve this purpose by examining the molecular electrostatic potential (MEP) that surrounds each Lewis acid unit. The σ-hole position is identified as the maximum of the MEP on an isodensity surface of ρ = 0.001 au, thought to be roughly comparable with the vdW surface. An example is illustrated in Figure 1 for SeFBr where Figure 1a locates the two principal maxima V max , one opposite each of the two halogen atoms. These points are both 2.03 Å from the central Se atom, somewhat further than the Bondi vdW radius of this atom which is equal to 1.90 Å. These maxima are not quite directly along the extensions of the XÀSe bond, with θ(XÀSeÀV max ) equal to 178°and 169°for X=F and Br, respectively.

The FÀYÀBr row of Table 1 shows the values of V max to be 39.3 and 34.8 kcal/mol, with the deeper of the two situated opposite the F. Perusal of the full contents of Table 1 shows certain trends that are consistent with concepts concerning electronegativity and polarizability. In the first place, these holes are uniformly deeper for positions opposite F than the less electronegative Br or I. Secondly, the diminishing electronegativity as the second halogen atom grows larger represents its lesser ability to pull density away from the central Y atom. This diminishing power results in a weakening of both σ-holes, not just the one opposite the non-F substituent. Another important trend is associated with the deepening of the two σholes as Y becomes larger: S < Se < Te. This pattern can be understood on the basis of the growing electropositivity of Y, along with its higher polarizability that better enables the attached X atoms to withdraw electron density. The replacement of an electron-withdrawing halogen atom by a donating tert-butyl (tBu) group has the reverse effect. The values of V max in the fourth row of Table 1 are considerably reduced relative to the preceding three rows, almost vanishing for FStBu. Again, this electron-releasing effect is manifested in the weakening of both σ-holes. Note also that there is a very substantial difference in the depths of the two σ-holes in these systems, 11 kcal/ mol for FStBu, up to 24 kcal/mol for FTetBu. These various trends are depicted graphically in Figure 2.

Turning to the chalcogenazole rings, the positioning of the two relevant σ-holes are shown in Figure 3a for the example of Y=Se. The two maxima are a bit further from Se than in Figure 1a, roughly 2.1 Å. Their angular placement is somewhat more distorted from the extensions of the RÀSe bonds. The small θ(NÀSeÀV max ) angle of 158°is likely influenced by the positive region surrounding the neighboring CH hydrogen center. The σ-holes are notably deeper opposite the electronwithdrawing N as opposed to the C. Adding the electronreleasing tBu substituent to the C adjacent to Y reduces V max for both positions, as witness the final row of Table 1. In fact, one of these maxima takes a slightly negative value.

In comparing the depths of the two relevant Y σ-holes for each monomer, there is a tendency for the deeper of the two to be the one opposite the more electronegative atom. The difference between the two holes is substantive but not overwhelming for the FSX units. This difference can be as small as 2 kcal/mol for FSBr and reaches a maximum of 8 kcal/mol for FTeI. The electron-releasing property of the tBu group leads to a more substantive hole depth difference, as large as 24 kcal/ mol for FTetBu. The σ-hole depths in the chalcogenazole ring are fairly deep for the one located opposite the N, much shallower for its analogue lying opposite a C.

Tables 2 and 3 contain the geometrical data concerning the dispositions of the V max positions for all of the Lewis acid molecules explored here. There is a clear pattern for the Table 1. Maximum of molecular electrostatic potential, V max (kcal/mol), on 0.001 au isodensity surface. F/N refers to the hole lying opposite the F or N atom of the Lewis acid; X/C places the hole opposite either the other X halogen atom of FYX or the C atom of the tBu group or the ring.

C FÀYÀF 38.4 48.1 60.8 FÀYÀBr 29.8 27.7 39.3 34.8 53.6 48.0 FÀYÀI 27.4 22.4 36.2 29.4 50.3 42.2 FÀYÀtBu 13.0 1.8 23.3 5.9 38.8 14.8 ring HCÀYÀN 22.3 3.1 24.2 8.5 31.6 19.6 ring tBuCÀYÀN 12.5 À0.9 15.8 4.2 23.1 14.7 distance from the central Y atom to V max in Table 2 to elongate as the depth of the hole diminishes. Taking the FÀSÀX series as an example, the distance corresponding to the hole opposite the F atom rises from 1.911 Å for FSF up to 1.980 for FSBr, then 2.007 and 2.125 Å for FYI and FYtBu, respectively. This pattern can be understood on the basis that a less electron-withdrawing substituent ought to leave more density on the Y atom, which will tend to expand its isodensity contour. The V max positions tend to be slightly closer to Y for the alternate hole, opposite the X atom, but also elongate as X becomes less electron-withdrawing. The position of each V max tends to lie roughly opposite the pertinent atom, with the θ(RY••V max ) angles in Table 3 approaching 180°. The deviation from linearity is smaller for the hole opposite the F than its counterpart opposite X.

Energetics of Chalcogen-Bonded Dyads

The ability of these various σ-holes to attract a nucleophile was realized by allowing each Lewis acid to interact with NH 3 .

Examples of the ensuing complexes are exhibited in Figures 1b and 1c for FSeBr and Figures 3b and 3c for selenazole. The approaching N aligns itself fairly closely with the position of V max . Despite the small size of NH 3 , there are certain weak secondary interactions that affect the final disposition of the molecules in certain cases. For example, the positive potential of the CH group in Figure 3b tends to exert an attractive force on the N lone pair, causing a slight rotation of the NH 3 , which would lead to a contamination of the desired ChB with a CH••Y HB if not corrected. [51] The N••H distance in this configuration is 2.834 Å, although the θ(CH••N) angle is as small as 107°.

Likewise the negative potential near the ring N tends to pull one of the NH 3 protons toward it in Figure 3c. Indeed, in some cases, it was necessary to impose a geometrical restriction so as to obtain a chalcogen-bonding interaction rather than an alternate H-bonded structure. Specifically, the lone pair of NH 3 , as defined by the molecule's C 3 rotation axis, was held so that it pointed directly at the Y atom, preventing an undesired rotation of the NH 3 . All other geometrical parameters were fully optimized. This restriction was required only when the base approached a shallow σ-hole that was unable to compete with a neighboring positive H. This situation arose when a tBu group was present or when the base approached the shallow CY σ-hole of the chalcogenazole ring.

The interaction energy for a NH 3 interacting with each of the two Y σ-holes is reported in Table 4. The deeper of the two σ-holes is listed first, which would place the base opposite the F for the first four rows, and the N of the ring in the last two rows. It is first clear that the chalcogen bond energies vary a great deal, from only 1 kcal/mol all the way up to nearly 20 kcal/mol. The trends of these energies largely mirror the σhole depths. In the first place, the deeper holes associated with Te manifest themselves in higher interaction energies, with S on the opposite end of this spectrum. The progressive replacement of the second F atom of FYF by Br, I, and then tBu which reduced V max , also lowers the interaction energy. In terms of the competition between the two σ-holes on each Y atom, it is the deeper of the two holes that is reflected by a higher interaction energy. And small differences in hole depth are indicative of similarly small differences in interaction energy for the most part although there are exceptions. For example, the N σ-hole of thioazole is deeper than its C analogue by a factor of 7, but there is only a three-fold difference in E int . And the two chalcogen bonds for the t-Bu derivative of selenazole are nearly equal despite a much deeper N than C hole. There is even a surprising pattern for tBu-tellurazole where the stronger chalcogen bond is associated with the shallower σ-hole. The perhaps disproportionate weakness of the N ChBs for the tBuring systems can be traced to the inability of the NH 3 to closely approach the Y center due to steric repulsion with the bulky tBu group (see below).

Geometries

In addition to the energetics, a second measure of ChB strength is the intermolecular distance. Given the varying size of each Y atom, it is preferable to consider the normalized distance R N in which the actual R(Y••N) is divided by the sum of the vdW radii of Y and N. These quantities are listed in Table 5 and are again reflective of the previous patterns. The weakening ChB with larger X in FYX or the addition of a tBu substituent appear as a growing R N , and this normalized distance diminishes with larger size of Y. On the other hand, these distances are not fully consistent when comparing the two σ-holes in a given system. In some cases, R N is shorter for the weaker of the two ChBs, particularly in the case of some of the ring systems. This anomaly is particularly obvious for the tBu ring systems in the last row where one again sees the steric bulkiness of the tBu group inhibiting the NH 3 from approaching as closely as it might otherwise do. These longer distances are also symptomatic of the presence of weak CH••N H-bonds to the NH 3 (see below).

A univalent halogen atom in a RÀX bonding situation can be thought of as containing three lone pairs, symmetrically disposed around the RÀX axis. The X σ-hole will thus lie directly along the extension of this axis, between the three lone pairs, with a θ(RÀXÀV max ) angle of 180°. The chalcogen atom in a divalent R 1 ÀYÀR 2 unit is different in that the two Y lone pairs lie above and below the molecular plane. Their high electron density will thereby tend to push the σ-hole lying opposite R 1 toward R 2 to a certain extent, and vice versa, so that the two θ(RÀYÀV max ) angles will be somewhat less than 180°, as reported in Table 3.

And indeed, this nonlinearity was found to be the case. For example, these angles were found to be equal to 173°, 169°, and 166°for FSF, FSeF, and FTeF, respectively. Overall, these angles were closest to 180°for the σ-hole lying opposite F, somewhat smaller for the shallower hole lying opposite the other halogen atom in FYX. The situation is somewhat different for the chalcogenazole rings where the hole lying opposite the N atom is displaced some 20-30°from the NÀY extension. A large part of this displacement occurs due to the proximity of the positive region surrounding the CH hydrogen center which partially merges with the σ-hole.

The specific position of the σ-hole is a primary force in guiding the geometry of the complex with NH 3 , but not the only factor. In most cases, the θ(RÀY••N) angle is a bit smaller, i. e. less linear, than would be predicted solely on the basis of V max location. This deviation, which amounts to several degrees, is partly due to the attraction between the positively charged NH 3 hydrogens and the negative charge of the neighboring halogen atom. These interactions do not amount to true Hbonds as judged by their geometrical aspects. Taking the FSeBr Lewis acid as an example, the H atoms of NH 3 lie 3.17 6, where their nonlinearity is evident. The deviation from 180°is quite small in many cases, although it can reach up to some 20°. With regard to the FYX Lewis acids, the deviation from linearity is larger for the weaker of the two ChBs, where the NH 3 is positioned opposite the less electronegative substituent. This pattern is consistent with the V max positions, where the σ-holes opposite these less electronegative groups also deviate by more from linearity.

Electronic Aspects

AIM analysis of the topology of the electron density furnishes an independent means of identifying the presence of both primary and secondary interactions, as well as a quantitative estimate of their strength. The electron densities are listed in Table 7 at the ChB bond critical points; any secondary bonds are placed in parentheses. These quantities generally reflect the energetic data. For example, ρ BCP diminishes as the X substituent in FYX transitions from F to Br to I to tBu. But there are exceptions as well. Whereas the FS••N ChBs are stronger than the XS••N bonds in the first four rows of the table, the same is not always true for Se and Te. Also there are two instances where the ρ BCP for ChBs involving Te are smaller than their Se correlates. In both of these instances, where FYF and FYBr interact with NH 3 through the σ-hole opposite the F atom, the R(Y••N) distance is considerably longer for Y=Te. The reduction in ρ BCP on going from Se to Te may thus reflect this ChB lengthening, since ρ BCP is well known to be very sensitive to the interatomic distance. [74] Certain of the systems also show evidence of a secondary bonding interaction in addition to the primary ChB. As In addition to providing insight into any charge transfers contributing to the stability of these dimers, NBO offers an independent means of identifying and quantifying any secondary bonding interactions. Table 8 lists the second-order perturbation energies E2 corresponding to the transfer of charge from the N lone pair of the NH 3 to the relevant σ* antibonding orbitals of the Lewis acid. The primary (1°) terms refer to the σ*(YR 1 ) orbital where R 1 lies opposite the NH 3 . There is also a certain amount of charge which accumulates in the other antibonding orbital involving Y and R 2 , where R 2 represents that atom not opposite the NH 3 , labeled 2°in Table 8.

The primary E2 in Table 8 are generally consistent with interaction energies. NBO correctly mirrors the weak interactions with the rings, as well as the rising ChB energy as the Y atom grows larger in these rings. On the other hand, some of the energetic trends are not duplicated correctly. For example, E2 is smaller for FTeX than for FSeX, even though the ChBs are stronger for the former. And E2 does not accurately reflect the diminishing E int as X in this series changes from F to Br to I to tBu, especially for Y=Te. Part of the reason for this different behavior of E int and E2 may arise as the electron density is drawn from the N lone pair of NH 3 for Se, but in the Te cases NBO extracts the required density from a σ-bond which it attaches between the Te and N atoms. There are also cases where E2 would predict a stronger ChB if the NH 3 were positioned opposite the less electronegative atom bound to Y. With regard to secondary interactions, the HBs identified for some of the complexes by AIM are confirmed by NBO. For example, both AIM and NBO suggest that the interactions between NH 3 and the tBu-rings are reinforced by HBs, which in some cases represent the stronger binding force.

It is clear that there are certain relationships between the interaction energy of a given ChB, and various geometrical and electronic parameters. The normalized intermolecular distance R N is indicated by the black points in Figure 4 that are plotted against E int as horizontal axis. (R N has been multiplied by 100 so as to allow inclusion of other quantities in Figure 4.) It is clear that stronger bonds to the right of the figure align with shorter distances. The curve of R N vs E int is not linear, with some divergence toward the left, so the linear correlation coefficient between these two quantities is only 0.75. Better linear correlations are achieved with the other three parameters included in Figure 4. The red points correspond to the depth of the σ-hole of the monomer, E2 is represented by the green points, and the bond critical point density by the blue points (with ρ multiplied by 1000 to again allow its inclusion in the figure). All these parameters grow along with the ChB strengthening, with linear correlation coefficients equal to 0.94, 0.81 and 0.86, respectively. So the best predictor as to the strength of any of these ChBs is the V max of the appropriate σhole within the Lewis acid monomer.

Internal Perturbations

With the formation of the ChB, and the associated transfer of charge into the YÀR 1 antibonding orbital of the Lewis acid, one would anticipate a certain degree of weakening of this internal covalent bond. This possibility can be assessed by examining the change in the bond critical point density arising when the two subunits combine to form a complex. As seen in Table 9, nearly all of these changes are negative and consistent with the idea of a bond weakening. These trends better reflect the E2 charge transfers in Table 8 than the interaction energies. For example, the density depletions of the YÀF bonds in the FÀYÀX series are largest for Se, followed next by Te and S, but both parameters have Te > Se for FÀYÀtBu. Consistent with the generally small E2 quantities for the S and Se rings, there are also small changes noted in Δρ BCP . There are several bonds which appear to undergo a slight strengthening upon dimerization, most notably the YÀC bonds to some of the tBu substituents.

The anticipated bond lengthening that ought to accompany a decrease of ρ BCP are in fact present, as evident by the positive values in Table 10. There is a solid if imperfect relationship between these bond elongations and the perturbation energies in Table 8 as well as the bond critical point density reductions in Table 9. As the R substituent in the FÀYÀR series transitions to a larger and less electronegative species, the degree of bond stretch is reduced. The bond lengths are more sensitive to ChB strength for the heavier R atoms, especially Br, as the YBr bond stretches more than does YÀF or YÀI. Bond length changes within the rings in the last two rows are generally quite small, consistent with the small changes in E2 or Δr. The relationship between these two measures of internal bond strength and the change in its length is pictured in Figure 5. (Δρ has been multiplied by 1000 so as to fit in the same diagram.) The correlation coefficient R 2 between Δr and E2 and Δρ are both equal to 0.81.

Possibility of Two Chalcogen Bonds

The formation of a ChB to one of the Y σ-holes will transfer a certain amount of charge to the Y atom, and thereby weaken its second σ-hole. In some cases, this hole will be so shallow that a second ChB is not possible, and in those cases where it occurs one can expect a good deal of negative cooperativity that ought to weaken the two ChBs. This issue was examined by placing one NH 3 near each of the two Y σ-holes and then optimizing the entire structure. (As in the dyad cases, it was necessary again to align the C 3 axis of the NH 3 along the N••C axis to avoid its rotation to unwanted interactions.) Several sample triads are pictured in Figures 1d and 3d.

Utilizing the Lewis acid as a double electron acceptor acts to lengthen each ChB within the triad relative to its length within each individual dyad in the absence of the other NH 3 . These bond elongations are enumerated in Table 11. Worthy of comment, the Lewis acids that cannot sustain both ChBs are indicated in Table 11 by an x. These systems comprise first the three S systems where the NH 3 would approach the position opposite a CÀS bond. This result is not surprising as the σ-holes were quite shallow to begin with in the monomer, only 3 kcal/ mol or less. And when complexed with NH 3 in the more stable position opposite the F or N, the V max of these holes sinks down below zero, as low as À6.5 kcal/mol. Also in this category is the tBu selenogenazole, again with a V max of only 4.2 kcal/mol, which drops down to À1.6 kcal/mol after the NH 3 has attached itself to the hole opposite the N. One might conclude from Tables 1 and 11 that the original V max of the uncomplexed monomer must be at least 6 kcal/mol for the molecule to sustain a second ChB.

Focusing first on the FÀYÀX units in the first three rows, the bond stretches are closely related to the strength of the other ChB. For example, the FSe••N ChB is stretched by 0.210 Å when a second FS••N bond is present, but this amount is drastically reduced to 0.117 Å if the second bond is the weaker BrSe••N, and down to only 0.065 Å for IS••N. Conversely, the weaker of the two ChBs, in this case BrSe••N and ISe••N are elongated by more than 0.16 Å by the addition of the stronger FSe••N ChB. These same trends are repeated for Y=Se and Te, although the magnitudes are reduced for Y=S. The ChBs to the chalcogenazole rings also elongate upon the addition of the second ChB, but by a smaller amount, less than 0.1 Å, consistent with their weaker nature.

The anticooperativity exerts an expected reduction in the interaction energies of each ChB. Table 12 lists the interaction energy between a given NH 3 unit and the Lewis acid-NH 3 dyad which it is approaching, all within the geometry of the fully optimized triad. The ChB energy reductions are quite sizable. For example, the FY••N ChBs in the first three rows of Table 12 are lower by some 9-37 % than the same bonds within the dyads. Although the magnitudes of the weaker XY••N ChB energies are smaller, their percentage drops remain high, between 22 and 28 %. Similar bond weakenings occur within those ring systems for which a triad is stable.

Discussion

The calculations described above show that both σ-holes connected to the central Y atom are deepened as either of the two R substituents becomes more electron-withdrawing. But there is a clear pattern that the deeper of these two holes, even if only by a little, is the one which lies opposite the more electron-withdrawing of the two substituents. This difference in hole depth is then reflected in a somewhat greater interaction energy. In the case where it is a C atom which is attached to Y, the σ-hole is rather shallow, particularly when Y is the lighter S chalcogen atom. In cases such as this, the ChB energy is small, on the order of only 1 kcal/mol. Indeed, the N lone pair must be forced to align with the Y atom or it is prone to rotate away from the C, toward a more favorable orientation. This ability of a shallow σ-hole, even one with a negative V max , to sustain a ChB was noted earlier [26] in the context of R 2 T=Y sorts of analogues of formaldehyde.

The preference of a base for the site on the chalcogen atom lying opposite the more electron-withdrawing substituent has been confirmed on numerous occasions [18,75] as have the deviations from linearity that are a common feature of ChBs. [10] In some of the cases discussed above, the difference in ChB energy between the two situations in which the base lies opposite the more electronegative atom, either F or N, was only slightly stronger than its position opposite that of lesser electronegativity. There was even one situation involving the tBu-tellurazole, where the two binding energies were reversed. This finding has certain similarities with an earlier examination of tetravalent S compounds, where Franconetti et al [76] had noted that a nucleophile can in certain instances prefer the σhole that lies opposite the less electron-withdrawing substituent. The authors were surprised to find that the hole opposite a NÀS bond is slightly deeper than that opposite a FÀS bond. They attributed this observation to substantial differences in polarizability between F and the competing substituent.

Given the importance of the relative depths of the two σholes on a given Y atom to their binding energies with a base, it is important to consider this issue in a bit more depth. The values reported in Table 1 were based on a single point, the maximum MEP on an arbitrarily assigned isodensity surface with ρ = 0.001 au. This point lies only roughly along the RÀY bond extension, at a variable distance from Y, which depends on the nature of the Lewis acid molecule and is somewhat different for the two σ-holes. In the case of FTeBr for example, V max opposite the F is situated 2.03 Å from Te, within 1°of FÀTeÀV max linearity. By way of comparison, the Br σ-hole is 2.42 Å from Te, and deviates from the BrÀTe axis by 12°.

In order to probe further, FSBr was taken as a representative case, as its two measured V max quantities are close to one another, 29.8 and 27.7 kcal/mol, respectively. The MEP around this molecule was mapped out at three specific distances from S, varying from 2.0 to 2.5 Å. As depicted in Figure 6, the θ angle measures the deviation of the point of reference from the Br-SÀF bisector; positive angles are displaced toward Br and negative toward F. For each of the three distances chosen, there are two maxima present. The precise position of the maximum shifts a bit as the distance d from S changes. For example, the maximum on the left, opposite Br, changes from about À52°for d = 2.0 Å, to À40°for d = 2.5 Å. But most importantly, for each distance d, the maximum on the right, lying roughly opposite the F atom, is higher than the Br maximum on the left. So the V max values in Table 1 which indicate that the σ-hole opposite the F is deeper than that for Br, is indeed a valid and more general conclusion, despite its evaluation on one specific and arbitrary isodensity surface. One might expect that the location of V max ought to dictate the angular positioning of the base. This supposition is largely supported by the computed data. In most cases, the θ(RY••N) angle is within a few degrees of θ(RY••V max ). The former tends to be slightly smaller than the latter, likely due to a weak electrostatic attraction between the halogen substituent of FÀYÀX and the H atoms of NH 3 . The situation is slightly different for the chalcogenazole rings. θ(RY••V max ) for the hole lying opposite the N is artificially small due to the partial coalescence of the Y σ-hole with the positive MEP surrounding the CH group of the ring, so is thus some 12°smaller than the ultimate θ(RY••N) within the ChB. This spurious angle reduction is removed when a tBu group is placed on the ring, leaving the hole nearly opposite the N. On the other hand, the NH 3 is drawn closer to the tBu by attractions between its N and the tBu H atoms so θ(RY••N) is some 10°less than θ(RY••V max ) for Y=S and Se. However, the greater strength of the Te••N ChB overcomes any tendency for the NH 3 to move toward the tBu, so this discrepancy vanishes.

The Lewis acids considered here cover a variety of different variations on the divalent binding theme. The FYX and FYtBu molecules offer a simple sp 3 hybridization and what might be thought of as a pair of "rabbit-ear" lone pairs, which reveal themselves as such in an ELF diagram for SeF 2 as an example in Figure 7a. The electronic structure within the chalcogenazole rings, on the other hand, is better characterized as sp 2 hybridization. One lone pair consists essentially of a p π orbital, perpendicular to the ring, and participating in the overall aromaticity. The second Y lone pair lies in the ring plane, roughly bisecting the CÀYÀN bond angle. The ELF diagram of selenazole in Figure 7b shows how these two lone pairs tend to merge with one another; comparison with Figure 7a clarifies the difference between the two lone pair dispositions. The overall similar behavior of the two sorts of Y bonding patterns suggests the generality of the principles discussed here.

One can apply these ideas in designing a system which will attract a nucleophile to a chosen site on a Lewis acid molecule. In the first place, a larger chalcogen atom such as Te would offer the deepest pair of σ-holes, and most strongly attract the base, although even a smaller S atom could serve this same purpose in the right circumstances. Secondly, the potential ChB would be strengthened by adding two electron-withdrawing substituents to the Y atom in question. If there is a preference as to which of the two σ-holes of Y is to be occupied, tuning down the electron-withdrawing power of one substituent would push the nucleophile toward the site opposite the other group, although there would be a small sacrifice in terms of the overall ChB strength.

There is quite a bit of support for the idea that the chalcogen atom can engage in two ChBs simultaneously, with one nucleophile attached to each of its two σ-holes. A recent review of crystal structures [77] indicated that chalcogen atoms, particularly Te, can be involved in two ChBs with N atoms at the same time. [78] Common examples arise in the context of chalcogenadiazoles [79][80][81] where negative cooperativity was observed. In fact, both of the electron donor atoms can be part of the same anionic electron donor, as in the case of (SO 4 ) 2À . [82] There are several other cases where Te appears to participate in more than two ChBs, although some of the intermolecular distances are perhaps too long to be considered as true bonds. [83] Multiple ChBs to the same Se have also been observed. [84] Other instances of multiple ChBs occur within the context of triangular arrangements of the three atoms, [64,85] Y=C = Y molecules, [86] or hypervalent bonding situations. [87] Tetravalent chalcogen atoms as in the context of YF 4 also appear capable of sustaining two ChBs, [88] with the binding energy rising quickly with the size of the Y atom. The single σhole present in a linear molecule such as OSY can also bind to two separate electron donor atoms in a bifurcated ChB. [89] However, it should be understood that participation in two simultaneous ChBs places the acid molecule in the unfavorable position of serving as a dual electron acceptor, and the attendant anti-cooperativity makes each such ChB weaker than it would be in the absence of the other. As a corollary of this effect, a normally weak ChB to a shallow σ-hole might disappear entirely if there is already an interaction involving the deeper of the two holes. Consequently, the possibility of a pair of ChBs is enhanced if the central Y atom is a large one like Te, or if the two substituents are electron-withdrawing.

It should be emphasized that the principles enunciated here were developed for a divalent chalcogen atom, characterized by two covalent bonds and a pair of σ-holes. When placed in a hypervalent situation, the principles must be adjusted accordingly. For example, in a tetravalent molecule like YF 4 the four YÀF bonds are arranged in a modified trigonal bipyramid shape, with only a single lone pair on Y, occupying one of the equatorial positions. [90][91][92][93] Either of the 2 σ-holes associated with the two equatorial YF bonds is capable of engaging in a strong ChB with NH 3 , [92] varying from 8 kcal/mol for SF 4 up to 22 kcal/ mol for TeF 4 . This bond induces a substantial deformation of the YF 4 unit into a sort of octahedral structure, with NH 3 occupying one leg, and the Y lone pair another. Hexavalent YF 6 , on the other hand, assumes an octahedral geometry in which each YÀF bond is directly opposite another. There are hence no σ-holes which preclude formation of a ChB.

Conclusions

Overall, the ChBs formed by the divalent R 1 YR 2 molecules considered here run a full gamut of interaction energy varying from only 1 kcal/mol all the way up to nearly 20 kcal/mol. The strengths of these bonds, which rise along with the size of the chalcogen Y atom: S < Se < Te, is closely related to the depth of the σ-hole to which the base, in this case NH 3 , is attached. The depth of each of the two σ-holes on Y is diminished by a lowering electronegativity of both groups R 1 and R 2 . The deeper of these two σ-holes is the one lying directly opposite the more electronegative substituent. This difference in depth is not particularly large when both substituents are halogen atoms, but becomes much more substantial if Y is connected to a considerably less electronegative C. This distinction in V max is reflected in the ChB energy which is larger when the base positions itself opposite to the more electronegative group. Nonetheless, the Y atom is capable of engaging in a ChB utilizing even its secondary shallow σ-holes, in some cases with a very small or even slightly negative V max .

The formation of each ChB induces a weakening of the internal covalent bonds within the R 1 YR 2 entity, which is reflected in a lowering of the bond critical point density as well as an elongation of the YÀR covalent bond. Likewise, the attachment of a base to one σ-hole weakens the other hole, and lessens its ability to engage in a second ChB. Consequently, those Lewis acids with a shallow hole in their monomer are unable to form a second ChB. Nevertheless, most of the R 1 YR 2 Lewis acids examined here are capable of engaging in two simultaneous ChBs of moderate strength, some exceeding 12 kcal/mol, despite an anticooperativity-induced weakening of between 10 % and 40 %.