Halogen bonds (XB) bear a striking resemblance to the more commonly observed and thoroughly studied H-bond (HB). As has been deduced over many years [1
], the latter is stabilized in large measure by an electrostatic attraction between the partial positive charge on the bridging proton of the acid and a negative region on the base, typically a lone pair. Therefore, the replacement of this H by a more electronegative X atom would at first sight seem counterintuitive, as one might initially conclude that the interaction ought to be repulsive. However, this paradox is resolved by the inspection of the disposition of the electrostatic potential about the X center, which includes a negative equator region surrounding a positive pole along the extension of the R-X bond, which can in turn attract the nucleophile. Due to its depletion of electron density, this latter positive region is commonly dubbed a σ-hole. As in the HB, the electrostatic attraction is complemented by other factors, most notably a charge transfer from the lone pair of the nucleophile to the σ*(RX) antibonding orbital of the Lewis acid unit [12
There have been numerous observations of XBs within the context of crystals over the years, encompassing close encounters between an X atom and a nucleophile. Of particular interest have been those in which the atom of the nucleophile which most closely approaches X is itself a halogen atom [26
]. An example of such an X··X halogen bond is illustrated in Figure 1
a for the FBr dimer, where the σ-hole of the Lewis acid on the left is indicated by a positive conical region which is also coincident with the σ*(BrF) orbital. One of the Br lone pairs on the base unit is illustrated by a negative region which is aligned with the positive σ-hole, as well as the σ*(BrF) orbital for optimal charge transfer. This sort of arrangement is commonly referred to as Type II (T2) in the crystallography literature.
This configuration contrasts with T1 in Figure 1
b, which is much more symmetrical with approximately equal FBr··Br angles. While the bending of the two molecules away from T2 deteriorates the alignment of the σ-hole of the molecule on the left and the lone pair on the right relative to T2, it also leads to a second and converse partial alignment of the lone pair on the left with a σ-hole on the right. Recent calculations [40
] have shown that this pair of distorted XBs in T1 is only slightly less stable than the perfectly aligned single XB in T2. In fact, T1 does not represent a true minimum for the potential energy surface of this dimer, but is rather a transition state for the conversion of the T2 pictured in Figure 1
a with its converse, where the two molecules reverse their role of electron donor and acceptor [40
]. However, importantly, the energy difference between T2 and T1 is quite small, on the order of only 1 kcal/mol or less, for a wide selection of FX1
F dimers. It is because of this small energy difference that there have been nearly as many observations of T1-like geometries of X··X contacts within crystals as for the slightly more stable T2.
The widespread occurrence of both T1 and T2 structures leads to the obvious question as to whether such competitive geometries are limited to only halogen-bonded systems. The recent literature is replete with many observations of the very closely related chalcogen bonds (YBs), where X is replaced by S, Se, or Te [14
]. Just as halogen atoms are typically univalent, the most common bonding pattern around a given Y chalcogen atom is divalent. In one such pattern, sp2
Y engages in a double bond with C, as in analogues to formaldehyde. One would expect a σ-hole on the Y, lying along the extension of the C=Y bond, flanked by a pair of lone pairs within the molecular plane. This sort of molecule can potentially form homodimers of both T2 and T1 type, much akin to XBs, as illustrated in Figure 1
c,d, respectively, for the F2
The chalcogen atom can forsake a double bond, engaging instead in a pair of single bonds, as in YR1
. This variation leads to not one but two σ-holes, one along the extension of each of the two YR bonds. The two lone pairs within this sp3
Y hybridization lie above and below the plane of the molecule. The T2 sort of classical chalcogen bond in Figure 1
e for the SeFH homodimer aligns one of the Se σ-holes of the Lewis acid on the left with one of the two Se lone pairs of the base on the right. The T1 arrangement in Figure 1
f again contains the essential elements of a duo of distorted YBs (this formulation is fundamentally unchanged if the two Y lone pairs arise from an alternate sp2
hybridization, with an occupied p-orbital perpendicular to the molecular plane, representing one of the lone pairs).
The work described below considers the potential of both T2 and T1 structures to serve as valid geometrical motifs for Y··Y chalcogen bonds in a fashion parallel to XBs. Units examined contain both sp2 and sp3 hybridizations of the Y atom, via R1R2C=Y and R1R2Y, where R1 and R2 refer to either H or the strongly electronegative F. Y atoms span the chalcogen family: S, Se, and Te. Homodimers of each of these molecules are examined to determine the stabilities of both T1 and T2 arrangements. Issues of concern include first whether such geometries constitute true minima on the potential energy surface, and how their stabilities compare with one another. Taking into account that most YBs in the literature are heterogeneous, in that the electron donor atom is much more electronegative than S, Se, or Te, how strong are the homogeneous Y··Y chalcogen bonds considered here? Is there a difference between S, Se, and Te with regard to these issues? Another question relates to how the substitution of H by F affects the binding, and how the overall energetics vary along the S, Se, Te sequence. Can one relate the stabilities of the T1 and T2 isomers, and their energy difference, to the maxima and minima of the electrostatic potential surrounding each monomer? As another issue, the bulk of earlier studies of chalcogen bonds include a highly electronegative atom such as O or N, or even an anion, as the electron donor. Consideration of YBs between pairs of like chalcogen atoms are much rarer. The work described below considers a much less electronegative chalcogen atom as both donor and acceptor.
A comparison of the minima on the surfaces of the chalcogen-bonded dimers here, and the previously studied halogen bonded analogues, reveals both similarities and differences. For the FX··XF dimers, the T2 geometries represented minima on the surface, whereas the symmetric T1 structures did not. Each of the latter instead comprised a transition state, separating one T2 geometry from its equivalent counterpart where the role of electron donor and acceptor were reversed. As such, the T2 structures are universally lower in energy than T1, although this energy difference is not necessarily very large.
The situation for the YB systems is more nuanced. Some T2 geometries are true minima, as for example TeCF2 and SeF2, whereas a number of others require a geometric restriction such as enforced FY··Y linearity. Unlike the FX dimers, some of the T1 geometries are true minima for the Y-bonded systems; others occur only if the symmetry is enforced by equal RY··Y angles. This restriction seems to be necessary only for the molecules with a poorly developed σ-hole, such as YH2 or YCH2.
One point of similarity between the XB and YB dimers lies in the greater stability of the T2 geometry as compared to T1, for the doubly bonded R1R2C=Y complexes. In most cases, this energy difference was a small one, considerably less than 1 kcal/mol. However, this situation reversed itself for the FX dimers, in that it was the symmetric T1 geometries that were more stable for the smaller R1R2Y homodimers. These singly bonded cases had stronger bonding overall, in addition to a large difference between T1 and T2. On the other hand, this exaggerated stability of the YF2 T1 homodimers must be considered in the light of the actual bonding pattern. These complexes forgo the Y··Y chalcogen bonds of the majority of the other structures considered here, in favor of a pair of Y··F interactions that take advantage of the negative MEP associated with the very electronegative F atom. They are perhaps supplemented by an AIM bond path between the same two F atoms, although this particular interaction is absent in NBO analysis.
As the Y atom grew larger, and more polarizable and electropositive, it is natural that its σ-hole deepened, as was indeed found to be the case. At the same time, one would expect that the MEP of the Y lone pair should change in the opposite direction, becoming less negative. If such were the case, then these two effects might counteract one another, and the Y··Y chalcogen bond strength ought not change much. However, it was found that the transition from S to Se to Te had very little effect upon the MEP of the Y lone pair. It was therefore the σ-hole depth that dominated the trend, causing the YB strength to increase with larger Y.
Conversely, one can consider the trends in MEP maximum and minimum as the F atoms were replaced by H. Taking the R1R2CY case first, each such replacement removed one electron-withdrawing substituent, thereby weakening the positive σ-hole. This same substitution allowed the lone pair MEP minimum to become more negative, so there was a certain degree of cancellation between these two trends. It is for this reason that the interaction energies of these R1R2CY homodimers were only mildly sensitive to these F→H replacements.
The patterns in the MEP extrema are a bit more complicated for the R1
Y units. There was, indeed, a substantially more negative Y lone pair MEP minimum as each F changed to H. However, the first such substitution from YF2
to YFH had very little effect on the Y σ-hole depth. This insensitivity was largely due to the proximity of the H atom of YFH to the σ-hole lying opposite the F. The positive MEP surrounding this H was able to partially blend in with this σ-hole (see Figure 2
e), thereby magnifying what would otherwise be a shallower hole. Consequently, this morphing of YF2
to YFH changed the interaction energy by less than it would have otherwise. The low polarizability of the SH bond left the SH2
molecule without a formal σ-hole, and those of SeH2
were considerably smaller than in their fluorinated counterparts. Even if the Y atom of one YH2
was restricted to the HY axis extension of the other, the former rotated around so as to present its positive H atoms toward the negative lone pairs of the latter molecule, forsaking any possible Y··Y YB in favor of YH··Y H-bonds. In other words, the very diffuse positive region of one Y is incapable of successfully engaging with the negative Y lone pair of its partner.
It was noted above that Lewis acids with shallow, or even nonexistent, σ-holes such as the YCH2
units here are able to engage in a YB with a base, albeit one with a small interaction energy of less than 2 kcal/mol. This ability confirms an earlier work [74
], where a similar finding extended to a range of other R1
T=Y units where T referred to a general tetrel atom. It was further found there that these shallow energy minima could be deepened if the system was immersed in a solvent. Reservations have been expressed with an overemphasis on MEP extrema such as σ-holes as a means to analyze some noncovalent bonds, as for example a recent work [75
] that stressed the importance of HOMO–LUMO interactions.
Chalcogen bonds between a pair of like Y atoms have also been examined in the context of thiophene, selenophene, and tellurophene homodimers [76
] where the Y atom is embedded within a C4
Y aromatic system. These optimized dimers closely resemble the symmetric T1 geometries and take on a similar bonding pattern, as introduced in Figure 3
d. Interaction energies of 1.5–2.3 kcal/mol were computed, in the same range as those of the simpler nonaromatic R1
T=Y systems studied here, where the Y atom was also sp2
-hybridized; the AIM bond critical point densities were also quite similar.
Although sparser than the ample literature regarding YBs with electronegative atoms, such as O and N as electron donors, there is some prior evidence of bonds involving S, Se, and Te as both donor and acceptor [77
]. A recent review [82
] of such Y··Y interactions summarized a good deal of the literature up through 2018, and demonstrated that such YBs between divalent chalcogen atoms are not uncommon in the solid state and solution, and they can play an active role as intramolecular bonds in molecular conformation. Those involving Te tend to be the strongest.
Buralli et al. [83
] examined (R1
C complexes where R1
refer to various small substituents. The calculations restricted these systems to a fully linear CSe··SeC arrangement, and arrived at interaction energies between 1 and 2 kcal/mol, although these structures were not true minima. S··S YBs occurred in a secondary minimum structure when dimethyl sulfide combined with 2,2,3,4-tetrafluoro-1,3-dithietane, with both S atoms in sp3
] in solution. The authors surmised that this S··S interaction was no weaker than that between S and O.
Recent quantum calculations [85
] considered Y=C=Y units in geometries akin to the T1 and T2 structures described above. Computed interaction energies were in the same range as noted above for R1
C=Y homodimers, and in another point of agreement the T1 and T2 stabilities were quite similar for these two geometry types. A search of the CSD carried out by these authors identified a number that they classified as T1, but T2 was less prevalent, despite its lower energy in their quantum calculations. Arrangements akin to T1 were observed in crystals and studied by model Te(CH2
] in tubular packing. An earlier survey of the CSD [87
] considered the C=S···S=C motif involving exclusively sulfur and identified quite a number of T1 sorts of geometric dispositions. Their quantum calculations found true T1 minima for X2
CS dimers for X=NH2
, OH, and F, but not for H and Cl. Their computed binding energies for (H2
closely match the data reported here for these homodimers.
Other studies of Y··Y interactions focused on the triangular variety involving three Y atoms in a roughly equilateral triangle arrangement, which occurs on occasion within the CSD [88
]. Calculations confirmed the strengthening effect of enlarging the three Y atoms.