Pseudo-Bifurcated Chalcogen Bond in Crystal Engineering

The concept of pseudo-bifurcated chalcogen bond has been proposed for the first time in this paper. It was found that the anticooperative effects between two chalcogen bonds of the pseudo-bifurcated chalcogen bond are not very large as compared to those of the true bifurcated noncovalent bond. According to the nature of pseudo-bifurcated chalcogen bond, we designed some strong pseudo-bifurcated chalcogen bond synthons. The binding energy of the strongest pseudo-bifurcated chalcogen bond attains about 27 kcal/mol. These strong pseudo-bifurcated chalcogen bond synthons have great potential as building blocks in crystal engineering.


Introduction
The effectiveness of the halogen bond in crystal engineering has been widely documented over the past decade [1][2][3][4][5][6][7][8][9][10][11][12].In contrast, the study of the chalcogen bond, another type of noncovalent bond in which chalcogen acts as an electron acceptor, is still in its infancy, and many more studies must be carried out to understand the value of the chalcogen bond in crystal engineering .Both the halogen bond and the chalcogen bond are of the σ-hole bond [39][40][41][42].It is the regions of positive electrostatic potential on the outer surfaces of halogens and chalcogens that lead to the formation of the halogen bond and chalcogen bond (Figure 1).The structures and properties of the halogen bond and chalcogen bond are very similar.For example, in most cases, both are highly directional, electrostatically-driven noncovalent interactions [41,42].However, as shown in Figure 1, halogens have only one electrophilic end whereas chalcogens always have two electrophilic ends, which causes that the structures and properties of the chalcogen bond may also be different from the ones of the halogen bond.At least, it is natural to suppose that the formation of the bifurcated chalcogen bond is much easier than the formation of the bifurcated halogen bond.
To better understand the difference between the halogen bond and the chalcogen bond, we carried out a statistical analysis of the iodine bonds and selenium bonds with nitrogen acceptors using the Cambridge Structural Database (CSD, version 5.27, November 2006 plus 31 updates, ConQuest version 1.8) [43,44].The iodine bond is a subset of the halogen bond and the selenium bond is a subset of the chalcogen bond [7].For simplicity, we did not consider the other subsets of the halogen bond and chalcogen bond.For the CSD search, only structures with not disordered, no errors, not polymeric, and no ions were considered.At the same time, the following general search filters were also chosen from the ConQuest search menu: 3D coordinates determined, only organics, and R factor < 0.05.It can be clearly seen from Scheme 1 that the CSD search yields 465 individual crystal structures containing the iodine bonds and 120 individual crystal structures containing the selenium bonds.Among each kind of crystal structures, the percentage of the crystal structures containing the bifurcated iodine bonds and bifurcated selenium bonds are 3% (16 hits) and 22% (26 hits), respectively.This result supports the above hypothesis that the formation of the bifurcated chalcogen bond is much easier than the formation of the bifurcated halogen bond.Considering that the selenium atoms have two electrophilic regions and a noncovalent bond is always defined as a net attractive interaction between an electrophilic region and a nucleophilic region [6], the 6 bifurcated selenium bonds actually are not true bifurcated selenium bonds.Evidently, each of them also cannot be regarded as a simple combination of two separate selenium bonds.Consequently, the term "pseudo-bifurcated" selenium bond should be a more accurate descriptor of this kind of noncovalent bonds.Similarly, the pseudo-bifurcated selenium bond is also a subset of the pseudo-bifurcated chalcogen bond.We did not find the pseudo-bifurcated chalcogen bonds with two bond angles less than 150 • in the CSD.Hence, the pseudo-bifurcated chalcogen bond can be defined as the bifurcated chalcogen bond which has two bond angles in the range of 150-180 • .
The aim of this paper is two-fold.First, we will compare the difference between the pseudo-bifurcated noncovalent bonds and the true bifurcated noncovalent bonds.Second, according to the nature of the pseudo-bifurcated chalcogen bond, we will design some strong pseudo-bifurcated chalcogen bond synthons which may have great potential in crystal engineering.

Computational Details
In the present study, selecting selenium dicyanide [(NC) 2 Se], sulfur dicyanide [(NC) 2 S], tellurium dicyanide [(NC) 2 Te] and iodine cyanide (NCI) as chalcogen (halogen) atom donors and hydrogen cyanide (HCN), 1,10-phenanthroline (Phen) and N,N,N ,N -tetramethyl-ethane-1,2-diamine (TMEDA) as chalcogen (halogen) atom acceptors, we studied the structures, energies and properties of the complexes formed by these chalcogen (halogen) atom donors with these chalcogen (halogen) atom acceptors.For all the model complexes considered in this paper, the geometries were fully optimized, and the binding energies were calculated at the B3LYP-D3/def2-TZVPP level of theory [45,46].Here, B3LYP-D3 is the standard B3LYP method which is added by the D3 version of Grimme's dispersion with Becke-Johnson damping [47].The reliability of the B3LYP-D3 method for the study of the noncovalent complexes can be found elsewhere [45].It is well known that the accuracy of density functional theory calculations also depends on the number of points used in the numerical integration.An "ultrafine" integration grid (99 radial, 590 angular points) is used for all the density functional theory calculations to avoid the possible integration grid errors.The binding energies were calculated with the supermolecule method and corrected for basis set superposition error using the counterpoise method of Boys and Bernardi [48].All the calculations were carried out with the GAUSSIAN 09 electronic structure program package [49].
Bader's "atoms in molecules" (AIM) theory, which is based on a topological analysis of the electron charge density and its Laplacian, has been widely applied in the study of the noncovalent bonds [50][51][52].In this study, AIM analysis was also performed with the AIM2000 software package using B3LYP-D3/def2-TZVPP wave functions as input [53].

Results and Discussion
What is the difference between the pseudo-bifurcated noncovalent bonds and the true bifurcated noncovalent bonds?To answer this question, we selected the complexes NCI   2 shows the bond lengths, bond angles and bond strengths of the noncovalent bonds in these complexes calculated at the B3LYP-D3/def2-TZVPP level of theory.From NCI•••NCH to NCI•••(NCH) 2 , the bond strength (binding energy) of the I•••N noncovalent bond varies from 6.17 to 2.00 kcal/mol, which means that the formation of the bifurcated iodine bond weakens the I•••N noncovalent bond by a surprising amount, about 68% of its magnitude.Along with this weakening, there is a large stretch of the bond length (I•••N distance) by 0.357 Å, and the bond angle (∠C−I•••N) becomes a lot more nonlinear.Like the case in the bifurcated hydrogen bond, it is the repulsion of two halogen bond acceptors that results in the weakening of each I•••N noncovalent bond [54].As a comparison, the formation of the pseudo-bifurcated selenium bond weakens the Se•••N noncovalent bond by only about 16%.The Se•••N distance is elongated by only a very small amount (0.049 Å) and the bond angle (∠C−Se•••N) is decreased by only 3 • upon the pseudo-bifurcated selenium bond formation.The results presented here illustrate that the two noncovalent bonds of either the true bifurcated noncovalent bond or the pseudo-bifurcated noncovalent bond reduce the strengths of each other, indicating anticooperativity.However, the anticooperative effects between two chalcogen bonds of the pseudo-bifurcated chalcogen bond are not very large as compared to those of the true bifurcated noncovalent bond.In fact, the nature of true bifurcated noncovalent bonds is that the directionality of two monocoordinate noncovalent bonds is largely destroyed.However, in the pseudo-bifurcated chalcogen bonds considered here, the directionality of two monocoordinate chalcogen bonds is kept very well, which is totally different from the true bifurcated noncovalent bonds.That is also why we use the term "pseudo-bifurcated chalcogen bond".It is clear from Figure 2 that the strength of the pseudo-bifurcated chalcogen bond is about twice that of the "two-centered" chalcogen bond.With this in mind, we can design some strong pseudo-bifurcated chalcogen bond synthons which may have great potential in supramolecular chemistry.Figure 3 shows six complexes containing the pseudo-bifurcated chalcogen bond synthons.In these complexes, (NC) 2 S, (NC) 2 Se and (NC) 2 Te are the chalcogen atom donors; Phen and TMEDA are the chalcogen atom acceptors.In a recent paper, Murray, Resnati and Politzer studied the network of (NC) 2 Te molecules linked by many Te•••N close contacts [55].The pseudo-bifurcated chalcogen bond synthons we designed here are formed between only two molecules.As can be seen in Figure 3, the strengths of the pseudo-bifurcated chalcogen bonds are all larger than 12 kcal/mol.Therefore, the pseudo-bifurcated chalcogen bonds designed here may be used as strong synthons in crystal engineering.Chalcogen polarizability increases in the order O < S < Se < Te [56].Thus, the strength of the pseudo-bifurcated chalcogen bond also increases in the order O < S < Se < Te.On the other hand, the sp 3 hybridized N atoms in TMEDA are much more nucleophilic than the sp 2 hybridized N atoms in Phen.Therefore, as expected, the strongest pseudo-bifurcated chalcogen bond is found in (NC) 2 Te•••TMEDA in which the binding energy is 25.34 kcal/mol.The S(Se,Te) •••N distances are also listed in Figure 3. Evidently, the strengths of the pseudo-bifurcated chalcogen bonds are inversely proportional to the S(Se,Te) •••N distances.
Both symmetric pseudo-bifurcated chalcogen bonds and asymmetrical pseudo-bifurcated chalcogen bonds have been found in the CSD.For example, the symmetric pseudo-bifurcated chalcogen bonds was found in the crystal structure of 4H,8H-4-(dicyanomethylene)benzo[l,2-c;4,5-c ]bis[l,2,5]thiadiazole (CSD entry code: GEFVOC10) [57]; the asymmetrical pseudo-bifurcated chalcogen bonds was found in the crystal structure of 4,7-difluoro-5,6-dimethoxy-2,1,3-benzoselenadiazole (CSD entry code: NABSER) [58].The pseudo-bifurcated chalcogen bonds considered in Figure 3 are all of symmetric type.Figure 4 lists the bond lengths, bond angles and binding energies of the symmetrical pseudo-bifurcated chalcogen bond and the asymmetrical pseudo-bifurcated chalcogen bond.Obviously, the strength of the symmetrical pseudo-bifurcated chalcogen bond is almost the same as the strength of the asymmetrical pseudo-bifurcated chalcogen bond.Although similar in strength, the number of asymmetrical pseudo-bifurcated chalcogen bonds is much larger than the number of symmetrical pseudo-bifurcated chalcogen bonds because of the entropy effect.5.For the noncovalent bond, the electron density at the BCP is relatively low in value, and the value of the electron density Laplacian is positive [50].As shown in Figure 5, the values of the electron density at the BCPs of the S(Se,Te)•••N contacts range from 0.0198 to 0.0312 au, and the corresponding values of the electron density Laplacian range from 0.0587 to 0.0671 au.These values appear to meet the two criteria above, indicating that the S(Se,Te)•••N contacts are typical noncovalent bonds.Except for the pseudo-bifurcated chalcogen bonds, there are no other noncovalent bonds in the four complexes.This is very important because it rules out the possible effects of other noncovalent bonds.The results of the AIM analyses also confirm that it is reasonable to use the binding energy of a complex as the strength of a pseudo-bifurcated chalcogen bond.

Conclusions
In the present study, we have proposed a new kind of noncovalent bond-pseudo-bifurcated chalcogen bond-since the chalcogens may have two electrophilic σ holes.The difference between the pseudo-bifurcated noncovalent bonds and the true bifurcated noncovalent bonds was investigated by using the dispersion-corrected density functional theory calculations.It was found that the anticooperative effects between two chalcogen bonds of the pseudo-bifurcated chalcogen bond are not very large comparing with those of the true bifurcated noncovalent bond.According to the nature of pseudo-bifurcated chalcogen bond, we designed a series of strong pseudo-bifurcated chalcogen bond synthons of which the strengths are all larger than 12 kcal/mol.We wish these strong pseudo-bifurcated chalcogen bond synthons to have great potential in crystal engineering.

Figure 1 .
Figure 1.The electrostatic potentials on the 0.0004 au isodensity surfaces of NCI and (NC) 2 Se with a scale of −28.24 to +40.79 kcal/mol.

Figure 4 .
Figure 4. Bond lengths (black numbers, in Å) and bond angles (blue numbers, in • ) of the symmetrical pseudo-bifurcated chalcogen bond and the asymmetrical pseudo-bifurcated chalcogen bond.The binding energies (in kcal/mol) are represented by red numbers.

Figure 5
Figure 5 shows the molecular graphs for the complexes (NC) 2 S•••Phen, (NC) 2 Se•••Phen, (NC) 2 Te•••Phen, (NC) 2 S•••TMEDA, (NC) 2 Se•••TMEDA and (NC) 2 Te•••TMEDA.The bond critical points (BCPs) of the S(Se,Te)•••N contacts and the bond paths associated with the S(Se,Te)•••N BCPs can be clearly seen in Figure5.For the noncovalent bond, the electron density at the BCP is relatively low in value, and the value of the electron density Laplacian is positive[50].As shown in Figure5, the values of the electron density at the BCPs of the S(Se,Te)•••N contacts range from 0.0198 to 0.0312 au, and the corresponding values of the electron density Laplacian range from 0.0587 to 0.0671 au.These values appear to meet the two criteria above, indicating that the S(Se,Te)•••N contacts are typical noncovalent bonds.Except for the pseudo-bifurcated chalcogen bonds, there are no other noncovalent bonds in the four complexes.This is very important because it rules out the possible effects of other noncovalent bonds.The results of the AIM analyses also confirm that it is reasonable to use the binding energy of a complex as the strength of a pseudo-bifurcated chalcogen bond.