Hydrogen Bonds of C=S, C=Se and C=Te with C-H in Small-Organic Molecule Compounds Derived from the Cambridge Structural Database (CSD)

Considerable interest in hydrogen bonding involving chalcogen has been growing since the IUPAC committee has redefined hydrogen bonding. Not only the focus is on unconventional acceptors, but also on donors not discussed before. It has been mentioned in previous studies that the proton of the H-C group could be involved in hydrogen bonding, but with conventional acceptors. In this study, we explored the ability of hydrogen bond formation of Se, S and Te acceptors with the H-C donor using Cambridge Structural Database in conjunction with Ab Initio calculations. In the CSD, there are respectively 256, 6249 and 11 R 1 ,R 2 ,-C=Se, R 1 ,R 2 ,-C=S and R 1 ,R 2 ,-C=Te structures that form hydrogen bonds, in which the N,N groups are majority. Except for C=S acceptor which can form a hydrogen bond with its C, C group, both C=Se and C=Te acceptors could form a hydrogen bond only with N,C and N,N groups. CSD analysis shows very similar d (norm) around −0.04 Å, while DFT-calculated interaction for N,C and N,N groups are also similar. Both interaction distances derived from CSD analysis and DFT-calculated interaction energies demonstrate that the acceptors form stable complexes with H-CF 3 . Besides hydrogen bonds,


Introduction
Selenium, sulphur and tellurium, of respectively atomic numbers 34, 16 and 52 are chalcogens and share properties with oxygen and polonium, all of which have six valence electrons, although oxygen is sometimes excluded from the collective term "chalcogen". The importance of chalcogen is known and has been demonstrated [1]- [8]. Significant interest in hydrogen bonding involving chalcogen has been growing since the IUPAC committee has redefined hydrogen bonding. Not only the focus is on unconventional acceptors, but also on donors not discussed before. It has been mentioned in previous studies [9] [10] that the proton of the H-C group could be involved in hydrogen bonding, but with conventional acceptors.
Due to the importance of both inorganic and organic chalcogens, we are embarking on a series of studies of the structural chemistry of small-molecule Se, S and Te compounds, with an emphasis on their intermolecular interactions in crystal structures. In this paper, we report a general survey of both three chalcogens in small-molecule crystal structures, before examining the ability of them to accept H-C hydrogen bonds in [(NH 2 ) 2 -C=X], [(NH 2 ),C-C=X, and [(C) 2 -C=X] models. This work builds on earlier studies of the hydrogen-bonding ability of analogous C=Se and C=S acceptors with O-H and N-H donors [14]. Surveys and analyses of the Cambridge Structural Database [15] [16] have been used in conjunction with Ab Initio and DFT calculations of model systems using Gaussian 09 [17] to probe hydrogen bonding in terms of structure, energetics and electrostatics.

CSD Analysis
We performed the CSD analysis using an analogous approach to that outlined elsewhere [14] using CSD version 5.41 (November 2019) including the November data update, which has a total of 1,034,174 structural entries. Geometric parameters (d distance, rho, phi and theta angles) for intermolecular interactions between H-bond acceptors (C=Se/S/Te) and donors (QA) were performed according to Figure 1.
In addition, we calculated the van der Waals normalized hydrogen-bond dis- where d is the hydrogen bond distance, H and X are respectively the hydrogen and acceptor atoms, vdW(H) and vdW(X) are the van der Waals radii of the H and acceptor atoms respectively.

Computational Studies
To complement the database results, a series of calculations were carried out with the density-functional theory (DFT) method using Gaussian 09 [17]. The B3LYP [18] [19] [20] three-parameter hybrid functional and the B3LYP augmented with the D3 dispersion correction [21] were used with the basis set of 6-311++G(3df,2p). Use of this large basis set should minimize the problem of correction for the basis set superposition error [22] [23] [24]. Both approaches were used to calculate atomic partial charges, molecular electrostatic potentials and energies of interaction, but also to perform NBO analysis.
The electrostatic potential V(r) in the space around a molecule, created by the electrons and nuclei at any point r, was calculated according to the Equation (2), written in atomic units, a.u.: and acceptor (E acceptor ) using optimised geometries: Vibrational analysis was also performed calculated with all DFT levels of theory to determine true minima and saddle points of different orders.

Initial Survey of Se Compounds in the CSD
We start with a brief overview of compounds containing the three chalcogens X (X = Se/S/Te) of CSD. The complete CSD (all inputs, without secondary filters applied) contains 13 Tables  1-3 together with the data for R 1 = C, and R 2 = C. Tables 1-3 generally show that the average lengths of the C=X and C-N bonds vary with the R 1 and R 2 substituents, and also with the hybridization of the carbon atom. This tendency is also presented by C=O acceptors [25] [26]. The length of the C=X bond increases in the sequence C 4 ,C 4 -C=X<N 3 ,C 4 -C=X<N 3 , C 3 -C=X <N 3 ,N 3 -C=X. The average C-N bond is longer for N,N-C=X than for  N,C-C=X, consistent with the data for the C=O and C=S analogues [26] and as expected from the resonance model.
In relation with our earlier work [14] and the previous studies by Allen [25] and Blessing [27], for ureas and thioureas respectively, but higher than the value of −0.645 [14] for selenoureas.

Occurrence of Hydrogen Bonds Involving C=S, C=Se and C=Te
An initial survey in the CSD showed that there are 7146 compounds R 1 ,R 2 -C=S, with R 1 and R 2 assigned as any type of atom (X), which formed hydrogen bonds with OH, NH or CH donors, and 6249 of these compounds formed hydrogen bonds with C-H. In all cases, one or both of R 1 , R 2 are three-coordinate nitrogen atoms. The overall frequency of occurrence (FoO) of hydrogen bond formation by C=S in CSD is 89.3% since we found 8002 structures in which a hydrogen bond to S could have been formed. The separate probability values for the structures of thioureas and thioamides, in which a hydrogen bond to S could have been formed, are quite different at 92.9% and 85.3% respectively. Of the 856 sulphur structures, where a hydrogen bond C=S···H is not formed, the available H donors bind to stronger acceptors in some cases, such as carbonyl and hydroxyl oxygen, in some others sulphur is involved in other types of interactions.
Furthermore, the equivalent frequencies of occurrence of hydrogen bond formation of the C=O analogues (urea and amide) were determined using CSD ver- The CSD survey also showed that 278 compounds R 1 ,R 2 -C=Se, with R 1 and R 2 assigned as any type of atom (X), formed hydrogen bonds withO-H, N-H and

Hydrogen Bond Geometry
Tables 4-6 give geometric data for intermolecular hydrogen bonds with the acceptors C=Se, C=S and C=Te for C-H donors on the basis of the parameters defined in Figure 1. For comparison, the tables also report data for O-H and N-H.
The first three rows of Tables 4-6 show hydrogen bonds for all angles ρ, while the rest of the tables only consider those structures where ρ ≥ 120.0˚, which is the recommended limit given by Wood [28]. Since the vast majority of the structures shown in these tables are those with N 3 (three-coordinate N) and bonded to C-H donors, where the hydrogen bond angle ρ ≥ 120.0˚, the following analysis and discussion are limited to those hydrogen bonds. Table 6 is approximately 0.16 Å and 0.25 Å longer than that of C=Se and C=S acceptors in Table 4 and Table 5 respectively, which is consistent with the larger van der Waals (vdW) radii of Te The angular directionality parameters (ρ, φ and θ, Figure 1) for the C=X acceptors show remarkably similar mean values to each other. Thus, the angle on the donor atom of H is completely linear (ρ tends towards 180˚).This is an expected behaviour for hydrogen bonds [28]. In addition, the tendency for the hydrogen bond donor vector (C-H) to approach X in the plane of the >C=X group is typical. The θ values in Tables 4-6 show mean deviations of coplanarity around 37 (23) Table 4 and Table 5, and all of these values can be attributed to interactions between H δ+ and the lone pairs on the atoms of Se, S and Te. The finding that hydrogen bonding at C=Te acceptors shows directional properties like hydrogen bonding at C=Se and C=S, should also make Te atoms versatile tools to directing and controlling the structure of molecular systems, with consequences for the use in crystal engineering [9] [31] [32] [33] and its integration in pharmaceutical agents [34] [35] [36]. Furthermore, we note that intramolecular hydrogen bonds of acceptors N-C=Se, N-C=S and N-C=Te are formed in 216, 4533 and 9 structures respectively, with very variable geometries. Structures forming 5 to 8 membered hydrogen bond rings are observed. For these structures, the distances Se···H, S···H and Te···H vary from from 2.32 to 3.10 Å, 1.85 to 3.00 Å and from 2.75 to 3.25 Å respectively, but the hydrogen bond angles are significantly distorted from the intermolecular normal values discussed above by the constraints of ring formation: ρ values are in the ranges 79˚ -174˚, 76˚ -178˚ and 86˚ -156˚, φ in the ranges 54˚ -116˚, 44˚ -173˚ and 58˚ -92˚ and θ in the ranges 0˚ -30˚, 0˚ -83˚ and 1˚ -62˚ respectively for Se, S and Te.

Hydrogen Bond Coordination
In the earlier comparative study by Allen [25], it was found that C=S and C=O normally accept one or two hydrogen bonds, but on rare occasions C=S accepts up to six hydrogen bonds, then C=O accepts up to five. This analysis was performed on all of the hydrogen bonds formed by the C=S or C=O acceptors at that time, and included both intramolecular and intermolecular hydrogen bonds. We performed a similar hydrogen bond coordination analysis of C=Se acceptors [14] and we saw that the coordination values 1 (66.3%) and 2 (25.5%) were the norm, while the maximum hydrogen bond coordination observed for C=Se was 3. The hydrogen bond coordination analysis performed for Se and S acceptors with C-H, N-H and O-H donors shows that these chalcogens can form up to eight and nine bonds respectively for Se and S. Table 7 reports the Mulliken and NBO partial charges on the O atom in formaldehyde, formamide and urea and on the Se and S atoms in their Se and S analogues, calculated using a variety of different methods, as described in section 2.2. Table 8 gives the Mulliken and NBO partial charges of Te.

Atomic Point Charges and Molecular Electrostatic Potential of Systems R 1 ,R 2 -C=X
The data in Table 7 show the expected trends in the electronegativity induced by the resonance in O, Se and S. The negative partial charge of the O atom increases due to the resonance moving from formaldehyde to formamide, then to urea, with both four theoretical levels and methods of calculating the partial charges, giving comparable results and trends. For Se and S with R 1 and R 2 as H atoms, the partial charges of the two atoms are quite small, in agreement with the similar electronegativities of Se, S and C. When we move to thioformamide and selenoformamide, then to thiourea and to selenourea, both Se and S have significant negative partial charges. These results and values are comparable to those previously reported for O and S by Allen [25] and for urea, thiourea and selenourea by Moudgil [37]. As for Te, the data in Table 8 show the same expected trend of electronegativity induced by resonance on Te. Indeed, the partial charge of Te tends more and more towards the negative when R 1 and R 2 move from C and C to N and N via C and N.
As shown by the above results, the Mulliken partial charges have lower values than the general NBO loads in Table 7, while in Table 8, the NBO partial charges have lower values than the Mulliken partial charges. This behaviour reflects the different approaches to obtaining atomic charges in each method. Indeed, all the methods of calculating the atomic charge are necessarily arbitrary, since it is not a quantum mechanical observable. There is then no rigorous physical basis for assigning charges to atoms in molecules, because assigning a single positive or negative value to each atom implicitly assumes that the charge distributions are spherical symmetrical [24].
The electrostatic potential has then been suggested as a significant representation of the electrostatic effects of molecular charge distribution [13]. Figure 5 shows the molecular electrostatic potential (MEP) for acetone, acetamide, urea and their selenium, sulphur and tellurium analogues. All molecules containing O exhibit a significant region of negative electrostatic potential, where the O atom will accept hydrogen bonds. For the Se, S and Te analogues, this region becomes more evident when the C atom bonded to the chalcogen has an N atom as a substituent. As previously reported for C=S [26], a marked fall-off in the negative charge density around Se and Te is observed in (CH 3 ,CH 3 )-C=Se and (CH 3 ,CH 3 )-C=Te, and explains the lack of hydrogen bonds to C=Se and C=Te in crystal structures when carbon bound to chalcogen has C as substituents. MEPs for selenourea, thiourea and, more clearly, for tellurourea also show a zone of positive electrostatic potential associated with the Se, S and Te atoms, which is directed outward along the C=Se, C=S and C=Te bondssuggesting the ability of chalcogen atoms to form both hydrogen bonds and positive hole-based bonds similar to sigma-hole interactions [24] [38] [39]. It was also find in chalcogen bonding in divalent Se, S and Te compounds [40] [41] [42] [43].
The methyl groups of the substituents were placed cis at the Y-H···X interaction to avoid an interaction between the N-H and the donor molecule, after which all three systems were able to relax completely.
The results of Table 9 and Table 10 show that the interaction strength C=Se Table 9. Values of total interaction energy (Eint) and geometric parameters d,φ and ρ for C-H···Se=C hydrogen bonds in N,N-, N,C-and C,C-disubstituted systems, as calculated using B3LYP/6-311++G(3df,2p) and B3LYP-GD3/6-311++G(3df,2p).  The geometries parameters (d, φ and ρ) obtained in the DFT calculations much well with the trends observed in CSD (Table 4 and Table 5), but we can note a difference by 30˚ -40˚ on φ angle for N,N groups. For example, an φ angle of 117 (26)˚ was found while the corresponding in calculation gives 89˚ for selenium acceptor.
The results of these Table 9 and Table 10  Furthermore, insights into the nature of interaction involved in the complex formation can be provided by NBO interaction analysis. Table 11 and Table 12 report NBO interactions with values of the associated second order perturbation energies E (2) for C=Se and C=S respectively.

Conclusions
The present study investigated the ability of C=Se, C=S and C=Te acceptors to form hydrogen bonds with C-H hydrogen bond donors using CSD analysis in conjunction with computational methods. Following relevant conclusions can be drawn: • There are respectively 256, 6249 and 11R 1 ,R 2 ,-C=Se, R 1 ,R 2 ,-C=S and R 1 ,R 2 ,-C=Te structures in CSD that form hydrogen bonds, in which the majority groups are N,N compounds. Except for the C=S acceptor which can form the hydrogen bond with its C,C group, both C=Se and C=Te could form a hydrogen bond only with N,C and N,N groups.
• C-H hydrogen-bond donors approach C=X acceptors at greater angles than their corresponding N-H and O-H donors, and the hydrogen bonding to C=X acceptors is highly directional, like to N-H and O-H donors.
• Partial charges and electrostatic potentials calculated for Te atoms in C=Te acceptors, as well as intramolecular geometries, suggest that the hydrogen bond D. D. Bibelayi et al. stems from the substituent groups inducing C δ+ =Te δdipole as occurs in hydrogen bonding C=Se and C=S acceptors.
• Molecular electrostatic potential surfaces calculated for C=Te acceptors show remarkably similar patterns to those for C=Se acceptors and C=S with a negative area and a positive hole suggesting the ability of chalcogen atoms to form both hydrogen bonds and positive hole-based bonds similar to sigma-hole.
• Both interaction distances derived from CSD analysis and DFT-calculated interaction energies demonstrate that the acceptors strongly interact with H-CF 3 . Besides hydrogen bonds, dispersion interactions are forces stabilizing the complexes since their contribution can reach 50%.
• NBO interaction analysis shows that C=Se···H-Cand C=S···H-C interactions are characterized by the transfer of charge from lone pair of the proton acceptor to the antibonding orbital of the C-H covalent bond.