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 distances d (norm) to explore the bond-strength bond-length relationship according to the Equation (1):

d ( norm ) = d − vdW ( H ) − vdW ( X ) (1)

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.

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.:

V ( r ) = ∑ A Z A | R A − r | − ∫ ρ ( r ′ ) d r ′ | r ′ − r | (2)

Z_A and ρ(r) are, respectively, the charge on nucleus A located at distance R and the electronic density of the molecule. | R A − r | and | r ′ − r | respectively represent the nucleus distance from r, the distance of each electronic charge increment ρ ( r ′ ) d r ′ from r.

Interaction energies were calculated for the interactions of trifluoro-methane molecules with the hydrogen bonding acceptors R₁,R₂-C=X, where R = CH₃CH₂ or NHCH₃ according to equation (3), as difference between the energy of the complex (E_complex) and the sum of the energies of the isolated h-bond donor (E_donor) and acceptor (E_acceptor) using optimised geometries:

E int = E complex − ( E donor + E acceptor ) (3)

E_complex, E_donor, and E_acceptor are the energy minima at 0 K.

Vibrational analysis was also performed calculated with all DFT levels of theory to determine true minima and saddle points of different orders.

An initial survey in the CSD showed that there are 7146 compounds R₁,R₂-C=S, with R₁ and R₂ 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 R₁, R₂ 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 version 5.41 with an R-factor limit of 0.05. This resulted in overall FoO values of 94.3% and 94.8% respectively for the urea and amide analogues of C=O. Although these values are almost the same as those obtained for the C=Se compounds and less than of C=Te compounds, they should not be taken as an indication of the relative strengths of hydrogen bonds.

The CSD survey also showed that 278 compounds R₁,R₂-C=Se, with R₁ and R₂ assigned as any type of atom (X), formed hydrogen bonds withO-H, N-H and C-H donors, while there are 256 which formed with C-H donors. In all cases, one or both of R₁, R₂ are three-coordinate nitrogen atoms. In a separate search, we found 300 crystal structures that also contained O-H, N-H or C-H donors, i.e., structures in which a hydrogen bond to Se could have been formed. Thus, the overall occurrence frequency (FoO) of hydrogen bond formation by C=Se in CSD is 92.6%. The separate probability values for the structures of selenoureas and selenoamides, in which a hydrogen bond to Se could have been formed, are quite similar at 92.0% and 90.8% respectively. These results confirm that C=Se is an efficient hydrogen bond acceptor when Se is activated by resonance effects. Of the 22 selenium structures where a hydrogen bond C=Se···H does not form, the majority of available H donors bind to stronger acceptors, such as carbonyl and hydroxyl oxygen, or selenium is involved in other types of interactions.

Interestingly, there are 11 compounds R₁,R₂-C=Te, with R₁ and R₂ assigned as any type of atom (X) in CSD that have formed hydrogen bonds with O-H, N-H or C-H donors. All 11 compounds formed hydrogen bonds with C-H. One or both of R₁, R₂ are three-coordinate nitrogen atoms. Crystal structures also containing OH, NH or CH donors in which a hydrogen bond to Te could have been formed are 11. Thus, the overall occurrence frequency (Fo) of hydrogen bond formation by C=Te in CSD is of 100%. The separate probability values for tellurourea and telluroamide structures, in which a hydrogen bond to Te could have been formed, are 100% and 100% respectively.

In the present work, we are concerned with hydrogen-bonding of C-H donors at the monovalent chalcogen atoms, since those bonds report marked values of FoO. A similar study of the hydrogen-bonding of O-H and N-H donors will be reported shortly.

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 N³ (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.

We can note that C=Se and C=S could form hydrogen bonds with O-H, N-H and C-H donors, but C=Te could form only with C-H donors. The average hydrogen bond distance (d) of C=Te acceptors in 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 (2.06 Å) with respect to S (1.80 Å) and Se (1.90 Å) [29]. There is no significant difference between the hydrogen bond distances (d) observed in subgroups (N³, N³), and the subgroups (N³, C) for all acceptors. However, there is some indication that the hydrogen bond distances for CH···X interactions are longer than their NH···X and OH···X counterparts up to 0.33 Å and 0.51 Å respectively for selenium, 0.38 Å and 0.49 Å for sulphur. This situation has also been observed in previous studies of the C=S acceptor [25] [26] and C=Se acceptor [14]. This is an indication that the differences between the interaction energies between N-H and C-H donors could be greater than those between O-H and N-H donors.

An earlier comparative analysis of C = O and C = S acceptors [26] used standard van der Waals hydrogen bond distances, i.e.

d ( norm ) = d ( Hbond ) − vdW ( H ) − vdW ( X ) , where X represents the acceptor atom (O or S) and vdW (X) is the vdW radius of this atom. The value of 1.10 Å determined by Rowland and Taylor [30] was used for vdW (H), while the values of 1.52 Å for vdW (O) and 1.80 Å for vdW (S) were taken from Bondi [29]. For hydrogen bonds from NH with oxygen O of ureido and sulphur S of thioureido, a large and homogeneous subgroup for both acceptors, d(norm) values were −0.692 Å and −0.449 Å for the acceptors C = O and C = S respectively, which clearly indicates that the hydrogen bonds formed with C = O are much stronger compared to those with C = S. Calculation of d(norm) using the d values of 2.95 Å for the Se···HC bonds of selenoureido, of 2.86 Å for the S···HC bonds of thioureido and of 3.12 Å for the Te···HC bonds of telluroureido from Tables 4-6, vdW (S) = 1.80 Å [29], vdW (Se) = 1.90 Å [29] and vdW (H) = 1.10 Å [30], d(norm) gives −0.05 Å, −0.04 Å and −0.04 Å respectively for Se···HC, S···HC and Te···HC which values are lower than the values of -0.44 Å and -0.45 Å respectively for Se···HO and S···HO [14] [26]. Thus, we can deduce that the stabilization energy of both three acceptors C=X···H bonds should be similar with the CH donor.

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)˚, 37 (24)˚ and 32 (22)˚ respectively. The most interesting angle is φ, the angle at which the hydrogen atom approaches with respect to the C=X bond, for which the mean values of 116 (26)˚, 119 (27)˚ and 116 (25)˚ are obtained for Se, S and Te acceptors respectively. These values, for the N-H and O-H donors, are slightly upper than those 103 (13)˚ and 97 (8) for selenium and than 107 (12)˚ and 103 (13)˚ for sulphur in 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.

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.

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 R₁ and R₂ 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 R₁ and R₂ 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 (CH₃,CH₃)-C=Se and (CH₃,CH₃)-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].

DFT calculations were performed to determine the geometry and energy of interaction with trifluoro-methane as donors according to the scheme shown in Figure 6. The number of vibration frequencies (Nv) shows that all the complexes were true minima (Nv = 0).

Structural information from the CSD and electrostatic data from AbInitio calculations suggest that the N-substituted C=Se acceptors should have hydrogen bond interaction strengths comparable to the corresponding C=S acceptors. Table 9 and Table 10 report the geometries and interaction energies (as defined in Figure 1 and Figure 6) of the complexes (NHCH₃,NHCH₃,)-C=Se···H-CF₃ (I1), (NHCH₃,CH₃CH₂)-C=Se···H-CF₃ (I2), (CH₃CH₂,CH₃CH₂)-C=Se···H-CF₃ (I3), (NHCH₃,NHCH₃,)-C=S···H-CF₃ (II1), (NHCH₃,CH₃CH₂)-C=S···H-CF₃ (II2) and (CH₃CH₂,CH₃CH₂)-C=S···H-CF₃ (II3) calculated with both B3LYP (EintB3LYP) and B3LYP-3D (EintB3LYP-3D). We were unable to calculate the interaction energies of the acceptor Te due to the failure of calculations.

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

is very similar to that C=S for systems (NHCH₃NHCH₃)-C=X···H-CF₃ and (NHCH₃,CH₃CH₂)-C=X···H-CF₃; and clearly shows that C=Se and C=S can form stabilizing hydrogen bonds. Indeed, values of −14.30 kJ/mole (EintB3LYP) and −27.76 kJ/mole (EintB3LYP-3D) of C=Se for the NN groups are similar with values of −14.29 kJ/mole (EintB3LYP) and −27.04 kJ/mole (EintB3LYP-3D) of C=S respectively, and those of −12.16 kJ/mole (EintB3LYP) and −22.37 kJ/mole (EintB3LYP-3D) of C=Se for the NC groups are similar with values of −12.55 kJ/mole (EintB3LYP) and −22.32 kJ/mole (EintB3LYP-3D) of C=S respectively.

As for the systems (CH₃CH₂,CH₃CH₂)-C=X···H-CF₃, we notice the difference in interaction strength for the two acceptors C=Se and C=S, values of −9.81 kJ/mole (EintB3LYP) and −20.45 kJ/mole (EintB3LYP-3D) of C=Se are different from −5.20 kJ/mole (EintB3LYP) and −16.71 kJ/mole (EintB3LYP −3D) of C=S respectively.

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 also show that the calculated energies follow the expected trend of the hydrogen bond strength already established on the basis of the geometry analysis of the structures in the CSD and are consistent with the partial charges and MEP of the groups C=Se and C=S substituted. Indeed, the trend of the interaction energies agrees well with that of CSD d (norm). One can expect from analysis of d (norm) values of three chalcogens that C=Te should be of comparable strength than C=Se.

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.

It appears from those Tables that all hydrogen bonds consist of charge transfer (CT) from a selenium or sulphur lone pair (LP) acting as hydrogen bond acceptor to a H-C antibonding orbital (BD*) of the hydrogen bond donor.

For C=Se acceptor, E⁽²⁾ values range from 4.10 to 16.19 kJ∙mol⁻¹ for B3LYP and from 2.85 to 21.13 kJ∙mol⁻¹ for B3LYP-D3 depending on the hydrogen-bond donor and substituents bonded to carbon in C=X acceptors. Those calculated for C=S acceptor with B3LYP and B3LYP-D3 respectively vary from 2.89 to 14.69 kJ∙mol⁻¹, and from 2.05 to 19.20 kJ∙mol⁻¹.