The results obtained in this study are presented below in five sections.
Section 1 addresses the equilibrium HN(CH)SX:SCO complexes that have C
1 symmetry. In the second section, corresponding complexes that have C
s symmetry are discussed. In
Section 3, the molecules found on the potential surfaces, and the transition structures that interconvert complexes and molecules are presented.
Section 4 presents spin-spin coupling constants for complexes, molecules, and transition structures. In the fifth section, some comparisons are made between HN(CH)SX:SCO complexes that are stabilized by N
…C tetrel and S
…S chalcogen bonds, and HN(CH)SX:OCS complexes that have N
…C tetrel and O
…S chalcogen bonds.
3.1. HN(CH)SX:SCO Complexes with C1 Symmetry
Searches of the HN(CH)SX:SCO potential energy surfaces yielded equilibrium complexes containing N
…C tetrel and S
…S chalcogen bonds. The structures, total energies, and molecular graphs of these complexes are given in
Table S1 of Supporting Information. In the molecular graphs, these complexes appear to have planar
Cs symmetry, but they do not. Rather, they have
C1 symmetry, as illustrated in
Figure 1 for complexes with X = F, NC, and H. In this figure, the S=C=O molecule has been oriented so that it is perpendicular to the N
…C tetrel bond, and the view is along that bond. This orientation illustrates the deviation of these complexes from
Cs symmetry. The complexes with X = F, Cl, CCH, H, and CN have dihedral S–C–N–C angles between 39 and 49°, and they are represented by HN(CH)SF:SCO and HN(CH)SH:SCO in
Figure 1a,b, respectively. The dihedral angle is reduced to 20° in the complex with X = NC, which is illustrated in
Figure 1c. The planar HN(CH)SH:SCO
Cs complex is shown in
Figure 1d.
Figure 1 also provides insight into the values of the S–S–A angles in these complexes. Complexes X = F, Cl, and NC have values of this angle between 166 and 169°. These values are consistent with a traditional S
…S chalcogen bond, in which a lone pair on S3 is directed toward the σ-hole on S6. Complexes with X = CCH, H, and CN have S–S–A angles of 123, 131, and 124°, respectively, which is not an optimum orientation for the formation of an S
…S chalcogen bond.
Table 1 provides structural and energetic data for complexes with
C1 symmetry, including binding energies; N–C and S–S distances across the tetrel and chalcogen bonds, respectively; the N–C–S and S–S–A angles; and the dihedral S–C–N–C angles. In the tables, atoms are given numbers that correspond to
Figure 1, but in the text, numbers are not used unless there might be some ambiguity. The binding energies of these complexes span a small range from 13.3 to 15.6 kJ·mol
–1, and they decrease with respect to X in the order F > Cl > NC = CCH > H ≈ CN. Thus, the complexes with the stronger electron-withdrawing substituents have the greater binding energies.
Further insight into these complexes can be gained by examining their S–S and N–C distances. The three most strongly bound complexes have S–S distances between 3.10 and 3.50 Å, with the most strongly bound complex having the shortest S–S distance. As noted previously, these three complexes have S–S–A angles of 169, 166, and 166°, respectively, values consistent with a chalcogen bond. In contrast, the S–S distance is much longer in the complexes with X = CCH, H, and CN, varying between 3.78 and 3.81 Å. These complexes also have reduced S–S–A angles of 123, 131, and 124°, respectively. These data indicate that the chalcogen bonds in the latter complexes are very weak or perhaps nonexistent.
The most strongly bound complex with X = F has an N–C distance of 3.01 Å. The N–C distances in the complexes with X = Cl and NC are 3.06 Å. This distance in the remaining complexes with X = CCH, H, and CN is shorter, with values between 3.02 and 3.04 Å. These short N–C distances suggest that in the complexes with the weaker S…S chalcogen bonds, the N…C tetrel bonds may be stronger. The values of the N–C–S angle are consistent with the formation of a tetrel bond at C through its local π-hole.
Figure 2 provides plots of the binding energies of the HN(CH)SX:SCO complexes versus the N–C and S–S distances. It is evident from this figure that the binding energies are essentially independent of the N–C distance. Moreover, there is not a good correlation between these binding energies and the S–S distance. This lack of correlation may be attributed to the differences primarily in the S
…S bonds in complexes with X = F, Cl, and NC compared to those having X = CCH, H, and CN.
The nature of the charge-transfer interactions and their energies for the
C1 complexes are reported in
Table 2. There are two lone pairs of electrons on S3, and each can be involved in charge-transfer. The strongest S3
lp1 → σ*S6–A interactions are found for the complexes with X = F, Cl, and NC, with values of 12.2, 8.0, and 5.9 kJ
.mol
–1, respectively. The charge-transfer energies drop to less than 1 kJ
.mol
–1 for the complexes with X = CCH, H, and CN. The second charge-transfer interaction has a value of about 2 kJ
.mol
–1 for the complexes with X = F, Cl, and NC, and it is less than 0.1 kJ
.mol
–1 for the complexes with X = CCH, H, and CN. Thus, these data for the S
…S bonds are consistent with the previous statements that chalcogen bonds in complexes with X = CCH, H, and CN are very weak or nonexistent.
There are also two charge-transfer interactions across the tetrel bonds. The dominant interaction arises from the donation of the lone pair on N to the local in-plane antibonding π C–O orbital. The charge-transfer energies range from 2.5 to 5.9 kJ·mol–1 and decrease in the order F > Cl = NC > H > CCH ≈ CN. There is also a second charge-transfer in the complexes with X = F, Cl, NC, and H arising from electron donation from the lone pair on N to the local π*C–S orbital, with energies of only 0.3 kJ·mol–1.
3.2. HN(CH)SX:SCO Complexes with Cs Symmetry
The structures, total energies, and molecular graphs of the optimized HN(CH)SX:SCO complexes with
Cs symmetry are reported in
Table S2 of Supporting Information.
Table 3 reports their binding energies, N–C and S–S distances, and N–C–S and S–S–A angles, and
Figure 3a depicts the planar HN(CH)SF:SCO complex. The
Cs complexes have one imaginary frequency and are thus the transition structures that connect the two equivalent
C1 complexes. However, the difference between the binding energies of corresponding
Cs and
C1 structures does not exceed 0.5 kJ
.mol
–1, found for the complexes with X = CCH and H. When X = NC, the binding energies of the
C1 and
Cs structures are the same. From these data, it is apparent that the potential energy surfaces are very flat in the region surrounding the equilibrium and transition structures. Thus, the
Cs structures may be viewed as vibrationally averaged structures, and these structures will be discussed below in this and the following sections.
Figure 2 also provides plots of the binding energies of the complexes with
Cs symmetry versus the N–C and S–S distances. Once again, it is apparent that these binding energies are essentially independent of the N–C distance, but they do depend on the S–S distance. The correlation coefficient of the second-order trend line for the complexes with
Cs symmetry is 0.922. This plot also shows the similarities between the binding energies and S–S distances for the
C1 and
Cs complexes when X = F, Cl, and NC, as well as the relatively small but noticeable differences when X = CCH, H, and CN.
It is interesting to compare the corresponding N–C and S–S distances across tetrel and chalcogen bonds, respectively, in the C1 and Cs complexes. The N–C distances in the Cs complexes with X = F, Cl, and NC are slightly shorter than in the corresponding C1 complexes, but the difference does not exceed 0.008 Å. In contrast, these distances are longer by 0.03–0.05 Å in the Cs complexes with X = CCH, H, and CN. For the complexes with X = F, Cl, and NC, the S–S distances in the Cs structures are longer by 0.01–0.04 Å compared to the corresponding C1 complexes, but this distance is shorter in the C1 complexes with X = CCH, H, and CN by 0.06–0.17 Å. The N4–C1–S3 angles in all of the complexes are consistent with tetrel-bond formation through the π-hole at C of S=C=O. The S–S–A angles are indicative of S…S chalcogen-bond formation in the all of the Cs complexes and in the C1 complexes with X = F, Cl, and NC through the σ-hole on S6, but indicate that this bond is distorted when X = CCH, H, and CN.
Table 2 reports the charge-transfer energies for the
Cs complexes. The dominant charge-transfer interaction across the tetrel bond arises from electron donation by N to the local in-plane antibonding π C–O orbital. The charge-transfer energy is 6.6 kJ
.mol
–1 for the complex with X = F which has an N–C distance of 3.004 Å, and 5.4 kJ
.mol
–1 at an N–C distance of 3.051 Å when X = Cl. In the remaining complexes, the charge-transfer energies are between 4.8 and 5.2 kJ
.mol
−1 at N–C distances between 3.060 and 3.075 Å. There is also a second charge-transfer of about 0.3 kJ
.mol
–1 across the tetrel bond from the lone pair on N to the local in-plane π antibonding C–S orbital.
There are two lone pairs of electrons on S3, and there are therefore two charge-transfer interactions across the S3…S6 chalcogen bonds. The primary charge transfer arises from donation of one of the lone pairs on S3 to a σ antibonding S–A orbital. These charge-transfer energies vary from 3.5 to 12.8 kJ.mol–1 and decrease with respect to X in the same order as the binding energies. A plot of these energies versus the S–S distance has a second-order trend line with a correlation coefficient of 0.935. It is noteworthy that all of these energies are greater than the charge-transfer energies in the corresponding C1 complexes, particularly for the complexes with X = CCH, H, and CN. The second charge-transfer interaction across the chalcogen bond is much weaker, with values between 0.4 and 1.7 kJ.mol–1.
3.3. HN(CH)SX:SCO Molecules and Transition Structures
Searches of the potential energy surfaces led to the identification of HN(CH)SX:SCO transition structures and molecules, which are illustrated by HN(CH)SF:OCS in
Figure 3b,c, respectively. The structures, total energies, and molecular graphs of the molecules and transition structures are given in
Tables S3 and S4, respectively, in Supporting Information. The binding energies, N–C and S–S distances, and N–C–S and S–S–A angles of the molecules are reported in
Table 4. The molecules have a significantly reduced N–C covalent bond distance of 1.44 Å when X = F, Cl, and NC. In the complexes with X = CCH, H, and CN, this distance is longer, varying between 1.52 and 1.55 Å. The S–S distances are also much shorter in the molecules than they are in the complexes, with a value of approximately 2.30 Å for the molecules with X = F, Cl, and NC, and values are between 2.67 and 2.89 Å in the remaining molecules. The reduced values of the S–S distance indicate that the chalcogen bonds have acquired increased covalent character in the molecules relative to the complexes. The data also suggest that the N–C covalent bond and the S
…S chalcogen bond are significantly weaker in the molecules when the substituents are CCH, H, and CN.
The data of
Table 4 illustrate that the distance changes are also accompanied by angular changes in the molecular geometries. The N4–C1–S3 angle increases dramatically from about 96° in the complexes to between 131 and 137° in the molecules. This is as expected as the N
…C tetrel bond becomes an N–C covalent bond. Except for HN(CH)SH:SCO, the S–S–A angle increases relative to its value in the complexes and approaches 180° in the molecules, the idealized value for a chalcogen bond.
The binding energies of the molecules are also reported in
Table 4. Only the molecules HN(CH)SF:SCO and HN(CH)SCl:SCO are bound relative to the corresponding isolated monomers, with binding energies of 48 and 24 kJ
.mol
–1, respectively. HN(CH)S(NC):SCO is unbound but by only −10 kJ·mol
–1. The remaining molecules with X = CCH, H, and CN are unbound by between −64 and −70 kJ·mol
–1. Thus, the covalent N–C bond and the S
…S chalcogen bond are sufficiently strong to overcome the distortion energies of the monomers only when X = F and Cl.
Figure 4 illustrates the stabilization energies of complexes, transition structures, and molecules as a function of the S–S distance. A similar plot can be obtained as a function of the N–C distance.
It is informative to examine the changes that occur in the geometries of HN(CH)SF:SCO and HN(CH)SCl:SCO as these complexes traverse the transition states and become molecules. For ease of comparison,
Table 5 presents the N–C, S–S, and S–A distances, as well as the N–C–S, S–S–A, and S–C–O angles for the complexes, transition structures, and molecules. As the two complexes become molecules, the N
…C tetrel bond becomes an N–C covalent bond. Thus, the N–C distance decreases dramatically from about 3.0 Å to 1.44 Å, the N–C–S angle increases from 95 to 109°, and the S=C=O molecule becomes nonlinear as the S–C–O angle decreases to 131°. The values of these geometric descriptors in the transition structure lie between the values found in the complex and corresponding molecule, except for the S–S–A angle, which is similar in the molecule and transition structure. Significant changes are also found for the S
…S chalcogen bond. In particular, the S–S distance decreases dramatically from 3.35 and 3.49 Å in the complexes with X = F and Cl to 2.29 and 2.31 Å, respectively, in the molecules as the S–S–A angle increases from 166 to about 176°. It is noteworthy that the S–F distance increases from 1.64 to 1.80 Å, while the S–Cl distance increases from 2.04 to 2.31 Å as the complexes become molecules. This suggests that the formation of the molecule leads to a weakening of the S–A bond.
The binding energies of the HN(CH)SF:SCO and HN(CH)SCl:SCO complexes, transition structures, and molecules are also reported in
Table 5. The binding energies increase to 48 and 24 kJ·mol
–1 for the molecules with X = F and Cl, respectively. The corresponding transition structures are unbound by −19 and −37 kJ·mol
–1. Thus, the barrier to convert the HN(CH)SF:SCO complex to the molecule is 34 kJ·mol
–1, while the barrier for the reverse reaction is 67 kJ·mol
–1. For HN(CH)SCl:SCO, the barrier to convert the complex to the molecule is 52 kJ·mol
–1, while the barrier for the reverse reaction is 61 kJ·mol
–1. These barriers are visible in
Figure 4. These data suggest that at low temperatures, the complexes would form as the two monomers approach each other. However, at higher temperatures, the HN(CH)SF:SCO molecule would be the dominant species, while both the HN(CH)SCl:SCO complex and molecule would have appreciable concentrations.
3.4. Spin-Spin Coupling Constants
Spin-spin coupling constants
1tJ(N–C) across the tetrel bonds and
1cJ(S–S) across the chalcogen bonds have been computed for all of the complexes having
Cs symmetry. For the transition structures HN(CH)SF:SCO and HN(CH)SCl:SCO coupling constants
1tJ(N–C) across the tetrel bonds and
1cJ(S–S) across the chalcogen bonds were evaluated. Coupling constants
1cJ(S–S) were computed for the molecules as well as
1J(N–C) for coupling across the covalent N–C bond. The components of these coupling constants are reported in
Table S5 of Supporting Information. As is usually the case, coupling constants
1tJ(N–C) across the tetrel bond and
1cJ(S–S) across the chalcogen bond for complexes and transition structures are determined by the FC term. This is not generally the case for molecules due to contributions from the PSO and SD terms.
Table S5 provides values of the coupling constants
1tJ(N–C) across the tetrel bonds and
1cJ(S–S) across the chalcogen bonds for all HN(CH)SX:SCO complexes. The
1tJ(N–C) values are very small at −0.3 Hz in all complexes. In contrast,
1cJ(S–S) values, which are reported in
Table 3, vary from 1.4 to 5.7 Hz and decrease with respect to the substituent X in the order F > Cl ≈ NC > CN ≈ CCH > H.
Figure 5 illustrates the strong dependence of this coupling constant on the S–S distance, with a correlation coefficient of 0.999 for a second-order trend line.
The values of
1tJ(N–C) and
1cJ(S–S) for the HN(CH)SF:SCO and HN(CH)SCl:SCO complexes and transition structures, as well as the values of
1cJ(S–S) and
1J(N–C) for the corresponding molecules, are reported in
Table 6. As the N–C distance decreases in going from the complex to the transition structure,
1tJ(N–C) increases to 18 and 21 Hz in transition structures with X = F and Cl, respectively. In the molecules, the N–C bond becomes a covalent bond, and
1J(N–C) decreases dramatically to −7.8 and −7.6 Hz, respectively, when X = F and Cl.
Figure 6 illustrates these changes as a function of the N–C distance. The correlation coefficient of the second-order trend line is 0.980.
A similar pattern can be observed for
1cJ(S–S) as a function of the S–S distance. This coupling constant increases from 5.7 and 3.8 Hz in the complexes to 22.7 and 21.5 Hz in the transition structures with X = F and Cl, respectively, as the S–S distance decreases. A further decrease in the S–S distance leads to a decrease in these two coupling constants to 13.1 and 12.7 Hz, respectively, but these two coupling constants do not change sign. The S···S bond gains covalent character in the transition structures and again in the molecules, but it remains an intermolecular chalcogen bond. The correlation coefficient is 0.939 for the second-order trend line in
Figure 6, which illustrates these changes.
3.5. Comparison of Cs Complexes, Molecules, and Transition Structures HN(CH)SX:SCO and HN(CH)SX:OCS
Data for the isomers HN(CH)SX:OCS with the same set of substituents X but which are stabilized by O…S chalcogen bonds instead of S…S bonds have been reported in Reference [Error! Bookmark not defined.]. The equilibrium HN(CH)SX:OCS complexes have Cs symmetry. The binding energies of HN(CH)SX:OCS and HN(CH)SX:SCO isomers with Cs symmetry are similar. Those with O…S chalcogen bonds have binding energies between 12.2 and 15.1 kJ.mol–1, while those with S…S chalcogen bonds have binding energies between 13.0 and 15.3 kJ.mol–1. In both series, the most strongly bound complexes have X = F, Cl, and NC. The C1–N4 distances in these two series are similar, with values of 3.03–3.09 Å in the complexes with O…S chalcogen bonds and 3.00–3.08 Å in complexes with S…S bonds. The O–S distance in the complexes with O…S chalcogen bonds varies by 0.363 Å, while the S–S distance varies by 0.399 Å in complexes with S…S chalcogen bonds. In both series of complexes, the binding energies are essentially independent of the N–C distance but exhibit a second-order dependence on the O–S and S–S distances.
There is only one HN(CH)SX:OCS potential energy surface that has a bound molecule, namely HN(CH)SF:OCS. The binding energy of this molecule is 15.2 kJ·mol–1 at the N–C and O–S distances of 1.431 and 1.948 Å, respectively. By comparison, there are bound molecules on two HN(CH)SX:SCO potential energy surfaces, those with X = F and Cl. The binding energies of these are 48.1 and 24.3 kJ·mol–1, respectively, at an N–C distance of 1.44 Å and an S–S distance of approximately 2.30 Å. Thus, the two bound molecules with X = F and Cl that are stabilized by S…S chalcogen bonds are significantly more stable than the HN(CH)SF:OCS molecule with an O…S chalcogen bond.
It is also possible to compare the changes in the coupling constants
1tJ(C–N) and
1cJ(S–S) for HN(CH)SX:SCO complexes with the changes in
1tJ(C–N) and
1cJ(O–S) for HN(CH)SX:OCS. In both series,
1tJ(N–C) is independent of the nature of the substituent and the N–C distance. In contrast, the second-order dependence of
1cJ(O–S) and
1cJ(S–S) on the O–S and S–S distances, respectively, is illustrated in
Figure 5. The correlation coefficients are greater than 0.990. This type of distance dependence across intermolecular bonds in a related series of complexes is common when the nature of this bond does not change significantly as the bond distance changes [
20,
22].
The effect of the changing nature of the O
…S bond in HN(CH)SF:OCS, the S
…S bonds in HN(CH)SF:SCO and HN(CH)SCl:SCO, and the N
…C bonds in these three complexes on C1–N4, O–S and S–S coupling constants is dramatic, as is illustrated in
Figure 6.
1tJ(N–C) increases in going from the complex to the transition structure as the N–C distance decreases, and then it decreases and changes sign in the molecule as a covalent N–C bond is formed.
1cJ(S–S) and
1cJ(O–S) show similar patterns as functions of the S–S and O–S distances, respectively, although these coupling constants do not change sign because the S
…S and O
…S bonds remain chalcogen bonds but with increased covalent character. In
Figure 6, the curve for
1cJ(S–S) is displaced to longer distances simply because the S atom has a larger van der Waals radius than O.