Enhancing Effects of the Cyano Group on the C-X∙∙∙N Hydrogen or Halogen Bond in Complexes of X-Cyanomethanes with Trimethyl Amine: CH3−n(CN)nX∙∙∙NMe3, (n = 0–3; X = H, Cl, Br, I)

In this paper, density functional theory and wave function theory calculations are carried out to investigate the strength and nature of the intermolecular C-X∙∙∙N bond interaction as a function of the number of cyano groups, CN, in the X-bond donor while maintaining the X-bond acceptor as fixed. Specifically, complexes of X-cyanomethanes with trimethyl amine CH3−n(CN)nX∙∙∙NMe3 (n = 0–3; X = H, Cl, Br, I) are used as model systems. Geometrical parameters and vibrational C-X-stretching frequencies as well as interaction energies are used as relevant indicators to gauge hydrogen or halogen bond strength in the complexes. Additional characteristics of interactions that link these complexes, i.e., hydrogen or halogen bonds, are calculated with the use of the following theoretical tools: the atoms in molecules (AIM) approach, the natural bond orbital (NBO) method, and energy decomposition analysis (EDA). The results show that, for the specified X-center, the strength of C-X∙∙∙N interaction increases significantly and in a non-additive fashion with the number of CN groups. Moreover, the nature (noncovalent or partly covalent) of the interactions is revealed via the AIM approach.


Introduction
A hydrogen bond, D-H···A, is commonly understood as the attractive, non-covalent interaction between a hydrogen bond donor, D-H, and a hydrogen bond acceptor, A [1][2][3][4][5][6][7][8]. Likewise, a halogen bond, D-Hal···A (Hal = F, Cl, Br, or I), is understood as the attractive, non-covalent interaction between a halogen bond donor, D-Hal, and a halogen bond acceptor, A [9][10][11][12][13][14][15][16]. Thus, a halogen bond could be considered in principle as an extension of the hydrogen bond concept. It has also been suggested that a hydrogen or a halogen bond could be thought of as a Lewis acid-base interaction, with the donor (D-H or D-Hal) as the Lewis acid, and the acceptor, A, as the Lewis base [13][14][15][16][17]. The distinctive characteristics of the hydrogen and halogen bond interactions, as well as their corresponding IUPAC (International Union of Pure and Applied Chemistry) definitions, have been provided recently [18,19].
Similarities and differences between hydrogen and the halogen bonds have been pointed out in a variety of studies [20][21][22][23][24][25]. For example, both interactions have been shown to be highly directional, although the halogen bond tends to be more linear than the hydrogen bond [26][27][28][29][30]. Additionally, both the hydrogen bond and the halogen bond have been shown to be highly tunable [14][15][16][17]31]. Tuning the strength of the hydrogen or halogen bond interaction for a fixed acceptor or Lewis base can be made through the interplay of a number of factors pertaining the D-H or the D-Hal donor group. With more Optimized geometries for all CH 3−n (CN) n X···NMe 3 (n = 0-3; X = H, Cl, Br, I) complexes were first obtained with the ωB97X-D/aug-cc-pVTZ level of theory. Harmonic vibrational frequency calculations, at the same level of theory, demonstrated that all the optimized geometries were minima in their respective potential energy surfaces (no imaginary frequencies present). Geometry optimizations and corresponding frequency calculations at the MP2/aug-cc-pVDZ level of theory also resulted in minimum energy structures for all complexes with no imaginary frequencies. Lastly, the MP2/aug-cc-pVDZ-optimized geometries were used as initial guess geometries for further geometry optimizations at the MP2/aug-cc-pVTZ level. Frequency calculations at the MP2/aug-cc-pVTZ were generally not possible given our computer capabilities, and thus were not performed. It should be noted that, in all calculations, either the aug-cc-pVDZ-PP or the aug-cc-pVTZ-PP basis set was used for the iodine atom, where applicable. Figures 1 and 2 show the ωB97X-D/augcc-pVTZ-optimized geometries of the CH 3−n (CN) n H···NMe 3 and CH 3−n (CN) n Cl···NMe 3 complexes; the X···N distances are also presented there for all complexes, X = H, Cl, Br, I. The corresponding relevant geometrical parameters for each complex at all levels of theory can be found in Tables 1-4. Accordingly, the inspection of Tables 1-4 shows that the ωB97X-D/aug-cc-pVTZ level of theory predicts C-X bond lengths and intermolecular X···N distances that are smaller and longer, respectively, than the corresponding results predicted in the MP2/aug-cc-pVDZ level of theory. Interestingly, the MP2/aug-cc-pVTZ results are closer to those of the ωB97XD/aug-cc-pVTZ level of theory for the C-X covalent bond lengths and to those of the MP2/aug-cc-pVDZ level of theory for the hydrogen or halogen bond distances and angles, X···N and C-X···N, respectively.
presented there for all complexes, X = H, Cl, Br, I. The corresponding relevant geometrical parameters for each complex at all levels of theory can be found in Tables 1-4. Accordingly, the inspection of Tables 1-4 shows that the B97X-D/aug-cc-pVTZ level of theory predicts C-X bond lengths and intermolecular X•••N distances that are smaller and longer, respectively, than the corresponding results predicted in the MP2/aug-cc-pVDZ level of theory. Interestingly, the MP2/aug-cc-pVTZ results are closer to those of the B97XD/aug-cc-pVTZ level of theory for the C-X covalent bond lengths and to those of the MP2/aug-cc-pVDZ level of theory for the hydrogen or halogen bond distances and angles, X•••N and C-X•••N, respectively.    presented there for all complexes, X = H, Cl, Br, I. The corresponding relevant geometrical parameters for each complex at all levels of theory can be found in Tables 1-4. Accordingly, the inspection of Tables 1-4 shows that the B97X-D/aug-cc-pVTZ level of theory predicts C-X bond lengths and intermolecular X•••N distances that are smaller and longer, respectively, than the corresponding results predicted in the MP2/aug-cc-pVDZ level of theory. Interestingly, the MP2/aug-cc-pVTZ results are closer to those of the B97XD/aug-cc-pVTZ level of theory for the C-X covalent bond lengths and to those of the MP2/aug-cc-pVDZ level of theory for the hydrogen or halogen bond distances and angles, X•••N and C-X•••N, respectively.     An inspection of Table 1 shows that, at all levels of theory, the covalent C-H bond length in CH 3−n (CN) n H···NMe 3 increases nonlinearly with the number of CN groups, relative to the bond length for the system with no CN groups, n = 3. For example, at the ωB97X-D/aug-cc-pVTZ level, the C-H bond increases by only 0.5% when n = 2, but then it increases more substantially when n = 1 (1.7%) and when n = 0 (5.7%). Concomitant with the C-H elongation there is a nonlinear reduction in the hydrogen bond distance, H···N, with the number of CN groups that is proportionally larger than the accompanying increase in the C-H bond length. Thus, at the ωB97X-D/aug-cc-pVTZ level, the H···N distance is decreased by 10.4%, 20.3% and 32.0% for n = 2, 1, and 0, respectively. Lastly, the C-H···N angle remains far from linear until all three CN groups are present. Overall, the geometrical changes suggest an important strengthening of the H···N hydrogen bond resulting from the cumulative electron-withdrawing effects of the CN groups. An inspection of Tables 2-4 reveals that the effects of the CN groups on the C-X bond lengths and the X···N halogen bond distances qualitatively mirror those in the hydrogen bond complexes, i.e., X = H. A graphical representation of the effects of the CN groups at the ωB97X-D/aug-cc-pVTZ level can be seen in Figure 3 (for the C-X bond lengths) and in Figure 4 (for the X···N interaction distances). It is worth noting that the halogen bond angles are linear for both X = Br and I, regardless of the number of CN groups. For X = Cl, the halogen bond angle increases from quasilinear 169 • (n = 3) to linear 180 • (n = 0). An inspection of Table 1 shows that, at all levels of theory, the covalent C-H bond length in CH3-n(CN)nH•••NMe3 increases nonlinearly with the number of CN groups, relative to the bond length for the system with no CN groups, n = 3. For example, at the ωB97X-D/aug-cc-pVTZ level, the C-H bond increases by only 0.5% when n = 2, but then it increases more substantially when n = 1 (1.7%) and when n = 0 (5.7%). Concomitant with the C-H elongation there is a nonlinear reduction in the hydrogen bond distance, H•••N, with the number of CN groups that is proportionally larger than the accompanying increase in the C-H bond length. Thus, at the ωB97X-D/aug-cc-pVTZ level, the H•••N distance is decreased by 10.4%, 20.3% and 32.0% for n = 2, 1, and 0, respectively. Lastly, the C-H•••N angle remains far from linear until all three CN groups are present. Overall, the geometrical changes suggest an important strengthening of the H•••N hydrogen bond resulting from the cumulative electron-withdrawing effects of the CN groups. An inspection of Tables 2-4 reveals that the effects of the CN groups on the C-X bond lengths and the X•••N halogen bond distances qualitatively mirror those in the hydrogen bond complexes, i.e., X = H. A graphical representation of the effects of the CN groups at the ωB97X-D/aug-cc-pVTZ level can be seen in Figure 3 (for the C-X bond lengths) and in Figure 4 (for the X•••N interaction distances). It is worth noting that the halogen bond angles are linear for both X = Br and I, regardless of the number of CN groups. For X = Cl, the halogen bond angle increases from quasilinear 169° (n = 3) to linear 180° (n = 0).  Changes in the strength of the hydrogen or halogen bond interactions revealed through geometrical parameters are also revealed in pertinent vibrational frequencies.
Specifically, for any given complex, the elongation of the C-X bond length with the number of CN groups brings about a reduction in the stretching C-X vibrational frequency, C-X, as can be seen in Table 5 for the frequencies calculated at both the Changes in the strength of the hydrogen or halogen bond interactions revealed through geometrical parameters are also revealed in pertinent vibrational frequencies. Specifically, for any given complex, the elongation of the C-X bond length with the number of CN groups brings about a reduction in the stretching C-X vibrational frequency, ν C-X , as can be seen in Table 5 for the frequencies calculated at both the ωB97X-D/aug-cc-pVTZ and the MP2/aug-cc-pVDZ levels of theory. In particular, the percent changes in ν C-X as a function of the number of CN groups for the CH 3−n (CN) n X···NMe 3 systems at the ωB97X-D/augcc-pVTZ level are displayed in Figure 5. Table 5. Stretching frequencies, ν C-X (cm −1 ), for CH 3−n (CN) n X···NMe 3 (X = H, Cl, Br, or I; n = 0-3).  Changes in the strength of the hydrogen or halogen bond interactions revealed through geometrical parameters are also revealed in pertinent vibrational frequencies.
Specifically, for any given complex, the elongation of the C-X bond length with the number of CN groups brings about a reduction in the stretching C-X vibrational frequency, C-X, as can be seen in Table 5 for the frequencies calculated at both the B97X-D/aug-cc-pVTZ and the MP2/aug-cc-pVDZ levels of theory. In particular, the percent changes in C-X as a function of the number of CN groups for the CH3-n(CN)nX•••NMe3 systems at the B97X-D/aug-cc-pVTZ level are displayed in Figure  5.   Table 6 displays the BSSE-corrected interaction energy associated with the formation of each complex calculated at the MP2/aug-cc-pVTZ level using the geometries optimized at the ωB97X-D/aug-cc-pVTZ level of theory. An inspection of Table 6 shows that, even in the absence of a CN group, all complexes are stabilized by the C-X···N interaction. In particular, the strength of the interaction follows the order H < Cl < Br < I when n = 0. However, H and Cl swap places when n = 1-3. Table 6 also shows that the increase in the magnitude of the interaction energy for any given complex increases nonlinearly with the number of CN groups. The rather substantial and non-additive increase in the interaction energy per CN group is presented in Figure 6. Specifically, the magnitude of the interaction energy per CN group increases with the number of CN groups for all halogen bonds. This increase also correlates with the size of the halogen. For the hydrogen bond, the magnitude of the interaction energy per CN group increases with one CN group but then shows a small decline with two CN groups followed by a somewhat large increase with three CN groups. It is worth noting that the increases in the magnitude of the interaction energies for the hydrogen bonds are consistently larger than in the chlorine bonds. In particular, the strength of the interaction follows the order H < Cl < Br < I when n = 0. However, H and Cl swap places when n = 1-3. Table 6 also shows that the increase in the magnitude of the interaction energy for any given complex increases nonlinearly with the number of CN groups. The rather substantial and non-additive increase in the interaction energy per CN group is presented in Figure 6. Specifically, the magnitude of the interaction energy per CN group increases with the number of CN groups for all halogen bonds. This increase also correlates with the size of the halogen. For the hydrogen bond, the magnitude of the interaction energy per CN group increases with one CN group but then shows a small decline with two CN groups followed by a somewhat large increase with three CN groups. It is worth noting that the increases in the magnitude of the interaction energies for the hydrogen bonds are consistently larger than in the chlorine bonds.   Table 7 displays the BSSE-corrected interaction energies associated with the formation of the C-H•••N and C-I•••N links in complexes calculated at the CCSD(T)/aug-cc-pVTZ level using the MP2/aug-cc-pVTZ-optimized geometries. An inspection of Table 7 shows similar qualitative trends in interaction energies as a function of the CN groups, as seen at the corresponding MP2 level. The magnitude of the interac-  Table 7 displays the BSSE-corrected interaction energies associated with the formation of the C-H···N and C-I···N links in complexes calculated at the CCSD(T)/aug-cc-pVTZ level using the MP2/aug-cc-pVTZ-optimized geometries. An inspection of Table 7 shows similar qualitative trends in interaction energies as a function of the CN groups, as seen at the corresponding MP2 level. The magnitude of the interaction energies in all cases, however, appears somewhat overestimated at the MP2 level when compared with the corresponding CCSD(T) results. The presence of a halogen (hydrogen) bond in each of the CH 3−n (CN) n X···NMe 3optimized complexes was further confirmed by the topology of the corresponding electron density [24,74]. In particular, a bond critical point was found for each of the C-X···N interactions along the path connecting the nitrogen atom with the related hydrogen (X = H) or halogen (X = Cl, Br, I). The strength and nature of the interaction was gauged by examining properties evaluated at the bond's critical point. In particular, the electron densities, ρ c , evaluated at the C-X···N bond critical points, are typically used as indicators of bond strength. Moreover, the total electron energy densities, H c , and their kinetic and potential energy density components, G c and V c , respectively, can provide insight on the nature of the hydrogen or halogen bond. [24,[74][75][76][77] Table 8 shows the relevant AIM parameters for the various complexes considered (X = H, Cl, Br, and I). Inspection across Table 8 shows, for any given complex system, an increase in ρ c with the number of CN groups, n. A closer examination of the data reveals a non-additive effect on ρ c . In the C-H···N hydrogen bond interaction, for example, ρ c increases by 0.0073 a.u. when n = 1, but more than twice this amount when n = 2 (0.0191 a.u.), and more than six times (0.0461 a.u.) when n = 3. Table 9 summarizes the non-additive changes in ρ c per CN group for any given C-X···N interaction. The strengthening of the C-X···N bond, reflected in the non-additive increase in ρ c with the number of CN groups, is further verified through the correlations found between ρ c and the corresponding magnitude of interaction energies, |∆E|, as shown in Figure 7. In general, for any X, the larger the magnitude of the interaction energy is, the larger the corresponding ρ c is. More specifically, ρ c and |∆E| correlate linearly when X = Cl or Br, and nonlinearly when X = I or H.   Insight into the nature of the C-X•••N bond in a given complex is gained by examining the sign of the corresponding electron energy density at the bond's critical point (Hc). [24,[74][75][76][77] Indeed, a positive sign of Hc would correspond to a closed-shell intermolecular interaction, but a negative sign would correspond to a partly covalent one. Further confirmation on the nature of the interaction can be found in the absolute ratio of the kinetic, Gc, and potential, Vc, electron energy density components of Hc |Gc/Vc|. Accordingly, if |Gc/Vc| > 1, then the interaction is noncovalent. On the other hand, if 0.5 < |Gc/Vc| < 1, then the nature of the interaction is deemed to be partly covalent. Accordingly, Table 8 shows that the nature of the C-H•••N hydrogen bond transition from a closed-shell noncovalent interaction into a partly covalent one when the number of CN groups is two. Likewise, the transition to the partly covalent interaction in C-Br•••N occurs when n = 2. The transition to partly covalent for the C-Cl•••N halogen bond interaction occurs only when there are three CN groups (Table 8). In turn, Table 8 reveals that only one CN group suffices for C-I•••N halogen bond interaction to exhibit a partly covalent nature. In general, the |Gc/Vc| ratio decreases with the number of CN groups in accord with a systematic strengthening of the C-X•••N bond interaction brought about by the electron-withdrawing CN groups.

Energy Decomposition Analysis
In the decomposition scheme [63,64], the total interaction energy is partitioned according to the equation given below.
The term ΔEelstat is usually attractive and it corresponds to the quasi-classical electrostatic interaction between the unperturbed charge distributions of atoms. The Pauli repulsion, ΔEPauli, is the energy change associated with the transformation from the superposition of the unperturbed electron densities of the isolated fragments to the wave function that properly obeys the Pauli principle through the antisymmetrization and renormalization of the product wave function. The orbital interaction, ΔEorb, corresponds Insight into the nature of the C-X···N bond in a given complex is gained by examining the sign of the corresponding electron energy density at the bond's critical point (H c ) [24,[74][75][76][77]. Indeed, a positive sign of H c would correspond to a closed-shell intermolecular interaction, but a negative sign would correspond to a partly covalent one. Further confirmation on the nature of the interaction can be found in the absolute ratio of the kinetic, G c , and potential, V c , electron energy density components of H c |G c /V c |. Accordingly, if |G c /V c | > 1, then the interaction is noncovalent. On the other hand, if 0.5 < |G c /V c | < 1, then the nature of the interaction is deemed to be partly covalent. Accordingly, Table 8 shows that the nature of the C-H···N hydrogen bond transition from a closed-shell noncovalent interaction into a partly covalent one when the number of CN groups is two. Likewise, the transition to the partly covalent interaction in C-Br···N occurs when n = 2. The transition to partly covalent for the C-Cl···N halogen bond interaction occurs only when there are three CN groups (Table 8). In turn, Table 8 reveals that only one CN group suffices for C-I···N halogen bond interaction to exhibit a partly covalent nature. In general, the |G c /V c | ratio decreases with the number of CN groups in accord with a systematic strengthening of the C-X···N bond interaction brought about by the electron-withdrawing CN groups.

Energy Decomposition Analysis
In the decomposition scheme [63,64], the total interaction energy is partitioned according to the equation given below.
The term ∆E elstat is usually attractive and it corresponds to the quasi-classical electrostatic interaction between the unperturbed charge distributions of atoms. The Pauli repulsion, ∆E Pauli , is the energy change associated with the transformation from the superposition of the unperturbed electron densities of the isolated fragments to the wave function that properly obeys the Pauli principle through the antisymmetrization and renormalization of the product wave function. The orbital interaction, ∆E orb , corresponds to the charge transfer and polarization phenomena, i.e., to electron charge shifts resulting from the complex formation; the dispersion interaction energy term, ∆E disp , is also included (Equation (1)). In agreement with the convention adopted in the majority of studies, the attractive energy terms are negative while the Pauli repulsion is positive. Table 10 presents the results of the decomposition of the energy of interaction (Equation (1)) for complexes analyzed in this study. The total BP86-D3/TZ2P interaction energies, ∆E int 's, are also inserted in Table 10. The latter energies are in good agreement with those calculated at the MP2/aug-cc-pVTZ level; for the complexes analyzed here, the linear correlation occurs between the MP2 and DFT(BP86-D3) interaction energies (R = 0.99). As pointed out earlier for the CH n (CN) 3−n X···N(CH 3 ) 3 complexes, the strength of interaction increases, i.e., |∆E int | value increases, for the specific substituent X with the increase in the number of CN substituents. On the other hand, for the specific number of CN substituents in the complex the strength of interaction increases (|∆E int |) with the increase in the atomic number of the halogen atom (X). Additionally, the interactions in CH 3−n (CN) n H···N(CH 3 ) 3 complexes are stronger than the corresponding interactions in the CH 3−n (CN) n Cl···N(CH 3 ) 3 systems. This means that the C-H···N hydrogen bonds are stronger than the C-Cl···N halogen bonds. However, the other C-X···N halogen bonds (X = Br, I) are stronger than the corresponding hydrogen bonds. This is in line with other studies where it was found that hydrogen bonds are stronger than halogen bonds if the chlorine atom is a Lewis acid halogen center, while for heavier halogens, in contrast, the halogen bonds are stronger than their hydrogen bond counterparts [21][22][23][24][25][26]. These findings are in agreement with those based on the DFT results that are described in the former section. However, there is only one exception: for the former DFT results, for systems without CN groups (n = 0) the chlorine bond is stronger than the corresponding hydrogen bond.
Concerning the interaction energy terms, some interesting observations can be made. For example, the corresponding ∆E Pauli , |∆E elstat | and |∆E orb | values increase with the number of CN groups in the following order of X substituents: H < Cl < Br < I; there are only slight disagreements sometimes. In the case of the increase in the |∆E disp | value, the order is slightly different, the same as for the |∆E int | values: Cl < H < Br < I. Table 10 also shows that the electrostatic term is the most important attractive contribution of the total interaction energy, followed by the orbital term and the dispersion interaction energy term. In other words, the following order of terms is observed: |∆E elstat | > |∆E orb | > |∆E disp |. However, there are few exceptions that concern the weaker interactions: in the CH 3 H···N(CH 3 ) 3 complex, the order of |∆E disp | > |∆E elstat | > |∆E orb | is observed, while for the CH 2 CNH···N(CH 3 ) 3 and CH 3 Cl···N(CH 3 ) 3 complexes, this order is |∆E elstat | > |∆E disp | > |∆E orb |. The latter three complexes are among those with the weakest interactions. It is worth noting that for these three complexes exhibiting "the unusual order", the repulsion interaction energy term, ∆E Pauli , is the lowest in comparison with its value for the remaining complexes (lower than 8 kcal/mol). Interestingly, the CH 2 CNCl···N(CH 3 ) 3 complex, with just one CN group, shows the same order of attraction interaction energy contributions as the majority of all other complexes.
One may expect that the most important electrostatic interaction for the majority of complexes analyzed here would be contrary to the covalent character of the links in these complexes. The orbital interaction, related to the electron charge shifts resulting from complexation, is often attributed to covalency [5,8,71,77,78]. However, in several studies, it was pointed out that the positive value of the Heitler-London interaction energy term, ∆E H-L = ∆E Pauli + ∆E elstat , indicates the at least the partial covalent character of the interaction [78]. A positive ∆E H-L indicates that the electrostatic attraction cannot balance the Pauli repulsion and that the stabilization is possible due to the electron charge density shifts expressed by the ∆E orb term. For all complexes analyzed here, the pertinent ∆E H-L values are always positive, indicating the covalent character of the interactions.
It is known that all interaction energy terms increase (repulsive Pauli term and absolute values of the attractive terms) with the increase in the strength of the interaction. However, the |∆E orb | increases faster than |∆E elstat | and |∆E disp | [78]. Hence, the |∆E elstat |/|∆E orb | ratio decreases with the increase in the strength of interaction, or more specifically, with the increase in the covalent character of interaction. It was found, for example, that for extremely strong hydrogen bonds this ratio is lower than unity [78]. Table 10 shows that, in the case of the complexes analyzed here, for the specified X substituent the |∆E elstat |/|∆E orb | ratio generally decreases with the increase in CN substituents. The lowest value of this ratio, of 1.1, occurs for the C(CN) 3 H···N(CH 3 ) 3 and C(CN) 3 Cl···N(CH 3 ) 3 complexes.
As mentioned above, all interaction energy terms increase with the increase in the strength of interaction (absolute values for attractive terms). Particularly, the attractive terms increase to compensate for the increase in the Pauli repulsion term [78].   Table 11 presents various parameters calculated with the use of the NBO6 program. These parameters include the NBO atomic charges of X and N centers that are in contact. The nitrogen center which belongs to the N(CH3)3 Lewis base unit is always negative. The most negative charges of nitrogen occur for complexes linked by the CH•••N hydrogen bonds, between −0.34 au and −0.37 au. For the remaining complexes, this charge is located between −0.25 au and −0.34 au. Various situations are observed for the X charge of the Lewis acid species. The hydrogen center (X = H) is always positive, which may indicate the electrostatic character of the C-H•••N hydrogen bond. The same goes for iodine as the Lewis acid center: it is characterized by a positive charge. This is in line with other studies where it was found that the Lewis acid properties of halogen increase with the increase in its atomic number [27,79]. Similarly, the atomic charge for another heavier halogen, bromine, is positive, although less so than the corresponding iodine of the Lewis  Table 11 presents various parameters calculated with the use of the NBO6 program. These parameters include the NBO atomic charges of X and N centers that are in contact. The nitrogen center which belongs to the N(CH 3 ) 3 Lewis base unit is always negative. The most negative charges of nitrogen occur for complexes linked by the CH···N hydrogen bonds, between −0.34 au and −0.37 au. For the remaining complexes, this charge is located between −0.25 au and −0.34 au. Various situations are observed for the X charge of the Lewis acid species. The hydrogen center (X = H) is always positive, which may indicate the electrostatic character of the C-H···N hydrogen bond. The same goes for iodine as the Lewis acid center: it is characterized by a positive charge. This is in line with other studies where it was found that the Lewis acid properties of halogen increase with the increase in its atomic number [27,79]. Similarly, the atomic charge for another heavier halogen, bromine, is positive, although less so than the corresponding iodine of the Lewis acid unit possessing the same number of CN substituents. There is one exception here: in the CH 3 Br···N(CH 3 ) 3 complex, the bromine center is negative. In the case of the chlorine center, its charge is negative except for the CH(CN) 2 Cl···N(CH 3 ) 3 complex, which shows a positive charge, albeit very close to zero. Table 11. CH 3−n (CN) n X···N(CH 3 ) 3 complexes (X = H, Cl, Br, I); the properties of X···N contact are given. Q(X)-NBO charge of X; Q(N)-NBO charge of N; WBI-Wiberg bond index; NBI-natural binding index; n→σ* is n(N)→σ CX * orbital-orbital interaction energy (in kcal/mol). It is worth noting, however, that electrostatic potentials are better indicators of the Lewis acidity-basicity than the charges [27,79]. The electrostatic potential (EP) surfaces of the CH 3−n (CN) n Cl units acting as the Lewis acids in the complexes analyzed here are presented in Figure 9. These EP calculations were performed at the ωB97XD/aug-cc-pVTZ level. The EP surfaces correspond to the electron density of the 0.001 au; this electron density value was proposed by Bader and coworkers as corresponding approximately to the van der Waals spheres [80]. The EP values corresponding to the σ-holes at the halogen centers of all CH 3−n (CN) n X units (X = Cl, Br, I) are presented in Figure 9. One can see that the EP value for the fixed halogen center increases with the increase in the number of CN substituents; similarly, for the fixed number of CN substituents, greater EP values are observed for a greater atomic number of the halogen center. The latter is in agreement with former studies where, for the same group elements, the EP value increased with the increase in atomic number [27,79]. One can see that the EP value refers approximately to the Lewis acid properties of the center considered. The EP value of the Lewis acid unit correlates often with the strength of interaction for complexes characterized by the same Lewis base units. For the halogen-bonded complexes analyzed in this study, a good second-order polynomial correlation is observed between the EP values presented in Figure 9 and the BP86-D3/TZ2P interaction energies (Table 10), R = 0.962. ments, the EP value increased with the increase in atomic number. [27,79] One can see that the EP value refers approximately to the Lewis acid properties of the center considered. The EP value of the Lewis acid unit correlates often with the strength of interaction for complexes characterized by the same Lewis base units. For the halogen-bonded complexes analyzed in this study, a good second-order polynomial correlation is observed between the EP values presented in Figure 9 and the BP86-D3/TZ2P interaction energies (Table 10), R = 0.962.  Table 11 presents the energies of the most important orbital-orbital interactions; they correspond to the n(N)  CX * overlaps ( * designates the atibonding orbital here  Table 11 presents the energies of the most important orbital-orbital interactions; they correspond to the n(N) → σ CX * overlaps (* designates the atibonding orbital here and further in the text). For the A-H···B hydrogen bond, the n B → σ AH * overlap is the most important orbital-orbital interaction [70,71]. n B designates the lone electron pair of the B proton-accepting centre; σ AH * is an antibonding orbital of the A-H bond of the Lewis acid unit. The interaction energy of this overlap is expressed by the following equation (Equation (2)):

Lewis Acid
∆E (n B →σ AH *) = q i n B |F|σ AH * 2 /(ε (σ AH *) − ε (n B )) (2) n B |F|σ AH * is the Fock matrix element, (ε (σ AH *) − ε (n B )) is the orbital energy difference and q i is the donor orbital occupancy. The n N →σ CH * overlaps occur for the C-H···N intermolecular interactions, i.e., for the hydrogen bonds discussed here in complexes where the hydrogen is the Lewis acid center. For the remaining complexes, the n N →σ CX * overlaps are observed with X being the halogen center. However, if all centers (X = H, Cl, Br and I) are considered for the n N →σ CX * overlaps, the following observations can be noted. For the specified substituent, the interaction energy corresponding to the orbital overlap discussed above increases with the increase in the number of CN substituents in the Lewis acid unit. For the specified number of CN substituents for the changing X, there is the following order of the increase in the interaction energy of this overlap Cl < H < Br < I. When the Lewis acid species do not contain CN substituents, the order is slightly different: H < Cl < Br < I. Table 11 presents also the Wiberg bond indices (WBIs) and the natural binding indices (NBIs) for the X···N intermolecular interactions discussed here. The Wiberg index [72,81] corresponds approximately to the bond order, while the NBI is an interaction parameter that can be expressed as the strength (matrix norm) of off-diagonal couplings between the atomic blocks of the natural atom orbital (NAO) density matrix. However, the NBI is also related to the Wiberg index and consequently to the bond order; approximately both indices correspond to the strength of the interatomic link. For all the results presented in Table 11, a linear correlation between the NBI and WBI indices (R 2 = 0.955) is found. The correlation is even better if the potential function is considered (R 2 = 1.000), as shown in Figure 10.
between the atomic blocks of the natural atom orbital (NAO) density matrix. However, the NBI is also related to the Wiberg index and consequently to the bond order; approximately both indices correspond to the strength of the interatomic link. For all the results presented in Table 11, a linear correlation between the NBI and WBI indices (R 2 = 0.955) is found. The correlation is even better if the potential function is considered (R 2 = 1.000), as shown in Figure 10. Both WBI and NBI indices correlate with other measures of the interaction strength. In particular, for the halogen-bonded systems, the Wiberg index correlates linearly with ΔEint (Table 10 R 2 = 0.993, as demonstrated in Figure 11. The systems linked by hydrogen bonds (not included in Figure 11) are excluded from this linear dependence, but show the same tendency, i.e., the increase in WBI index for stronger interactions. A similar linear Both WBI and NBI indices correlate with other measures of the interaction strength. In particular, for the halogen-bonded systems, the Wiberg index correlates linearly with ∆E int (Table 10 R 2 = 0.993, as demonstrated in Figure 11. The systems linked by hydrogen bonds (not included in Figure 11) are excluded from this linear dependence, but show the same tendency, i.e., the increase in WBI index for stronger interactions. A similar linear correlation is observed between NBI and ∆E int (R 2 = 0.961) when only the halogenbonded complexes are considered; again, the H-bonded systems do not follow a linear correlation but show the same tendency, i.e., an increase in the NBI index with increasing interaction strength. correlation is observed between NBI and ΔEint (R 2 = 0.961) when only the halogen-bonded complexes are considered; again, the H-bonded systems do not follow a linear correlation but show the same tendency, i.e., an increase in the NBI index with increasing interaction strength. Figure 11. The linear correlation between the Wiberg index and the interaction energy, ΔEint (Equation (1) and Table 10); the hydrogen-bonded systems are excluded from this correlation.

Conclusions
Density functional theory and wave function theory calculations were performed to examine the effects that the electron-withdrawing cyano group CN have on the hydrogen donor ability of methane and the halogen bond donor ability of halomethane. Trimethyl amine was used throughout as the hydrogen or the halogen bond acceptor. Specifically, the equilibrium geometries, vibrational frequencies, and BSSE interaction energies for the complexes CH3-n(CN)nX•••NMe3 (n = 0-3; X = H, Cl, Br, I) were investigated.
The computational results reveal a substantial and non-additive strengthening of the C-X•••N interaction with the number of CN groups in the X-bond donor molecule. This interaction strengthening is indicated, for example, by a large increase in the covalent C-X bond, concomitant with a sizeable decrease in the intermolecular X•••N distance. The increase in the covalent C-X bond brings about a corresponding shift to the red in the corresponding vibrational C-X-stretching frequency. Moreover, direct evidence of the

Wiberg index
E int (kcal/mol) Figure 11. The linear correlation between the Wiberg index and the interaction energy, ∆E int (Equation (1) and Table 10); the hydrogen-bonded systems are excluded from this correlation.

Conclusions
Density functional theory and wave function theory calculations were performed to examine the effects that the electron-withdrawing cyano group CN have on the hydrogen donor ability of methane and the halogen bond donor ability of halomethane. Trimethyl amine was used throughout as the hydrogen or the halogen bond acceptor. Specifically, the equilibrium geometries, vibrational frequencies, and BSSE interaction energies for the complexes CH 3−n (CN) n X···NMe 3 (n = 0-3; X = H, Cl, Br, I) were investigated.
The computational results reveal a substantial and non-additive strengthening of the C-X···N interaction with the number of CN groups in the X-bond donor molecule. This interaction strengthening is indicated, for example, by a large increase in the covalent C-X bond, concomitant with a sizeable decrease in the intermolecular X···N distance. The increase in the covalent C-X bond brings about a corresponding shift to the red in the corresponding vibrational C-X-stretching frequency. Moreover, direct evidence of the nonadditive strengthening of the C-X···N bond is provided by changes in the BSSE interaction energies per CN group, relative to the interaction when there are no CN groups (n = 0). Both the strength and the nature of the C-X···N bond interactions as a function of the number of CN groups were examined within the framework of the atoms in molecules theory.
Further evidence of the enhancement effects of the CN group on the C-X···N bond is given by the results of both the energy decomposition and the NBO analyses. Particularly, the absolute values of all interaction energy terms increase with the increase in the number of CN groups for the specified X-center. The electrostatic interactions accompanied by the electron charge shifts follow the increase in the Pauli repulsion with the decrease in the C-X···N bond length, since the sum of attractive interaction energies correlates with the repulsion interaction energy. The electrostatic interaction is the most important attractive term for all complexes, except for the species where methane acts as the Lewis acid unit where the dispersion interaction plays the crucial role. For the majority of complexes investigated here, the next important factor is the orbital-orbital interaction energy; only for the weakest interactions is the dispersion more pronounced than orbital interaction. The NBO approach shows that the n→σ* orbital-orbital overlap is a signature of both hydrogen and halogen bonds. This kind of interaction is strengthened for the specified X-center with the increase in the number of CN groups.