Next Article in Journal
The Stimulation of Macrophages by Systematical Administration of GM-CSF Can Accelerate Adult Wound Healing Process
Previous Article in Journal
Roles of Exosomes in Chronic Rhinosinusitis: A Systematic Review
Previous Article in Special Issue
Uracil Derivatives for Halogen-Bonded Cocrystals
 
 
Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
Journals
IJMS
Volume 23
Issue 19
10.3390/ijms231911289
ijms-logo
Submit to this Journal Review for this Journal Propose a Special Issue
► Article Menu

Article Menu

share Share announcement Help format_quote Cite question_answer Discuss in SciProfiles thumb_up
...
Endorse textsms
...
Comment
first_page
settings
Order Article Reprints
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
Article

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)

by
Rubén D. Parra
1,* and
Sławomir J. Grabowski
2,3,*
1
Department of Chemistry and Biochemistry, DePaul University, Chicago, IL 60614, USA
2
Polimero eta Material Aurreratuak: Fisika, Kimika eta Teknologia, Kimika Fakultatea, Euskal Herriko Unibertsitatea UPV/EHU, Donostia International Physics Center (DIPC), P.O. Box 1072, 20080 Donostia, Spain
3
Ikerbasque, Basque Foundation for Science, 48011 Bilbao, Spain
*
Authors to whom correspondence should be addressed.
Int. J. Mol. Sci. 2022, 23(19), 11289; https://doi.org/10.3390/ijms231911289
Submission received: 23 August 2022 / Revised: 15 September 2022 / Accepted: 20 September 2022 / Published: 25 September 2022
(This article belongs to the Special Issue Synthesis or Assembly in Supramolecules)
Browse Figures
Versions Notes

Abstract

:
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.

1. 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 than one type of halogen atom that can be used in D-Hal, the halogen bond also renders greater flexibility for fine-tuning compared with the hydrogen bond [32,33,34,35,36,37,38,39,40,41,42,43,44]. One factor that can be used to fine tune the D-H or the D-Hal donor ability is the electronegativity of the atom covalently bonded to hydrogen or halogen. In the case of the hydrogen bond donor, an increase in electronegativity reduces electron density in the hydrogen atom in D-H, making it more susceptible to interact with a Lewis base. Thus, C-H is considered a weak hydrogen bond donor when compared with either the O-H or the N-H hydrogen bond donor. In the case of the halogen bond donor ability of D-Hal, it has been found that both the size and the magnitude of the positive electrostatic potential (known as the σ-hole) of the halogen atom increases with the increasing electronegativity of the atom covalently bonded to the halogen atom in D-Hal. It is worth noting that the σ-hole on the halogen atom acts as the Lewis acid site that interacts with a suitable electron donor species acting as the Lewis base, and that the location of the σ-hole (opposite to the covalent D-Hal bond) results in the highly distinctive linearity of the halogen bond [9,32,44]. Further studies have demonstrated that the ability of a halogen atom to engage in halogen bonding correlates with the size of the σ-hole. Accordingly, the C-Hal is deemed a weak halogen bond donor when compared with either the O-Hal or the N-Hal donor. Moreover, it has also been found that for the same D, the size of the σ-hole increases with the size of the halogen (F ≪ Cl < Br < I). The correlation between the halogen atom size and the σ-hole adds flexibility for fine-tuning the halogen bond donor ability of D-Hal when compared with the fine-tuning of the hydrogen bond donor ability of D-H. Another factor that has been shown to influence hydrogen or halogen bond donor ability is the hybridization of the atom covalently bonded to the hydrogen (in D-H) or halogen atom in (D-Hal). Specifically, the donor ability of C-H or C-Hal tends to increase with the increasing s-character of the hybridized carbon, i.e., C(sp3) < C(sp2) < C(sp) [45,46,47,48]. The presence of electron-withdrawing groups have also been shown to enhance the donor ability of either the D-H or the D-Hal group. Thus, even a weak hydrogen (C-H) or halogen (C-Hal) bond donor with hybridized sp3 carbon can increase its donor ability by adding suitable electron-withdrawing groups to the carbon atom [40,42,45].
In this work, the enhancing effect on the hydrogen bond or the halogen bond donor ability of methane or halomethane is investigated by sequentially adding up to three electron-withdrawing cyano groups, CN, as substituents on the hybridized sp3 carbon of the methane or the halomethane. Specifically, the strengthening of the hydrogen or the halogen bond is examined as a function of the number of cyano groups in the complexes CH3−n(CN)nX∙∙∙NMe3 (n = 0–3; X = H, Cl, Br, I). The following are the reasons for the choice of the CN group as a substituent: It is known as a strong electron-withdrawing substituent that also possesses simple structure. Moreover, this group has not been analyzed extensively as a factor influencing halogen bond strength, and not as extensively as fluorine and other halogens, for example.
For convenience, the hydrogen or the halogen bond interaction studied in this work is jointly represented as C-X∙∙∙N. Moreover, the relatively strong and neutral Lewis base trimethyl amine, NMe3, is used throughout as the halogen bond acceptor. Lastly, in this work, the correlation between the halogen bond strength and the halogen atom size is also examined. The choice of small Lewis acid (CH3−n(CN)nX) and Lewis base (NMe3) units allow us to apply various theoretical tools and consequently to analyze different characteristics of interactions. The particular attention is paid here on the comparison between hydrogen and halogen-bonded systems. The competition between these interactions is often observed in crystal structures; thus, the results presented here allow us to understand the influence of these interactions on the arrangement of molecules and ions in crystals.

2. Computational Details

Geometry optimizations, frequency calculations, and interaction energies were carried out using the GAUSSIAN 16 program [49]. Geometry optimizations for all complexes, CH3−n(CN)nX∙∙∙NMe3 (n = 0–3; X = H, Cl, Br, I) and constituent monomers were first carried out using the ωB97X-D [50] density functional method and the aug-cc-pVTZ-PP [51] basis set for the iodine atom and the aug-cc-pVTZ [52,53,54,55] basis set for all other atoms. Corresponding frequency calculations demonstrated that the ωB97X-D-optimized geometries were minimum energy structures with no imaginary frequencies. Subsequent geometry optimizations for all monomers and complexes were carried out using the MP2 [56,57] method with both the aug-cc-pVTZ-PP and the aug-cc-pVDZ-PP [58] basis sets for the iodine atom and the corresponding aug-cc-pVTZ or aug-cc-PVDZ basis sets for all other atoms. The MP2 geometries optimized with the smaller of the two basis sets (aug-cc-pVDZ-PP, aug-cc-pVDZ) were shown to be minimum energy structures with no imaginary frequencies calculated at the same level of theory.
The ωB97X-D geometries of complexes optimized with the larger basis set (aug-cc-pVTZ-PP, aug-cc-pVTZ) were used for all subsequent analyses including interaction energy, NBO, and AIM analyses. In particular, topological features of electron density according to the theory of atoms in molecules (AIM) of Bader [59] were obtained with the AIMALL [60] software package. MP2 interaction energies were obtained for all complexes and corrected for basis set superposition error, BSSE, using the counterpoise method [61]. BSSE-corrected interaction energies were also obtained with the CCSD(T) [62] method for the X = H- or X = I-containing systems.
The BP86-D3/TZ2P calculations were carried out with the ADF 2019.302 program codes [63] for the decomposition of interaction energies [64,65] for the ωB97X-D-optimized dimer complexes described previously. That is, the BP86 functional [66,67] with Grimme dispersion corrections [68] was applied, and for all elements the uncontracted Slater-type orbitals (STOs) as basis functions with triple-ζ quality [69] were applied. Relativistic scalar ZORA corrections [65] were applied for species containing heavier atoms (Br and I).
The NBO method [70,71] was used to calculate the atomic charges, the energies of orbital–orbital interactions, the Wiberg bond indices [72], and the natural binding indices. The NBO 6.0 program [73] implemented in the ADF2019 set of codes [63] was applied to perform NBO calculations.
The calculations of interaction energies were performed with the splitting of the complexes CH3−n(CN)nX∙∙∙NMe3 into the CH3−n(CN)nX and NMe3 units. The same splitting was carried out in the decomposition of interaction energies as well as in other calculations where interactions between Lewis acid and Lewis base units were considered.

3. Results and Discussion

3.1. Geometries and Vibrational Frequencies

Optimized geometries for all CH3−n(CN)nX∙∙∙NMe3 (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. Figure 1 and Figure 2 show the ωB97X-D/aug-cc-pVTZ-optimized geometries of the CH3−n(CN)nH∙∙∙NMe3 and CH3−n(CN)nCl∙∙∙NMe3 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 Table 1, Table 2, Table 3 and Table 4. Accordingly, the inspection of Table 1, Table 2, Table 3 and Table 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.
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 Table 2, Table 3 and Table 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, νC-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 νC-X as a function of the number of CN groups for the CH3−n(CN)nX∙∙∙NMe3 systems at the ωB97X-D/aug-cc-pVTZ level are displayed in Figure 5.

3.2. Intermolecular Interaction Energies and AIM Analyses

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.
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 CH3−n(CN)nX∙∙∙NMe3-optimized 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, ρc, evaluated at the C-X∙∙∙N bond critical points, are typically used as indicators of bond strength. Moreover, the total electron energy densities, Hc, and their kinetic and potential energy density components, Gc and Vc, 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 ρc with the number of CN groups, n. A closer examination of the data reveals a non-additive effect on ρc. In the C-H∙∙∙N hydrogen bond interaction, for example, ρc 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 ρc 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 ρc with the number of CN groups, is further verified through the correlations found between ρc and the corresponding magnitude of interaction energies, |ΔE|, as shown in Figure 7. In general, for any X, the larger the magnitude of the interaction energy is, the larger the corresponding ρc is. More specifically, ρc and |ΔE| 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.

3.3. Energy Decomposition Analysis

In the decomposition scheme [63,64], the total interaction energy is partitioned according to the equation given below.
ΔEint = ΔEelstat + ΔEPauli + ΔEorb + ΔEdisp
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 to the charge transfer and polarization phenomena, i.e., to electron charge shifts resulting from the complex formation; the dispersion interaction energy term, ΔEdisp, 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, ΔEint’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 CHn(CN)3−nX∙∙∙N(CH3)3 complexes, the strength of interaction increases, i.e., |ΔEint| 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 (|ΔEint|) with the increase in the atomic number of the halogen atom (X). Additionally, the interactions in CH3−n(CN)nH∙∙∙N(CH3)3 complexes are stronger than the corresponding interactions in the CH3−n(CN)nCl∙∙∙N(CH3)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 ΔEPauli, |ΔEelstat| and |ΔEorb| 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 |ΔEdisp| value, the order is slightly different, the same as for the |ΔEint| 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: |ΔEelstat| > |ΔEorb| > |ΔEdisp|. However, there are few exceptions that concern the weaker interactions: in the CH3H∙∙∙N(CH3)3 complex, the order of |ΔEdisp| > |ΔEelstat| > |ΔEorb| is observed, while for the CH2CNH∙∙∙N(CH3)3 and CH3Cl∙∙∙N(CH3)3 complexes, this order is |ΔEelstat| > |ΔEdisp| > |ΔEorb|. 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, ΔEPauli, is the lowest in comparison with its value for the remaining complexes (lower than 8 kcal/mol). Interestingly, the CH2CNCl∙∙∙N(CH3)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, ΔEH-L = ΔEPauli + ΔEelstat, indicates the at least the partial covalent character of the interaction [78]. A positive ΔEH-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 ΔEorb term. For all complexes analyzed here, the pertinent ΔEH-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 |ΔEorb| increases faster than |ΔEelstat| and |ΔEdisp| [78]. Hence, the |ΔEelstat|/|ΔEorb| 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 |ΔEelstat|/|ΔEorb| ratio generally decreases with the increase in CN substituents. The lowest value of this ratio, of 1.1, occurs for the C(CN)3H∙∙∙N(CH3)3 and C(CN)3Cl∙∙∙N(CH3)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]. Figure 8 presents an excellent linear correlation (R = 1.000) between the repulsion term and the sum of attractive terms if the halogen is the Lewis acid center, i.e., if the complexes are linked by halogen bonds. However, the hydrogen-bonded systems not presented in this figure are not so far from this linear correlation.

3.4. NBO Analyses

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 acid unit possessing the same number of CN substituents. There is one exception here: in the CH3Br∙∙∙N(CH3)3 complex, the bromine center is negative. In the case of the chlorine center, its charge is negative except for the CH(CN)2Cl∙∙∙N(CH3)3 complex, which shows a positive charge, albeit very close to zero.
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 CH3−n(CN)nCl 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 CH3−n(CN)nX 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.
Table 11 presents the energies of the most important orbital–orbital interactions; they correspond to the n(N) → σCX* overlaps (* designates the atibonding orbital here and further in the text). For the A-H∙∙∙B hydrogen bond, the nB → σAH* overlap is the most important orbital–orbital interaction [70,71]. nB designates the lone electron pair of the B proton-accepting centre; σAH* 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)):
ΔE (nB→σAH*) = qi〈nB|F|σAH*〉2/(ε (σAH*) − ε (nB))
〈nB|F|σAH*〉 is the Fock matrix element, (ε (σAH*) − ε (nB)) is the orbital energy difference and qi is the donor orbital occupancy. The nN→σCH* 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 nN→σCX* overlaps are observed with X being the halogen center. However, if all centers (X = H, Cl, Br and I) are considered for the nN→σCX* 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 (R2 = 0.955) is found. The correlation is even better if the potential function is considered (R2 = 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 R2 = 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 ΔEint (R2 = 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.

4. 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 non-additive 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.

Author Contributions

Conceptualization, R.D.P. and S.J.G.; Investigation, R.D.P. and S.J.G.; Writing original draft, R.D.P. and S.J.G. All authors have read and agreed to the published version of the manuscript.

Funding

S.J.G. thanks Eusko Jaurlaritza, grant number IT-1254-19, for funding support.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Not applicable.

Acknowledgments

R.D.P. is grateful to the Department of Chemistry and Biochemistry at DePaul University for its continuing support.

Conflicts of Interest

The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.

References

  1. Pimentel, G.C.; McClellan, A.L. The Hydrogen Bond; Freeman: San Francisco, CA, USA, 1960. [Google Scholar]
  2. Desiraju, G.R.; Steiner, T. The Weak Hydrogen Bond; Oxford University Press: New York, NY, USA, 1999. [Google Scholar]
  3. Jeffrey, G.A. An Introduction to Hydrogen Bonding; Oxford University Press: New York, NY, USA, 1997. [Google Scholar]
  4. Scheiner, S. Hydrogen Bonding: A Theoretical Perspective; Oxford University Press: New York, NY, USA, 1997. [Google Scholar]
  5. Gilli, G.; Gilli, P. The Nature of the Hydrogen Bond; Oxford University Press: Oxford, UK, 2009. [Google Scholar]
  6. Scheiner, S. New ideas from an Old Concept: The Hydrogen Bond. Biochem 2019, 4, 6–9. [Google Scholar] [CrossRef]
  7. Scheiner, S. The Hydrogen Bond: A Hundred Years and Counting. J. Indian Inst. Sci. 2020, 100, 61–76. [Google Scholar] [CrossRef]
  8. Grabowski, S.J. Understanding Hydrogen Bonds: Theoretical and Experimental Views; The Royal Society of Chemistry: Cambridge, UK, 2021. [Google Scholar]
  9. Clark, T.; Hennemann, M.; Murray, J.S.; Politzer, P. Halogen Bonding: The σ-Hole. J. Mol. Model. 2007, 13, 291–296. [Google Scholar] [CrossRef] [PubMed]
  10. Politzer, P.; Lane, P.; Concha, M.C.; Ma, Y.; Murray, J.S. An Overview of Halogen Bonding. J. Mol. Model. 2007, 13, 305–311. [Google Scholar] [CrossRef] [PubMed]
  11. Legon, A.C. The Halogen Bond: An Interim Perspective. Phys. Chem. Chem. Phys. 2010, 12, 7736–7747. [Google Scholar] [CrossRef]
  12. Wang, C.; Danovich, D.; Mo, Y.; Sahik, S. On the Nature of the Halogen Bond. J. Chem. Theory Comput. 2014, 10, 3726–3737. [Google Scholar] [CrossRef]
  13. Cavallo, G.; Metrangolo, P.; Milani, R.; Pilati, T.; Priimagi, A.; Resnati, G.; Terraneo, G. The Halogen Bond. Chem. Rev. 2016, 116, 2478–2601. [Google Scholar] [CrossRef]
  14. Costa, P.J. The Halogen Bond: Nature and Applications. Phys. Sci. Rev. 2017, 2, 2017-0136. [Google Scholar] [CrossRef]
  15. Varadwaj, P.R.; Varadwaj, A.; Marques, H.M. Halogen Bonding: A Halogen-Centered Noncovalent Interaction Yet to Be Understood. Inorganics 2019, 7, 40. [Google Scholar] [CrossRef]
  16. Riley, K.E.; Murray, J.S.; Fanfrlík, J.; Řezáč, J.; Solá, R.J.; Concha, M.C.; Ramos, F.M.; Politzer, P. Halogen Bond Tunability I: The Effects of Aromatic Fluorine Substitution on the Strengths of Halogen-Bonding Interactions Involving Chlorine, Bromine, and Iodine. J. Mol. Model. 2011, 17, 3309–3318. [Google Scholar] [CrossRef]
  17. Akorta, I.; Legon, A.C. Nucleophilicities of Lewis Bases B and Electrophilicities of Lewis Acids A Determined from the Dissociation Energies of Complexes B· · ·A Involving Hydrogen Bonds, Tetrel Bonds, Pnictogen Bonds, Chalcogen Bonds and Halogen Bonds. Molecules 2017, 10, 1786. [Google Scholar] [CrossRef] [PubMed]
  18. Arunan, E.; Desiraju, G.R.; Klein, R.A.; Sadlej, J.; Scheiner, S.; Alkorta, I.; Clary, D.C.; Crabtree, R.H.; Dannenberg, J.J.; Hobza, P.; et al. Definition of the Hydrogen Bond. Pure Appl. Chem. 2011, 83, 1637–1641. [Google Scholar] [CrossRef]
  19. Desiraju, G.R.; Ho, P.S.; Kloo, L.; Legon, A.C.; Marquardt, R.; Metrangolo, P.; Politzer, P.; Resnati, G.; Rissanen, K. Definition of the Halogen Bond. Pure Appl. Chem. 2013, 85, 1711–1713. [Google Scholar] [CrossRef]
  20. Metrangolo, P.; Neukirch, H.; Pilati, T.; Resnati, G. Halogen Bonding Based Recognition Processes: A World Parallel to Hydrogen Bonding. Acc. Chem. Res. 2005, 38, 386–395. [Google Scholar] [CrossRef]
  21. Grabowski, S.J. Hydrogen and Halogen Bonds are Ruled by the Same Mechanisms. Phys.Chem. Chem. Phys. 2013, 15, 7249–7259. [Google Scholar] [CrossRef]
  22. Walters, L.P.; Bickelhaupt, F.M. Halogen Bonding versus Hydrogen Bonding: A Molecular Orbital Perspective. ChemistryOpen 2012, 1, 96–105. [Google Scholar] [CrossRef] [PubMed]
  23. Robertson, C.C.; Wright, J.S.; Carrington, E.J.; Perutz, R.N.; Hunter, C.A.; Brammer, L. Hydrogen Bonding vs. Halogen Bonding: The Solvent Decides. Chem. Sci. 2017, 8, 5392–5398. [Google Scholar] [CrossRef]
  24. Grabowski, S.J. QTAIM Characteristics of Halogen Bond and Related Interactions. J. Phys. Chem. A 2012, 116, 1838–1845. [Google Scholar] [CrossRef]
  25. Quiñonero, D.; Frontera, A. Hydrogen Bond versus Halogen Bond in HXOn (X = F, Cl, Br, and I) Complexes with Lewis Bases. Inorganics 2019, 7, 9. [Google Scholar] [CrossRef]
  26. Shields, Z.P.; Murray, J.S.; Politzer, P. Directional Tendencies of Halogen and Hydrogen Bonds. Int. J. Quantum Chem. 2010, 110, 2823–2832. [Google Scholar] [CrossRef]
  27. Politzer, P.; Murray, J.S.; Clark, T. Halogen Bonding: An Electrostatically Driven Highly Directional Noncovalent Interaction. Phys. Chem. Chem. Phys. 2010, 12, 7748–7757. [Google Scholar] [CrossRef] [PubMed]
  28. Shahi, A.; Arunan, E. Why Are Hydrogen Bonds Directional? J. Chem. Sci. 2016, 128, 1571–1577. [Google Scholar] [CrossRef]
  29. Saccone, M.; Cavallo, G.; Metrangolo, P.; Pace, A.; Pibiri, I.; Pilati, T.; Resnati, G.; Terraneo, G. Halogen Bond Directionality Translates Tecton Geometry into Self-Assembled Architecture Geometry. CrystEngComm 2013, 15, 3102–3105. [Google Scholar] [CrossRef]
  30. Riley, K.E. Critical Comparison of R-X∙∙∙Y and R-H∙∙∙Y Directionality in Halogen and Hydrogen Bonds using Modern Computational Chemistry Methods. Chem. Phys. Lett. 2020, 744, 137221. [Google Scholar] [CrossRef]
  31. Bauzá, A.; Quiñonero, D.; Frontera, A. Substituent Effects in Multivalent Halogen Bonding Complexes: A Combined Theoretical and Crystallographic Study. Molecules 2018, 23, 18. [Google Scholar] [CrossRef] [PubMed]
  32. Murray, J.S.; Macaveiua, L.; Politzer, P. Factors Affecting the Strengths of σ-Hole Electrostatic Potentials. J. Chem. Theory Comput. 2014, 5, 590–596. [Google Scholar] [CrossRef]
  33. Ibrahim, M.A.A.; Hasb, A.A.M. Polarization Plays the Key Role in Halogen Bonding: A Point-of-Charge-Based Quantum Mechanical Study. Theor. Chem. Acc. 2019, 138, 1–12. [Google Scholar] [CrossRef]
  34. Brinck, T.; Borrfors, A.N. Electrostatics and Polarization Determine the Strength of the Halogen Bond: A Red card for Charge Transfer. J. Mol. Model. 2019, 25, 125. [Google Scholar] [CrossRef]
  35. Oliveira, V.; Kraka, E.; Cremer, D. The Intrinsic Strength of the Halogen Bond: Electrostatic and Covalent Contributions Described by Coupled Cluster Theory. Phys. Chem. Chem. Phys. 2016, 18, 33031–33046. [Google Scholar] [CrossRef]
  36. Riley, K.E.; Hobza, P. The Relative Roles of Electrostatics and Dispersion in the Stabilization of Halogen Bonds. Phys. Chem. Chem. Phys. 2013, 15, 17742–17751. [Google Scholar] [CrossRef]
  37. Orlova, A.P.; Jasien, P.G. Halogen Bonding in Self-Assembling Systems: A Comparison of Intra- and Interchain Binding Energies. Comput. Theor. Chem. 2018, 1139, 63–69. [Google Scholar] [CrossRef]
  38. Nepal, B.; Scheiner, S. NX···Y Halogen Bonds. Comparison with NH···Y H-Bonds and CX···Y Halogen Bonds. Phys. Chem. Chem. Phys. 2016, 18, 18015–18023. [Google Scholar] [CrossRef] [PubMed]
  39. Riley, K.E.; Murray, J.S.; Politzer, P.; Concha, M.C.; Hobza, P. Br···O Complexes as Probes of Factors Affecting Halogen Bonding: Interactions of Bromobenzenes and Bromopyrimidines with Acetone. J. Chem. Theory Comput. 2009, 5, 155–163. [Google Scholar] [CrossRef] [PubMed]
  40. Han, N.; Zeng, Y.; Li, X.; Zheng, S.; Meng, L. Enhancing Effects of Electron-Withdrawing Groups and Metallic Ions on Halogen Bonding in the YC6F4X···C2H8N2 (X = Cl, Br, I., Y = F, CN, NO2, LiNC+, NaNC+) Complex. J. Phys. Chem. A 2013, 117, 12959–12968. [Google Scholar] [CrossRef] [PubMed]
  41. Ebrahimia, A.; Razmazma, H.; Delarami, H.S. The Nature of Halogen Bonds in [N∙∙∙X∙∙∙N]+ Complexes: A Theoretical Study. Phys. Chem. Res. 2016, 4, 1–15. [Google Scholar]
  42. Tian, W.; Huang, X.; Li, Q.; Li, W.; Cheng, J.; Gong, B. Effect of Superalkali Substituents on the Strengths and Properties of Hydrogen and Halogen bonds. J. Mol. Model. 2013, 19, 1311–1318. [Google Scholar] [CrossRef]
  43. Zhang, Y.; Li, A.-Y.; Cao, L.-J. Electronic Properties of the Halogen Bonds Z3CX···Y- Between Halide Anions and Methyl Halides. Struct. Chem. 2012, 23, 627–636. [Google Scholar] [CrossRef]
  44. Franchini, D.; Forni, A.; Genoni, A.; Pieraccini, S.; Gandini, E.; Sironi, M. The Origin of the σ-Hole in Halogen Atoms: A Valence Bond Perspective. ChemistryOpen 2020, 9, 445–450. [Google Scholar] [CrossRef]
  45. Scheiner, S.; Grabowski, S.J.; Kar, T. Influence of Hybridization and Substitution upon the Properties of the CH··O Hydrogen Bond. J. Phys. Chem. A 2001, 105, 10607–10612. [Google Scholar] [CrossRef]
  46. Metrangolo, P.; Meyer, F.; Pilati, T.; Resnati, G.; Terraneo, G. Halogen Bonding in Supramolecular Chemistry. Angew. Chem. Int. Ed. 2008, 47, 6114–6127. [Google Scholar] [CrossRef]
  47. Rege, P.D.; Malkina, O.L.; Goroff, N.S. The Effect of Lewis Bases on the 13C NMR of Iodoalkynes. J. Am. Chem. Soc. 2002, 124, 370–371. [Google Scholar] [CrossRef] [PubMed]
  48. Perkins, C.; Libri, S.; Adams, H.; Brammer, L. Diiodoacetylene: Compact, Strong Ditopic Halogen Bond Donor. CrystEngComm 2012, 14, 3033–3038. [Google Scholar] [CrossRef]
  49. Frisch, M.J.; Trucks, G.W.; Schlegel, H.B.; Scuseria, G.E.; Robb, M.A.; Cheeseman, J.R.; Scalmani, G.; Barone, V.; Petersson, G.A.; Nakatsuji, H.; et al. Gaussian 16, Revision A.03; Gaussian Inc.: Wallingford, CT, USA, 2016. [Google Scholar]
  50. Minenkov, Y.; Singstad, A.; Occhipinti, G.; Jensen, V.R. The accuracy of DFT-optimized geometries of functional transition metal compounds: A validation study of catalysts for olefin metathesis and other reactions in the homogeneous phase. Dalton Trans. 2012, 41, 5526–5541. [Google Scholar] [CrossRef]
  51. Yurieva, A.G.; Poleshchuk, O.K.; Filimonov, V.D. Comparative Analysis of a Full-Electron Basis Set and Pseudopotential for the Iodine Atom in DFT Quantum-Chemical Calculations of Iodine-Containing Compounds. J. Struct. Chem. 2008, 49, 548–552. [Google Scholar] [CrossRef]
  52. Dunning, T.H., Jr. Gaussian Basis Sets for Use in Correlated Molecular Calculations. I. The Atoms Boron through Neon and Hydrogen. J. Chem. Phys. 1989, 90, 1007–1023. [Google Scholar] [CrossRef]
  53. Kendall, R.A.; Dunning, T.H.; Harrison, R.J. Electron Affinities of the First-Row Atoms Revisited. Systematic Basis Sets and Wave Functions. J. Chem. Phys. 1992, 96, 6796–6806. [Google Scholar] [CrossRef]
  54. Woon, D.E.; Dunning, T.H., Jr. Gaussian Basis Sets for Use in Correlated Molecular Calculations. 3. The Atoms Aluminum through Argon. J. Chem. Phys. 1993, 98, 1358–1371. [Google Scholar] [CrossRef]
  55. Woon, D.E.; Dunning, T.H., Jr. Gaussian Basis Sets for Use in Correlated Molecular Calculations. V. Core-Valence Basis Sets for Boron through Neon. J. Chem. Phys. 1995, 103, 4572–4585. [Google Scholar] [CrossRef]
  56. Møller, C.; Plesset, M.S. Note on the Approximation Treatment for Many-Electron Systems. Phys. Rev. 1934, 46, 618–622. [Google Scholar] [CrossRef]
  57. Frisch, M.J.; Head-Gordon, M.; Pople, J.A. Direct MP2 gradient method. Chem. Phys. Lett. 1990, 166, 275–280. [Google Scholar] [CrossRef]
  58. Peterson, K.A.; Figgen, D.; Goll, E.; Stoll, H.; Dolg, M. Systematically Convergent Basis Sets with Relativistic Pseudopotentials. II. Small-Core Pseudopotentials and Correlation Consistent Basis Sets for the Post-D Group 16−18 Elements. J. Chem. Phys. 2003, 119, 11113–11123. [Google Scholar]
  59. Bader, R.F.W. Atoms in Molecules: A Quantum Theory; Oxford University Press: Oxford, UK, 1990. [Google Scholar]
  60. Todd, A.; Keith, T.K. AIMAll (Version 11.08.23); Overland Park, KS, USA. Gristmill Software. 2011. Available online: aim.tkgristmill.com (accessed on 22 September 2022).
  61. Boys, S.F.; Bernardi, F. Calculation of Small Molecular Interactions by Differences of Separate Total Energies—Some Procedures with Reduced Errors. Mol. Phys. 1970, 19, 553–566. [Google Scholar] [CrossRef]
  62. Watts, J.D.; Barlett, R.J. Triple Excitations in Coupled-Cluster Theory: Energies and Analytical Derivatives. Int. J. Quantum Chem. 1993, 48, 51–66. [Google Scholar] [CrossRef]
  63. Baerends, E.J.; Ziegler, T.; Atkins, A.J.; Autschbach, J.; Baseggio, O.; Bashford, D.; Bérces, A.; Bickelhaupt, F.M.; Bo, C.; Boerrigter, P.M.; et al. ADF2019, SCM, Theoretical Chemistry; Vrije Universiteit: Amsterdam, The Netherlands; Available online: http://www.scm.com (accessed on 22 September 2022).
  64. Ziegler, T.; Rauk, A. CO, CS, N2, PF3, and CNCH3 as σ Donors and π Acceptors. A Theoretical Study by the Hartree-Fock-Slater Transition-State Method. Inorg. Chem. 1979, 18, 1755–1759. [Google Scholar] [CrossRef]
  65. Velde, G.T.E.; Bickelhaupt, F.M.; Baerends, E.J.; Guerra, C.F.; van Gisbergen, S.J.A.; Snijders, J.G.; Ziegler, T. Chemistry with ADF. J. Comput. Chem. 2001, 22, 931–967. [Google Scholar] [CrossRef]
  66. Becke, A.D. Density-Functional Exchange-Energy Approximation with Correct Asymptotic Behavior. Phys. Rev. A 1988, 38, 3098–3100. [Google Scholar] [CrossRef]
  67. Perdew, J.P. Density-functional approximation for the correlation energy of the inhomogeneous electron gas. Phys. Rev. B 1986, 33, 8822–8824. [Google Scholar] [CrossRef]
  68. Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H.A. A Consistent and Accurate ab initio Parametrization of Density Functional Dispersion Correction (DFT-D) for the 94 elements H-Pu. J. Chem. Phys. 2010, 132, 154104. [Google Scholar] [CrossRef]
  69. Van Lenthe, E.; Baerends, E.J. Optimized Slater-type Basis Sets for the Elements 1-118. J. Comput. Chem. 2003, 24, 1142–1156. [Google Scholar] [CrossRef]
  70. Reed, E.; Curtiss, L.A.; Weinhold, F. Intermolecular Interactions from a Natural Bond Orbital, Donor-Acceptor Viewpoint. Chem. Rev. 1988, 88, 899–926. [Google Scholar] [CrossRef]
  71. Weinhold, F.; Landis, C. Valency and Bonding, A Natural Bond Orbital Donor-Acceptor Perspective; Cambridge University Press: Cambridge, UK, 2005. [Google Scholar]
  72. Wiberg, K. Application of the Pople-Santry-Segal CNDO Method to the Cyclopropylcarbinyl and Cyclobutyl Cation and to Bicyclobutane. Tetrahedron 1968, 24, 1083–1096. [Google Scholar] [CrossRef]
  73. Glendening, E.D.; Badenhoop, J.K.; Reed, A.E.; Carpenter, J.E.; Bohmann, J.A.; Morales, C.M.; Landis, C.R.; Weinhold, F. NBO 6.0; Theoretical Chemistry Institute, University of Wisconsin: Madison, WI, USA, 2013; Available online: https://nbo6.chem.wisc.edu/ (accessed on 22 September 2022).
  74. Zou, J.-W.; Lu, Y.-X.; Yu, Q.-S.; Zhang, H.-X.; Jiang, Y.-J. Halogen Bonding: An AIM Analysis of the Weak Interactions. Chin. J. Chem. 2006, 24, 1709–1715. [Google Scholar] [CrossRef]
  75. Espinosa, E.; Molins, E.; Lecomte, C. Hydrogen Bond Strengths Revealed by Topological Analyses of Experimentally Observed Electron Densities. Chem. Phys. Lett. 1998, 285, 170–173. [Google Scholar] [CrossRef]
  76. Espinosa, E.; Alkorta, I.; Rozas, I.; Elguero, J.; Molins, E. About the Evaluation of the Local Kinetic, Potential and Total Energy Densities in Closed-Shell Interactions. Chem. Phys. Lett. 2001, 336, 457–461. [Google Scholar] [CrossRef]
  77. Espinosa, E.; Alkorta, I.; Elguero, J.; Molins, E. From Weak to Strong Interactions: A Comprehensive Analysis of the Topological and Energetic Properties of the Electron Density Distribution Involving X-H∙∙∙F-Y Systems. J. Chem. Phys. 2002, 117, 5529–5542. [Google Scholar] [CrossRef]
  78. Grabowski, S.J. What is the Covalency of Hydrogen Bonding? Chem. Rev. 2011, 11, 2597–2625. [Google Scholar] [CrossRef] [PubMed]
  79. Politzer, P.; Murray, J.S.; Clark, T. Halogen bonding and other σ-hole interactions: A perspective. Phys.Chem. Chem. Phys. 2013, 15, 11178–11189. [Google Scholar] [CrossRef] [PubMed]
  80. Bader, R.F.W.; Carrol, M.T.; Cheeseman, J.R.; Chang, C. Properties of atoms in molecules: Atomic volumes. J. Am. Chem. Soc. 1987, 109, 7968–7979. [Google Scholar] [CrossRef]
  81. Mayer, I. Bond Order and Valence Indices: A Personal Account. J. Comput. Chem. 2007, 28, 204–221. [Google Scholar] [CrossRef]
Ijms 23 11289 g001 550
Figure 1. ωB97X-D/aug-cc-pVTZ-optimized geometries of the CH3−n(CN)nH∙∙∙NMe3 (n = 0–3) complexes.
Figure 1. ωB97X-D/aug-cc-pVTZ-optimized geometries of the CH3−n(CN)nH∙∙∙NMe3 (n = 0–3) complexes.
Ijms 23 11289 g001
Ijms 23 11289 g002 550
Figure 2. ωB97X-D/aug-cc-pVTZ-optimized geometries of the CH3−n(CN)nCl∙∙∙NMe3 (n = 0–3) complexes; X∙∙∙N distances for X = Cl, Br, I are presented in the figure.
Figure 2. ωB97X-D/aug-cc-pVTZ-optimized geometries of the CH3−n(CN)nCl∙∙∙NMe3 (n = 0–3) complexes; X∙∙∙N distances for X = Cl, Br, I are presented in the figure.
Ijms 23 11289 g002
Ijms 23 11289 g003 550
Figure 3. Percent change in the covalent C-X bond as a function of the number of CN groups in the CH3−n(CN)nX∙∙∙NMe3 (X = H, Cl, Br, or I; n = 0–3) complexes optimized at the ωB97X-D/aug-cc-pVTZ level of theory.
Figure 3. Percent change in the covalent C-X bond as a function of the number of CN groups in the CH3−n(CN)nX∙∙∙NMe3 (X = H, Cl, Br, or I; n = 0–3) complexes optimized at the ωB97X-D/aug-cc-pVTZ level of theory.
Ijms 23 11289 g003
Ijms 23 11289 g004 550
Figure 4. Percent change in the intermolecular X∙∙∙N distance as a function of the number of CN groups in the CH3−n(CN)nX∙∙∙NMe3 (X = H, Cl, Br, or I; n = 0–3) complexes optimized at the ωB97X-D/aug-cc-pVTZ level of theory.
Figure 4. Percent change in the intermolecular X∙∙∙N distance as a function of the number of CN groups in the CH3−n(CN)nX∙∙∙NMe3 (X = H, Cl, Br, or I; n = 0–3) complexes optimized at the ωB97X-D/aug-cc-pVTZ level of theory.
Ijms 23 11289 g004
Ijms 23 11289 g005 550
Figure 5. Percent change in the harmonic stretching frequency of the C-X bond, νC-X, as a function of the number of CN groups in the CH3−n(CN)nX∙∙∙NMe3 (X = H, Cl, Br, or I; n = 0–3) complexes optimized at the ωB97X-D/aug-cc-pVTZ level of theory.
Figure 5. Percent change in the harmonic stretching frequency of the C-X bond, νC-X, as a function of the number of CN groups in the CH3−n(CN)nX∙∙∙NMe3 (X = H, Cl, Br, or I; n = 0–3) complexes optimized at the ωB97X-D/aug-cc-pVTZ level of theory.
Ijms 23 11289 g005
Ijms 23 11289 g006 550
Figure 6. Changes in the magnitude of the interaction energy per CN group added in the CH3−n(CN)nX∙∙∙NMe3 (X = H, Cl, Br, or I; n = 0–3) dimer complexes. Values calculated at MP2//ωB97X-D/aug-cc-pVTZ level of theory.
Figure 6. Changes in the magnitude of the interaction energy per CN group added in the CH3−n(CN)nX∙∙∙NMe3 (X = H, Cl, Br, or I; n = 0–3) dimer complexes. Values calculated at MP2//ωB97X-D/aug-cc-pVTZ level of theory.
Ijms 23 11289 g006
Ijms 23 11289 g007 550
Figure 7. Correlations between ρc and the corresponding magnitude of interaction energies, |ΔE|, in the CH3−n(CN)nX∙∙∙NMe3 (X = H, Cl, Br, or I; n = 0–3) dimer complexes.
Figure 7. Correlations between ρc and the corresponding magnitude of interaction energies, |ΔE|, in the CH3−n(CN)nX∙∙∙NMe3 (X = H, Cl, Br, or I; n = 0–3) dimer complexes.
Ijms 23 11289 g007
Ijms 23 11289 g008 550
Figure 8. The linear correlation between the Pauli repulsion interaction energy and the sum of all attractive interaction energy terms for halogen-bonded dimers.
Figure 8. The linear correlation between the Pauli repulsion interaction energy and the sum of all attractive interaction energy terms for halogen-bonded dimers.
Ijms 23 11289 g008
Ijms 23 11289 g009 550
Figure 9. The EP surfaces of the CHn-3(CN)nCl monomers. The EP maxima on the halogen σ-holes are listed (in au) for X = Cl, Br, I. The number of CN groups increases from 0 to 3.
Figure 9. The EP surfaces of the CHn-3(CN)nCl monomers. The EP maxima on the halogen σ-holes are listed (in au) for X = Cl, Br, I. The number of CN groups increases from 0 to 3.
Ijms 23 11289 g009
Ijms 23 11289 g010 550
Figure 10. Correlation between NBI and Wiberg indices. Potential regression is applied; all dimers linked by halogen (black circles) and hydrogen (open circles) bonds are taken into account in this correlation.
Figure 10. Correlation between NBI and Wiberg indices. Potential regression is applied; all dimers linked by halogen (black circles) and hydrogen (open circles) bonds are taken into account in this correlation.
Ijms 23 11289 g010
Ijms 23 11289 g011 550
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.
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.
Ijms 23 11289 g011
Table
Table 1. Optimized geometries for the CH3−n(CN)nH∙∙∙NMe3 complexes; C-H bond lengths, H⋅⋅⋅N distances and C-H⋅⋅⋅N angles are given.
Table 1. Optimized geometries for the CH3−n(CN)nH∙∙∙NMe3 complexes; C-H bond lengths, H⋅⋅⋅N distances and C-H⋅⋅⋅N angles are given.
nC-H (Å)H∙∙∙N (Å)C-H∙∙∙N (°)
ωB97X-D/aug-cc-pVTZ
01.0892.595151.2
11.0942.326151.0
21.1082.067157.2
31.1511.765180.0
MP2/aug-cc-pVTZ
01.0882.569155.8
11.0922.370145.1
21.1062.066153.2
31.1591.711180.0
MP2/aug-cc-pVDZ
01.0992.522158.3
11.1042.292151.8
21.1182.043154.5
31.1721.693180.0
Table
Table 2. Optimized geometries for the CH3−n(CN)nCl∙∙∙NMe3 complexes; C-Cl bond lengths, Cl⋅⋅⋅N distances and C-Cl⋅⋅⋅N angles are given.
Table 2. Optimized geometries for the CH3−n(CN)nCl∙∙∙NMe3 complexes; C-Cl bond lengths, Cl⋅⋅⋅N distances and C-Cl⋅⋅⋅N angles are given.
nC-Cl (Å)Cl∙∙∙N (Å)C-Cl∙∙∙N (°)
ωB97X-D/aug-cc-pVTZ
01.7873.321168.6
11.7893.018175.5
21.8042.810178.9
31.8382.620180.0
MP2/aug-cc-pVTZ
01.7813.115169.1
11.7852.896171.1
21.8042.679177.5
31.8762.385180.0
MP2/aug-cc-pVDZ
01.7983.116169.5
11.8032.903171.7
21.8232.700177.8
31.8882.439180.0
Table
Table 3. Optimized geometries for the CH3−n(CN)nBr∙∙∙NMe3 complexes; C-Br bond lengths, Br⋅⋅⋅N distances and C-Br⋅⋅⋅N angles are given.
Table 3. Optimized geometries for the CH3−n(CN)nBr∙∙∙NMe3 complexes; C-Br bond lengths, Br⋅⋅⋅N distances and C-Br⋅⋅⋅N angles are given.
nC-Br (Å)Br∙∙∙N (Å)C-Br∙∙∙N (°)
ωB97X-D/aug-cc-pVTZ
01.9413.102179.9
11.9532.911179.2
21.9812.725179.7
32.0462.506180.0
MP2/aug-cc-pVTZ
01.9332.896179.5
11.9512.711178.7
21.9972.505179.3
32.0992.302180.0
MP2/aug-cc-pVDZ
01.9512.925180.0
11.9692.747179.2
22.0132.548179.5
32.1062.347180.0
Table
Table 4. Optimized geometries for the CH3−n(CN)nI∙∙∙NMe3 complexes; C-I bond lengths, I⋅⋅⋅N distances and C-I⋅⋅⋅N angles are given.
Table 4. Optimized geometries for the CH3−n(CN)nI∙∙∙NMe3 complexes; C-I bond lengths, I⋅⋅⋅N distances and C-I⋅⋅⋅N angles are given.
nC-I (Å)I∙∙∙N (Å)C-I∙∙∙N (°)
ωB97X-D/aug-cc-pVTZ
02.1453.099179.9
12.1712.890180.0
22.2172.715180.0
32.3002.536180.0
MP2/aug-cc-pVTZ
02.1382.875179.9
12.1702.697179.7
22.2222.543179.5
32.2922.424180.0
MP2/aug-cc-pVDZ
02.1642.889179.9
12.1982.710179.8
22.2482.565179.7
32.3102.457180.0
Table
Table 5. Stretching frequencies, νC-X (cm−1), for CH3−n(CN)nX∙∙∙NMe3 (X = H, Cl, Br, or I; n = 0–3).
Table 5. Stretching frequencies, νC-X (cm−1), for CH3−n(CN)nX∙∙∙NMe3 (X = H, Cl, Br, or I; n = 0–3).
nνC-HνC-ClνC-BrνC-I
ωB97X-D/aug-cc-pVTZ
03033748632556
13024762452418
22846493411358
32210465345298
MP2/aug-cc-pVDZ
03045747624542
13034747427389
22854473374340
32160387308302
Table
Table 6. BSSE-corrected MP2//ωB97X-D/aug-cc-pVTZ interaction energies, ΔE(kcal/mol), for CH3−n(CN)nX∙∙∙NMe3 (X = H, Cl, Br, or I; n = 0–3).
Table 6. BSSE-corrected MP2//ωB97X-D/aug-cc-pVTZ interaction energies, ΔE(kcal/mol), for CH3−n(CN)nX∙∙∙NMe3 (X = H, Cl, Br, or I; n = 0–3).
nHClBrI
0−1.47−1.73−3.10−5.41
1−4.90−3.28−5.50−8.94
2−8.02−5.33−8.89−13.89
3−13.17−8.50−15.03−21.49
Table
Table 7. BSSE-corrected CCSD(T)//MP2/aug-cc-pVTZ interaction energies, ΔEs (kcal/mol), for CH3−n(CN)nX∙∙∙NMe3 (X = H, I; n = 0–3).
Table 7. BSSE-corrected CCSD(T)//MP2/aug-cc-pVTZ interaction energies, ΔEs (kcal/mol), for CH3−n(CN)nX∙∙∙NMe3 (X = H, I; n = 0–3).
nHI
0−1.46−4.30
1−4.69−7.53
2−7.49−12.19
3−12.21−18.93
Table
Table 8. MP2//wB97X-D/aug-cc-pVTZ topological parameters (a.u.) for CH3−n(CN)nX∙∙∙NMe3 (X = H, Cl, Br, I).
Table 8. MP2//wB97X-D/aug-cc-pVTZ topological parameters (a.u.) for CH3−n(CN)nX∙∙∙NMe3 (X = H, Cl, Br, I).
nρcGcVcHc|Gc/Vc|
CH3−n(CN)nH∙∙∙NMe3
00.00890.0058−0.00480.00101.21
10.01620.0106−0.00950.00111.12
20.02800.0183−0.0198−0.00150.92
30.05500.0322−0.0485−0.01630.66
CH3−n(CN)nCl∙∙∙NMe3
00.00710.0049−0.00370.00121.32
10.01340.0097−0.00810.00161.20
20.02080.0153−0.01410.00121.09
30.03200.0230−0.0240−0.00100.96
CH3−n(CN)nBr∙∙∙NMe3
00.01370.0093−0.00810.00121.15
10.02000.0138−0.01300.00081.06
20.02960.0200−0.0209−0.00090.96
30.04730.0302−0.0372−0.00700.81
CH3−n(CN)nI∙∙∙NMe3
00.01760.0110−0.01040.00061.06
10.02630.0166−0.0175−0.00090.95
20.03720.0231−0.0275−0.00440.84
30.09000.0407−0.0786−0.03790.52
Table
Table 9. Changes in electron density at C-X…N bond critical points (a.u.) per number of CN groups, Δρc/n, present in CH3−n(CN)nX∙∙∙NMe3.
Table 9. Changes in electron density at C-X…N bond critical points (a.u.) per number of CN groups, Δρc/n, present in CH3−n(CN)nX∙∙∙NMe3.
CN GroupsHClBrI
10.00730.00630.00630.0087
20.00960.00690.00800.0098
30.01540.00830.01120.0241
Table
Table 10. The interaction energy terms (in kcal/mol) and the ΔEorb/ΔEelstat ratio for the CH3−n(CN)nX∙∙∙N(CH3)3 complexes (X = H, Cl, Br, I).
Table 10. The interaction energy terms (in kcal/mol) and the ΔEorb/ΔEelstat ratio for the CH3−n(CN)nX∙∙∙N(CH3)3 complexes (X = H, Cl, Br, I).
Lewis Acid UnitΔEintΔEPauliΔEelstatΔEorbΔEdispΔEelstat/ΔEorb
CH3H−1.763.56−1.91−1.12−2.291.7
CH2CNH−5.607.87−6.56−3.05−3.852.2
CH(CN)2H−9.5214.13−11.47−7.22−4.961.6
C(CN)3H−17.0933.66−23.78−21.54−5.441.1
CH3Cl−1.315.41−2.65−1.81−2.261.5
CH2CNCl−3.419.38−6.21−4.12−2.471.5
CH(CN)2Cl−6.9917.86−12.42−9.75−2.681.3
C(CN)3Cl−13.7945.54−28.65−27.26−3.411.1
CH3Br−3.7012.95−8.76−5.00−2.891.8
CH2CNBr−7.4022.39−15.97−10.41−3.421.5
CH(CN)2Br−12.7641.85−28.96−21.75−3.911.3
C(CN)3Br−20.8779.17−51.76−44.13−4.141.2
CH3I−6.4022.76−16.37−8.74−4.051.9
CH2CNHI−10.9037.87−27.52−16.75−4.491.6
CH(CN)2I−16.4859.10−42.28−28.61−4.691.5
C(CN)3I−23.3583.70−58.90−43.38−4.771.4
Table
Table 11. CH3−n(CN)nX∙∙∙N(CH3)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)→σCX* orbital–orbital interaction energy (in kcal/mol).
Table 11. CH3−n(CN)nX∙∙∙N(CH3)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)→σCX* orbital–orbital interaction energy (in kcal/mol).
Lewis Acid UnitQ(X)Q(N)WBINBIn→σ*
CH3H0.230−0.3480.00550.07430.69
CH2CNH0.283−0.3630.01510.12272.49
CH(CN)2H0.320−0.3670.04740.21778.07
C(CN)3H0.344−0.3440.14790.384529.15
CH3Cl−0.082−0.3390.01590.12630.89
CH2CNCl−0.026−0.3360.04240.20592.22
CH(CN)2Cl0.004−0.3150.09720.31185.02
C(CN)3Cl−0.012−0.2600.21900.468013.65
CH3Br−0.039−0.3350.04860.22043.78
CH2CNBr0.013−0.3250.09750.31236.99
CH(CN)2Br0.040−0.2960.18200.426713.55
C(CN)3Br0.059−0.2500.30910.556027.98
CH3I0.039−0.3370.08580.29296.51
CH2CNHI0.097−0.3260.15130.389011.84
CH(CN)2I0.143−0.3080.23380.483519.74
C(CN)3I0.187−0.2900.32350.568830.21
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Share and Cite

MDPI and ACS Style

Parra, R.D.; Grabowski, S.J. 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). Int. J. Mol. Sci. 2022, 23, 11289. https://doi.org/10.3390/ijms231911289

AMA Style

Parra RD, Grabowski SJ. 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). International Journal of Molecular Sciences. 2022; 23(19):11289. https://doi.org/10.3390/ijms231911289

Chicago/Turabian Style

Parra, Rubén D., and Sławomir J. Grabowski. 2022. "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)" International Journal of Molecular Sciences 23, no. 19: 11289. https://doi.org/10.3390/ijms231911289

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Metrics

Back to TopTop