*3.2. N(d') plots*

The data characterized by α = 160◦–180◦ was inspected further by means of *N*(*d'*) plots as described in the methods and materials section. A numerical overview of the amount of data in each dataset as well as the (relative) amount of van der Waals overlap found in each dataset is given in Table S2. Shown in Figure 3 are plots of the hit fractions (in %) as a function of *d'* (the van der Waals corrected *d*) for X = C, N, O and ElR = water or amide. The same data plotted as cumulative hit fractions is shown in Figure S2 and the *N*(*d'*) plots for all datasets containing >500 hits are shown in Figure S3.

**Figure 3.** Hit fraction (in %) as a function of the van der Waals corrected XCH3···ElR distance *d'* (in Å) for several datasets from Table S2 (α ≥ 160◦, as illustrated by the inset figure). The interacting pairs involve water-O (red, empty) or amide-O (blue, half-filled) with X = C (squares), N (diamonds), or O (circles). See Figure S2 for the same data plotted as a cumulative hit fraction. *N* (CSD/PDB) = 2,376/1,622 (C, water); 1,089/1,186 (N, water); 452/757 (O, water); 2,599/1,179 (C, amide); 504/650 (N, amide); 640/483 (O, amide).

In the CSD (left), The data involving N/O–CH3···Oamides are very similarly distributed and grouped near *d'* <sup>≈</sup> 0 Å with about 30% of all the data involved in van der Waals overlap. Likewise, data involving N/O–CH3···Owaters are also very similarly distributed but group near the larger *d'* <sup>≈</sup> 0.25 Å with 15% van der Waals overlap. The C–CH3···Oamides/waters data hardly displays van der Waals overlap (3–4%) and is broadly grouped around *d'* = 0.4 Å for waters and not grouped at all for amides. Similar trends are present in the PDB (right), albeit the features are much less pronounced and the N/O–CH3···O datasets with amides and waters are very similar.

The data presented in Figure <sup>3</sup> thus imply a somewhat directional nature of X–CH3···Oamides/waters interactions for X = N and O, but not at all for X = C. These findings are in line with the lack of directionality observed in the *P*(α) plots for X = C and the somewhat directional behavior for X = N or O (see Figure 2). A likely explanation for this is the larger (Pauling) electronegativity of N (3.04) and O (3.44) compared to C (2.55), resulting in a larger degree of polarization of the X–CH3 bond for X = N or O. Another conceivable manner to make a methyl group pore electropositive is to bind it to a cationic fragment such as in protonated or quaternary R3N<sup>+</sup>–CH3 fragments. Thus, an additional dataset was retrieved from the CSD involving R3N<sup>+</sup>–CH3···ElR pairs that fulfilled the *<sup>d</sup>* <sup>≤</sup> 5 Å and <sup>α</sup> <sup>=</sup> <sup>160</sup>◦–180◦ criteria (see bottom entries in Tables S1 and S2). Shown in Figure 4 are the *N*(*d'*) plots of the most numerous datasets involving R3N<sup>+</sup>–CH3 (hexagonals, N+) together with similar datasets involving all possible N–CH3 fragments (diamonds, N). In all three cases (ElR = water, carboxy or aryl), the distribution is shifted to lower *d'* distances for cationic R3N<sup>+</sup>–CH3, which means that relatively more van der Waals overlap is present in these datasets. As can be seen especially from the cumulative *N*(*d'*) plots (left), the grouping is tightest with carboxy O-atoms (green), followed by water O-atoms (red) and aryl rings centroids (grey) are not grouped at all (nearly linear).

**Figure 4.** Cumulative (**left**) and regular (**right**) hit fraction (in %) as a function of the van der Waals corrected XCH3···ElR distance *d'* (in Å) for the datasets from Table S2 (<sup>α</sup> <sup>=</sup> <sup>160</sup>◦–180◦ as illustrated in the inset figure). The interacting pairs involve water-O (red, empty), carboxy-O (green, right-filled) or the centroid of an aryl ring (grey, left-filled). X can be any N (diamond) or a cationic (tetravalent) N<sup>+</sup> (hexagonal). *N* (N/N+) = 1,809/290 (water, red); 2,062/274 (carboxy, green); 10,585/527 (aryl, grey).

#### *3.3. Computations*

In order to gain insight into the nature and energetics of possible non-covalent Carbon bonding interactions involving various methyl groups and water or amide O-atoms, DFT calculations were performed of X–CH3 adducts with water and with dimethylacetamide (dma, see methods section for details). An overview of these adducts is given in Table 1, together with α of the optimized structures, the total interaction energy of the adducts in kcal·mol−<sup>1</sup> and the percentages of electrostatic (E), orbital (O), and dispersion (D) interactions that contribute to this total energy [79]. Perspective views and atoms-in-molecules analyses of all converged structures are shown in Figure S4 and several representative examples are shown in Figure 5.

**Figure 5.** Ball and stick representations of molecular adducts selected from Table 1 that were optimized by DFT (B3LYP-D3/def2-TZVP). The thin lines are bond paths (bp's) and the small red spheres are bond critical points (bcp's) obtained from an 'atoms-in-molecules' analysis. The bond density (ρ) is in arbitrary units ·10<sup>2</sup> and bcp's indicative of non-covalent Carbon bonding have been highlighted in yellow.

**Table 1.** Numerical overview of adducts computed with DFT between an indicated X-CH3 methyls and water (adducts 'a') or dimethylacetamide (dma, adducts 'b'). Using ADF at the B3LYP-D3/def2-TZVP level of theory, interaction energies (in kcal·mol<sup>−</sup>1) were computed and an energy decomposition analyses is shown as a percentage of the total amount of interaction energies split up as electrostatic (E), orbital (O) and dispersion (D) interactions. Entries in grey are not consistent with a Carbon bonding geometry. See Figure S4 for perspective views and atoms in molecules analyses.


<sup>a</sup> One of the water H-atoms and one of the RCH3 C-atoms are closest to each other; <sup>b</sup> Carbon bonding interaction geometry; cInteraction with the cationic C; <sup>d</sup> Hydrogen bonding interaction(s); <sup>e</sup> Interaction with cationic N; <sup>f</sup> CH-π interaction; <sup>g</sup> The interaction energy with benzene was also computed, starting from a geometry with X–CH3···benzene centroid = 180◦. All adducts converged at a geometry where this angle was about 90◦ degrees. Interaction energies are about 4–5 kcal·mol−<sup>1</sup> and dominated by electrostatics (35–40%) and dispersion (40–50%, see Figure S5 for details).

For comparison purposes, adducts with ethane were computed as shown in entries 1 of Table 1. Both structures converged to a hydrogen bonding interaction. <sup>Δ</sup><sup>E</sup> <sup>=</sup> <sup>−</sup>1.2 kcal·mol−<sup>1</sup> in **1a** and a methyl acts as electron donating site; i.e., an O–H···C hydrogen bonding interaction. This can be understood due to the polarization in ethane, where both C's are most electronegative and are polarized by the H-atoms. Adduct **1b** is about twice as stable with <sup>Δ</sup><sup>E</sup> <sup>=</sup> <sup>−</sup>2.8 kcal·mol−<sup>1</sup> and also features a hydrogen bonding interaction, but now between a methyl CH and a π-bond in dma. Both **1a** and **1b** are stabilized mainly by dispersion (46–58%), then electrostatics (32–26%) and least by orbital interactions (22–16%). The neutral water adducts where X = permethylated N, O, P, or S are energetically nearly identical to the ethane adduct (**2a**–**5a**). Like with ethane, **4a** converged in a O–H···C hydrogen bonding interaction, which can be rationalized by the lower (Pauling) electronegativity of P (2.19) compared to C (2.55). **2a**, **3a** and **5a** converged at a geometry consistent with a Carbon bonding interaction. This is illustrated for structure **3a** in Figure 5, where a single bond critical point (bcp) is located between C and O with a bond density of 0.60 · 102 a.u.. This can be rationalized by the higher (Pauling) electronegativity of N (3.05), O (3.44) and S (2.58) compared to C (2.55). Electrostatics or dispersion are the main energetic stabilizing factor in adducts **2a**–**5a** which is typical for weak and non-directional interactions like in adduct

**1a**. A similar series with dma was computed as adducts **2b**–**5b**. Only **2b** converged in a geometry consistent with a Carbon bonding interaction (with dispersion as main driver) while the others are C–H···O hydrogen bonding interactions. Carbon bonding interactions with regular permethylated main group elements are thus comparable to very weak C–H hydrogen bonding interactions and less than about <sup>−</sup>1.5 kcal·mol−<sup>1</sup> in strength. These energies are in line with earlier computations with the adducts [H2N-CH3···OCH2] [47] and [HO-CH3···OH2] [48] of <sup>−</sup>0.7 and <sup>−</sup>1.0 kcal·mol-1 respectively.

The cationic adducts **6**–**11a** were computed as well and the most stable of these involved the Me3C<sup>+</sup> carbocation in **6** (adducts with pentamethylated Carbon are unstable). The bonding interaction in **6b** is largely covalent, as evidenced by the interaction energy of <sup>−</sup>82.4 kcal·mol<sup>−</sup>1, the large orbital contribution (55%), a dense bond critical point (18.4 · <sup>10</sup><sup>2</sup> a.u.) and a clear pyramidalization of the central C-atom (see Figure S4). Of the other adducts, all except **6a** (Me3C<sup>+</sup>···O interaction) and **<sup>9</sup>** (with the least electronegative P) converged into an X–CH3···O Carbon bonding geometry. This is illustrated for **8a** and **11a** in Figure 4, where a clear bcp can be seen in between methylC and Owater with a bond density of 1.15 · <sup>10</sup><sup>2</sup> and 0.98 · 102 a.u. for **8a** and **11a** respectively. The bonding energies in **<sup>7</sup>**–**11a** are mainly electrostatic in origin (~70%) and about <sup>−</sup>8 kcal·mol−<sup>1</sup> for water and <sup>−</sup>15 kcal·mol−<sup>1</sup> for dma. The most stable adducts in both series involved the most electronegative O (3.44) in Me3O<sup>+</sup> (**8**). Two alternative configurations with *N*-methylpyridinium were also computed (**12** and **13**). In **12**, the O points in between two CH hydrogens as is illustrated for **12a** in Figure 4. In adducts **13** the O atom is located directly above the cationic N+. Both **12** and **13** are more stable than the Carbon bonding geometry found in **11**, suggesting that hydrogen bonding interactions are most preferred. The interaction energies of Carbon bonding interaction with cationic species is similar to previous data of the adducts: [H3N<sup>+</sup>-CH3···OCH2] (−9.7 kcal·mol−1); [47] [Me3N<sup>+</sup>-CH3···OC(H)NH2] (−13 kcal·mol−1); [49] [Me2S<sup>+</sup>-CH3···OH2/NH3/OCH2] (about <sup>−</sup>8–9 kcal·mol<sup>−</sup>1); [47,49] and [R2S<sup>+</sup>-CH3···various lone-pairs] (about <sup>−</sup>9.0 kcal·mol<sup>−</sup>1) [50].

As the calculations with cationic species imply that electron withdrawing substituents amplify the Carbon bonding interaction, it was decided to compute adducts with small molecules that have an electron withdrawing group: Iodomethane (**14**), 1,1,1-trifluoroethane (**16**), acetonitrile (**18**) and nitromethane (**20**). All these adducts converged as a Carbon bonding geometry and are energetically favorable by 1.6–2.8 kcal·mol−<sup>1</sup> for water and 3.0–4.9 kcal·mol−<sup>1</sup> for dma. The adducts involving nitromethane (**20**) were most stable and are shown in Figure 5, together with an aim analysis revealing a single C···O bcp (<sup>ρ</sup> <sup>=</sup> 0.79 · 102 and 0.83 · <sup>10</sup><sup>2</sup> a.u. for **20a** and **20a** respectively). For the water adducts, H-bonding geometries were also optimized: **15a**, **17a**, **19a** and **21a**. All these adducts were about twice as stable and the Carbon bonding geometry. This can be ascribed to the fact that besides a C–H···O hydrogen bonding interaction, another weak hydrogen bonding interaction is present as well (i.e., C–H···I in **15a**, C–H···F in **17a** and C–H···π in **19a**, see also see also Figure S4). For example, a dimer of HCF3 is estimated at <sup>−</sup>2.6 kcal·mol−<sup>1</sup> and exhibits two weak C–H···F hydrogen bonding interactions (not shown). The interaction energies with neutral yet polarized methyl groups (**14**–**20**) liken those reported by others for: [F-CH3···OH2/NH3/PH3] (about <sup>−</sup>2–3 kcal·mol−1); [48,51–53] [F-CH3···C2H2] (−1.2 kcal·mol−1); [54] [Hlg-CH3···C2H4/NH3/PH3] (−1–4 kcal·mol−1); [53,55] [NC-CH3···C2H4/dma] (−3–5 kcal·mol<sup>−</sup>1); [55,56] and [O2N-CH3···dma] (−4.9 kcal·mol<sup>−</sup>1) [56].

#### *3.4. General Discussion*

From all the calculations collected in Table 1 it is evident that the interaction energies of Carbon bonding geometries with the sp2-O in dma (adducts 'b') is consistently about twice as strong as the interaction with sp3-O in water (adducts 'a'). This is in line with the larger amount of van der Waals overlap observed in the *N*(*d'*) plots (Figure 2, ~30% for amides vs ~15% for water). The interaction energies of adducts with a Carbon bonding geometry range from very weak (below <sup>−</sup>1.5 kcal·mol−<sup>1</sup> in **<sup>2</sup>**, **<sup>3</sup>**, **<sup>5</sup>**), to moderately weak (between <sup>−</sup>1.5 and <sup>−</sup>5 kcal·mol−<sup>1</sup> in **<sup>14</sup>**, **<sup>16</sup>**, **<sup>18</sup>** and **<sup>20</sup>**) to fairly strong in the cationic adducts (between <sup>−</sup>7 and <sup>−</sup>18 kcal·mol−<sup>1</sup> in **<sup>6</sup>**–**11**). <sup>Δ</sup>E becomes smaller (more stable) in the order **2** < **14** < **16** < **18** < **20** < **7** < **8**. Within this series, the orbital contribution remains constant at about 15–20%, while the electrostatic component increases from 30–35% in **2** to about 65% in **8**. This implies that stronger Carbon bonding interactions are mainly driven by electrostatic interactions and that weaker such adducts are driven by dispersion. These computational results are consistent with recent literature reports [47–59] and the database analyses presented here; neutral adducts are very weak and thus hardly (or non) directional but can be made stronger (and thus presumably more directional) when X in X–CH3 is strongly polarized (see especially Figure 4). The relevance of Carbon bonding interactions with methyl groups is thus likely limited to highly polarized and/or cationic species. While this limits the scope considerably, it is worth pointing out that ligands with methyl groups related to those in adducts **2**–**10** and **14**–**21** are abundant within proteins structures and that cationic methyl groups also occur. For example, methylated methionine residues in methyl transferases [80] and nicotinamide derivatives such as nicotinamide adenine dinucleotide [81,82].

#### **4. Summary and Conclusions**

The CSD and the PDB were systematically evaluated for potential directional behavior of intermolecular non-covalent Carbon bonding interactions involving X–CH3 and electron rich entities such as O/S atoms or an aryl ring (ElR) within a hemisphere of 5 Å basal radius (centered on C). It was found that X–CH3···ElR interactions can be as directional as very weak hydrogen bonding interaction involving C–H (*P*max ≤ 1.50) but not directional at all when X = C. Grouping of data with significant amounts of van der Waals overlap (up to ~30%) was observed in various sub-datasets in the region where the X–CH3···ElR angle α is 160◦–180◦. These distributions were significantly shifted to shorter distances (i.e., more van der Waals overlap) in the case of cationic R3N<sup>+</sup>–CH3···Owater/amide compared to charge-neutral R2N–CH3···Owater/amide interactions.

Model DFT calculations revealed that charge neutral X–CH3···O adducts with water and dimethylacetamide are very weak (<sup>≤</sup> –1.5 kcal·mol−<sup>1</sup> in **<sup>2</sup>**, **3a**, **5a**) and are often not the energy minima of the adducts (**1**, **3b**, **4**, **5b**). The interaction energies can be increased by deploying a more electron withdrawing X (–1.5 to –5 kcal·mol−<sup>1</sup> in **<sup>14</sup>**, **<sup>16</sup>**, **<sup>18</sup>** and **<sup>20</sup>**). Rendering X cationic leads to even more stable adducts (–7.0 to –18 kcal·mol−1) in **<sup>7</sup>**, **<sup>8</sup>**, **<sup>10</sup>** and **<sup>11</sup>**). Carbon-bonding adducts with dimethylacetamide are consistently twice as stable as those with water. Energy decomposition analyses showed that increased stability is driven by electrostatics and atom-in-molecule analyses regularly gave a clear bond critical point involving the methyl C-atom.

It is thus concluded that this combined database / DFT study reaffirms that intermolecular non-covalent Carbon interactions with X–CH3 is electrostatically driven and can be significant. The interaction can even by mildly directional in the solid state (comparable to weak CH hydrogen bonding interactions), provided X is sufficiently electron withdrawing.

**Supplementary Materials:** The following are available online, Table S1. Numerical overview of datasets retrieved from the CSD and the PDB. See Figure S1 and Figure 2 for P (α) directionality plots. For data of refined datasets see Table S2 (α ≥ 160◦ and van der Waals overlap). 'n.a.' stands for 'not assessed'. The data for quaternary (cationic) N-atoms is not used in the paper for P(α) plot but they were used in N(d') plots. Table S2. Numerical overview of the amount of data in each dataset from Table S1 characterized by α ≥ 160◦ (Nα ≥ 160◦), together with the amount of data within that dataset where van der Waals radii overlap (NΣvdW). 'n.a.' stands for 'not assessed'. Datasets with Nα ≥ 160◦ larger than 100 were inspected further by means of the N(d') plots shown in Figures S2–S3. As a guide to the eye, datasets with less than 100 hits are in grey, those between 100 and 500 hits are in blue and those above 500 are in regular black. Figure S1. P (α) directionality plots for the data retrieved from the CSD (left) and the PDB (right) using the general query shown in the top-left inset figure for X–CH3···ElR pairs. X can be C, N, O, P, or S and 'ElR' can be a water, amide or carboxyl O-atom, an RyCS S-atom (y = 2 or 3, R = any non-metal) or the centroid of an aryl ring, as is indicated in the right-hand side of the figure. The insert figure in the top right is intended as a guide to the eye to interpret the spatial location of data with a certain value of α. Due to the amount of data per dataset (see Table S1 for numerical overview), the top four P (α) plots are given at a 5◦ resolution for α and the bottom six at a 10◦ resolution. NB: Interestingly, in the P(α) plots for X = S and ElR = water, P is above unity at α = 160◦–180◦ for the CSD data, while P < 1 for the PDB data in this same region. In both databases, the P-values are ≥ 1 around α = 105◦. This indicates that the H-bonding geometry (α ≈ 105◦) is somewhat directional on both databases but that the carbon bonding geometry is more directional only in the CSD. However, the dataset retrieved from the CSD is much smaller (1,546 hits) than the dataset from the PDB (30,725 hits) and the observed feature α = 160◦–180◦ in the CSD might well be an artefact. Similarly, the P(α) plots with X = S and an amide O-atom reveal that P ≥ 1 at α = 90◦–105◦, again congruent with a hydrogen bonding geometry. P ≥ 1 also at α = 170◦–180, but only for the PDB data. As this dataset is more voluminous (N = 11,215 vs

2,175 in the CSD), this implies that a carbon bonding geometry is more directional (at least in protein structures). A possible reason for this discrepancy might be that many cysteine and methionine residues are involved in metal coordination or directly methylated thus polarizing the S–C bond. For example, iron-sulphur clusters are held in place by cysteine–Fe coordination bonds [1] and methylated methionine residues are a (crystallographically known) intermediate in methyl transferases. [2]. Figure S2. Cumulative hit fraction (in %) as a function of the van der Waals corrected XCH3···ElR distance d' (in Å) for several datasets from Table S2 (α ≥ 160◦, as illustrated by the inset figure). The interacting pairs involve water-O (red, empty) or amide-O (blue, half-filled) with X = C (squares), N (diamonds), or O (circles). See Figure 2 for the same data plotted as a regular hit fraction. Figure S3. Cumulative (top) and regular (bottom) hit fraction (in %) as a function of the van der Waals corrected XCH3···ElR distance d' (in Å) for all the datasets from Table S2 (α ≥ 160◦, illustrated with the inset figure) that contain ≥ 500 data points. The inset legends show the nature of X (horizontally) and ElR (vertically). NB: In addition to the trends observed and discussed in the main text according to Figure 2, It is interesting to note that in all cases, for X = C the plot is shifted most to longer d' and has the least van der Waals overlap. Moreover, carboxy O-atoms are distributed about the same as amide O-atoms and thio S-atoms about the same as water. Aryls are always randomly distributed with the least amount of van der Waals overlap. Figure S4. Ball and stick representations of perspective views of all molecular adducts listed in Table 1 that were optimized by DFT (B3LYP-D3/def2-TZVP). The thin lines are bond paths (bp's) and the small red spheres are bond critical points (bcp's) obtained from an 'atoms-in-molecules' analysis. The bond density (ρ) is in arbitrary units 102 and bcp's indicative of non-covalent carbon bonding have been highlighted in yellow. Figure S5. Ball and stick representations of molecular adducts selected from Table 1 that were optimized by DFT (B3LYP-D3/def2-TZVP). The thin lines are bond paths (bp's) and the small red spheres are bond critical points (bcp's) obtained from an 'atoms-in-molecules' analysis. The bond density (ρ) is in arbitrary units ·102 and bcp's indicative of non-covalent carbon bonding have been highlighted in yellow.

**Funding:** This research was funded by the Netherlands Organization for Scientific Research (NWO) grant number 723.015.006.

**Conflicts of Interest:** The author declares no conflict of interest.

## **References**


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