Charge Anisotropy of Nitrogen: Where Chemical Intuition Fails

For more than half a century computer simulations were developed and employed to study ensemble properties of a wide variety of atomic and molecular systems with tremendous success. Nowadays, a selection of force-fields is available that describe the interactions in such systems. A key feature of force-fields is an adequate description of the electrostatic potential (ESP). Several force-fields model the ESP via point charges positioned at the atom centers. A major shortcoming of this approach, its inability to model anisotropies in the ESP, can be mitigated using additional charge sites. It has been shown that nitrogen is the most problematic element abundant in many polymers as well as large molecules of biological origin. To tackle this issue, small organic molecules containing a single nitrogen atom were studied. In performing rigorous scans of the surroundings of these nitrogen atoms, positions where a single extra charge can enhance the ESP description the most were identified. Significant improvements are found for ammonia, amines, and amides. Interestingly, the optimal location for the extra charge does not correlate with the chemically intuitive position of the nitrogen lone pair. In fact, the placement of an extra charge in the lone-pair location does not lead to significant improvements in most cases.

performed, the placement of a single EC in this minimum reduces the RMSE even by ≈ 60% when compared to the respective APC reference. At the most favorable minimum two groups are also found for qEC, the charge of the EC. While calculations with the 6-31G* basis set yield -0.082 ≤ qEC ≤ -0.079 e, all other calculations yield ECs with larger magnitudes (-0.188 ≤ qEC ≤ -0.164 e). Figure S1 RMSE of the 1D scan for ammonia. At r = 0 the RMSE corresponds to the plain atomic point charge (APC) reference. The different data sets correspond to different QM levels of theory as indicated in the legend.
In Figure S2 the results are shown for trimethylamine. Here, the situation is more complex.
Similar RMSE data are found for B3LYP calculations when the basis sets aug-cc-pVDZ, augcc-pVTZ, or 6-311++G(3df,3pd) are used. The results for HF and CCSD with the 6-31G* basis set are located at lower RMSE, but they are similar to each other. All other QM calculations yield RMSE values between those two groups. Despite the added complexity, when compared to ammonia still two minima are found in all cases. A rather broad minimum appears between -2.0 and -1.0 Å and a more localized minimum is visible at ≈ 2.0 Å. Yet, the lowest minimum is not the same for all QM calculations. The B3LYP calculations yield the lower minimum at negative distances (-1.6 ≤ r ≤ -1.4 Å), while in all other cases the minimum at positive distances is lower (1.9 ≤ r ≤ 2.1 Å). That is, depending on the QM calculation a different optimal EC location is proposed. In contrast to the location of the minimum, the charges obtained for the EC at the respective minima do not fall into two separate groups, but rather are distributed in the range -0.020 ≤ qEC ≤ -0.053 e. For the B3LYP calculations, the optimal EC placement leads to a RMSE reduction between 30 and 35%, for CCSD calculations between 20 and 30%, and for HF calculations between 15 and 25% when compared to the respective APC reference.
Note that QM-ESP calculations with basis-sets larger than 6-31G* yield similar results (cf. Figure 3A in the main document). In addition, the optimal location for the EC placement for ammonia is insensitive to the QM calculation used. For trimethylamine, different locations are proposed by different QM variants. While all B3LYP calculations indicate the optimal spot for EC placement in the direction of the methyl groups, all other calculations suggest that the optimal spot is in the lone-pair direction. In any case, all QM variants used indicate two minima at similar locations for trimethylamine. Moreover, irrespective of the optimal EC location the improvement of the ESP upon EC introduction is small when compared to ammonia.

S-II Influence of the EC position on the point charges 1D scans
In this section, we provide additional figures related to the 1D scans of ammonia, trimethylamine and triethylamine. In these figures (Figures S3-S5) the values of all point charges are shown as a function of EC distance r from the nitrogen atom. The data shown correspond to QM calculations at B3LYP/6-311++G(3df,3pd) level. For ammonia, the results are shown in Figure S3. The EC itself is negative at almost all scanned distances, only at positive r ≤ 0.7 Å the EC assumes a positive charge. Conversely, the nitrogen point charge is negative at all distances except for the point scanned at r = -0.1 Å. The hydrogen point charge is positive and comparably small (< 0.6 e) for all scanned distances r.  The data for triethylamine is shown in Figure S5. As in the previous two cases, the EC is negative at negative r and it changes sign at positive r. The point charge of the nitrogen atom shows a similar trend as for ammonia, i.e., it is negative for the majority of scanned distances.
Positive values for the nitrogen atom are found at negative r ≥ -1.

2D scans
In this section, additional figures related to the 2D scans of the primary and secondary amines as well as the amides are provided. In particular, these figures show the influence of the EC position (defined by r and ϕ; cf. Figure   Only the point charge associated with the carbonyl hydrogen of formamide changes sign if the EC approaches its location. Note that since the hydrogens bound to the nitrogen share the atom type, they have equal point charges. Therefore, the approach of the EC to either one of the two hydrogen atoms is not reflected in the charge plots.  In Figure S9 the results for N-methylformamide are presented. For this molecule, we also studied the influence of internal rotations on the ESP fitting. Hence, data for three different rotamers of N-methylformamide are shown in Figure S9. The first column shows the RMSE of the 2D scans of the rotamer considered in the main manuscript (cf. Figure 9). Here a hydrogen of the methyl group and the carbonyl group are eclipsed (0°). The second column shows the RMSE for a methyl group rotation of 30° and the third column shows the RMSE for a methyl group rotation of 60°. While the APC RMSE is similar in all three structures, it is found that the area between the methyl and the carbonyl group is significantly affected by the rotation. In the eclipsed case, an EC in this area can improve the ESP approximation by ≈ 50%, while only ≈ 20% can be achieved for the other two rotamers. Moreover, the area where such an improvement is possible shrinks as the methyl group is rotated. In contrast, the area around the N-H bond is hardly affected by the rotation and an EC in this area can improve the ESP approximation by ≈ 50% in all cases. This suggests that this area is to be favored for EC placement since it significantly enhances the ESP description for all rotamers considered.

S-III Comparison to literature data
Figures S11 and S12 are reproductions of Figures 7 and 8 of the main document, respectively.
Shown are the RMSE results of the 2D scans for methyl-and ethylamine ( Figure S11) as well as dimethyl-, diethylamine, aziridine and pyrrolidine ( Figure S12). Added to these figures are black arrows indicating the vector on which the first EC is placed according to the approach presented by Horton et al. 1 In no case these vectors coincide with one of the minima identified in the present survey.  Figure 2C and D in the main document). The coloring indicates the RMSE and the maximum of the color scale is the RMSE of the plain atomic point charge (APC) reference. Note that for clarity the CH3 group is not shown in the case of diethylamine (B). The results are based on B3LYP/6-311++G(3df,3pd) calculations. The black arrow indicates the direction in which the first EC would be placed according to the method introduced by Horton et al. 1