CHEMPHYSCHEM ARTICLES DOI: 10.1002/cphc.201301176

Clusters of Ammonium Cation—Hydrogen Bond versus sHole Bond Sławomir J. Grabowski*[a, b] MP2/6-311 + + G(d,p) calculations were performed on the NH4 + ···(HCN)n and NH4 + ···(N2)n clusters (n = 1–8), and interactions within them were analyzed. It was found that for molecules of N2 and HCN, the N centers play the role of the Lewis bases, whereas the ammonium cation acts as the Lewis acid, as it is characterized by sites of positive electrostatic potential, that is, H atoms and the sites located at the N atom in the extension of the HN bonds. Hence, the coordination number for the ammonium cation is eight, and two types of interactions of this cation with the Lewis base centers are possible: NH···N hydrogen bonds and HN···N interactions that are classified as s-hole bonds. Redistribution of the electronic charge resulting from complexation of the ammonium cation was analyzed. On the one hand, the interactions are similar, as

they lead to electronic charge transfer from the Lewis base (HCN or N2 in this study) to NH4 + . On the other hand, the hydrogen bond results in the accumulation of electronic charge on the N atom of the NH4 + ion, whereas the s-hole bond results in the depletion of the electronic charge on this atom. Quantum theory of “atoms in molecules” and the natural bond orbital method were applied to deepen the understanding of the nature of the interactions analyzed. Density functional theory/natural energy decomposition analysis was used to analyze the interactions of the ammonium ion with various types of Lewis bases. Different correlations between the geometrical, energetic, and topological parameters were found and discussed.

1. Introduction There are different so-called noncovalent interactions described recently in numerous studies.[1–4] The hydrogen bond is analyzed most often due to its importance in numerous chemical, physical, and biochemical processes.[5] However, it was also pointed out that other noncovalent interactions play an important role in various reactions and processes.[2, 4, 6] One can mention such interactions as the hydride bond, for which the negatively charged H atom acts as the Lewis base center, and it is situated between two electropositive centers,[7–10] and the beryllium bond[11] or the dihydrogen bond, which is the contact between negatively and positively charged H atoms.[12] The latter interaction may be classified as a hydrogen bond from one side and also as a hydride bond from the other side.[7] It seems that the s-hole concept explains the nature of numerous noncovalent interactions.[2, 4, 13–16] For example, atoms of groups V, VI, and VII, due to sites of positive electrostatic potential, may interact with Lewis bases to form connections through pnicogen, chalcogen, and halogen bonds, respectively.[16] Even an atom of group IV may act as the Lewis acid

[a] Prof. S. J. Grabowski Faculty of Chemistry University of the Basque Country and Donostia International Physics Center (DIPC) P.K. 1072, 20080 Donostia (Spain) E-mail: [email protected] [b] Prof. S. J. Grabowski IKERBASQUE, Basque Foundation for Science 48011 Bilbao (Spain) Supporting Information for this article is available on the WWW under http://dx.doi.org/10.1002/cphc.201301176.

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center due to the existence of sites characterized by positive electrostatic potential.[16, 17] Such interactions were analyzed recently, and it was pointed out that they may be considered as a preliminary stage of the SN2 reaction.[18] The latter interactions were named recently as tetrel bonds,[18, 19] and specifically for situations in which the carbon atom acts as a Lewis acid center, the term carbon bond was proposed.[20] In general, if the noncovalent interaction is connected with a meaningful shift in the electronic charge resulting from complexation, it may be often treated as a preliminary stage of the chemical process; for example, the hydrogen bond of a proton transfer[21] or the dihydrogen bond in the creation of molecular hydrogen.[22] Very recently, complexes of ZH4 + , ZFH3 + , and ZF4 + (Z = N, P, and As) with Lewis bases were analyzed,[23] and it was found that these cations, similarly to species of the above-mentioned group IV atoms, possess two types of Lewis acid sites characterized by positive electrostatic potential: the H atoms and parts of the molecular surface located at the Z atom in the extension of HZ and FZ bonds. In such a way, two types of interactions were found: ZH···B hydrogen bonds and (F)HZ···B s-hole bonds (B designates the Lewis base center).[23] It is interesting that the ZH4 + , ZFH3 + , and ZF4 + cations are characterized by positive electrostatic potential on the whole molecular surface, and thus, they always act as Lewis acids. The only question is which interaction sites are preferable. It was found that for the ammonium cation, NH4 + , these are the H atoms, as they possess greater positive electrostatic potential than sites attributed to the N atom, that is, to the extension of HN bonds.[23] In the case of ammonium cation anaChemPhysChem 2014, 15, 876 – 884

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CHEMPHYSCHEM ARTICLES logues, such as PH4 + and AsH4 + , interactions through the central atoms are preferable, as the P and As sites possess greater positive electrostatic potential than the H atoms. For substituted ammonium ions, for example, NFH3 + , the electrostatic potential in the extension of the FN bond is more positive than the electrostatic potential of the H atoms and still more positive than the N atom sites located in the extension of HN bonds. According to those findings, it is interesting to analyze larger clusters in which a cation moiety is characterized by various Lewis acid sites. Notably, NH4 + ···(H2)n[24] and NH4 + ···(C2H2)n[25] clusters (n = 1–8) have been analyzed before; however, they were not analyzed in the context of s-hole-bond interactions or in the context of the analysis of the electronic charge redistribution resulting from complexation. For the NH4 + ···(C2H2)n clusters, acetylene could act as the Lewis base owing to the basic properties of the p electrons, and similarly, the s electrons of molecular hydrogen may be treated as a weak Lewis base in the NH4 + ···(H2)n clusters. The corresponding NH···p and NH···s hydrogen bonds were analyzed, as well as the N··· p and N···s interactions.[24, 25] However, the latter N···p(s) interactions were not considered as s-hole bonds. In another study, AH···p and AH···s hydrogen bonds were compared (AH is the proton-donating bond), and it was found that for cases of extremely strong charge assisted interactions, even if the s electrons of the H2 molecule played the role of the Lewis base, they sometimes possessed characteristics typical for covalent bonds.[26] Notably, there are numerous studies in which larger clusters were analyzed, and specifically, water clusters were considered very often.[27] However, one can also mention studies on other systems: those in which stronger ionic interactions exist, for example, in the (LiHHHLi) + and (NaHHHNa) + species,[28] and those in which weaker noncovalent interactions exist, such as in acetylene[29] or molecular hydrogen clusters.[30] However, for larger systems molecular dynamics methods are usually used, whereas time-consuming ab initio calculations are not common. Hence, the aim of this study is the analysis of NH4 + ···(HCN)n and NH4 + ···(N2)n clusters on the basis of ab initio calculations. Especially, the coexistence of two kinds of interactions, that is, the NH···N hydrogen bond and the N···N s-hole bond, are considered. Two types of Lewis bases were chosen, the stronger hydrogen cyanide, HCN, which acts through the N center, and the weaker N2 Lewis base to study their influence on the electronic charge distribution in the ammonium ion. Given that there are eight sites of extreme (positive) electrostatic potential in the NH4 + cation, clusters with up to eight Lewis base units were analyzed.

2. Results and Discussion 2.1. The Structure of the NH4 + ···(HCN)n and NH4 + ···(N2)n Clusters Ab initio calculations were performed for the NH4 + ···(HCN)n and NH4 + ···(N2)n clusters, and optimizations led to energetic minima for all systems considered (n = 1–8). For the clusters  2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

www.chemphyschem.org containing up to four ligands (HCN or N2 molecules), complexation led to the formation of NH···N hydrogen bonds in which NH was the proton-donating bond of the ammonium cation. In the case of the NH4 + ···(HCN)4 and NH4 + ···(N2)4 clusters, all of the NH bonds of the cation were involved in hydrogen-bonding interactions, which could suggest that the coordination number of NH4 + is four. However, the ammonium cation, similarly to phosphorus and arsenic analogues[23] and to analogues with a group IV central atom,[17, 18, 20] possesses sites of positive electrostatic potential on the terminal H atoms and at the N center in the elongation of the HN bonds (the sholes). Consequently, for the NH4 + ion there are eight Lewis acid centers, which suggests that the coordination number for the ammonium ion is eight. However, one can expect that interactions through the s-holes are weaker than those through the NH···N hydrogen bonds, because a greater positive electrostatic potential (i.e. 0.286 a.u.) is observed for the H atoms than for the nitrogen s-holes (i.e. 0.263 a.u.) for the ammonium cation (MP2/aug-cc-pVTZ results, see Figure 1).[23] Additionally, previous studies showed that the NH···B hydrogen bond is a stronger interaction than the HN···B s-hole bond for complexes of ammonium cations.[23]

Figure 1. Computed electrostatic potential on the 0.001 a.u. molecular surface of NH4 + . Blue color corresponds to the maximum and red corresponds to the minimum electrostatic potential. Black points designate the extremes of the electrostatic potential, that is, 0.286 a.u. for elongation of the NH bonds (H atoms) and 0.263 a.u. for elongation of the HN bonds (N atom). Positive electrostatic potential is observed for the whole molecular surface.

The results of the calculations confirm these expectations; Figure 2 presents, as examples, the molecular graphs of the NH4 + ···(HCN)5 and NH4 + ···(N2)5 clusters. For the former, there are four hydrogen bonds, and the corresponding H···N bond paths (BPs) are observed. There is also the N···N BP between the nitrogen attractors of the NH4 + ion and of the HCN molecule corresponding to the s-hole bond. A similar arrangement is observed for the NH4 + ···(N2)5 cluster, but there are also additional BPs between the nitrogen atoms of the N2 molecules, and hence, ring critical points are also observed (Figure 2). In general, for larger clusters containing more than four ligands, there are four hydrogen bonds, and additional s-hole bonds are created; finally, for eight ligands in the case of the NH4 + ···(HCN)8 and NH4 + ···(N2)8 clusters, all Lewis acid sites are “satuChemPhysChem 2014, 15, 876 – 884

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Figure 3. The relationship between the H···N distance [] and the electron density at the corresponding bond critical point [a.u.]: NH4 + ···(HCN)n clusters (*), NH4 + ···(N2)n clusters (*).

Figure 2. Molecular graphs of the NH4 + ···(HCN)5 (top) and NH4 + ···(N2)5 (bottom) clusters; big circles correspond to attractors attributed to atoms, and small circles correspond to the bond and ring critical points. Solid and broken lines correspond to bond paths: solid to those attributed to covalent bonds and broken to intermolecular contacts.

rated” by four hydrogen bonds and four s-hole bonds (see the Supporting Information for molecular graphs of selected clusters). If the number of ligands does not exceed four, only N H···N hydrogen bonds are created between the ammonium ion and the nitrogen centers of the N2 and HCN molecules. Figure 3 presents a good exponential relationship (R = 0.998) between the H···N distance and the electron density at the corresponding bond critical point (BCP). Both types of clusters were considered, that is, NH4 + ···(HCN)n and NH4 + ···(N2)n, and both were taken into account in the above-mentioned relationship. One can observe shorter H···N distances and greater values for the electron density at the BCPs for the NH4 + ···(HCN)n clusters than for the NH4 + ···(N2)n clusters. Thus, in general, the hydrogen-bonding interactions are stronger in the former clusters than in the latter clusters. Only H···N contacts corresponding to NH···N hydrogen bonds are included in Figure 3, because for the N···N contacts, the corresponding shole bonds are much weaker than the hydrogen bonds and there is no good correlation between the N···N distance and the electron density at the corresponding BCP (see the Supporting Information for electron densities at the BCPs of H···N and N···N).  2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

Optimizations were performed without any symmetry constraints; however, the geometries of the clusters were at energy minima and were considered to be very close to highsymmetry objects. Geometry close to Td symmetry was observed for clusters containing four and eight ligands. For two and six ligands in the clusters, C2v symmetry was observed; for one, three, five, and seven ligands, C3v symmetry was characteristic. The discrepancies between the idealized geometry characterized by symmetry constraints and the observed geometry were greater for clusters with N2 ligands than for those with HCN species. Also, this discrepancy was greater if the number of ligands in the cluster increased. The greater discrepancy for clusters with nitrogen molecules is probably the effect of the additional interactions between the N2 molecules (see Figure 2). Similarly, it seems that a greater number of ligands in the cluster results in denser packing and additional intermolecular interactions. Notably, the properties of the ammonium cation are in agreement with the experimental studies; a search through the Cambridge Structural Database was performed, and the results showed the existence of crystal structures in which the NH4 + cation acts as a Lewis acid through the H atoms and additionally through the N center s-hole sites.[23] Table 1 presents selected parameters for the clusters considered. As expected, the HCN molecules interact more strongly with the ammonium ion than do the nitrogen molecules. For example, for complexes containing one ligand, the binding energy, Ebin, is 21.2 and 6.0 kcal mol1 for the HCN and N2 ligand, respectively. The strength of the interaction between the ammonium cation and the ligand increases if the number of ligands increases; however, the mean interaction between the cation and the ligand in the cluster, Emean = Ebin/n, decreases if n increases (n = number of ligands). There is the greater decrease in the latter value for clusters containing more than four ligands, because in such cases, additional shole-bond interactions occur, which are weaker than the corresponding hydrogen bonds. For the NH4 + ···NCH and NH4 + ···N2 complexes characterized by C3v symmetry and linked through ChemPhysChem 2014, 15, 876 – 884

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Table 1. The binding energy, the mean energy of the interaction between the ligand and the ammonium ion, the QTAIM integrated charge of NH4 + , the charge of the N atom of NH4 + , and the corresponding atomic volume. Cluster

Ebin [kcal mol1]

Emean [kcal mol1]

QNH4 + [a.u.]

QN[a] [a.u.]

VN[b] [3]

NH4 + ···HCN NH4 + ···(HCN)2 NH4 + ···(HCN)3 NH4 + ···(HCN)4 NH4 + ···(HCN)5 NH4 + ···(HCN)6 NH4 + ···(HCN)7 NH4 + ···(HCN)8 NH4 + ···HCN[c] NH4 + ···N2 NH4 + ···(N2)2 NH4 + ···(N2)3 NH4 + ···(N2)4 NH4 + ···(N2)5 NH4 + ···(N2)6 NH4 + ···(N2)7 NH4 + ···(N2)8 NH4 + ···N2[c]

21.2 38.5 53.2 65.9 73.8 81.0 87.5 93.4 17.0 6.0 11.5 16.8 21.8 26.0 30.6 35.0 39.9 4.2

21.2 19.3 17.7 16.5 14.8 13.5 12.5 11.7 17.0 6.0 5.8 5.6 5.5 5.2 5.1 5.0 5.0 4.2

0.942 0.911 0.891 0.879 0.884 0.888 0.893 0.894 0.985 0.977 0.950 0.944 0.931 0.928 0.928 0.924 0.922 0.991

1.072 1.103 1.129 1.150 1.133 1.118 1.106 1.096 1.027 1.051 1.068 1.083 1.097 1.094 1.090 1.087 1.084 1.032

16.26 16.40 16.53 16.64 16.03 15.53 15.08 14.62 15.66 16.17 16.24 16.30 16.35 16.01 15.75 15.42 15.12 15.73

[a] The value for NH4 + that is not involved in any interaction is 1.033 a.u. [b] 16.08 3 for free NH4 + . [c] The complex is linked through the N···N s-hole bonds.

N···N s-hole bonds, the Ebin energy is 17.0 and 4.2 kcal mol1, respectively. However, the latter species do not correspond to energy minima but to second-order transition states. The maxima of the electrostatic potential for the ammonium cation are attributed to the H atoms, and this is why clusters of NH4 + in energy minima and containing s-hole bonds exist only if all of the H atom centers are saturated by hydrogen bonds, that is, for n > 4. Table 1 presents results concerning electronic charge redistribution as an effect of complexation. The charge of the ammonium cation not involved in any interaction, QNH4 + , is + 1, and this charge decreases in clusters. For the HCN clusters, this charge decreases to + 0.942 a.u. for the NH4 + ···NCH complex, and it decreases further to + 0.879 a.u. if the number of HCN molecules increases up to four. However, a slight increase in this charge is observed for any further increase in the number of HCN molecules in the cluster, in spite of the fact that all of the HCN molecules act as Lewis bases. A different situation is observed for clusters with N2 molecules; a decrease in the value of QNH4 + is observed if the number of N2 molecules increases up to eight. However, the N2 molecule delivers a lower negative charge to the ammonium cation than the HCN molecule, which is a stronger Lewis base. One can conclude that there is a limit in the electronic charge shift from the Lewis base units into the ammonium cation and that for the NH4 + ···(HCN)4 cluster such a limit is achieved. Table 1 also shows the accumulation of the negative charge on the nitrogen atom, QN, of the NH4 + cation. Such an accumulation is observed if the number of ligands increases to four for complexes in which the ammonium ion is connected only through hydrogen bonds. The latter is accompanied by an in 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

crease in the nitrogen atom volume, VN. This is in line with other studies on complexes linked through hydrogen bonds. It was pointed out that the formation of AH···B hydrogen bonds is connected to the hyperconjugation effect, which is attributed to n(B)!sAH* orbital–orbital interactions and further to a rehybridization process.[31] These effects are accompanied by electronic charge transfer from the Lewis base to the Lewis acid, an increase in the negative charge of the A atom, and consequently an increase in its volume. The rehybridization process for the hydrogen bond also leads to an increase in the positive charge of the H atom and to a decrease in its volume. The latter features, among eight other ones, were described as QTAIM (quantum theory of “atoms in molecules”) characteristics attributed to hydrogen bonds.[32] One can see that for a greater number of ligands (n  5), the above-mentioned values of QN and VN change in opposite directions. This may be suggestive of the different natures of the N···N s-hole bond and the NH···N hydrogen bond. Figure 4 shows the relationships between the charge of the NH4 + cation and the charge of the N center of this moiety. One can clearly see the minimum negative charge of the N atom of the four ligands for both the HCN and N2 clusters. In contrast, as previously mentioned above, the minimum value

Figure 4. The relationships between the QTAIM charge [a.u.] of the ammonium cation and the QTAIM charge [a.u.] of its N center for HCN (top, *) and N2 (bottom, *) clusters; the number of ligands is indicated in these plots.

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of the NH4 + charge is observed for four ligands in the case of the HCN clusters, whereas in the case of the N2 clusters, such a minimum value of the charge of the cation is observed for eight ligands. Table 1 presents parameters for the NH4 + ···NCH and NH4 + ···N2 complexes that are not in energy minima and for which C3v symmetry and links through the N···N s-hole bonds were fixed. There is also electronic charge transfer from the Lewis base (HCN or N2) to the Lewis acid (the ammonium ion) for these complexes; however, it is much lower than that for analogues linked through hydrogen bonds. Nonetheless, for the shole bonds the negative charge of the N atom of NH4 + decreases with an accompanying decrease in the volume of the N atom. Similar changes as an effect of complexation were observed recently for simple complexes of the ammonium cation and its group V analogues[23] as well as for complexes of ZH4, ZFH3, and ZF4 (Z = group IV atom).[17, 18, 20] It is discussed further below. Tables 2 and 3 show parameters of the NH bonds involved in the hydrogen bond and/or the s-hole bond for the HCN and N2 clusters, respectively. The NH bond length for the ammonium cation not involved in any interaction is 1.024 . One can see the elongation of this bond in almost all clusters of

Table 2. Selected parameters for the NH4 + ···(HCN)n clusters: the bond length, the polarization of the NH bond, the energy of the n(N)!sNH* interaction, the charge of the H atom of NH4 + , and the corresponding atomic volume. The values given in the row correspond to the NH bond involved in the NH···N hydrogen bond and/or in the N···NH s-hole bond.[a] rNH[b] []

Pol[c] [% at N atom]

ENBO (H-bond) [kcal mol1]

ENBO (s-hole) [kcal mol1]

QH[d] [a.u.]

VH[e] [3]

1.053(1) 1.042(2) 1.035(3) 1.030(4) 1.028(5) 1.028(5) 1.028(5) 1.028(5) 1.026(6) 1.026(6) 1.026(6) 1.026(6) 1.025(7) 1.024(7) 1.025(7) 1.025(7) 1.023(8) 1.023(8) 1.023(8) 1.023(8) 1.022(1)[f]

76.05 75.01 74.22 73.57 73.07 73.6 73.6 73.6 73.18 73.58 73.18 73.58 73.11 73.46 73.11 73.67 73.3 73.3 73.3 73.3 72.25

28.71 20.58 15.82 12.73 10.78 11.15 11.15 11.15 9.37 9.55 9.37 9.55 8.56 7.54 8.56 9.11 7.53 7.54 7.53 7.54 0

– – – – 0.37 – – – 0.35 – 0.35 – 0.31 0.35 0.31 – 0.32 0.32 0.32 0.32 1.05

0.564 0.542 0.523 0.507 0.496 0.507 0.507 0.507 0.498 0.506 0.498 0.506 0.496 0.501 0.496 0.506 0.497 0.497 0.497 0.497 0.488

2.27 2.51 2.71 2.88 3.00 2.88 2.87 2.88 2.97 2.87 2.97 2.87 3.00 2.82 3.00 2.79 2.88 2.88 2.88 2.88 3.84

[a] For the clusters containing up to four ligands, similar values were obtained for all hydrogen bonds in the cluster considered, and thus, the mean values are presented. [b] The number of HCN molecules in the corresponding cluster is given in parentheses; the NH bond length for free NH4 + is 1.024 . [c] The polarization of the NH bond for free NH4 + is 72.89. [d] This value for the H atom of NH4 + that is not involved in any interaction is 0.508 a.u. [e] 3.68 3 for free NH4 + . [f] The complex is linked through the N···N s-hole bond.

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Table 3. Selected parameters for the NH4 + ···(N2)n clusters: the bond length, the polarization of the NH bond, the energy of the n(N)!sNH* interaction, the charge of the H atom of NH4 + , and the corresponding atomic volume. The values given in the row correspond to the NH bond involved in the NH···N hydrogen bond and/or in the N···NH s-hole bond.[a] rNH[b] []

Pol[c] [% at N atom]

ENBO (H-bond) [kcal mol1]

ENBO (s-hole) [kcal mol1]

QH[c] [a.u.]

VH[c] [3]

1.032(1) 1.030(2) 1.028(3) 1.027(4) 1.026(5) 1.026(5) 1.026(5) 1.026(5) 1.026(6) 1.025(6) 1.026(6) 1.025(6) 1.025(7) 1.024(7) 1.025(7) 1.025(7) 1.024(8) 1.024(8) 1.024(8) 1.024(8) 1.024(1)[d]

74.15 73.82 73.52 73.24 73.03 73.28 73.28 73.23 72.93 73.37 73.11 73.37 72.95 73.09 73.19 73.48 73 73 73.38 73.38 72.68

8.65 7.74 6.94 6.42 6.06 6.33 6.33 6.31 5.99 5.73 6.17 5.73 5.99 5.65 5.89 5.39 5.85 5.85 5.29 5.29 0

– – – – 0.27 – – – 0.27 – 0.10 – 0.28 0.28 0.13 – 0.29 0.29 0.19 0.19 0.36

0.531 0.522 0.514 0.507 0.503 0.507 0.507 0.506 0.503 0.507 0.500 0.507 0.500 0.501 0.503 0.507 0.499 0.499 0.504 0.504 0.502

2.92 3.01 3.09 3.17 3.21 3.13 3.13 3.15 3.17 3.02 3.22 3.03 3.20 3.12 3.12 2.93 3.13 3.13 2.92 2.92 3.71

[a] For clusters containing up to four ligands, similar values were obtained for all hydrogen bonds in the cluster considered; thus, the mean values are presented. [b] The number of N2 molecules in the corresponding cluster is given in parentheses. [c] These values for the NH4 + cation not involved in any interaction are given in the footnote of Table 2. [d] The complex is linked through the N···N s-hole bond.

HCN and N2. The greatest elongation of about 0.01  is observed for the NH4 + ···NCH complex, and it decreases if the number of HCN molecules in the cluster increases. For seven and eight ligands, changes of the NH bond length are negligible. There are two reasons for the smaller elongation of the NH bonds with an increase in the number of ligands. For the NH4 + ···NCH complex linked through the s-hole bond, shortening of the NH bond as a result of complexation is observed, and thus, the additional s-hole bonds for n  5 result in a smaller elongation effect. The second reason is connected with weakening of intermolecular hydrogen-bonding interactions (see Table 1) with an increase in the number of ligands. Tables 2 and 3 show other changes resulting from interactions in the clusters. Polarization (percentage of the electron density on the N atom) of the NH bonds of the cation increases, which is a result of the formation of hydrogen bonds. This is connected with a shift in the electron density from the Lewis base to the cation and next to the central N atom. Hence, an increase in the positive charge of the H atom is observed as is an increase in the negative charge of the N atom (Tables 1–3). The latter changes, which are typical for hydrogen-bonding interactions,[31, 33] are accompanied by a decrease in the volume of the H atom and an increase in the volume of the N atom. ChemPhysChem 2014, 15, 876 – 884

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CHEMPHYSCHEM ARTICLES For the NH4 + ···NCH and NH4 + ···N2 complexes linked through the s-hole bond, changes opposite to those described above and resulting from the formation of hydrogen bonds are observed. Formation of the s-hole bond leads to a decrease in the polarization of the NH bond, a decrease in the positive charge of the H atom, a decrease in the negative charge of the N atom, and so on (Tables 1–3). Hence, the effects of the formation of hydrogen bonds are reduced for clusters containing five or more ligands, because s-hole bonds are formed. Additionally, it was previously mentioned that an increase in the number of ligands is connected with the formation of weaker hydrogen bonds. The changes described above and resulting from complexation are much smaller for clusters of N2 than for clusters of HCN, as the nitrogen molecule is a weaker Lewis base than hydrogen cyanide (Tables 2 and 3). For example, for the NH4 + ···NCH complexes, there is an increase in the polarization of the NH bond by 3.2 for a link through the hydrogen bond, and this values decreases by 0.6 for a link through a s-hole bond. For the NH4 + ···N2 complexes, the corresponding changes amount to 1.3 and 0.2, respectively. Tables 2 and 3 also present the orbital–orbital n(N)!sNH* interaction energies (designated as ENBO) for the hydrogen bond and the s-hole bond. For the HCN clusters, such energies connected with hydrogen-bond formation are in the range from 28.7 to 7.5 kcal mol1, whereas for the N2 clusters, the values are within the range from 8.7 to 5.3 kcal mol1. The following ranges are observed for the s-hole bonds: 1.05–0.31 and 0.36– 0.10 kcal mol1, respectively. The greatest orbital–orbital interactions are for complexes containing one ligand. In general, the ENBO energies are greater for clusters containing HCN ligands than for those containing N2 molecules. Also, the orbital–orbital interactions attributed to hydrogen bonds are much stronger than those attributed to the s-hole bonds. Figure 5 presents the correlation between the NH bond length and the polarization of this bond for the hydrogen cyanide clusters; similar relations are observed for the NH4 + ···(N2)n clusters. A greater polarization occurs for larger elongations of the NH bond as a result of complexation. One can see that

Figure 5. The relationship between the length of the NH bond [] and the corresponding polarization [% at N atom]: free ammonium cation and clusters containing up to four HCN molecules (*) and the remaining clusters (~). The numbers 1–4 show the number of ligands in the cluster.

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www.chemphyschem.org for free ammonium cations and clusters containing up to four ligands, there is good linear correlation. For clusters containing five ligands or more, we did not observe significant changes in the NH bond length or the corresponding polarization (Figure 5, ~). This was mentioned above: s-hole bonds existing in large clusters (n  5) reduce the effects of hydrogen-bond formation, and for such clusters, the hydrogen bonds are weaker than those in clusters containing fewer ligands. Figure 6 shows the correlation between the NH bond length and the ENBO orbital–orbital energy connected with the formation of hydrogen bonds. Opposite to the relation presented in Figure 5, a linear correlation is observed for all NH bonds in all of the clusters, even in clusters for which n  5

Figure 6. The relationship between the length of the NH bond [] and the corresponding energy of the n(N)!sNH* interaction [kcal mol1]: free ammonium cation and clusters containing up to four HCN molecules (*) and the remaining clusters (~). The numbers 1–4 show the number of ligands in the cluster. An excellent correlation for the whole sample is observed if the free cation with no orbital–orbital interaction corresponding to the hydrogen bond (* on the horizontal axis) is excluded.

(Figure 6). Consequently, the hydrogen bond and the n(N)! sNH* orbital–orbital covering attributed to this interaction are mainly responsible for the change in the NH bond length, that is, its elongation, whereas the influence of the weak orbital–orbital interaction related to the s-hole bond is negligible. Note that for NH4 + ···NCH complexes linked through the hydrogen bond and the s-hole bond (see Table 2) there is a change in the NH bond length of 0.029 and 0.002 , respectively. A similar situation is observed for clusters containing N2 ligands, as a change in the NH bond length for the NH4 + ···N2 complex configurations amount to less than 0.0005  for the s-hole link and to less than 0.008  for the hydrogen bond. These results show that the analyzed hydrogen bonds are to a great extent steered by charge-transfer processes. It was previously pointed out that charge-transfer interactions, mainly the n(B)!sAH* orbital–orbital contribution attributed to the AH···B hydrogen bond, is responsible for the stability of related complexes.[31, 33] A different situation usually occurs for the s-hole bonds, for which electrostatic interactions followed by polarization are the most important factors that contribute to stabilizing the complexes.[4, 16]

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For large clusters (n  5), there are two types of interactions: drogen bond and the N···s s-hole bond. For complexes of the for the hydrogen bond, a meaningful shift in the electronic acetylene analogues, NH···p and N···p interactions are obcharge is observed, whereas for the s-hole bond, it is negligiserved. Similarly for complexes of HCN and N2, there are N ble. Hence, the n(N)!sNH* orbital–orbital interaction is much H···N and N···N interactions, as discussed in the previous section. stronger for the former than for the latter, and this is why the The results of DFT/NEDA for the complexes mentioned interaction energy terms related to electronic shift are often above are presented in Table 4. One can see that for the hydrocomparable to the electrostatic energy for the hydrogen bond, gen-bonded configurations, the charge transfer (CT) interaction whereas for the s-hole bond, the electrostatic interaction is energy term is the most important attractive contribution folusually dominant. Notably, the hydrogen bond is considered to be classified as a type of s-hole bond.[2, 4, 15] However, it seems that there are Table 4. DFT/NEDA decomposition of the energy of interaction and the terms of the decomdifferences between the hydrogen bond and position: the total energy (TOT), charge transfer (CT), electrostatic (ES), polarization (PL), the exchange term containing dispersion energy (XC), and the deformation energy (DEF). the other types of s-hole bonds, such as the halogen,[34] pnicogen,[35] chalcogen,[36] and Complex TOT ES CT PL XC DEF tetrel bonds.[17–19] In the case of the AH···B [kcal mol1] [kcal mol1 [kcal mol1 [kcal mol1 [kcal mol1 [kcal mol1 hydrogen bond, an enhancement in the posNH4 + ···HCN[a] 21.81 23.58 36.48 12.16 4.83 55.24 itive electrostatic potential on the edge of NH4 + ···HCN[b] 16.04 15.14 2.86 13.17 2.98 18.11 the H atom is connected to a shift in the 5.46 4.34 12.13 7.22 2.17 20.40 NH4 + ···N2[a] + [b] 3.51 2.65 2.32 8.45 1.83 11.74 NH electron density from the H atom to the A 4 ···N2 + [a] ···C H 10.63 10.01 17.19 3.5 2.81 22.88 NH 4 2 2 center, whereas for the above-mentioned 6.57 5.76 2.41 6.28 1.74 9.62 NH4 + ···C2H2[b] other s-hole bonds, the electronic charge on 2.21 1.46 4.9 0.16 0.83 5.14 NH4 + ···H2[a] the Z atom (Z = group IV, V, VI, or VII atom) 0.95 0.6 0.93 0.89 0.38 1.85 NH4 + ···H2[b] depends on the nature of the hybrid orbital [a] Complexes linked through the hydrogen bond. [b] Complexes linked through the s-hole of the Z atom that contributes to the covabond. lent bond (NH bond in the case of the ammonia cation considered in this study). The lowed by the electrostatic and polarization terms. This is in line depletion of this electronic charge on the Z atom increases if with the former statements that the charge-transfer interaction the contribution of the p orbital to this hybrid orbital increasis a signature of the hydrogen bond and that it is responsible es.[37] In spite of the fact that the hydrogen bond may be probfor the stability of complexes linked through this interaction.[31] ably classified as the s-hole bond, two terms are used in this study: the hydrogen bond and the s-hole bond (for HN···N In contrast, for complexes linked through the s-hole bond, the interactions) to distinguish them in the above and below diselectrostatic or polarization interaction energy is the most imcussions. portant attractive term. This is in line with the results presented in the former section, in which it was discussed that the n(N)!sNH* orbital–orbital interaction is much more important + 2.2. Complexes of NH4 Linked through the Hydrogen Bond for hydrogen bonds than for s-hole bonds and that for the and the s-Hole Bond latter interactions the electrostatic interactions should play the To deepen the understanding of the nature of the interactions dominant role. in the clusters analyzed, density functional theory (DFT)/natural There is a very good correlation between the total interacenergy decomposition analysis (NEDA)[38] of the energy of intion energy and the electrostatic energy (R = 1.00 for linear reteraction was applied for different dyads linked through the gression, see the Supporting Information). This may suggest hydrogen bond or the s-hole bond. The NH4 + ion acts similarly that for both the hydrogen bond and the s-hole bond considto the clusters analyzed in this study, that is, as the Lewis acid ered in this study, the electrostatic interaction plays a very immoiety, and the following molecules were chosen as the Lewis portant role. It was stated in recent studies that for s-hole bases: HCN, N2, C2H2, and H2. All dyads linked through the hybonds the electrostatic interactions play the dominant role followed by the polarization and sometimes dispersive contribudrogen bond correspond to minima, whereas configurations tions.[2, 4, 15, 16] It seems that for numerous noncovalent interaclinked through the s-hole bond correspond to the transition state. The geometries of the latter configurations were taken tions, the arrangement of the molecules is steered by electrofrom the corresponding clusters at energy minima and constatic potential and next by effects connected with the shift in taining five ligands, as for n  5 all of the NH bonds are satuthe electronic charge that takes place in the process of the rated by hydrogen bonds and the next ligand is attached complexation. These shifts are very important for AH···B hythrough the s-hole bond. The geometries for complexes of drogen bonds, for which significant movement of the proton HCN and N2 were taken from the results here presented, and shift of the electronic charge from the H atom to the A center is observed. For the other s-hole bonds, also those obwhereas the geometries for the H2 and C2H2 complexes were served here, such shifts are not so large. This is why CT energy taken from earlier studies.[24, 25] In the case of the H2 complexes is very important for hydrogen bonds, whereas for other non(see the Supporting Information), one can see the NH···s hy 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

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CHEMPHYSCHEM ARTICLES covalent interactions, the electrostatic term is usually the most important attractive one. The latter statements are supported by a very good correlation between the positive deformation energy and the energy terms related to electronic shift, that is, polarization and charge transfer (R = 1.00 for linear regression, see the Supporting Information). This is also in line with previous studies, in which it was observed that for stronger interactions the repulsive exchange effects overwhelm the electrostatic attraction, and thus, to “keep” the system stable, contributions related to electronic shift are more significant. This was analyzed mostly for hydrogen-bonded systems,[39] but it was also observed for other noncovalent interactions.[40] However, one should be careful in analyzing the results of the decomposition of the interaction energy. There are different decomposition schemes for which there are different physical meanings for the decomposition terms. However, the DFT/NEDA results presented here are in line with earlier studies, and in general, they are in agreement with the s-hole concept.

3. Conclusions The NH4 + ···(HCN)n and NH4 + ···(N2)n clusters were considered, and it was found that two types of interactions exist between the ammonia cation and the ligands: NH···N hydrogen bonds and N···N s-hole bonds. The existence of such interactions is connected with the Lewis acid sites of the ammonia ion. Namely, the NH4 + species is characterized by four maxima of positive electrostatic potential for the H atoms and four positive electrostatic potential sites situated in elongations of the HN bonds at the N center. In such a way, the coordination number for the ammonia cation is eight. If the number of ligands does not exceed four, only hydrogen bonds are created, as the positive potential at the H atoms is greater than the potential at the N sites. For clusters in which the number of ligands amounts to five or more, both hydrogen bonds and shole bonds are formed. The complexation, in the case of ammonia ion clusters, is connected with a shift in the electronic charge from the ligands to the cation; this effect is greater for the HCN Lewis base than for the N2 molecule, and it is also greater for the hydrogen bond than for the s-hole bond. It is interesting that the shift in the electronic charge for the hydrogen bond is opposite to the shift for the s-hole bond. For the former, there is the shift from the ligand to NH4 + and next within the cation from the H atom to the N center. For the latter, there is similarly a shift from the ligand to the cation, but next within the cation from the N center to the corresponding H atom. Simple complexes of the ammonia cation were also analyzed, and within DFT/NEDA it was found that for the hydrogen-bonded complexes the energy of the charge-transfer interaction is the most important attractive term, whereas for the s-hole-bonded complexes it is the electrostatic interaction that is the most important attractive term. However, the geometries of the molecules in the clusters show that distribution of the electrostatic potential for the interacting subunits (Lewis acid and Lewis base units) steers the arrangement of the moieties  2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

www.chemphyschem.org and that complexation leads to shifts in the electronic charge within them.

Computational details The MP2/6-311 + + G(d,p) calculations on clusters of the NH4 + cation [NH4 + ···(HCN)n and NH4 + ···(N2)n, n = 1–8] were performed, which led to energy minima, as no imaginary frequencies were detected. The calculations were performed with the use of the Gaussian09 set of codes.[41] Additionally, complexes of the ammonia ion with selected Lewis base units were analyzed, and the calculations were performed at the same level as that for the clusters. The quantum theory of “atoms in molecules” (QTAIM) was applied.[42] The QTAIM calculations were performed with the use of the AIMAll program.[43] The molecular graphs of the considered clusters and dyads were analyzed, especially the bond paths related to the intermolecular interactions and the electron densities at the corresponding bond critical points (BCPs, 1BCP). The integrated atomic charges and atomic volumes were also calculated within the QTAIM approach. The natural bond orbital (NBO) method[31, 33] was applied to calculate selected orbital–orbital interactions as well as the polarizations of selected bonds directly participating in the hydrogen-bonds and s-hole-bond interactions. Natural energy decomposition analysis (NEDA) of the interaction energy is often used to analyze intermolecular interactions.[44] However, this decomposition is performed on the Hartree–Fock wavefunction, for which correlation effects are neglected. Thus, an extended DFT/NEDA approach[38] was used to include the correlation effects. For DFT/NEDA, the B3LYP functional and the 6-311 + + G(d,p) basis set were used. The interaction energy within the DFT/ NEDA approach may be expressed in the following way [Eq. (1)]: DE DFT ðTOTÞ ¼ ES þ PL þ CT þ XC þ DEF

ð1Þ

For a complex composed of A and B units, DEDFT is the DFT interaction energy, and ES is the classical electrostatic interaction. PL is the polarization term, which arises from the extra electrostatic interaction connected with the polarization of the unperturbed molecular orbitals of the separated A and B fragments to those of the complex. CT is the charge transfer contribution, and it is the stabilizing component that arises from delocalization of the electrons between the A and B units of the complex. XC is an attractive contribution accounting for intermolecular electron exchange and correlation. DEF designates the deformation energy having a contribution from each fragment, DEF(A) and DEF(B). DEF(A or B) is a repulsive term, as yA(B), the wavefunction converged for A(B), is of lower energy than yA(B)def in the complex. DFT/NEDA was chosen because the extended basis sets calculations showed the numerical stability of this approach.[38] For the NBO and DFT/NEDA calculations, the NBO 5.0 program[45] implemented in the GAMESS set of codes[46] was used.

Acknowledgements Financial support comes from Eusko Jaurlaritza (GIC 07/85 IT330-07) and the Spanish Office for Scientific Research (CTQ201127374). Technical and human support provided by Informatikako Zerbitzu Orokora – Servicio General de Informatica de la Universidad del Pais Vasco (SGI/IZO-SGIker UPV/EHU), Ministerio de ChemPhysChem 2014, 15, 876 – 884

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Received: December 11, 2013 Published online on February 24, 2014

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