Understanding the Hydrogen-Bonded Clusters of Ammonia (NH3) n (n = 3-6): Insights from the Electronic Structure Theory.

Although it is well known that hydrogen bonds commonly exist in ammonia clusters and play an important role, there are still many challenges in understanding the electronic structure properties of hydrogen bonds. In this paper, the geometric and electronic structure properties of cyclic ammonia clusters are investigated by using first-principles density functional theory (DFT) and the Møller-Plesset perturbation theory (MP2). The calculation results show that the pentamer and hexamer have deviated from the perfect plane, while the trimer and tetramer present planarization that has been confirmed by infrared (IR) spectra. The electronic structure analysis further shows that the covalent properties play a non-negligible role in hydrogen bonding. The results also indicate that the electronic structure facilitates structure planarization. Our work not only provides insight into the role and nature of hydrogen bonds in ammonia clusters but also provides a theoretical basis for frontier science in fields such as atmospheric haze and biomolecular functions.

Introduction

Ammonia is a colorless gas with a characteristic pungent smell. It is very soluble in water and can easily be condensed to a liquid by cold and pressure.[1,2] Ammonia is also a building block for the synthesis of many pharmaceuticals and is used in many commercial cleaning products. In addition, ammonia gas can provide nitrogen raw materials for production and life, such as fertilizer production, medicine preparation, synthetic fiber, etc.[3] Ammonia clusters can be used to synthesize the third major nitride film in materials science.[4,5] Meanwhile, ammonia clusters can also be used to prepare nitrogen-doped graphene.[6] Moreover, ammonia has received worldwide attention as energy storage media, which is generally more economical.[7] Therefore, understanding the existence of ammonia in the atmosphere and its property is an important scientific and engineering objective, which can be supported by geometric and electronic structure investigations. These fundamental studies require detailed explanations at the atomic level.

An ammonia molecule can donate and accept up to three hydrogen bonds. Ammonia clusters are constituted of ammonia molecules linked by hydrogen bonds. The hydrogen bond network of ammonia clusters is related to ammonia’s properties. Previous experimental studies show the covalent-like characteristics of hydrogen bonds in two 8-hydroxyquiline molecules and liquid water.[8,9] The covalent-like characteristics of hydrogen bonds are also shown in our early theoretical works.[10,11] Hence, it is a critical task to have an insight into structures of hydrogen bonds in ammonia clusters. Several studies have been carried out to understand the hydrogen bond network in ammonia clusters and a mixed ammonia/water cluster.[12] Some specific and relevant issues in ammonia clusters concern geometrical structures,[13−23] energetics,[14,15,19,24] spectroscopy,[25−32] and so on. Despite these studies, the hydrogen bond network in ammonia clusters is still not understood perfectly. So far, less attention has been attracted to the intermolecular interaction between ammonia molecules from the perspective of electronic structures. Therefore, we investigated the electronic properties of cyclic ammonia clusters.

To solve the atmospheric haze, the structures of ammonia clusters have been extensively studied before,[13−20] such as the ammonia dimer. In this work, a systematic investigation on cyclic ammonia clusters in the (NH3) (n = 3–6) clusters is presented by employing first-principles density functional theory (DFT) and the Møller–Plesset perturbation theory. This study addresses the degree of structural planarization and fingerprint recognition by an infrared spectrum in ammonia clusters as well as the nature of bonding in a hydrogen bond. This work has broad potential to be implicated in explaining the mechanism of hydrogen bond interaction in the ammonia cluster, thereby facilitating the understanding of the important role of ammonia in the atmospheric environment and industrial catalysis.

Method

In this paper, we present a systematic study aiming to understand the electronic structure properties of the hydrogen bond mechanism of cyclic ammonia clusters from the perspective of quantum chemistry. We have carried out structural optimizations for cyclic ammonia (NH3) (n = 3–6) clusters at the MP2/6-311++g(2df,2pd) level, as shown in Figure . Moreover, we considered the empirical dispersion-corrected density functional theory (DFT-D3) method with hybrid generalized gradient approximation (hybrid GGA) at the PBE0-D3[33] and B3LYP-D3[34,35] level with 6-311++g(2df,2pd) basis sets. In addition, the performances of MP2/aug-cc-pvdz, MP2/aug-cc-pvtz, and MP2/6-31++g(d,p) were also tested on a geometric structure. To confirm if the obtained final optimized structures are truly energy minimum, vibrational frequency verifications have also been carried out at the same level of theory. All calculations were performed using the Gaussian 09 package.[36]

Figure 1

Optimized structures of cyclic ammonia clusters (NH3) (n = 3–6) at the MP2/6-311++g(2df,2pd) level of theory. Nitrogen atoms appear in purple, hydrogen appears in white, and the broken purple dotted lines denote the N···H bonds.

To obtain detailed information of the intermolecular interaction in cyclic ammonia clusters (NH3) (n = 3–6), we analyzed the interaction energy using the energy decomposition scheme of the ADF 2016 package.[37] In this work, ADF calculations were carried out using the PBE0-D3 functional with the ET-QZ3P-1DIFFUSE basis set. The interaction energy ΔEint can be decomposed into the following physically relevant componentswhere the ΔEelstat describes the classical Coulomb interaction between the fragments; ΔEPauli corresponds to the Pauli repulsion (positive value); ΔEorb is from the orbital interaction, which represents the polarization effects of the electrons among fragments; and ΔEdis takes into account the dispersion forces. ΔEelstat, ΔEorb, and ΔEdis are the total attractive interactions (negative value).

Results and Discussion

Figure presents the stable structures of cyclic ammonia clusters (NH3) (n = 3–6). For n = 3–4, the clusters are nearly a planar structure. Meanwhile, in n = 5–6, the clusters are non-planar. Hydrogen bonds are formed in cyclic ammonia clusters, with each ammonia molecule acting simultaneously as a H atom donor and acceptor. The geometric parameters of cyclic ammonia clusters (NH3) (n = 3–6) are displayed in Figure (the geometric parameters of the dimer are given in Table S1). The average values of intermolecular lengths, R(N···N), are calculated to be 3.176, 3.159, 3.157, and 3.156 Å for n = 3–6, respectively. We note the contraction of the average intermolecular N···N bond length separation by 0.020 Å from the trimer (3.176 Å) to the hexamer (3.156 Å). The average N···H bond lengths, R(N···H), for n = 3–6 were calculated to be 2.223, 2.149, 2.141, and 2.138 Å, respectively. An increase in n leads to a gradual decrease in the average intermolecular N···H bond lengths for n = 3–6. A similar tendency is obtained at the PBE0-D3/6-311++g(2df,2pd), B3LYP-D3/6-311++g(2df,2pd), MP2/aug-cc-pvdz, MP2/aug-cc-pvtz, and MP2/6-31++g(d,p) levels, as shown in Table S1 in the Supporting Information. These geometric structure parameters of MP2 with basis set investigations are in good agreement with DFT.[16,38−40] The trend is consistent with the previous view that bond lengths decrease gradually with the increase of the number of n.[16,38−40] Moreover, we present the average O–H bond lengths as well as the average ∠H···NH bond angles in Figure . As the n value increases, the N–H bond lengths and ∠H···NH bond angles increase, leading to a decrease of N···H bond lengths. Meanwhile, the N–H bond lengths with increased n in the ammonia clusters are close to liquid ammonia.[23]

Figure 2

Geometric structure parameters for cyclic ammonia clusters (NH3) (n = 3–6) at the MP2/6-311++g(2df,2pd) level of theory. The black solid circles represent the average intermolecular N···N bond length, the blue solid circles represent the average intermolecular N···H bond length, the red solid circles represent the average N–H bond length, and the green solid circles represent the average ∠H···NH bond angle.

Infrared (IR) spectra are useful tools for understanding the role of hydrogen bond interactions in ammonia clusters, so we calculated the IR spectra, as shown in Figure . It has been demonstrated that, with the size increase from n = 3 to 6, the band intensity of the 3400 cm–1 regions is remarkably broadened, while smooth shifts are observed for the position of both the 3200 and 3300 cm–1 region bands. This mainly originates from the vibrational mode of N–H stretching in the corresponding clusters. N–H stretching involves symmetric stretching and anti-symmetric stretching (for details, see Figure ). With an increasing cluster size, the number of calculated spectral lines increases correspondingly. The spectra of the planar trimer and the nearly planar tetramer are very simple, which compose of a single degenerate line. Meanwhile, in the pentamer and hexamer, the planar structures are broken, which compose of complicated dependency. We notice that there is no obvious shift in the spectrum for n = 5 and 6 because the hydrogen bond strength is almost saturated in these clusters. The result is consistent with the previous work.[14,32,38]

Figure 3

IR spectra for cyclic ammonia clusters (NH3) (n = 3–6) at the MP2/6-311++g(2df,2pd) level of theory with a scaling factor of 0.95. The black curve lines represent the broadened data (Lorentzian), and the blue solid lines represent the IR intensity.

In ammonia clusters, the formation of hydrogen bonds will break the C3v symmetry, but there still remains the symmetry with respect to the mirror plane.[32] The planar symmetry is broken in (NH3)5 and (NH3)6; they deviate from planarization. From the spectra, we found a splitting of symmetric stretches in n = 5 and 6. However, the peak strength is very weak in n = 4, and it may be because of the strong repulsive force hindering the symmetric stretching of N–H. To explain the signature, we present the IR spectra for the cyclic and tail structure of (NH3)4 at the MP2/6-311++g(2df,2pd) level of theory (see Figures S1 and S2). In the case of symmetric stretches, we found a marked split for the non-planar structure. As one can see, the tail structure is composed of a cyclic cluster of ammonia and a free ammonia molecule, which deviates from the plane structure significantly. This non-planar structure leads to an active symmetric stretching pattern of N–H.

To compare NH3 and (NH3)2 with n = 3–6, we calculated the IR spectra for NH3 and (NH3)2, as shown in Figure S4. Figure S3 shows the vibrational modes of symmetric and anti-symmetric stretching vibrations for NH3. In the IR spectra for ammonia clusters (NH3) (n = 1–6), we notice that the anti-symmetric stretches decrease by roughly 15 cm–1 from n = 2 to 3, by roughly 10 cm–1 from n = 4 to 5, and by roughly 20 cm–1 from n = 5 to 6; the frequency shifts are found to be larger from n = 3 to 4 at about 50 cm–1. There is no obvious shift in n = 4 and 5. Therefore, the hydrogen bond strength is almost saturated. This is consistent with the previous work.[26,32] Thus, the presence of the vibrational signature could be used as an indication of the transition from a planar ring-like structure to a 3D one.

Furthermore, we analyze the electronic structures of cyclic ammonia clusters (NH3) (n = 3–6). Figure shows the energy level diagrams of cyclic ammonia clusters. Lowest unoccupied molecular orbitals (LUMO) display that there are some electrons distributed in H and N atoms of n = 3. For n = 4–6, the electrons are located in N atoms. The result supports that the electronic structure is related to structural planarization. Furthermore, we analyze the highest unoccupied molecular orbital (HOMO)-LUMO gap values. The trimer has the largest HOMO-LUMO gap among cyclic ammonia clusters (NH3) (n = 3–6). This indicates that n = 3 is a stable structure. The MOs with energies at the red line positions present delocalization characteristics in the ammonia clusters. Among them, the energy level has three regions: MOs-I (about −13 eV), MOs-II (about −17 eV), and MOs-III (about −30 eV). The detailed compositions of delocalized MOs in Figure are presented in Table . MOs-I consists of 2s and the lone pair electrons in N atoms. MOs-II is mainly from the 2p bonding electrons of N and the 1s electrons of H. MOs-III is composed of the 2s electrons of N. Moreover, the orbital composition of each region almost has no change with the increasing cluster size.

Figure 4

Energy level diagrams of cyclic ammonia clusters (NH3) (n = 3–6) at the MP2/6-311++g(2df,2pd) level of theory. The red lines indicate the energy levels of the occupied delocalized MOs. The red numbers are HOMO-LUMO gap values.

Table 1

Detailed Atomic Orbital Contributions (%) to Delocalized MOs in the Various Ammonia Clusters

	N		HO–Ha	HO···Hb		N		HO–Ha	HO···Hb
(NH3)3	2s	2p	1s	1s	(NH3)4	2s	2p	1s	1s
HOMO	4.8	93.0	0.0	0.0	HOMO	4.5	93.4	0.0	0.0
HOMO-8	0.0	69.0	18.0	12.4	HOMO-11	0.0	69.2	17.3	12.8
HOMO-11	66.9	0.0	11.0	19.4	HOMO-15	66.8	0.0	11.0	19.5

The H-bonding 1s electrons of H atoms.

The 1s electrons of free H atoms. Note that all Rydberg NAOs/shells or contributions ≤ 0.50% will not be printed.

As shown in Figure (more detailed MO diagrams for these ammonia clusters are given in Table S2 in Part 5 of the Supporting Information), the electrons of MOs-II are delocalized over the whole central regions of n = 3. For n = 4, the reduction of electron delocalization is in the central region of MOs-II. Such electron delocalization results in a high degree of planarization in n = 3. However, in the case of n = 5 and 6, they are further weakened in the electron delocalization in the central area, causing the geometric structure to deviate from the planar structure. Interestingly, as n increases, the delocalization characteristic of MOs-II causes the largest downshifts of MO energies. This strongly highlights the significant role of MOs-II delocalized orbitals in the structural planarization of n = 3 and 4, showing a sharp contrast to n = 5 and 6. The delocalization characteristic of the MOs is revealed to be important in driving the structure planarization. The result is in accordance with water clusters.[10,11]

To show the significant role of these orbitals in the intermolecular interaction of cyclic ammonia clusters (NH3) (n = 3–6), the energy decomposition analysis is calculated, as shown in Table . The total attractive interactions are dominated by the electrostatic (ΔEelstat) and orbital (ΔEorb) interaction energies as well as the dispersion (ΔEdis) energy. For the ΔEelstat term that contributes 61.48–63.77% on account of the total attractive interactions, the ΔEorb term contributes 32.18–33.22% while 3.01–5.88% for the ΔEdis term. The ΔEPauli term constitutes the destabilization factor of cyclic ammonia clusters. It is well known that the orbital interaction reflects the overlap between ammonia molecules. In cyclic ammonia clusters (NH3) (n = 3–6), the corresponding orbital interactions are −2.55, −3.62, −3.78, and −3.84 kcal/mol, respectively. For n = 3–6, with the increase of n, the values of the orbital interaction are increased in which the relatively orbital overlap exists. This is consistent with the previous results in water clusters where the structure planarization is related to the orbital interaction.[10,11] Meanwhile, the total interaction energy increases and N···H bond lengths decrease with the n increase. Moreover, we calculated mixed water/ammonia clusters, as shown in Figure S6. Energy decomposition analysis (see Table S3) reveals that the total interaction increases with the increase of the number of water molecules in the mixed water/ammonia clusters. This is because O is sp3-hybridized in H2O, and there are two lone pairs of electrons outside O, which makes the spatial repulsive force smaller, thus leading to the increase of the total interaction energy. Meanwhile, in NH3, although N is also sp3-hybridized, there is only one lone pair electron outside, which increases the spatial repulsive force, so the total interaction energy decreases. The hydrogen bond interaction in ammonia clusters proved to be much weaker than that in water clusters.

Table 2

Energy Decomposition Analysis of Cyclic Ammonia Clusters (NH3) (n = 3–6)a

geom	ΔEelstat	ΔEPauli	ΔEorb	ΔEdis	ΔEint
(NH3)3	–5.78(65.09%)	4.97	–2.55(28.72%)	–0.55(6.19%)	–3.97
(NH3)4	–6.99(62.13%)	6.50	–3.62(32.18%)	–0.64(5.69%)	–4.75
(NH3)5	–7.16(61.62%)	6.75	–3.78(32.53%)	–0.68(5.85%)	–4.78
(NH3)6	–7.23(61.48%)	6.84	–3.84(32.65%)	–0.69(5.88%)	–4.92

Energy contributions per NH3 in kcal/mol. The percentage values represent the contribution to the total attractive interactions.

To get more in-depth information about intermolecular interactions in cyclic ammonia clusters, we performed the calculations for electron density difference of the cyclic ammonia cluster, as shown in Figure , which are defined as ρ=ρtotal – ∑ ρmolecule where ρtotal is the electron density of cyclic ammonia clusters and ρmolecule is the electron density of each molecule. It is clear that the electron density is enriched around N atoms, and the electronic charge distribution in H atoms is decreased. It means that the electron density shifts from H atoms to the N atom. It can be clearly seen that the central region electronic distribution decreases with the increase of the ammonia molecule. Nevertheless, the electron density of N atoms is almost unchanged. The results for n ≥ 5 suggested that these larger clusters may have the tendency to form three-dimensional isomeric structures very close in energy. The result also indicates that the electronic structure facilitates structure planarization. To compare (NH3)2, we calculated the energy density difference of (NH3)2 (see Figure S7), and there are more charge depletions in H of the hydrogen bond relative to free H, indicating that H atoms of the hydrogen bond act as donors, which are consistent with n = 3–6.

Figure 5

Electron density difference of cyclic ammonia clusters (NH3) (n = 3–6) at the MP2/6-311++g(2df,2pd) level of theory. The blue and yellow regions represent an increase and decrease of electron density, respectively. The isosurface value is ±0.0004 a.u.

Conclusions

In summary, cyclic ammonia clusters (NH3) (n = 3–6) were explored using first-principles DFT and the Møller–Plesset perturbation theory. We study the electronic structure of cyclic ammonia clusters. The calculation results demonstrate that three kinds of MOs play important roles in structural planarization. On further analyzing the geometric structure parameters, IR spectra, and electron density difference, the obvious difference is in n = 3 and n = 4–6. Moreover, the orbital interactions (covalent properties) play a non-negligible role in hydrogen bonding. This work provides a new perspective to understand the electronic structure of the gas ammonia cluster and to encourage the experimental exploration of these promising characteristics in the future.