Dismantlement of ammonia upon interaction with Ben (n ≤ 10) clusters

The interaction of ammonia with Ben (n < 1–10) clusters has been investigated by density functional theory and ab initio calculations. The main conclusion is that, regardless of the size of the Be cluster, neither the structure of ammonia nor that of the Be clusters are preserved due to a systematic dissociation of its NH bonds and a spontaneous H‐shift toward the available Be atoms. This H migration not only leads to rather stable BeH bonds, but dramatically enhances the strength of the BeN bonds as well. Accordingly, the maximum stability is found for the interaction with the beryllium trimer, leading to a complex with three NBe and three BeH bonds. Another maximum in stability, although lower than that reached for n = 3, is found for the Be heptamer, since from n = 6, a new NBe bond is formed, so that complexes from n = 6 to n = 10 are characterized by the formation of a NBe4 moiety, whose stability reaches a maximum at n = 7. The bonding characteristics of the different species formed are analyzed by means of AIM, NBO, ELF and AdNDP approaches.


| INTRODUCTION
The so-called electron-deficient compounds are molecules that do not have enough valence electrons to form two-center two-electron bonds to keep the atoms bonded. The simplest case is probably one of the most abundant ions in the universe and one of the most important molecules in the interstellar medium, the H 3 + cation, in which only one pair of electrons binds three protons. Thompson discovered this molecule in 1911, 1 and 24 years later, Coulson concluded, using the MO theory, that H 3 + existed in a stable equilateral form. 2 Nowadays, these initial ideas are confirmed and the bonding in H 3 + is viewed as the result of locating the two electrons of the system in a symmetric three-center bonding orbital. 3 However, many more complicated molecules can be classified as electron-deficient systems. This often occurs when the molecule contains elements, such as boron, that have too few electrons to form an octet, as was established in some seminal papers published by Longuet-Higgins in the mid-20th century. 4,5 The interest in these systems, which are generally excellent Lewis acids, grew steadily since then, as their high-electron affinity was behind a very reach chemistry. It suffices to cite a small selection of papers published over the last decade to illustrate the versatility of boron-containing systems, from their electrophilicity, Dedicated to Gernot Frenking on the occasion of his 75th birthday.
antiferroelectricity, aromaticity, fluxionality, hydrophilicity, ion storage properties, catalytic effects to their fluorescence or versatile reactivity. [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] Although the information on beryllium-containing systems is much scarcer due to the high toxicity of this element, pioneering papers written by Rundle et al., again at the middle of the last century, clearly established the connection between the electron-deficient nature of this element and the characteristics of the crystals of dimethylberyllium 21 or beryllium chloride. 22 The electrondeficient nature of both Be-and B-containing compounds is also behind the acidity enhancement they induce by acting as Lewis acids when interacting with different Lewis bases. This explains, for instance, the enhanced acidity of phosphine-boranes 23 and amineboranes, 24 or the fact that even common hydrocarbons become strong acids in the gas-phase when interacting with Be compounds, 25 which can also induce spontaneous ion-pair formations, 26 or proton transfers. 27 The high-electron affinity of Be also allows the formation of Be-based anion sponges 28 as close relatives of the well-known proton sponges. 29 The electron-deficiency of Be and its electronegativity also help stabilize molecules containing planar hypercoordinate atoms [30][31][32][33] and noble gas compounds, and even with suitable ligands, it is possible to stabilize viable systems that feature a neutral Be 2 moiety with a single Be Be covalent bond. 34 During these last four decades, many exciting and unusual characteristics of beryllium derivatives, such as the stability and bonding of CBe 2 , C 2 Be, C 2 Be 2 , NNBeO, OCBeO, and COBeO compounds, the role of Be in a variety of donor-acceptor complexes, the bonding peculiarities in Be 2 F 2 , Be 2 B 8 and Be 2 B 7 À systems with unusually short Be Be distances or the existence of beryllium dinitrogen complexes have been reported in the literature by Frenking and coworkers. [35][36][37][38][39][40][41][42][43][44][45][46] In the first decade of this century, it became clear how the electron-deficient nature of Be is responsible for the formation of so-called beryllium bonds, relatively strong non-covalent interactions that would take place in the gas phase. 47 These bonds were found to modulate the strength of other non-covalent interactions, such as hydrogen bonds, 48 halogen bonds, 49 and other weak intermolecular interactions. 50 It was also found that beryllium bonds can spontaneously produce radicals, 51 or very strong one-electron three-center bonds. 52 Many other characteristics can be found in a recent compilation on this bond. 53 Some attention has also been paid to Be clusters, where already the simplest, Be 2 , was the subject of a long-standing controversy as to its stability since early CI calculations predicted its ground state of being repulsive, 54 whereas more recent studies indicate that the bonding in Be 2 is essentially due to non-dynamical correlation effects. 55 A more detailed discussion of this and other larger Be n (n = 2-12) clusters can also be found in Reference [50]. One of the signatures of beryllium bonds is the significant distortion they produce in the electron densities of interacting systems, leading to changes in the reactivity and strength of other interactions (vide supra). However, so far, the reactivity of Be n clusters has not been explored in detail, except for a recent theoretical study by some of us on the interaction of ammonia with the Be tetramer. 56 In that paper, we have found that such interaction leads to spontaneous bond dissociation cascades of the Lewis base, 56 so this left us wondering whether this is a general feature of beryllium clusters or a peculiarity of the tetramer. Hence, in the present paper, we will attempt to answer this question by investigating the behavior if the cluster size increases systematically from the isolated Be atom to the Be 10 decamer.

| COMPUTATIONAL DETAILS
The systematic exploration of the potential energy surface for clusters with formula Be n NH 3 (n > 10) was carried out through a modified genetic algorithm, as implemented in the GLobal Optimization of MOlecular Systems (GLOMOS). [57][58][59] GLOMOS is written in Python and includes stochastic and evolutive methodologies to carry out the global optimization of atomic and molecular clusters, where the local optimizations are solved through an electronic structure code. The initial screening was done using the TPSS non-empirical meta-generalized gradient approximation, 60 together with a def2-SVP basis set.
The most energetically stable structures found in the screening were reminimized using the TPPSh, which is a hybrid method 61 based on TPSS 60 and which has been proved to provide a high-quality description for the type of systems included in this study. 61 We have also used, for the sake of completeness, the M06-2X functional, 62 which has been shown to give accurate and balanced binding energies for Be clusters when compared with ab initio CCSD(T) calculations. 63 Finally, taking into account that a reliable description of weakly bound systems, such as some of the structures we are dealing with, requires the inclusion of high-order correlation corrections to be accounted for, we have also used a CCSD(T) procedure in our optimizations. In all cases, a def2-TZVP basis set 64 has been used.
Since Be 4 clusters have been found to exhibit an RHF-UHF instability, 56 we have also checked whether the other systems under investigation present any instability in the wavefunction. The result of this survey is that the most stable complexes between Be n (n = 1-10) and ammonia do not have any kind of wavefunction instability, and only for the Be 8 cluster an RHF-UHF instability was detected.
As we will discuss in the forthcoming sections, the interaction of

| RESULTS AND DISCUSSION
The optimized CCSD(T)/def2-TZVP geometries of the most stable structure of the complexes formed by the interaction of ammonia with Be n (n = 1-10) clusters are shown in Figure 1, while the geometries of the isolated Be n (n = 2-10) clusters are given in Figure S1 of the Supporting information.
The corresponding binding energies defined by the reaction (1), where Be n /NH 3 corresponds to the structure shown in Figure 1 and Be n to the most stable isolated Be n cluster (see Figure S1 of the Supporting Information), are given in Table 1.
It can be seen that both DFT approaches slightly overestimate the CCSD(T) binding energies, although the best agreement is obtained when the TPSSh functional is used. The advantage is that the DFT computations do not present any instability of the wavefunction. It should also be noticed that, regardless of the method, the dissociation energy goes through two maxima, one for n = 3 and one for n = 7 (see Figure 2).
To understand this behavior, it is worth noting that the association of the different Be clusters to ammonia is accompanied by a migration of its hydrogen atoms onto the Be atoms of the cluster.
Accordingly, when the interaction involves a single Be atom, only one of these migrations occurs, whereas for Be n clusters in which n ≥3, vs. 225.9 kJ mol À1 ) shown in Figure 3. Again consistently, for the  F I G U R E 3 Diabatic dissociation energies (kJ mol À1 ) calculated at the CCSD(T)/def2-TZVP level between Be and ammonia should yield a Be NH 3 complex, this structure evolves into the HBeNH 2 global minimum, which has much stronger bonds.
The results obtained using both the NBO and the ELF approaches for the HBeNH 2 complex are fully consistent with the aforementioned energetics. The NBO identifies four polar covalent bonds, two corresponding to the two N H bonds and two more centered at the Be atom. One of these is an N Be covalent bond, connecting the NH 2 and the BeH groups (94% sp hybrid from the NH 2 moiety and 6% sp hybrid from the BeH moiety), whereas the other is the Be H bond of the latter (82% s orbital from the H atom and 18% sp hybrid from the Be atom). The ELF analysis shows (see Figure 4) the presence of a disynaptic Be H basin with a population of 2.01 e, and two N Be basins, with a population of 2.05 e each, corresponding to an H 2 N Be covalent bond and the interaction of the N lone-pair of the amino group with the empty orbitals of Be, consistent with the high strength of the Be N bond. Therefore, although the initial step of the interaction between Be and ammonia should yield a Be NH 3 complex, this structure evolves into the HBeNH 2 global minimum, which has much stronger bonds.
The same arguments apply to the cases where ammonia interacts with Be 2 and Be 3 clusters. In the HN(BeH) 2 system the planar central N atom forms tree σ bonds, two with the two Be H groups and a third one with the H atom. These bonds, according to the NBO method, are described by the 0.973 N(sp 2 ) + 0.232 Be(sp) and 0.836 N(sp 2 ) + 0.548 H(1s) and 0.973 N(sp 2 ) + 0.232 Be(sp) linear combinations of hybrid atomic orbitals, respectively, confirming that the N Be bonds are very polar. Concomitantly, a 3c-2e π-bond is also formed by the delocalization of the N lone pair into the empty p(π) orbitals of the two Be atoms. When the interaction involves Be 3 , three N Be bonds, rather than two, are formed and the nitrogen lone-pair is again delocalized into the empty p(π) orbitals of three Be atoms, leading to a 4c-2e π-bond. This bonding features are consistent with the ELF analysis (Figure 4). For the HN(BeH) 2 system the dysinaptic N Be basins, due to the symmetry around the N H bond, form a torus because of the contribution of the 3c-2e π-bond, with a total population of 5.96 e, four electrons coming from the N Be σ-bonds and another two from the 3c-2e π-bond. For the N(BeH) 3 cluster, the three N Be σ-bonds combined with the 4c-2e π-bond lead to the three tori (dysinaptic N Be basins), around each N Be bond with a total population very near to eight electrons. Coherently, if one compares the molecular graphs of these three complexes (see The situation changes when we go to the system in which ammonia interacts with a Be tetramer. As is illustrated in both Figures 1 and   5, the additional Be does not attach directly to the nitrogen, which is already tricoordinated, with a bonding scheme similar to the N(BeH) 3 F I G U R E 4 ELF functions, with an isovalue of 0.83, calculated for the HBe NH 2 , HN(BeH) 2 and N(BeH) 3 structures. The population of each basin is indicated in electrons. Core basins are shown in blue, disynaptic in green and X H (X = Be, N) basins in yellow F I G U R E 5 Molecular graphs of the most stable Be n /NH 3 (n = 1-4) complexes. The electron densities at the BCPs (green dots) are in a.u. For n = 4 we show the presence of NNAs and the value of the electron density at these points Y complex, that is, three N Be σ-bonds combined with a 4c-2e π-bond, but it inserts into one of the Be H bonds. The consequence is that while the dissociation energy of a Be N bond is around 500 kJ mol À1 (see Figure 3) (only 2.9 kJ mol À1 higher that the G3 value reported by M o et al. 73 in 2005), the diabatic dissociation energy of the new Be Be bond in the Be 4 /NH 3 complex is only 314 kJ mol À1 . This is again consistent with the ELF of this (HBe) 2 N-BeBeH cluster (see Figure S2 of the Supporting Information) which shows that the disynaptic Be Be basin population is 25% smaller than that of the N Be ones. It is also noteworthy that in this latter case, which is the first to show a Be Be bond, the molecular graph features two non-nuclear attractors (NNA) associated with the Be Be bond. Recently Haiduke et al. 74 have investigated the characteristics of NNAs for a large set of diatomic molecules as a function of the internuclear distance, as Martín-Pendás et al. 75,76 have shown, in two seminal papers, that NNA points appear in this type of interactions when the internuclear distances decrease. This is indeed the situation here, where, as shown in Figure S3 of the Supporting Information, when going from the beryllium dimer with an internuclear distance of 2.787 Å, which has no NNAs, to the Be 4 /NH 3 complex, where the Be Be internuclear distance decreases to 2.098 Å, the NNAs appear. This feature will also emerge in the larger Be n /NH 3 (n = 6-10) clusters, as all of them show Be Be interactions. In fact, they are also already present in these Be clusters before the interaction with ammonia, as illustrated in the beautiful image of Figure 6 for Be 10 .
The tricoordination of the N atom remains in the most stable form of the Be 5 /NH 3 complex, where again the additional Be atom inserts into the other Be H bond, resulting in the two hydrogen atoms bridging both Be atoms, and as in the two previous cases (three and four Be atoms), the nitrogen lone pair is engaged in a 4c-2e π-bond. However, differently to what was found in Be 4 /NH 3 cluster, in the Be 5 /NH 3 system the N Be Be arrangements are not linear to favor the interaction of the terminal Be H groups, so that each H atom interacts with both Be atoms and a HÁ Á ÁH dihydrogen bond is also formed. Consequently, the new Be Be bonds formed in this case, with an electron density of 0.058 a.u. at the BCP, are weaker than the one formed in the Be 4 /NH 3 complex, where the electron density at the Be Be BCP is 0.066 a.u. This explains why Be 5 /NH 3 has slightly lower binding energy than Be 4 /NH 3 (see Table 1).
Since for some of the larger clusters, the CCSD(T), as mentioned above, has RHF/UHF instabilities that do not allow us to obtain reliable energies for these cases, for the discussion, we will use instead the binding energies calculated by TPSSh. The situation described above for the Be 5 /NH 3 global minimum changes again when switching to Be 6 /NH 3 . The corresponding molecular graph (see When the NBO approach is used we obtain similar conclusions in the sense that two of the four N Be bonds (WBI = 0.187, 0.180) are stronger than the strongest ones in Be 6 /NH 3 (see above) and in Be 8 /NH 3 (WBI = 0.178, 0.169), and the other two (WBI = 0.159, 0.142) are also stronger than the weakest one in Be 6 /NH 3 and in Be 8 /NH 3 (WBI = 0.155), so it not surprising that the binding energy for Be 7 /NH 3 global minimum is 5 and 43 kJ mol À1 higher, respectively, than those of Be 6 /NH 3 and Be 8 /NH 3 . As a matter of fact, as shown in Figure S4 of the Supporting Information, there is a relatively good linear correlation between the changes in the binding energy of Be n /NH 3 global minima and the changes in the relative stability their NBe 4 moiety for n = 6-10.
Finally, there are two potential solutions in AdNDP. One is where the orbitals around the N are classified as lone pairs and the other where overlap with the Be orbitals gives rise to orbitals located along the bonds involving the N atom. The best solution, in principle, is the one with the lowest number of residual electrons, that is, the second one, so we will focus on it. However, the results indicate the high F I G U R E 6 Molecular graph of the Be 10 cluster, showing the presence of NNAs associated with the different Be Be bonds in the cluster. Red and green dots correspond to ring critical points and BCPs, respectively polarity of the N Be bonds. The electron pair distribution provided by AdNDP is as follows (see Figure S5 of the Supporting Information): Up to the Be 5 /NH 3 complex, AdNDP shows one electron pair located on the nitrogen atom and the rest are involved in 2c-2e N H or Be N σ-bonds. From Be 6 /NH 3 to Be 10 /NH 3 (see Figure S6 of the Supporting Information), the nitrogen atom is tetracoordinate, and there is one electron pair per N Be bond. Be 6 /NH 3 is the only system where a 2c-2e Be H σ-bond is present. The 3c-2e Be H Be bonds are located from the system with five Be atoms. The remaining electrons are found in 3c-2e bonds among Be atoms. The only system showing a 3c-2e Be N Be bond is Be 10 /NH 3 .

| CONCLUDING REMARKS
The main conclusion of this study is that when ammonia interacts with Be n (n = 1-10), a spontaneous hydrogen shift from the N to the available Be atoms strongly stabilizes the complex. This migration dramatically enhances the strength of the Be N bond, with the result that maximum stability is found for the interaction with the beryllium trimer, where besides the three σ N Be bonds an additional 3c-2e π-bond is formed. For n = 4 and 5, the nitrogen is still tricoordinated, keeping the additional 3c-2e π-bond, whereas the additional beryllium atoms insert into the available Be H bonds forming a Be Be bonds, which are weaker than the Be N bonds. Consequently, the stabilization of these complexes decreases with respect to the case where n = 3. A new change is noted when the number of Be atoms increase further, and for n = 6-10, a NBe 4 group with four σ N Be bonds, is systematically formed. The stability of this group reaches a maximum at n = 7, and the same trend occurs for the binding energies. In summary, regardless of the size of Be n (n = 1-10), neither the structure of these clusters nor that of ammonia are preserved when they interact. For clusters with n ≤5, the N atom is coordinated with a maximum of three Be atoms, favoring the formation of a 3c-2e π-bond (n = 2) or 4c-2e π-bond (n = 3-5), the most stable complex being the one with n = 3. For n ≥6, all the complexes are less stable than the system with n = 3, and the N atom is linked to four Be atoms, the n = 7 complex being the most stable of this second series of complexes.
F I G U R E 7 Molecular graphs of the most stable Be n /NH 3 (n = 5-10) complexes. The electron densities at the BCPs are in a.u. Red and green dots correspond to ring critical points and BCPs, respectively F I G U R E 8 ELF function, with an isovalue of 0.80, calculated for the Be 7 /NH 3 most stable cluster. The population of each basin is indicated in electrons. Core basins are shown in blue, disynaptic in green and X H (X = Be, N) basins in yellow