Ab initio study on the stability of Ng(n)Be₂N₂, Ng(n)Be₃N₂ and NgBeSiN₂ clusters

DOI: 10.1002/cphc.201402101

Ab Initio Study on the Stability of NgnBe2N2, NgnBe3N2 andNgBeSiN2 Clusters**Sudip Pan,[a] Diego Moreno,[b] Jos� Luis Cabellos,[b] Gabriel Merino,*[b] andPratim K. Chattaraj*[a]

1. Introduction

The enthusiasm to enrich a less developed field always acts asa driving force for scientists. Noble gas (Ng) chemistry is onesuch field.[1] The low reactivity of an Ng with other elementsmakes discovering new Ng compounds a challenge. To devel-op this field, theoreticians try to build proper theory to under-stand the reactivity and bonding pattern and use this to pre-dict new stable Ng compounds, whereas experimentalistsdevote their efforts to synthesize Ng compounds dependingon the knowledge provided by these theories. In 1933, basedon the fundamental understanding of chemical bonding, Paul-ing[2] predicted the chemical binding ability of elements at thebottom of Group 18. Chemical bonding is a phenomenon ofelectron donation or sharing, therefore the unreactivity shoulddiminish gradually on descending Group 18 from He to Rn,due to the steady increase and decrease of polarizability andionization energy, respectively. The first molecule classified asan Ng compound, was xenon hexafluoroplatinate, Xe+[PtF6]� ,synthesized by Bartlett in 1962.[3] His experiments directly chal-lenged the long-held belief that Ng atoms were truly inert andsoon after the field of Ng chemistry was born. Following Bar-tlett’s synthesis, various research groups achieved success in

synthesizing a number of compounds containing heaviermembers of Group 18.[4] The successful syntheses of com-pounds of type HNgY (Y = electron-withdrawing group) andNg hydrides by R�s�nen et al.[5] and Feldman et al.[6] are alsoconsidered as significant contributions in this field. Theoreticalstudies on several Ng compounds by various groups must alsobe acknowledged.[7–11] The computational study on the stabilityof NgBeO molecules (Ng = He–Xe) by Frenking’s group[7a, d]

shed light on the Ng-binding ability of a positively charged Becenter ; such compounds were later synthesized by Andrews’group.[12] The dominant contributors to the attraction betweenan electropositive center and Ng atoms are polarization andcharge transfer.[13] In general, with an increase in the positivecharge, the Ng-binding ability improves although this variationis not a directly proportional relationship. Therefore, if wewant to search for Be-containing clusters that bind Ng atoms,we have to look towards clusters in which Be is linked withelectronegative atoms and hence acquires a high positivecharge. To build an effective interaction with Ng atoms, thepositive charge at the Be center should be large enough topull the electron clouds of Ng atoms despite their low polariza-bilities and high ionization potentials. Based on this simple un-derstanding about the Be–Ng interaction, Grandinetti et al.[14]

have shown the Ng-binding ability of a series of Be clusters inwhich Be is bonded to electronegative atoms and/or which arecationic clusters.

We have recently studied the stability of (NgBeY)0/1 + (Y = O,S, Se, Te) clusters, in which the dissociation energy of the Be�Ng bond is found to be higher in monocationic clusters thanthe corresponding neutral analogues.[15] We have also shownthat BeCN2 and BeNBO have better Ng-binding ability than thewell-known BeO, BeS, BeNH systems.[13] Prompted by thisknowledge, here we have looked for viable Be-containing clus-ters, in which the Be centers have large positive charge due tobonding with electronegative atoms.

The global minima of Be2N2, Be3N2 and BeSiN2 clusters areidentified using a modified stochastic kick methodology. Thestructure, stability and bonding nature of these clusters boundto noble gas (Ng) atoms are studied at the MP2/def2-QZVPPDlevel of theory. Positive Be�Ng bond dissociation energy,which gradually increases down Group 18 from He to Rn, indi-cates the bound nature of Ng atoms. All of the Ng-binding

processes are exothermic in nature. The Xe and Rn binding toBe2N2 and Be3N2 clusters and Ar�Rn binding to BeSiN2 are exer-gonic processes at room temperature; however, for the lighterNg atoms, lower temperatures are needed. Natural populationanalysis, Wiberg bond index computations, electron densityanalysis, and energy decomposition analysis are performed tobetter understand the nature of Be�Ng bonds.

[a] S. Pan, Prof. P. K. ChattarajDepartment of Chemistry and Centre for Theoretical StudiesIndian Institute of Technology Kharagpur 721302 (India)E-mail : [email protected]

[b] D. Moreno, Dr. J. L. Cabellos, Prof. G. MerinoDepartamento de F�sica AplicadaCentro de Investigaci�n y Estudios AvanzadosUnidad M�rida, km 6 Antigua carretera a ProgresoApartado Postal 73, Cordemex97310 M�rida, Yucat�n (M�xico)E-mail : [email protected]

[**] Ng = Noble Gas (He, Ne, Ar, Kr, Xe, Rn)

Supporting Information for this article is available on the WWW underhttp://dx.doi.org/10.1002/cphc.201402101.

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Be3N2 and BeSiN2 are well-known experimentally availablecompounds in their different polymorphic forms.[16, 17] Severaltheoretical studies have also been carried out exploring char-acteristics such as their semiconductor properties.[18, 19] The de-tection of Be2N2 was first reported in 1917 by Vournasos.[16a]

Thompson and Andrews further identified Be2N2 from IR spec-tra.[20] In addition, several derivatives of Be2N2, namelyBa[Be2N2][21] and E[Be2N2] (E = Mg, Ca, Sr, Ba),[22] have also beenprepared. The aromaticity in the planar conformer of Be2N2

was also a matter of interest to theoreticians.[23] In our study,we performed the search of global minimum-energy structuresfor Be2N2, Be3N2 and BeSiN2 clusters and owing to the highelectropositive nature of Be, their Ng-binding ability was stud-ied. The nature of Be�Ng bonds was also explored. It shouldbe noted that although previous studies considered a planarstructure of Be2N2 clusters,[23] our global minimum search re-vealed that the planar isomer is a local minimum and not theglobal one.

Computational Details

A modified stochastic kick methodology called Bilatu[24] was usedfor searching the global minimum-energy structures by consider-ing both singlet- and triplet-spin states of Be2N2, Be3N2 and BeSiN2

clusters. The working principle of this methodology s described indetail elsewhere.[13] In this study, the initial search for the globalminima of Be2N2, Be3N2, and BeSiN2 was performed at the PBE0/LanL2DZ level and optimized further at the MP2/def2-QZVPPDlevel. All of the Ng-bound analogues were also studied at theMP2/def2-QZVPPD level. We also carried out computations at theCCSD(T)/def2-QZVPPD//MP2/def2-QZVPPD level to compute Be–Ngdissociation values. For the core electrons of Xe and Rn atoms,a quasi-relativistic pseudopotential was used.[25] Natural populationanalysis (NPA) and calculation of Wiberg bond index (WBI)[26] werecarried out to assess the atomic charge q at each center and toevaluate the bond order, respectively. We carried out all the MP2and CCSD(T) computations using the Gaussian 09 package.[27] Theenergy decomposition analysis (EDA) was performed at theCCSD(T)/def2-TZVP level of theory by using the method proposedby Su and Li[28] , as implemented in Gamess.[29]

Multiwfn software[30] was used for detailed electron density analy-sis.[31] Generally, a negative value of the Laplacian of electron densi-ty gN> 21(rc) at the bond critical point (BCP) can be interpreted asa covalent interaction, whereas positive value as a noncovalent in-teraction. The failure of this criterion to characterize typical cova-lent molecules has also been reported.[31, 32] Several other parame-ters, such as local kinetic energy density G(rc), local potentialenergy density V(rc), local electron energy density H(rc), and ratios�G(rc)/V(rc) and G(rc)/1 (rc), were introduced to describe the natureof bonding. It has been reported in the literature that a bond canbe considered to have partial covalent character if gN> 21(rc)>0and H(rc)<0.[33] H(rc) can be calculated as the sum of G(rc) and V(rc).If �G(rc)/V(rc)>1, then the bond is of a noncovalent type and if itis within the range 0.5–1.0, then that bond may be called partiallycovalent.[34] Note that the criteria H(rc)<0 and �G(rc)/V(rc)<1 fora partial covalent bond are the same. Furthermore, G(rc)/1(rc)<1 in-dicates a covalent bond.[32]

2. Results and Discussion

2.1. NgnBe2N2 and NgnBe3N2 Clusters

The six most-stable isomers of Be2N2 and Be3N2 are displayedin Figure 1. The global minimum of Be2N2 at the studied levelis found to be a singlet nonplanar C2v structure rather than theplanar D2h structure considered in previous studies[23] to assessits aromaticity. In fact, Nigam et al.[23a] claimed that Be2N2

favors a planar configuration as the lowest-energy structure,but this is not the case. The C2v form is 6.6 kcal mol�1 morestable than the corresponding D2h analogue. The second-lowest energy isomer is a triplet with a planar C2v structure,which is only 1.0 kcal mol�1 less stable than that of the globalminimum. In the case of Be3N2, the most-stable isomer is a sin-glet D3h structure, in which two N atoms reside above andbelow the triangular Be3 ring (Figure 1). It is only 1.8 kcal mol�1

more stable than its nearest-energy triplet C2v isomer. Notethat such a small energy difference between the lowest- andthe second-lowest-energy structures in the cases of Be2N2 andBe3N2 indicates that in an experimental situation, the finalproducts might consist of both isomers in different propor-tions. Here we have only considered the lowest-energy isomersas the second-lowest energy isomers would not be good can-didates to bind Ng atoms.[35] NPA reveals that each Be and Ncenter in a Be2N2 cluster possess + 1.19 e� and �1.19 e� , re-spectively, whereas those in a Be3N2 cluster have + 1.14 e� and�1.71 e� , respectively. Therefore, each center might be expect-ed to bind Ng atoms as the positive charges at Be centers aresomewhat large.

The structures of NgnBe2N2 and NgnBe3N2 clusters are depict-ed in Figure 2. The NgBe2N2 clusters adopt Cs point groups,whereas Ng2Be2N2 clusters have C2v point groups.[36] The corre-sponding detailed results for NgnBe2N2 and NgnBe3N2 clustersare provided in Tables 1 and 2, respectively. The zero-pointenergy (ZPE)-corrected dissociation energy values (D0) for Be�Ng bonds are small for He and Ne compounds, however itgradually increases from Ar to Rn. For a particular Ng binding,the corresponding D0 values slowly decrease with each succes-sive binding. In fact, for the third He atom binding ontoa Be3N2 cluster, the D0 value reaches zero. The dissociationenergy values at the CCSD(T)/def2-QZVPPD/MP2/def2-QZVPPDlevel (DCCSD(T)) are also provided in Tables 1 and 2.

The reaction enthalpy (DH) values for all Ng-binding pro-cesses by Be2N2 and Be3N2 clusters are negative (Tables 1 and2). From He to Rn, the processes gradually become more exo-thermic. The second Ng-binding events are slightly less exo-thermic than the first in NgnBe2N2 (except binding of He). ForNgnBe3N2, the corresponding DH value also decreases with theincreased number of Ng atoms. The free-energy change (DG)for all Xe and Rn and the first Kr-binding processes are exer-gonic in nature at 298 K. However, the other Ng-bindingevents are not spontaneous at room temperature. Therefore,for those processes, lower temperature is needed to make theunfavorable TDS term less important. Initially, we calculatedDG values for all these processes at the temperature of liquidN2 (77 K) and, for those processes not spontaneous at that

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Figure 1. Optimized structures of six low-lying isomers of Be2N2 and Be3N2 clusters studied at the MP2/def2-QZVPPD level. The ZPE-corrected relative energiesin kcal mol�1 are also given.

Figure 2. Optimized structures of NgnBe2N2 and NgnBe3N2 clusters studied at the MP2/def2-QZVPPD level.

Table 1. The dissociation energy De [kcal mol�1] , ZPE-corrected dissociation energy D0 [kcal mol�1] of Be�Ng bonds for the dissociation process NgnBe2N2!Ng + Ngn-1Be2N2, reaction enthalpy DH [kcal mol�1] and free-energy change DG [kcal mol�1] for the process Ng + Ngn-1Be2N2!NgnBe2N2 at 298 K, HOMO–LUMO gap (Gap [eV]), NPA charges at Be and Ng centers q [a.u.] , WBIs of Be�Ng bonds, Be�Ng bond distances rBe�Ng, [�] and the lowest frequency nmin

[cm�1] of the studied clusters at the MP2/def2-QZVPPD level.

Cluster PG De D0 DCCSD(T)[a] DH DG Gap q (Ng) q (Be) WBI rBe�Ng nmin

Be2N2 C2v 9.17 1.19 406HeBe2N2 Cs 1.2 0.4 0.8 �0.7 5.2 9.23 0.09 1.08 0.16 1.718 119He2Be2N2 C2v 1.1 0.3 0.6 �0.7 6.1 10.17 0.09 1.09 0.16 1.715 83NeBe2N2 Cs 1.9 1.4 1.6 �1.5 4.3 9.21 0.06 1.13 0.12 1.963 94Ne2Be2N2 C2v 1.8 1.3 1.4 �1.4 5.2 9.58 0.06 1.13 0.12 1.976 38ArBe2N2 Cs 6.0 5.5 5.2 �5.7 0.5 9.09 0.18 0.99 0.32 2.192 104Ar2Be2N2 C2v 5.4 5.0 4.5 �5.1 1.8 9.02 0.17 1.00 0.30 2.209 33KrBe2N2 Cs 7.7 7.2 6.6 �7.3 �1.2 9.07 0.22 0.94 0.38 2.323 101Kr2Be2N2 C2v 6.9 6.5 5.8 �6.6 0.3 8.90 0.21 0.96 0.36 2.337 25XeBe2N2 Cs 9.7 9.2 8.3 �9.4 �3.3 9.02 0.26 0.89 0.45 2.485 99Xe2Be2N2 C2v 8.7 8.4 7.3 �8.4 �1.7 8.61 0.25 0.91 0.43 2.499 21RnBe2N2 Cs 11.0 10.5 9.6 �10.7 �4.7 8.96 0.27 0.88 0.47 2.550 101Rn2Be2N2 C2v 10.0 9.7 8.5 �9.7 �3.0 8.38 0.26 0.90 0.44 2.564 17

[a] DCCSD(T) is the dissociation energy [kcal mol�1] at the CCSD(T)/def2-QZVPPD//MP2/def2-QZVPPD level.

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temperature, DG values were calculated at 4 K. The corre-sponding values (Table S1 in the Supporting Information) showthat all Ar- and Kr-binding processes by Be2N2 and Be3N2 clus-ters become exergonic at 77 K and for the other systems,much lower temperatures are needed. Note that low dissocia-tion energy values and the spontaneity of Ng-binding process-es at low temperature (4 K) for He and Ne compounds implythat they are unlikely to be synthesized, although other sys-tems might be viable, particularly in cold matrices.

The HOMO–LUMO gap values of Be2N2 (9.17 eV) and Be3N2

(8.11 eV) clusters are somewhat high, indicating the stability ofthese compounds. Note that, similar to their parent moieties,all the Ng-bound analogues have high HOMO–LUMO gapvalues. In NgnBe2N2 clusters, the HOMO–LUMO gap slightly in-creases for Ng = He and Ne but for the larger Ng analogues itdecreases to some extent with respect to that of the Be2N2

cluster ; however, in cases of NgnBe3N2 clusters, with the excep-tion of Rn3Be3N2, this value is larger than that of Be3N2 cluster.

2.2. NgBeSiN2 Clusters

The global minimum of the BeSiN2 cluster is found to be a trip-let having linear structure (C1v), which is 4.6 kcal mol�1 morestable than the second-lowest energy singlet Cs isomer (seeFigure 3). In the global minimum, the Be center is located inbetween two N atoms in a linear configuration, hence there isno available binding site for Ng atoms. However, the secondisomer is more likely to bind Ng atoms because the Be centerpossesses a positive charge of + 1.28 e� and is available forfurther coordination by Ng atoms. The Cs isomer of BeSiN2 haseven better Ng-binding ability than the Be2N2 and Be3N2 clus-ters (Table S2). The corresponding dissociation energy values

Table 2. The dissociation energy De [kcal mol�1] , ZPE-corrected dissociation energy D0 [kcal mol�1] of Be�Ng bonds for the dissociation process NgnBe3N2!Ng + Ngn-1Be3N2, reaction enthalpy DH [kcal mol�1] and free energy change DG [kcal mol�1] for the process Ng + Ngn-1Be3N2!NgnBe3N2 at 298 K, HOMO–LUMO gap (Gap [eV]), NPA charges at Be and Ng centers q [a.u.] , WBIs of Be�Ng bonds, Be�Ng bond distances rBe�Ng, [�] and the lowest frequency nmin

[cm�1] of the studied clusters at the MP2/def2-QZVPPD level.

Cluster PG De D0 DCCSD(T)[a] DH DG Gap q (Ng) q (Be) WBI rBe�Ng nmin

Be3N2 D3h 8.11 1.14 528HeBe3N2 C2v 1.1 0.1 1.2 �0.5 5.4 8.34 0.10 1.00 0.18 1.705 136He2Be3N2 C2v 0.9 0.1 1.0 �0.4 6.0 8.65 0.10 1.00 0.18 1.722 99He3Be3N2 D3h 0.8 0.0 0.9 �0.3 6.7 9.42 0.09 1.01 0.17 1.740 98NeBe3N2 C2v 1.7 1.1 1.8 �1.3 4.4 8.27 0.07 1.06 0.13 1.979 96Ne2Be3N2 C2v 1.5 1.0 1.7 �1.1 5.1 8.48 0.07 1.06 0.13 1.998 41Ne3Be3N2 D3h 1.4 0.9 1.5 �1.0 5.7 8.82 0.07 1.06 0.12 2.020 39ArBe3N2 C2v 6.1 5.4 5.8 �5.7 0.4 8.26 0.20 0.90 0.35 2.187 109Ar2Be3N2 C2v 5.4 4.8 5.0 �4.9 1.7 8.43 0.19 0.91 0.33 2.208 36Ar3Be3N2 D3h 4.7 4.2 4.4 �4.2 2.9 8.52 0.18 0.91 0.32 2.231 33KrBe3N2 C2v 7.9 7.3 7.3 �7.5 �1.4 8.26 0.24 0.85 0.42 2.312 102Kr2Be3N2 C2v 7.0 6.5 6.4 �6.5 0.0 8.41 0.23 0.86 0.40 2.333 27Kr3Be3N2 D3h 6.2 5.7 5.6 �5.7 1.0 8.41 0.22 0.87 0.38 2.356 23XeBe3N2 C2v 10.2 9.6 9.3 �9.8 �3.9 8.26 0.30 0.79 0.50 2.469 92Xe2Be3N2 C2v 9.1 8.6 8.1 �8.6 �2.2 8.42 0.28 0.80 0.47 2.489 20Xe3Be3N2 D3h 8.1 7.7 7.2 �7.7 �0.7 8.18 0.27 0.81 0.45 2.510 17RnBe3N2 C2v 11.7 11.1 10.6 �11.3 �5.4 8.22 0.31 0.78 0.51 2.534 85Rn2Be3N2 C2v 10.5 10.0 9.4 �10.1 �3.7 8.28 0.29 0.80 0.49 2.552 15Rn3Be3N2 D3h 9.5 9.1 8.5 �9.1 �2.1 7.95 0.28 0.81 0.46 2.572 13

[a] DCCSD(T) is the dissociation energy [kcal mol�1] at the CCSD(T)/def2-QZVPPD//MP2/def2-QZVPPD level.

Figure 3. Optimized geometries of six low-lying isomers of a BeSiN2 cluster studied at the MP2/def2-QZVPPD level. The ZPE-corrected relative energies in kcalmol�1 are also given.

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of NgBeSiN2 clusters are largerthan those of NgBe2N2 andNgBe3N2 clusters. All the Ng-binding processes are exother-mic in nature; however only Ar–Rn-binding processes are spon-taneous at the studied tempera-ture (298 K). The He- and Ne-binding events can be exergonicat low temperature (Table S1).However, due to its higher-energy structure, BeSiN2 is lesslikely to exist in the singlet Cs

form. We have also studied theinteraction of Ng atoms with thelinear global-minimum energystructure of BeSiN2 (Table S3).Low Be�Ng bond dissociationenergies are found in thesecases. We would like to highlightthat in the presence of anNg atom, the energy differencebetween the lowest-energy andthe second-lowest-energy iso-mers gradually decreases fromHe to Ne and for Ar–Rn the cor-responding Ng-bound Cs isomersbecome more stable than theNg-bound C1v isomers (Figure 4).Therefore, the presence of Ng a-toms can stabilize less stableforms of clusters.

2.3. NPA Charges and WBIs

NPA reveals that some degree ofelectron transfer takes placefrom Ng atoms to positively charged Be centers. The extent ofshifting of electron density from Ng to the Be center is low forlighter Ng atoms. However, it is considerably large for heavierNg atoms, especially Xe and Rn (�0.3 e�). It follows the orderRn>Xe>Kr>Ar>He>Ne (see Tables 1, 2 and S2). Note thatthe electron shift from Ne is smaller than that from He, al-though based on the polarizability and ionization energyvalues, the reverse is expected. Such off-trend behavior of Neis not new in the literature. To resolve this anomaly, Bent,[37]

Scerri,[38] Grochala[10b] and recently Grandinetti[39] argued infavor of moving He to the top of Group 2 in the periodic table.Grandinetti explained the lower reactivity of Ne compared toHe: “Neon is bigger than helium, and possesses occupied p or-bitals. This is thought to produce less effective electrostatic in-teractions and higher orbital repulsions, which typically makethe neon compounds either unstable or only marginally stable,although the contributions of these factors are still to be fur-ther investigated”.[39] In our EDA (see below), in all cases theelectrostatic contribution for Ne is higher than that of He. Infact, the lower reactivity of Ne compared to He is a matter of

debate. Furthermore, the Be–Ne dissociation values are alwayshigher than those of Be�He bonds, although in our previousstudy,[13] in a few instances the Be�Ne bonds had higher disso-ciation energies than that of He, whereas in others the reversewas true. Therefore, this topic is open for further discussion.

In this study, the WBI calculation corresponding to Be�Ngbonds gives a small value for lighter Ng atoms, and a consider-ably larger value for heavier analogues. WBIs of Be�Ng bondsfollow the order Rn>Xe>Kr>Ar>He>Ne (see Tables 1–3).These values further indicate that almost a half bond is formedin between Be and Ng atoms for Ng = Xe and Rn. A low WBIprovides a hint to the existence of dominant van der Waalstype of interaction (this is the case for lighter Ng atoms), how-ever, a large value reveals that some degree of covalent char-acter exists between them (for heavier analogues).

2.4. Electron Density Analysis

The different topological parameters computed at the BCPs ofBe�Ng bonds from the electron density analysis[31] are present-

Figure 4. Optimized structures of NgBeSiN2 clusters studied at the MP2/def2-QZVPPD level. The ZPE-corrected rel-ative energies in kcal mol�1 are also given.

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ed in Table S4. Caution should be exercised with this analy-sis.[40] Recently, Boggs et al.[41] reported electron density analy-sis of a series of Ng-loaded clusters to characterize the natureof the interaction. They also considered NgBeO in their study.Based on the outputs of different topological descriptors andthe Ng�Be bond distances being between those of covalentand van der Waals distances, they have introduced two newtypes of bonding, Wn (weak interaction having noncovalentcharacter) and Wc (weak interaction having some degree of co-valent character). In our study, the Ng-binding center is also Be(similar to NgBeO) and the Ng�Be distances are less than thevan der Waals distances but larger than the corresponding co-valent distances. Typical Ng�Be covalent and van der Waalsdistances can be found in ref. [41] . We have adopted thesetypes to assign the nature of interaction. Table S4 shows thatin our study, r21(rc)>0 and G(rc)/1(rc)>1; however H(rc) is onlynegative for Xe and Rn (and consequently �G(rc)/V(rc)<1 forthese cases). Therefore, Be�Xe and Be�Rn bonds can be con-sidered to be of type Wc and the remaining Be�Ng (Ng = He–Kr) bonds of type Wn.

2.5. Energy Decomposition Analysis

The results of the EDA of these Ng–Be clusters carried out atthe CCSD(T)/def2-TZVP level, taking Ng as one fragment andthe Be cluster as another, are provided in Table 3. The total in-teraction energy (DEtotal) is divided into the electrostatic (DEele),exchange (DEex), repulsive (DErep), polarization and chargetransfer (DEpol + ct), and dispersion (DEdisp) energy terms.

Positive and negative values of DE imply that the interactionterms between two fragments are repulsive and attractive innature, respectively. Here, DEtotal represents the energy differ-ence between the “supermolecule” and the monomers havingthe geometries of those in the supermolecule. Of all the attrac-

tive terms, for NgBe2N2 and NgBe3N2 clusters, DEex contributesthe most (�42–48 %) towards the total attraction energywhereas the DEpol + ct term is the second leading contributor(�28–36 %). With the exception of HeBeSiN2 and NeBeSiN2,DEpol + ct (�44–46 %) and DEex (�37–38 %) are found to be thelargest and the second-largest contributions, respectively, instabilizing NgBeSiN2 clusters. It is notable that in our previousstudy, DEpol + ct was more dominant over DEex for NgBeCN2 andNgBeNBO clusters.[13] In such Ng–Be clusters, the relative domi-nance of DEpol+ ct and DEex over each other depends on thepositive charges at the Be centers. One Be center havinga higher positive charge can behave as a better polarizingcenter than that possessing a lower positive charge. The charg-es at Be centers in Be2N2, Be3N2 and BeSiN2 are + 1.19, + 1.14and + 1.28 e� , respectively. Therefore, the Be center in BeSiN2

can polarize the orbitals of Ng atoms to a greater extent thanthose in Be2N2 and Be3N2 clusters. This makes DEpol+ ct a largercontributor than the corresponding DEex term. Owing to thelow polarizability values of He and Ne, we have equal contribu-tions from DEpol + ct and DEex in HeBeSiN2 and slightly smallercontribution from DEpol+ ct than DEex in NeBeSiN2. Note that inBeCN2 (+ 1.39 e�) and BeNBO (+ 1.45 e�), the positive chargeswere also high on the Be centers.[13] The DEele and DEdisp termscontribute towards the total attraction energy, approximately5–17 % and 4–14 %, respectively. Compared to the DEtotal

values it is clear that although the contribution from the DEdisp

term is significantly less, it is not negligible. This further high-lights the necessity of taking a proper dispersion correctioninto account when representing such clusters. From He to Rn,both the repulsive (DErep) and the attractive (DEex, DEpol+ ct andDEdisp) terms increase gradually, with the exception of DEpol + ct

for Ne, which is always smaller than that of He. This is due tothe fact that for Ne donating an electron to the positivelycharged Be center is less likely than He. Note that in all cases,

Table 3. EDA results of the NgBe2N2, NgBe3N2 and NgBeSiN2 clusters studied at the CCSD(T)/def2-TZVP level. All energy terms are expressed in kcal mol�1.[a]

System Fragments DEtotal DEelec DEex DErep DEpol + ct DEdisp

HeBe2N2 He + Be2N2 �0.19 �1.29 (9.5 %) �6.61 (48.5 %) 13.44 �4.89 (35.9 %) �0.84 (6.2 %)NeBe2N2 Ne + Be2N2 �1.02 �2.49 (16.8 %) �6.64 (44.8 %) 13.81 �4.14 (27.9 %) �1.56 (10.5 %)ArBe2N2 Ar + Be2N2 �5.17 �4.26 (12.6 %) �14.20 (41.9 %) 28.70 �11.70 (34.5 %) �3.72 (11.0 %)KrBe2N2 Kr + Be2N2 �6.12 �4.56 (11.7 %) �16.41 (42.3 %) 32.71 �13.80 (35.5 %) �4.07 (10.5 %)XeBe2N2 Xe + Be2N2 �7.57 �3.93 (8.8 %) �19.12 (42.9 %) 36.98 �16.22 (36.4 %) �5.27 (11.8 %)RnBe2N2 Rn + Be2N2 �8.22 �3.86 (8.3 %) �19.91 (42.7 %) 38.37 �16.98 (36.4 %) �5.85 (12.6 %)

HeBe3N2 He + Be3N2 �0.61 �1.23 (9.3 %) �6.37 (48.1 %) 12.64 �4.79 (36.2 %) �0.86 (6.5 %)NeBe3N2 Ne + Be3N2 �1.55 �2.15 (15.4 %) �6.05 (43.4 %) 12.40 �3.85 (27.6 %) �1.90 (13.6 %)ArBe3N2 Ar + Be3N2 �5.93 �3.97 (11.5 %) �14.47 (41.7 %) 28.74 �11.69 (33.7 %) �4.54 (13.1 %)KrBe3N2 Kr + Be3N2 �7.08 �4.24 (10.5 %) �17.11 (42.3 %) 33.36 �13.99 (34.6 %) �5.10 (12.6 %)XeBe3N2 Xe + Be3N2 �8.65 �3.80 (8.1 %) �20.37 (43.2 %) 38.53 �16.55 (35.1 %) �6.47 (13.7 %)RnBe3N2 Rn + Be3N2 �9.35 �3.75 (7.6 %) �21.33 (43.1 %) 40.15 �17.30 (34.9 %) �7.13 (14.4 %)

HeBeSiN2 He + BeSiN2 �1.04 �1.10 (7.8 %) �6.20 (44.0 %) 13.05 �6.20 (44.0 %) �0.59 (4.2 %)NeBeSiN2 Ne + BeSiN2 �1.94 �2.10 (13.8 %) �6.20 (40.7 %) 13.29 �5.56 (36.5 %) �1.37 (9.0 %)ArBeSiN2 Ar + BeSiN2 �7.38 �2.99 (8.9 %) �12.57 (37.4 %) 26.26 �14.68 (43.6 %) �3.41 (10.1 %)KrBeSiN2 Kr + BeSiN2 �8.61 �2.95 (7.7 %) �14.51 (37.8 %) 29.76 �17.20 (44.8 %) �3.73 (9.7 %)XeBeSiN2 Xe + BeSiN2 �10.45 �2.25 (5.1 %) �16.79 (38.2 %) 33.50 �19.97 (45.4 %) �4.93 (11.2 %)RnBeSiN2 Rn + BeSiN2 �11.28 �2.05 (4.5 %) �17.35 (37.9 %) 34.47 �20.84 (45.5 %) �5.52 (12.1 %)

[a] The percentage values within parentheses show the contribution towards the total attractive interaction DEelec +DEex +DEpol + ct +DEdisp.

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the shift of electron density from Ne to Be is smaller than thatfrom He. The DEele term gradually improves from He to Kr butdecreases in the case of Xe and Rn. In general, a large DEpol + ct

term indicates that the orbitals undergo considerable transfor-mation in their shapes, which is akin to a covalent bond. Thehigh values of DEpol + ct, particularly in the case of Xe and Rnimply that there might be some degree of covalent characterin Be�Xe/Rn bonds (also Be–Kr in KrBeSiN2).

3. Conclusions

We have identified the global minimum-energy structures ofexperimentally achievable Be2N2, Be3N2 and BeSiN2 clusters.The lowest-energy isomer of Be2N2 has a singlet nonplanar C2v

structure. Therefore, a different global minimum-energy struc-ture for a Be2N2 cluster was obtained when compared to thatreported in a previous study.[23a] Be3N2 has a singlet D3h geome-try in which two N atoms reside above and below the triangu-lar Be3 ring. In the case of BeSiN2, the global minimum corre-sponds to a triplet linear structure in which the Be center is lo-cated in between two N atoms. Owing to the high positivecharges, the Be center in the global minimum geometries ofBe2N2 and Be3N2 clusters can bind Ng atoms. In the linear ge-ometry of BeSiN2, the Be center interacts weakly with Ng atomsdue to the absence of an appropriate binding site. However,the second-lowest energy Cs isomer has greater Ng-bindingability compared to Be2N2 and Be3N2 clusters. The presence ofNg atoms reduces the energy difference between the lowest-and the second-lowest-energy isomers of a BeSiN2 cluster. Infact, in the presence of Ar–Rn, the Cs isomer becomes morestable than the corresponding linear isomer. All the Ng-bindingevents are exothermic in nature and become more exothermicon descending Group 18. All the Xe, Rn- and first Kr-bindingevents at Be2N2 and Be3N2 clusters are exergonic at room tem-perature, whereas in case of the BeSiN2 cluster, Ar–Rn-bindingprocesses are spontaneous at room temperature. For the re-maining systems, lower temperatures are required. The He-and Ne-bound clusters are not promising candidates for syn-thesis. Electron transfer takes place from Ng atoms to Be cen-ters by approximately 0.3 e� for the heavier Ng atoms and lessfor the lighter analogues. The WBIs for Be�Xe/Rn bonds areapproximately 0.50. Electron density analysis shows that theBe�Xe/Rn bond can be considered as type Wc, whereas theother Be�Ng (Ng = He–Kr) bonds can be considered as Wn.EDA suggests that for NgBe2N2 and NgBe3N2 clusters, the termDEex contributes the most (�42–48 %) towards the total attrac-tion energy, whereas DEpol + ct is the most dominating term (�44–46 %) in the case of NgBeSiN2 (except Ng = He and Ne).The charge at the Be center appears to be responsible for this.

Acknowledgements

P.K.C. would like to thank DST, New Delhi for the J. C. Bose Na-tional Fellowship. S.P. thanks CSIR, New Delhi for his fellowship.D.M. thanks Conacyt for the Ph.D. fellowship. Conacyt (GrantINFRA-2013-01-204586) and Moshinsky Foundation supported the

work in M�rida. The CGSTIC (Xiuhcoalt) at Cinvestav is gratefullyacknowledged for generous allocation of computational resour-ces.

Keywords: bonding · electron density · energy decompositionanalysis · HOMO–LUMO gap · noble gas

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Received: March 6, 2014Revised: April 24, 2014Published online on May 30, 2014

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