CHEMPHYSCHEM ARTICLES DOI: 10.1002/cphc.201402101
Ab Initio Study on the Stability of NgnBe2N2, NgnBe3N2 and NgBeSiN2 Clusters** Sudip Pan,[a] Diego Moreno,[b] Jos Luis Cabellos,[b] Gabriel Merino,*[b] and Pratim K. Chattaraj*[a] The global minima of Be2N2, Be3N2 and BeSiN2 clusters are identified using a modified stochastic kick methodology. The structure, stability and bonding nature of these clusters bound to noble gas (Ng) atoms are studied at the MP2/def2-QZVPPD level of theory. Positive BeNg bond dissociation energy, which gradually increases down Group 18 from He to Rn, indicates the bound nature of Ng atoms. All of the Ng-binding
processes are exothermic in nature. The Xe and Rn binding to Be2N2 and Be3N2 clusters and ArRn binding to BeSiN2 are exergonic processes at room temperature; however, for the lighter Ng atoms, lower temperatures are needed. Natural population analysis, Wiberg bond index computations, electron density analysis, and energy decomposition analysis are performed to better understand the nature of BeNg bonds.
1. Introduction The enthusiasm to enrich a less developed field always acts as a driving force for scientists. Noble gas (Ng) chemistry is one such field.[1] The low reactivity of an Ng with other elements makes discovering new Ng compounds a challenge. To develop this field, theoreticians try to build proper theory to understand the reactivity and bonding pattern and use this to predict new stable Ng compounds, whereas experimentalists devote their efforts to synthesize Ng compounds depending on the knowledge provided by these theories. In 1933, based on the fundamental understanding of chemical bonding, Pauling[2] predicted the chemical binding ability of elements at the bottom of Group 18. Chemical bonding is a phenomenon of electron donation or sharing, therefore the unreactivity should diminish gradually on descending Group 18 from He to Rn, due to the steady increase and decrease of polarizability and ionization energy, respectively. The first molecule classified as an Ng compound, was xenon hexafluoroplatinate, Xe + [PtF6] , synthesized by Bartlett in 1962.[3] His experiments directly challenged the long-held belief that Ng atoms were truly inert and soon after the field of Ng chemistry was born. Following Bartlett’s synthesis, various research groups achieved success in
[a] S. Pan, Prof. P. K. Chattaraj Department of Chemistry and Centre for Theoretical Studies Indian Institute of Technology Kharagpur 721302 (India) E-mail: [email protected] [b] D. Moreno, Dr. J. L. Cabellos, Prof. G. Merino Departamento de Fsica Aplicada Centro de Investigacin y Estudios Avanzados Unidad Mrida, km 6 Antigua carretera a Progreso Apartado Postal 73, Cordemex 97310 Mrida, Yucatn (Mxico) E-mail: [email protected] [**] Ng = Noble Gas (He, Ne, Ar, Kr, Xe, Rn) Supporting Information for this article is available on the WWW under http://dx.doi.org/10.1002/cphc.201402101.
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synthesizing a number of compounds containing heavier members of Group 18.[4] The successful syntheses of compounds of type HNgY (Y = electron-withdrawing group) and Ng hydrides by Rsnen et al.[5] and Feldman et al.[6] are also considered as significant contributions in this field. Theoretical studies on several Ng compounds by various groups must also be acknowledged.[7–11] The computational study on the stability of NgBeO molecules (Ng = He–Xe) by Frenking’s group[7a, d] shed light on the Ng-binding ability of a positively charged Be center; such compounds were later synthesized by Andrews’ group.[12] The dominant contributors to the attraction between an electropositive center and Ng atoms are polarization and charge transfer.[13] In general, with an increase in the positive charge, the Ng-binding ability improves although this variation is not a directly proportional relationship. Therefore, if we want to search for Be-containing clusters that bind Ng atoms, we have to look towards clusters in which Be is linked with electronegative atoms and hence acquires a high positive charge. To build an effective interaction with Ng atoms, the positive charge at the Be center should be large enough to pull the electron clouds of Ng atoms despite their low polarizabilities and high ionization potentials. Based on this simple understanding about the Be–Ng interaction, Grandinetti et al.[14] have shown the Ng-binding ability of a series of Be clusters in which Be is bonded to electronegative atoms and/or which are cationic 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 than the corresponding neutral analogues.[15] We have also shown that BeCN2 and BeNBO have better Ng-binding ability than the well-known BeO, BeS, BeNH systems.[13] Prompted by this knowledge, here we have looked for viable Be-containing clusters, in which the Be centers have large positive charge due to bonding with electronegative atoms. ChemPhysChem 2014, 15, 2618 – 2625
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CHEMPHYSCHEM ARTICLES Be3N2 and BeSiN2 are well-known experimentally available compounds in their different polymorphic forms.[16, 17] Several theoretical studies have also been carried out exploring characteristics such as their semiconductor properties.[18, 19] The detection of Be2N2 was first reported in 1917 by Vournasos.[16a] Thompson and Andrews further identified Be2N2 from IR spectra.[20] In addition, several derivatives of Be2N2, namely Ba[Be2N2][21] and E[Be2N2] (E = Mg, Ca, Sr, Ba),[22] have also been prepared. 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 structures for Be2N2, Be3N2 and BeSiN2 clusters and owing to the high electropositive nature of Be, their Ng-binding ability was studied. The nature of BeNg bonds was also explored. It should be noted that although previous studies considered a planar structure of Be2N2 clusters,[23] our global minimum search revealed that the planar isomer is a local minimum and not the global one.
Computational Details A modified stochastic kick methodology called Bilatu[24] was used for searching the global minimum-energy structures by considering both singlet- and triplet-spin states of Be2N2, Be3N2 and BeSiN2 clusters. The working principle of this methodology s described in detail elsewhere.[13] In this study, the initial search for the global minima of Be2N2, Be3N2, and BeSiN2 was performed at the PBE0/ LanL2DZ level and optimized further at the MP2/def2-QZVPPD level. All of the Ng-bound analogues were also studied at the MP2/def2-QZVPPD level. We also carried out computations at the CCSD(T)/def2-QZVPPD//MP2/def2-QZVPPD level to compute Be–Ng dissociation values. For the core electrons of Xe and Rn atoms, a quasi-relativistic pseudopotential was used.[25] Natural population analysis (NPA) and calculation of Wiberg bond index (WBI)[26] were carried out to assess the atomic charge q at each center and to evaluate the bond order, respectively. We carried out all the MP2 and CCSD(T) computations using the Gaussian 09 package.[27] The energy decomposition analysis (EDA) was performed at the CCSD(T)/def2-TZVP level of theory by using the method proposed by Su and Li[28] , as implemented in Gamess.[29] Multiwfn software[30] was used for detailed electron density analysis.[31] Generally, a negative value of the Laplacian of electron density gN > 21(rc) at the bond critical point (BCP) can be interpreted as a covalent interaction, whereas positive value as a noncovalent interaction. The failure of this criterion to characterize typical covalent molecules has also been reported.[31, 32] Several other parameters, such as local kinetic energy density G(rc), local potential energy 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 nature of bonding. It has been reported in the literature that a bond can be considered to have partial covalent character if gN > 21(rc) > 0 and 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 it is within the range 0.5–1.0, then that bond may be called partially covalent.[34] Note that the criteria H(rc) < 0 and G(rc)/V(rc) < 1 for a partial covalent bond are the same. Furthermore, G(rc)/1(rc) < 1 indicates a covalent bond.[32] 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
www.chemphyschem.org 2. Results and Discussion 2.1. NgnBe2N2 and NgnBe3N2 Clusters The six most-stable isomers of Be2N2 and Be3N2 are displayed in Figure 1. The global minimum of Be2N2 at the studied level is found to be a singlet nonplanar C2v structure rather than the planar D2h structure considered in previous studies[23] to assess its 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 mol1 more stable than the corresponding D2h analogue. The secondlowest energy isomer is a triplet with a planar C2v structure, which is only 1.0 kcal mol1 less stable than that of the global minimum. In the case of Be3N2, the most-stable isomer is a singlet D3h structure, in which two N atoms reside above and below the triangular Be3 ring (Figure 1). It is only 1.8 kcal mol1 more stable than its nearest-energy triplet C2v isomer. Note that such a small energy difference between the lowest- and the second-lowest-energy structures in the cases of Be2N2 and Be3N2 indicates that in an experimental situation, the final products might consist of both isomers in different proportions. Here we have only considered the lowest-energy isomers as the second-lowest energy isomers would not be good candidates to bind Ng atoms.[35] NPA reveals that each Be and N center in a Be2N2 cluster possess + 1.19 e and 1.19 e , respectively, whereas those in a Be3N2 cluster have + 1.14 e and 1.71 e , respectively. Therefore, each center might be expected to bind Ng atoms as the positive charges at Be centers are somewhat large. The structures of NgnBe2N2 and NgnBe3N2 clusters are depicted in Figure 2. The NgBe2N2 clusters adopt Cs point groups, whereas Ng2Be2N2 clusters have C2v point groups.[36] The corresponding detailed results for NgnBe2N2 and NgnBe3N2 clusters are provided in Tables 1 and 2, respectively. The zero-point energy (ZPE)-corrected dissociation energy values (D0) for Be Ng bonds are small for He and Ne compounds, however it gradually increases from Ar to Rn. For a particular Ng binding, the corresponding D0 values slowly decrease with each successive binding. In fact, for the third He atom binding onto a Be3N2 cluster, the D0 value reaches zero. The dissociation energy values at the CCSD(T)/def2-QZVPPD/MP2/def2-QZVPPD level (DCCSD(T)) are also provided in Tables 1 and 2. The reaction enthalpy (DH) values for all Ng-binding processes by Be2N2 and Be3N2 clusters are negative (Tables 1 and 2). From He to Rn, the processes gradually become more exothermic. The second Ng-binding events are slightly less exothermic than the first in NgnBe2N2 (except binding of He). For NgnBe3N2, the corresponding DH value also decreases with the increased number of Ng atoms. The free-energy change (DG) for all Xe and Rn and the first Kr-binding processes are exergonic in nature at 298 K. However, the other Ng-binding events are not spontaneous at room temperature. Therefore, for those processes, lower temperature is needed to make the unfavorable TDS term less important. Initially, we calculated DG values for all these processes at the temperature of liquid N2 (77 K) and, for those processes not spontaneous at that ChemPhysChem 2014, 15, 2618 – 2625
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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 energies in kcal mol1 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 mol1], ZPE-corrected dissociation energy D0 [kcal mol1] of BeNg bonds for the dissociation process NgnBe2N2 ! Ng + Ngn-1Be2N2, reaction enthalpy DH [kcal mol1] and free-energy change DG [kcal mol1] 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 BeNg bonds, BeNg bond distances rBeNg, [] and the lowest frequency nmin [cm1] 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
rBeNg
nmin
Be2N2 HeBe2N2 He2Be2N2 NeBe2N2 Ne2Be2N2 ArBe2N2 Ar2Be2N2 KrBe2N2 Kr2Be2N2 XeBe2N2 Xe2Be2N2 RnBe2N2 Rn2Be2N2
C2v Cs C2v Cs C2v Cs C2v Cs C2v Cs C2v Cs C2v
1.2 1.1 1.9 1.8 6.0 5.4 7.7 6.9 9.7 8.7 11.0 10.0
0.4 0.3 1.4 1.3 5.5 5.0 7.2 6.5 9.2 8.4 10.5 9.7
0.8 0.6 1.6 1.4 5.2 4.5 6.6 5.8 8.3 7.3 9.6 8.5
0.7 0.7 1.5 1.4 5.7 5.1 7.3 6.6 9.4 8.4 10.7 9.7
5.2 6.1 4.3 5.2 0.5 1.8 1.2 0.3 3.3 1.7 4.7 3.0
9.17 9.23 10.17 9.21 9.58 9.09 9.02 9.07 8.90 9.02 8.61 8.96 8.38
0.09 0.09 0.06 0.06 0.18 0.17 0.22 0.21 0.26 0.25 0.27 0.26
1.19 1.08 1.09 1.13 1.13 0.99 1.00 0.94 0.96 0.89 0.91 0.88 0.90
0.16 0.16 0.12 0.12 0.32 0.30 0.38 0.36 0.45 0.43 0.47 0.44
1.718 1.715 1.963 1.976 2.192 2.209 2.323 2.337 2.485 2.499 2.550 2.564
406 119 83 94 38 104 33 101 25 99 21 101 17
[a] DCCSD(T) is the dissociation energy [kcal mol1] at the CCSD(T)/def2-QZVPPD//MP2/def2-QZVPPD level.
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Table 2. The dissociation energy De [kcal mol1], ZPE-corrected dissociation energy D0 [kcal mol1] of BeNg bonds for the dissociation process NgnBe3N2 ! Ng + Ngn-1Be3N2, reaction enthalpy DH [kcal mol1] and free energy change DG [kcal mol1] 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 BeNg bonds, BeNg bond distances rBeNg, [] and the lowest frequency nmin [cm1] 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
rBeNg
nmin
Be3N2 HeBe3N2 He2Be3N2 He3Be3N2 NeBe3N2 Ne2Be3N2 Ne3Be3N2 ArBe3N2 Ar2Be3N2 Ar3Be3N2 KrBe3N2 Kr2Be3N2 Kr3Be3N2 XeBe3N2 Xe2Be3N2 Xe3Be3N2 RnBe3N2 Rn2Be3N2 Rn3Be3N2
D3h C2v C2v D3h C2v C2v D3h C2v C2v D3h C2v C2v D3h C2v C2v D3h C2v C2v D3h
1.1 0.9 0.8 1.7 1.5 1.4 6.1 5.4 4.7 7.9 7.0 6.2 10.2 9.1 8.1 11.7 10.5 9.5
0.1 0.1 0.0 1.1 1.0 0.9 5.4 4.8 4.2 7.3 6.5 5.7 9.6 8.6 7.7 11.1 10.0 9.1
1.2 1.0 0.9 1.8 1.7 1.5 5.8 5.0 4.4 7.3 6.4 5.6 9.3 8.1 7.2 10.6 9.4 8.5
0.5 0.4 0.3 1.3 1.1 1.0 5.7 4.9 4.2 7.5 6.5 5.7 9.8 8.6 7.7 11.3 10.1 9.1
5.4 6.0 6.7 4.4 5.1 5.7 0.4 1.7 2.9 1.4 0.0 1.0 3.9 2.2 0.7 5.4 3.7 2.1
8.11 8.34 8.65 9.42 8.27 8.48 8.82 8.26 8.43 8.52 8.26 8.41 8.41 8.26 8.42 8.18 8.22 8.28 7.95
0.10 0.10 0.09 0.07 0.07 0.07 0.20 0.19 0.18 0.24 0.23 0.22 0.30 0.28 0.27 0.31 0.29 0.28
1.14 1.00 1.00 1.01 1.06 1.06 1.06 0.90 0.91 0.91 0.85 0.86 0.87 0.79 0.80 0.81 0.78 0.80 0.81
0.18 0.18 0.17 0.13 0.13 0.12 0.35 0.33 0.32 0.42 0.40 0.38 0.50 0.47 0.45 0.51 0.49 0.46
1.705 1.722 1.740 1.979 1.998 2.020 2.187 2.208 2.231 2.312 2.333 2.356 2.469 2.489 2.510 2.534 2.552 2.572
528 136 99 98 96 41 39 109 36 33 102 27 23 92 20 17 85 15 13
[a] DCCSD(T) is the dissociation energy [kcal mol1] at the CCSD(T)/def2-QZVPPD//MP2/def2-QZVPPD level.
temperature, DG values were calculated at 4 K. The corresponding values (Table S1 in the Supporting Information) show that all Ar- and Kr-binding processes by Be2N2 and Be3N2 clusters become exergonic at 77 K and for the other systems, much lower temperatures are needed. Note that low dissociation energy values and the spontaneity of Ng-binding processes at low temperature (4 K) for He and Ne compounds imply that they are unlikely to be synthesized, although other systems 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 of these compounds. Note that, similar to their parent moieties, all the Ng-bound analogues have high HOMO–LUMO gap values. In NgnBe2N2 clusters, the HOMO–LUMO gap slightly increases for Ng = He and Ne but for the larger Ng analogues it decreases to some extent with respect to that of the Be2N2
cluster; however, in cases of NgnBe3N2 clusters, with the exception 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 triplet having linear structure (C1v), which is 4.6 kcal mol1 more stable than the second-lowest energy singlet Cs isomer (see Figure 3). In the global minimum, the Be center is located in between two N atoms in a linear configuration, hence there is no available binding site for Ng atoms. However, the second isomer is more likely to bind Ng atoms because the Be center possesses a positive charge of + 1.28 e and is available for further coordination by Ng atoms. The Cs isomer of BeSiN2 has even better Ng-binding ability than the Be2N2 and Be3N2 clusters (Table S2). The corresponding dissociation energy values
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 kcal mol1 are also given.
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of NgBeSiN2 clusters are larger than those of NgBe2N2 and NgBe3N2 clusters. All the Ngbinding processes are exothermic in nature; however only Ar– Rn-binding processes are spontaneous at the studied temperature (298 K). The He- and Nebinding events can be exergonic at low temperature (Table S1). However, due to its higherenergy structure, BeSiN2 is less likely to exist in the singlet Cs form. We have also studied the interaction of Ng atoms with the linear global-minimum energy structure of BeSiN2 (Table S3). Low BeNg bond dissociation energies are found in these cases. We would like to highlight that in the presence of an Ng atom, the energy difference between the lowest-energy and the second-lowest-energy isomers gradually decreases from He to Ne and for Ar–Rn the corresponding Ng-bound Cs isomers become more stable than the Ng-bound C1v isomers (Figure 4). Therefore, the presence of Ng atoms can stabilize less stable forms of clusters. 2.3. NPA Charges and WBIs
Figure 4. Optimized structures of NgBeSiN2 clusters studied at the MP2/def2-QZVPPD level. The ZPE-corrected relative energies in kcal mol1 are also given.
NPA reveals that some degree of electron transfer takes place from Ng atoms to positively charged Be centers. The extent of shifting of electron density from Ng to the Be center is low for lighter Ng atoms. However, it is considerably large for heavier Ng atoms, especially Xe and Rn ( 0.3 e). It follows the order Rn > Xe > Kr > Ar > He > Ne (see Tables 1, 2 and S2). Note that the electron shift from Ne is smaller than that from He, although based on the polarizability and ionization energy values, the reverse is expected. Such off-trend behavior of Ne is not new in the literature. To resolve this anomaly, Bent,[37] Scerri,[38] Grochala[10b] and recently Grandinetti[39] argued in favor of moving He to the top of Group 2 in the periodic table. Grandinetti explained the lower reactivity of Ne compared to He: “Neon is bigger than helium, and possesses occupied p orbitals. This is thought to produce less effective electrostatic interactions and higher orbital repulsions, which typically make the neon compounds either unstable or only marginally stable, although the contributions of these factors are still to be further investigated”.[39] In our EDA (see below), in all cases the electrostatic contribution for Ne is higher than that of He. In fact, the lower reactivity of Ne compared to He is a matter of 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
debate. Furthermore, the Be–Ne dissociation values are always higher than those of BeHe bonds, although in our previous study,[13] in a few instances the BeNe bonds had higher dissociation energies than that of He, whereas in others the reverse was true. Therefore, this topic is open for further discussion. In this study, the WBI calculation corresponding to BeNg bonds gives a small value for lighter Ng atoms, and a considerably larger value for heavier analogues. WBIs of BeNg bonds follow the order Rn > Xe > Kr > Ar > He > Ne (see Tables 1–3). These values further indicate that almost a half bond is formed in between Be and Ng atoms for Ng = Xe and Rn. A low WBI provides a hint to the existence of dominant van der Waals type of interaction (this is the case for lighter Ng atoms), however, a large value reveals that some degree of covalent character exists between them (for heavier analogues). 2.4. Electron Density Analysis The different topological parameters computed at the BCPs of BeNg bonds from the electron density analysis[31] are presentChemPhysChem 2014, 15, 2618 – 2625
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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 mol1.[a] System
Fragments
DEtotal
DEelec
DEex
DErep
DEpol + ct
DEdisp
HeBe2N2 NeBe2N2 ArBe2N2 KrBe2N2 XeBe2N2 RnBe2N2
He + Be2N2 Ne + Be2N2 Ar + Be2N2 Kr + Be2N2 Xe + Be2N2 Rn + Be2N2
0.19 1.02 5.17 6.12 7.57 8.22
1.29 (9.5 %) 2.49 (16.8 %) 4.26 (12.6 %) 4.56 (11.7 %) 3.93 (8.8 %) 3.86 (8.3 %)
6.61 (48.5 %) 6.64 (44.8 %) 14.20 (41.9 %) 16.41 (42.3 %) 19.12 (42.9 %) 19.91 (42.7 %)
13.44 13.81 28.70 32.71 36.98 38.37
4.89 (35.9 %) 4.14 (27.9 %) 11.70 (34.5 %) 13.80 (35.5 %) 16.22 (36.4 %) 16.98 (36.4 %)
0.84 1.56 3.72 4.07 5.27 5.85
(6.2 %) (10.5 %) (11.0 %) (10.5 %) (11.8 %) (12.6 %)
HeBe3N2 NeBe3N2 ArBe3N2 KrBe3N2 XeBe3N2 RnBe3N2
He + Be3N2 Ne + Be3N2 Ar + Be3N2 Kr + Be3N2 Xe + Be3N2 Rn + Be3N2
0.61 1.55 5.93 7.08 8.65 9.35
1.23 (9.3 %) 2.15 (15.4 %) 3.97 (11.5 %) 4.24 (10.5 %) 3.80 (8.1 %) 3.75 (7.6 %)
6.37 (48.1 %) 6.05 (43.4 %) 14.47 (41.7 %) 17.11 (42.3 %) 20.37 (43.2 %) 21.33 (43.1 %)
12.64 12.40 28.74 33.36 38.53 40.15
4.79 (36.2 %) 3.85 (27.6 %) 11.69 (33.7 %) 13.99 (34.6 %) 16.55 (35.1 %) 17.30 (34.9 %)
0.86 1.90 4.54 5.10 6.47 7.13
(6.5 %) (13.6 %) (13.1 %) (12.6 %) (13.7 %) (14.4 %)
HeBeSiN2 NeBeSiN2 ArBeSiN2 KrBeSiN2 XeBeSiN2 RnBeSiN2
He + BeSiN2 Ne + BeSiN2 Ar + BeSiN2 Kr + BeSiN2 Xe + BeSiN2 Rn + BeSiN2
1.04 1.94 7.38 8.61 10.45 11.28
1.10 (7.8 %) 2.10 (13.8 %) 2.99 (8.9 %) 2.95 (7.7 %) 2.25 (5.1 %) 2.05 (4.5 %)
6.20 (44.0 %) 6.20 (40.7 %) 12.57 (37.4 %) 14.51 (37.8 %) 16.79 (38.2 %) 17.35 (37.9 %)
13.05 13.29 26.26 29.76 33.50 34.47
6.20 (44.0 %) 5.56 (36.5 %) 14.68 (43.6 %) 17.20 (44.8 %) 19.97 (45.4 %) 20.84 (45.5 %)
0.59 1.37 3.41 3.73 4.93 5.52
(4.2 %) (9.0 %) (10.1 %) (9.7 %) (11.2 %) (12.1 %)
[a] The percentage values within parentheses show the contribution towards the total attractive interaction DEelec + DEex + DEpol + ct + DEdisp.
ed in Table S4. Caution should be exercised with this analysis.[40] Recently, Boggs et al.[41] reported electron density analysis of a series of Ng-loaded clusters to characterize the nature of the interaction. They also considered NgBeO in their study. Based on the outputs of different topological descriptors and the NgBe bond distances being between those of covalent and van der Waals distances, they have introduced two new types of bonding, Wn (weak interaction having noncovalent character) and Wc (weak interaction having some degree of covalent character). In our study, the Ng-binding center is also Be (similar to NgBeO) and the NgBe distances are less than the van der Waals distances but larger than the corresponding covalent distances. Typical NgBe covalent and van der Waals distances can be found in ref. [41]. We have adopted these types to assign the nature of interaction. Table S4 shows that in our study, r21(rc) > 0 and G(rc)/1(rc) > 1; however H(rc) is only negative for Xe and Rn (and consequently G(rc)/V(rc) < 1 for these cases). Therefore, BeXe and BeRn bonds can be considered to be of type Wc and the remaining BeNg (Ng = He– Kr) bonds of type Wn. 2.5. Energy Decomposition Analysis The results of the EDA of these Ng–Be clusters carried out at the CCSD(T)/def2-TZVP level, taking Ng as one fragment and the Be cluster as another, are provided in Table 3. The total interaction energy (DEtotal) is divided into the electrostatic (DEele), exchange (DEex), repulsive (DErep), polarization and charge transfer (DEpol + ct), and dispersion (DEdisp) energy terms. Positive and negative values of DE imply that the interaction terms between two fragments are repulsive and attractive in nature, respectively. Here, DEtotal represents the energy difference between the “supermolecule” and the monomers having the geometries of those in the supermolecule. Of all the attrac 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
tive terms, for NgBe2N2 and NgBe3N2 clusters, DEex contributes the most ( 42–48 %) towards the total attraction energy whereas 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 the largest and the second-largest contributions, respectively, in stabilizing NgBeSiN2 clusters. It is notable that in our previous study, DEpol + ct was more dominant over DEex for NgBeCN2 and NgBeNBO clusters.[13] In such Ng–Be clusters, the relative dominance of DEpol + ct and DEex over each other depends on the positive charges at the Be centers. One Be center having a higher positive charge can behave as a better polarizing center than that possessing a lower positive charge. The charges at Be centers in Be2N2, Be3N2 and BeSiN2 are + 1.19, + 1.14 and + 1.28 e , respectively. Therefore, the Be center in BeSiN2 can polarize the orbitals of Ng atoms to a greater extent than those in Be2N2 and Be3N2 clusters. This makes DEpol + ct a larger contributor than the corresponding DEex term. Owing to the low polarizability values of He and Ne, we have equal contributions from DEpol + ct and DEex in HeBeSiN2 and slightly smaller contribution from DEpol + ct than DEex in NeBeSiN2. Note that in BeCN2 (+ 1.39 e) and BeNBO (+ 1.45 e), the positive charges were also high on the Be centers.[13] The DEele and DEdisp terms contribute towards the total attraction energy, approximately 5–17 % 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 highlights the necessity of taking a proper dispersion correction into account when representing such clusters. From He to Rn, both the repulsive (DErep) and the attractive (DEex, DEpol + ct and DEdisp) terms increase gradually, with the exception of DEpol + ct for Ne, which is always smaller than that of He. This is due to the fact that for Ne donating an electron to the positively charged Be center is less likely than He. Note that in all cases, ChemPhysChem 2014, 15, 2618 – 2625
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CHEMPHYSCHEM ARTICLES the shift of electron density from Ne to Be is smaller than that from He. The DEele term gradually improves from He to Kr but decreases in the case of Xe and Rn. In general, a large DEpol + ct term indicates that the orbitals undergo considerable transformation in their shapes, which is akin to a covalent bond. The high values of DEpol + ct, particularly in the case of Xe and Rn imply that there might be some degree of covalent character in BeXe/Rn bonds (also Be–Kr in KrBeSiN2).
3. Conclusions We have identified the global minimum-energy structures of experimentally achievable Be2N2, Be3N2 and BeSiN2 clusters. The lowest-energy isomer of Be2N2 has a singlet nonplanar C2v structure. Therefore, a different global minimum-energy structure for a Be2N2 cluster was obtained when compared to that reported in a previous study.[23a] Be3N2 has a singlet D3h geometry in which two N atoms reside above and below the triangular Be3 ring. In the case of BeSiN2, the global minimum corresponds to a triplet linear structure in which the Be center is located in between two N atoms. Owing to the high positive charges, the Be center in the global minimum geometries of Be2N2 and Be3N2 clusters can bind Ng atoms. In the linear geometry of BeSiN2, the Be center interacts weakly with Ng atoms due to the absence of an appropriate binding site. However, the second-lowest energy Cs isomer has greater Ng-binding ability compared to Be2N2 and Be3N2 clusters. The presence of Ng atoms reduces the energy difference between the lowestand the second-lowest-energy isomers of a BeSiN2 cluster. In fact, in the presence of Ar–Rn, the Cs isomer becomes more stable than the corresponding linear isomer. All the Ng-binding events are exothermic in nature and become more exothermic on descending Group 18. All the Xe, Rn- and first Kr-binding events at Be2N2 and Be3N2 clusters are exergonic at room temperature, whereas in case of the BeSiN2 cluster, Ar–Rn-binding processes are spontaneous at room temperature. For the remaining systems, lower temperatures are required. The Heand Ne-bound clusters are not promising candidates for synthesis. Electron transfer takes place from Ng atoms to Be centers by approximately 0.3 e for the heavier Ng atoms and less for the lighter analogues. The WBIs for BeXe/Rn bonds are approximately 0.50. Electron density analysis shows that the BeXe/Rn bond can be considered as type Wc, whereas the other BeNg (Ng = He–Kr) bonds can be considered as Wn. EDA suggests that for NgBe2N2 and NgBe3N2 clusters, the term DEex contributes the most ( 42–48 %) towards the total attraction 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 National Fellowship. S.P. thanks CSIR, New Delhi for his fellowship. D.M. thanks Conacyt for the Ph.D. fellowship. Conacyt (Grant INFRA-2013-01-204586) and Moshinsky Foundation supported the 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
www.chemphyschem.org work in Mrida. The CGSTIC (Xiuhcoalt) at Cinvestav is gratefully acknowledged for generous allocation of computational resources. Keywords: bonding · electron density · energy decomposition analysis · HOMO–LUMO gap · noble gas
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S. Dapprich, A. D. Daniels, . Farkas, J. B. Foresman, J. V. Ortiz, J. Cioslowski, D. J. Fox, Gaussian, Inc., Wallingford CT, 2009. P. Su, H. Li, J. Chem. Phys. 2009, 131, 014102 – 014116. M. W. Schmidt, K. K. Baldridge, J. A. Boatz, S. T. Elbert, M. S. Gordon, J. H. Jensen, S. Koseki, N. Matsunga, K. A. Nguyen, S. J. Su, M. Dupuis, J. A. Montgomery, J. Comput. Chem. 1993, 14, 1347 – 1363. T. Lu, F. W. Chen, J. Comput. Chem. 2012, 33, 580 – 592. R. F. W. Bader, Atoms in Molecules: A Quantum Theory, Clarendon, Oxford, 1990. a) P. Macchi, D. M. Proserpio, A. Sironi, J. Am. Chem. Soc. 1998, 120, 13429 – 13435; b) P. Macchi, L. Garlaschelli, S. Martinengo, A. Sironi, J. Am. Chem. Soc. 1999, 121, 10428 – 10429; c) I. V. Novozhilova, A. V. Volkov, P. Coppens, J. Am. Chem. Soc. 2003, 125, 1079 – 1087; d) L. J. Farrugia, H. M. Senn, J. Phys. Chem. A 2010, 114, 13418 – 13433. D. Cremer, E. Kraka, Angew. Chem. Int. Ed. Engl. 1984, 23, 627 – 628; Angew. Chem. 1984, 96, 612 – 614. M. Ziołkowski, S. J. Grabowski, J. Leszczynski, J. Phys. Chem. A 2006, 110, 6514 – 6521. The Be centers in the second-lowest energy isomer, i.e. the triplet C2v isomer of the Be2N2 cluster have low positive charges (+ 0.25 and + 0.29 e). Therefore, it cannot bind Ng atoms. In the case of the second-lowest-energy isomer of the Be3N2 cluster, each of the two Be centers located between two N atoms has + 1.23 e charge whereas the Be atom bonded to only one N atom has + 0.76 e charge. We have seen that the Be centers having + 1.23 e charge can bind Ng atoms (Ng = Ne–Rn) but the corresponding BeNg bond dissociation energies De are smaller than that of the D3h isomer. In this case, for the first Ng atom that binds, the De values are 0.5, 3.4, 4.9, 6.7 and 8.0 kcal mol1 for Ne, Ar, Kr, Xe and Rn, respectively. We have first performed full optimization in all cases without imposing any symmetry, then taking the final structures, we have imposed those point groups which appear under default or loose tolerance. H. A. Bent, New Ideas in Chemistry from Fresh Energy for the Periodic Law, Author House, Bloomington, IN, 2006.. E. R. Scerri, The Periodic Table: Its Story and Its Significance, Oxford University Press, New York, 2007. F. Grandinetti, Nat. Chem. 2013, 5, 438. a) J. Cioslowski, S. T. Mixon, Can. J. Chem. 1992, 70, 443 – 449; b) J. Cioslowski, S. T. Mixon, J. Am. Chem. Soc. 1992, 114, 4382 – 4387; c) A. Haaland, D. J. Shorokhov, N. V. Tverdova, Chem. Eur. J. 2004, 10, 4416 – 4421; d) A. Krapp, G. Frenking, Chem. Eur. J. 2007, 13, 8256 – 8270; e) J. Poater, R. Visser, M. Sola, F. M. Bickelhaupt, J. Org. Chem. 2007, 72, 1134 – 1142; f) E. Cerpa, A. Krapp, A. Vela, G. Merino, Chem. Eur. J. 2008, 14, 10232 – 10234; g) E. Cerpa, A. Krapp, R. Flores-Moreno, K. J. Donald, G. Merino, Chem. Eur. J. 2009, 15, 1985 – 1990. W. Zou, D. Nori-Shargh, J. E. Boggs, J. Phys. Chem. A 2013, 117, 207 – 212.
Received: March 6, 2014 Revised: April 24, 2014 Published online on May 30, 2014
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Ab Initio Study on the Stability of NgnBe2N2, NgnBe3N2 and NgBeSiN2 Clusters** Sudip Pan,[a] Diego Moreno,[b] Jos Luis Cabellos,[b] Gabriel Merino,*[b] and Pratim K. Chattaraj*[a] The global minima of Be2N2, Be3N2 and BeSiN2 clusters are identified using a modified stochastic kick methodology. The structure, stability and bonding nature of these clusters bound to noble gas (Ng) atoms are studied at the MP2/def2-QZVPPD level of theory. Positive BeNg bond dissociation energy, which gradually increases down Group 18 from He to Rn, indicates the bound nature of Ng atoms. All of the Ng-binding
processes are exothermic in nature. The Xe and Rn binding to Be2N2 and Be3N2 clusters and ArRn binding to BeSiN2 are exergonic processes at room temperature; however, for the lighter Ng atoms, lower temperatures are needed. Natural population analysis, Wiberg bond index computations, electron density analysis, and energy decomposition analysis are performed to better understand the nature of BeNg bonds.
1. Introduction The enthusiasm to enrich a less developed field always acts as a driving force for scientists. Noble gas (Ng) chemistry is one such field.[1] The low reactivity of an Ng with other elements makes discovering new Ng compounds a challenge. To develop this field, theoreticians try to build proper theory to understand the reactivity and bonding pattern and use this to predict new stable Ng compounds, whereas experimentalists devote their efforts to synthesize Ng compounds depending on the knowledge provided by these theories. In 1933, based on the fundamental understanding of chemical bonding, Pauling[2] predicted the chemical binding ability of elements at the bottom of Group 18. Chemical bonding is a phenomenon of electron donation or sharing, therefore the unreactivity should diminish gradually on descending Group 18 from He to Rn, due to the steady increase and decrease of polarizability and ionization energy, respectively. The first molecule classified as an Ng compound, was xenon hexafluoroplatinate, Xe + [PtF6] , synthesized by Bartlett in 1962.[3] His experiments directly challenged the long-held belief that Ng atoms were truly inert and soon after the field of Ng chemistry was born. Following Bartlett’s synthesis, various research groups achieved success in
[a] S. Pan, Prof. P. K. Chattaraj Department of Chemistry and Centre for Theoretical Studies Indian Institute of Technology Kharagpur 721302 (India) E-mail: [email protected] [b] D. Moreno, Dr. J. L. Cabellos, Prof. G. Merino Departamento de Fsica Aplicada Centro de Investigacin y Estudios Avanzados Unidad Mrida, km 6 Antigua carretera a Progreso Apartado Postal 73, Cordemex 97310 Mrida, Yucatn (Mxico) E-mail: [email protected] [**] Ng = Noble Gas (He, Ne, Ar, Kr, Xe, Rn) Supporting Information for this article is available on the WWW under http://dx.doi.org/10.1002/cphc.201402101.
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synthesizing a number of compounds containing heavier members of Group 18.[4] The successful syntheses of compounds of type HNgY (Y = electron-withdrawing group) and Ng hydrides by Rsnen et al.[5] and Feldman et al.[6] are also considered as significant contributions in this field. Theoretical studies on several Ng compounds by various groups must also be acknowledged.[7–11] The computational study on the stability of NgBeO molecules (Ng = He–Xe) by Frenking’s group[7a, d] shed light on the Ng-binding ability of a positively charged Be center; such compounds were later synthesized by Andrews’ group.[12] The dominant contributors to the attraction between an electropositive center and Ng atoms are polarization and charge transfer.[13] In general, with an increase in the positive charge, the Ng-binding ability improves although this variation is not a directly proportional relationship. Therefore, if we want to search for Be-containing clusters that bind Ng atoms, we have to look towards clusters in which Be is linked with electronegative atoms and hence acquires a high positive charge. To build an effective interaction with Ng atoms, the positive charge at the Be center should be large enough to pull the electron clouds of Ng atoms despite their low polarizabilities and high ionization potentials. Based on this simple understanding about the Be–Ng interaction, Grandinetti et al.[14] have shown the Ng-binding ability of a series of Be clusters in which Be is bonded to electronegative atoms and/or which are cationic 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 than the corresponding neutral analogues.[15] We have also shown that BeCN2 and BeNBO have better Ng-binding ability than the well-known BeO, BeS, BeNH systems.[13] Prompted by this knowledge, here we have looked for viable Be-containing clusters, in which the Be centers have large positive charge due to bonding with electronegative atoms. ChemPhysChem 2014, 15, 2618 – 2625
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CHEMPHYSCHEM ARTICLES Be3N2 and BeSiN2 are well-known experimentally available compounds in their different polymorphic forms.[16, 17] Several theoretical studies have also been carried out exploring characteristics such as their semiconductor properties.[18, 19] The detection of Be2N2 was first reported in 1917 by Vournasos.[16a] Thompson and Andrews further identified Be2N2 from IR spectra.[20] In addition, several derivatives of Be2N2, namely Ba[Be2N2][21] and E[Be2N2] (E = Mg, Ca, Sr, Ba),[22] have also been prepared. 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 structures for Be2N2, Be3N2 and BeSiN2 clusters and owing to the high electropositive nature of Be, their Ng-binding ability was studied. The nature of BeNg bonds was also explored. It should be noted that although previous studies considered a planar structure of Be2N2 clusters,[23] our global minimum search revealed that the planar isomer is a local minimum and not the global one.
Computational Details A modified stochastic kick methodology called Bilatu[24] was used for searching the global minimum-energy structures by considering both singlet- and triplet-spin states of Be2N2, Be3N2 and BeSiN2 clusters. The working principle of this methodology s described in detail elsewhere.[13] In this study, the initial search for the global minima of Be2N2, Be3N2, and BeSiN2 was performed at the PBE0/ LanL2DZ level and optimized further at the MP2/def2-QZVPPD level. All of the Ng-bound analogues were also studied at the MP2/def2-QZVPPD level. We also carried out computations at the CCSD(T)/def2-QZVPPD//MP2/def2-QZVPPD level to compute Be–Ng dissociation values. For the core electrons of Xe and Rn atoms, a quasi-relativistic pseudopotential was used.[25] Natural population analysis (NPA) and calculation of Wiberg bond index (WBI)[26] were carried out to assess the atomic charge q at each center and to evaluate the bond order, respectively. We carried out all the MP2 and CCSD(T) computations using the Gaussian 09 package.[27] The energy decomposition analysis (EDA) was performed at the CCSD(T)/def2-TZVP level of theory by using the method proposed by Su and Li[28] , as implemented in Gamess.[29] Multiwfn software[30] was used for detailed electron density analysis.[31] Generally, a negative value of the Laplacian of electron density gN > 21(rc) at the bond critical point (BCP) can be interpreted as a covalent interaction, whereas positive value as a noncovalent interaction. The failure of this criterion to characterize typical covalent molecules has also been reported.[31, 32] Several other parameters, such as local kinetic energy density G(rc), local potential energy 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 nature of bonding. It has been reported in the literature that a bond can be considered to have partial covalent character if gN > 21(rc) > 0 and 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 it is within the range 0.5–1.0, then that bond may be called partially covalent.[34] Note that the criteria H(rc) < 0 and G(rc)/V(rc) < 1 for a partial covalent bond are the same. Furthermore, G(rc)/1(rc) < 1 indicates a covalent bond.[32] 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
www.chemphyschem.org 2. Results and Discussion 2.1. NgnBe2N2 and NgnBe3N2 Clusters The six most-stable isomers of Be2N2 and Be3N2 are displayed in Figure 1. The global minimum of Be2N2 at the studied level is found to be a singlet nonplanar C2v structure rather than the planar D2h structure considered in previous studies[23] to assess its 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 mol1 more stable than the corresponding D2h analogue. The secondlowest energy isomer is a triplet with a planar C2v structure, which is only 1.0 kcal mol1 less stable than that of the global minimum. In the case of Be3N2, the most-stable isomer is a singlet D3h structure, in which two N atoms reside above and below the triangular Be3 ring (Figure 1). It is only 1.8 kcal mol1 more stable than its nearest-energy triplet C2v isomer. Note that such a small energy difference between the lowest- and the second-lowest-energy structures in the cases of Be2N2 and Be3N2 indicates that in an experimental situation, the final products might consist of both isomers in different proportions. Here we have only considered the lowest-energy isomers as the second-lowest energy isomers would not be good candidates to bind Ng atoms.[35] NPA reveals that each Be and N center in a Be2N2 cluster possess + 1.19 e and 1.19 e , respectively, whereas those in a Be3N2 cluster have + 1.14 e and 1.71 e , respectively. Therefore, each center might be expected to bind Ng atoms as the positive charges at Be centers are somewhat large. The structures of NgnBe2N2 and NgnBe3N2 clusters are depicted in Figure 2. The NgBe2N2 clusters adopt Cs point groups, whereas Ng2Be2N2 clusters have C2v point groups.[36] The corresponding detailed results for NgnBe2N2 and NgnBe3N2 clusters are provided in Tables 1 and 2, respectively. The zero-point energy (ZPE)-corrected dissociation energy values (D0) for Be Ng bonds are small for He and Ne compounds, however it gradually increases from Ar to Rn. For a particular Ng binding, the corresponding D0 values slowly decrease with each successive binding. In fact, for the third He atom binding onto a Be3N2 cluster, the D0 value reaches zero. The dissociation energy values at the CCSD(T)/def2-QZVPPD/MP2/def2-QZVPPD level (DCCSD(T)) are also provided in Tables 1 and 2. The reaction enthalpy (DH) values for all Ng-binding processes by Be2N2 and Be3N2 clusters are negative (Tables 1 and 2). From He to Rn, the processes gradually become more exothermic. The second Ng-binding events are slightly less exothermic than the first in NgnBe2N2 (except binding of He). For NgnBe3N2, the corresponding DH value also decreases with the increased number of Ng atoms. The free-energy change (DG) for all Xe and Rn and the first Kr-binding processes are exergonic in nature at 298 K. However, the other Ng-binding events are not spontaneous at room temperature. Therefore, for those processes, lower temperature is needed to make the unfavorable TDS term less important. Initially, we calculated DG values for all these processes at the temperature of liquid N2 (77 K) and, for those processes not spontaneous at that ChemPhysChem 2014, 15, 2618 – 2625
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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 energies in kcal mol1 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 mol1], ZPE-corrected dissociation energy D0 [kcal mol1] of BeNg bonds for the dissociation process NgnBe2N2 ! Ng + Ngn-1Be2N2, reaction enthalpy DH [kcal mol1] and free-energy change DG [kcal mol1] 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 BeNg bonds, BeNg bond distances rBeNg, [] and the lowest frequency nmin [cm1] 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
rBeNg
nmin
Be2N2 HeBe2N2 He2Be2N2 NeBe2N2 Ne2Be2N2 ArBe2N2 Ar2Be2N2 KrBe2N2 Kr2Be2N2 XeBe2N2 Xe2Be2N2 RnBe2N2 Rn2Be2N2
C2v Cs C2v Cs C2v Cs C2v Cs C2v Cs C2v Cs C2v
1.2 1.1 1.9 1.8 6.0 5.4 7.7 6.9 9.7 8.7 11.0 10.0
0.4 0.3 1.4 1.3 5.5 5.0 7.2 6.5 9.2 8.4 10.5 9.7
0.8 0.6 1.6 1.4 5.2 4.5 6.6 5.8 8.3 7.3 9.6 8.5
0.7 0.7 1.5 1.4 5.7 5.1 7.3 6.6 9.4 8.4 10.7 9.7
5.2 6.1 4.3 5.2 0.5 1.8 1.2 0.3 3.3 1.7 4.7 3.0
9.17 9.23 10.17 9.21 9.58 9.09 9.02 9.07 8.90 9.02 8.61 8.96 8.38
0.09 0.09 0.06 0.06 0.18 0.17 0.22 0.21 0.26 0.25 0.27 0.26
1.19 1.08 1.09 1.13 1.13 0.99 1.00 0.94 0.96 0.89 0.91 0.88 0.90
0.16 0.16 0.12 0.12 0.32 0.30 0.38 0.36 0.45 0.43 0.47 0.44
1.718 1.715 1.963 1.976 2.192 2.209 2.323 2.337 2.485 2.499 2.550 2.564
406 119 83 94 38 104 33 101 25 99 21 101 17
[a] DCCSD(T) is the dissociation energy [kcal mol1] at the CCSD(T)/def2-QZVPPD//MP2/def2-QZVPPD level.
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Table 2. The dissociation energy De [kcal mol1], ZPE-corrected dissociation energy D0 [kcal mol1] of BeNg bonds for the dissociation process NgnBe3N2 ! Ng + Ngn-1Be3N2, reaction enthalpy DH [kcal mol1] and free energy change DG [kcal mol1] 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 BeNg bonds, BeNg bond distances rBeNg, [] and the lowest frequency nmin [cm1] 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
rBeNg
nmin
Be3N2 HeBe3N2 He2Be3N2 He3Be3N2 NeBe3N2 Ne2Be3N2 Ne3Be3N2 ArBe3N2 Ar2Be3N2 Ar3Be3N2 KrBe3N2 Kr2Be3N2 Kr3Be3N2 XeBe3N2 Xe2Be3N2 Xe3Be3N2 RnBe3N2 Rn2Be3N2 Rn3Be3N2
D3h C2v C2v D3h C2v C2v D3h C2v C2v D3h C2v C2v D3h C2v C2v D3h C2v C2v D3h
1.1 0.9 0.8 1.7 1.5 1.4 6.1 5.4 4.7 7.9 7.0 6.2 10.2 9.1 8.1 11.7 10.5 9.5
0.1 0.1 0.0 1.1 1.0 0.9 5.4 4.8 4.2 7.3 6.5 5.7 9.6 8.6 7.7 11.1 10.0 9.1
1.2 1.0 0.9 1.8 1.7 1.5 5.8 5.0 4.4 7.3 6.4 5.6 9.3 8.1 7.2 10.6 9.4 8.5
0.5 0.4 0.3 1.3 1.1 1.0 5.7 4.9 4.2 7.5 6.5 5.7 9.8 8.6 7.7 11.3 10.1 9.1
5.4 6.0 6.7 4.4 5.1 5.7 0.4 1.7 2.9 1.4 0.0 1.0 3.9 2.2 0.7 5.4 3.7 2.1
8.11 8.34 8.65 9.42 8.27 8.48 8.82 8.26 8.43 8.52 8.26 8.41 8.41 8.26 8.42 8.18 8.22 8.28 7.95
0.10 0.10 0.09 0.07 0.07 0.07 0.20 0.19 0.18 0.24 0.23 0.22 0.30 0.28 0.27 0.31 0.29 0.28
1.14 1.00 1.00 1.01 1.06 1.06 1.06 0.90 0.91 0.91 0.85 0.86 0.87 0.79 0.80 0.81 0.78 0.80 0.81
0.18 0.18 0.17 0.13 0.13 0.12 0.35 0.33 0.32 0.42 0.40 0.38 0.50 0.47 0.45 0.51 0.49 0.46
1.705 1.722 1.740 1.979 1.998 2.020 2.187 2.208 2.231 2.312 2.333 2.356 2.469 2.489 2.510 2.534 2.552 2.572
528 136 99 98 96 41 39 109 36 33 102 27 23 92 20 17 85 15 13
[a] DCCSD(T) is the dissociation energy [kcal mol1] at the CCSD(T)/def2-QZVPPD//MP2/def2-QZVPPD level.
temperature, DG values were calculated at 4 K. The corresponding values (Table S1 in the Supporting Information) show that all Ar- and Kr-binding processes by Be2N2 and Be3N2 clusters become exergonic at 77 K and for the other systems, much lower temperatures are needed. Note that low dissociation energy values and the spontaneity of Ng-binding processes at low temperature (4 K) for He and Ne compounds imply that they are unlikely to be synthesized, although other systems 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 of these compounds. Note that, similar to their parent moieties, all the Ng-bound analogues have high HOMO–LUMO gap values. In NgnBe2N2 clusters, the HOMO–LUMO gap slightly increases for Ng = He and Ne but for the larger Ng analogues it decreases to some extent with respect to that of the Be2N2
cluster; however, in cases of NgnBe3N2 clusters, with the exception 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 triplet having linear structure (C1v), which is 4.6 kcal mol1 more stable than the second-lowest energy singlet Cs isomer (see Figure 3). In the global minimum, the Be center is located in between two N atoms in a linear configuration, hence there is no available binding site for Ng atoms. However, the second isomer is more likely to bind Ng atoms because the Be center possesses a positive charge of + 1.28 e and is available for further coordination by Ng atoms. The Cs isomer of BeSiN2 has even better Ng-binding ability than the Be2N2 and Be3N2 clusters (Table S2). The corresponding dissociation energy values
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 kcal mol1 are also given.
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of NgBeSiN2 clusters are larger than those of NgBe2N2 and NgBe3N2 clusters. All the Ngbinding processes are exothermic in nature; however only Ar– Rn-binding processes are spontaneous at the studied temperature (298 K). The He- and Nebinding events can be exergonic at low temperature (Table S1). However, due to its higherenergy structure, BeSiN2 is less likely to exist in the singlet Cs form. We have also studied the interaction of Ng atoms with the linear global-minimum energy structure of BeSiN2 (Table S3). Low BeNg bond dissociation energies are found in these cases. We would like to highlight that in the presence of an Ng atom, the energy difference between the lowest-energy and the second-lowest-energy isomers gradually decreases from He to Ne and for Ar–Rn the corresponding Ng-bound Cs isomers become more stable than the Ng-bound C1v isomers (Figure 4). Therefore, the presence of Ng atoms can stabilize less stable forms of clusters. 2.3. NPA Charges and WBIs
Figure 4. Optimized structures of NgBeSiN2 clusters studied at the MP2/def2-QZVPPD level. The ZPE-corrected relative energies in kcal mol1 are also given.
NPA reveals that some degree of electron transfer takes place from Ng atoms to positively charged Be centers. The extent of shifting of electron density from Ng to the Be center is low for lighter Ng atoms. However, it is considerably large for heavier Ng atoms, especially Xe and Rn ( 0.3 e). It follows the order Rn > Xe > Kr > Ar > He > Ne (see Tables 1, 2 and S2). Note that the electron shift from Ne is smaller than that from He, although based on the polarizability and ionization energy values, the reverse is expected. Such off-trend behavior of Ne is not new in the literature. To resolve this anomaly, Bent,[37] Scerri,[38] Grochala[10b] and recently Grandinetti[39] argued in favor of moving He to the top of Group 2 in the periodic table. Grandinetti explained the lower reactivity of Ne compared to He: “Neon is bigger than helium, and possesses occupied p orbitals. This is thought to produce less effective electrostatic interactions and higher orbital repulsions, which typically make the neon compounds either unstable or only marginally stable, although the contributions of these factors are still to be further investigated”.[39] In our EDA (see below), in all cases the electrostatic contribution for Ne is higher than that of He. In fact, the lower reactivity of Ne compared to He is a matter of 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
debate. Furthermore, the Be–Ne dissociation values are always higher than those of BeHe bonds, although in our previous study,[13] in a few instances the BeNe bonds had higher dissociation energies than that of He, whereas in others the reverse was true. Therefore, this topic is open for further discussion. In this study, the WBI calculation corresponding to BeNg bonds gives a small value for lighter Ng atoms, and a considerably larger value for heavier analogues. WBIs of BeNg bonds follow the order Rn > Xe > Kr > Ar > He > Ne (see Tables 1–3). These values further indicate that almost a half bond is formed in between Be and Ng atoms for Ng = Xe and Rn. A low WBI provides a hint to the existence of dominant van der Waals type of interaction (this is the case for lighter Ng atoms), however, a large value reveals that some degree of covalent character exists between them (for heavier analogues). 2.4. Electron Density Analysis The different topological parameters computed at the BCPs of BeNg bonds from the electron density analysis[31] are presentChemPhysChem 2014, 15, 2618 – 2625
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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 mol1.[a] System
Fragments
DEtotal
DEelec
DEex
DErep
DEpol + ct
DEdisp
HeBe2N2 NeBe2N2 ArBe2N2 KrBe2N2 XeBe2N2 RnBe2N2
He + Be2N2 Ne + Be2N2 Ar + Be2N2 Kr + Be2N2 Xe + Be2N2 Rn + Be2N2
0.19 1.02 5.17 6.12 7.57 8.22
1.29 (9.5 %) 2.49 (16.8 %) 4.26 (12.6 %) 4.56 (11.7 %) 3.93 (8.8 %) 3.86 (8.3 %)
6.61 (48.5 %) 6.64 (44.8 %) 14.20 (41.9 %) 16.41 (42.3 %) 19.12 (42.9 %) 19.91 (42.7 %)
13.44 13.81 28.70 32.71 36.98 38.37
4.89 (35.9 %) 4.14 (27.9 %) 11.70 (34.5 %) 13.80 (35.5 %) 16.22 (36.4 %) 16.98 (36.4 %)
0.84 1.56 3.72 4.07 5.27 5.85
(6.2 %) (10.5 %) (11.0 %) (10.5 %) (11.8 %) (12.6 %)
HeBe3N2 NeBe3N2 ArBe3N2 KrBe3N2 XeBe3N2 RnBe3N2
He + Be3N2 Ne + Be3N2 Ar + Be3N2 Kr + Be3N2 Xe + Be3N2 Rn + Be3N2
0.61 1.55 5.93 7.08 8.65 9.35
1.23 (9.3 %) 2.15 (15.4 %) 3.97 (11.5 %) 4.24 (10.5 %) 3.80 (8.1 %) 3.75 (7.6 %)
6.37 (48.1 %) 6.05 (43.4 %) 14.47 (41.7 %) 17.11 (42.3 %) 20.37 (43.2 %) 21.33 (43.1 %)
12.64 12.40 28.74 33.36 38.53 40.15
4.79 (36.2 %) 3.85 (27.6 %) 11.69 (33.7 %) 13.99 (34.6 %) 16.55 (35.1 %) 17.30 (34.9 %)
0.86 1.90 4.54 5.10 6.47 7.13
(6.5 %) (13.6 %) (13.1 %) (12.6 %) (13.7 %) (14.4 %)
HeBeSiN2 NeBeSiN2 ArBeSiN2 KrBeSiN2 XeBeSiN2 RnBeSiN2
He + BeSiN2 Ne + BeSiN2 Ar + BeSiN2 Kr + BeSiN2 Xe + BeSiN2 Rn + BeSiN2
1.04 1.94 7.38 8.61 10.45 11.28
1.10 (7.8 %) 2.10 (13.8 %) 2.99 (8.9 %) 2.95 (7.7 %) 2.25 (5.1 %) 2.05 (4.5 %)
6.20 (44.0 %) 6.20 (40.7 %) 12.57 (37.4 %) 14.51 (37.8 %) 16.79 (38.2 %) 17.35 (37.9 %)
13.05 13.29 26.26 29.76 33.50 34.47
6.20 (44.0 %) 5.56 (36.5 %) 14.68 (43.6 %) 17.20 (44.8 %) 19.97 (45.4 %) 20.84 (45.5 %)
0.59 1.37 3.41 3.73 4.93 5.52
(4.2 %) (9.0 %) (10.1 %) (9.7 %) (11.2 %) (12.1 %)
[a] The percentage values within parentheses show the contribution towards the total attractive interaction DEelec + DEex + DEpol + ct + DEdisp.
ed in Table S4. Caution should be exercised with this analysis.[40] Recently, Boggs et al.[41] reported electron density analysis of a series of Ng-loaded clusters to characterize the nature of the interaction. They also considered NgBeO in their study. Based on the outputs of different topological descriptors and the NgBe bond distances being between those of covalent and van der Waals distances, they have introduced two new types of bonding, Wn (weak interaction having noncovalent character) and Wc (weak interaction having some degree of covalent character). In our study, the Ng-binding center is also Be (similar to NgBeO) and the NgBe distances are less than the van der Waals distances but larger than the corresponding covalent distances. Typical NgBe covalent and van der Waals distances can be found in ref. [41]. We have adopted these types to assign the nature of interaction. Table S4 shows that in our study, r21(rc) > 0 and G(rc)/1(rc) > 1; however H(rc) is only negative for Xe and Rn (and consequently G(rc)/V(rc) < 1 for these cases). Therefore, BeXe and BeRn bonds can be considered to be of type Wc and the remaining BeNg (Ng = He– Kr) bonds of type Wn. 2.5. Energy Decomposition Analysis The results of the EDA of these Ng–Be clusters carried out at the CCSD(T)/def2-TZVP level, taking Ng as one fragment and the Be cluster as another, are provided in Table 3. The total interaction energy (DEtotal) is divided into the electrostatic (DEele), exchange (DEex), repulsive (DErep), polarization and charge transfer (DEpol + ct), and dispersion (DEdisp) energy terms. Positive and negative values of DE imply that the interaction terms between two fragments are repulsive and attractive in nature, respectively. Here, DEtotal represents the energy difference between the “supermolecule” and the monomers having the geometries of those in the supermolecule. Of all the attrac 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
tive terms, for NgBe2N2 and NgBe3N2 clusters, DEex contributes the most ( 42–48 %) towards the total attraction energy whereas 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 the largest and the second-largest contributions, respectively, in stabilizing NgBeSiN2 clusters. It is notable that in our previous study, DEpol + ct was more dominant over DEex for NgBeCN2 and NgBeNBO clusters.[13] In such Ng–Be clusters, the relative dominance of DEpol + ct and DEex over each other depends on the positive charges at the Be centers. One Be center having a higher positive charge can behave as a better polarizing center than that possessing a lower positive charge. The charges at Be centers in Be2N2, Be3N2 and BeSiN2 are + 1.19, + 1.14 and + 1.28 e , respectively. Therefore, the Be center in BeSiN2 can polarize the orbitals of Ng atoms to a greater extent than those in Be2N2 and Be3N2 clusters. This makes DEpol + ct a larger contributor than the corresponding DEex term. Owing to the low polarizability values of He and Ne, we have equal contributions from DEpol + ct and DEex in HeBeSiN2 and slightly smaller contribution from DEpol + ct than DEex in NeBeSiN2. Note that in BeCN2 (+ 1.39 e) and BeNBO (+ 1.45 e), the positive charges were also high on the Be centers.[13] The DEele and DEdisp terms contribute towards the total attraction energy, approximately 5–17 % 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 highlights the necessity of taking a proper dispersion correction into account when representing such clusters. From He to Rn, both the repulsive (DErep) and the attractive (DEex, DEpol + ct and DEdisp) terms increase gradually, with the exception of DEpol + ct for Ne, which is always smaller than that of He. This is due to the fact that for Ne donating an electron to the positively charged Be center is less likely than He. Note that in all cases, ChemPhysChem 2014, 15, 2618 – 2625
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CHEMPHYSCHEM ARTICLES the shift of electron density from Ne to Be is smaller than that from He. The DEele term gradually improves from He to Kr but decreases in the case of Xe and Rn. In general, a large DEpol + ct term indicates that the orbitals undergo considerable transformation in their shapes, which is akin to a covalent bond. The high values of DEpol + ct, particularly in the case of Xe and Rn imply that there might be some degree of covalent character in BeXe/Rn bonds (also Be–Kr in KrBeSiN2).
3. Conclusions We have identified the global minimum-energy structures of experimentally achievable Be2N2, Be3N2 and BeSiN2 clusters. The lowest-energy isomer of Be2N2 has a singlet nonplanar C2v structure. Therefore, a different global minimum-energy structure for a Be2N2 cluster was obtained when compared to that reported in a previous study.[23a] Be3N2 has a singlet D3h geometry in which two N atoms reside above and below the triangular Be3 ring. In the case of BeSiN2, the global minimum corresponds to a triplet linear structure in which the Be center is located in between two N atoms. Owing to the high positive charges, the Be center in the global minimum geometries of Be2N2 and Be3N2 clusters can bind Ng atoms. In the linear geometry of BeSiN2, the Be center interacts weakly with Ng atoms due to the absence of an appropriate binding site. However, the second-lowest energy Cs isomer has greater Ng-binding ability compared to Be2N2 and Be3N2 clusters. The presence of Ng atoms reduces the energy difference between the lowestand the second-lowest-energy isomers of a BeSiN2 cluster. In fact, in the presence of Ar–Rn, the Cs isomer becomes more stable than the corresponding linear isomer. All the Ng-binding events are exothermic in nature and become more exothermic on descending Group 18. All the Xe, Rn- and first Kr-binding events at Be2N2 and Be3N2 clusters are exergonic at room temperature, whereas in case of the BeSiN2 cluster, Ar–Rn-binding processes are spontaneous at room temperature. For the remaining systems, lower temperatures are required. The Heand Ne-bound clusters are not promising candidates for synthesis. Electron transfer takes place from Ng atoms to Be centers by approximately 0.3 e for the heavier Ng atoms and less for the lighter analogues. The WBIs for BeXe/Rn bonds are approximately 0.50. Electron density analysis shows that the BeXe/Rn bond can be considered as type Wc, whereas the other BeNg (Ng = He–Kr) bonds can be considered as Wn. EDA suggests that for NgBe2N2 and NgBe3N2 clusters, the term DEex contributes the most ( 42–48 %) towards the total attraction 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 National Fellowship. S.P. thanks CSIR, New Delhi for his fellowship. D.M. thanks Conacyt for the Ph.D. fellowship. Conacyt (Grant INFRA-2013-01-204586) and Moshinsky Foundation supported the 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
www.chemphyschem.org work in Mrida. The CGSTIC (Xiuhcoalt) at Cinvestav is gratefully acknowledged for generous allocation of computational resources. Keywords: bonding · electron density · energy decomposition analysis · HOMO–LUMO gap · noble gas
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Received: March 6, 2014 Revised: April 24, 2014 Published online on May 30, 2014
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