Noble Gas Encapsulated Endohedral Zintl Ions Ng@Pb122â and Ng

Subscriber access provided by UB + Fachbibliothek Chemie | (FU-Bibliothekssystem)

Article 122-

Noble Gas Encapsulated Endohedral Zintl Ions Ng@Pb and Ng@Sn (Ng = He, Ne, Ar, and Kr): A Theoretical Investigation 122-

Pooja Sekhar, Ayan Ghosh, Meenakshi Joshi, and Tapan K. Ghanty J. Phys. Chem. C, Just Accepted Manuscript • Publication Date (Web): 28 Apr 2017 Downloaded from http://pubs.acs.org on April 30, 2017

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

The Journal of Physical Chemistry C is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 53 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

Noble Gas Encapsulated Endohedral Zintl Ions Ng@Pb122 and Ng@Sn122 (Ng = He, Ne, Ar, and Kr): A Theoretical Investigation

Pooja Sekhar†,§, Ayan Ghosh#,‡, Meenakshi Joshi†,‡, and Tapan K. Ghanty†,‡,*

†

Theoretical Chemistry Section, Chemistry Group, Bhabha Atomic Research Centre, Mumbai 400 085, INDIA. #

Laser and Plasma Technology Division, Beam Technology Development Group, Bhabha Atomic Research Centre, Mumbai 400 085, INDIA.

§

Present address: Indian Institute of Science Education and Research Tiruvananthapuram,

CET Campus, Computer Science Building, Sreekaryam, Tiruvananthapuram 695016, Kerala, INDIA. ‡

Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, INDIA.

Page 1 of 53 ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 53

ABSTRACT The stability of the molecular cage clusters formed by noble gas (Ng) encapsulation in negatively charged Zintl ions like Pb122– and Sn122– has been investigated through density functional theory and ab initio molecular dynamics simulation studies. The computed structural parameters, energetics and natural population values along with the simulation results suggest that they are thermodynamically unstable with respect to dissociation into the respective Ng atom and the parent cage; however, most of these endohedral Zintl clusters are kinetically stable. He@Pb122–, He@Sn122–, Ne@Pb122–, Ne@Sn122–, and H2 encapsulated Pb122– and Sn122– clusters preserve their structural integrity throughout the simulation even at 700 K, while Ar@Sn122–, He2@Pb122–, Ar@Pb122– and Kr@Pb122– are found to retain their structures only at lower temperatures of 150 K, 500 K, 500 K and 77 K, respectively. Among all the Ng atom encapsulated clusters, Kr@Sn122– is found to be the least stable as the encapsulated Kr atom comes out from the cage, even at 20 K. These results suggest that the stability of these endohedral clusters is truly dependent on the size of the encapsulated atom. Despite high positive electron affinity values of the Ng atoms, the computed NPA results reveal that they gain electrons when encapsulated in an electron-rich cluster. These meagre negative charges developed on the Ng atoms indicate a weak van der Waals interaction between the noble gas atoms and the cage atoms, thus making plumbaspherene (Pb122–) and stannaspherene (Sn122–) as possible molecular devices to store noble gases. Effect of countercation(s) has been found to be insignificant on the structural parameters and calculated properties of the Ng@Pb122– and Ng@Sn122– Zintl ions. However, it is important to note that unlike the Ng atom encapsulated doubly charged Zintl ions, which are only kinetically stable, K+ salt of the Ng atom encapsulated negatively charged Zintl ions are found to be thermodynamically stable. Therefore, our results would incite further studies into the experimental methods through which these molecular carriers for noble gas atoms can be produced.

*

Author to whom correspondence should be addressed. Telephone: (+) 91-22-25595089;

Fax: (+) 91-22-25505151; Electronic mail: [email protected].


Page 3 of 53 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1. INTRODUCTION It is well known that the Zintl ions of Group 14 and 15 have been considered as incredible chemical systems with unexpected stoichiometries, and intriguing structures leading to a unique and unusual chemical behavior and potential applications. 1 Among them, lead and tin clusters, namely plumbaspherene Pb122– and stannaspherene Sn122– are of considerable interests because of their hollow and spherical nature, high stability and large diameter. It was discovered that plumbaspherene Pb122–

2

and stannaspherene Sn122–

3

form a highly stable

icosahedral cage cluster bonded by four delocalized radial π bonds and nine delocalized onsphere σ bonds from 6p, 6s and 5p, 5s orbitals, respectively. Moreover, Sn122– and Pb122– cage diameters are 6.1 and 6.3 Å, respectively, that are slightly smaller than that of C60 (7.1 Å). This large interior volume of Sn122– and Pb122– cages accounts for the existence of many endohedral clusters analogous to that of fullerenes. Thus the spherically symmetric 26electron systems, plumbaspherene and stannaspherene can be considered as inorganic analogues of fullerenes. In fact, Sn122– and Pb122– cage based several endohedral clusters, 4-18 encapsulating different atom/ion have been investigated experimentally as well as theoretically. Apart from the endohedral Sn122– and Pb122– clusters, in recent years, metal atom/ion encapsulated silicon and germanium clusters have also attracted considerable attention.19-28 After the successful synthesis of the first noble gas compound Xe+[PtF6]– by Bartlett in 1962,29 researchers have developed a keen interest in a new arena named noble gas chemistry. Several novel molecules containing one or more noble gas atoms have been studied to analyze the nature of interaction existing between them.30-38 Confinement has become an important methodology in this direction.39-51 Endohedrally confined noble gas atoms in fullerene cages, Ngn@C60 and Ngn@C70, have been investigated theoretically and experimentally.39,40,52-56 Noble gas atoms have been successfully incorporated into the fullerene cages by employing techniques like ion bombardment,57 high temperature/high pressure methods and ‘molecular surgery’.58 Studies on He@C60 and Ne@C60 by Saunders and co-workers have proposed a “window” mechanism which involves reversible breaking of one or more bonds of the cage resulting in the incorporation of 3He and Ne atoms on heating fullerenes in their presence even though some controversies still exist.39 The presence of encapsulated noble gas atoms in fullerenes have been detected by observing chemical shifts in the helium NMR spectrum of He-labelled C70 species,42,52 mass spectrometric evidence of 129

Xe NMR spectrum40 and by probing the internal magnetic fields inside fullerenes through

the analysis of downfield 3He chemical shifts.55 These experimental evidences instigate the Page 3 of 53 ACS Paragon Plus Environment


Page 4 of 53

preparation of other stable endohedral clusters in a similar fashion. Ng@C60 complexes have also been reported to possess a high activation barrier of 90 kcal mol1 with respect to dissociation.59 It was found that noble gas atoms can be successfully inserted into cavities even smaller than that of C60 like C10H10, C20H20 and Mo6Cl8F6.60-63 Cross and co-workers61 has incorporated helium atom into a smaller cage dodecahedrane, C20H20, even though theoretical studies revealed that He@C20H20 is less stable by 33.8 kcal mol1 with respect to isolated C20H20 and He atom. The correlation between the stability of endohedral clusters and ionization potential of the encapsulated atoms has been established by Moran et al. by introducing a variety of guest atoms inside C4H4, C8H8, C8H14, C10H16, C12H12 and C16H16.64 Recently, Chattaraj and co-workers have studied confinement induced binding of noble gas atoms within magic BN-fullerenes like B12N12 and B16N1643 and

BN doped carbon

65

nanotube. Moreover, Chakraborty and co-workers has founded slightly higher reactivity of noble gas atoms as well as some other guests (C2H2, C2H4, C2H6, CO2, CO, H2, NO2, NO) in their confined state inside the octa acid cavitand.66 Although most of the noble gas encapsulated cages have been found to be thermodynamically unstable, they exist due to their high kinetic stability. Several bonds involving cage atoms must be broken to knock out the Ng atom from any Ng@cage composite system, which results into this high kinetic stability. In addition to the noble gas encapsulation into various cages, movement of small molecules inside a fullerene has also been investigated experimentally in the recent past.67-70 H2, HD and D2 encapsulated C60 clusters have been studied experimentally by Ge et al. by using infrared spectroscopy.71-73 Dynamics of hydrogen molecules trapped inside anisotropic fullerene cages has also been investigated experimentally by using inelastic neutron scattering method.74 Ab initio studies on confinement of noble gas dimers (Ng2) in C60 75 and other cages reveal that NgNg bond distances in Ng2@C60 are shorter than those in free noble gas dimers. Krapp and Frenking46 reported the existence of a real XeXe chemical bond in fullerenes while weak van der Waals interaction has been shown to exist between the lighter analogues, He and Ne. Cerpa et al.47 have identified that shorter He–He interaction does not always imply the existence of a chemical bond. Furthermore, ab initio molecular dynamics studies on Ngn@B12N12 and Ngn@B16N16 showed that He–He dimer undergoes translation, rotation and vibration inside the cavity.43 These theoretical investigations on confinement of noble gas atoms reveal how Ng atoms with completely filled valence orbitals behave when they are forced to confine themselves within a host at its equilibrium geometry. This kind of studies Page 4 of 53 ACS Paragon Plus Environment

Page 5 of 53 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


attracted considerable attention from researchers since noble gas atoms are widely used in gas storage, gas filtration76-78 etc. Apart from ab initio studies, London–type new formulations have been derived to describe the dispersion interaction in endohedral systems like A@B, where the interaction energy is expressed in terms of the properties of the monomers, and applied on several atom/molecule encapsulated C60 systems including Ng@C60 systems.79,80 Discovery of the Zintl ions viz., Pb122– and Sn122– motivate the scientists to investigate the atom encapsulation within these cages. Through experiments as well as theoretical calculations it has been demonstrated that Pb122–

10-18

and Sn122–

4-9

can trap not only alkali,

alkaline earth and rare-earth atoms but also more interesting transition metals. Highly stable 32-electron system of Pu@Pb12 and other actinide encapsulated Pb122 15,16 clusters have also been investigated. In contrast to M@Au12 and encapsulated Ge and Si clusters where dopants are critical in stabilizing cage structures,19-25 M@Pb12 and M@Sn12 derive its stability from the intrinsic stability of parent clusters, Pb122– and Sn122– due to their more aromaticity as compared to Ge122–.26-28 Zintl-like ions composed of only transition metal atoms such as [Ni@Au6]2– and [Ti@Au12]2– have also been proposed recently81 based on the 18-electron rule. All these aspects have motivated us to explore the stability of noble gas encapsulated Pb122– and Sn122– clusters. For a long time noble gases were considered to be highly inert and they were unable to form any chemical compounds, which had been attributed to their closed electronic shell configuration. However, in recent years various compounds involving noble gas atom have been observed. Thus the reactive nature of noble gas atoms has prompted us to predict new Ng–compounds. Moreover, not only the noble gas encapsulated fullerenes but also several new species involving noble gas atoms have been reported from time to time since past decade. For instance, noble gas filled Group 14 clathrates82 (Ngn[M136], Ng=Ar, Kr, Xe and M=Si, Ge, Sn, n=8, 24) have been reported to be stable. Noble gas compounds with main group elements under high pressure (ArLin, XeLin, Ng–Mg, Na2He, Na2HeO etc)83-86 show peculiar chemistry where noble gas atom has been found to be anionic in nature, which is highly counter-intuitive. Surprisingly, under high pressure, noble gas atoms have tendency of accepting electron because of the energy reordering of the atomic orbitals of noble gas atoms and orbitals of the main group atoms. Thus, noble gas atom has been found to become more reactive and acquire high negative charge under high pressure condition.83-86 Apart from fundamental interests on the structure and bonding of noble gas compounds, in recent years, trapping of noble gas atom into various novel materials has attracted considerable attention Page 5 of 53 ACS Paragon Plus Environment


Page 6 of 53

from applications point of view.48,87-90 It may be noted here that the presently investigated host anions (Pb122– and Sn122–) possess highest symmetry, namely, Ih point group (analogous to Buckminsterfullerene, C60). All these aspects made us curious to know whether noble gas atom can be trapped into Pb122– and Sn122– ions resulting into endohedrally encapsulated Zintl ions. To the best of our knowledge, encapsulation of noble gas atoms in negatively charged lead and tin clusters has never been reported before. The present work attempts to explore whether noble gas atoms with high positive electron affinity values can be encapsulated within a negatively charged cluster in its di-anionic state. Therefore, in this paper, the optimized structures, energetics and stability of noble gas encapsulated Pb122– and Sn122– clusters have been investigated through electronic structure calculations as well as ab initio molecular dynamics simulations.91 Molecular dynamics simulation studies has been carried out at different temperatures like 298 K, 500 K etc. to infer the dependence of temperature on the interaction pattern between the concerned atoms and stability of the clusters over the course of time. Moreover, Ng@KPb12–, Ng@KSn12–, Ng@K2Pb12 and Ng@K2Sn12 systems have also been investigated to see the effect of counter ion(s) on the structure and stability of these noble gas encapsulated clusters. 2. COMPUTATIONAL DETAILS In this study, all the theoretical computations including electronic structure optimizations and ab initio molecular dynamics simulations have been performed using TURBOMOLE-6.6 package92 and a hybrid density functional, B3LYP (Becke 3-parameter exchange with LeeYang-Parr correlation),93,94 has been used to describe the exchange and correlation interactions. We have employed def-TZVP basis sets for lighter atoms in our endohedral cluster like He, Ne, Ar, Kr, and H whereas the effective core potential (ECP) along with defTZVP basis set has been utilized for heavier elements like Pb, Sn, and Xe during the calculations.95,96 This combination of basis set is denoted as DEF2 throughout the text unless otherwise mentioned. Initial geometries have been optimized at B3LYP/DEF2 level of theory. The harmonic vibrational frequencies have been calculated with the same level of theory and all real frequency values confirm the minima state of the clusters studied here on their respective potential energy surfaces (PES). The thermodynamic stability of the noble gas encapsulated clusters has been determined based on their binding energy values. It has been calculated according to the equation: BE = – [E(Ng@Pb122–/Ng@Sn122–) – E(Ng) – E(Pb122–/Sn122–)]

(1) Page 6 of 53

ACS Paragon Plus Environment

Page 7 of 53 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Furthermore, natural population analysis (NPA) has been employed to calculate the charges on noble gas and cage atoms. In order to determine the dynamics of the noble gas encapsulated molecular cage clusters of our study, ab initio molecular dynamics simulation has been performed based on Born Oppenheimer molecular dynamics (BOMD) as implemented in TURBOMOLE92 with B3LYP/DEF2 optimized geometries as the starting point. Default random velocity generator in TURBOMOLE has been utilized to generate initial mass-weighted Cartesian velocities based on Boltzmann velocity distribution at a particular temperature. Temperature has been maintained at specific values of 100, 298, 500 and 700 K for finite temperature simulations of clusters using a Nosé-Hoover thermostat for a total simulation time of 5000 fs with a time step of 1 fs. 3. RESULTS AND DISCUSSIONS 3.1. Optimized Geometrical Parameters and Vibrational Frequencies of Ng@Zintl Ions The clusters of our study, Ng@Pb122– and Ng@Sn122–, exhibit icosahedral (Ih) structure similar to their parent clusters while He2@Pb122–, H2@Pb122– and H2@Sn122– exhibit D5d symmetric structure at their respective minima. The pictorial representation for bare Pb122–, Ng encapsulated plumbaspherene Ng@Pb122–, and Ng2 encapsulated plumbaspherene Ng2@Pb122– are shown in Figure 1. Encapsulation of xenon dimers in these clusters is not theoretically possible because their cavity size cannot afford the insertion of a large atom like xenon. Except He2@Pb122–, the optimized geometries obtained after the encapsulation of other noble gas dimers in plumbaspherene are found to be unstable since they exhibit imaginary frequencies. Also, the He2@Sn122– system is found to be unstable at the same computational level. This suggests a greater stability of encapsulated plumbaspherene clusters as compared to those of stannaspherene. This observation may be attributed to the greater cavity size and larger HOMO-LUMO gap in Pb122– as compared to that in the Sn122– cluster. In case of bare Pb122– and Sn122– clusters, the cage diameters are computed to be 6.303 Å and 6.061 Å, respectively, while the size is increased to some extent after noble gas encapsulation. It shows that the cages get distorted slightly while accommodating the noble gas atoms. The computed results reveal that the cage diameter increases in the range of 6.3446.764 Å for Ng@Pb122– and 6.1116.555 Å for Ng@Sn122– as we go from He to Kr. The distortion has been found to be the largest in case of He2@Pb122– with a cage diameter of 6.808 Å (i.e., maximum Pb–Pb distance). The distance between the inserted noble gas atom Page 7 of 53 ACS Paragon Plus Environment


Page 8 of 53

and the cage atom is also found to increase from He to Kr in both the clusters as reported in Table 1. The Ng–Pb distances are found to be 3.172, 3.209, 3.321 and 3.382 Å for He, Ne, Ar and Kr, respectively. It is worth mentioning here that the Pu–Pb distance was reported to be 3.33 Å by Pyykkö and co-workers for the Pu@Pb12 cluster. We have also evaluated the distance between the dopant at the centre and the cage atoms by encapsulating a dummy atom inside Pb122– and Sn122– clusters. As expected, the calculated distances of 3.151 Å and 3.030 Å for Pb122– and Sn122– clusters are found to be lower than the Ng–Pb and Ng–Sn distance values of noble gas encapsulated clusters. A remarkable observation is that the He–He bond length in [He2@Pb12]2– cluster is shorter than that in free He–He dimer as reported in previous papers of Ng2 encapsulated clusters.43,44,65 The B3LYP/DEF2 computed optimized structural parameters for He2@Pb122–, H2@Pb122– and H2@Sn122– clusters are reported in Table 2. Here, the He–He bond distance in [He2@Pb12]2– is observed to be 1.561 Å while that in free helium dimer is 3.852 Å at B3LYP/DEF2 level. For the purpose of comparison, we have optimized the geometries of [He2@Pb12]2– and free helium dimer using PBE functional with DEF2 basis set and the computed values are found to be 1.554 Å and 2.667 Å, respectively. We have also performed electronic structure optimizations of H2@Pb122– and H2@Sn122– clusters at the same computational level. The H–H bond distances in H2@Pb122– and H2@Sn122– are found to be 0.738 Å and 0.739 Å, respectively as compared to the bond length of 0.744 Å in free H2 molecule at the B3LYP/DEF2 level of theory. It indicates that helium atoms come closer to each other on confinement into the Zintl ion cages than that of the hydrogen atoms. Furthermore, the distortion in cage diameter is found to be higher in He2@Pb122– than that in H2@Pb122–, as expected. These results expose the fact that the stability of encapsulated clusters is strongly dependent on the size of the entrapped atom. In this context, it is of interest to compare the H–H and He–He bond lengths in the Zintl ion cages with the corresponding covalent (cov) and van der Waals (vdW) limits following the approach of Gerry and co–workers.33 For an AB bond these are defined as Rcov [= rcov (A) + rcov(B)] and RvdW [= rvdW(A) + rvdW(B)]. Here rcov and rvdW refers to the respective covalent and van der Waals radius of an atom and the terms Rcov and RvdW are the covalent and van der Waals limits, respectively, for the AB bond. Standard values reported in the literature have been taken for these calculations. The covalent97 and van der Waals98 limits of the H bond are 0.64 and 2.40 Å, respectively, while the corresponding Hee bond length values are 0.92 and 2.86 Å considering the single bond radii of the H and He Page 8 of 53 ACS Paragon Plus Environment

Page 9 of 53 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


atoms. On comparison with the B3LYP/DEF2 computed values, it is found that the H bond length (0.738 Å in H2@Pb122– and 0.739 Å in H2@Sn122–) is very close to the covalent limit whereas the Hee bond length (1.561 Å in He2@Pb122–) is in between the covalent and van der Waals limit. Nevertheless, the H bond length in H2 encapsulated Zintl ion cages is even slightly smaller than that in free H2 molecule (0.744 Å) indicating a strong covalent bonding between the H atoms inside the cages. On the other hand, although the Hee bond length in He2@Pb122– are very small as compared to the free helium dimer (3.852 Å), the nature of Hee bonding inside the cages is in between the covalent and van der Waals interactions. To characterize the noble gas and H2 encapsulated Zintl ion clusters further, a harmonic vibrational frequency analysis is performed for all the cage clusters. B3LYP/DEF2 method has been employed to calculate the IR frequency values along with their intensity for the present systems. The vibrational frequency values for bare and Ng encapsulated cage clusters are reported in Table 3 and Table 4 for Pb and Sn cages, respectively, while the Table 5 lists the vibrational frequencies for H2@Pb122–, H2@Sn122– and He2@Pb122– clusters. Now, it is very interesting to compare the H and Hee stretching vibrational frequencies inside the cages with the free H2 molecule and helium dimer, respectively. The H stretching vibrational frequency have been found to be 4380.5 and 4323.9 cm1 for H2@Pb122– and H2@Sn122–, respectively, while the corresponding value in free H2 molecule is slightly higher (4417.1 cm1). On contrary, the Hee stretching vibrational frequency is 1026.9 cm1 for He2@Pb122– whereas the corresponding value in free helium dimer is 31.5 cm1. This trend provides a clear signature of strong interaction playing between the two He atoms inside the plumbaspherene cage as compared to that of the free helium dimer. In this circumstance, it is worthwhile to mention that the frequency values correlate well with the optimized structural parameters. Here it is interesting to compare the experimentally observed red-shift in the IR frequency of the H2 molecule encapsulated inside a C60 cluster. Our calculated red-shift for the H2@Sn122– cluster (93.2 cm–1) is very close to the corresponding experimentally observed shift of 98.8 cm–1 for the H2@C60 system.72 Now it is important to include the dispersion correction term for accurate calculation of the structural parameters and binding energy in the Ng encapsulated Zintl ions. Therefore we have used Grimme’s approach for inclusion of this term (DFT-D3),99 which has been highly successful

100,101

for the description of weakly interacting chemical systems.

Therefore, we have done the optimization of the noble gas atom encapsulated Pb122– and Page 9 of 53 ACS Paragon Plus Environment


Page 10 of 53

Sn122– clusters: Ng@Pb122– and Ng@Sn122– using dispersion corrected B3LYP functional with def-TZVP basis set to take into account the dispersion correction caused by weak interaction between the noble gas atom and the Pb122– / Sn122– cluster. In He@Pb122–, He–Pb and Pb–Pb bond distances are calculated to be 3.175 and 3.339 Å, respectively, which are quite similar to the corresponding He–Pb and Pb–Pb bond length values of 3.172 and 3.335 Å, calculated without employing the dispersion correction. Similarly, in all other noble gas encapsulated Pb122– and Sn122– clusters, Ng–Pb and Ng–Sn bond length values using dispersion corrected B3LYP functional are found to be very close to the Ng–Pb and Ng–Sn bond length values calculated without dispersion correction. All the calculated values of dispersion corrected Ng–Pb and Ng–Sn bond distances are shown in Table 1. Furthermore, we have performed frequency calculations for all the noble gas atom encapsulated Pb122– and Sn122– clusters using dispersion correction D3 method. We found that all the noble gas atom encapsulated clusters are optimized with real frequency values, which represents the icosahedral structure to be true minima structure for all the mentioned clusters. Later on, to check the effect of basis set size on the structural and energetic parameters of Ng@Pb122– and Ng@Sn122– clusters, we have used aug-cc-pVTZ and aug-ccpV(T+d)Z basis sets for noble gas atoms, while for Pb and Sn, we have used aug-cc-pVTZPP basis set. For Ar@Pb122– systems the structural and energetic parameters are calculated to be almost the same for both these basis sets. Therefore we have used only aug-cc-pVTZ (denoted as AVTZ) basis sets for checking the effect of basis set on the structure and properties of these systems. Accordingly, we have calculated all the parameters for noble gas atom encapsulated Pb122– and Sn122– clusters, namely, Ng@Pb122– and Ng@Sn122– systems using large basis set AVTZ. Noble gas atoms encapsulated Pb122– and Sn122– clusters have been optimized in icosahedral geometry with real frequency values using AVTZ basis set. However, we found very small change in Ng–Pb/Ng–Sn and Pb–Pb/Sn–Sn bond length values calculated using large basis set AVTZ with same B3LYP functional. In He@Pb122–, the He–Pb and Pb–Pb bond distances are found to be 3.131 and 3.292 Å, respectively, which are slightly smaller than the corresponding DEF2 level calculated He–Pb and Pb–Pb bond distances of 3.172 and 3.335 Å. Similarly we have observed the similar Ng–Pb/Ng–Sn and Pb–Pb/Sn–Sn bond length trends for other noble gas atom encapsulated clusters as shown in Table 1. 3.2. Energetics and Stabilities of Ng@Zintl Ions


Page 11 of 53 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


The stability of the molecular cage clusters can be inferred from their binding energies and the HOMO-LUMO energy gaps. The calculated values of binding energies or dissociation energies in kcal mol–1 and HOMO-LUMO gap in eV of the clusters of our study at B3LYP/DEF2 level have been reported in Table 1. The negative values of binding energy indicate that the process of encapsulation of noble gas atoms in Pb122– and Sn122– clusters is thermodynamically unfavourable. However, these negatively charged noble gas inserted clusters are kinetically stable, can be prepared and are of significant importance due to their kinetic stability which is more elaborately dealt with in the molecular dynamics section of this paper. The binding energies corresponding to the Eqn.(1) for Ng@Pb122– and Ng@Sn122– clusters are –15.2, –34.6, –107.4, –147.2 kcal mol–1 and –19.5, –43.1, –126.4, –169.8 kcal mol–1, respectively, from He to Kr. These values suggest that the destabilization caused by noble gas encapsulation in Pb122– and Sn122– clusters increases with increase in the size of the noble gas atom. It may be due to the less space available inside the Pb122– and Sn122– cages for the encapsulation of a larger atom like Kr. As reported in the previous papers on noble gas encapsulation, it is imperative to suggest that destabilization originates from distortion in the cages as well as repulsion between electrons of the dopant and the cage atoms, both of which increase with increase in the size of the encapsulated atom. This trend of decrease in dissociation energies of Ng@Pb122– and Ng@Sn122– has been observed to comply well with the increase in the bond lengths of cage atoms (Pb/Sn) along the series He–Ne–Ar–Kr. As mentioned earlier, HOMO-LUMO gap is a good indicator of the electronic stability of the system. It is well known that higher the value of HOMO-LUMO gap, greater is the stability of a system. The computed values of HOMO–LUMO gap are 3.081, 2.825, 2.288, 1.974 eV for Ng@Pb122– and 2.720, 2.617, 2.073, 1.763 eV for Ng@Sn122– along the series He–Ne–Ar–Kr while the corresponding values for bare Pb122– and Sn122– clusters are 3.047 and 2.720 eV, respectively. It has also been found that HOMO-LUMO gap in He@Pb122– is slightly higher than that in the bare Pb122– cluster. It is noteworthy to mention that the calculated values of HOMO-LUMO gap of Ng encapsulated clusters further support our hypothesis that the stability of Ng@Pb122– and Ng@Sn122– clusters is found to reduce with increase in the size of the noble gas atom. The larger binding energies and higher HOMO–LUMO gap values of Ng@Pb122– as compared to that of Ng@Sn122– indicate that noble gas entrapped Pb122– clusters are more stable than the corresponding Sn122– clusters. The dissociation energy and HOMO–LUMO energy gap for He2@Pb122–, H2@Pb122– H2@Sn122– clusters have been reported in the Table 2. He2@Pb122– cluster also maintains quite high HOMO-LUMO gap (2.422 eV), and the dissociation energy with respect to two He Page 11 of 53 ACS Paragon Plus Environment


Page 12 of 53

atoms and bare Pb122– cluster is computed to be –63.4 kcal mol–1 while the corresponding value for H2@Pb122– is found to be –23.4 kcal mol–1, with a HOMO-LUMO gap of 3.079 eV. It indicates that encapsulation of helium dimer in Pb122– cluster results in a less stable product as compared to that of hydrogen dimer in Pb122–. Likewise, lower binding energy and HOMO–LUMO gap values of H2@Sn122– in comparison with H2@Pb122– further reveal the greater stability of H2 encapsulated plumbaspherene than the corresponding stannaspherene. We have found very similar HOMO-LUMO gaps, calculated using dispersion corrected B3LYP functional with def-TZVP basis set. The computed values of HOMO-LUMO gap are 3.073, 2.833, 2.282, 1.968 eV for Ng@Pb122– and 2.714, 2.611, 2.055, 1.762 eV for Ng@Sn122– along the series He–Ne–Ar–Kr. While in bare Pb122– and Sn122– clusters HOMOLUMO gaps are 3.032 and 2.715 eV, respectively. Instead of similar HOMO-LUMO gaps and similar Ng–Pb/Ng–Sn and Pb–Pb/Sn–Sn bond length values, we observe slightly different binding energy in Ng@Pb122– and Ng@Sn122– clusters. Binding energy calculated for Ng@Pb122– and Ng@Sn122– clusters are –11.7, –27.4, –100.4, –139.9 kcal mol–1 and –16.4, – 36.7, –119.1, –161.7 kcal mol–1, respectively, from He to Kr. HOMO-LUMO gaps and binding energy calculated using Dispersion corrected D3 method are given in Table 1. Furthermore, we have used aug-cc-pVTZ basis sets (AVTZ) to check the effect of basis set size on energetic parameters of Ng@Pb122– and Ng@Sn122– clusters. Using, AVTZ basis set with B3LYP functional we have found slightly smaller HOMO-LUMO gaps in Ng@Pb122– and Ng@Sn122– clusters, except in Sn122–, He@Sn122– and Ne@Sn122– clusters. The calculated values of HOMO-LUMO gaps are found to be 2.821, 2.585, 2.067,1.755 eV for Ng@Pb122– and 2.767, 2.657, 2.062, 1.734 eV for Ng@Sn122– along the series He–Ne–Ar–Kr while for bare Pb122– and Sn122– clusters calculated values of HOMO-LUMO gaps are 2.767 and 2.771 eV, respectively. Similarly the calculated values of binding energies using AVTZ basis set for He and Ng encapsulated clusters are very close to the def-TZVP basis set calculated binding energy values. The binding energy calculated for Ng@Pb122– and Ng@Sn122– clusters are –16.1, –36.4, –108.2 and –147.4 kcal mol–1 and –20.3, –46.6, –131.9 and –176.8 kcal mol–1, respectively, from He to Kr. The values of HOMO–LUMO gaps and binding energy calculated using AVTZ basis set with B3LYP functional are reported in Table 1. 3.3. Natural Population Analysis (NPA) of Ng@Zintl Ions Charge distribution in the charged clusters is found to be quite different from that of neutral ones. In contrary to the previous studies on noble gas encapsulation in neutral and positively Page 12 of 53 ACS Paragon Plus Environment

Page 13 of 53 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


charged clusters, here the encapsulated noble gas atom develops slightly negative charge. This implies that the negative (2) charge of the bare cluster is being shared by the Ng atoms via electron transfer from the cage atoms to the Ng atoms. The computed net NPA charges on encapsulated noble gas atoms have been reported in Table 1. The charges acquired by the Ng atoms are found to be –0.028, –0.024, –0.021 and –0.024 for He, Ne, Ar, and Kr, respectively, in Ng@Pb122– while the corresponding values are –0.027, –0.024, –0.020, – 0.022 in Ng@Sn122– along the series He–Ne–Ar–Kr. These values clearly reveal that the noble gas atom acquire small negative charge irrespective of the nature of the Ng atom or the cage atoms. This finding is in contrast to the earlier works where the Ng@cage has been charge neutral. Electron transfer from Pb/Sn atom to the Ng atom decreases from He–Ar except Kr as expected from their increasing positive electron affinity values. Earlier works on encapsulation in clusters have established the fact that the interaction between the dopant and the cage atoms increases with increase in the size of the encapsulated atom. This holds true in our case also since the shared electron density values are found to be the maximum for Kr–Pb and Kr–Sn among all Ng–Pb and Ng–Sn bonds. However, it is to be noted that here Kr develops negative charge whose magnitude is similar to that of Ne in both Ng@Pb122– and Ng@Sn122– clusters. This may be attributed to the high polarizability of Kr atom due to its large size. Correspondingly, the negative charges on the cage atoms vary from He–Kr encapsulated clusters and their absolute charges are found to be less as compared to that in the empty cages. It is observed that Ng atoms inserted into Pb122– clusters develop slightly more negative charge than those in Ng@Sn122– although the cage diameter of Sn122– is less as compared to that of Pb122– and the fact that atoms in a smaller cavity are supposed to interact more strongly. The observed result may be due to the more electropositive nature of Pb in comparison with Sn. The computed NPA values further support our previous conclusion that the noble encapsulated Pb122– clusters are more stable than the corresponding Sn122– ones. In this context we have also analyzed the charge distribution on H2@Pb122–, H2@Sn122–, and He2@Pb122– clusters as reported in the Table 2. The calculated NPA charge on each He atom in He2@Pb122– is –0.022 whereas that on each H atom in H2@Pb122– is found to be – 0.057. The individual NPA charges and shared electron density values suggest more electron transfer from Pb to H atoms than to He atoms in He2@Pb122– which in turn reflects strong interaction and more stable nature of H2@Pb122–as compared to He2@Pb122–. As expected from the smaller cavity size of Sn122– clusters, the H atoms on H2@Sn122– develop more Page 13 of 53 ACS Paragon Plus Environment


Page 14 of 53

negative charge than that in H2@Pb122– indicating stronger interaction between H and Sn atoms in H2@Sn122– than the corresponding atoms in H2@Pb122–. The shared electron density values of 1.213 for H–H in H2@Pb122– and 1.113 for H–H in H2@Sn122– suggest strong covalent kind of interaction between the two hydrogen atoms in these clusters. However, feeble negative charges developed on the Ng atoms imply a weak van der Waals interaction between the encapsulated noble gas atom and the cage atoms. Thus, through this work we have established the fact that noble gas on confinement in electron rich species can gain electrons in spite of their positive electron affinity values. Very recently it has been shown that the noble gas atom can acquire negative charge in various Ng compounds with main group elements under high pressure (ArLin, XeLin, Ng–Mg, Na2He and Na2HeO etc)83-86 Therefore, effect of high pressure is somewhat similar to the confinement effect in the present work as far as charge distribution is concerned. 3.4. Molecular Orbital Ordering of Ng@Zintl Ions The molecular orbital energy diagrams for Pb122–, Ng@Pb122– and Sn122–, Ng@Sn122– are represented in Figure 2 and Figure 3, respectively, as obtained by using B3LYP/DEF2 level of theory and Turbomole program. The symmetry of the HOMO and LUMO for bare plumbaspherene has been found to be t1u and gg molecular orbitals (MOs), respectively. On the other hand for the bare stannaspherene the corresponding MOs are hg and gg, although the energy difference between the t1u and hg orbitals are negligibly small. Similar to the Pb122– cluster, the HOMO and LUMO in all the Ng@Pb122– systems are found to be the t1u and gg orbitals. However, for the Ng@Sn122– systems the HOMO-LUMO ordering does not remain the same. Similar to the bare Sn122– system, the hg MO is found to be the HOMO in the He@Sn122– cluster; on the other hand, the t1u MO is found to be the HOMO for the other Ng@Sn122– systems. As mentioned, the t1u and hg MOs are almost degenerate in the cases of Pb122– and He@Pb122– systems, and the energy gap between these two MOs is found to increase gradually in going from He to Kr since the hg MO is stabilized more and more in going from He to Kr. The energy of the HOMO is almost the same for all the Ng@Pb122– systems including the bare Pb122– cluster. Similar to the hg MO, the LUMO (gg) is found to be stabilized in going from He to Kr. As a result, the HOMO–LUMO gap is decreased in going from He@Pb122– to Kr@Pb122– cluster. Similar trends are found in the case of Ng@Sn122– systems. Nevertheless, it is to be emphasized here that the HOMO and LUMO state may vary from one cluster to another depending on the encapsulated species into the respective plumbaspherene and stannaspherene cages. Page 14 of 53 ACS Paragon Plus Environment

Page 15 of 53 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


3.5. Density of States of Ng@Zintl Ions The density of states (DOS) of bare Pb122– and Sn122– cages and their noble gas and hydrogen molecule entrapped clusters are plotted in Figure 4 and Figure S1 (in the Supporting Information), respectively. A profound band structure is observed around 0.00 eV (Relative energy of HOMO) in both Pb122– and Sn122– corresponding to their valence orbitals 6p and 5p, respectively. Similar band structure is observed in all the noble gas encapsulated clusters excluding some differences. The curves for Pb122–, He@Pb122– and Sn122–, He@Sn122– are very similar with their peaks coinciding whereas for the neon inserted ones the DOS is slightly shifted deeper in energy although the peak positions almost remain the same. In case of Ar@Pb122–, Ar@Sn122–, Kr@Pb122–, and Kr@Sn122– more energy levels are seen to be profound as compared to its lower analogues and DOS is shifted more deeply in energy. It is observed that larger the atomic radius of the encapsulated atom, extent of shift is more for the occupied levels. Similar to the He@Pb122– system, the DOS plot for the H2@Pb122– system remains almost the same as in the bare Pb122– cluster. Moreover, the density of states plot of He2@Pb122– is found to be similar to that of Ar@Pb122– in terms of the number of occupied energy levels near HOMO as well as the shift in the energy levels. All the DOS results clearly indicate that the extent of increase of cage size is increased with the increase in the size of the encapsulated atom/molecule, which in turn modifies energies of different MOs. These results also indicate that the interaction between the cage atoms and Ng atoms becomes stronger as the size of Ng atom increases. 3.6. Ab initio Molecular Dynamics Simulation of Ng@Zintl Ions In order to determine the kinetic stability and dynamical behaviour of the aforementioned clusters, ab initio molecular dynamics simulation has been carried out at 298 and 500 K, and their trajectories have been analyzed for 5 ps. The average Pb–Pb/Sn–Sn and Ng–Pb/Ng–Sn distances have been computed for a better analysis of these simulations. The time evolution of total energies of Ng@Pb122– and Ng@Sn122– clusters have been depicted in Figures S2 and S3 in the Supporting Information. The variation in average bond distances are presented in Figure 5 for Pb–Pb bond and Figure 6 for Ng–Pb bond for the Ng@Pb122– cluster while the corresponding Sn–Sn and Ng–Sn bond distances for the Ng@Sn122– cluster are represented in Figure S4 and Figure S5 (Supporting Information), respectively. The variation in these parameters with respect to time gives an idea about the distortion caused by the interaction between the encapsulated atoms and the cage as well as the forces at play inside the cage. The interplay between the internal force stabilizing the system and centrifugal force inflating the Page 15 of 53 ACS Paragon Plus Environment


Page 16 of 53

cage determines the stability of encapsulated clusters. It is observed that total energies and average Pb–Pb/Sn–Sn and Ng–Pb/Ng–Sn distances oscillate around a mean value depending on the temperature that is maintained during the simulation. These oscillations are assumed to have resulted from the increase in nuclear kinetic energies as the noble gas atom approaches the wall of the cage which causes distortion in Pb122–/Sn122– cluster producing higher energy structures. It is evident from the plots that both the fluctuations and the average values of total energy and bond distances increase with rise in temperature. This may be due to the fact that kinetic energy increases with temperature which causes larger amplitudes in stretching and compression modes of vibration in bonds resulting in larger bond lengths and total energy. For a better understanding of the temperature dependence on the stability of the cage clusters, we have performed MD simulations at higher temperature (700 K) as well as lower temperatures (50, 77, 100, and 150 K). Throughout the simulation, He and Ne atoms and H2 remain within the cavity of the cages concerned and the structural integrity of the cages are retained, except for the loss of symmetry, even at a temperature as high as 700 K. This reveals the high stability of these encapsulated clusters. However, fluctuations in the average Ng–Pb/Ng–Sn and Pb–Pb/Sn–Sn distances are found to be larger for He encapsulated clusters as compared to other Ng entrapped ones as shown in Figure 5 and 6 and Figures S2–S6. It is due to smaller mass of the helium atom and the larger space available inside the cage for this atom resulting in its higher degree of movement. Ar@Pb122–, Ar@Sn122–, Kr@Pb122–, and Kr@Sn122– clusters are found to be less stable. It is observed that Ar@Pb122– cluster fragments at high temperature of 700 K as argon atom emerges out of the cage. However, Ar@Sn122– cluster fragments in the course of MD simulation at 298 K and 500 K and is stable only at lower temperatures like 150 K and 100 K. The Kr encapsulated clusters are found to be even less stable. Krypton atom is observed to emerge out of Sn122– cage through “window” mechanism as reported in fullerenes,39 even at 20 K indicating its very low stability whereas Kr@Pb122– cluster retains its structure at 77 K. It is also interesting to note that the Ng atoms come out of the distorted cage in a shorter time during simulation at higher temperatures. Here, on analyzing the simulation of Kr@Pb122– at 100 K, it is observed that one of the triangular faces of the cage gets distorted as Kr approaches that part of the wall of the cage. These results demonstrate that the stable clusters exist at least kinetically even if they are thermodynamically unstable. The simulation results have been observed to be in good agreement with the geometrical parameters and energetics data. This further confirms the better stability of Ng@Pb122– over Ng@Sn122– clusters. Page 16 of 53 ACS Paragon Plus Environment

Page 17 of 53 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


In addition to the Ng atom encapsulated clusters, we have also performed simulations for the He2@Pb122–and H2@Pb122– clusters. The He2@Pb122– cluster has been observed to retain its structure at temperatures as high as 500 K as shown in the Figure S6 in the Supporting Information whereas at 700 K both He atoms remain enclosed within the cage only for duration of approximately 3970 fs after which one of the He atoms leave the cage producing a large local minimum on the energy surface. For the purpose of comparison, we have analyzed the simulation of He2@Pb122–, H2@Pb122–, and H2@Sn122– clusters and the average bond distances with respect to time have been depicted in Figure 5 and Figures S2S4 and S6 in the Supporting Information. It is clear that the oscillations in this parameter is present for dimer encapsulated clusters also and the amplitude of vibration of H–H/He–He and X–Pb/X–Sn (where X = H/He) distances get enhanced with rise in temperature. In the graphs of average He–He distance vs time (Figure S6 in the Supporting Information), no abrupt peaks are observed. It indicates that He–He dimer inside Pb122– undergoes only usual processes of stretching and compression. From this, we can infer the existence of some sort of bonding between the two He atoms inside the cage. Therefore, we can conclude from these results that the formation and kinetic stability of the aforementioned Ng encapsulated clusters primarily depend on the size of the encapsulated moiety. A glimpse of the MD simulations for the noble gas and hydrogen molecule encapsulated Zintl ion clusters is further obtained by noting the snapshots at different times during the simulation. Therefore, we have provided the snapshots at 0, 100, 500, 1000, 1500, 2000, 2500, and 3000 fs at 50 K of temperature for Kr@Pb122– cluster and at 298 K for other Ng@Pb122– clusters as depicted in Figures S7–S13 in the Supporting Information. 3.7. Electron Density Analysis of Ng@Zintl Ions Following Bader’s quantum theory of atomsinmolecules (QTAIM), 102 we have carried out the electron density analysis to get a better understanding of the nature of interaction between the noble gas atom and the cage atoms as well as between the two trapped gas atoms in the noble gas encapsulated plumbaspherene and stannaspherene cage clusters. The electron density based topological properties viz., electron density [], Laplacian of the electron density [2], the local kinetic energy density [G(r)], the local potential energy density [V(r)], the local energy density [Ed], and the ratio of electron kinetic energy density and electron density [G(r)/] have been reported in Table 6 and Table 7 for Pb and Sn clusters, respectively. At the bond critical point (BCP), the negative and positive values of 2(rc) are Page 17 of 53 ACS Paragon Plus Environment


Page 18 of 53

related to the concentration and depletion of electron density, respectively. In general, a high value of (rc) and negative value of 2(rc) at the BCP emphasize the covalent interaction whereas a low value of (rc) and positive values of 2(rc) represent a “closed–shell type bonding”. In the present cases, all the bonds are associated with low value of (rc) and positive value of 2(rc) indicating the closed-shell type bonding, except the HH bond in both H2@Pb122 and H2@Sn122 clusters, which is covalent in nature. According to Boggs and co-workers,103 the “Type C” and “Type D” bonds, which are associated with a small amount of covalent characteristics, have to satisfy the criteria [Ed(rc) < 0; G(rc)/(rc) < 1] and [|Ed(rc)| < 0.005; G(rc)/(rc) < 1], respectively, at their corresponding BCPs. From the results it has been found that the PbPb and SnSn bonds are combination of “Type C” and “Type D” bonds in all the presently studied clusters while the NgPb and NgSn bonds are considered as “Type D” bond in case of all Ng encapsulated Zintl ion clusters. Therefore, it is evident that the PbPb and SnSn bonds are associated with a comparatively higher degree of covalency as compared to that of the corresponding NgPb and NgSn bonds. In case of H2 trapped Pb122 and Sn122 cage clusters, the corresponding HPb and HSn bonds are found to be “Type D” covalent bonds, while the HH bond is of “Type A” covalent bond fulfilling the condition [2(rc) < 0; (rc) > 0.1 au] in both the H2@Pb122 and H2@Sn122. On the contrary in case of He2@Pb122 cluster, the HePb bond can be attributed to “Type D” covalent bond whereas the HeHe bond can be assigned to be a “Wn” type bond, which is due to weak interactions with some noncovalent properties. Here it may be noted that Ng–Sn and Ng–Pb bonds are noncovalent bond of “Type C” with the positive value of 2 in FNgSnF3 , FNgPbF3, FNgSnF and FNgPbF systems as reported by Chattaraj and co-workers104 recently, while in our systems, Ng–Sn and Ng–Pb bonds are comparatively weaker noncovalent bond of “Type D” with a positive value of 2. Electron localization function (ELF)105 is another very important parameter to find out the nature of bonding that exists in between the constituent atoms of the concerned molecular systems. It is worthwhile to mention that a high value of ELF indicates the presence of localized electrons in between the bonding atoms which in turn implies the existence of covalent bonds. On the contrary, a low value of ELF signifies a noncovalent interaction between the constituent atoms. The color-filled maps of ELF for H2@Pb122, H2@Sn122, and He2@Pb122 clusters are depicted in Figure S14 (Supporting Information). It is clearly evident from the figure that there is maximum electron localization between the H Page 18 of 53 ACS Paragon Plus Environment

Page 19 of 53 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


atoms in both the H2@Pb122 and H2@Sn122 clusters while almost no electron localization has been found in between the He atoms in He2@Pb122 cluster. The BCP parameters as well as the ELF maps clearly indicate the existence of closed-shell type bonding in between two He atoms or in between He and cage Pb atoms. Therefore, we can emphasize that the bonding between the H atoms bear strong covalent character while the nature of bonding between the He atoms are of noncovalent type, which correlates well with the HH and HeHe bond length values. 3.8. Effect of Counter ion on the Structure and Properties of Ng@Pb122– and Ng@Sn122– clusters Experimentally it may be difficult to investigate the doubly negative charged Ng@Pb122– and Ng@Sn122– clusters because of increase in the electron-electron repulsion. Therefore, we have used alkali metal cation as the counter ion for balancing the excess electrons and investigated the structure and properties of anionic Ng@MPb12– and Ng@MSn12– and neutral Ng@M2Pb12 and Ng@M2Sn12 clusters (M=Li and K). The structures of these systems are depicted in Figure 7. It has been found that the Ih structure of LiPb12– and LiSn12– anions, where Li occupies the centre of the icosahedron, is the most stable one. On the other hand, in the KPb12– and KSn12– anions, the K+ ion at the exohedral position with C3v symmetry is the most stable one, where the K+ ion is placed on the triangular face of the icosahedron. Here it may be noted that the KPb12– and KSn12– species have been investigated experimentally2,3 correspond to the C3v structure, as reported earlier2,3 and also obtained by us. Similarly, in the case of Li2Pb12 and Li2Sn12 clusters, the most stable structure corresponds to the one with one Li+ ion occupying the center of the icosahedron cage. In contrast, both the K+ ion are found to occupy the exohedral position in the most stable structure of K2Pb12 and K2Sn12 clusters, where two K+ ions are placed at each of the opposite triangular face of the icosahedron resulting into D3d symmetry. Here it may be noted that the higher energy C5v and D5d structures (Figure 7) are associated with imaginary frequency. Therefore, it is clear that endohedral encapsulation of an Ng atom is not possible within the LiPb12–, LiSn12–, Li2Pb12 and Li2Sn12 cages. Accordingly, we have investigated the Ng encapsulated structures of KPb12–, KSn12–, K2Pb12 and K2Sn12 clusters, and the results are reported in Table 8. The addition of K+ ion(s) does not lead to any significant change in the Pb–Pb or Sn–Sn bond length. However, slightly smaller HOMO-LUMO gaps have been found after the addition of K+ ion (s) in the Ng@Pb122– and Ng@Sn122– clusters. Charge on the K atom in these clusters Page 19 of 53 ACS Paragon Plus Environment


Page 20 of 53

are found to be in the range of 0.80–0.87 and 0.91–0.94 for the mono–potassium and di– potassium clusters, indicating that all these clusters can best be described as [K+Ng@M122–]– and [2K+Ng@M122–]. It is important to note that the calculated binding energy values reported in Table 8 are found to be positive, which indicate that the K+ ion(s) stabilized noble gas encapsulated Zintl clusters are thermodynamically stable. It is in contrast to the Ng encapsulated bare Zintl ions. 3.9 Energy Decomposition Analysis Energy decomposition analysis (EDA) is a very powerful method for analyzing the intermolecular interaction in any system using either Hartree–Fock method or density functional theory. To know the nature of interaction between the Ng atom and the host cluster (Pb122/Sn122) in Ng@Pb122 and Ng@Sn122 systems, we have performed energy decomposition analysis as implemented in GAMESS106 by Su and Li 107 using B3LYP/DEF2 level of theory including dispersion interaction. For EDA calculations, clusters have been considered to dissociate into two fragments namely, Ng atom and Pb122/ Sn122 cluster, and the interaction energy is decomposed into electrostatic, exchange, repulsion, polarization and dispersion terms. Thus, decomposition energy can be expressed as ∆E= ∆Eele + ∆Eex + ∆Erep + ∆Epol +∆Edisp. The energy terms, ∆Eele, ∆Eex , ∆Epol and ∆Edisp are all attractive in nature while, ∆Erep term is repulsive in nature. The percentage contribution of the attractive energy term, ∆Eele to the total attractive interaction has been found to be 21.5, 35.5, 37.1, 37.4, 21.8 and 22.9 for the Ng@Pb122 systems (Ng= He, Ne, Ar, Kr), and the He2@Pb122 and H2@Pb122 systems, respectively while the same has been found to be 23.4, 38.5, 40.4,40.3, 22.6 for the corresponding Sn122 systems. However, in all these systems, the percentage of the exchange term is higher and in the range of 41.4 – 45.0 and 41.9–42.7. Very small percentage contribution has been found for the polarization and dispersion terms as shown in Table 9. Among all terms, the repulsive term has been found to be most dominating term that makes the overall interaction energy to be repulsive in nature as reported in Table 9. Thus, the larger repulsion between the noble gas atom and the cluster leads to thermodynamically unstable noble gas atom encapsulated Zintl ions. Furthermore, all energy terms are found to increase with the size of noble gas atom. However, we have found tremendous increase in the repulsive term (∆Erep ) as compared to increase in attractive energy terms (∆Eele, ∆Eex, ∆Epol and ∆Edisp taken together). Consequently, large size Ng atom encapsulated systems are found to be more unstable. All Page 20 of 53 ACS Paragon Plus Environment

Page 21 of 53 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


the calculated energy terms for Ng@Pb122 and Ng@Sn122 system and their corresponding percentage contribution (given in square brackets) and basis set superposition error (BSSE) corrected energies (given in parenthesis) are reported in Table 9. Subsequently, we have done the energy decomposition analysis for the Ng@KPb12, Ng@KSn12, Ng@K2Pb12 and Ng@K2Pb12 systems. For the EDA calculation, chosen fragments are Ng atom, K+ ion and Pb122 or Sn122 cluster. In Ng@KPb12 and Ng@KSn12 clusters, the ∆Eele term has percentage contribution of 67.5, 63.8, 59 and 64.9, 61.8, 51.1, respectively, in the total attractive interaction energy of the systems along the series, He–Ne– Ar. Unlike Ng@Pb122 and Ng@Sn122 systems, in Ng@K2Pb12 and Ng@K2Pb12 systems percentage contribution from the ∆Eele term has been found to be tremendously higher with percentage contributions of 76.5, 73.2 and 64.8 in Ng@K2Pb12 systems, and 74.9, 71.5 and 63.0 in Ng@K2Pb12 systems along He–Ne–Ar series. Besides, repulsive term (∆Erep) is found to be smaller as compared to the attractive term (∆Eele), in Ng@KPb12, Ng@KSn12 , Ng@K2Pb12 and Ng@K2Pb12 systems. In all the systems the ∆Eele is the most negative, therefore, makes the overall energy of the system to be attractive in nature. However, with increase in the size of noble gas atom, we have found significant decrease in percent contribution from ∆Eele terms, which in turn reduces the attractive interaction between the large size noble gas atom and the Zintl ions. Therefore, large size noble gas encapsulated Zintl ion clusters are found to be less stable as compared to the small size noble gas atom encapsulated Zintl ion clusters. All the calculated energy term for Ng@KPb12, Ng@KSn12, Ng@K2Pb12 and Ng@K2Sn12 systems and their corresponding percentage contribution (shown in square brackets) and BSSE corrected energies (given in parenthesis) are reported in Table 10. Moreover, to know the nature of chemical bonding between NgPb/NgSn, PbPb/SnSn and KPb/KSn, we have also calculated the bond critical properties for Ng@KPb12–, Ng@KSn12–, Ng@K2Pb12 and Ng@K2Sn12 systems. In Ng@KPb12– and Ng@KSn12– systems Pb–Pb/Sn–Sn bonding are of “Type C” and “Type D” with Ed(rc) < 0; G(rc)/(rc) < 1, while Ng–Pb/Ng–Sn chemical bonding are of “D Type” with |Ed(rc)| < 0.005; G(rc)/(rc) < 1 , analogous to the same in the Ng@Pb122– and Ng@Sn122– systems. Also, the K–Pb/K–Sn bonding is of “D Type”. Similar bonding trends are found in the Ng@K2Pb12 and Ng@K2Sn12 clusters. All the BCP properties of the K+ ion stabilized noble gas atom encapsulated clusters are reported in Tables S1–S4 in the Supporting Information.



Page 22 of 53

3.10. Energy Barrier Calculation Energy barrier provides an important aspect regarding the kinetic stability of clusters. We have calculated energy barrier for the He–encapsulated clusters namely He@Pb122–, He@Sn122–, He@KPb12–, He@KSn12–, He@K2Pb12 and He@K2Sn12 by moving the He atom from its equilibrium position to outside the cage through the triangular face of the C3V and D3d structures for the mono- and di-potassium cases, respectively. Naturally, when the He atom is located at the surface, the energy of the system attains its maximum value, and the difference between this energy and the energy corresponding to the He atom encapsulated equilibrium geometry can be considered as the approximate energy barrier. The calculated value of energy barrier are 141.6, 138.6, 134.5, 139.6, 141.3 and 150.2 kcal mol1 for He@Pb122–, He@Sn122–, He@KPb12–, He@KSn12–, He@K2Pb12 and He@K2Sn12 clusters respectively. Thus, all the He–encapsulated clusters are found to be kinetically stable because of very high energy barrier. Therefore, once the He-encapsulated clusters are formed, they cannot dissociate into its fragments due to the very high energy barrier. The barrier height will be even larger for other Ng encapsulated clusters because of the larger size of the Ng atom. 4. CONCLUSION In a nutshell, we have predicted the theoretical existence and kinetic stability of noble gas encapsulated plumbaspherene and stannaspherene cage clusters, Ng@Pb122– and Ng@Sn122– through systematic calculations of the electronic structure optimization and ab initio molecular dynamics simulation. Similar to the bare Pb122– and Sn122– clusters, the Ng encapsulated analogues are also found to maintain comparable HOMO-LUMO energy gap values revealing their electronic stability. Structural parameters, calculated at B3LYP/AVTZ level and dispersion corrected B3LYP/DEF2 level, are found to be in good agreement with the B3LYP/DEF2 level calculated parameters. Moreover, we have also predicted the structural parameters corresponding to the counter ion containing Ng@KPb12–, Ng@KSn12–, Ng@K2Pb12 and Ng@K2Sn12 systems, which are found to be very similar with the structural parameters of Ng@Pb122– and Ng@Sn122– systems and are found to be bonded by weak noncovalent type of interaction similar to Ng@Pb122– and Ng@Sn122– systems. The possible existence of He2@Pb122– has also been established through the DFT and ab initio MD simulation based techniques. The basic concept that noble gas atoms with highly positive Page 22 of 53 ACS Paragon Plus Environment

Page 23 of 53 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


electron affinity values cannot gain electrons, is not obeyed here since Ng atoms in the present systems develop small negative charge via electron transfer from Pb/Sn atoms to the Ng atom. The computed values of structural parameters, energetics and natural population analysis suggest the existence of a weak van der Waals interaction between the Ng and the cage atoms. Ab initio molecular dynamics simulation shows that He, Ne, and H2 encapsulated Pb122– and Sn122– clusters remain intact up to 5000 fs even at temperatures as high as 700 K. However, Kr@Sn122– cluster is found to fragment at 20 K itself while Kr@Pb122–, Ar@Pb122–, Ar@Sn122– and He2@Pb122– are found to retain their structures at 77 K, 500 K, 150 K, and 500 K, respectively. The fact that encapsulated atoms with larger atomic radii distort the cage to a greater extent has been established through geometrical parameters and simulation data. EDA has revealed that in all the Ng encapsulated clusters, repulsive term is more predominant as compared to the attractive terms, except in Ng@KPb12–, Ng@KSn12–, Ng@K2Pb12 and Ng@K2Sn12 systems. Furthermore, very high energy barrier has been observed for He@Pb122–, He@Sn122–, He@KPb12–, He@KSn12–, He@K2Pb12 and He@K2Sn12 systems. All these findings indicate that although the Ng encapsulated dianionic cage clusters are thermodynamically unstable with respect to dissociation into noble gas atoms, they are kinetically stable. Nevertheless, Ng@KPb12–, Ng@KSn12–, Ng@K2Pb12 and Ng@K2Sn12 systems are found to be kinetically as well as thermodynamically stable. The insertion of noble gas atoms into C60 fullerenes and synthesis of He@C20H20 have already been reported.58,60 Experimental observations2,3 of KPb12– and KSn12– and very recent experimental preparations85 of noble gas compounds with main group elements under high pressure along with recent theoretical investigations82–84 suggest that it might be possible to identify the alkali metal cation stabilized endohedral noble gas encapsulated Zintl ions experimentally. Our present work will encourage further studies towards the possible realization of Ng@Pb122– and Ng@Sn122– clusters experimentally, analogous to noble gas atom encapsulated fullerenes and related systems. Supporting Information The variation of density of states (DOS) as a function of orbital energies for Ng@Sn122−, total energy with respect to time at different temperatures of Ng encapsulated Pb122− and Sn122− clusters (Figures S1S3). The average SnSn and NgSn bond distances in Ng@Sn122− and average HeHe bond distances in He2@Pb122− with respect to time at different temperatures during the course of MD simulation (Figures S4S6). The MD simulated snapshots at Page 23 of 53 ACS Paragon Plus Environment


Page 24 of 53

different time scale at a particular temperature for noble gas and hydrogen molecule encapsulated Pb clusters (Figures S7S13). The color–filled ELF maps for H2@Pb122, H2@Sn122, and He2@Pb122 clusters (Figure S14). BCP properties of Ng@KSn12–, Ng@KPb12–, Ng@K2Sn12, Ng@K2Pb12 (Tables S1-S4) This material is available free of charge via the Internet at http://pubs.acs.org.

ACKNOWLEDGMENTS The authors gratefully acknowledge the generous support provided by their host institution, Bhabha Atomic Research Centre, Mumbai. The authors would like to thank the Computer Division, Bhabha Atomic Research Centre for providing computational facilities. P.S. gratefully acknowledges the support of NIUS (HBCSE−TIFR, Mumbai). M.J. would like to thank Homi Bhabha National Institute for the Ph.D. fellowship in Chemical Sciences. It is a pleasure to thank Dr. A. K. Nayak and Shri R. K. Rajawat for their kind interest and continuous encouragements.

REFERENCES 1. Scharfe, S.; Kraus, F.; Stegmaier, S.; Schier, A.; and Fässler, T. F. Zintl Ions, Cage Compounds, and Intermetalloid Clusters of Group 14 and Group 15 Elements. Angew. Chem. Int. Ed. 2011, 50, 36303670. 2. Cui, L. F.; Huang, X.; Wang, L. M.; Li, J.; Wang, L. S. Pb122: Plumbaspherene. J. Phys. Chem. A 2006, 110, 1016910172. 3. Cui, L. F.; Huang, X.; Wang, L. M.; Zubarev, D. Y.; Boldyrev, A. I.; Li, J.; Wang, L. S. Sn122: Stannaspherene. J. Am. Chem. Soc. 2006, 128, 83908391. 4. Cui, L. F.; Huang, X.; Wang, L. M.; Li, J.; Wang, L. S. Endohedral Stannaspherenes M@Sn12: A Rich Class of Stable Molecular Cage Clusters. Angew. Chem. Int. Ed. 2007, 119, 756759. 5. Schäfer, S.; Assadollahzadeh, B.; Mehring, M.; Schwerdtfeger, P.; Schäfer, R. Structure and Electric Properties of SnN Clusters (N = 6–20) from Combined Electric Deflection Experiments and Quantum Theoretical Studies. J. Phys. Chem. A 2008, 112, 12312–12319. 6. Kandalam, A. K.; Chen, G.; Jena, P. Unique Magnetic Coupling between Mn Doped Stannaspherenes Mn@Sn12. Appl. Phys. Lett. 2008, 92, 143109. Page 24 of 53 ACS Paragon Plus Environment

Page 25 of 53 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


7. Wang J. –Q.; Stegmaier, S.; Wahl, B.; Fässler, T. F. Step-by-Step Synthesis of the Endohedral Stannaspherene [Ir@Sn12]3– via the Capped Cluster Anion [Sn9Ir(cod)]3–. Chem. Eur. J. 2010, 16, 1793–1798. 8. Rohrmann, U.; Schäfer, R. Stern-Gerlach Experiments on Mn@Sn12: Identification of a Paramagnetic Superatom and Vibrationally Induced Spin Orientation. Phys. Rev. Lett. 2013, 111, 133401. 9. Rohrmann, U.; Schäfer, R. Stren-Gerlach Experiments on Fe@Sn12: Magnetic Response of a Jahn-Teller Distorted Endohedrally Doped Molecular Cage Cluster. J. Phys. Chem. C 2015, 119, 10958–10961. 10. Zhang, X.; Li, G.; Xing, X.; Zhao, X.; Tang, Z.; Gao, Z. Formation of Binary Alloy Cluster Anions from Group-14 Elements and Cobalt and Comparison With SolidState Alloys. Rapid Commun. Mass Spectrom. 2001, 15, 23992403. 11. Esenturk, E. N.; Fettinger, J.; Lam, Y. F.; Bryan, E. [Pt@Pb12]2–. Angew. Chem. Int. Ed. 2004, 43, 21322134. 12. Fässler, T. F.; Hoffmann, S. D. Endohedral Zintl Ions: Intermetalloid Clusters. Angew. Chem. Int. Ed. 2004, 43, 6242–6247. 13. Neukermans, S.; Janssens, E.; Chen, Z. F.; Silverans, R. E.; Schleyer, P. v. R.; Lievens, P. Extremely Stable Metal-Encapsulated AlPb10+ and AlPb12+ Clusters: Mass-Spectrometric Discovery and Density Functional Theory Study. Phys. Rev. Lett. 2004, 92, 163401. 14. Esenturk, E. N.; Fettinger, J.; Eichhorn, B. The Pb122– and Pb102– Zintl Ions and the M@Pb122– and M@Pb102– Cluster Series Where M = Ni, Pd, Pt. J. Am. Chem. Soc. 2006, 128, 9178–9186. 15. Dognon, J. P.; Clavaguera, C.; Pyykkö, P. Towards a 32-Electron Principle: Pu@Pb12 and Related Systems. Angew. Chem. Int. Ed. 2007, 46, 14271430. 16. Dognon, J. P.; Clavaguéra, C.; Pyykkö, P. Chemical Properties of the Predicted 32Electron Systems Pu@Sn12 and Pu@Pb12. C. R. Chimie. 2010, 13, 884–888. 17. Zhou, B.; Krämer, T.; Thompson, A. L.; McGrady, J. E.; Goicoechea, J. M. A Highly Distorted Open-Shell Endohedral Zintl Cluster: [Mn@Pb12]3. Inorg. Chem. 2011, 50, 8028–8037. 18. Bhattacharyya, S.; Nguyen, T. T.; Haeck, K.; Lievens, P.; Janssens, E. Mass–Selected Photodissociation Studies of AlPbn+ Clusters (n = 7–16): Evidence for the Extraordinary Stability of AlPb10+ and AlPb12+. Phys. Rev. B 2013, 87, 054103. Page 25 of 53 ACS Paragon Plus Environment


Page 26 of 53

19. Hiura, H.; Miyazaki, T.; Kanayama, T. Formation of Metal Encapsulating Si Cage Clusters. Phy. Rev. Lett. 2001, 86, 17331736. 20. Kumar, V.; Kawazoe, Y. Metal-Encapsulated Fullerene like and Cubic Caged Clusters of Silicon. Phy. Rev. Lett. 2001, 87, 045503. 21. Kumar, V.; Kawazoe, Y. Metal–Encapsulated Icosahedral Superatoms of Germanium and Tin with Large Gaps: Zn@Ge12 and Cd@Ge12. Appl. Phys. Lett. 2002, 80, 859861. 22. Kumar, V.; Singh, A. K.; Kawazoe, Y. Smallest Magic Caged Clusters of Si, Ge, Sn and Pb by Encapsulation of Transition Metal Atom. Nano Lett. 2004, 4, 677681. 23. Koyasu, K.; Akutsu, M.; Mitsui, M.; Nakajima, A. Selective Formation of MSi16 (M = Sc, Ti, and V). J. Am. Chem. Soc. 2005, 127, 49984999. 24. Atobe, J.; Koyasu, K.; Furuse, S.; Nakajima, A. Anion Photoelectron Spectroscopy of Germanium and Tin Clusters Containing a Transition– or Lanthanide–Metal Atom; MGen– (n = 8–20) and MSnn– (n = 15–17) (M = Sc–V, Y–Nb, and Lu–Ta). Phys. Chem. Chem. Phys. 2012, 14, 9403–9410. 25. Espinoza-Quintero, G.; Duckworth, J. C. A.; Myers, W. K.; McGrady, J. E.; Goicoechea, J. M. Synthesis and Characterization of [Ru@Ge12]3−: An Endohedral 3– Connected Cluster. J. Am. Chem. Soc. 2014, 136, 1210−1213. 26. Shao, N.; Bulusu, S.; Zeng, X. C. Search for Lowest–Energy Structure of Zintl Dianion Si122–, Ge122–, and Sn122–. J. Chem. Phys. 2008, 128, 154326. 27. Castro, A. C.; Osorio, E.; Jiménez-Halla, J. O. C.; Matito, E.; Tiznado, W.; Merino, G. Scalar and Spin-Orbit Relativistic Corrections to the NICS and the Induced Magnetic Field: The case of the E122 Spherenes (E = Ge, Sn, Pb). J. Chem. Theory Comput. 2010, 6, 2701–2705. 28. Tai, T. B.; Nguyen, M. T. A Stochastic Search for the Structures of Small Germanium Clusters and Their Anions: Enhanced Stability by Spherical Aromaticity of the Ge10 and Ge122– Systems. J. Chem. Theory Comput. 2011, 7, 1119–1130. 29. Bartlett, N. Xenon Hexafluoroplatinate (V) Xe+[PtF6]–. Proc. Chem. Soc. 1962, 27, 218. 30. Khriachtchev, L.; Pettersson, M.; Runeberg, N.; Lundell, J.; Räsänen, M. A Stable Argon Compound. Nature (London) 2000, 406, 874–876.


Page 27 of 53 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


31. Khriachtchev, L.; Isokoski, K.; Cohen, A.; Räsänen, M.; Gerber, R. B. A Small Neutral Molecule with two Noble-Gas Atoms: HXeOXeH. J. Am. Chem. Soc. 2008, 130, 6114−6118. 32. Li, T. −H.; Mou, C. −H.; Hui−Ru Chen, H. –R.; Hu, W. –P. Theoretical Prediction of Noble Gas Containing Anions FNgO– (Ng = He, Ar, and Kr). J. Am. Chem. Soc. 2005, 127, 9241−9245. 33. Michaud, J. M.; Gerry, M. C. L. XeCu Covalent Bonding in XeCuF and XeCuCl, Characterised by Fourier Transform Microwave Spectroscopy Supported by Quantum Chemical Calculations. J. Am. Chem. Soc. 2006, 128, 76137621, and references therein. 34. Jayasekharan, T.; Ghanty, T. K. Insertion of Rare Gas Atoms into BF3 and AlF3 Molecules: An ab initio Investigation. J. Chem. Phys. 2006, 125, 234106. 35. Ghosh, A.; Manna D.; Ghanty, T. K. Theoretical Prediction of Noble Gas Inserted Thioformyl Cations: HNgCS+ (Ng = He, Ne, Ar, Kr, and Xe). J. Phys. Chem. A. 2014, 119, 22332243. 36. Pan, S.; Jalife, S.; Romero, J.; Reyes, A.; Merino, G.; Chattaraj, P. K. Attractive Xe– Li interaction in Li-decorated clusters. Comput. Theor. Chem. 2013, 1021, 6269. 37. Jiménez-Halla, C. O. C.; Fernández, I.; Frenking, G. Is it Possible to Synthesize a Neutral Noble Gas Compound Containing a NgNg Bond? A Theoretical Study of HNgNgF (Ng = Ar, Kr, Xe). Angew. Chem. Int. Ed. 2009, 48, 366369. 38. Pan, S.; Moreno, D.; Cabellos, J. L.; Romero, J.; Reyes, A.; Merino, G.; Chattaraj, P. K. In Quest of Strong BeNg Bonds among the Neutral BeNg Complexes. J. Phys. Chem. A 2014, 118, 487494. 39. Saunders, M.; Jiménez-Vázquez, H. A.; Cross, R. J.; Poreda, R. J. Stable Compounds of Helium and Neon: He@C60 and Ne@C60. Science 1993, 259, 14281430. 40. Syamala, M. S.; Cross, R. J.; Saunders, M. 129Xe NMR Spectrum of Xe inside C60. J. Am. Chem. Soc. 2002, 124, 62166219. 41. Cross, R. J.; Khong, A.; Saunders, M. Using Cyanide to put Noble Gases inside C60. J. Org. Chem. 2003, 68, 82818283. 42. Khong, A.; Jiménez-Vázquez, H. A.; Saundres, M.; Cross, R. J.; Laskin, J.; Peres, T.; Lifshitz, C.; Strongin, R.; Smith, A. B. An NMR Study of He2 inside C70. J. Am. Chem. Soc. 1998, 120, 63806383.



Page 28 of 53

43. Khatua, M.; Pan, S.; Chattaraj, P. K. Confinement Induced Binding of Noble Gas Atoms. J. Chem. Phys. 2014, 140, 164306. 44. Khatua, M.; Pan, S.; Chattaraj, P. K. Movement of Ng2 Molecules Confined in a C60 Cage: An ab initio Molecular Dynamics Study. Chem. Phys. Lett. 2014, 610611, 351356. 45. Mondal, S.; Chattaraj, P. K. Noble Gas Encapsulation: Clathrate Hydrates and their HF Doped Analogues. Phys. Chem. Chem. Phys. 2014, 16, 1794317954. 46. Krapp, A.; Frenking, G. Is This a Chemical Bond? A Theoretical Study of Ng2@C60 (Ng = He, Ne, Ar, Kr, Xe). Chem. Eur. J. 2007, 13, 82568270. 47. Cerpa, E.; Krapp, A.; Flores-Moreno, R.; Donald, K. J.; Merino, G. Influence of Endohedral Confinement on the Electronic Interaction between He Atoms: A He2@C20H20 Case Study. Chem. Eur. J. 2009, 15, 19851990. 48. Pan, S.; Mandal, S.; Chattaraj, P.K. Cucurbit[6]uril: A Possible Host for Noble Gas Atoms. J. Phys. Chem. B 2015, 119, 1096210974. 49. Ohtsuki, T.; Ohno, K.; Shiga, K.; Kawazoe, Y.; Maruyama, Y.; Masumoto, K. Insertion of Xe and Kr Atoms into C60 and C70 Fullerenes and the Formation of Dimers. Phys. Rev. Lett. 1998, 81, 967970. 50. Albert, V. V.; Sabin, J. R.; Harris, F. E. Simulated Structure and Energetics of Endohedral Complexes of Noble Gas Atoms in Buckminsterfullerene. Int. J. Quant. Chem. 2007, 107, 30613066. 51. Ravinder, P.; Subramanian, V. Studies on the Encapsulation of Various Anions in Different Fullerenes Using Density Functional Theory Calculations and BornOppenheimer Molecular Dynamics Simulation. J. Phys. Chem. A 2011, 115, 1172311733. 52. Bühl, M.; Patchkovskii, S.; Thiel, W. Interaction Energies and NMR Chemical Shifts of Noble Gases in C60. Chem. Phys. Lett. 1997, 275, 1418. 53. Peres, T.; Cao, B. P.; Cui, W. D.; Khong, A.; Cross, R. J.; Saunders, M.; Lifshitz, C. Some New Diatomic Molecule Containing Endohedral Fullerenes. Int. J. Mass Spectrom. 2001, 210–211, 241247. 54. Laskin, J.; Peres, T.; Lifshitz, C.; Saunders, M.; Cross, R. J.; Khong, A. An Artificial Molecule of Ne2 inside C70. Chem. Phys. Lett. 1998, 285, 79.


Page 29 of 53 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


55. Sternfeld, T.; Hoffman, R. E.; Saunders, M.; Cross, R. J.; Syamala, M. S.; Rabinovitz, M. Two Helium Atoms inside Fullerenes: Probing the Internal Magnetic Field in C606 and C706. J. Am. Chem. Soc. 2002, 124, 87868787. 56. Manna, D.; Ghanty, T.K. Prediction of a New Series of Thermodynamically Stable Actinide Encapsulated Fullerene Systems Fulfilling the 32-Electron Principle. J. Phys. Chem. C 2012, 116, 2563025641. 57. Weiske, T.; Bohme, D. K.; Schwartz, H. Injection of Helium Atoms into Doubly and Triply Charged Carbon (C60) Cations. J. Phys. Chem. 1991, 95, 84518452. 58. Saunders, M.; Jiménez-Vázquez, H. A.; Cross, R. J.; Mroczkowski, S.; Gross, M. L.; Giblin, D. E.; Poreda, R. J. Incorporation of Helium, Neon, Argon, Krypton and Xenon into Fullerenes Using High Pressure. J. Am. Chem. Soc. 1994, 116, 21932194. 59. Becker, L.; Poreda, R. J.; Bada, J. L. Extraterrestrial Helium Trapped in Fullerenes in the Sudbury Impact Structure. Science 1996, 271, 249252. 60. Cross, R. J.; Saunders, M.; Prinzbach, H. Putting Helium inside Dodecahedrane. Org. Lett. 1999, 1, 14791481. 61. Jiménez-Vázquez, H. A.; Tamariz, J.; Cross, R.J. Binding Energy in and Equilibrium Constant of Formation for the Dodecahedrane Compounds He@C20H20 and Ne@C20H20. J. Phys. Chem. A 2001, 105, 13151319. 62. Zou, W.; Liu, Y.; Liu, W.; Wang, T.; Boggs, J. E. He@Mo6Cl8F6: A Stable Complex of Helium. J. Phys. Chem. A 2010, 114, 646651. 63. Darzynkiewicz, R. B.; Scuseria, G. E. Noble Gas Endohedral Complexes of C60 Buckministerfullerene. J. Phys. Chem. A 1997, 101, 71417144. 64. Moran, D.; Woodcock, H. L.; Chen, Z. F.; Schaefer, H. F.; Schleyer, P. V. R. On the Viability of Small Endohedral Hydrocarbon Cage Complexes: X@C4H4, X@C8H8, X@C8H14, X@C10H16, X@C12H12, and X@C16H16. J. Am. Chem. Soc. 2003, 125, 11442–11451. 65. Chakraborty, D.; Chattaraj, P.K. Confinement Induced Binding in Noble Gas Atoms within a BN-Doped Carbon Nanotube. Chem. Phys. Lett. 2015, 621, 2934. 66. Chakraborty, D.; Pan, S.; Chattaraj, P.K. Encapsulation of Small Gas Molecules and Rare Gas Atoms Inside the Octa Acid Cavitand. Theor. Chem. Acc. 2016, 135, 119.



Page 30 of 53

67. Whitener, K. E. Jr.; Cross, R. J.; Saunders, M.; Iwamatsu, S.; Murata, S.; Mizorogi, N.; Nagase, S. Methane in an Open Cage[60] Fullerene. J. Am. Chem. Soc. 2009, 131, 6338−6339. 68. Whitener, K. E. Jr.; Frunzi, M.; Iwamatsu, S.; Murata, S.; Cross, R. J.; Saunders, M. Putting Ammonia into Chemically Opened Fullerene. J. Am. Chem. Soc. 2008, 130, 13996−13999. 69. Stanisky, C. M.; Cross, R. J.; Saunders, M. Putting Atoms and Molecules into Chemically Opened Fullerenes. J. Am. Chem. Soc. 2009, 131, 3392−3395. 70. Krachmalnicoff, A.; Bounds, R.; Mamone, S.; Alom, S.; Concistrè, M.; Meier, B.; Kouřil, K.; Light, M. E.; Johnson, M. R.; Rols, S.; Horsewill, A. J.; Shugai, A.; Nagel, U.; Rõõm, T.; Carravetta, M.; Levitt, M. H.; Whitby, R. J. The Dipolar Endofullerene HF@C60. Nat. Chem. 2016, 8, 953–957. 71. Ge, M.; Nagel, U.; Hüvonen, D.; Rõõm, T.; Mamone, S.; Levitt, M. H.; Carravetta, M.; Murata, Y.; Komatsu, K.; Lei, X.; and Turro, N. J. Infrared Spectroscopy of Endohedral HD and D2 in C60. J. Chem. Phys. 2011, 135, 114511. 72. Ge, M.; Nagel, U.; Hüvonen, D.; Rõõm, T.; Mamone, S.; Levitt, M. H.; Carravetta, M.; Murata, Y.; Komatsu, K.; Chen, J. Y.–C.; Turro, N. J. Interaction Potential and Infrared Absorption of Endohedral H2 in C60. J. Chem. Phys. 2011, 134, 054507. 73. Mamone, S.; Ge, M.; Hüvonen, D.; Nagel, U.; Danquigny, A.; Cuda, F.; Grossel, M. C.; Murata, Y.; Komatsu, K.; Levitt, M. H.; Rõõm, T.; Carravetta, M. Rotor in a Cage: Infrared Spectroscopy of an Endohedral Hydrogen–fullerene complex. J. Chem. Phys. 2009, 130, 081103. 74. Horsewill, A. J.; Panesar, K. S.; Rols, S.; Johnson, M. R.; Murata, Y.; Komatsu, K.; Mamone, S.; Danquigny, A.; Cuda, F.; Maltsev, S.; Grossel, M. C.; Carravetta, M., Levitt, M. H. Quantum Translator–Rotator: Inelastic Neutron Scattering of Dihydrogen Molecules Trapped inside Anisotropic Fullerene Cages. Phys. Rev. Lett. 2009, 102, 013001. 75. Straka, M.; Vaara, J. Density Functional Calculations 3He Chemical Shift in Endohedral Helium Fullerenes: Neutral, Anionic and Di-Helium Species. J. Phys. Chem. A 2006, 110, 1233812341. 76. Arash, B.; Wang, Q. Detection of Gas Atoms with Carbon Nanotubes. Sci. Rep. 2013, 3, 1782.


Page 31 of 53 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


77. Foroutan, M.; Nasrabadi, A. T. Adsorption Behaviour of Ternary Mixtures of Noble Gases inside Single-Walled Carbon Nanotube Bundles. Chem. Phys. Lett. 2010, 497, 213217. 78. Foroutan, M.; Nasrabadi, A. T. Adsorption and Separation of Binary Mixtures of Noble Gases on Single-Walled Carbon Nanotube Bundles. Physica E 2011, 43, 851856. 79. Pyykkö, P.; Wang, C.; Straka M.; Vaara, J. A. London–Type Formula for the Dispersion Interactions of Endohedral A@B Systems. Phys. Chem. Chem. Phys. 2007, 9, 2954–2958. 80. Wang, C.; Straka, M.; Pyykkö, P. Formulations of the Closed–Shell Interactions in Endohedral Systems. Phys. Chem. Chem. Phys. 2010, 12, 6187–6203. 81. Zhou, J.; Giri, S.; Jena, P. 18-Electron Rule Inspired Zintl-like Ions Composed of All Transition Metals. Phys. Chem. Chem. Phys. 2014, 16, 2024120247. 82. Karttunen, A. J.; Fässler , T. F. Semiconducting Clathrates Meet Gas Hydrates: Xe24[Sn136]. Chem. Eur. J. 2014, 20, 6693 – 6698. 83. Li, X.; Hermann, A.; Peng, F.; Lv, J.; Wang, Y.; Wang, H.; Ma, Y. Stable Lithium Argon Compounds under High Pressure. Sci. Rep. 2015, 5, 16675. 84. Liu, Z.; Botana, J.; Miao, M.; Yan, D. Unexpected Xe Anions in XeLin Intermetallic Compounds. Europhys. Lett. 2017, 117, 26002. 85. Miao, M.–S.; Wang, X.–L.; Brgoch, J., Spera, F.; Jackson, M. G.; Kresse, G.; Lin, H.–Q. Anionic Chemistry of Noble Gases: Formation of Mg−NG (NG = Xe, Kr, Ar) Compounds under Pressure. J. Am. Chem. Soc. 2015, 137, 14122−14128. 86. Dong, X.; Oganov, A. R.; Goncharov, A. F.; Stavrou, E.; Lobanov, S.; Saleh, G.; Qian, G.–R.; Zhu, Q; Gatti, C.; Deringer, V. L.; Dronskowski, R.; Zhou, X.–F.; Prakapenka, V. B.; Konôpková, Z., Popov, I. A.; Boldyrev, A. I.; Wang, H.–T. A. Stable Compound of Helium and Sodium at High Pressure. Nat. Chem. 2017 (ASAP) doi:10.1038/nchem.2716 87. Ghose, S. K.; Li, Y.; Yakovenko, A.; Dooryhee, E.; Ehm, L.; Ecker, L. E.; Dippel, A.–C.; Halder, G. J.; Strachan, D. M.; Thallapally, P. K. Understanding the Adsorption Mechanism of Xe and Kr in a Metal Organic Framework from X‑ray Structural Analysis and First-Principles Calculations. J. Phys. Chem. Lett. 2015, 6, 1790−1794.



Page 32 of 53

88. Vazhappilly, T.; Ghanty, T. K.; Jagatap, B. N. Computational Modeling of Adsorption of Xe and Kr in M‑MOF-74 Metal Organic Frame Works with Different Metal Atoms. J. Phys. Chem. C 2016, 120, 10968−10974. 89. Banerjee, D.; Simon, C. M.; Plonka, A. M.; Motkuri, R. K.; Liu, J.; Chen, X.; Smit, B.; Parise, J. B.; Haranczyk, M., Thallapally , P. K. Metal-organic framework with optimally selective xenon adsorption and separation. Nat. Comm. 2016, 7, 11831. 90. Banerjee, D.; Cairns, A. J.; Liu, J.; Motkuri, R. K.; Nune, S. K.; Fernandez, C. A.; Krishna, R.; Strachan, D. M.; Thallapally, P. K. Potential of Metal-Organic Frameworks for Separation of Xenon and Krypton. Acc. Chem. Res. 2015, 48, 211−219. 91. Marx, D.; Hutler, J. Ab Initio Molecular Dynamics: Theory and Implementation. In Modern Methods and Algorithms of Quantum Chemistry; Grotendorst, J., Eds.; John von Neumann Institute for Computing (NIC); Germany, 2000; Vol. 3, pp 329446. 92. TURBOMOLE is program package developed by the Quantum Chemistry Group at the University of Karlsruhe, Germany, 1988: Ahlrichs, R.; Bär, M.; Häser, M.; Horn, H.; Kölmel, C. Chem. Phys. Lett. 1989, 162, 165169. 93. Becke, A. D. A New Mixing of Hartree−Fock and Local Density−Functional Theories. J. Chem. Phys. 1993, 98, 13721377. 94. Lee,

C.;

Yang,

W.;

Parr,

R.

G.

Development

of

the

Colle−Salvetti

Correlation−Energy Formula into a Functional of the Electron Density. Phys. Rev. B 1988, 37, 785−789. 95. Peterson, K. A.; Figgen, D.; Goll, E.; Stoll, H.; Dolg, M. Systematically Convergent Basis Sets with Relativistic Pseudopotentials. II. Small-Core Pseudopotentials and Correlation Consistent Basis Sets for the Post-d Group 16−18 Elements. J. Chem. Phys. 2003, 119, 11113−11123. 96. Peterson,

K.

A.

Systematically

Convergent

Basis

Sets

with

Relativistic

Pseudopotentials. II. Small-Core Pseudopotentials and Correlation Consistent Basis Sets for the Post d-Group 13-15 Elements. J. Chem. Phys. 2003, 119, 11099. 97. Pyykkö, P. Additive Covalent Radii for Single, Double, and Triple Bonded Molecules and Tetrahedrally Bonded Crystals: A Summary. J. Phys. Chem. A 2015, 119, 23262337. 98. Vogt, J.; Alvarez, S. van der Waals Radii of Noble Gases. Inorg. Chem. 2014, 53, 92609266. Page 32 of 53 ACS Paragon Plus Environment

Page 33 of 53 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


99. Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. A Consistent and Accurate ab initio Parametrization of Density Functional Dispersion Correction (DFT–D) for the 94 Elements H–Pu. J. Chem. Phys. 2010, 132, 154104. 100. Grimme, S.; Hansen, A.; Brandenburg, J. G.; Bannwarth, C. Dispersion–Corrected Mean–Field Electronic Structure Methods. Chem. Rev. 2016, 116, 5105–5154. 101. Reimers, J. R.; Ford, M. J.; Marcuccio, S. M.; Ulstrup, J.; Hush, N. S. Competition of van der Waals and Chemical Forces on Gold–Sulfur Surfaces and Nanoparticles. Nat. Rev. Chem. 2017, 1, 0017. 102. Bader, R. F. W. Atoms in MoleculesA Quantum Theory; Oxford University Press: Oxford, U. K., 1990. 103. Zou, W.; NoriShargh, D.; Boggs, J. On the Covalent Character of Rare Gas Bonding Interactions: A New Kind of Weak Interaction. J. Phys. Chem. A 2013, 117, 207212. 104. Pan, S.; Gupta, A.; Mandal, S.; Moreno, D.; Merino, G.; Chattaraj, P.K. Metastable Behavior of Noble Gas Inserted Tin and Lead Fluorides. Phys. Chem. Chem. Phys., 2015, 17, 972982. 105. Becke, A. D.; Edgecombe, K. E. A Simple Measure of Electron Localization in Atomic and Molecular Systems. J. Chem. Phys. 1990, 92, 5397−5403. 106. Su, P; Li, H. Energy Decomposition Analysis of Covalent Bonds and Intermolecular Interactions. J. Chem. Phys. Chem. 2009, 131, 014102. 107. Schmidt, M. W.; Baldridge, K. K.; Boatz, J. A.; Elbert, S. T.; Gordon, M. S.; Jensen, J. H.; Koseki, S.; Matsunaga, N.; Nguyen, K. A.; Su, S. et al. General Atomic and Molecular Electronic Structure System. J. Comput. Chem. 1993, 14, 1347−1363.



Page 34 of 53

FIGURE CAPTION Figure 1. Optimized structures of (a) plumbaspherene (Pb122–), (b) noble gas encapsulated Pb122–, Ng@Pb122–, and (c) noble gas dimer encapsulated Pb122–, Ng2@Pb122– as obtained by B3LYP/DEF2 levels of theory. Figure 2. Orbital energies of bare Pb cluster (a) Pb122−, and noble gas encapsulated Pb clusters (b) He@Pb122−, (c) Ne@Pb122−, (d) Ar@Pb122−, and (e) Kr@Pb122−. Figure 3. Orbital energies of bare Sn cluster (a) Sn122−, and noble gas encapsulated Sn clusters (b)He@Sn122−, (c) Ne@Sn122−, (d) Ar@Sn122−, and (e) Kr@Sn122−. Figure 4. The variation of density of states (DOS) as a function of orbital energies of noble gas encapsulated Pb clusters for (a) He@Pb122−, (b) Ne@Pb122−, (c) Ar@Pb122−, (d) Kr@Pb122−, (e) H2@Pb122−, and (f) He2@Pb122− considering the HOMO energy set to zero in all the cases where the blue legend representing the bare cluster and the red one corresponds to the noble gas encapsulated Pb clusters. Figure 5. The variation in average Pb−Pb distances of noble gas encapsulated Pb clusters for (a) He@Pb122−, (b) Ne@Pb122−, (c) Ar@Pb122−, (d) Kr@Pb122−, (e) H2@Pb122−, (f) He2@Pb122−, and bare Pb cluster (g) Pb122− with respect to time at different temperatures during the course of molecular dynamics simulation. Figure 6. The variation in Ng−Pb distances of noble gas encapsulated Pb clusters for (a) He@Pb122−, (b) Ne@Pb122−, (c) Ar@Pb122−, and (d) Kr@Pb122− with respect to time at different temperatures during the course of molecular dynamics simulations. Figure 7. Optimized structures of (a) C5v Ng@KPb12–, (b) C3v Ng@KPb12–, (c) D5d Ng@K2Pb12 and (d) D3d Ng@K2Pb12 as obtained by B3LYP/DEF2 levels of theory.


Page 35 of 53 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(a)

(b)

(c)

Figure 1. Optimized structures of (a) plumbaspherene (Pb122–), (b) noble gas encapsulated Pb122–, Ng@Pb122–, and (c) noble gas dimer encapsulated Pb122–, Ng2@Pb122– as obtained by B3LYP/DEF2 levels of theory.



Page 36 of 53

Figure 2. Orbital energies of bare Pb cluster (a) Pb122−, and noble gas encapsulated Pb clusters (b) He@Pb122−, (c) Ne@Pb122−, (d) Ar@Pb122−, and (e) Kr@Pb122−.


Page 37 of 53 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 3. Orbital energies of bare Sn cluster (a) Sn122−, and noble gas encapsulated Sn clusters (b)He@Sn122−, (c) Ne@Sn122−, (d) Ar@Sn122−, and (e) Kr@Sn122−.



Page 38 of 53

(a)

(b)

(c)

(d)

(e)

(f)

Figure 4. The variation of density of states (DOS) as a function of orbital energies of noble gas encapsulated Pb clusters for (a) He@Pb122−, (b) Ne@Pb122−, (c) Ar@Pb122−, (d) Kr@Pb122−, (e) H2@Pb122−, and (f) He2@Pb122− considering the HOMO energy set to zero in all the cases where the blue legend representing the bare cluster and the red one corresponds to the noble gas encapsulated Pb clusters. Page 38 of 53 ACS Paragon Plus Environment

Page 39 of 53 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(a)

(b)

(c)

(d)

(e)

(f)



Page 40 of 53

(g) Figure 5. The variation in average Pb−Pb distances of noble gas encapsulated Pb clusters for (a) He@Pb122−, (b) Ne@Pb122−, (c) Ar@Pb122−, (d) Kr@Pb122−, (e) H2@Pb122−, (f) He2@Pb122−, and bare Pb cluster (g) Pb122− with respect to time at different temperatures during the course of molecular dynamics simulation.


Page 41 of 53 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(a)

(b)

(c)

(d)

Figure 6. The variation in Ng−Pb distances of noble gas encapsulated Pb clusters for (a) He@Pb122−, (b) Ne@Pb122−, (c) Ar@Pb122−, and (d) Kr@Pb122− with respect to time at different temperatures during the course of molecular dynamics simulations.



(a)

(c)

Page 42 of 53

(b)

(d)

Figure 7. Optimized structures of (a) C5v Ng@KPb12–, (b) C3v Ng@KPb12–, (c) D5d Ng@K2Pb12 and (d) D3d Ng@K2Pb12 as obtained by B3LYP/DEF2 levels of theory.


Page 43 of 53 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 1. Optimized Ng−Pb/Ng−Sn Distances (R(Ng−Pb/Ng−Sn), in Å)a, Shortest Pb−Pb/Sn−Sn Distances (R(Pb–Pb/Sn–Sn), in Å), Dissociation Energies (BE, in kcal mol−1), HOMO-LUMO Gap (EGap, in eV) and NPA Charge at Noble Gas Atom (q(Ng)) of Ng@Pb122− and Ng@Sn122− (Ng = He, Ne, Ar, and Kr) Clusters Calculated at B3LYP Level with DEF2 basis set ,aug-cc-pVTZ basis setb and dispersion correctedb B3LYP Method with DEF2 basis set

Cluster

R(Ng−Pb/Ng−Sn)

R(Pb−Pb/Sn−Sn)

BE

EGap

q(Ng)

2− a

3.151 (3.158) [3.110]

3.314 (3.321) [3.270]

...

3.047 (3.032) [2.767]

...

He@Pb122−

3.172 (3.175) [3.131]

3.335 (3.339) [3.292]

15.2 (11.7) [16.1]

3.081 (3.073) [2.821]

0.028 (0.028) [0.055]

Ne@Pb122−

3.209 (3.204) [3.168]

3.375 (3.369) [3.331]

34.6 (27.4) [36.4]

2.825 (2.833) [2.585]

0.024 (0.023) [0.037]

Ar@Pb122−

3.321 (3.327) [3.272]

3.492 (3.498) 107.4 (100.4) [3.441] [108.2]

2.288 (2.282) [2.067]

0.021 (0.022) [0.022]

Kr@Pb122−

3.382 (3.395) [3.330]

3.556 (3.570) 147.2 (139.9) [3.501] [147.4]

1.974 (1.968) [1.755]

0.024 (0.025) [0.022]

Sn122− a

3.030 (3.043) [2.987]

3.186 (3.199) [3.141]

...

2.720 (2.715) [2.771]

...

He@Sn122−

3.056 (3.069) [3.012]

3.213 (3.227) [3.167]

19.5 (16.4) [20.3]

2.720 (2.714) [2.767]

0.027 (0.027) [0.055]

Ne@Sn122−

3.098 (3.102) [3.056]

3.258 (3.262) [3.214]

43.1 (36.7) [46.6]

2.617 (2.611) [2.657]

0.024 (0.024) [0.032]

Ar@Sn122−

3.216 (3.254) [3.170]

3.382 (3.421) 126.4 (119.1) [3.333] [131.9]

2.073 (2.055) [2.062]

0.020 (0.021) [0.022]

Pb12

Kr@Sn122−

3.277 (3.310) 3.446 (3.480) 169.8 (161.7) 1.763 (1.762) 0.022 (0.022) [3.230] [3.397] [176.8] [1.734] [0.052] 2− 2− a In the case of Pb12 and Sn12 , R(Ng−Pb/Ng−Sn) refers to the distance from the centre to the cage atoms. b

Dispersion corrected values are written in parenthesis and AVTZ basis set calculated values

are given in the square bracket



Page 44 of 53

Table 2. Calculated Values of He−He/H−H Distances (R(He−He/H−H), in Å), Shortest Pb−Pb/Sn−Sn Distances (R(Pb−Pb/Sn−Sn), in Å), Dissociation Energies (BE, in kcal mol−1), HOMO−LUMO Gap (EGap, in eV) and NPA Charge at Encapsulated Atoms (q(He)/q(H)) of He2@Pb122−, H2@Pb122− and H2@Sn122− Clusters as Performed using B3LYP Method with def–TZVP basis set Cluster

Symmetry

R(He−He/H−H)

R(Pb−Pb/Sn−Sn)

BE

EGap

q(He)/q(H)

He2@Pb122−

D5d

1.561

3.347

63.4

2.422

0.022

H2@Pb122−

D5d

0.738

3.339

23.4

3.079

0.057

H2@Sn122−

D5d

0.739

3.216

27.9

2.702

0.062


Page 45 of 53 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 3. Harmonic Vibrational Frequencies (in cm–1) and Intensities (in km mol−1) as given in Parenthesis of Bare Pb122− and Ng@Pb122− (Ng = He, Ne, Ar, and Kr) Clusters Calculated by using B3LYP Method with DEF2 Basis Set. Pb122−

He@Pb122−

Ne@Pb122−

Ar@Pb122−

Kr@Pb122−

48.5(0)

47.1(0)

44.5(0)

37.1(0)

33.2(0)

51.4(0)

52.6(0)

52.1(0)

44.6(0)

37.7(0)

68.9(0)

66.9(0)

63.4(0)

49.7(0)

38.4(0)

75.1(0)

75.2(0)

68.8(0)

53.7(0)

38.9(2.966)

78.8(0)

77.2(0)

78.2(0.011)

56.0(0.873)

48.7(0)

85.8(0)

84.6(0)

78.4(0)

76.8(0)

73.9(0)

86.6(0)

86.0(0)

81.6(0)

77.9(0)

74.7(0)

89.9(0.004)

86.5(0.021)

85.6(0)

81.4(0)

78.8(0)

...

376.2(18.341)

190.3(0.054)

187.8(6.785)

140.4(10.708)



Page 46 of 53

Table 4. Harmonic Vibrational Frequencies (in cm−1) and Intensities (in km mol−1) as given in Parenthesis of Bare Sn122− and Ng@Sn122− (Ng = He, Ne, Ar, and Kr) Clusters Calculated by using B3LYP Method with DEF2 Basis Set.

Sn122− 62.8(0)

He@Sn122− 60.4(0)

Ne@Sn122− 56.4(0)

Ar@Sn122− 45.7(0)

Kr@Sn122− 35.6(7.686)

70.5(0)

71.0(0)

68.4(0)

53.9(0)

40.1(0)

91.6(0)

88.2(0)

82.8(0)

59.9(0)

40.7(0)

103.0(0)

99.2(0)

89.0(0)

66.1(3.381)

44.2(0)

105.8(0)

105.9(0)

100.9(0.566)

68.8(0)

61.8(0)

114.6(0)

113.3(0)

108.3(0)

104.6(0)

100.1(0)

118.6(0)

115.8(0.144)

109.8(0)

107.4(0)

102.1(0)

121.8(0.343)

117.2(0)

116.3(0)

109.3(0)

105.3(0)

...

418.5(18.801)

211.2(0.017)

203.7(5.551)

156.5(7.418)


Page 47 of 53 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 5. Harmonic Vibrational Frequencies (in cm−1) and Intensities (in km mol–1) as given in Parenthesis of He2@Pb122−, H2@Pb122−and H2@Sn122− Clusters Calculated by using B3LYP Method with DEF2 Basis Set.

He2@Pb122− 22.7 (0)

H2@Pb122− 46.5(0)

H2@Sn122− 59.3(0)

42.3(0)

46.8(0)

59.4(0)

42.6(0)

47.2(0)

59.6(0)

43.8(0)

51.6(0)

66.1(0)

53.2(0)

52.1(0)

68.8(0)

53.5(0)

52.5(0)

69.3(0)

53.5(0)

65.8(0)

86.8(0)

59.6(0.013)

66.7(0)

86.8(0)

61.6(0)

73.8(0)

96.0(0)

66.9(0)

73.8(0.021)

96.2(0.006)

69.3(0)

76.9(0)

103.4(0)

72.5(0.016)

77.0(0.005)

103.5(0.002)

78.4(0)

82.8(0)

109.5(0)

79.0(0.011)

84.7(0)

112.2(0)

80.3(0)

85.3(0)

113.1(0.081)

80.8(0)

85.4(0)

113.2(0)

82.6(0.268)

85.8(0.024)

114.1(0.065)

83.4(0)

86.2(0.018)

115.8(0)

242.6(0)

378.5(0)

264.9(0)

380.7(4.454)

680.9(126.006)

700.2(127.557)

392.5(0)

683.5(110.625)

708.5(116.202)

1026.9(0)

4380.5(0)

4323.9(0)



Page 48 of 53

Table 6. Calculated Values of Bond Critical Point Electron Density (ρ in e a0–3), Laplacian (2ρ in e a0–5), the Local Electron Energy Density (Ed in au), and Ratio of Local Electron Kinetic Energy Density and Electron Density (G/ρ in au) in Bare Pb122− and Ng@Pb122− Clusters (Ng = He, Ne, Ar, and Kr) as Obtained Using B3LYP Method with DEF2 Basis Set. Clusters

Bond



2

G(r)a

V(r)b

Ed(r)

G(r)/

Typec

Pb122

PbPb

0.022

0.008

0.005

0.008

0.003

0.227

C, D

PbPb

0.022

0.008

0.005

0.008

0.003

0.227

C, D

HePb

0.008

0.023

0.005

0.004

0.001

0.625

D

PbPb

0.021

0.008

0.005

0.007

0.003

0.238

C, D

NePb

0.009

0.030

0.006

0.005

0.001

0.667

D

PbPb

0.019

0.008

0.004

0.006

0.002

0.211

C, D

ArPb

0.012

0.034

0.008

0.007

0.0006

0.667

D

PbPb

0.018

0.007

0.003

0.005

0.002

0.167

C, D

KrPb

0.013

0.032

0.008

0.008

0.0001

0.615

D

PbPb

0.022

0.008

0.005

0.008

0.003

0.227

C, D

HPb

0.013

0.022

0.005

0.005

0.00005

0.385

D

HH

0.272

1.093

0.008

0.290

0.281

0.029

A

PbPb

0.022

0.008

0.005

0.008

0.003

0.227

C, D

HePb

0.014

0.050

0.011

0.010

0.001

0.786

D

HeHe

0.042

0.254

0.059

0.055

0.004

1.405

Wn

He@Pb122 Ne@Pb122 Ar@Pb122 Kr@Pb122

H2@Pb122

He2@Pb122 a

G(r) represents the local electron kinetic energy density; bV(r) signifies the local electron

potential energy density; c“Type” is an indication of type of bonding exists in between the corresponding pair of bonding atoms.


Page 49 of 53 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 7. Calculated Values of Bond Critical Point Electron Density (ρ in e a0–3), Laplacian (2ρ in e a0–5), the Local Electron Energy Density (Ed in au), and Ratio of Local Electron Kinetic Energy Density and Electron Density (G/ρ in au) in Bare Sn122− and Ng@Sn122− Clusters (Ng = He, Ne, Ar, and Kr) Species as Obtained Using B3LYP Method with DEF2 Basis Set. Clusters

Bond



2

G(r)a

V(r)b

Ed(r)

G(r)/

Typec

Sn122

SnSn

0.026

0.005

0.006

0.010

0.004

0.231

C, D

SnSn

0.025

0.006

0.005

0.010

0.004

0.200

C, D

HeSn

0.009

0.029

0.006

0.005

0.001

0.667

D

SnSn

0.024

0.006

0.005

0.009

0.004

0.208

C, D

NeSn

0.011

0.036

0.008

0.007

0.001

0.727

D

SnSn

0.021

0.006

0.004

0.007

0.003

0.190

C, D

ArSn

0.014

0.038

0.009

0.009

0.0003

0.643

D

SnSn

0.020

0.006

0.004

0.006

0.002

0.200

C, D

KrSn

0.015

0.036

0.009

0.010

0.0004

0.600

D

SnSn

0.025

0.006

0.005

0.009

0.004

0.200

C, D

HSn

0.015

0.024

0.007

0.007

0.0005

0.467

D

HH

0.272

1.080

0.010

0.290

0.280

0.037

A

He@Sn122 Ne@Sn122 Ar@Sn122 Kr@Sn122

H2@Sn122 a

G(r) represents the local electron kinetic energy density; bV(r) signifies the local electron

potential energy density; c“Type” is an indication of type of bonding exists in between the corresponding pair of bonding atoms.



Page 50 of 53

Table 8. Optimized Ng−Pb/Ng−Sn Distances (R(Ng−Pb/Ng−Sn), in Å)a, Shortest and Longest Pb−Pb/Sn−Sn Distances (R(Pb–Pb/Sn–Sn), in Å), Dissociation Energies (BE, in kcal mol−1), HOMO-LUMO Gap (EGap, in eV) and NPA Charge at Noble Gas Atom and counter ion (q(Ng) and q(K)) of Bare and Ng Encapsulated KPb12–, KSn12–, K2Pb12 and K2Sn12 Clusters Calculated at B3LYP/DEF Computational Level (Ng = He, Ne, Ar, and Kr). Cluster

Sym

R(Ng−Pb/Ng−Sn)

R(Pb−Pb/Sn−Sn)

R(K−Pb/K−Sn)

BE

EGap

q(Ng)

q(K+)

KPb12− a

C3v

2.797/3.456

3.240/3.368

3.612/8.156

−

1.778

−

0.868

He@KPb12−

C3v

3.101/3.207

3.262/ 3.402

3.612/8.190

116.5

1.840

−0.021

0.871

Ne@KPb12−

C3v

3.180/3.240

3.298/3.444

3.625/8.252

97.2

1.681

−0.017

0.856

Ar@KPb12−

C3v

3.266/3.352

3.403/3.550

3.653/7.014

24.5

1.388

−0.003

0.806

Kr@KPb12−

C3v

Exob

−

−

−

−

−

KSn12− a

C3v

2.671/3.333

3.115/3.224

3.577/7.965

−

1.860

−

0.861

He@KSn12−

C3v

2.983/3.092

3.140/3.256

3.573/7.999

111.9

1.920

−0.021

0.861

Ne@KSn12−

C3v

3.064/3.138

3.180/3.300

3.587/8.072

88.2

1.874

−0.018

0.848

Ar@KSn12−

C3v

3.145/3.260

3.286/3.492

3.618/8.277

5.0

1.555

−0.001

0.798

Kr@KSn12−

C3v

Exob

−

−

−

−

−

K2Pb12 a

D3d

3.088/3.213

3.229/ 3.375

3.670/8.140

−

2.156

−

0.944

He@K2Pb12

D3d

3.120/3.224

3.255/3.403

3.675/8.191

199.4

2.237

−0.018

0.940

Ne@K2Pb12

D3d

3.162/3.259

3.289/3.457

3.680/8.241

179.7

1.992

−0.015

0.937

Ar@K2Pb12

D3d

3.288/3.361

3.386/3.627

3.701/8.387

105.9

1.547

−0.003

0.922

Kr@K2Pb12

D3d

Img(−38)c

−

−

−

−

−

K2Sn12a

D3d

2.955/3.105

3.098/3.258

3.641/7.933

−

2.282

−

0.932

He@K2Sn12

D3d

2.992/3.119

3.128/3.274

3.642/7.987

194.8

2.332

−0.018

0.927

Ne@K2Sn12

D3d

3.042/3.158

3.165/ 3.333

3.651/ 8.048

170.3

2.212

−0.015

0.925

Ar@K2Sn12

D3d

3.177/3.267

3.258/3.526

3.672/ 8.191

85.6

1.688

−0.002

0.913

Kr@K2Sn12

D3d

Img(−52) c

−

−

−

−

−

−

a

In the case of bare clusters R(Ng−Pb/Ng−Sn) refers to the distance from the centre to the cage

atoms; bStructure becomes exohedral; cEndohedral structure is associated with imaginary frequency.


Page 51 of 53 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 9. Calculated Values of Electrostatic Energy (Eele), Exchange Energy (Eex), Repulsion Energy (Erep), Polarization Energy (Epol), Dispersion Energy (Edisp) and the Total Interaction Energy (E) (in kcal mol1) in Ng@Pb122−, Ng@Sn122−, H2@Pb122−, He2@Pb122−, and H2@Sn122− Clusters (Ng = He, Ne, Ar, and Kr) as obtained using B3LYP Method with DEF2 Basis Set.a Complexes

Eele

Eex

Erep

Epol

Edisp

E

He@Pb122

6.6[21.5] (6.8)

12.7[41.4] (13.3)

45.3 (46.9)

5.5[17.9] (5.5)

5.9[19.2] (6.0)

14.6 (15.3)

Ne@Pb122

24.3[35.5] (24.1)

29.2[42.6] (29.6)

100.8 (101.8)

5.0[7.3] (4.2)

10.0[14.6] (10.4)

32.2 (33.5)

Ar@Pb122

65.6[37.1] (63.2)

77.6[43.8] (77.5)

266.2 (265.4)

17.1[9.7] (17.5)

16.7[9.5] (17.3)

89.3 (89.9)

Kr@Pb122

92.8[37.4] (87.4)

106.0[42.7] (102.4)

362.0 (353.7)

29.6[11.9] (28.6)

19.8[8.0] (20.2)

113.8 (115.1)

H2@Pb122

15.9[21.8] (15.2)

32.0[43.9] (31.1)

96.2 (94.7)

16.3[22.3] (16.1)

8.8[12.0] (8.9)

23.2 (23.4)

He2@Pb122

19.2[22.9] (19.1)

37.8[45.0] (38.2)

132.3 (133.1)

15.9[18.9] (15.6)

11.1[13.2] (11.3)

48.4 (49.0)

He@Sn122

10.7[23.4] (9.2)

19.2[41.9] (16.7)

64.4 (59.2)

9.4[20.4] (6.7)

6.6[14.3] (6.7)

18.5 (19.9)

Ne@Sn122

38.6[38.5] (31.5)

41.8[41.6] (37.0)

139.6 (127.4)

8.8[8.7] (6.3)

11.2[11.2] (11.5)

39.2 (41.1)

Ar@Sn122

101.0[40.4] (79.2)

104.2[41.7] (93.6)

351.7 (322.0)

26.6[10.6] (26.6)

18.4[7.3] (18.9)

101.5 (103.8)

Kr@Sn122

138.7[40.3] (106.8)

138.2[40.2] (122.6)

472.2 (425.9)

45.7[13.3] (43.8)

21.6[6.3] (22.0)

128.1 (130.7)

23.1[22.6] 43.7[42.7] 129.0 25.7[25.1] 9.8[9.5] 26.8 (19.5) (38.3) (117.4) (21.8) (10.0) (27.8) a Percentage contributions of each attractive energy terms are written in square brackets; BSSE corrected energy components are reported in the parenthesis

H2@Sn122



Page 52 of 53

Table 10. Calculated Values of Electrostatic Energy (Eele), Exchange Energy (Eex), Repulsion Energy (Erep), Polarization Energy (Epol), Dispersion Energy (Edisp) and the Total Interaction Energy (E) (in kcal mol1) in Ng@KPb12−, Ng@KSn12−, Ng@K2Pb12 and Ng@K2Sn12, Clusters (Ng = He, Ne, Ar, and Kr) as obtained using B3LYP Method with DEF2 Basis Set.a Complexes

Eele

Eex

Erep

Epol

Edisp

E

He@KPb12

129.0[67.5] (129.9)

18.88[9.9] (19.8)

73.5 (75.8)

33.0[17.2] (32.3)

10.3[5.4] (10.6)

117.7 (116.8)

Ne@KPb12

146.2[63.8] (146.4)

35.6[15.5] (36.0)

128.6 (130.2)

32.8[14.3] (31.5)

14.49[6.3] (15.0)

100.5 (98.7)

Ar@KPb12

186.6[59.4] (184.3)

85.6[25.2] (84.2)

295.5 (294.6)

46.5[13.7] (46.4)

21.1[6.2] (21.7)

44.4 (41.9)

He@KSn12

133.1[64.9] (131.7)

25.1[12.2] (22.8)

91.6 (86.4)

35.7[13.6] (32.34)

11.3[5.5] (11.6)

113.5 (112.1)

Ne@KSn12

160.4[61.8] (153.1)

48.0[18.5] (42.9)

166.5 (153.9)

35.2[13.6] (32.1)

15.9[6.1] (16.3)

93.0 (90.6)

Ar@KSn12

221.2[54.1] (199.5)

110.1[26.9] (99.6)

378.5 (349.1)

54.6[13.3] (54.2)

22.9[5.6] (23.5)

30.3 (27.7)

He@K2Pb12

249.1[76.5] (250.3)

23.3[7.2] (24.7)

93.7 (96.9)

38.9[11.9] (37.9)

14.1[4.3] (14.6)

231.6 (230.6)

Ne@K2Pb12

266.3[73.2] (266.7)

40.1[11.0] (41.1)

149.6 (152.0)

38.8[10.7] (37.4)

18.4[5.1] (19.1)

214.0 (212.2)

Ar@K2Pb12

305.9[64.8] (303.6)

89.0[18.8] (88.6)

315.4 (315.2)

52.2[11.0] (52.0)

25.1[5.3] (25.9)

156.7 (154.9)

He@K2Sn12

254.3[74.9] (252.8)

29.3[8.6] (27.4)

111.4 (106.2)

40.9[12.0] (37.3)

15.1[4.5] (15.5)

228.2 (226.8)

Ne@K2Sn12

281.2[71.5] (273.7)

52.1[13.3] (47.5)

186.7 (174.0)

40.2[10.2] (37.0)

19.7[5.0] (20.3)

206.6 (204.4)

340.3[63.0] 113.7[21.1] 396.6 59.0[10.9] 27.0[5.0] 143.1 (318.4) (103.4) (367.2) (58.3) (27.5) (140.3) a Percentage contributions of each attractive energy terms are written in square brackets; BSSE corrected energy components are reported in the parenthesis

Ar@K2Sn12


Page 53 of 53 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table of Content Graphics

K+

K+


Noble Gas Encapsulated Endohedral Zintl Ions Ng@Pb122â and Ng

Recommend Documents

Noble Gas Encapsulated Endohedral Zintl Ions Ng@Pb122â and Ng