CounterâIntuitive Stability in Actinide Encapsulated Metalloid Clusters

Subscriber access provided by Kaohsiung Medical University

C: Surfaces, Interfaces, Porous Materials, and Catalysis

Counter–Intuitive Stability in Actinide Encapsulated Metalloid Clusters with Broken Aromaticity Meenakshi Joshi, Ayan Ghosh, Aditi Chandrasekar, and Tapan K. Ghanty J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b05883 • Publication Date (Web): 27 Aug 2018 Downloaded from http://pubs.acs.org on September 2, 2018

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 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 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.

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 34 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

Counter–intuitive Stability in Actinide Encapsulated Metalloid Clusters with Broken Aromaticity Meenakshi Joshi†,§ Ayan Ghosh#,§, Aditi Chandrasekar‡,§ and Tapan K. Ghanty†,§,* †

Theoretical Chemistry Section, Chemistry Group, Bhabha Atomic Research Centre, Mumbai 400085, India. #

Laser and Plasma Technology Division, Beam Technology Development Group, Bhabha Atomic Research Centre, Mumbai 400085, India.

‡

Fuel Chemistry Division, Indira Gandhi Centre for Atomic Research, Kalpakkam 603102, India.

§

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

AUTHOR INFORMATION Corresponding Author *

Email: [email protected]; Fax: 0091–22–25505151

Page 1 of 34 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 34

ABSTRACT Aromaticity has been traditionally used for decades to explain the exceptional stability of certain conjugated organic compounds. Only in the recent past, this concept has crossed the bounds of organic chemistry and been employed in understanding inorganic ring systems with conjugation. In the present work, actinide element doped E126– (E= Sb, Bi) clusters formed from the combination of an actinide ion and aromatic Bi42– or Sb42– rings are thoroughly investigated using density functional theory (DFT) to explore their geometric, electronic and bonding properties in comparison with the bare cluster. The aromatic E42– rings in the bare clusters lost their aromaticity due to loss in planarity of the E42– rings on interaction with the central atom/ion. Although the extent of non−planarity of the three E42– rings is increased considerably on moving along the valence−isoelectronic series, Th4+– Pa5+– U6+– Np7+ in the doped clusters, the stability of the clusters is increased significantly. Valence–isoelectronic lanthanide ion doped metalloid clusters, viz., La3+, Ce4+, Pr5+ and Nd6+ have also been investigated for the sake of comparison, among which experimental and theoretical study of [La(η4–Sb4)3]3– cluster has been reported recently. The highlight of the entire investigation is that the metal atom/ion doped clusters nevertheless, displayed higher stability than the bare clusters in spite of losing their valuable aromatic stabilization. The various factors responsible for the stability of the lanthanide and actinide doped non–aromatic clusters including electronic shell–closing are elucidated in the present research.

*

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

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


Page 3 of 34 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 Over the past few years, clusters have attracted considerable attention from many researchers due to their unusual optoelectronic behaviour, magnetism, catalytic activities, as well as their similarity with super atomic systems.1−9 Among all the clusters, particularly metalloid anion clusters usually known as Zintl ions, possess striking chemical and physical peculiarities that make them inspiring specimens for experimentalists and theorists alike.10−16 Additionally, the inclusion of different metal atoms or ions into the host clusters can result in new types of cluster systems with different properties that were absent in the bare cluster. Thus, a multitude of intriguing metal−doped clusters with entirely different and unexpected characteristics become possible.17−19 Moreover, encapsulation of metals in the bare cluster stabilizes the cluster cage, which on certain occasions would have been unstable standing alone. An example of such a system is metal encapsulated [Co@Ge10]3– and [Fe@Ge10]3– clusters which are stable, whereas the bare Ge10n– cluster has not been successfully isolated.20,21 Another example is W@Au12, where the 12−atom gold cage is stabilized by placing a W atom at the cage center.22 Consequently, just by functionalizing the cluster with different dopants new stable clusters with novel properties can be prepared via synthetic routes.23−26 Although the formation mechanism of large bio–organic and organometallic compounds with complex chemical systems has been understood a decade ago27−33, the formation mechanism of the ligand−free inorganic chemical species are not clear due to the structural dissimilarities of the constituent species and their complexes. Only recently in the work done by Mitzinger and co – workers34, an attempt has been made to comprehend the formation mechanism of ligand−free inorganic chemical compounds containing Zintl ions and it has attracted the attention of scientists in this advancing field of research. Thorough knowledge of the mechanistic pathways is beneficial for the optimization of reaction conditions leading to better yields and cost effective synthesis.34 A large number of studies have been carried out in the past on a range of multi– metallic clusters doped with transition metal atoms or ions.9−33 Rare–earth doped metalloid clusters, [Ln@Pb6Bi8]3–, [Ln@Pb3Bi10]3–, [Ln@Pb7Bi7]4–,[Ln@Pb4Bi9]4– etc. have also been studied experimentally as well as quantum mechanically.35−39 Examining lanthanide (Ln) and actinide (An) doped clusters, gives insights about their structure, bonding, and magnetic properties. Recently, U doped metalloid clusters, [U@Bi12]3−, [U@Tl2Bi11]3−, [U@Pb7Bi7]3−, and [U@Pb4Bi9]3− have been synthesized and characterized experimentally as well as theoretically and have been shown to have unique anti–ferromagnetic coupling between the metal–actinide atoms.40 Apart from the uranium doped clusters, lanthanide doped metalloids Page 3 of 34 ACS Paragon Plus Environment


Page 4 of 34

clusters, [Ln@Sb12]3– (Ln = La, Y, Ho, Er, Lu) have also been synthesized by Xue Min et. al. and were further isolated as the K([2.2.2]crypt) salts and characterised by single–crystal X– ray diffraction techniques.41 Very recently Rookes et al. have synthesised and characterized the [An(TrenDMBS){Pn(SiMe3)2}] and [An(TrenTIPS){Pn(SiMe3)2}] systems, (where, TrenDMBS = N(CH2CH2NSiMe2But)3, An = U, Pn = P, As, Sb, Bi; An = Th, Pn = P, As; and TrenTIPS = N(CH2CH2NSiPri3)3, An = U, Pn = P, As, Sb; An = Th, Pn = P, As, Sb) and investigated the thermal and photolytic reactivity of U–Pn and Th–Pn bonds.42 It is worthwhile to mention that the concept of ''Magic Number'' is one of the most important parameters for explaining the stability of a large number of cluster systems. Structures containing 18, 32 and 42–electrons in their valence shells are called ''Magic Number'' species. Magic number behaviour of any system can be understood using two factors of stability: one of them is high structural symmetry and the other is electronic shell closure.43 The Langmuir 18–electron principle successfully explains the stability of a range of systems containing 18– electrons corresponding to fully occupied ns2np6(n−1)d10 configurations.44,45 Conversely, the stability of actinide and lanthanide containing systems is often explained by invoking the 32– electron principle because of a further addition of 14–electrons to the system from the 4f/5f orbitals of lanthanides or actinides, respectively. There are many cases of stable 32–electron containing systems such as An@C28,46, Pu@Pb12,47 Pu@Sn12,47 [U@Si20]6–,48 M@C26,49 and Pu@C2450 which have been reported in recent years. The endohedral cluster U@C28 following the 32–electron principle51 has been studied experimentally and found to form spontaneously in the vapour phase,52 confirming the validity of the 32–electron principle in explaining the stability of lanthanide and actinide doped cluster systems. Moreover, stable clusters associated with intermediate magic number of 26–electron are also reported in the literature.53–55 Although the ligand free inorganic chemical compound containing lanthanum, [La@Sb12]3– is synthesized and characterized experimentally as well as studied theoretcially41, encapsulation of actinide (Th4+, Pa5+, U6+ and Np7+) ions in the negatively charged antimony and bismuth clusters (Sb126– and Bi126– ) have not been reported before. Thus, the present work not only attempts to provide a thorough analysis on the stability of the experimentally observed [La@Sb12]3– cluster41 within the framework of electronic shell closing principles but also to predict the stability of actinide centered clusters and other valence−isoelectronic lanthanide centered clusters through quantum chemical calculations. For this purpose, we have Page 4 of 34 ACS Paragon Plus Environment

Page 5 of 34 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


investigated the optimized geometrical parameters, binding energies as well as the electronic properties of all Ln@E126– and An@E126– clusters using density functional theory (DFT) based techniques. Another interesting feature in this work is to study the dependence of charge on the metal ion towards the extent of non–planarity of the three E42–. The encapsulated forms denoted as Ln@E126 and An@E126 clusters have been examined with respect to their stability order with variation of the central metal atom/ion in different metalloid clusters (Sb126 and Bi126). In the present theoretical study, metal atom or ion encapsulated clusters have been rendered stable in spite of losing the aromaticity of their parent E42 (E= Bi, Sb) rings. Thus, it is of immense interest to explore the reasons behind the unusually high stability of these clusters, notwithstanding their conversion into what is expected to be a less stable anti–aromatic cluster. Importance of the concepts of aromaticity and anti–aromaticity in guiding experimental synthesis and rationalizing geometrical and electronic structures of some Zintl clusters has been emphasized very recently.56 2. COMPUTATIONAL MEHODOLOGY In this study, all the theoretical computations including electronic structure optimizations, calculations of binding energies, HOMO–LUMO energy gap and charges have been performed using TURBOMOLE–6.6 package.57 All the calculations have been carried out using generalized gradient approximation type Perdew–Burke–Ernzerhof (PBE)58 and Becke 3–parameter exchange and Lee−Yang−Parr correlation (B3LYP) hybrid functionals.59,60 For all heavy atoms viz., Sb (ECP−46), Bi (ECP−78), La (ECP−46), Ce, Pr, Nd (ECP−28) and Th, Pa, U, Np (ECP−60), effective core potential along with def−TZVPP61–68 basis set have been used. This combination of basis set is denoted as DEF throughout the text unless otherwise mentioned. For the purpose of comparison, we have also used small core ECP for all the heavy atoms viz., Ln (ECP−28), An (ECP−60), Sb ( ECP−28) and Bi (ECP−60) along with def−TZVPP (for Ln and An) and def2−TZVPP (for Sb and Bi) basis sets.61–69 However, for La we have used Stuttgart basis set.70,71This combination of small core ECP along with the corresponding basis set is represented as DEF2. The harmonic vibrational frequencies have been calculated with the same level of theory and all real frequency values confirm the true minima state of the clusters studied here on their respective potential energy surfaces (PES). The thermodynamic stability of the early lanthanide and actinide encapsulated metalloid clusters has been determined based on their binding energy values. In addition, natural population analysis (NPA)72 has been performed to calculate the natural population on Page 5 of 34 ACS Paragon Plus Environment


Page 6 of 34

f orbitals of the central metal atom. The VDD charge on doped metal atom is also calculated by using Voronoi deformation density (VDD)73 method with ADF2016 software.74−76 Furthermore, the Atoms–in–Molecules (AIM) analysis77,78 has been adopted to understand the nature of bonding that exists between the lanthanide or actinide elements with the elements present in the Zintl ions by employing PBE method using Multiwfn program.79 The use of densities obtained using a pseudopotential may cause problems like lack of nuclear maxima and appearance of spurious critical points. Therefore, to avoid these problems we have used an approximation recently developed by Keith and Frisch80 in which the missing core electron density is modelled by an energy density function (EDF). Since, the inclusion of EDF is sufficient to avoid the interference of spurious electron density critical points in case of small core ECP81−84, therefore, the AIM properties of all the clusters are calculated using small core ECP augmented with EDF. Further, to analyse the nature of interaction between the central atom and ring atoms, energy decomposition analysis85−87 is performed at PBE/TZ2P level88 using scalar relativistic zeroth order regular approximation89,90 (ZORA) with ADF2016 software. Moreover, we also studied the effect of spin orbit coupling91 on the few systems. 3. RESULTS AND DISCUSSIONS 3.1. Bare E126– Systems Both the bare metalloid Zintl ion clusters, E126– (E = Sb and Bi) contain three E42– rings. The Sb42– and Bi42– rings have been optimized using PBE method with DEF basis set and are found to have all real frequencies in D4h symmetry confirming their minimum energy state structures. Both the Sb42– and Bi42– rings are aromatic and have already been synthesized in the past.92–94 The pictorial representation of E42– ring is shown in Figure 1a. The bare E126– systems are found to be highly unstable because of the weak interactions between the neighbouring E42– units in the absence of a metal ion. In these Zintl ions (E126–), there are two types of bonding, one is intra–ring bonding (Rintra), that is bonding within the E42– rings and the second is inter–ring bonding (Rinter), that is bonding between the neighbouring rings (E42– –E42–). In both the Sb126– and Bi126– clusters intra–ring bonding is found to be much stronger, while inter–ring bonding is observed to be extremely weak which clearly represents the highly stable and less reactive aromatic nature of the Sb42– and Bi42– rings.


Page 7 of 34 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


3.2. Geometries and Chemical Stabilities of Ln@E126– and An@E126– Systems To begin with, we optimized the U@Bi123− and La@Sb123− clusters with PBE/DEF and B3LYP/DEF methods. For comparison purpose U@Bi123− and La@Sb123− clusters are also optimized with small core ECP using PBE/DEF2 and B3LYP/DEF2 methods. The calculated bond lengths of [U@Bi12]3− and La@Sb123− clusters are reported in Table S1. Similar to the earlier work40, [U@Bi12]3− system contains one unpaired electron in the f orbital of the central atom. In the optimized structure of the Ln@E126 and An@E126 clusters, six atoms (E = Sb or Bi) of the E126 clusters are in the plane while for the remaining six atoms, three atoms are above the plane and three lie below the plane. In addition to Rintra and Rinter bond distances, metal doped clusters also possess two other type of bonding; one is the bonding of central metal atom with the six in−plane atoms of E126 clusters known as equatorial bonding (Req) and the second is the bonding of central metal ion with the six out of plane atoms of the E126 clusters, which is mentioned as axial bonding (Rax) throughout the paper. It is noteworthy to mention that for La@Sb123– and U@Bi123– clusters, the Rax and Req corresponding to M−E bond as well as Rinter and Rintra, corresponding to E–E (E = Sb, Bi) bond calculated using PBE/DEF and PBE/DEF2 methods are somewhat close to the corresponding experimental values.40,41 Whereas, the B3LYP calculated Rax, Req, Rinter and Rintra values of La@Sb123– and U@Bi123– clusters are significantly different than the corresponding reported experimental values.40,41 Further, from Table S1, it can be seen that the HOMO–LUMO energy gap values calculated using PBE/DEF and PBE/DEF2 methods are very close. The HOMO–LUMO gap calculated using B3LYP functional is relatively higher for both systems.95 Since, the PBE calculated bond lengths are in good agreement with the experimentally reported values, therefore various properties of all the clusters have been investigated using PBE/DEF method. After performing the benchmark study for U@Bi123− and La@Sb123− clusters, all the lanthanide and actinide doped metalloid clusters viz., Ln@E126 and An@E126 (Ln = La3+, Ce4+, Pr5+, Nd6+; An = Th4+, Pa5+, U6+, Np7+; E = Sb, Bi) are optimized in D3h symmetry with real frequency values using PBE/DEF method (Figure 1b). In addition to the D3h symmetry, all the Ln@E126 and An@E126 clusters except Nd@E126 are also optimized in Cs symmetry with real frequencies (Figure 1c). However, this particular geometry with Cs symmetry is energetically less stable as compared to the corresponding D3h geometry isomer (Table S2). Moreover, we have also optimized all the Ln@Sb126 and An@Sb126 clusters using Page 7 of 34 ACS Paragon Plus Environment


Page 8 of 34

icosahedral geometry without any symmetry constrain using PBE/DEF method. However, all the systems are found to be optimized in highly distorted icosahedral structure. Furthermore, these distorted icosahedral geometries for all the Ln@Sb126 and An@Sb126 clusters are found to be energetically less stable (by 0.05–1.6 eV) as compared to their corresponding D3h isomer, which is consistent with the experimentally41 observed D3h structure of [Ln@Sb12]3– clusters reported recently. Therefore, D3h geometry represents the true minimum structure for all the Ln@E126 and An@E126 clusters. In general, the intra–ring bond distances are found to be smaller than that of the inter–ring bond distances indicating a stronger intra–ring bonding as compared to inter–ring bonding in most of the metalloid systems (Table 1). This trend is in agreement with the intra− and inter−ring bond distances for the K([2.2.2]crypt) salts of [Ln@Sb12]3– (Ln = La, Y, Ho, Er, Lu) systems, which have been synthesized and characterized recently.41 However, in the U@Bi12, Np@Bi12+, Np@Sb12+ and Nd@Bi12 clusters, the inter−ring bonding turns out to be stronger than the intra−ring, indicating a greater extent of interaction between the three neighbouring E42– rings in the presence of U6+, Np7+ and Nd6+ metal ions. This alternative trend has also been found in the recently synthesized K([2.2.2]crypt) salts of [U@Bi12]3–.40 Furthermore, on moving from La3+ to Nd6+ and Th4+ to Np7+ in Ln@E126 and An@E126 clusters, respectively, the values of Rax and Req are found to increase monotonically. It is interesting to observe that as we move from La3+ to Nd6+ and Th4+ to Np7+ in Ln@E126 and An@E126 clusters the bonding between the neighbouring rings (Rinter) is progressively increasing whereas the bonding within the rings (Rintra) is decreasing. The variation of the Rax, Req, Rintra and Rinter are reported in Table 1. These bond length values clearly indicate that the central metal ion plays a vital role to stabilize these clusters. For comparison purpose all the clusters are also optimized using B3LYP/DEF method. The B3LYP/DEF calculated Rax, Req, Rintra and Rinter values also follow the same stability trend as we discussed above for the PBE calculated bond distances of the Ln@E126– and An@E126– clusters (Table S3 ). 3.3. Binding Energy Estimation The stability of the lanthanide (Ln = La3+, Ce4+, Pr5+, and Nd6+) as well as actinide (An = Th4+, Pa5+, U6+, and Np7+) doped metalloids (E = Sb126– and Bi126–) systems can be determined based on their binding energy values, which are calculated by using the following pathway (path1): Mn+ + 3 [E4]2–  [M@E12]n–6 Page 8 of 34 ACS Paragon Plus Environment

Page 9 of 34 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


B.E. = E ([M@E12]n–6) – E (Mn+) – 3E (E42–) All the encapsulations are found to be exothermic in nature with negative binding energy values, which is indicative of the feasibility of bond formation between the central metal atom with the E42– rings atoms, thus favouring the formation of all Ln@E126– and An@E126– clusters. For all the systems, calculated binding energies are very high (Table 2). The calculated binding energies for the Ln@Sb126– systems (with Ln = La3+, Ce4+, Pr5+ and Nd6+) are 46.6, 90.0, 151.7 and 234.8 eV, respectively. The binding energies values for the corresponding Ln@Bi126– systems are 46.9, 90.4, 152.3 and 235.6 eV. The two set of values are very close to each other indicating that for a particular central metal ion, the binding energy value remains almost the same with change in the Zintl ion ligand from Sb42– to Bi42–. However, for a particular ligand there is an enormous change in the binding energy value along the La3+  Ce4+  Pr5+  Nd6+ series, which is consistent with the calculated structural trends. Similar trends are observed for the An@Sb126– and An@Bi126– systems, where the binding energy values are 82.4, 131.2, 196.0 and 278.7 eV and 82.6, 131.5, 196.5 and 279.5 eV, respectively, along the Th4+  Pa5+  U6+  Np7+ series. The B3LYP calculated binding energies of Ln@E126– and An@E126– clusters reported in Table S4 also follow the similar stability trend. For neutral U@Sb12, U@Bi12, Nd@Sb12 and Nd@Bi12 systems, we again calculated the binding energy using another pathway (path2) that is shown below: M + 3 [E4]  M@E12 B.E. = E (M@E12) – E (M) – 3E (E4) The binding energy values calculated using the path2 are −13.84 and −13.89 eV for U@Bi12 and U@Sb12 systems, respectively. And for Nd@Bi12 and Nd@Sb12 systems binding energies are −8.75 and −8.47 eV, respectively. These values clearly indicate that the binding energy values are overestimated in case of highly charged fragments (path1). We anticipate higher binding energy by following the path1 as we are separating the highly charged species in the gas phase. However, we have not used path2 for other systems because defining fragments for path2 becomes difficult for the charged systems studied here. In the present study, initially three planar and aromatic E42– rings (E = Sb and Bi) are considered to interact with each other as well as with the central metal ion to form Ln@E126– and An@E126– clusters. However, three rings (E42– unit) considerably deviate from their Page 9 of 34 ACS Paragon Plus Environment


Page 10 of 34

planarity in the corresponding Ln@E126– and An@E126– clusters similar to the experimentally reported [La(η4–Sb4)3]3– system.41 It is worthwhile to mention that the stability of metal−doped clusters has been significantly affected by the non−planarity of the three E42– rings present in their respective M@E126– clusters. On going from La@E123– to Nd@E12 and Th@E122– to Np@E12+ clusters, the extent of non−planarity of three metalloid rings (E42–) in their corresponding systems tend to increase considerably, where the dihedral angle varies from 12.9 to 25.2 degree and 17.2 to 28.5 degree for each of the Sb42– and Bi42– units in the corresponding complexes, as reported in Table 2. Thus, it is revealed that an increase in the dihedral angle on going from valence−isoelectronic La3+ to Nd6+ and Th4+ to Np7+ doped Zintl ion clusters, is associated with an increase in the strength of inter–ring bonding as well as bonding of central metal atom with the ring atoms, which in turn enhance the stability of these metalloid clusters. Similar trends are observed in the B3LYP/DEF calculated dihedral angles (Table S4). Consequently, all the clusters studied in this work are stable even after losing the aromaticity of their parent E42– rings, similar to the experimentally observed [Ln@Sb12]3– (Ln=La, Y, Ho, Er, Lu) clusters.41 3.4. Molecular orbital diagram and charge distribution The molecular orbital (MO) energy level diagrams of An@Sb126– and Ln@Sb126– clusters are shown in Figure 2 and Figure S1, respectively. For a better comparison, the orbital energies of the An@Sb126– and the Ln@Sb126– clusters are scaled to match the HOMO energies of U@Sb12 and Nd@Sb12 clusters, respectively. The HOMO–LUMO energy gap of all the actinide (An) and lanthanide (Ln) doped Zintl ion systems calculated by PBE/DEF method are listed in Table 2. The corresponding B3LYP/DEF calculated values are found to be relatively higher (Table S4). The sufficiently large HOMO–LUMO energy gap points to the significant chemical stability of all the studied clusters. It is to be noted that in all the An and Ln doped clusters the energy difference between the 6s/5s orbital and the 6p/5p orbitals of Sb/Bi atom is very large, therefore, only 6p/5p orbitals are considered as outer valence orbitals for bonding with doped metal atom. The Th4+ and La3+ doped Zintl ion clusters alone behave differently in comparison to the remaining An (An = Pa5+, U6+ and Np7+) and Ln (Ln = Ce4+, Pr5+ and Nd6+) doped clusters, as no f atomic orbitals of Th and La atom are involved in bonding with the valence atomic orbitals of ring atoms. It has been shown earlier that the f–function can significantly affect the bond length and dissociation energy of Th–O.96 Therefore, to see the effect of f function on the optimized parameters, binding energy and electronic property, we optimized Th@Sb122– and La@Sb123– clusters with and without f basis Page 10 of 34 ACS Paragon Plus Environment

Page 11 of 34 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


function61,97 in a systematic way. For this purpose we have used def–TZVPP basis set with f function and def–TZVP basis set without f function for the La atom,61 which are available in Turbomole–6.6 basis set library. For Th, we have used ECP78MWB–AVDZ without f function (represented as AVDZ) and ECP78MWB–AVTZ (represented as AVTZ) with f function basis sets.97 Both the basis sets are taken from Stuttgart basis set library.98 Furthermore, we have also optimized Th–O with and without f basis function using AVTZ and AVDZ basis sets97, respectively, for the purpose of comparison. We have found very small effect of f function on the optimized bond length, electronic count, and binding energy values of Th@Sb122– and La@Sb123– clusters, whereas significant effect of f–function is found for Th–O system as shown in Table S5. Thus, for Th@Sb122– and La@Sb123– clusters the molecular calculations with and without f functions on La/Th provides almost the same result. Furthermore, in both the La@Sb123– and Th@Sb122– systems, no f–orbital of La and Th is involved in bonding with Sb atom of the cage, using basis set with f–function as well as without f–function. It is to be noted that in case of U@Sb12, Np@Sb12+, Ce@Sb122– and Pr@Sb12–, the LUMO are localized on the f orbital of the doped atom, whereas in Pa@Sb12–, Nd@Sb12, the LUMO contains orbital contribution from the ring atoms as well as from the f–orbitals of doped atom. Conversely, the LUMO of Th@Sb122– and La@Sb123– is localized on the ring atoms alone. From Figure S2, one can see the participation of the valence 7s, 7p, 6d, orbitals of Th in bonding with the 6p orbitals of ring atoms in 10e', 8a1', 5a2", 5e", 9e', 8e', 7e' and 7a1' MOs. As a consequence, these hybrid MOs fulfil the 26–electron count53–55 around the Th. Similarly the La@Sb123– cluster forms a stable 26–electron system corresponding to completely filled 6a1', 8e', 4e", 4a2", 7e', 6e', 5e', and 5a1' mixed MOs (Figure S3), which are formed by the overlapping of the valence orbitals of La (6s, 6p, 5d) and the valence orbitals of ring (6p) atoms. While the remaining occupied MOs in both the clusters are due to the pure ring (Sb126–) orbitals. Unlike in the case of Th4+ and La3+, the f orbitals of remaining An (An = Pa5+, U6+ and Np7+) and Ln (Ln = Ce4+, Pr5+, Nd6+) are involved in bonding with the p orbitals of the rings. From Figures S4 and S5, one can see that in U@Sb12 and Nd@Sb12 clusters, the ns, np, (n−1) d, and (n−2)f (where, n =7, 6 for An and Ln, respectively) orbitals of An and Ln overlap with the 6p orbitals of cage to from a stable 32–electron system46–51 corresponding to completely filled 10e', 5a2", 2a2', 8a1', 5e", 9e', 4e", 8e', 7e' and 7a1' mixed MOs. However, in the Ln doped clusters the rings–central atom mixing in 4e" orbital is small. In all the An@Sb126 and Ln@Sb126 clusters, 1a1'', 4a2", 3e" and 6a1' MOs correspond Page 11 of 34 ACS Paragon Plus Environment


Page 12 of 34

to the 6p orbitals of ring atoms and do not contribute to the bonding with the central atom. In the same way An and Ln doped Bi clusters also fulfil the 26–electron count around Th and La, and 32–electron count around the remaining An (Pa5+, U6+ and Np7+) and Ln (Ce4+, Pr5+, Nd6+) in their respective clusters. Thus the absence of the involvement of the f–orbitals in the bonding with the ring atoms causes the difference of 6 electrons in the total electron count of Th4+ and La3+ containing E126– ring. Therefore, larger involvement of the f–orbitals of An (U6+ and Np7+) and Ln (Nd6+) in bonding with the ring atoms is responsible for the stronger inter ring bonding as compared to the intra ring bonding in Np@Sb12+, U@Bi12, Np@Bi12 and Nd@Bi12 systems, which clearly shows the impact of f–orbitals of An and Ln on the geometrical parameters of these systems. Further the VDD73 charges on central atoms as well as on the ring atoms of Ln@E126– and An@E126– clusters are calculated using PBE/TZ2P method (Table S6). The calculated VDD charges on the central atoms are in the range of 0.01 to −0.06 for An (Th4+ to Np7+) and −0.05 to −0.06 for Ln (La3+ to Nd6+), which is significantly smaller than the initial charge on the central atoms (i.e., +3 to +7). On the other hand, the overall negative charge of ring (i.e., −6) has been reduced to the range of −2.95 to 0.06, from La3+ to Nd6+ doped clusters and −2.01 to 1.07 from Th4+ to Np7+ doped clusters. The increase in the negative charge on the An and Ln metal ions and decrease in the negative charge of ring in the M@Sb126– and M@Bi126– clusters indicates that some amount of electron density has been transferred from the ring to the central atoms, where the charge transfer from ring orbitals to central atom orbitals is maximum in case of Np7+, U6+ and Nd6+ doped clusters. Further, the population of the valence s, p, d and f orbitals of the central atom in all metal−doped clusters are calculated using natural population analysis (NPA)72 scheme. On moving from Th4+ to Np7+ and La3+ to Nd6+ metal ions, it has been found that s and p populations on central atom are more or less similar while there is a significant variation in its f population for both lanthanide and actinide doped clusters as shown in Table S6. The 4f population of lanthanide ions in the Ln@E126– systems is observed to be smaller as compared to 5f–population of actinides in the corresponding An@E126– clusters. 3.5. Density of States Density of states plots (DOS) for the M@Sb126– (M = An, Ln) clusters are represented in Figure 3 and Figure S6, respectively. For, M@Bi126– clusters the DOS plots are given in Figure S7. All the bands appearing at the right side of the HOMO (HOMO is pointed by the Page 12 of 34 ACS Paragon Plus Environment

Page 13 of 34 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


vertical arrow) correspond to the unoccupied MOs. While the bands appearing at the left side of the HOMO correspond to the mixed occupied MOs (associated with the valence orbital of central atom (s, p, d and f) as well as ring orbitals (p)) and pure occupied MOs (associated with the ring atomic orbital only). It is to be noted that the DOS are shifted deeper in energy from Th4+ − Np7+ and La3+ − Nd6+ doped clusters, indicative of increasing extent of hybridization of central atom with ring atoms. Furthermore, as compared to the actinide– doped systems, the lanthanide doped Ln@E126− systems are shifted less deep in energy, because of the slightly smaller mixing of their less diffuse 4f orbitals with the p orbitals of Sb/Bi compared to the stronger hybridization of the more diffuse 5f orbitals of actinides with the p orbitals of Sb/Bi atoms. 3.6. Analysis of topological properties of M@E126– clusters To analyze the nature of chemical bonding between the ring atoms as well as between the central metal atom (Ln/An) and ring atoms (Sb/Bi) in Ln@E126– and An@E126– clusters, bond critical point (BCP) properties have been calculated using Bader's quantum theory of atomsinmolecules (QTAIM)77 with small core ECP augmented with EDF using PBE/DEF2 method. The electron density plots and Laplacian of electron density plots of M@Sb126– and M@Bi126– (M = Ln and An) clusters are represented in Figure S8 and Figure S9, respectively. The various bond critical point (BCP) properties of are listed in Tables S7– S1. Usually the values of electron density and Laplacian of electron density allows us to distinguish between covalent (for large density and 2ρ(rc) < 0 ) and non–covalent interactions (for small density and 2ρ(rc) > 0). However, according to Boggs78 sometimes the use of 2ρ(rc) can produce conflicting results. According to Boggs, if the local electron energy density i.e., Ed < 0 or |Ed| < 0.005 and G(rc)/ρ(rc) < 1, the interaction possess some degree of covalency even if the value of 2ρ(rc) > 0. It is to be noted that the value of 2ρ(rc) > 0 and density is very small at BCP the for all the studied clusters. Therefore, the Rax and Req bonds as well as inter and intra–ring bonding are not true covalent bond. However, at BCP the value of Ed(rc) < 0 and G(rc)/ρ(rc) < 1, which suggest a small amount of covalent character in all four type of bonds. It is interesting to observe that at BCP the value of electron density () corresponding to Rax, Req and Rinter bonds increases slightly on moving from La3+ to Nd6+ and Th4+ to Np7+ doped E126– (E= Sb or Bi) clusters (Tables S7–S10). However, the electron density for Rintra bonds tend to decrease on moving from La3+ to Nd6+ and Th4+ to Np7+ doped E126– (E= Sb or Bi) clusters. Consequently, the strength of Rax , Req Page 13 of 34 ACS Paragon Plus Environment


Page 14 of 34

and Rinter bonds increases along La3+ – Ce4+ – Pr5+ – Nd6+ and Th4+ – Pa5+ – U5+ – Np7+ series in their respective clusters while the strength of Rintra bonds decreases along the same series. All these trends are in agreement with the corresponding structural parameters. 3.7. Vibration Frequency Analysis A detailed IR spectroscopic analysis of the lanthanide and actinides encapsulated Sb126– and Bi126– clusters has been performed using Turbomole 6.6 program and the results are reported in Tables S11 and S12. The harmonic vibrational spectra for M@Sb126– and M@Bi126– clusters (where M = Th4+, Pa5+, U6+, Np7+ and La3+, Ce4+, Pr5+, Nd6+ ) are shown in Figure S10 and Figure S11, respectively. In all the metal encapsulated clusters with D3h point group, only the normal modes with a2'' and e' symmetries are IR active, while the remaining modes are IR inactive. Most of the peaks appearing at the higher frequencies correspond to the combined motion of the central metal atom and ring atoms. However, the peaks corresponding to the lower frequencies are mainly due to the bending involving ring atoms. In general, the frequency peaks are blue shifted on moving from La@Sb123– to Nd@Sb12 and Th@Sb122– to Np@Sb12+ clusters. 3.8 Energy Decomposition Analysis To analyze the nature of interaction in M@E126− clusters, a detailed account of energy decomposition analysis (EDA)85−87 has been performed in ADF2016 package74−76 using PBE/TZ2P method along with scalar relativistic zeroth order regular approximation (ZORA).89,90 In EDA, The total energy (ΔE) is decomposed into Pauli repulsion (ΔEPauli), electrostatic interaction (ΔEelec), orbital interaction (ΔEorb) and preparatory energy (ΔEprep) terms. Thus, the total interaction energy, ΔEint can be represented as. ΔEint = ΔEPauli + ΔEelec + ΔEorb + ΔEprep The ΔEelec and ΔEorb are attractive energy (stabilizing) terms while ΔEPauli is repulsive energy (destabilizing) term. The ΔEprep is the preparatory energy term (also known as deformation energy of E42– rings in the presence of doped metal ion) , which is calculated by taking the energy difference between the distorted rings (3 E42– unit) of M@E126– with the relaxed bare 3E42– rings. We can see from Table 3, that the ΔEprep term increases as we move from Th4+ to Np7+ and La3+ to Nd6+ centered E126− clusters, which is in agreement with dihedral angle Page 14 of 34 ACS Paragon Plus Environment

Page 15 of 34 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


variation (Table 2). Thus E42– rings of the M@E126– get more distorted as we move from Th4+ to Np7+ and La3+ to Nd6+ centered E126− clusters. For EDA calculations, M@E126− clusters are partioned into four fragments viz., central ion (M) and three identical E42− rings (E = Sb, Bi). The EDA results of M@E126− clusters are provided in Table 3. It is to be noted that the bonding energy of all the Ln@E126− and An@E126− clusters are strongly affected by the nature and type of central metal atom, however insignificant effect of ring type (Sb42− or Bi42−) has been observed in the bonding energies of all the clusters. In case of An@E126− and Ln@E126− (E = Sb, Bi) clusters, the bonding energy has been drastically increased from Th4+ − Np7+ and La3+ − Nd6+ metal doped clusters. Note that in all the cases the major contribution of the attractive energy components makes the overall interaction energy attractive in nature. Further, as we move from Th4+ to Np7+ and La3+ to Nd6+ centered E126− clusters, the percentage contribution from the electrostatic terms become smaller while the contribution of ΔEorb term is found to be increased, leading to more stability for the Np@E12+ and Nd@E12 clusters as compared to the remaining clusters. The increase in the ΔEorb contribution along these series is clearly due to an increase in the Rax, Req and Rinter bonding. 3.9 Spin Orbit Coupling Effect We studied the effect of spin orbit coupling for four systems namely, U@Sb12, U@Bi12, Nd@Sb12, and Nd@Bi12. The U@Sb12 system has been optimized using spin orbit coupling and scalar relativistic effect using PBE functional and TZ2P88 basis set. The bond lengths calculated incorporating spin orbit coupling (Rax = 3.082, Req = 3.372, Rinter = 2.968, Rintra = 2.960) and scalar relativistic effects (Rax =3.054, Req = 3.343, Rinter =2.948, Rintra =2.949) are relatively close in value, indicating a very small effect of spin orbit coupling on the structural parameter of U@Sb12 system. Similarly, the HOMO−LUMO gap calculated using spin orbit coupling (0.839 eV) is relatively smaller than that obtained by the scalar relativistic calculation (0.993 eV) due to the splitting of the energy levels. The calculated bond lengths of U@Sb12 (Rax = 3.029, Req = 3.295, Rinter = 2.914, Rintra = 2.902) using PBE/DEF2 method are relatively close to the bond lengths calculated using the scalar relativistic effects. Since the variation in the optimized bond length is not large, for the remaining systems we have performed single point energy calculations using scalar relativistic and spin orbit coupling by taking the optimized geometry obtained by the PBE/DEF method. We have also plotted the MO energy level diagram to see the effect of spin orbit interaction on the energy levels of all the above–mentioned clusters. In the presence of spin orbit coupling, the Page 15 of 34 ACS Paragon Plus Environment


Page 16 of 34

HOMO−LUMO gaps are slightly lowered in all the systems because of splitting of the energy levels. The HOMO−LUMO gap calculated using both methods are shown in Figure 4 and Figures S12−14. Because of the spin orbit coupling, the molecular orbitals energy levels split, although the extent of splitting of MO energy levels is very small. From Figure 4 and Figures S12−S14, one can see that the effect of spin orbit coupling on the energy levels of MOs of U@Sb12, U@Bi12, Nd@Sb12, and Nd@Bi12 is too small to affect their electronic properties. 4. Conclusions Theoretical existence of an entire series of early lanthanide (La3+, Ce4+, Pr5+, Nd6+) and actinide (Th4+, Pa5+, U6+, Np7+) doped metalloid M@Sb126– and M@Bi126– clusters has been comprehensively investigated in the present work. Despite the loss of aromatic stabilization in the bare metalloid cages, a new class of valence iso–electronic series of actinides viz., Pa@Sb12–, U@Sb12, and Np@Sb12+ and lanthanides (Ce@Sb122–, Pr@Sb12–, and Nd@Sb12) following the 32–electron principle have been revealed, however, in the Ce@Sb122–, Pr@Sb12–, and Nd@Sb12 clusters the possibility of fulfilment of 32–electron count around the central atom is comparatively less as compared to the actinides doped clusters. Similar trends are observed for the corresponding bismuth clusters, viz., M@Bi126– (M = Ln and An). In the La@Sb123– and Th@Sb122– clusters the f–orbitals of La and Th do not participate in bonding with the ring orbitals, therefore, both the clusters follow 26–electron principle. Thus, the greater involvement of the f–orbitals of U, Np and Nd in bonding with ring atoms is responsible for the elongation of intra bonds (Rintra) of the three E42– rings and shortening of inter ring bonds (Rinter) of the U@Bi12, Np@Bi12+, Np@Sb12+ and Nd@Bi12 systems. In M@Sb126– and M@Bi126– clusters, all the three–aromatic rings of the bare cluster lose their planarity and in turn their aromaticity. However, the formation of closed shell 32−electron and 26−electron systems in addition to their favourable geometric as well as energetic parameters provides them with unusually high stability. An increased strength in inter–ring bonding as well as bonding of metal with cage atoms results in this phenomenon. On moving from valence iso−electronic Th4+ to Np7+ and La3+ to Nd6+ in the doped clusters, though the non−planarity of the three E42– rings is increased, the stability of the clusters is increased, indicating that less planar rings are more reactive and are hence responsible for increased interaction between the ring atoms as well as between the ring and the central atom. Our work uncovers the reasons behind the unexpectedly high stability of lanthanide doped anti– aromatic clusters as well as the stability of actinide doped metalloid clusters in many aspects. Further the clusters reported in this work have potential application in cluster–assembled Page 16 of 34 ACS Paragon Plus Environment

Page 17 of 34 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


material research owing to their tunable electronic properties across the rare earth and the actinide series. ASSOCIATED CONTENT Supporting Information Bond length, Binding energy and HOMO–LUMO gap of U@Bi123− and La@Sb123− Clusters using PBE (B3LYP) Methods along with DEF and DEF2 basis sets. Relative Energy, Bond length, Binding energy, HOMO–LUMO gap, NPA, VDD charge distributions, AIM properties, BCP plots, molecular orbital energy level diagram, molecular orbital pictures, DOS plots, Vibration frequency and Scalar relativistic and SOC molecular orbital energy level diagram of various M@Sb126− and M@Bi126− clusters. 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. M.J. and A.C. would like to thank Homi Bhabha National Institute for the Ph.D. fellowship in Chemical Sciences. A.C acknowledges Dr. N. Sivaraman for his constant support and the Computer Division, IGCAR for providing HPC facilities. It is a pleasure to thank Dr. A. K. Nayak, Shri R. K. Rajawat and Dr. P. D. Naik for their kind interest and continuous encouragement. References 1. Reveles, J. U.; Khanna, S. N. Electronic Counting Rules for the Stability of Metal−Silicon Clusters. Phys. Rev. B 2006, 74, 035435. 2. Wang, J.; Bai, J.; Jellinek, J.; Zeng, X. C. Gold−Coated Transition−Metal Anion [Mn13@Au20]− with Ultrahigh Magnetic Moment. J. Am. Chem. Soc. 2007, 129, 4110−4111. 3. Jing, Q.; Tian, F. Y.; Wang,Y. X. No Quenching of Magnetic Moment for the GenCO (n=1−13) Clusters: First−Principles Calculations. J. Chem. Phys. 2008, 128, 124319. 4. Korber, N. The Shape of Germanium Clusters to Come. Angew. Chem., Int. Ed. 2009, 48, 3216–3217



Page 18 of 34

5. Reveles, J. U.; Clayborne, P. A.; Reber, A. C.; Khanna, S. N.; Pradhan, K.; Sen, P.; Pederson, M. R. Designer Magnetic Superatoms. Nat. chem. 2009, 1, 310−315. 6. Medel, V. M.; Reveles, J. U.; Khanna, S. N.; Chauhan, V.; Sen, P.; Castleman, A. W. Hund's Rule in Superatoms with Transition Metal Impurities. Proc. Natl. Acad. Sci. U.S.A. 2011, 108, 10062−10066. 7. Jena, P. Beyond the Periodic Table of Elements: The Role of Superatoms. J. Phys. Chem. Lett. 2013, 4, 1432−1442. 8. Luo, Z.; Castleman. A. W. Special and General Superatoms. Acc. Chem. Res. 2014, 47, 2931−2940. 9. Zhou, S.; McIlwrath, K.; Jackson, G.; Eichhorn, B. Enhanced CO Tolerance for Hydrogen Activation in Au−Pt Dendritic Heteroaggregate Nanostructures J. Am. Chem. Soc. 2006, 128, 1780–1781. 10. Guo, L. J.; Zhao, G. F.; Gu, Y. Z.; Liu, X.; Zeng, Z. Density−Functional Investigation of Metal−Silicon Cage Clusters MSin (M= Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn; n= 8–16). Phys. Rev. B 2008, 77, 195417. 11. Ohara, M.; Koyasu, K.; Nakajima, A.; Kaya, K. Geometric and Electronic Structures of Metal (M)−Doped Silicon Clusters (M= Ti, Hf, Mo and W). Chem. Phys. Lett. 2003, 371, 490−497. 12. Kumar, V.; Kawazoe, Y. Metal−Encapsulated Icosahedral Superatoms of Germanium and Tin with Large Gaps: Zn@Ge12 and Cd@Sn12. Appl. Phys. Lett. 2002, 80, 859−861. 13. McCoy, R. S.; Choi, S.; Collins, G.; Ackerson, B. J.; Ackerson, C. J. Superatom Paramagnetism Enables Gold Nanocluster Heating in Applied Radiofrequency Fields. ACS nano 2013, 7, 2610−2616. 14. Okrut, A.; Runnebaum, R. C.; Ouyang, X.; Lu, J.; Aydin, C.; Hwang, S. J.; Zhang, S.; Olatunji−Ojo, O. A.; Durkin, K. A.; Dixon, D. A.; Gates, B. C. Selective Molecular Recognition by Nanoscale Environments in a Supported Iridium Cluster Catalyst. Nature nanotech. 2014, 9, 459−465. 15. Bals, S.; Van Aert, S.; Romero, C. P.; Lauwaet, K.; Van Bael, M. J.; Schoeters, B.; Partoens, B.; Yücelen, E.; Lievens, P.; Van Tendeloo, G. Atomic Scale Dynamics of Ultrasmall Germanium Clusters. Nat. Commun. 2012, 3, 897. 16. Qian, M.; Reber, A. C.; Ugrinov, A.; Chaki, N. K.; Mandal, S.; Saavedra, H. M.; Khanna, S. N.; Sen, A.; Weiss, P. S. Cluster−Assembled Materials: Toward Nanomaterials with Precise Control over Properties. ACS nano 2009, 4, 235−240. Page 18 of 34 ACS Paragon Plus Environment

Page 19 of 34 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


17. Fässler, T. F.; Hoffmann, S. D. Endohedral Zintl Ions: Intermetalloid Clusters. Angew. Chem., Int. Ed. 2004, 43, 6242−6247. 18. Schnöckel, H. Formation, Structure and Bonding of Metalloid Al and Ga Clusters. A Challenge for Chemical Efforts in Nanosciences. Dalton Trans. 2008, 4344−4362. 19. Lips, F.; Dehnen, S. Neither Electron−Precise nor in Accordance with Wade−Mingos rules: The Ternary Cluster Anion [Ni2Sn7Bi5]3–. Angew. Chem., Int. Ed. 2011, 50, 955−959. 20. Wang, J. Q.; Stegmaier, S.; Fässler, T. F. [Co@Ge10]3−: An Intermetalloid Cluster with Archimedean Pentagonal Prismatic Structure. Angew. Chem., Int. Ed. 2009, 48, 1998–2002. 21. Zhou, B.; Denning, M. S.; Kays, D. L.; Goicoechea, J. M. Synthesis and Isolation of [Fe@Ge10]3−: A Pentagonal Prismatic Zintl Ion Cage Encapsulating an Interstitial Iron Atom. J. Am. Chem. Soc. 2009, 131, 2802–2803. 22. Pyykkö P.; Runeberg, N. Icosahedral WAu12 A Predicted Closed‐Shell Species, Stabilized by Aurophilic Attraction and Relativity and in Accord with the 18‐Electron Rule. Angew. Chem., Int. Ed. 2002, 12, 2174–2176. 23. Goicoechea, J. M.; Sevov, S. C. Deltahedral Germanium Clusters: Insertion of Transition−Metal Atoms and Addition of Organometallic Fragments. J. Am. Chem. Soc. 2006, 128, 4155−4161. 24. Scharfe, S.; Fässler, T. F.; Stegmaier, S.; Hoffmann, S. D.; Ruhland, K. [Cu@Sn9]3− and [Cu@Pb9]3−: Intermetalloid Clusters with Endohedral Cu Atoms in Spherical Environments. Chem. Euro. J. 2008, 14, 4479−4483. 25. Krämer, T.; Duckworth, J. C.; Ingram, M. D.; Zhou, B.; McGrady, J. E.; Goicoechea, J. M. Structural Trends in Ten−Vertex Endohedral Clusters, M@E10 and the Synthesis of a New Member of the Family,[Fe@Sn10]3−. Dalton Trans. 2013, 42, 12120−12129. 26. Corey, E. J. The Logic of Chemical Synthesis: Multistep Synthesis of Complex Carbogenic Molecules (Nobel Lecture). Angew. Chem., Int. Ed. 1991, 30, 455−465. 27. 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. 28. Esenturk, E. N.; Fettinger, J.; Eichhorn, B. The Closo− Pb102– Zintl Ion in the [Ni@Pb10]2− Cluster. Chem. Commun. 2005, 247−249. 29. Esenturk, E. N.; Fettinger, J.; Lam, Y. F.; Eichhorn, B. [Pt@Pb12]2−. Angew. Chem., Int. Ed. 2004, 43, 2132−2134. Page 19 of 34 ACS Paragon Plus Environment


Page 20 of 34

30. Goicoechea, J. M.; Sevov, S. C. [(Ni−Ni−Ni)@(Ge9)2]4−: A Linear Triatomic Nickel Filament Enclosed in a Dimer of Nine−Atom Germanium Clusters. Angew. Chem., Int. Ed. 2005, 44, 4026−4028. 31. Goicoechea, J. M.; Sevov, S. C. [Zn9Bi11]5−: A Ligand−Free Intermetalloid Cluster. Angew. Chem., Int. Ed. 2006, 45, 5147−5150. 32. Moses, M. J.; Fettinger, J. C.; Eichhorn, B. W. Interpenetrating As20 Fullerene and Ni12 Icosahedra in the Onion−Skin [As@Ni12@As20]3– Ion. Science 2003, 300, 778−780. 33. Goicoechea, J. M.; Sevov, S. C. [(Pd − Pd)@Ge18]4–: A Palladium Dimer Inside the Largest Single−Cage Deltahedron. J. Am. Chem. Soc. 2005, 127, 7676−7677. 34. Mitzinger, S.; Broeckaert, L.; Massa, W.; Weigend, F.; Dehnen, S. Understanding of Multimetallic Cluster Growth. Nat. Commun. 2016, 7, 10480. 35. Grubisic, A.; Ko, Y. J.; Wang, H.; Bowen, K. H. Photoelectron Spectroscopy of Lanthanide− Silicon Cluster Anions LnSin− (3 ≤ n ≤ 13; Ln=Ho, Gd, Pr, Sm,Eu, Yb): Prospect for Magnetic Silicon−Based Clusters. J. Am. Chem. Soc. 2009, 131, 10783−10790. 36. Lips, F.; Clérac, R.; Dehnen, S. [Eu@Sn6Bi8]4−: A Mini−Fullerane−Type Zintl Anion Containing a Lanthanide ion. Angew. Chem., Int. Ed. 2010, 50, 960–964 37. Lips, F.; Hołyńska, M.; Clérac, R.; Linne, U.; Schellenberg, I.; Pöttgen, R.; Weigend, F.; Dehnen, S. Doped Semimetal Clusters: Ternary, Intermetalloid Anions [Ln@Sn7Bi7]4– and [Ln@Sn4Bi9]4– (Ln=La, Ce) with Adjustable Magnetic Properties. J. Am. Chem. Soc. 2012, 134, 1181–1191. 38. Weinert, B.; Weigend, F.; Dehnen, S. Subtle Impact of Atomic Ratio, Charge and Lewis

Basicity

on

Structure

Selection

and

Stability:

The

Zintl

Anion

[(La@In2Bi11)(µ−Bi)2(La@In2Bi11)]6–. Chem. Eur. J. 2012, 18, 13589–13595. 39. Ababei, R.; Massa, W.; Weinert, B.; Pollak, P.; Xie, X.; Clérac, R.; Weigend, F.; Dehnen, S. Ionic−Radius−Driven Selection of the Main−Group−Metal Cage for Intermetalloid Clusters [Ln@PbxBi14−x]q− and [Ln@PbyBi13−y]q− (x/q= 7/4, 6/3; y/q= 4/4, 3/3). Chem. Euro. J. 2014, 1, 386−394. 40. Lichtenberger, N.; Wilson, R. J.; Eulenstein, A. R.; Massa, W.; Clérac, R.; Weigend, F.; Dehnen, S. Main Group Metal–Actinide Magnetic Coupling and Structural Response Upon U4+ Inclusion Into Bi, Tl/Bi, or Pb/Bi Cages. J. Am. Chem. Soc. 2016, 138, 9033−9036.


Page 21 of 34 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


41. Min, X.; Popov, I. A.; Pan, F. X.; Li, L. J.; Matito, E.; Sun, Z. M.; Wang, L. S.; Boldyrev, A. I. All−Metal Antiaromaticity in Sb4−Type Lanthanocene Anions. Angew. Chem., Int. Ed. 2016, 55, 5531−5535. 42. Rookes, T. M.; Wildman, E. P.; Balázs, G.; Gardner, B. M.; Wooles, A. J.; Gregson, M.; Tuna, F.; Scheer, M.; Liddle, S. T. Actinide−Pnictide (An−Pn) Bonds Spanning Non−Metal, Metalloid, and Metal Combinations (An = U, Th; Pn = P, As, Sb, Bi). Angew. Chem., Int. Ed. 2017, 56, 1−6. 43. Lau, J. T.; Hirsch, K.; Klar, P.; Langenberg, A.; Lofink, F.; Richter, R.; Rittmann, J.; Vogel, M.; Zamudio−Bayer, V.; Möller, T.; Issendorff, B. V. X−ray Spectroscopy Reveals High Symmetry and Electronic Shell Structure of Transition−Metal−Doped Silicon Clusters. Phys. Rev. A 2009, 79, 053201. 44. Langmuir, I. Types of Valence. Science 1921, 54, 59−67. 45. Pyykkö, P. Understanding the Eighteen–Electron Rule. J. Organomet. Chem. 2006, 691, 4336−4340. 46. Dognon, J. P.; Clavaguéra, C.; Pyykkö, P. A Predicted Organometallic Series Following a 32−Electron Principle: An@C28 (An= Th, Pa+, U2+, Pu4+). J. Am. Chem. Soc. 2008, 131, 238−243. 47. Dognon, J. P.; Clavaguéra, C.; Pyykkö, P. Chemical Properties of the Predicted 32−Electron Systems Pu@Sn12 and Pu@Pb12. Comptes. Rendus. Chimie. 2010, 13, 884−888. 48. Dognon, J. P.; Clavaguéra, C.; Pyykkö, P. A New, Centered 32−Electron System: The Predicted [U@Si20]6− −Like Isoelectronic Series. Chem. Sci. 2012, 3, 2843−2848. 49. 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. 50. Manna, D.; Sirohiwal, A.; Ghanty, T. K. Pu@C24: A New Example Satisfying the 32−Electron Principle. J. Phys. Chem. C 2014, 118, 7211−7221. 51. Xing, D.; Yang, G.; Wanrun, J.; Yanyu, L.; Zhigang, W. U@C28: The Electronic Structure Induced by the 32−electron Principle. Phys. Chem. Chem. Phys. 2015, 17, 23308−23311. 52. Guo, T.; Diener, M. D.; Chai, Y.; Alford, M. J.; Haufler, R. E.; McClure, S. M.; Ohno, T.; Weaver, J. H.; Scuseria G. E.; Smalley, R. E. Uranium Stabilization of C28: A Tetravalent Fullerene. Science 1992, 257, 1661−1664.



Page 22 of 34

53. Manna, D.; Ghanty, T. K. Theoretical Prediction of Icosahedral U@C20 and Analogous Systems with High HOMO–LUMO Gap. J. Phys. Chem. C 2012, 116, 16716−16725. 54. Cui, L. – F.; Huang, X.; Wang, L. –M.; Zubarev, D. Y.; Boldyrev, A. I.; Li, J.; Wang, L. –S. Sn122–: Stannaspherence. J. Am. Chem. Soc. 2006, 128, 8390–8391. 55. Cui, L. – F.; Huang, X.; Wang, L. –M.; Li, J.; Wang, L. –S. Pb122–: Plumbaspherence. J. Phys. Chem. A 2006, 110, 10169–10172. 56. Liu, C.; Popov, I. A; Chen, Z.; Boldyrev, A. I.; Sun, Z.−M. Aromaticity and Antiaromaticity in Zintl Clusters. Chem. Eur. J. 10.1002/chem.201801715. 57. Ahlrichs, R.; Bär, M.; Häser, M.; Horn, H.; Kölmel, C. Chem. Phys. Lett. 1989, 162, 165. TURBOMOLE V6.6 2014, a Development of University of Karlsruhe and Forschungszentrum Karlsruhe GmbH, 1989−2007, TURBOMOLE GmbH, since 2007, available from http://www.turbomole.com 58. Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865−3868. 59. Becke, A. D. A New Mixing of Hartree−Fock and Local Density−Functional Theories. J. Chem. Phys. 1993, 98, 13721377. 60. 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. 61. Weigenda, F.; Ahlrichsb, R. Balanced Basis Sets of Split Valence, Triple Zeta Valence and Quadruple Zeta Valence Quality for H To Rn: Design And Assessment Of Accuracy. Phys. Chem. Chem. Phys. 2005, 7, 3297–3305. 62. Weigend, F.; Häser, M.; Patzelt, H.; Ahlrichs, R. RI−MP2: Optimized Auxiliary Basis Sets and Demonstration of efficiency. Chem. Phys. Lett. 1998, 294, 143–152. 63. Bergner, A.; Dolg, M.; Küchle, W.; Stoll, H.; Preuß, H. Ab Initio Energy−Adjusted Pseudopotentials for Elements of Groups 13−17. Mol. Phys. 1993, 80, 1431–1441. 64. Cao, X.; Dolg, M. Segmented Contraction Scheme for Small−Core Actinide Pseudopotential Basis Sets. J. Molec. Struct. 2004, 673, 203–209. 65. Dolg, M.; Stoll, H.; Savin, A.; Preuss; H. Energy–Adjusted Pseudopotentials for the Rare Earth Elements. Theor. Chim. Acta 1989, 75, 173–194. 66. Dolg, M.; Stoll, H.; Preuss; H. Energy–Adjusted ab initio Pseudopotentials for the Rare Earth Elements. J. Chem. Phys. 1989, 90, 1730–1734. Page 22 of 34 ACS Paragon Plus Environment

Page 23 of 34 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


67. Cao, X.; Dolg, M.; Stoll; H. Valence Basis Sets for Relativistic Energy–Consistent Small–Core Actinide Pseudopotentials. J. Chem. Phys. 2003, 118, 487–496. 68. Küchle, W.; Dolg, M.; Stoll, H.; Preuss; H. Ab initio Pseudopotentials for Hg through Rn. Mol. Phys. 1991, 74, 1245–1263. 69. Metz,

B.;

Stoll,

H.;

Dolg,

M.

J.

Small−Core

Multiconfiguration−Dirac−Hartree−Fock−Adjusted Pseudopotentials for Post−d Main Group Elements: Application to PbH to PbO. Chem. Phys. 2000, 113, 2563–2569. 70. Feller, D. The Role of Databases in Support of Computational Chemistry Calculations. J. Comp. Chem. 1996, 17, 1571–1586. 71. Cao, X.; Dolg, M. Valence Basis Sets for Relativistic Energy–Consistent Small–Core Lanthanide Pseudopotentials. J. Chem. Phys. 2001, 115, 7348–7355. 72. Reed, A. E.; Weinstock, R. B.; Weinhold, F. A. Natural population analysis. J. Chem. Phys. 1985, 83, 735. 73. Guerra, C. F.; Handgraaf, J. W.; Baerends, E. J.; Bickelhaupt, F. M. Voronoi Deformation Density (VDD) Charges: Assessment of the Mulliken, Bader, Hirshfeld, Weinhold, and VDD Methods for Charge Analysis. J. Comput. Chem. 2004, 25, 189– 210. 74. ADF2016; SCM, Theoretical Chemistry, Vrije Universiteit: Amsterdam, The Netherlands. http://www.scm.com. 75. te Velde, G.; Bickelhaupt, F. M.; van Gisbergen, S. A.; Fonseca Guerra, C.; Baerends, E. J.; Snijders, J. G.; Ziegler, T. Chemistry with ADF. J. Comput. Chem. 2001, 22, 931−967. 76. Fonseca Guerra, C.; Snijders, J. G.; te Velde, G.; Baerends, E. J. Towards an Order−N DFT Method. Theor. Chem. Acc. 1998, 99, 391−403. 77. Bader, R. F. W. Atoms in Molecules−A Quantum Theory; Oxford University Press: Oxford, U.K., 1990. 78. 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. 79. Lu, T.; Chen, F. W. Multiwfn: A Multifunctional Wavefunction Analyzer. J. Comput. Chem. 2012, 33, 580−592. 80. Keith, T. A.; Frisch M. J. Subshell Fitting of Relativistic Atomic Core Electron Densities for Use in QTAIM Analyses of ECP–Based Wave Functions. J. Phys. Chem. A. 2011, 115, 12879–12894.



Page 24 of 34

81. Sadjadi, S. A.; Matta, C. F.; Lemke, K. H.; Hamilton, I. P. Relativistic–Consistent Electron Densities of the Coinage Metal Clusters M2, M4, M42–, and M4Na2 (M = Cu, Ag, Au): A QTAIM Study. J. Phys. Chem. A. 2011, 115, 13204–12035. 82. Borocci, S.; Giordani, M.; Grandinetti, F. Complexes of XeHXe+ with Simple Ligands: A Theoretical Investigation on (XeHXe+)L (L = N2, CO, H2O, NH3). J. Phys. Chem. A. 2015, 119, 2383–2392. 83. Borocci, S.; Giordani, M.; Grandinetti, F. Neutral Compound with Xenon– Germanium Bonds: A Theoretical Investigation on FXeGeF and FXeGeF3. J. Phys. Chem. A. 2014, 118, 3326–3334. 84. Zhang, M.; Gao, K.; Sheng, L. Predicted Organic Noble–Gas Hydrides Derived from Acrylic Acid. J. Phys. Chem. A. 2015, 119, 2393–2400. 85. Baerends, E. J.; Branchadell, V.; Sodupe, M. Atomic Reference Energies for Density Functional Calculations. Chem. Phys. Lett. 1997, 265, 481−489. 86. Ziegler, T.; Rauk, A. On the Calculation of Bonding Energies by the Hartree−Fock−Slater Method−I. The Transition State Method. Theor. Chim. Acta 1977, 46, 1−10. 87. Bickelhaupt, F. M.; Baerends, E. J. ''Kohn−Sham Density Functional Theory: Predicting and Understanding Chemistry'' Lipkowitz, K. B.; Boyd, D. B. (Eds.), Rev. Comput. Chem. 2007, 15, 1–86. 88. van Lenthe, E.; Baerends, E. J. Optimized Slater−type Basis Sets for the Elements. 1−118. J. Comput. Chem. 2003, 24, 1142–1156. 89. van Lenthe, E.; Baerends, E. J.; Snijders, J. G. Relativistic Total Energy using Regular Approximations. J. Chem. Phys. 1994, 101, 9783–9792. 90. van Lenthe, E.; Ehlers, A. E.; Baerends, E. J. Geometry Optimization in the Zero Order Regular Approximation for Relativistic Effects. J. Chem. Phys. 1999, 110, 8943–8953. 91. van Lenthe, E.; Snijders. J. G.; Baerends, E. J. The Zero−Order Regular Approximation for Relativistic Effects: The Effect of Spin−Orbit Coupling in Closed Shell Molecules. J. Chem. Phys. 1996, 105, 6505−6516. 92. Critchlow, S. C.; Corbett, J. D. Homopolyatomic Anions of the Post Transition Elements. Synthesis and Structure of Potassium−crypt Salts of the Tetraantimonide( 2−) and Heptaantimonide(3−) Anions, Sb42− and Sb73−. Inorg. Chem. 1984, 23, 770−774.


Page 25 of 34 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


93. Cisar, A.; Corbett, J. D. Polybismuth Anions. Synthesis and Crystal Structure of a Salt of the Tetrabismuthide (2−) ion, Bi42−. A Basis for the Interpretation of the Structure of Some Complex Intermetallic Phases. Inorg. Chem. 1977, 16, 2482−2487. 94. Lohr Jr, L. L.; Pyykkö, P. Relativistically Parameterized Extended Hückel Theory. Chem. Phys. Lett. 1979, 62, 333−338. 95. Zhang, G.; Musgrave, C. B. Comparison of DFT Methods for Molecular Orbital Eigenvalue Calculations. J. Phys. Chem. A 2007, 111, 1554−1561. 96. Küchle, W.; Dolg, M.; Stoll, H; Preuss, H. Energy–Adjusted Pseudopotentials for the Actinides. Parameter Sets and Test Calculations for Thorium and Thorium Monoxide. J. Chem. Phys. 1994, 100, 7535–7542. 97. Moritz, A.; Cao, X.; Dolg, M. Quasirelativistic Energy–Consistent 5f–in–Core Pseudopotentials for Divalent and Tetravalent Actinide Elements. Theor Chem Account 2007, 118, 845–854. 98. http://www.tc.uni-koeln.de/PP/index.en.html (accessed July 22, 2018)



Page 26 of 34

FIGURE CAPTION Figure 1. Optimized structures of (a) bare E42− ring in D4h symmetry, (b) An@E126− and Ln@E126− clusters in D3h symmetry, (c) An@E126− and Ln@E126− clusters in Cs symmetry obtained by using PBE/DEF method. (Where, An = Th4+, Pa5+, U6+, Np7+; Ln = La3+, Ce4+, Pr5+, Nd6+; and E = Sb and Bi). Figure 2. Molecular orbital energy level diagram of An@Sb126− (An = Th4+, Pa5+, U6+, Np7+) clusters in D3h symmetry obtained by using PBE/DEF method. The HOMO energy of all the clusters is scaled with the HOMO energy of U@Sb12 cluster. (Here blue lines stands for mixed MOs which have orbital contribution from central metal atom and ring atoms, red lines stands for the MOs corresponding to the pure orbitals of ring atoms.) Figure 3. Density of states plot of An@Sb126− (An = Th4+, Pa5+, U6+, Np7+) clusters in D3h symmetry as obtained by using PBE/DEF method. (Arrows are showing peak corresponding to HOMO) Figure 4. Scalar relativistic (left panel) and spin orbit splitting (right panel) diagram of the valence molecular orbital energy levels of U@Sb12 system


Page 27 of 34 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)

or

(b)

(c) Figure 1. Optimized structures of (a) bare E42− ring in D4h symmetry, (b) An@E126− and Ln@E126− clusters in D3h symmetry, (c) An@E126− and Ln@E126− clusters in Cs symmetry obtained by using PBE/DEF method. (Where, An = Th4+, Pa5+, U6+, Np7+; Ln = La3+, Ce4+, Pr5+, Nd6+; and E = Sb and Bi).



6a"2

-4 -5 -6 Energy (eV)

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

5a''2 5e'' 9e' 8e'

7e' -8 3e''

6a"2

9a'1

9a'1

10e' ' 8a'1 2a2 4e'' 4a''2 1a''1

10e' ' '' 2, 5a2 '' 2a ' 5e , 8a1 4e'', 9e' 1a''1, 8e'  7e', 4a''2

7a'1 6a'1

7a'1, 3e''  6a'1

-9

-10 -12 -14 -16

Page 28 of 34

Sb12 s block

Sb12 Sb12 Sb12 s block s block s block

Th@Sb122-

Pa@Sb12- U@Sb12 Np@Sb12+

Figure 2. Molecular orbital energy level diagram of An@Sb126− (An = Th4+, Pa5+, U6+, Np7+) clusters in D3h symmetry obtained by using PBE/DEF method. The HOMO energy of all the clusters is scaled with the HOMO energy of U@Sb12 cluster. (Here blue lines stand for mixed MOs which have orbital contributions from central metal atom and ring atoms, red line stands for the MOs corresponding to the pure orbitals of ring atoms and s block refers to the valence s–orbitals of Sb atoms)


Page 29 of 34

Th@Sb122-

DOS

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


Pa@Sb12U@Sb12 Np@Sb12+ -12

-9

-6

-3

Energy(eV)

0

3

Figure 3. Density of states plot of An@Sb126− (An = Th4+, Pa5+, U6+, Np7+) clusters in D3h symmetry as obtained by using PBE/DEF method. (Arrows are showing peak corresponding to HOMO.)



e1/2

9a'1

-4 -5 Energy (eV)

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 30 of 34

0.776 eV

0.982 eV

e1/2 e1/2 a 3/2, 3/2 ea1/2, e1/2 a3/2,a3/2 e1/2 a3/2,a3/2,e1/2 e1/2 ee1/2,a3/2,a3/2 1/2 a3/2, a3/2 a3/2,a3/2 e1/2 e1/2, e1/2 ae3/2,a3/2 1/2 e1/2

10e' 2a'2,5e" 5a''2 8a'1,9e' { 4e'',1a''1{

-6

8e'

-7

7e' 4a''2 3e'' 7a'1 6a'1

-8

U@Bi12(C3V) Scalar

U@Bi12(C*3V) Spin Orbit

Figure 4. Scalar relativistic (left panel) and spin orbit splitting (right panel) diagram of the valence molecular orbital energy levels of U@Sb12 system.


Page 31 of 34 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. Calculated Values of Inter–Ring (Rinter), Intra–Ring (Rintra) Bond Distances (in Å) as well as Axial (Rax) and Equatorial (Req) Bond distances (in Å) of Central Atom with Ring Atoms in An@E126− and Ln@E126− (An = Th4+, Pa5+, U6+, Np7+; Ln = La3+, Ce4+, Pr5+, Nd6+; and E = Sb and Bi) Clusters in D3h Symmetry as obtained by using PBE/DEF Method.

Systems Th@Bi122− Pa@Bi12− U@Bi12 Np@Bi12+ Th@Sb122− Pa@Sb12− U@Sb12 Np@Sb12+ La@Bi123− Ce@Bi122− Pr@Bi12− Nd@Bi12 Ce@Sb122− Pr@Sb12− Nd@Sb12

Req 3.553 3.457 3.426 3.419 3.456 3.340 3.295 3.283 3.655 3.498 3.449 3.427 3.398 3.328 3.297

Rax 3.259 3.151 3.110 3.099 3.218 3.085 3.029 3.012 3.380 3.187 3.137 3.121 3.146 3.070 3.041

Rintra 3.040 3.053 3.056 3.064 2.872 2.893 2.902 2.908 3.030 3.052 3.061 3.068 2.880 2.899 2.909

Rinter 3.138 3.074 3.054 3.054 3.053 2.955 2.914 2.903 3.209 3.104 3.074 3.065 3.003 2.944 2.920



Page 32 of 34

Table 2. Calculated Values of Binding Energy (BE, in eV), HOMO−LUMO Energy Gap (ΔEgap, in eV), and Dihedral Angle (DA, in degree) of E42− rings of An@E126− and Ln@E126− (An = Th4+, Pa5+, U6+, Np7+; Ln = La3+, Ce4+, Pr5+, Nd6+; and E = Sb and Bi) Clusters in D3h Symmetry as obtained by using PBE/DEF Method. Systems

BE

ΔEgap

DA

Systems

BE

ΔEgap

DA

Th@Bi122−

−82.58

1.21

21.8

Th@Sb122−

−82.36

1.50

17.0

Pa@Bi12−

−131.53

1.31

26.1

Pa@Sb12−

−131.23

1.47

22.2

U@Bi12

−196.51

0.99

27.7

U@Sb12

−196.02

1.00

24.4

Np@Bi12+

−279.53

0.71

28.5

Np@Sb12+

−278.65

0.73

25.2

U@Bi123−

−40.17

0.20

25.7

…

….

…

…

La@Bi123−

−46.93

1.10

17.2

La@Sb123−

−46.64

1.17

12.9

Ce@Bi122−

−90.37

0.98

24.9

Ce@Sb122−

−90.02

0.99

19.7

Pr@Bi12−

−152.27

0.74

27.0

Pr@Sb12−

−151.74

0.69

22.9

Nd@Bi12

−235.60

0.69

27.9

Nd@Sb12

−234.76

0.70

24.3


Page 33 of 34 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. The Calculated Values of Electrostatic Energy (ΔEelec, in eV), Pauli Repulsion Energy (ΔEPauli, in eV), Orbital Interactions Energy (ΔEorb, in eV), Preparatory Energy (ΔEPrep, in eV) and Total Bonding Energy (ΔE, in eV) as obtained from Energy Decomposition Analysis using the ADF Software with TZ2P Basis Set and PBE Method. (Percentage Contribution of ΔEelec and ΔEorb Energy to the Total Bonding Energy are Provided within Parenthesis) Cluster

ΔEPauli

ΔEelec

ΔEorb

ΔEprep

ΔE

Th@Bi122−

56.16

−92.12 (66.30)

−46.82 (33.70)

0.906

−81.87

Pa@Bi12−

73.91

−123.44 (59.83)

−82.87 (40.17)

1.483

−130.92

U@Bi12

83.47

−150.01 (53.28)

−131.52 (46.72)

1.714

−196.35

Np@Bi12+

88.51

−174.14 (47.04)

−196.02 (52.96)

1.844

−279.81

Th@Sb122−

47.65

−86.43 (66.62)

−43.30 (33.38)

0.516

−81.56

Pa@Sb12−

67.31

−119.05 (59.92)

−79.63 (40.08)

1.182

−130.19

U@Sb12

79.48

−147.70 (53.46)

−128.56 (46.54)

1.526

−195.25

Np@Sb12+

85.39

−173.13 (47.40)

−192.15 (52.60)

1.651

−278.24

La@Bi123−

39.05

−61.64 (71.14)

−25.00 (28.86)

0.483

−47.11

Ce@Bi122−

61.02

−96.06 (61.75)

−59.50 (38.25)

1.290

−93.25

Pr@Bi12−

71.78

−123.79 (52.25)

−113.15 (47.75)

1.621

−163.54

Nd@Bi12

76.75

−149.16 (43.92)

−190.43 (56.08)

1.822

−261.02

La@Sb123−

32.89

−56.91 (71.13)

−23.10 (28.87)

0.250

−46.87

Ce@Sb122−

51.81

−89.88 (61.82)

−55.52 (38.18)

0.806

−92.78

Pr@Sb12−

65.31

−119.79 (52.20)

−109.68 (47.80)

1.294

−162.87

Nd@Sb12

71.77

−146.79 (44.05)

−186.42 (55.95)

1.560

−259.88



TOC GRAPHICS

Binding Energy (eV)

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 34 of 34

300 250

Nd@Sb12

200

100

U@Sb12

Pr@Sb-12

150

Th@Sb212La@Sb312-

Np@Sb+12

Pa@Sb-12 Ce@Sb212-

50 10

12

14

16

18

20

22 2 4 26 28 30 Dihedral Angle of Sb2- ring (degree) 4


CounterâIntuitive Stability in Actinide Encapsulated Metalloid Clusters

Recommend Documents

CounterâIntuitive Stability in Actinide Encapsulated Metalloid Clusters