Structure and bonding in endohedral transition metal clusters

CHAPTER EIGHT

Structure and bonding in endohedral transition metal clusters Xiao Jin, John E. McGrady* Department of Chemistry, University of Oxford, Oxford, United Kingdom *Corresponding author: e-mail address: [email protected]

Contents 1. Introduction 2. Survey of experimental data 3. Models of cluster electronic structure 4. Methodology 5. The emergence of paramagnetism: [Mn@Pb12]3
and [Mn@Si12]+ 6. The 10-vertex family, M@E10 7. The 14-vertex family, M@E14 8. Summary and future perspectives Acknowledgments References

266 267 272 273 281 288 292 298 301 301

Abstract Endohedral clusters of the tetrel elements, M@En, provide a diverse platform for exploring chemical bonding, simply because the cluster does not necessarily depend on strong M–E bonding for its integrity. The interaction between the metal and the cluster can therefore range from strongly covalent all the way to cases where the metal is simply trapped inside the cage by virtue of the strong E-E bonds, with little or no direct bonding. This spectrum of bond types leads to unusual structural, spectroscopic and magnetic properties that we seek to rationalize in this review. The clusters of interest are drawn from the field of Zintl-ion chemistry, typically containing the heavier tetrels, and also from the gas-phase spectroscopy of metal-silicon clusters. By highlighting the close relationships between the molecules studied in these two rather different disciplines, we establish a continuum framework that places all of the available experimental data in context.

Advances in Inorganic Chemistry, Volume 73 ISSN 0898-8838 https://doi.org/10.1016/bs.adioch.2018.11.003

#

2019 Elsevier Inc. All rights reserved.

265

266

Xiao Jin and John E. McGrady

1. Introduction Nearly 50 years on from Wade’s seminal work on boron clusters,1 the properties of cluster compounds continue to intrigue both chemists and physicists. This is due, at least in part, to the esthetic appeal of these clusters, many of which adopt highly symmetric structures, but increasingly applications are being found which bridge the gap between the molecular and solid-state domains. The small size of these clusters means that “every atom counts,” and magnetic and catalytic properties can be changed beyond recognition by the addition or substitution of a single atom.2 This then places a very high premium on a detailed understanding of the connections between electronic structure, magnetism and spectroscopy. In this review we are concerned with the electronic structure of a specific class of pseudo-spherical clusters, the endohedrally encapsulated M@En family where M is a transition metal and E one of the tetrel elements, Si, Ge, Sn or Pb. Members of this family typically emerge from two quite distinct spheres of research, one very much the domain of inorganic chemistry, the other largely the preserve of chemical physics. In the first category, the chemistry of highly anionic Zintlion clusters, [Mx@En]q
(E ¼ Ge, Sn, Pb), has been developed extensively over the past two decades, and many of these anions have been crystallized, typically in combination with very large counter-cations. As a result, X-ray crystallography has been the tool of choice, yielding direct information on the arrangement of the atoms. The traditional spectroscopic tools of the inorganic chemist, notably EPR spectroscopy, have also provided important insights into the arrangement of electrons. Much of this research is driven by an innate curiosity about the nature of the bonding in these clusters, but they can also be viewed as building blocks for even larger endohedral clusters with nanometer dimensions which may, ultimately, have important technological applications. The second research area of interest, largely populated by chemical physicists, focuses on the gas-phase properties of endohedral clusters of silicon (and, to a lesser extent, the heavier tetrels), typically in neutral or low-charged states. Progress in this field has been based on extensive use of mass spectrometry to identify the composition of the clusters, along with mass selection and an array of vibrational and electronic spectroscopies to interrogate their structure and bonding. The primary motivation is again a curiosity about the structure and bonding in these clusters, but also the prospect that they represent the simplest available models for point defects in the silicon wafers that are ubiquitous in

Structure and bonding in endohedral clusters

267

modern electronic devices.3 Transition metal impurities, particularly iron, copper and nickel, are present in high concentrations following the manufacturing of bulk silicon wafers, and diffusion of these impurities leads to the formation of metal silicide islands at isolated lattice irregularities.4 This can have a substantial detrimental impact on the performance of electronic devices, and the removal of impurities is a costly problem for the industry. The “gettering” process involves the introduction of defect sites into non-critical regions of the wafer to seed the growth of these silicide islands, and the study of small isolated clusters may shed some light on the diffusion pathways that lead to silicide formation.5 The fact that there are two quite distinct research communities making independent progress in this field, using very different experimental techniques, means that important connections between the two areas tend to be overlooked. Our work over the past 5 years has sought to develop a model of bonding based on valence-electron count that can rationalize the wealth of structural and spectroscopic data that has emerged from the two communities. The review starts with a brief introduction to the key experimental advances, and we then deal in turn with the three families of clusters that have been the focus of much of our work, M@E10, M@E12 and M@E14 with a single endohedral transition metal ion and 10, 12 or 14 tetrel vertices, respectively. The tool of choice for much of our work has been density functional theory (DFT), but it is becoming increasingly clear that many of the most interesting clusters have ground states that are poorly described by a single-determinant wavefunction. We therefore also describe some very recent results using multiconfigurational techniques (CASSCF).

2. Survey of experimental data Before setting out our electronic structure model for this diverse family of clusters, we first present a brief survey of the diverse body of experimental data that has motivated much of our work. As noted above, this work falls into two very different categories, Zintl-ion chemistry and gasphase chemistry, primarily of silicon clusters. Many of the recent developments in Zintl-ion chemistry have been made by reaction of anionic group 14 clusters (K4Sn9 or K4Pb9, for example) with a source of low-valent transition metal (a metal alkyl, for example). In the presence of a cryptand ligand such as [2.2.2]crypt which binds the alkali metal cation, the large Zintl anion

268

Xiao Jin and John E. McGrady

and large [K([2.2.2]crypt)]+ cations co-crystallize, often yielding materials suitable for analysis by X-ray diffraction. Among these, the 12-vertex family [M@E12]q
is the most abundant and the most common structural motif is the icosahedron. Examples include [M@Pb12]2
, M ¼ Ni, Pd, Pt,6,7 [Ir@Sn12]3
,8 and [Rh@Pb12]3
,9 all of which have 60 valence electrons, and also 62-electron [Au@Pb12]3
,10 (throughout this review, we include all nd electrons on the transition metal in the valence electron count). Photoelectron spectra of the empty clusters [Sn12]2
and [Pb12]2
are also consistent with icosahedral structures,11 but as yet no crystallographic data are available. Further to the left in the periodic table, the 58-electron [Mn@Pb12]3
cluster is also recognizably icosahedral, but is strongly distorted along a C2 axis that bisects two opposing edges, giving a prolate D2h-symmetric geometry.12 For the lighter tetrels, crystallographic data are scarce and in fact the only M@Ge12 cluster yet to be characterized fully is the 59-electron [Ru@Ge12]3
anion13 which adopts a remarkable D2dsymmetric structure, sometimes described as a bicapped pentagonal prism. This structure had been proposed as the most stable isomer for Au@Ge12,14 Ni@Si1215 and Ni@Ge1216 in different computational studies, and has subsequently been found in the X-ray structure of the mixed group 14/15 cluster [Ta@Ge8As4]3
(Fig. 1).17 For the smaller M@E10 clusters, the structural chemistry is similarly diverse. Eichhorn has reported the 52-electron [Ni@Pb10]2
anion, a bicapped square antiprism with D4d point symmetry.18 The empty

Fig. 1 High-symmetry structures for the M@E10, M@E12 and M@E14 families.

Structure and bonding in endohedral clusters

269

[Pb10]2
cage is also stable in its own right,19 and the Pb–Pb bond lengths in ˚ for [Ni@Pb10]2
, the two clusters are very similar (3.07–3.31 A 2
˚ 3.09–3.41 A for [Pb10] ) suggesting that the presence of the endohedral metal does not perturb the cage to any significant extent. Sevov and Corbett have also described the structures of highly anionic [M@In10]n
clusters in the alloys K8In10M, M ¼ Zn, Ni, Pd, Pt,20 all of which have 50 valence electrons, two fewer than the [Ni@Pb10]2
cluster. The [Zn@In10]8
cluster is also approximately D4d-symmetric, but strongly compressed along the fourfold axis, giving 10 almost identical Zn–In bond lengths (2.84, 2.82 A˚) but a much wider spread of In–In distances ˚ ). The isoelectronic [Ni@In10]10
unit in K10In10Ni is even (3.04–3.64 A more distorted, and has been described as a tetra-capped trigonal prism (C3v), but the differences between the [Zn@In10]8
and [Ni@In10]10
are subtle and the most important feature is that both are significantly distorted from the bicapped square antiprism. The structural chemistry of the M@E10 family took a new turn in 2009 with the concurrent reports of crystal structures of 51-electron [Fe@Ge10]3
,21 and 52-electron [Co@Ge10]3
,22 both of which adopt a previously unprecedented pentagonal prismatic geometry (D5h). The 3-connected nature of the Ge vertices in these two clusters marks an abrupt departure from the more highly connected vertices of the deltahedral clusters, and invites comparison to the D2d-symmetric structure of [Ru@Ge12]3
, the vertices of which are similarly 3-connected. The admittedly limited data available therefore suggest that the shift toward 3-connected structures is intimately connected to the presence of elements from the middle of the transition series (Fe, Co, Ru) rather than their later counterparts. We note in this context Korber’s prescient commentary on the [Fe@Ge10]3
/[Co@Ge10]3
clusters where he stated that, “some kind of border seems to have been crossed when moving from Group 10 to Group 9 endohedral atoms, and the encapsulated transition metal atom clearly is not as innocent a template as it was assumed to be from the earlier results.”23 The M@E10 family was further expanded in 2013 with the isolation of the [Fe@Sn10]3
anion, isoelectronic with [Fe@Ge10]3
, as its [K([2.2.2]crypt)]+ salt.24 All attempts to achieve atomic resolution of the cluster unit have been frustrated by disorder, but the presence of three charge-balancing cations leaves no doubt that the cluster is present as a trianion. Our DFT calculations revealed that the equilibrium structure of the [Fe@Sn10]3
cluster anion is not a pentagonal prism like isoelectronic [Fe@Ge10]3
, but rather a distorted bicapped square antiprism with a C2v symmetry. Thus it seems that the precise position of

270

Xiao Jin and John E. McGrady

Korber’s borderline depends not only on the metal, but also on the identity of the tetrel elements forming the cage. The second sphere of experimental work of relevance to this review revolves around the gas-phase chemistry of neutral or singly charged clusters, primarily but not exclusively of silicon. Typically these are characterized using mass spectrometry in conjunction with a range of spectroscopies rather than the X-ray crystallography which is the tool of choice in the Zintl-ion field. Despite the use of very different techniques, there is considerable overlap between the two fields with many examples of isoelectronic and/or isostructural clusters from both sides of the divide. The study of endohedral gas-phase clusters containing both silicon and a transition element can be traced back to Beck’s work in the late 1980s25 where laser vaporization of a silicon wafer was used to generate clusters in a molecular beam which is then quenched with helium carrier gas. Seeding of the carrier gas with metal carbonyl species generated a series of cationic clusters with formula M@Sin that can be detected by mass spectrometry. The group 6 hexacarbonyls Cr(CO)6 and Mo(CO)6, for example, generated a range of clusters with n ¼ 14–17. In a complementary set of experiments, Hiura, Miyazaki and Kanayama used a quadrupole ion trap to isolate [M@SinHx]+ clusters from the reaction of SiH4 with metal vapor generated by resistive heating.26 The resulting time-resolved mass spectra show the stepwise growth of clusters with increasing n but the envelope for [W@SinHx]+, for example, terminates at n ¼ 12, with no evidence for the larger 15- and 16-vertex clusters seen in Beck’s experiments. Moreover, high-resolution spectra showed that the clusters with the highest Si content (n ¼ 12) had lost all hydrogen atoms (x ¼ 0), suggesting that the metal satisfies the valence of all 12 silicon atoms: i.e., it is fully encapsulated and not on the surface of the cluster. Preliminary DFT calculations on W@Si12, suggested a “basketlike” structure where the metal is encapsulated within the cluster and each silicon atom is bonded to three others, but a note added in proof proposed a hexagonal prismatic structure (D6h). Scanning tunneling microscopy experiments on [Ta@Si12]+ clusters absorbed on reconstructed Si (111) surfaces showed features consistent with intact hexagonal prismatic clusters,27 and XANES and EXAFS spectroscopy at the W L3 edge of surface-absorbed W@Six clusters are also consistent with the presence of hexagonal prismatic [email protected] Computational work by Khanna, Rao and Jena identified the hexagonal prism as the equilibrium structure for Cr@Si12,29 and predicted the presence of two peaks in the photo-detachment spectrum of the [Cr@Si12]
anion corresponding to singlet and triplet states of the neutral

Structure and bonding in endohedral clusters

271

species. Data subsequently published by Bowen and co-workers confirmed the presence of a narrow peak in the predicted region, at 3.18 eV.30 Janssens and co-workers have made extensive use of infra-red multiple photon dissociation (IRMPD) spectroscopy to study clusters bound to the noble gas, Xe.31 Resonant absorption of photons by the cluster results in local heating and desorption of the Xe atom, allowing the infra-red spectrum to be probed through frequency-dependent variations in ion intensities. Comparison of the measured vibrational spectrum with DFT-computed spectroscopic fingerprints then provides structural information, and their work on [Mn@Si12]+ offers compelling evidence that it also adopts a hexagonal prismatic structure.32 The multiplicity of the ground state of [Mn@Si12]+ has, however, proven to be a controversial issue: the computed vibrational frequencies were only in agreement with the experimental infra-red spectrum if the cluster was assumed to be in a triplet state, apparently in conflict with independent X-ray MCD spectroscopy studies by Zamudio-Bayer et al. which concluded that [Mn@Si12]+ is in fact diamagnetic.33 Despite the absence of definitive crystallographic evidence, the hexagonal prismatic geometry is now widely accepted as the equilibrium geometry in the M@Si12 clusters of group 6 (Cr, Mo, W) and other isoelectronic species, naturally inviting comparison to [Fe/Co@Ge10]3
and [Ru@Ge12]3
, all of which also have 3-connected vertices. Although less well studied than the silicon clusters, the gas-phase chemistry of clusters of the heavier tetrels has also been discussed in the literature. Gao and co-workers have used mass spectrometry to detect a range of mixed Co/Ge clusters, the dominant species being [Co@Ge10]
.34 Lower intensities for [Co@Ge11]
and all larger clusters were interpreted as evidence that the cobalt center occupies an endohedral position in the Ge10 cluster. Similar experiments on Co/Sn/Pb powder mixtures generated large quantities of [Co@Sn10]
and [Co@Pb10]
, along with the 12-vertex analogue [Co@Pb12]
.35 A subsequent paper extended the series of [M@Pbn]
clusters to include the entire first transition series from Ti to Cu, along with Pd and Ag from the second series, the results again suggesting high local stabilities for the 12-vertex clusters.36 Gas-phase photoelectron spectroscopy on the 12-vertex Sn clusters, [M@Sn12]1
(M ¼ Ti, V, Cr, Fe, Co, Ni, Cu, Nb, Pt, Au), confirms that they share a common icosahedral structure, and all are best formulated as M+@[Sn12]2
.37 Clusters of higher nuclearity have also been observed in mass spectrometric studies, and the M@Ge16 stoichiometry proves to be particularly abundant for the group 4 metals, Ti, Zr and Hf.38 The authors of this study proposed a Td-symmetric Frank-Kasper type

272

Xiao Jin and John E. McGrady

polyhedron. Similarly, mass spectra of Cr@Gen and Mn@Gen show maximum abundances for n ¼ 15/16. Neukermans et al. have also reported a survey of the cationic tin and lead clusters of Cr, Mn, Cu and Zn, where high abundances of [Cr@Snn]+ and [Mn@Snn]+ were observed for n ¼ 13–16.39

3. Models of cluster electronic structure The jellium model is perhaps the simplest model of cluster electronic structure and assumes that the n valence electrons move in an approximately spherical potential defined by the positive charges of the ion cores. The resulting 1-electron wavefunctions are classified according to spherical symmetry as s, p or d. This model has been applied with conspicuous success to the sodium clusters, Nan, where peaks in the abundance are observed for particular values of n (8, 18, 20).40 The “magic” stability of these clusters can be rationalized by the filling of spherical jellium orbitals in the order 1s21p61d102s2, and, through the work of Castleman and others, this has led to the idea of a cluster as a “superatom.”41 For example, mass spectrometry on anionic clusters of aluminum shows that the 40-electron [Al13]
cluster, which has a closed-shell jellium configuration of 1s21p61d102s22p61f14, is far more resistant to etching by dioxygen than its neighbors.42 Extensions of these ideas have led to the concept of a “3-dimensional periodic table,” which now features “super-alkalis” such as K3O,43 “super-halogens” such as Al1344 and even a cluster mimic of carbon or silicon, [Al7]
.45 The jellium model is clearly most applicable to clusters of the alkali metals, where the positive charge on the ionic cores is low, but it is more difficult to extend it to clusters of more electronegative elements where electrons tend to become localized. Perhaps the most famous qualitative model of cluster electronic structure was developed by Wade in the 1970s, initially in the context of borane chemistry.1 His eponymous rules are used extensively to rationalize structural trends as the vertex count is varied while maintaining a constant number of cluster bonding electrons. For example, the series [B6H6]2
, B5H9 and B4H10 share a common 14 skeletal electron count, and the evolution from closo ([B6H6]2
) to nido (B5H9) and arachno (B4H10) corresponds to successive removal of vertices from an octahedral starting point. Wade’s rules have been applied widely and are now a textbook piece of electronic structure theory. Their use in the context of this work is, however, somewhat limited because our focus is primarily on understanding trends within families of clusters with a constant vertex count and a varying number

Structure and bonding in endohedral clusters

273

of valence electrons, rather than a constant electron count and variable number of vertices. The structural relationships between members of the M@Si12 family, for example, are defined by how the cluster responds to changes in the number of valence electrons. In a localized (2-center) model of bonding, the successive removal of pairs of electrons typically leads to the formation of additional bonds—either π (as in S2 ➔ [S2]2+) or σ (as in S8 ➔ [S8]2+). If instead the electrons are highly delocalized, loss of successive pairs can lead to an increase in the connectivity of the vertices, the typical signature of electron deficiency, rather than a shortening of one particular bond. The balance between these two possible outcomes is central to much of the discussion in this review. When trying to put these ideas into action in the context of endohedral clusters, the major difficulty comes in defining exactly what is meant by “valence electrons”: should the metal d electrons be treated as valence or as part of the core? In the case of the late transition metals the answer seems clear—the d orbitals are typically core-like and the metal adopts a closed-shell d10 configuration that is largely inert in a structural sense. The situation is less clear-cut as we move progressively to the left of the periodic table because the d electrons become less numerous, but also higher in energy and therefore more available for bonding. It is not, therefore, a priori obvious whether the amount of d-electron density available to the cluster increases or decreases as we move across the periodic table.

4. Methodology Density functional theory has been the tool of choice for much of the work described in this review, and most calculations were performed with various versions of the Amsterdam Density Functional package.46 This code makes optimal use of high symmetry which has been invaluable in many of our studies. Our typical protocol uses Slater-type basis sets of triple-ζ quality, extended with one polarization function (TZP) on transition metals and a DZP basis for the tetrel elements. A variety of different functionals and frozen cores have been used—the reader is referred to original papers for details. For anionic clusters, the confining effect of cations in the crystal lattice was modeled by surrounding the clusters with a continuum dielectric model (COSMO).47 The chosen dielectric constant is typically ε ¼ 78.4 (water) although results are not strongly dependent on this choice. Single point CASSCF/CASPT2 calculations were performed with the MOLCAS 8.0 package.48 Atomic natural orbitals optimized for relativistic

274

Xiao Jin and John E. McGrady

corrections and core correlation (ANO-RCC) basis sets were used to expand the orbitals.49 The 12-vertex family: The M@E12 clusters are by far the most extensively studied from a theoretical perspective, and a number of significant contributions have emerged from different groups. Salient points from several of these papers will be drawn out in the following discussion, but an important point to emphasize from the outset is that the relative stability of different isomers appears to be highly sensitive to the choice of exchange correlation functional. As an illustrative example, the structure of the Ni@Ge12 cluster has been variously claimed to be a pseudo-icosahedral triplet,50 a D2dsymmetric singlet16a or a puckered hexagonal prismatic singlet51 (BLYP, B3PW91 or PW91 functionals, respectively). Similarly, icosahedral sextet50 and hexagonal prismatic doublet51 ground states have been reported for Mn@Ge12. Given that density functionals differ in their treatment of electron-electron repulsions, this extreme variability tends to suggest that the nature of these repulsions differs from structure to structure. The following discussion will revolve around the relative stabilities of the three key isomers that dominate the structural landscape in the 12-vertex family, namely the icosahedron (Ih), the hexagonal prism (D6h) and the bicapped pentagonal prism (D2d).52 Archetypes of each class are [Ni@Pb12]2
, Cr@Si12 and [Ru@Ge12]3
.6,13,29 The first of these is clearly deltahedral (i.e., it has exclusively triangular faces) while the other two have 3-connected vertices and are sometimes referred to in the literature as “fullerene-like” by analogy to carbon-based fullerenes where the vertices are also 3-connected. The degree to which this structural analogy extends to the underlying electronic structure remains to be established. The M@E12 Zintl ions [Ni@Pb12]2
, [Pd@Pb12]2
, [Pt@Pb12]2
, [Rh@Pb12]3
and [Ir@Sn12]3
all have a 60 valence electron count, and all are almost perfectly icosahedral. It is significant in this context that the empty 50-electron [Sn12]2
and [Pb12]2
cages are also stable entities in their own right,7 indicating that the interactions between the endohedral metal and the cluster unit are not critical to the integrity of the M@E12 unit. Wade’s rules predict a closo icosahedral structure for a system with 4n + 2 ¼ 50 valence electrons, 4n ¼ 48 coming from the E12 cluster itself and the other two from the net anionic charge. We can therefore partition the 60 valence electrons of the endohedral clusters cleanly into 50 for the [E12]2
cluster and 10 to complete the closed d shell configuration at the metal. The Kohn-Sham molecular orbital diagram for [Ni@Pb12]2
in Fig. 2 confirms this qualitative picture: the Ni 3d character is localized

Structure and bonding in endohedral clusters

275

Fig. 2 Kohn-Sham MO diagram for [Ni@Pb12]2
, showing the 60 valence electrons.

primarily in the 3hg orbital, which lies approximately 2 eV below the 4hg LUMO + 1 which is localized almost entirely on the Pb12 cluster. The large separation of the 3hg and 4hg orbitals renders back-bonding from metal to cluster ineffective, and interactions between the metal d orbitals and the cage are therefore primarily antibonding in nature, as they are in typical coordination complexes of d10 transition metals ([Zn(H2O)6]2+, for example). We therefore anticipate a stable icosahedral structure only when metal d orbitals are sufficiently contracted to render these antibonding interactions insignificant.

276

Xiao Jin and John E. McGrady

The second structural archetype for the M@E12 family is the D2dsymmetric bicapped pentagonal prism which has been discussed in several computational papers,14–16 but was only very recently identified crystallographically in 59-valence electron [Ru@Ge12]3
and 60-electron [Ta@Ge8As4]3
.13,17 The 3-connected vertices of the bicapped pentagonal prism are characteristic of electron-precise electron counts, and indeed the 5n rule for 12-vertex clusters demands precisely 60 electrons. These 60 electrons can be divided into 24 electrons in lone pairs at each vertex and 36 (¼3n) in edge-localized Ge–Ge 2-center-2-electron bond. The vertices and edges of the bicapped pentagonal prism span the {6a1 + 2a2 + 3b1 + 5b2 + 7e} representations, precisely the configuration shown in the KohnSham molecular orbital diagram in Fig. 3. The highest-lying of these 30 orbitals, 2a2, is the SOMO of [Ru@Ge12]3
. It is important to emphasize a fundamental difference from the icosahedral case discussed above, where the 60 available electrons can be partitioned cleanly into metal- and clusterbased components (10 and 50, respectively). Here, the characteristic 60-electron count at the cluster can only be attained if all electrons, including those on the metal, are assumed to contribute to the bonding between the Ge atoms—in other words, the electrons that we assign formally to metal d orbitals are also integral to the stability of the E12 unit. In the Kohn-Sham molecular orbital diagram, 5 of the 30 occupied orbitals (3b2, 4a1, 4e, and 2b1) have substantial Ru 4d character and are Ru–Ge bonding as well as Ge–Ge bonding. We can draw an analogy to the pieces of a jigsaw puzzle: the electron densities on metal and cage interpenetrate, and the five pairs highlighted above are integral to the stability of both the metal and the cluster. Put another way, a D2d-symmetric [Ge12]2
cage is most definitely not stable in its own right, and in this sense we can make a useful comparison to the classic coordination chemistry of the Schrock carbenes, M ¼ CR2, where two electrons from the metal are absolutely integral to the stability of the CR2 unit. As in the case of the carbenes, the sharing of electron density makes it very difficult (and perhaps, therefore, not useful) to assign formal oxidation states to either the metal or the cluster: if all 10 shared electrons are assigned to the metal, it is Ru(-II) with a 49-electron {Ge12}1
cage, while if they are allocated to the cage, it is Ru(VIII) with a 59-electron {Ge12}11
cage. The true electron density distribution is clearly somewhere between these two limits! Our initial interest in the 59-electron [Ru@Ge12]3
cluster was driven by the EPR spectrum, shown inset in Fig. 3, which shows strong hyperfine coupling (33 MHz) to only 8 of the 12 Ge nuclei—the coupling to the

Fig. 3 Structure, EPR spectrum and Kohn-Sham MO diagram for [Ru@Ge12]3
.13

278

Xiao Jin and John E. McGrady

other four is an order of magnitude smaller at 3 MHz. By symmetry, the SOMO of the cluster, 2a2, is localized entirely on the Ge12 cage, and [Ru@Ge12]3
can therefore be regarded without ambiguity as a Ge radical species and not a paramagnetic metal center. Moreover, the contributions of the four Ge centers, Ge1, Ge2, Ge7 and Ge8 in Fig. 3, to the SOMO are exclusively 3p in character, again by symmetry, leading to vanishingly small contact shifts from these four nuclei. Finally, we note that the 2a2 SOMO has Ge–Ge π* character, most obviously between the Ge1–Ge2 and Ge7–Ge8 pairs. The presence of a single vacancy in this orbital in [Ru@Ge12]3
therefore implies the presence of a small degree of Ge–Ge π bonding in the cluster. We return to this point in the discussion of the hexagonal prism. The third member of the 12-vertex family is the D6h-symmetric hexagonal prism. Although there is no definitive crystal structure of any species with this structure, Hiura’s original proposal for W@Si12 has been supported by a wealth of spectroscopic and computational data, at least for elements of group 6 (Cr, Mo, W). The 3-connected nature of the vertices again invites comparisons to the fullerenes, but the origins of its stability have proven rather controversial. In their initial report, Hiura et al. suggested that the hexagonal prismatic structure of W@Si12 could be understood in terms of an 18-electron rule: donation of 12 electrons from the Si12 cage to the metal raises the electron count to 18, leaving 3 electrons per Si center to form the 3 Si–Si bonds.26 This model is immediately problematic in the sense that it implies that all valence electrons of silicon lie in one hemisphere of the atom (i.e., directed toward the metal), leaving the vertices susceptible to attack by nucleophiles. Such a model would contrast dramatically with the Wade’s rules paradigm, a fundamental component of which is the presence of a pair of electrons directed radially outwards from each vertex. It would also run counter to Lewis’ ideas of an octet symmetrically distributed around the atom. The jellium model offers an alternative perspective, and a 1s21p61d10 configuration (18 electrons) has been proposed for [email protected] In contrast, Abreu et al. have argued that in fact a 16-electron count was more appropriate for Cr@Si12,54 and the presence of a low-lying vacant orbital with almost pure 3dz2 character (4a1g in the Kohn-Sham molecular orbital diagram in Fig. 4) supports this argument. The Cr–Si bonding is dominated by two degenerate orbitals, 2e1g and 2e2g orbitals (shown in bold in Fig. 4) which have substantial Cr dx2
y2/xy and dxz/yz character, respectively: the antibonding counterparts are 3e1g and 4e2g. It is tempting to draw an analogy to the very common square-planar 16-electron complexes of groups 9 and

Structure and bonding in endohedral clusters

279

Fig. 4 Kohn-Sham MO diagram for hexagonal prismatic Cr@Si12.

10 but this is somewhat misleading because in [Ni(CN)4]2
, for example, all five d orbitals are used, either to form Ni-CN bonds or to hold metal-based lone pairs: only the pz orbital of the {nd, (n + 1)s, (n + 1)p} manifold is unused in either sense. In the hexagonal prisms, it is the much lower-lying dz2 orbital that is unused in the sense that it is not involved in bonding and it does not hold a lone pair. As we show in the following section, this hole in the 3d manifold has a dramatic impact on the magnetic properties of these clusters. Looking at the Kohn-Sham MO diagram from the perspective of the Si12 cluster, we note that an electron-precise cluster with 3-connected vertices should, like the D2d-symmetric analogue, demand 5n ¼ 60 valence electrons (n lone pairs + 3n/2 bonding pairs), considerably more than the 54 available in Cr@Si12. A symmetry analysis is again useful: in D6h point symmetry the

280

Xiao Jin and John E. McGrady

12 vertices and 18 edges of a hexagonal prism transform as 3a1g + b1g + b2g + 2e1g + 3e2g + 2a2u + 2b1u + b2u + 2e2u + 3e1u, and in Fig. 4 the 54 valence electrons occupy 27 of these, leaving 2e2u and 2b1u vacant. Just like the 2a2 SOMO in [Ru@Ge12]3
, the three vacant orbitals have zero amplitude on the metal d orbitals, but substantial Si–Si π* character (within the Si6 rings in the case of 2b1u, between the rings in the case of 2e2u). Thus while the Ge–Ge π* character is marginal in [Ru@Ge12]3
, where there is only a single vacancy in the valence manifold of the cluster, it is much more developed in Cr@Si12, with a net π bond order of 3, delocalized over the 18 edges of the cluster. With an understanding of each of the three key structural types in place, we can now consider how their stabilities vary in a periodic sense. The relative stabilities of the key high-symmetry structural types shown in Fig. 1 are summarized in Fig. 5 as a function of total electron count. The icosahedral (Ih) structure is taken as an energetic reference point, and so the energies plotted in Fig. 5 are the differences between the energy of the structure in question and that of the perfect icosahedron for the cluster of the same composition. The plots in Fig. 5 highlight the close relationship between the M@Si12 clusters on the one hand and the anionic Zintl-ion clusters on the other—the trends in stability of the three main structural classes are very similar in the two plots. There is a broad island of stability for the hexagonal prism (HP) centered around electron counts of 54 (Cr/Y), which gives way to a region of relative stability for the bicapped pentagonal prism (BPP) for higher counts before finally the icosahedron becomes the most stable isomer as the d electrons descend into the core. The structural landscape reflects of the ability of electrons in the metal d

Fig. 5 Relative energies of the three structural classes, Ih, HP (D6h) and BPP (D2d), for (A) the M@Si12 family and (B) the [M@Ge12]3
family.

Structure and bonding in endohedral clusters

281

orbitals to mix with those on the cage. The hexagonal prism is favored when there is a small number (up to 6) high-energy electrons, the bicapped pentagonal prism is favored when there are more electrons but they are still relatively high in energy while the icosahedron prevails when the metal d electrons descend into the core. The region of relative stability for the bicapped pentagonal prism is much wider for the anionic Zintl-ion clusters than it is for the neutral M@Si12 clusters because the negative charge ensures that the metal d electrons remain in the valence region as far right as group VIII. These observations are consistent with the fact that there is as yet no experimental evidence for hexagonal prisms in the sphere of Zintl-ion chemistry, nor for bicapped pentagonal prisms in the M@Si12 family. The origins of this distinct trend may lie in the greater π bond order in the hexagonal prisms, which will be a more effective stabilizing mechanism for Si than for the heavier tetrels.

5. The emergence of paramagnetism: [Mn@Pb12]32 and [Mn@Si12]+ The discussion of the properties of [Ru@Ge12]3
highlights the fact that stable paramagnetic clusters can be isolated, although in that case the DFT calculations in combination with the EPR spectroscopy confirm that the radical character is localized entirely on the cage and not on the metal. From a technological perspective, one of the most exciting prospects in this field is the possibility of isolating clusters which retain large paramagnetic moments at the metal: these are highly desirable targets as they have potential applications in molecular magnetism. Transition metals from the middle of the first period are the most obvious candidates in this regard because the substantial 3d–3d exchange energies tend to enforce high-spin configurations, and computational work by Deng and co-workers has predicted a sextet ground state for the as-yet unknown neutral 55-electron cluster Mn@Pb12,55 with 4.34 unpaired electrons localized on the Mn center. This cluster is perfectly icosahedral, and by analogy to the [Ni@Pb12]2
case shown in Fig. 2, the natural formulation is as a Mn(II) ion with a 3hg5 configuration (S ¼ 5/2) encapsulated in an icosahedral [Pb12]2
cage. Kumar and co-workers have also referred to the germanium and tin analogues, Mn@E12 (E ¼ Ge, Sn) as a “magnetic superatoms,”56 where the high local moment at the metal center is shielded from the environment by the E12 cluster. The first experimental realization of such a cluster came in 2011 with the synthesis and characterization of the anionic 58-electron species

282

Xiao Jin and John E. McGrady

[Mn@Pb12]3
, formed from the reaction of K4Pb9 with a source of Mn(II), Mn3Mes6.12 The anion crystallized along with three charge-balancing [K([2.2.2]crypt)]+ cations, and while its structure is identifiably pseudoicosahedral, there is a very distinct prolate distortion along one C2 axis, leading to a D2h-symmetric structure with Mn–Pb distances that vary over a much wider range (2.869(3)–3.308(4) A˚) than seen in any of the other structurally characterized pseudo-icosahedral species. The X-ray data were, however, of rather low quality and so we conducted an exhaustive survey of the potential energy surface using DFT, identifying two almost isoenergetic stationary points, both spin triplets, one of which has D2h symmetry and resembles the X-ray structure rather closely: the Mn–Pb distances split into ˚ from three distinct sets of 2.91, 3.15, and 3.35 A˚ (c.f. 2.90, 3.10, and 3.30 A ˚ X-ray), while the computed Pb–Pb separations range from 3.16 to 3.76 A ˚ (c.f. 3.10–3.75 A from X-ray). The second structure, with D3d point symmetry, is also prolate, but in this case there are only two distinct Mn–Pb ˚ (in a 6:6 ratio) and Pb–Pb bond lengths rangbond lengths, 2.94 and 3.33 A ˚ ing from 3.16 to 3.64 A. The D3d isomer proves to be the global minimum, but only by 0.02 eV compared to the D2h-symmetric alternative, well within the anticipated accuracy limits of the computational method, from which we conclude that the potential energy surface is very flat in the region connecting D2h- and D3d-symmetric structures. For reference, a structure with perfect icosahedral symmetry lies 0.64 eV higher in energy, indicating that while the balance between D2h- and D3d-symmetric structures is delicate, the presence of a strong driving force for a prolate distortion of some kind is not in doubt. We noted above that the neutral Mn@Pb12 can be formulated rather obviously as Mn(II) inside a {Pb12}2
cage, so the key to understanding the structural chemistry of [Mn@Pb12]3
lies in establishing the location of the additional three electrons. In principle there are two limiting scenarios: either the metal ion is reduced to Mn(–I) or the Pb12 cage is reduced to {Pb12}5
. The Mn(–I) inside a {Pb12}2
cage limit would generate net spin densities of +2.0 and 0.0 at Mn and {Pb12}, respectively, while a Mn(II) ion inside a {Pb12}5
cage would give +5.0 and
3.0. In the Kohn-Sham MO diagram for [Mn@Pb12]3
shown in Fig. 6, the three additional electrons occupy the spin-β components of the 2hg orbital, and the net spin densities of +3.21 on the Mn center and
1.21 electrons on the Pb12 cage are almost exactly half way between the two limits identified above. In the discussion of [Ni@Pb12]2
we highlighted the point that back-bonding from Ni to the vacant orbitals of the Pb12 cage was negligible because of the stability of

Structure and bonding in endohedral clusters

283

Fig. 6 Spin-polarized Kohn-Sham diagram for [Mn@Pb12]3
(in icosahedral symmetry).

the Ni 3d orbitals. In the case of [Mn@Pb12]3
, the lower charge on the transition metal nucleus and the very strong exchange interactions between the 3d electrons combine to drive the spin-β components of the d orbitals up in energy, such that they now lie close to vacant orbitals of the cluster (4hg in Fig. 6): mixing between metal- and cluster-based orbitals of hg symmetry is therefore much more prominent in the spin-β manifold (note the much greater amplitude on Pb12 in 3hgβ compared to 2hgα). In effect, the formally Mn(–I) ion is able to relieve some of its excess electron density by transferring it into vacant orbitals on the cluster: complete transfer of all three spin-β electrons to the cage would generate a Mn(II) ion with its characteristic half-filled d shell. The situation described here is in fact very typical of the increasingly diverse family of ligand-centered radicals which are particularly common for the first row transition metals and the lanthanides, and have an important role in many biological electron transfer processes. If we now allow the geometry to relax from icosahedral symmetry to the prolate D2h-symmetric structure, we find a further increase of 0.14 in the magnitudes of the spin densities on both Mn and {Pb12} (ρ(Mn) ¼ +3.35, ρ(Pb12) ¼
1.35), suggesting that enhanced charge transfer from Mn to the cage provides the driving force for the distortion. The origin

284

Xiao Jin and John E. McGrady

of this trend can be traced to the presence of the vacant 1gg LUMO in Fig. 6, a cage-based orbital which is very close in energy to 3hg in the β manifold, but orthogonal to it, so unable to relieve the high electron density at the metal. However, any distortion that allows one or more component of hg and gg to transform as the same reducible representation will open up a very effective electron transfer channel (a second-order Jahn-Teller distortion). Either a D3d or a D2h-symmetric distortion achieves precisely this result, and the result is more effective transfer of electron density and a closer approach to the limit of the stable half-filled d shell. The discussion of the [Mn@Pb12]3
cluster highlights the ability of the E12 cage to support substantial radical character when the endohedral metal is itself strongly paramagnetic. This observation encouraged us to survey the electronic structure of clusters containing metals from near the middle of the first transition series for related phenomena. The question of the electronic structure of Cr@Si12 appears to be largely resolved, but some recent experimental observations on the isoelectronic cationic manganese cluster cation, [Mn@Si12]+, suggest a more complex picture. Infra-red multiple photon dissociation spectra of [Mn@Si12]+Xe, complemented by DFT calculations performed with the hybrid B3P86 functional, have been interpreted in terms of a triplet, rather than a singlet, ground state with a structure that is marginally distorted from perfect hexagonal prismatic.32 X-ray MCD spectra of the same cluster, however, tell a rather different story, and suggest that there is no spin moment on the Mn center.33 To understand this apparent dichotomy, we need to consider how the orbital array for Cr@Si12 in Fig. 4 is modified for isoelectronic [Mn@Si12]+.57 The increased positive charge at the central nucleus will stabilize all the orbitals, but particularly those with dominant metal 3d character. The non-bonding 4a1g LUMO, with Mn 3dz2 character, will therefore be stabilized with respect to 2a2u, which is localized entirely on the Si12 cage. As a result, a charge transfer state with 1A2u symmetry (Fig. 7) is relatively stabilized in the case of [Mn@Si12]+, and in fact lies below the closed-shell 1A1g state that was the unambiguous ground state of Cr@Si12. The value of hS2i in this 1A2u state (2.11 for B3LYP) is indicative of strong biradical character, as are the Mulliken spin densities, ρ(Mn) ¼ +2.69 and ρ(Si12) ¼
2.69. A simple singlet biradical with one unpaired electron on the metal and one on the Si12 cage should have hS2i ¼ 1.0 and spin densities of 1.0, so the rather larger computed values are indicative of substantial polarization of the electrons in the Mn–Si bonding 2e1g and 2e2g orbitals. Within an unrestricted Kohn-Sham ansatz, the presence of a single spin-α electron

Fig. 7 Two complementary perspectives on the seeding of spin polarization in [Mn@Si12]+: (A) the unrestricted DFT picture and (B) CASSCF natural orbitals and populations.57

286

Xiao Jin and John E. McGrady

in the 4a1g orbital makes it more favorable for electrons of the same spin to move closer to the Mn nucleus while the opposite-spin electrons are expelled outwards onto the Si12 cage. In effect, the promotion of one electron into the 4a1g orbital “seeds” the localization of these four bonding pairs, allowing the Mn center to shed the spin-β electrons and approach the half-filled shell configuration. The initially surprising observation that the 1A2u state is more stable than the triplet, 3A2u, is also a reflection of this electronic reorganization. The two formally singly occupied orbitals, 4a1g and 2a2u, are localized in completely different regions of the molecule: 4a1g is almost entirely Mn dz2 in character while 2a2u is almost entirely localized on the silicon cage. The direct exchange interaction between the two unpaired electrons, which would favor a triplet, is therefore very small and the dominant exchange interaction is instead between the single electron in 4a1g and those in the four Mn–Si bonding orbitals (2e1g, 2e2g in Fig. 4). The heavy spin contamination in the 1A2u state is, ultimately, a warning that a single-determinant is a poor approximation to the true wavefunction. In such circumstances, we can turn to the CASSCF approach for an alternative perspective on the bonding. Based on the Kohn-Sham MO diagram, the natural choice of active space is CAS(10,10), including the 4a1g and 2a2u orbitals, the four M–Si bonding orbitals (2e2g and 2e1g) and their antibonding counterparts.38,39 The 10 CAS orbitals and their occupation numbers in the 1 A1g and 1A2u states are shown in Fig. 7B. In the closed-shell singlet state 1 ( A1g), the 4a1g orbital (dz2) is vacant (natural orbital occupation ¼ 0.05) while in the 1A2u state it is singly occupied (0.99). The promotion of an electron into the 4a1g orbital has a significant knock-on effect on the occupations of the four Mn–Si bonding orbitals, which decrease from 1.86 in the 1A1g state to 1.78 in 1A2u, while the occupations of the antibonding orbitals show the opposite trend, increasing from 0.12 in 1A1g to 0.22 in 1A2u: the correlation of the Mn–Si bonding electrons is enhanced by the transfer of an electron into the non-bonding 4a1g orbital. This is precisely the same “seeding” phenomenon that led to the high spin densities in the unrestricted DFT calculations, viewed from the alternative perspective of the CASSCF wavefunction. Equipped with this deeper understanding of the underlying electronic structure, we can now revisit the experimental data for [Mn@Si12]+, in particular the vibrational spectroscopy, to see whether we can identify the signature of the unusual biradical character. The measured vibrational spectrum shows two broad absorptions centered at 260 and 330 cm
1 (Fig. 8, top) which can readily be assigned to the two IR-allowed vibrational

Structure and bonding in endohedral clusters

287

Fig. 8 Experimental infra-red multi-photon dissociation (IRMPD) spectrum of [Mn@Si12]+,32 and simulated vibrational spectra of the 1A1g and 1A2u states.

modes of the D6h-symmetric hexagonal prism, one corresponding to in-plane motion of the Mn atom (e1u) and one to motion along the principal axis (a2u). The computed spectrum of the closed-shell singlet state 1A1g state confirms that these two peaks dominate the low-frequency region, but the separation between the e1u band at 222 cm
1 and the a2u band at 333 cm
1 is

288

Xiao Jin and John E. McGrady

111 cm
1, much higher than the experimental difference of 70 cm
1. In the 1 A2u state, the same two intense bands are apparent in the spectrum, but the e1u band is now blue-shifted by 16 cm
1 while the a2u mode is red-shifted by 23 cm
1 giving an almost perfect agreement with the experimental separation of 70 cm
1. The experimental data are therefore much more consistent with the biradical ground state rather than a closed-shell singlet. The separation between the e1u (xy) and a2u (z) modes is in fact a very sensitive measure of the anisotropy of the Mn center (the two would merge in the limit of a perfectly symmetric coordination environment) and the overestimation of this separation for the 1A1g state is therefore a clear signal that the anisotropy of the Mn center is also overestimated due to the absence of electron density in the dz2 orbital. The transfer of a single electron into this dz2 orbital in the 1A2u state, along with the polarization of the other bonding electrons, leads to a much more isotropic distribution and hence to the smaller separation of the bands.

6. The 10-vertex family, M@E10 The family of 10-vertex endohedral clusters of the tetrels, M@E10, is also a structurally diverse one, and includes deltahedral examples (bicapped square antiprismatic 52-electron [Ni@Pb10]2
), intermediate structures that can be considered as distorted bicapped square antiprisms (50-electron [Ni@In10]10
) and “fullerene-like” examples (51-electron [Fe@Ge10]3
and 52-electron [Co@Ge10]3
). The periodic trends are also striking similar to those set out for the 12-vertex analogues—the deltahedra typically contain late transition metals while the fullerene-like structures contain earlier transition metals where the metal d orbitals are higher in energy. In this section we follow the same format adopted for the 12-vertex family—we first identify the key electronic features of the main sub-classes, and then establish the connections between them. The archetypal deltahedral cluster is D4d-symmetric [Ni@Pb10]2
with two quite distinct Ni–Pb bond lengths, ˚ (equatorial).6 In this case the empty cage, 3.21 A˚ (apical) and 2.72 A [Pb10]2
, has also been crystallographically characterized: it has the same bicapped square antiprismatic structure, with Pb–Pb distances in the range ˚ , very similar to those of [Ni@Pb10]2
(3.09–3.41 A ˚ ). All of the 3.07–3.31 A above points toward the presence of an inert Ni(0) center encapsulated in a closo [Pb10]2
cage and, just like in [Ni@Pb12]2
, we can partition the 52 available valence electrons cleanly into 10 for the Ni(0) center and 42 (¼4n + 2) for the closo 10-vertex cage. Various computational studies

Structure and bonding in endohedral clusters

289

of [Ni@Pb10]2
all confirm that the global minimum is indeed D4dsymmetric, with all alternative structures lying substantially higher in energy. Concurrent reports in 2009 of the structures of 51-electron [Fe@Ge10]3–,21 and 52-electron [Co@Ge10]3–,22 both of which adopt unprecedented pentagonal prismatic geometries (D5h in Fig. 1), introduced a new dimension to the structural chemistry of this family. This structural motif is strikingly reminiscent of hexagonal prismatic Cr@Si12, and also of [Ru@Ge12]3
, in so much as they all have 3-connected vertices and can loosely be described as “fullerene-like.” The presence of metals from the middle of the transition series in all cases suggests a common electronic origin for these clusters, connected to the availability of d-electron density. A number of calculations reported in the literature by us and others have established that the D5h-symmetric structures are indeed the global minima, lying substantially below the D4d-symmetric bicapped square antiprismatic alternative in both cases.52 King and co-workers have also shown that the pentagonal prism is preferred for [Pd@Ge10]2
and [Pt@Ge10]2
, but not for first-row analogue [Ni@Ge10]2
, again suggesting a link to the availability of electron density.58 An analysis of the electron density in [Co@Ge10]3
by F€assler and co-workers indicates a highly delocalized picture of bonding, leading the authors to conclude that the cluster is best described as an intermetalloid.22 The frontier molecular orbitals for [Co@Ge10]3
shown in Fig. 9 highlight the close relationship to hexagonal prismatic Cr@Si12 (Fig. 4). The Co–Ge bonding interaction is dominated by four electron pairs, 3e20 and 2e100 (compare with 3e2g and 2e1g in Fig. 4) while the dz2 orbital aligned along the principal axis, 4a10 , is again non-bonding. The most conspicuous difference between the two systems is that the dz2 orbital is occupied in [Co@Ge10]3
but empty in Cr@Si12, bringing the electron count at the metal up to 18. From the perspective of the cluster, an electron-precise 10-vertex structure demands 5n ¼ 50 valence electrons, two fewer than the total number of valence electrons available. The 4a10 orbital is, however, clearly non-bonding, and it is the remaining 50 electrons, including the 8 in the Co–Ge bonding orbitals, that make up the closed-shell configuration. Thus the electron density is again like the pieces of the jigsaw, with these eight electrons contributing both to the count at the metal and to the count at the cluster, and it is not possible to partition the electron density cleanly in the way that it is for [Ni@Pb10]2
. We can again place the electron counting on a more formal footing with a symmetry analysis using the vertices and the edges of pentagonal prism as a basis: the 3n/2 (¼15) edges span 2a10 + a200 + 2e10 + 2e20 + e100 + e200 while the n (¼10) vertices span

290

Xiao Jin and John E. McGrady

Fig. 9 Kohn-Sham diagram for pentagonal prismatic [Co@Ge10]3
.

a10 + a200 + e10 + e20 + e100 + e200 . Assuming that each edge corresponds to a 2-center-2-electron bond and each vertex carries a lone pair, we predict a 50-electron configuration of 3a10 + 2a200 + 3e10 + 3e20 + 2e100 + 2e200 , precisely the configuration shown in Fig. 9, with the two surplus electrons in the non-bonding Co dz2 orbital (4a10 ). The electron-precise count of 50 at the cluster means that there is no incipient E–E π bonding analogous to that in Cr@Si12, and there is a stronger analogy in this sense to D2d-symmetric [Ru@Ge12]3
, where the electron-precise count is almost complete, and to [Ta@Ge8As4]3
, where the full complement of 60 electrons is present. The comparison of 52-electron [Co@Ge10]3
with 51-electron [Fe@Ge10]3
also highlights a synergy with [Mn@Si12]+, where the presence of a single electron in a metal-centered non-bonding dz2 orbital acted as a seed, promoting the polarization of the electron density in the Mn–Si

Structure and bonding in endohedral clusters

291

bonding orbitals. The ground state of [Fe@Ge10]3
is an approximate doublet with a single electron in the 4a10 orbital, but the large value of hS2i (0.84 vs 0.75 for a pure doublet) and the presence of minority-spin density on the Ge10 cage (ρ(Fe) ¼ 1.45, ρ(Ge10) ¼
0.45) are both indicative of precisely the type of biradical character found in both [Mn@Si12]+ and [Mn@Pb12]3
. The limit of complete spin polarization of the four Fe–Ge bonding orbitals would leave an Fe3+ ion in an S ¼ 5/2 state, antiferromagnetically coupled to highly reduced {Ge10}6
cage in a local quintet configuration. Such high degrees of charge separation are clearly not consistent with the computed spin densities, but the emergence of negative spin density on the cage is nevertheless indicative of a shift toward the Fe3+@{Ge10}6
limit, driven by the local exchange energy available to the high-spin Fe3+ ion. The final member of the M@E10 family is the [Fe@Sn10]3
anion, isolated as its [K([2.2.2]crypt)]+ salt in 2013. We noted in the introduction that our DFT calculations suggest that the equilibrium structure of the [Fe@Sn10]3
anion is neither a pentagonal prism, like isoelectronic [Fe@Ge10]3
, nor a bicapped square antiprism, but rather a C2v-symmetric structure with two square faces.24 The bicapped square antiprism is, however, only very marginally less stable, suggesting that the potential energy surface is very flat. In fact the C2v-symmetric isomer can be considered as an intermediate in the concerted rearrangement of a pentagonal prism to a bicapped square antiprism. The B€ urgi-Dunitz structural correlation model59 holds that such flat surfaces allow for substantial deformations of the cluster in response to environmental effects, and this may be the root cause of the disorder problems encountered in the structure refinement. Motivated by a curiosity about how this new structure fits into the structural landscape, we have conducted a broader survey of isoelectronic 51- and 52-electron clusters, [M@Ge10]n and [M@Sn10]n with the first row transition metals Fe, Co, Ni, Cu, Zn (Fig. 10). The patterns establish a clear trend toward stabilization of the pentagonal prism in the earlier transition elements, just as the corresponding plots for the 12-vertex family established the preference for hexagonal prism over the icosahedron in the same region of the periodic table. The plots in Fig. 10 show that [Fe@Sn10]3
is unique among the 51-electron clusters in having a C2v-symmmetric equilibrium structure: in all other cases this isomer rearranges spontaneously to either the pentagonal prism or the bicapped square antiprism. In this sense, [Fe@Sn10]3
occupies an intermediate position in the structural landscape: it lies in a region where transfer of electron density from the metal to the cage is sufficient to drive a distortion away from the deltahedron, but not to the

292

Xiao Jin and John E. McGrady

Fig. 10 Relative energies of the D5h-, D4d- and C2v-symmetric isomers for isoelectronic [M@E10]n series: (A) 51-electron M@Ge10, (B) 51-electron M@Sn10, (C) 52-electron M@Ge10 and (D) 52-electron M@Sn10. In all cases, the bicapped square antiprismatic structure (D4d) is taken as the energetic reference.

extent that it causes a gross rearrangement to the “fullerene-like” pentagonal prism. In this sense there are many similarities between [Fe@Sn10]3
and [Mn@Pb12]3
, where charge transfer is also significant yet the cluster retains a recognizably deltahedral geometry.

7. The 14-vertex family, M@E14 In contrast to the M@E10 family, where the discussion focused largely on crystallographically characterized Zintl-ion species, the chemistry and physics of the 14-vertex analogues are dominated by the gas-phase chemistry of silicon and germanium. Beck’s early mass spectrometry data suggest that these clusters, along with M@Si15 and M@Si16, are produced in large quantities when a silicon wafer is ablated in the presence of metal carbonyls.25 In the absence of definitive results from diffraction, structural information can only be inferred from a combination of spectroscopic and computational

Structure and bonding in endohedral clusters

293

results and, perhaps inevitably, there seems to be no clear consensus in the literature on the identity of the global minimum for many members of the M@Si14 family. Taking the case of W@Si14 as an example, Hiura has proposed a D3h-symmetric “fullerene-like” isomer with characteristic 3-connected vertices (Fig. 1) as the global minimum using the PerdewWang (PW91) functional with a Gaussian basis set.60 In contrast, Kumar’s group concluded that a C2v-symmetric structure was more stable,61 also using PW91 but with a plane-wave basis. The landscape is similarly confusing for the lighter congener Cr@Si14, where the Perdew-Burke-Ernzerhof (PBE) functional predicts the C2v-symmetric to be most stable,62 while B3LYP favors the fullerene-like isomer (D3h).63 In group 8, we again find conflicting claims for Fe@Si14: with either the PBE or PW91 functional it is proposed to have octahedral symmetry (Oh),64 while B3LYP again favors the fullerene-like isomer.63 Experimental data to test these predictions are available in only a few cases, including the cationic clusters [Mn@Si14]+ and [V@Si14]+ which have been studied using infra-red multi-photon dissociation (IR-MPD) spectroscopy, in conjunction with DFT studies performed using the B3P86 functional.32 The calculations identify two candidate structures for [Mn@Si14]+, a D3h-symmetric fullerene-like isomer (in both singlet and triplet states) and a distorted bicapped hexagonal prism with a dimer unit capping a square face. All three states lie within 0.3 eV, precluding any definitive conclusions on the true ground states, and comparison of the computed spectra with experiment did not give a definitive match in any case. Nguyen and co-workers have also explored the relative stabilities of singlet and triplet states of the D3h-symmetric [Mn@Si14]+ using CASPT2, although this does not offer further insight into the structural preferences.65 It is abundantly clear from this brief survey that the choice of functional plays a defining role in the identity of the global minimum in these clusters, just as it did in the M@E12 family. When considering the relative energies of different isomers, we anticipate that the conclusions should be relatively independent of functional if, and only if, the bonding is qualitatively similar in all isomers of interest, because only then can we hope that errors should cancel, at least approximately. The fact that this is clearly not the case in the M@Si14 family suggests that despite their similar stabilities, the nature of the M–Si and Si–Si bonding in the different isomers of the M@Si14 family is very different. In the face of this “functional roulette,” it is particularly important to develop qualitative models of bonding that allow us to understand the factors that stabilize the different isomers. We again follow the protocol of first understanding the electronic factors

294

Xiao Jin and John E. McGrady

that stabilize the individual isomeric forms (D3h, C2v and Oh in Fig. 1) before considering how periodic trends control the balance between the three.66 Like [Ru@Ge12]3
, Cr@Si12 and [Co@Ge10]3
, the D3h-symmetric isomer is often referred to in the literature as “fullerene-like” because of its resemblance to the archetypal fullerene, C60, and also to an (unstable) isomer of 56-electron C14 with the same structure.67 Our discussion of 10- and 12-vertex families has highlighted the point that 3-connected vertices are in principle consistent with electron counts between 4n (the fullerenes) and 5n (electron-precise clusters), and indeed a D3h-symmetric isomer of 70-electron phosphorus cluster, P14 is topologically equivalent to C14.68 The difference between the fullerene-like and electron-precise limits lies in the π bond order (1/2 per bond in fullerenes, 0 in electron-precise structures), which affects bond lengths and angles but not the connectivity of the vertices. The “fullerene-like” series of endohedral clusters Cr@Si12, [Ru@Ge12]3
and [Co@Ge10]3
show a progressive decrease in π bond order (1/6, 1/36 and 0 per bond, respectively), but in this regard all three lie much closer to the electron-precise limit than a truly fullerene-like electronic structure. In short, the topology of the D3h-symmetic isomer is tolerant of a wide range of electron counts between 56 and 70, and so the adoption of a “fullerene-like” geometry should not be taken as a priori evidence of a truly “fullerene-like” electronic structure. The Kohn-Sham molecular orbital diagram for the D3h-symmetric isomer of Cr@Si14 is shown in Fig. 11, from which it is clear that all five Cr 3d orbitals are involved in Cr–Si bonding (6a10 , 7e0 , 4e00 ). There are, however, three vacant Si–Si π* orbitals, 2a20 , 8e0 , localized around the equator of the cluster and the three equatorial Si–Si bond lengths are accordingly shorter than those in the ˚ ). A fourth vacant Si–Si π* orbital, polar region of the cluster (2.34 vs 2.43 A 00 5a2 , is localized at the poles of the cluster, where the high curvature of the surface precludes significant overlap, but nevertheless this also confers some additional π character to the Si–Si bonds. So in comparison to the “fullerene-like” isomers of the 10- and 12-vertex families, the “fullerenelike” character, as measured by the π bond order, is rather better developed in Cr@Si14, particularly in the equatorial region. Turning to the C2v-symmetric isomer, the relatively high connectivities of its vertices are typical of electron-deficient clusters (the boranes, for example), and so it seems logical to turn to Wade’s rules for guidance. For a 14-vertex cluster, a 62-electron count corresponds to an arachno-architecture (62 ¼ 4n + 6), and so we can rationalize the structure as an arachno- cluster based on a 16-vertex parent polyhedron. The (unknown) closo-borane

Structure and bonding in endohedral clusters

295

Fig. 11 Kohn-Sham molecular orbitals for the D3h-symmetric “fullerene-like” isomer of Cr@Si14.

[B16H16]2
(isoelectronic with [Si16]2
) is predicted to be a D4d-symmetric octa-capped square antiprism, and removing two of the caps from this structure exposes the pentagonal faces found in the C2v-symmetric isomer. The role of the metal d orbitals is made clear if we make an isolobal comparison to the hypothetical empty arachno cluster [Si14]6
: the six 3d electrons of Cr (8b1, 8b2 and 4a2 in Fig. 12) simply replace the 6
charge, forcing the cluster to adopt a structure characteristic of a 62-electron count. Again we see a dual role for the metal 3d electrons: they contribute to the 18-electron count of the metal and to the 4n + 6 count of the cluster.9,10 This dual role can, however, be fulfilled only if the metal d orbitals have significant amplitude at the radius defined by the 14 silicon atoms (in other words, only if the isolobal analogies captured in the box in Fig. 12 are valid). Thus we should anticipate that as the metal d orbitals become increasingly contracted, the stability of this isomer should be compromised very rapidly. For the octahedral isomer, we find that the metal d orbitals play a very different role compared the two alternative structures. A first significant point to note is that the same isomer has been identified as the global minimum for the empty germanium cluster [Ge14]2
. The 58 valence

296

Xiao Jin and John E. McGrady

Fig. 12 Kohn-Sham molecular orbitals for the C2v-symmetric “arachno” isomer of Cr@Si14 and the isolobal relationship between Cr@Si14, arachno-[Si14]6
and closo[Si16]2
.

electrons equate to the classic 4n + 2 count for closo clusters, and indeed the high symmetry and high vertex connectivities of the octahedral isomer are precisely the structural features that characterize highly electrondeficient closo boranes such as [B6H6]2
. All of this invites comparison to [Ni@Pb12]2
and [Ni@Pb10]2
, where the empty closo cluster units, [Pb12]2
and [Pb10]2
, are also stable entities in their own right. The KohnSham molecular orbital diagram in Fig. 13 confirms this perspective: the 2eg orbitals, which are an integral part of the 4n + 2 ¼ 58 closo electron count, carry substantial Fe–Si and Si–Si bonding character. They therefore play a similar dual role as the 8b1, 8b2 and 4a2 orbitals of the C2v-symmetric isomer (Fig. 12), contributing to the characteristic electron count of the Si14 unit. The six remaining electrons of Fe@Si14 are, however, surplus to the requirements of the Si14 cluster, and the 3t2g orbital is Fe–Si antibonding. In this sense the situation is very similar to that in [Ni@Pb10]2
and [Ni@Pb12]2
(Fig. 2) and the octahedral [Si14]2
unit can be considered as a net π donor rather than an acceptor. Periodic variations in the stabilities of the three different isomers are shown in Fig. 14, for two of the contrasting functionals that lie at the center of the controversy in the literature: PBE and B3LYP. The octahedral isomer

Structure and bonding in endohedral clusters

297

Fig. 13 Kohn-Sham molecular orbitals for the “closo” octahedral isomer of Fe@Si14.

(Oh) is selected as an (arbitrary) reference point in all plots (green line). The plots again emphasize the point that the relative stabilities of the various isomers vary smoothly as a function of electron count. The Oh-symmetric isomer, where the interactions between the metal d electrons and the cluster are antibonding, becomes relatively stable as the d orbitals descend into the core to the right hand side of the period. Both the D3h- and C2v-symmetric isomers, in contrast, reach maximum stability around the 62-electron count of Cr@Si14, and the energies of the two are close enough to allow functional choice to reverse the order: the B3LYP functional (plot b) places D3h below C2v for Cr@Si14, as reported by Hiura and He, while PBE (plot a) reverses the order, as reported by Kumar and Khanna. Equally, 64-electron Fe@Si14 lies close to the intersection of the curves for D3h and Oh, and switching from PBE to B3LYP reverses the order. If we compare the relative stabilities for an isoelectronic series with different charges but a common 62 valence electron count (Fig. 14C and D), we note that the C2v isomer (red line) is very strongly destabilized relative to both D3h and Oh as the positive charge increases. We highlighted in the

298

Xiao Jin and John E. McGrady

Fig. 14 Functional dependence of the relative energies of the three isomers of MSi14 clusters: (A) neutral M@Si14 with the PBE functional, (B) neutral M@Si14 with the B3LYP functional, (C) 62-electron [M@Si14]n with the PBE functional and (D) 62-electron [M@Si14]n with the B3LYP functional. The octahedral isomer (green line) is taken as the energetic reference point in all cases.

discussion of the electronic structure that hybridization of the d orbitals on the metal with those on the cluster was absolutely integral to the C2v-symmetric arachno structure: the structure simply does not make sense without six d electrons to bring the count up to 62. The “fullerene-like” isomer (D3h), in contrast, is much more tolerant to changes in the electron density at the metal because the 3d electrons only interact weakly with the π components of the Si–Si bonds. Thus as the d orbitals contract and sink into the core, the stability of the C2v-symmetric isomer is compromised most rapidly.

8. Summary and future perspectives The aim of this review has been to highlight the close electronic relationships between apparently rather unrelated molecules. In particular, we

Structure and bonding in endohedral clusters

299

have emphasized the links between anionic Zintl ions of the heavier tetrels and neutral gas-phase clusters of silicon, which share many common features in terms of electronic structure. The plots of periodic stability trends for the three main families of cluster lay bare the fact that while the absolute stability of different isomers depends critically on composition, charge and theoretical model, the underlying trends do not. We can therefore identify islands of stability in chemical space where particular structural motifs will dominate. Perhaps most importantly, we have established the underlying electronic factors that determine these trends. Within each family of cluster, M@E10, M@E12 and M@E14, we find that deltahedral structures with high vertex connectivity dominate for the late transition metals, where the d orbitals are core-like. These clusters can be viewed through the lens of Wade’s rules: they contain an inert d10 ion which fills the internal void in a closo cluster. As we move to the left in the periodic table the metal d orbitals rise in energy and begin to impose their fingerprint on the structural chemistry. The 3-connected “fullerene-like” cluster geometries that dominate this region are characteristic of very high electron counts, and these can only be attained if the metal d electrons are assumed to contribute to the cluster. The “fullerene-like” and Wade’s rules paradigms of cluster bonding are typically applied to very different families of clusters (carbon-based clusters and the borane family, for example) and there is rarely any conflict between the two. It seems, however, that in the case of these endohedral clusters the factors that stabilize the two paradigms are very finely balanced, to the extent that the two isomers have very similar energies. We see this most clearly in isoelectronic pairs, where the geometry and electronic structure nevertheless prove to be very different: D5h-symmetric [Fe@Ge10]3
vs C2v-symmetric [Fe@Sn10]3
is a case in point, as is closed-shell Cr@Si12 vs biradical [Mn@Si12]+. The same issue leads directly to the extreme functional dependence found in the DFT literature, best exemplified by the M@Si14 family, where different choices lead to completely different conclusions regarding the equilibrium structure. We can understand the tension between the “fullerene-like” and Wade’s rules paradigms by linking the two models through a common electronprecise reference point (we take 14-vertex P14, as an example but similar arguments apply to any of the families). The electron-precise cluster has 5n ¼ 70 valence electrons (second column of Fig. 15)69 which can be partitioned into 3n ¼ 42 in the 21 σ bonds and 2n ¼ 28 in the 14 radially directed lone pairs (or E–H bonding orbitals if the vertices are diatomic fragments such as B–H). This then leaves only two ways to accommodate lower

300

Xiao Jin and John E. McGrady

Fig. 15 Schematic representation of the fullerene and Wade’s rules routes to accommodating electron deficiency in M@Si14 clusters. The numbers below each band indicate the number of orbitals.

electron counts: (i) by depleting the electron density in the lone pairs with concomitant generation of multiple bonds (the “fullerene route,” to the left in Fig. 15) or (ii) by leaving the lone pairs intact and depleting the σ framework (the “Wade’s rules route” to the right in Fig. 15). The first option leads to contraction of individual bonds but conserves the overall topology of the cluster, while the second option drives the formation of triangular faces and an increase in vertex connectivity. As the electron count is reduced from 5n to 4n + 2, the “fullerene-like” and Wade’s rules paradigms represent alternative solutions to the common problem of accommodating increasing electron deficiency. In carbon-based materials such as C60, the strong 2p–2p π overlap and the low surface curvature combine to stabilize the π bonding orbitals, and so make the fullerene solution favorable. In the

Structure and bonding in endohedral clusters

301

boranes, in contrast, depopulation of the radial orbitals is strongly disfavored because these are in fact B–H bonding orbitals rather than lone pairs. Any reduction in electron count can therefore only be absorbed by depletion of the B–B σ framework (i.e., the Wade’s rules route). The increasing stability of the ns2np2 configuration over ns1np3 down group 14 (the inert pair effect) has a similar effect, favoring double occupation of the radial orbital (the ns2 lone pair), and hence the Wade’s rules route over the fullerene alternative. As a result, the cluster chemistry of the heavier tetrels is dominated by deltahedral structures (Ni@Pb12, [Fe@Sn10]3
, [Mn@Pb12]3
) rather than fullerene-like alternatives. The endohedral silicon clusters appear to be rare intermediate cases where the two bonding paradigms collide, giving rise to near-degenerate isomers which make use of the limited metal-based electron density available in fundamentally different ways. While a thorough understanding of the factors that stabilize the different isomers brings us no closer to an answer to the question of which density functional is “best,” it does at least allow us to understand why functional roulette is such a dangerous game in the M@Si14 family. In the future, it seems likely that systematic bottom-up approaches will allow for the synthesis of ever larger clusters through the controlled coalescence of smaller building blocks. These protocols will offer opportunities to tune the macroscopic properties of the resultant materials through control of the interactions between the metal and the cage. The fact that these interactions can span the entire range from repulsive to strongly covalent offers a uniquely flexible platform for exploring the nature of the chemical bond. It is also clear that our ability to understand these clusters from a theoretical perspective will depend critically on an accurate treatment of the electronelectron repulsion problem.

Acknowledgments We acknowledge Professor Jose M. Goicoechea for many helpful discussions.

References 1. (a) Wade, K. J. Chem. Soc. D—Chem. Commun. 1971, 792. https://doi.org/10.1039/ C29710000792; (b) Wade, K. Adv. Inorg. Chem. Radiochem. 1976, 18, 1. 2. Tyo, E. C.; Vajda, S. Nat. Nanotechnol. 2015, 10, 577–588. 3. (a) Bernardini, F.; Picozzi, S.; Continenza, A. Appl. Phys. Lett. 2004, 84, 2289; (b) Dalpian, G. M.; da Silva, A. J. R.; Fazzio, A. Phys. Rev. B 2003, 68, 113310; (c) da Silva, A. J. R.; Fazzio, A.; Antonelli, A. Phys. Rev. B 2004, 70, 193205; (d) Zhang, Z. Z.; Partoens, B.; Chang, K.; Peeters, F. M. Phys. Rev. B 2008, 77, 155201. 4. Cheng, J.-Y.; Fisher, B. L.; Guisinger, N. P.; Lilley, C. M. npj Quant. Mater. 2017, 2, 25. 5. Myers, S. M. J. Appl. Phys. 2000, 88, 3795–3819.

302

Xiao Jin and John E. McGrady

6. Esenturk, E. N.; Fettinger, J.; Lam, Y. F.; Eichhorn, B. Angew. Chem. Int. Ed. 2004, 43, 2132–2134. 7. Esenturk, E. N.; Fettinger, J.; Eichhorn, B. J. Am. Chem. Soc. 2006, 128, 9178–9186. 8. Wang, J. Q.; Stegmaier, S.; Wahl, B.; F€assler, T. F. Chem. Eur. J. 2010, 16, 1793–1798. 9. Wang, Y.; Wang, L. L.; Ruan, H. P.; Luo, B. L.; Sang, R. L.; Xu, L. Chin. J. Struct. Chem. 2015, 34, 1253. 10. Li, L.-J.; Pan, F.-X.; Li, F.-Y.; Chen, Z.-F.; Sun, Z.-M. Inorg. Chem. Front. 2017, 4, 1393–1396. 11. (a) Cui, L. F.; Huang, X.; Wang, L. M.; Li, J.; Wang, L. S. J. Phys. Chem. A 2006, 110, 10169; (b) Cui, L. F.; Huang, X.; Wang, L. M.; Zubarev, D. Y.; Boldyrev, A. I.; Li, J.; Wang, L. S. J. Am. Chem. Soc. 2006, 128, 8390. 12. Zhou, B.; Kr€amer, T.; Thompson, A. L.; McGrady, J. E.; Goicoechea, J. M. Inorg. Chem. 2011, 50, 8028. 13. Espinoza-Quintero, G.; Duckworth, J. C. A.; Myers, W. K.; McGrady, J. E.; Goicoechea, J. M. J. Am. Chem. Soc. 2014, 136, 1210. 14. (a) Li, X.-J.; Su, K.-H. Theor. Chem. Acc. 2009, 124, 345; (b) Li, X.-J.; Ren, H.-J.; Yang, L.-M. J. Nanomater. 2012, 2012, 518593 (8 pp). 15. (a) Zdetsis, A. D.; Houkaras, E. N.; Garoufalis, C. S. J. Math. Chem. 2009, 46, 971; (b) Koukouras, E. N.; Garoufalis, C. S.; Zdetsis, A. D. Phys. Rev. B 2006, 73, 235417. 16. (a) Bandyopadhyay, D.; Sen, P. J. Phys. Chem. A 2010, 114, 1835; (b) Sen, P.; Mitas, L. Phys. Rev. B 2003, 68, 155404. 17. Mitzinger, S.; Broeckaert, L.; Massa, W.; Weigend, F.; Dehnen, S. Nat. Commun. 2016, 7, 10480–10489. 18. Esenturk, E. N.; Fettinger, J.; Eichhorn, B. Chem. Commun. 2005, 247–249. https://doi. org/10.1039/B412082E. 19. Spiekermann, A.; Hoffmann, S. D.; F€assler, T. F. Angew. Chem. Int. Ed. 2006, 45, 3459. 20. (a) Sevov, S. C.; Corbett, J. D. Inorg. Chem. 1993, 32, 1059; (b) Sevov, S. C.; Corbett, J. D.; Ostenton, J. E. J. Alloys Compd. 1993, 202, 289; (c) Sevov, S. C.; Corbett, J. D. J. Am. Chem. Soc. 1993, 115, 9089. 21. Zhou, B.; Denning, M. S.; Kays, D. L.; Goicoechea, J. M. J. Am. Chem. Soc. 2009, 131, 2802. 22. Wang, J.-Q.; Stegmaier, S.; F€assler, T. F. Angew. Chem. Int. Ed. 2009, 48, 1998. 23. Korber, N. Angew. Chem. Int. Ed. 2009, 48, 3216–3217. 24. Kr€amer, T.; Duckworth, J. C.; Ingram, M. D.; Zhou, B.; McGrady, J. E.; Goicoechea, J. M. Dalton Trans. 2013, 42, 12120–12129. 25. (a) Beck, S. M. J. Chem. Phys. 1987, 87, 4233–4234; (b) Beck, S. M. J. Chem. Phys. 1989, 90, 6306–6312. 26. Hiura, H.; Miyazaki, T.; Kanayama, T. Phys. Rev. Lett. 2001, 86, 1733–1736. 27. Uchida, N.; Bolotov, L.; Miyazaki, T.; Kanayama, T. J. Phys. D: Appl. Phys. 2003, 36, L43–L46. 28. Sun, Z.; Oyanagi, H.; Uchida, N.; Miyazaki, T.; Kanayama, T. J. Phys. D: Appl. Phys. 2009, 42, 015412. 29. Khanna, S. N.; Rao, B. K.; Jena, P. Phys. Rev. Lett. 2002, 89, 016803. 30. Zheng, W.; Nilles, J. M.; Radisic, D.; Bowen, K. H., Jr. J. Chem. Phys. 2005, 122, 071101. 31. Claes, P.; Janssens, E.; Ngan, V. T.; Gruene, P.; Lyon, J. T.; Harding, D. J.; Fielicke, A.; Nguyen, M. T.; Lievens, P. Phys. Rev. Lett. 2011, 107, 173401. 32. Ngan, V. T.; Janssens, E.; Claes, P.; Lyon, J. T.; Fielicke, A.; Nguyen, M. T.; Lievens, P. Chem. Eur. J. 2012, 18, 15788–15793. 33. Zamudio-Bayer, V.; Leppert, L.; Hirsch, K.; Langenberg, A.; Rittmann, J.; Kossick, M.; oller, T.; v. Issendorff, B.; K€ ummel, S.; Lau, J. T. Vogel, M.; Richter, R.; Terasaki, A.; M€ Phys. Rev. B 2013, 88, 115425.

Structure and bonding in endohedral clusters

303

34. Zhang, X.; Li, G. L.; Gao, Z. Rapid Commun. Mass Spectrom. 2001, 15, 1573. 35. Zhang, X.; Li, G. L.; Xing, X. P.; Zhao, X.; Tang, Z. C.; Gao, Z. Rapid Commun. Mass Spectrom. 2001, 15, 2399. 36. Zhang, X.; Tang, Z.; Gao, Z. Rapid Commun. Mass Spectrom. 2003, 17, 621. 37. Cui, L. F.; Huang, X.; Wang, L. M.; Li, J.; Wang, L. S. Angew. Chem. Int. Ed. 2007, 46, 742. 38. Ohara, M.; Koyasu, K.; Nakajima, A.; Kaya, K. Chem. Phys. Lett. 2003, 371, 490–497. 39. Neukermans, S.; Wang, X.; Veldeman, N.; Janssens, E.; Silverans, R. E.; Lievens, P. Int. J. Mass Spectrom. 2006, 252, 145–150. 40. Knight, W. D.; Clemenger, K.; de Heer, W. A.; Saunders, W. A.; Chou, M. Y.; Cohen, M. L. Phys. Rev. Lett. 1984, 52, 2141. 41. Luo, Z.; Castleman, A. W., Jr. Acc. Chem. Res. 2014, 47, 2931. 42. Leuchtner, R. E.; Harms, A. C.; Castleman, A. W., Jr. J. Chem. Phys. 1989, 91, 2753. 43. Reber, A. C.; Khanna, S. N.; Castleman, A. W., Jr. J. Am. Chem. Soc. 2007, 129, 10189. 44. Bergeron, D. E.; Castleman, A. W., Jr.; Morisato, T.; Khanna, S. N. Science 2004, 304, 84. 45. Reveles, J. U.; Khanna, S. N.; Roach, P. J.; Castleman, A. W., Jr. PNAS 2006, 103, 18405. 46. (a)Baerends, E. J. SCM, Theoretical Chemistry, Vrije Universiteit, Amsterdam, The Netherlands, 2013, ADF2013, http://www.scm.com.; (b) Fonseca Guerra, C.; Snijders, J. G.; te Velde, G.; Baerends, E. J. Theor. Chem. Acc. 1998, 99, 391–403; (c) te Velde, G.; Bickelhaupt, F. M.; Baerends, E. J.; Fonseca Guerra, C.; Van Gisbergen, S. J. A.; Snijders, J. G.; Ziegler, T. J. Comput. Chem. 2001, 22, 931–967. 47. (a) Klamt, A.; Jonas, V. J. Chem. Phys. 1996, 105, 9972–9981; (b) Klamt, A. J. Phys. Chem. 1995, 99, 2224–2235. 48. Aquilante, F.; Autschbach, J.; Carlson, R. K.; Chibotaru, L. F.; Delcey, M. G.; De Vico, L.; Galva´n, I. F.; Ferre, N.; Frutos, L. M.; Gagliardi, L.; Garavelli, M.; Giussani, A.; Hoyer, C. E.; Li Manni, G.; Lischka, H.; Ma, D. X.; Malmqvist, P. A.; M€ uller, T.; Nenov, A.; Olivucci, M.; Pedersen, T. B.; Peng, D. L.; Plasser, F.; Pritchard, B.; Reiher, M.; Rivalta, I.; Schapiro, I.; Segarra-Marti, J.; Stenrup, M.; Truhlar, D. G.; Ungur, L.; Valentini, A.; Vancoillie, S.; Veryazov, V.; Vysotskiy, V. P.; Weingart, O.; Zapata, F.; Lindh, R. J. Comput. Chem. 2016, 37, 506–541. 49. Roos, O. B.; Veryazov, V.; Widmark, P. O. Theor. Chem. Acc. 2003, 111, 345–351. 50. Tang, C.; Liu, M.; Zhu, W.; Deng, K. Comput. Theor. Chem. 2011, 969, 56. 51. Kapila, N.; Jindhal, V. K.; Sharma, H. Physica B 2011, 406, 4612. 52. Goicoechea, J. M.; McGrady, J. E. Dalton Trans. 2015, 44, 6755–6766. 53. Reveles, J. U.; Khanna, S. N. Phys. Rev. B 2005, 72, 165413. 54. Abreu, M. B.; Reber, A. C.; Khanna, S. N. J. Phys. Chem. Lett. 2014, 5, 3492–3496. 55. Chen, X.; Deng, K.; Liu, Y.; Tang, C.; Yuan, Y.; Hu, F.; Wu, H.; Huang, D.; Tan, W.; Wang, X. Chem. Phys. Lett. 2008, 462, 275. 56. Kumar, V.; Kawazoe, Y. Appl. Phys. Lett. 2003, 83, 2677. 57. Arcisauskaite, V.; Fijan, D.; Spivak, M.; de Graaf, C.; McGrady, J. E. Phys. Chem. Chem. Phys. 2016, 18, 24006–24014. 58. (a) King, R. B. In Zintl Ions: Principles and Recent Developments; F€assler, T. F. Ed.; 140; Springer-Verlag Berlin: Berlin, 2011; pp 1–24; (b) King, R. B.; Silaghi-Dumitrescu, I.; Ut¸a˘, M. M. Eur. J. Inorg. Chem. 2008, 25, 3996–4003; (c) King, R. B.; SilaghiDumitrescu, I.; Uta, M. M. Dalton Trans. 2007, 364–372. https://doi.org/10.1039/ B615225B. 59. B€ urgi, H. B.; Dunitz, J. Structural Correlation. Wiley, 1994. 60. Miyazaki, T.; Hiura, H.; Kanayama, T. Phys. Rev. B 2002, 66, 121403. 61. Kumar, V.; Kawazoe, Y. Phys. Rev. B 2002, 65, 073404.

304

Xiao Jin and John E. McGrady

62. Reveles, J. U.; Khanna, S. N. Phys. Rev. B 2006, 74, 035435. 63. He, J.; Wu, K.; Liu, C.; Sa, R. Chem. Phys. Lett. 2009, 483, 30–34. 64. (a) Chauhan, V.; Abreu, M. B.; Reber, A. C.; Khanna, S. N. Phys. Chem. Chem. Phys. 2015, 17, 15718–15724; (b) Kumar, V.; Kawazoe, Y. Phys. Rev. Lett. 2001, 87, 045503. 65. Ngan, V. T.; Pierloot, K.; Nguyen, M. T. Phys. Chem. Chem. Phys. 2013, 15, 5493–5498. 66. Jin, X.; Arcisauskaite, V.; McGrady, J. E. Dalton Trans. 2017, 46, 11636–11644. 67. Jones, R. O.; Seifert, G. Phys. Rev. Lett. 1997, 79, 443–446. 68. H€aser, M.; Schneifer, U.; Ahlrichs, R. J. Am. Chem. Soc. 1992, 114, 9551–9559. 69. McGrady, J. E. J. Chem. Educ. 2004, 81, 733–737.