Letter pubs.acs.org/JPCL
Does the 18-Electron Rule Apply to CrSi12? Marissa Baddick Abreu, Arthur C. Reber, and Shiv N. Khanna* Department of Physics, Virginia Commonwealth University, 1020 West Main Street, Richmond, Virginia 23284-2000, United States S Supporting Information *
ABSTRACT: Understanding the bonding between silicon and transition metals is valuable for devising strategies for incorporating magnetic species into silicon. CrSi12 is the standard example of a cluster whose apparent high stability has been explained by the 18-electron rule. We critically examine the bonding and nature of stability of CrSi12 and show that its electronic structure does not conform to the 18-electron rule. Through theoretical studies, we find that CrSi12 has 16 effective valence electrons assigned to the Cr atom and an unoccupied 3dz2 orbital. We demonstrate that the cluster’s apparent stability is rooted in a crystal field-like splitting of the 3d orbitals analogous to that of square planar complexes. CrSi14 is shown to follow the 18-electron rule and exhibits all conventional markers characteristic of a magic cluster. SECTION: Molecular Structure, Quantum Chemistry, and General Theory
M
clusters and showed that the energy gained in adding a Si atom to the CrSin clusters does peak at CrSi12, confirming its increased stability compared with its neighbors. These studies debated the utility of the 18-electron rule in predicting the stability of the clusters; however, determining if the 18-electron rule actually applies to CrSi 12 has not been examined.5,18−26,34,35 The purpose of this paper is to revisit the applicability of the 18-electron rule to CrSi12 and to critically investigate its magic nature. Two developments motivate this inquiry; first, photoelectron spectroscopy experiments on the CrSin− species have recently been carried out providing a direct window to the electronic structure of these clusters.35,36 Second, CrSi12 was not found to be unusually stable in the mass spectra found in the laser vaporization of silicon and chromium.3,37 These experiments find that CrSin+ with n = 14 to 15 have a higher intensity in the mass spectra than n = 12. We investigate the stability of CrSi12 using first-principles theoretical methods38−40 and find it has the second largest Si binding energy and a HOMO−LUMO gap that is smaller than most of the neighboring CrSin species, for n = 6−16, while CrSi14 has the largest Si binding energy and HOMO−LUMO gap in this size range. CrSi12 is also found to have a larger electron affinity and smaller ionization potential than CrSi14, indicating that the most stable neutral cluster in the series is CrSi14. Second, an analysis of the molecular orbitals of CrSi12 demonstrates that it does not conform to the 18-electron rule. The 3dz2 orbital of Cr is found to be unoccupied in CrSi12, and the oblate D6h structure of the cluster introduces a gap through crystal field splitting with an effective electron valence count on the Cr atom of 16 electrons. CrSi14 is found to have filled Cr 3d
etal silicon clusters have attracted a great deal of interest because the incorporation of large quantities of transition metal atoms into bulk silicon is difficult and overcoming this limitation could offer new materials for the microelectronics industry. Assembling solids using metal silicon clusters would alleviate this difficulty, and this started a vigorous search for stable metal silicon magic clusters almost 20 years ago.1−4 One of the areas of potential interest was silicon cages encapsulating metal atoms.3,4 The bonding between the silicon and the transition-metal dopant stabilizes the cage structure when the electronic shells of both the transition metal and silicon cages are closed. This work was originally motivated by Hiura et al.,5 who generated a series of hydrogenated silicon clusters containing several 5d transition metal atoms. The nonreactivity with silane and the preponderance of WSi12 prompted Hiura et al. to argue that WSi12 is a highly stable magic species. Hiura et al. also proposed that the stability of WSi12 could be rationalized within the 18-electron rule. It is well-known that main group elements are electronically stable when they follow the octet rule with filled ns2 np6 outer electronic shells, while transition metals have maximum stability with 18 electrons that corresponds to a closed shell of ns2 (n − 1)d10np6.6−11 Hiura et al. argued that WSi12 stability could also be attributed to the 18-electron rule assuming that each Si atom contributes one valence electron while the W contributes six electrons. The ground-state structure of WSi12 is a hexagonal prism with an endohedral W atom. Each Si is bonded to three other Si atoms and the central Cr atom, so by assuming electron-precise bonding, each Si donates 1 e− to the Cr atom. Furthermore, these clusters were thought to be analogous to transition-metal aromatic complexes that are most stable when the central atom has 18 effective valence electrons.12−17 These findings sparked a flurry of activities in MSin clusters and, in particular, on the congener cluster CrSi12.18−33 Numerous works including several from one of the present authors have examined the stability of CrSin © 2014 American Chemical Society
Received: September 3, 2014 Accepted: September 26, 2014 Published: September 26, 2014 3492
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and the ionization potential (I.P.). Some of these energies are defined by
orbitals and does conform to the 18-electron rule. CrSi14 is the smallest CrSin cluster with both a closed electronic and geometric shell. This is consistent with the observed and calculated enhanced stability of CrSi14 and reveals that the bonding between silicon and chromium is not electron precise. Figure 1 shows the equilibrium geometries of CrSin clusters, and the Supplementary Figure S1a−d in the Supporting
ΔSi = −[E(CrSi n) − E(CrSi n − 1) − E(Si)]
(1)
ΔCr = − [E(CrSi n) − E(Si n) − E(Cr)]
(2)
I. P. = −[E(CrSi n+) − E(CrSi n)]
(3)
Here E(CrSin) is the total energy of the CrSin cluster, while E(Si) and E(Cr) are the total energy of a Si and Cr atom, respectively. The Cr embedding energy was calculated using the ground-state geometries of Sin (n = 6−16), which are in agreement with previous theoretical studies on pure silicon clusters.45−49 The I.P. was calculated using the ground-state energies of the neutral and cationic clusters and thus corresponds to the adiabatic I.P. (the ground state cationic structures are shown in Figure S4 in the Supporting Information). Figure 2 shows the variation of these energies, and a table of all values in Figure 2 is given in the Supporting Information (Table S2).
Figure 1. Ground-state structures of neutral CrSin (n = 6−16). Silicon atoms are shown in gray and chromium atoms are shown in dark blue. The average bond lengths are shown for Si−Si in gray, and Cr−Si in blue.
Information contains information on higher energy structures for each size. The corresponding information on the groundstate geometries for the anions is given in Figure S2 in the Supporting Information. The atomic structures for neutral species are similar to the ones obtained in previous theoretical studies, and the calculated photoelectron spectra based off of these structures show good agreement with experiments.18,20−22,25,32,34,36,41−43 The calculated spectra are shown in Figure S3 in the Supporting Information. In Table S1 in the Supporting Information, we compare the ADE, VDE (position of the first peak in the photodetachment spectra), and the relative position of the second peak in the experimental spectra with those obtained in this work. In all cases, the calculated values differ from the experimental values by only few %, validating our theory. The ground state of CrSi12 is a hexagonal prism with an endohedral Cr atom sandwiched between two hexagons of Si atoms. This structure has been confirmed by scanning tunneling microscopy (STM) on deposited clusters44 and also obtained in several previous theoretical works including our own studies. CrSi6 has a multiplicity of five, while all of the larger CrSin clusters have quenched magnetic moments. CrSin, where n = 6−9, has the Cr atom on the outside of the silicon cage. CrSi10 and CrSi11 have structures in which the Cr is mostly embedded within the silicon cage; however, the Cr is partially exposed. CrSi12 is the smallest cluster with a completely encapsulated interior Cr atom. To detect signatures of special stability, we examined the energy gain, ΔSi, as a Si atom is added to the preceding size, the embedding energy, ΔCr, representing the gain in energy as a Cr atom is added to a Sin cluster, the gap between the highest occupied molecular orbital (HOMO), and the lowest unoccupied molecular orbital (LUMO), the VDE and ADE,
Figure 2. Properties of CrSin (n = 6−16) ground states. (a) Silicon binding energy, ΔSi, for n = 7−16. (b) Chromium embedding energy, ΔCr. (c) Adiabatic and vertical detachment energy. ADE is shown as blue squares and VDE is shown as red circles. (d) Ionization potential, IP. (e) HOMO−LUMO gap. (f) Hydrogen binding energy. The horizontal dotted line is the binding energy per H atom in H2. In panels a−f, the x axis is the number of silicon atoms.
Figure 2 summarizes the trends in the binding energies, detachment energies, and HOMO−LUMO gaps of the CrSin, n = 6−16. The ΔSi binding energies shown in Figure 2a show that CrSi12 has the second largest binding energy and that CrSi14 has the largest. The progression in ΔSi is consistent with stability, as observed in experiments. CrSi14 is the other strong magic species but is not observed in the experiment where clusters are grown from silane. ΔCr shows a monotonic increase with CrSi14 having a larger than trend embedding energy. Figure 2c shows the ADE and VDE, and CrSi12 has the largest ADE and third largest VDE. It is surprising that CrSi12 3493
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nodes of the orbitals, as shown on the left side of Figure 3. This analysis revealed that a simple jellium model is inconsistent with the observed electronic structure. The assigned shell structure is |1S2| 1P4|1P2 1D8| 1F8 1D2 2S2|1F4 2P6 2D12 1G4∥ 1D2 |, with the | indicating distinct sets of orbitals with similar energies and the ∥ indicating the line between filled and unfilled orbitals. The 2D12 occupation occurs because of covalent bonding between the silicon cage and the Cr atom, demonstrating that a simple split jellium model with charge transfer is unable to explain the electronic structure of the cluster. We now analyze the nature of one-electron orbitals in CrSi12 to determine if the 18-electron rule applies. The LUMO is the 3dz2 orbital of Cr, and an analysis of the filled orbitals reveals that the 3dz2 orbital is unoccupied. If the 18 electron rule applied to CrSi12, then all 5 3d orbitals must be occupied. We next used a fragment analysis where the cluster was divided into Cr and Si12 fragments.38,51 This allowed us to identify states that contained appreciable contributions from Cr or Si sites. The Cr atom is found to have an electronic configuration of 4s24p63d8, indicating that the Cr atom has 16 effective valence electrons. To understand why the cluster has an appreciable HOMO−LUMO gap with 16 valence electrons, we look to the geometric structure of the cluster. The hexagonal structure of the CrSi12 is oblate with no silicon atoms along the primary axis of rotation. This causes a crystal field-like splitting52 of the 3d orbitals, with the 3dz2 orbital being pushed up in energy. Much like a square-planar transition metal complex, the cluster becomes electronically stable with 16 effective valence electrons rather than the previously expected 18 effective valence electrons. A similar crystal field-like splitting marks the Cr 4p orbitals, although they are filled. While the oblate D6h structure causes crystal field splitting to give CrSi12 an appreciable HOMO−LUMO gap, the cluster is not characterized by a filled 3d electronic shell. This is the reason, we believe, that CrSi12 does not exhibit all of the electronic markers of a magic species. CrSi14 has the largest HOMO−LUMO gap and ΔSi, making it the most stable cluster, so does the 18 electron rule apply to this magic cluster? Figure 4 shows the electronic orbitals of CrSi14. The electronic structure of CrSi14 is found to be 4s24p63d10 with all five of the 3d orbitals being occupied. There is significant hybridization between the 3dxz and the 4px orbitals, resulting in two mixed orbitals, and the 3dxy and 3dyz orbitals hybridize with the Si14 cage to produce two sets of orbitals each. The spherical shape of the Si14 cage results in the 3d orbitals all being within 0.8 eV of each other and no dramatic crystal field splitting is observed. The LUMO is found to be a mixture of the 3dx2−y2 and 3dz2 orbitals, lying 1.48 eV above the HOMO. CrSi14 is found to have 18 effective valence electrons and to follow the 18-electron rule. The 18-electron rule does not apply to CrSi12, while it does apply to CrSi14. Previous work has assumed that electron precise bonding between the silicon cage and the endohedral Cr atom results in an accurate effective electron count on the Cr atom. This is an important reminder that our intuition involving bonding from traditional chemistry may not always apply to nonelectron precise clusters. These findings also explain why CrSi12 is not seen as a magic species under all experimental conditions. While CrSi12 has relatively large silicon binding energies and appears as a magic species in experiments that use silane as a precursor, it does not possess a closed electronic shell. We suspect that the high abundance of CrSi12 in silane precursor experiments is due to the exohedral
has a very high ADE because magic neutral species are expected to have low ADE. The I.P. shown in Figure 2d also shows CrSi14 to have the highest I.P., and CrSi12 to have the second highest. Figure 2e shows the HOMO−LUMO gaps, which is the strongest signature of a closed electronic shell. CrSi12 has a relatively small HOMO−LUMO gap of 0.97 eV, while CrSi14 has the largest HOMO−LUMO gap of 1.48 eV. The final criterion studied was the H binding energy because some of the experiments used silane, SiH4, as a precursor to generate CrSin clusters. Thus, clusters that bind H strongly are likely to remain hydrogenated, while those with weak H binding energies are likely to be pristine CrSin species. CrSi14 and CrSi15 are found to have quite low H-binding energies, indicating that H2 has the energy to autodissociate. CrSi12 binds hydrogen with 2.35 eV, slightly too strongly to allow autodissociation, although it binds H much more weakly than n = 7−9. The previously described results bring out two stable clusters, namely, CrSi12 and CrSi14. The fact that the binding energies of CrSi12 are relatively large suggests it is thermodynamically stable; however, the electronic criteria of the HOMO−LUMO gap and electron detachment energy suggest that CrSi12 does not possess high electronic stability. CrSi14 appears to possess both electronic and thermodynamic stability. One would expect that a cluster that is stabilized by the 18-electron rule would be electronically stable, even if it did not have a particularly high thermodynamic stability. The valence electrons of the Cr atom are 3d5 4s1 and those of Si are 3s2 3p2. CrSi12 then has 54 valence electrons. CrSi12 is spin singlet, indicating a quenching of the Cr spin moment and leading to 27 filled states with paired electrons, as shown in Figure 3. Figure S6a−c in the Supporting Information shows the wave functions in all of these orbitals to help visualize the nature of electron distributions. We attempted to assign each orbital according to the jellium model50 for a confined nearly free electron gas through the symmetry and by inspecting the
Figure 3. CrSi12 energy levels and selected orbitals. On the left hand, the orbital energy levels are assigned as S, P, D, F, or G delocalized orbitals as per the jellium model. On the right, the orbital energy levels are assigned based on orbital composition as predominantly silicon, shown in gray, or having chromium s, p, or d character. Occupied orbitals are shown as solid lines and unoccupied orbitals are shown with dashed lines. The orbitals pictured are those with high Cr character, and the contributing Cr orbital is noted. All orbitals are shown in Figure S7 in the Supporting Information. 3494
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ACKNOWLEDGMENTS
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REFERENCES
Letter
We gratefully acknowledge support from the U.S. Department of Energy (DOE) through grant DE-SC 0006420 for this work.
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Figure 4. CrSi14 energy levels and selected orbitals. The orbital energy levels of CrSi14 are shown and are assigned based on orbital composition as predominantly silicon, shown in gray, or having chromium s, p, d, or p-d hybrid character, shown in black, blue, red, and purple, respectively. Occupied orbital energy levels are shown with solid lines, and unoccupied orbital energy levels are shown with dashed lines. The orbitals pictured are those with high Cr character, and the contributing Cr orbital is noted.
Cr causing the cleavage of Si−H bond of silane; because CrSi12 is the smallest cluster in which Cr is endohedral, the addition of silane stops once the cluster size reaches CrSi12. It also explains the similar findings with WSi12, which is isoelectronic and isostructural with CrSi12. WSi12 also has an unoccupied 5dz2 orbital and is stabilized through crystal-field splitting. Because the crystal field splitting of 5d orbitals is larger than 3d orbitals, it has a large HOMO−LUMO gap of 1.42 eV, although it is smaller than the 1.80 eV gap of WSi14. The studies also bring out that metal−silicon clusters with filled electronic shells (CrSi14) exhibit the same electronic markers of stability as shown by the metal clusters. We have just become aware of the experimental investigations of the reactivity of WSin clusters with oxygen. The investigations indicate that while WSi12 reacts with oxygen, WSi14 is resilient to reacting with oxygen.53 We have previously shown that the reactivity of clusters with oxygen is governed by the HOMO−LUMO gap.9,54 Because W is a congener element to Cr, these finding are consistent with our theoretical results that indicate that CrSi14 has higher HOMO−LUMO gap than CrSi12. We hope that the present findings would encourage experimental investigations of the reactivity of CrSin clusters with oxygen.
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ASSOCIATED CONTENT
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AUTHOR INFORMATION
S Supporting Information *
Alternate isomers of CrSin, n = 6−16, simulated photoelectron spectra, the geometries of CrSin+, CrSin−, and CrSinH. Cartesian coordinates and frequencies of the clusters are also given. This material is available free of charge via the Internet at http:// pubs.acs.org. Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest. 3495
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