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Oct 8, 2003 - metal encapsulated Si-cage-clusters using ab initio pseudo- potential plane ... man et al.9 proposed using a fullerene type Si24 cluster ini-.

JOURNAL OF CHEMICAL PHYSICS

VOLUME 119, NUMBER 14

8 OCTOBER 2003

Understanding the structure of metal encapsulated Si cages and nanotubes: Role of symmetry and d -band filling Giannis Mpourmpakis and George E. Froudakisa) Department of Chemistry, University of Crete, P.O. Box 1470, Heraklio, Crete, Greece 71409

Antonis N. Andriotisb) Institute of Electronic Structure and Laser, Foundation for Research and Technology—Hellas, P.O. Box 1527, 71110 Heraklio, Crete, Greece

Madhu Menonc) Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky 40506-0055 and Center for Computational Sciences, University of Kentucky, Lexington, Kentucky 40506-0045

共Received 25 April 2003; accepted 17 July 2003兲 Using ab initio calculations we study the stability of Si-based cages and nanotubes stabilized by encapsulated transition metal atoms 共TMAs兲. It is demonstrated that the stabilization of these cages and nanotubes as well as their magnetic properties are strongly guided by a delicate interplay between the attainable symmetry of the system and the d-band filling of the encapsulated TMA. As a result, encapsulated TMAs of the early 3-d series lead to tubular stuctures of C6 symmetry and anti-ferromagnetic alignment between the magnetic moment of the TMA and that of the Si atoms. On the other hand, the encapsulated late 3-d elements lead to tubules of the C5 symmetry and to a ferromagnetic alignment of the metal and Si magnetic moments. Encapsulated Fe atoms 共being near the middle of the 3-d series兲 lead to tubular structures of either C6 or C5 symmetry. © 2003 American Institute of Physics. 关DOI: 10.1063/1.1607309兴

The interaction of transition metal atoms 共TMAs兲 with low-dimensional forms of carbon and silicon systems can lead to the formation of exotic new materials of immense technological interest. In particular, the versatility of these materials makes tailoring of their electronic properties relatively easy and, consequently, could find potential use in technologically important optoelectronic materials. Much research efforts have been devoted to the synthesis of Si-based nanotubes and quantum wires, the latter made of a variety of materials and grown using single wall carbon nanotubes 共SWCN兲 as templates 共either using the external surface of the SWCN or filling in its interior region with metal atoms兲.1–11 Recent experimental and theoretical findings have demonstrated that the encapsulation of TMAs by Si-atoms leads to stable Si-cages, the structure of which depends on many factors.10,11 Kumar and Kawazoe have reported results for metal encapsulated Si-cage-clusters using ab initio pseudopotential plane wave calculations using density functional theory 共DFT兲 in the generalized gradient approximation 共GGA兲 for the exchange-correlation energy.5 Depending upon the size of the metal atom, they find that silicon forms fullerene-like [email protected] , M⫽Hf, Zr, and cubic [email protected] , M ⫽Fe, Ru, Os cage clusters 共CC兲. Additionally, they reported stable clusters of type Sin M (n⫽14– 17, M⫽Cr, Mo, W兲 in the cubic, fullerene-like, decahedral and Frank-Kasperpolyhedron type of geometry.6

On the other hand, Andriotis et al.10,11 have pointed out that the most significant factor which determines the ground state properties of the TMA-encapsulating Si-clusters is the d-band filling factor of the TMA rather than its size when the TMA is taken from the 3-d series. They have also demonstrated that the d-band filling is mainly responsible for the symmetry of the ground state of these clusters. However, a minor contribution to the ground state properties may be attributed, among other factors, to the number of encapsulated TMAs, the number of encapsulating Si atoms and the temperature. Another interesting feature of TMA-encapsulated Siclusters was reported recently by Andriotis et al.10,11 In particular, they showed that Si-based nanotubes can be stabilized by the encapsulation of a linear chain of TMAs. Sibased nanotubes 共NTs兲 have previously been investigated as a possible precursor to Si nanowires. The basic idea is to find a small stable Si-cluster which could be used as a building block in constructing Si nanowires.4,8,9,12 In particular, Landman et al.9 proposed using a fullerene type Si24 cluster 共initially used by Marsen et al.13兲 as the building block. Li et al.,8 on the other hand, recently proposed using the uncapped trigonal Si6 prism and the tricapped Si9 trigonal prism as possible building blocks and showed that the thus built Si-nanowires exhibit energy gaps that get vanishingly small as the length of the wire increases. In order to improve the stability of their proposed Si-nanowire, Landman et al. included a core of Al atoms in the form of a linear chain within the Si24 building block and showed that the conductivity of the Al-encapsulating Si-nanowire depends on the length and the doping. The most interesting feature of the

a兲

Electronic mail: [email protected] Electronic mail: [email protected] c兲 Electronic mail: [email protected] b兲

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J. Chem. Phys., Vol. 119, No. 14, 8 October 2003

results of Andriotis et al. is their finding that the symmetry of the Si-nanotube depends very sensitively on the type of encapsulated TMA. Specifically, it was shown that a chain of Ni-atoms could stabilize a Si-nanotube with C5 v symmetry, while a chain of V-atoms could stabilize a Si-nanotube in the C6 v symmetry. It is worth noting that in both cases the Sinanotubes exhibit small energy gaps at the Fermi energy, E F , which approaches zero as the length of the tube becomes infinite. A detailed analysis of the electron density of states 共DOS兲 of these systems has revealed that the contribution of the d-orbitals to the electron DOS at the Fermi energy, ␳ (E F), is vanishingly small in the case of the encapsulated Ni-chain but is quite pronounced in the case of the V-chain. The contrasting behavior of Ni and V in their interaction with Si was reminiscent of the similar contrasting behavior found in the bonding of Ni and V with carbon surfaces of low dimension.14 –16 In the case of carbon it was found that the TMAs of the early 3d-series act as ␩ 2 or ␩ 3 ligands, while the elements of the late 3d-series act as ␩ 6 ligands. Such behavior was attributed to the filling factor of the 3d-band of each transition metal, the point group symmetry of the bonding site and some other factors of more or less minor importance. In this article, we present a detailed justification for the trends observed in the formation of TMA encapsulated Sicages. We found this to be a necessary next step in our investigations in order to identify the basic physics that elucidates the role of the d-band filling in explaining the differences in the behavior between early-3d and the late-3d elements when encapsulated by Si-based NTs. We, thus, focus on the reasoning why the d-band filling of the TMA plays such a crucial role in the properties of the metal encapsulated Si-based NT to such an extent. For this reason we examine in detail the effect of the d-band filling in the bonding configuration of the TMA-encapsulated Si-cages and investigate its consequences on the obtainable ground state symmetry. Furthermore, in order to provide additional support to our conclusions we include results for Feencapsulating Si–CC in the C5 or C6 symmetry configurations. This is because we expect, according to our previous investigations, a gradual variation of the properties of the TMA-encapsulated Si-CC and Si-based NTs as the encapsulated TMA changes from Ti 共early 3d-series兲 to Ni 共late 3d-series兲. It is, thus, reasonable to expect that TMAs close to the middle of the 3d-series 共like Fe兲, when encapsulated, would exhibit both tendencies, i.e., that of the early 3d-elements 共like the studied case of V11兲 and that of the late 3d-elements 共like the case of Ni studied10兲. Our conclusions are derived from a detailed investigation of the inter-relation between the type of the TMA and the resulting point group symmetry of Si-cages and Si-based nanotubes stabilized by the encapsulation of TMAs. Our study is based on ab initio density functional theory 共DFT兲 calculations at the level of the B3LYP approximation 共Becke’s three parameter method using the Lee, Yang, and Parr functional for the electron correlations兲. The Los Alamos LANL2DZ basis functions together with Effective Core Potential that include relativistic corrections to heavy elements were used and all calculations were performed without

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any symmetry constraint using the GAUSSIAN code.17 It should be noted that for most third row elements the relativistic corrections are relatively more important and basis sets that include relativistic corrections give a more accurate description. Taking into account the fact that Si-based nanotubes can be stabilized either in the C5 or the C6 symmetry, and that the bonding behavior of the 3d-TMAs with Si 共and/or C兲 changes as one moves from the left to the right of the 3d-series in the Periodic Table, we investigated the factors that affect the bonding behavior of Si-nanotubes stabilized by the encapsulation of a chain of either V, Fe, or Ni, either in C5 or the C6 symmetry. These simulations, thus, provide us an opportunity to follow the dependence of TMA’s bonding behavior with Si on the type of the stabilizing TMA and allow a detailed investigation of the effect of the filling factor of the d-band on the stabilization symmetry of the Si-cage or the Si-nanotube. For this purpose, some representative members of the following cluster-classes were investigated: Fen Si5(n⫹1)⫹k , Fen Si6(n⫹1)⫹k , and Vn Si6(n⫹1)⫹k , Nin Si5(n⫹1)⫹k , n⫽1, 2, 3 and k⫽0, 2. The cluster-classes with k⫽0 correspond to Si-nanotubes which are open at both ends while those with k⫽2 correspond to Si-nanotubes capped with Si atoms at both ends. Our results are summarized in Table I and include such cluster features as the spin state, the highest occupied molecular orbital 共HOMO兲-lowest unoccupied molecular orbital 共LUMO兲 gap, the character of the HOMO and LUMO states and the charge state of the metal atoms. We performed a series of total energy calculations of the clusters in different spin states and chose the lowest energy configuration. All calculations were spin-unrestricted calculations, i.e., LSB3LYP calculations. For completeness, results for the infinite Si-based nanotubes are also included.10,11 For the Si10Fe cluster we find a spin multiplicity of 5, the HOMOLUMO gap HLg is more than 1 eV and the BE/atom⫽ ⫺2.82 eV. In a recently reported work, Lu and Nagase18 using the same method and basis set, but with the nonhybrid BLYP functional found this system to have a magnetic moment of 2 ␮ B 共spin multiplicity⫽3), HLg⫽0.25 eV, binding energy with similar values as ours and charge transfer towards the Fe atom of 0.80 兩 e 兩 . The differences in the multiplicity values between our result and those in Ref. 18 may be attributed to the different functional used and the different values of the distances between the Fe atom and the pentagons. It should also be noted that as the number of Si atoms increases, the energy differences between the states of various spin multiplicity decrease. This necessitates a detailed search of the configuration space in order to locate the true ground state of these clusters as was shown in the case of the Si14Fe cluster for which a new ground state energetically more favorable 共by 1.6 eV兲 than previously reported6 was found in the present work. From Table I, we observe the following trends: 共1兲 In almost all systems studied, the ground state appears to be of low spin multiplicity when compared to that of the

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TABLE I. Ab initio results for representative members of the following cluster-classes: Vn Si6(n⫹1)⫹k , Fen Si5(n⫹1)⫹k , Fen Si6(n⫹1)⫹k , and Nin Si5(n⫹1)⫹k , n⫽1, 2, 3 and k⫽0, 2. The results include the spin state, the HOMO–LUMO gap, the character of the HOMO and LUMO states and the charge state of the metal atoms.

2S⫹1

HOMO–LUMO gap 共eV兲

HOMO character

LUMO character

Charge statea for metal ( 兩 e 兩 )

VSi12(C6 ) V2 Si18(C6 ) FeSi10(C5 ) FeSi12(C6 ) Fe2 Si15(C5 ) Fe2 Si18(C6 ) c Fe3 Si20(C5 ) Fe3 Si24(C6 )

2 1 5 3 3 3 NOT 3

1.30 1.50 1.01 1.10 1.25 0.95 STABLE 1.10

V p y – Sisp Vd – (Sisp ) b Sisp Fed – Sisp Sisp (2) Fe(1) d – Fes – Sisp

Vd – Sisp Vd – (Sisp ) Fed – (Sisp ) Fed – Sisp Fep – Sisp Fes – Sisp

⫺2.62 ⫺2.27, ⫺2.27 ⫺3.8 ⫺2.62 ⫺2.95, ⫺2.95 ⫺2.05, ⫺2.05

3共1兲d 1

1.25 1.50 0.00 0.00

(1) Fespd – Fe(2) pd (3) ⫺Fepd – Sisp Sisp Nid – Sisp Vd – Sisp Sisp

⫺2.15, ⫺1.19, ⫺2.02

NiSi10(C5 ) Ni2 Si15(C5 ) e tube- 关 VSi6 兴 x⫽13 inf-tube- 关 NiSi5 兴 x

(2) Fe(1) pd – Fes (3) ⫺Fes – Sisp Sisp Sisp Vd – Sisp Sisp

Cluster 共symmetry兲

⫺3.3 ⫺2.42, ⫺2.42 ⫺0.50 ⫹0.35

a

Negative charge state indicates gain of electrons by metals. Orbitals appeared in parentheses indicate that these orbitals have very little contribution to the character of the indicated level. c Structure slightly distorted. d The energy difference between the singlet and the triplet states is found to be 0.06 eV. e Another geometry of distorted C5 symmetry was found more stable by 0.09 eV than the symmetric state. b

free state of the encapsulated TMAs; it also exhibits quite large HOMO–LUMO gap, an indication of its stability. 共2兲 In all clusters, the TMAs gain a significant number of electrons from the surrounding Si-atoms. This is in contrast to the results we obtained11 for small MSin clusters, n⭐3 and M⫽V, Fe, Ni and indicates strong dependence of the charge transfer on the coordination number of the TMAs. 共3兲 The character of the HOMO and LUMO orbitals depends strongly on the type of the TMA. It is worth noting that in going from left to right of the 3d-series of the transition metals, the character of the HOMO and LUMO orbitals changes from metal-d like to Si-sp like. 共4兲 The systems with n⫽1 and k⫽0 共i.e., those Si-cages which include only one TMA兲 can be used as building blocks for the construction of stable Si-based nanotubes.10,11 These nanotubes become conducting as their length increases. Our findings for the HOMO and LUMO orbital character are in agreement with our previous reports obtained for long Si-tubes stabilized by a chain of V or Ni atoms.10,11 As mentioned earlier, in those cases it was found that ␳ (E F) is dominated by the d-orbitals of V 共in the V-stabilized tube兲, while it is dominated by Si s p-orbitals in the Ni-stabilized tube. Some additional information can be obtained from the electron-DOS for the clusters studied. In particular, we have noted that the contribution of the d-orbitals appears in groups 共bands兲; these bands are found at the edges of the HOMO– LUMO gap in the VSi12 cluster 共see Fig. 1兲. The same grouping appears in the case of the NiSi10 cluster but the d-bands in this case are situated much lower than the HOMO level and much higher than the LUMO levels 共see Fig. 2兲. In the case of FeSi10 we also observe d-band formation significantly below the HOMO level. Quite surprisingly, in the

FeSi12 case the d-orbitals are not found to form well defined d-bands; instead they are spread in a large energy range mostly below the HOMO level, and to a lesser extent, above the LUMO level. As the number of the encapsulated Fe atoms increases, the Fe-contribution to the HOMO and LUMO orbitals becomes more appreciable. One observation of major importance is the existence of a correlation between the symmetry of the system and the appearance of d-character in the HOMO orbitals. In fact, it is observed that the d-character of the HOMO level appears only in the systems of C6 symmetry. In the systems exhibiting the C5 symmetry, the character of the HOMO level is dominated by the ligand 共Si兲 orbitals.

FIG. 1. Electron DOS 共continuous curve兲 and eigenvalues-spectrum 共at the bottom of the figure兲 of the ground state structure of the VSi12 complex in the D6h symmetry as obtained by ab initio calculations. The zero energy corresponds to the midpoint of the HOMO–LUMO gap. In the upper left portion we show the obtained relaxed structure, while in the upper right portion we indicate the character of the HOMO orbital. As shown in Table I, there is no contribution from the d orbitals to the HOMO orbital.

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J. Chem. Phys., Vol. 119, No. 14, 8 October 2003

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TABLE II. Calculated magnetic moments of the encapsulated TMA in representative clusters of Table I. Cluster 共symmetry兲 VSi12(C6 ) FeSi10(C5 ) FeSi12(C6 ) Fe2 Si15(C5 ) Fe2 Si18(C6 ) Fe3 Si24(C6 ) NiSi10(C5 ) tube- 关 VSi6 兴 x⫽13 inf-tube- 关 NiSi5 兴 x a

FIG. 2. As in Fig. 1 for the NiSi10 complex in the D5h symmetry. Again, the HOMO level derives no contribution from the d orbital.

In Table II we give the calculated values of the magnetic moment of the encapsulated TMA in some representative members of the systems described in Table I. Some additional information can be also obtained by examining these values in relation to their corresponding spin-multiplicity. In all systems it was found that the major contribution to the spin multiplicity comes from the TMA while the Si atoms contribute to a lesser extent. However, quite surprisingly, we observed that the Si-contribution is more pronounced in the systems exhibiting the C5 symmetry. In these systems we find a ferromagnetic spin arrangement of the magnetic moments of the Si atoms with respect to that of the TMA. On the other hand, it was found that in systems with the C6 symmetry the magnetic moments of the Si-atoms are arranged anti-ferromagnetically with respect to the magnetic moment of the TMA and the Si-contribution is much smaller as compared to that of the C5 systems. It is worth noting that the values found for the magnetic moments of the encapsulated Ni and V atoms are in very good agreement with the values found 共vanishingly small per Ni atom and 0.65 ␮ B per V atom兲 using our tight-binding molecular-dynamics 共TBMD兲 simulations for Si-based nanotubes stabilized by the encapsulation of a linear chain consisting either of Ni or V.10,11 Furthermore, the present results support our previous findings that the interaction of TMAs with Si leads to a significant reduction of the magnetic moment of the TMA when compared to the magnetic moment of the free TMA. In order to get a better understanding of the contrasting bonding behavior observed in the clusters investigated, one can recall the similarity between the systems studied in the present work and those of the ferrocene (C5 symmetry兲 and the dibenzenechromium (C6 symmetry兲 that have been extensively discussed in the literature.19 It should be noted, however, that the systems included in Table I differ substantially from ferrocene and dibenzenechromium. That is, the systems in Table I exhibit strong Si–Si interactions between Si atoms belonging to different Si-rings. Even then, comparing the two cases, it becomes apparent that the 共re兲hybridized carbon-ring and metal orbitals change their sequence order as

2S⫹1 2 5 3 3 3 3 3

Magnetic moment ( ␮ B ) 0.75 1.87 2.36 1.92, 1.92 2.16, 2.60 2.44, 0.58,a 2.34 0.21 0.65 0.03

This corresponds to the middle Fe-atom.

the symmetry changes.20 Thus, as a result of the symmetry, the HOMO level may exhibit different symmetry while the filling factor of the TMA-d-band will specify the magnetic character and the bonding features between the TMA and the surrounding Si-atoms. These are very well demonstrated in the case of the V-encapsulation where we can see that both symmetries lead to structures with open outer electron shell configuration. However, in the C5 symmetry, the partially occupied MO is the e 2g 共of d xy and d x 2 ⫺y 2 character leading to ␦ bonds兲, while in the C6 symmetry the partially occupied ⬘ 共which has p y character leading to MO appears to be of e 1u ␲ bonds—see Fig. 2兲.21 As a result, the C6 symmetry appears preferable. It is worth noting that in this system, the rehybridization process leads to a partial occupation of the V p-orbitals (sd→p promotion兲. In the absence of strong electron correlations one could use arguments of closed outer electron-shell configurations to justify why Ni shows preference for the C5 symmetry and why Fe-stabilized Si-cages can form structures in both C5 and C6 symmetries. However, in the systems studied it appears that electron correlations play dominant role leading to higher than the singlet spin multiplicities. The symmetry in this case, in addition to specifying the symmetry of the HOMO orbital plays the key role of specifying the energy shift of the spin-up electrons relative to those of spin-down. In Fig. 1, the HOMO level appears to exhibit the e 2u symmetry and does not have any contribution from the Ni atom. In conclusion, we have demonstrated that the symmetry and the magnetic moment of the ground state structure of the Si-based cages and nanotubes encapsulating TMAs depend strongly on the filling factor of the d-band of the TMA. This, in turn, affects the re-hybridization level of the Si and TMA orbitals leading to large charge transfers towards the TMAs. This reorganization has as a result the reduction of the magnetic moment of the TMAs as compared to their free-state value. ACKNOWLEDGMENTS

The present work is supported through grants by the EUGROWTH research project AMMARE 共G5RD-CT-200100478兲, NSF 共NER-0165121, ITR-0221916兲, DOE Grant 共00-63857兲, NASA Grant 共00-463937兲, and the University of Kentucky Center for Computational Sciences.

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B. Marsen and K. Sattler, Phys. Rev. B 60, 11593 共1999兲. A. N. Andriotis, M. Menon, G. E. Froudakis, and J. E. Lowther, Chem. Phys. Lett. 301, 503 共1999兲. 15 A. N. Andriotis and M. Menon, Phys. Rev. B 60, 4521 共1999兲. 16 A. N. Andriotis, M. Menon, and G. E. Froudakis, Phys. Rev. B 62, 9867 共2000兲. 17 M. J. Frisch, G. W. Trucks, H. B. Schlegel et al., GAUSSIAN 98, Revision A.6, Gaussian, Inc., Pittsburgh PA, 1998. 18 J. Lu and S. Nagase, Phys. Rev. Lett. 90, 115506 共2003兲. 19 F. A. Cotton, in Chemical Applications of Group Theory 共Wiley, New York, 1990兲. 20 Provided that the same level of approximation is used in all these calculations; in general, the ordering depends on the approximation employed in each calculation. 21 ⬘ symmetry ␴-type bonds may also occur if the HOMO orbital is of a 1g 共i.e., of s and d z 2 character兲. 共The z-axis has been taken perpendicular to the planes of Si-hexagons or pentagons i.e., along the Si-tube axis.兲

1

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