Silicon Clusters

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Silicon Clusters with Metal Atom Impurities A
THEORETICAL STUDY
Frank Hagelberg Computational Center for
Molecular Structure and Interactions Jackson
State University
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Silicon Clusters with Metal Atom Impurities.

• Pure silicon clusters.
• II. Experimental evidence for Metal-Silicon
  clusters.
• III. Computational methods.
• Silicon Clusters enclosing metal atom
  impurities.
• Polyhedral Oligomeric Silsesquioxane (POSS)
  clusters
• with endohedral and exohedral impurities.

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I. Rata, A. Shvartsburg, M. Horoi, T. Frauenheim,
K. Michael Siu, K. Jackson, Phys. Rev. Lett. 85,
546 (2000).
From extensive collaborations of theorists and
experimentalists Equilibrium structures of
Silicon cluster (SiN) with N ? 20 for SiN ground
states and low-lying isomers.
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- SiN (N ? 100) geometries differ from those
of bulk fragments.
Si6 bulk fragment (D3d)
Si6 cluster (D4h)

• Reactivities of SiN interacting with O2 display
  oscillatory behavior
• for cluster sizes N ? 40.

From M. Jarrold, U.Ray, K.M. Creegan,
J.Chem.Phys. 93(1), 224 (1990).
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Si and C share the atomic valence electron
configuration (s2 p2) Si prefers sp3 over sp2
bonding formation of compact structures. Excepti
on Si4. No SiN clusters with fullerene
structures detected so far.
Si4 (D2h)
Si10 (C3v)
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Endohedral metallofullerenes Metal impurities
encapsulated in Fullerene cages.
Silicon analogues of endohedral
metallofullerenes? Stabilization of regular SiN
cage structures?
Fullerene-like Si60 structures through
incorporation of quasi-spherical clusters? Q.
Sun, S. Wang, P. Jena, B. K. Rao, Y.
Kawazoe, Phys. Rev. Lett. 90, 133503 (2003).
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Mass-spectrometric Studies of Silicon Clusters
with Metal Atom Impurities.
Observation of mixed metal-silicon clusters
formed by chemical reaction in a supersonic beam
by use of a laser vaporization technique (S. M.
Beck, 1989).
Silicon atom counts of maximally abundant CuSiN
and SiN clusters deviate markedly from each other.
From S. M. Beck, J. Chem. Phys. 90, 6306 (1989)
TMSiN, N 15,16 TM Cr, Mo, W. M. Ohara, K.
Koyasu, A. Nakajima, K. Kaya, Chem. Phys. Lett.
371, 490 (2003)
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Hiura, Miyazaki, Kanayama (2001)Experimental
evidence for silicon clusters encapsulating metal
atoms. Use of ion trap method to study the
gradual emergence of various MSiN (M metal
atom) species.
Example WSi12
Observation of the growth of WSiN (N 1, 2, 3
.) .
At N 12, the growth process terminates 12 Si
atoms surround a W ion.

From H. Hiura, T. Miyazaki and T. Kanayama,
Phys. Rev. Lett. 86, 1733 (2001).
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Geometry Optimization for finite
systems. Minimization of the total cluster
energy in Born - Oppenheimer approximation
ET lt ? H ? gt
Minimum. ? electronic wavefunction of
the cluster. H Hamiltonian of the cluster Te
VeN Vee VNN Te Kinetic Energy of the
electrons, VeN Electron Nuclear
Interaction, Vee Interelectronic
Repulsion, VNN Internuclear
Repulsion. Minimum of ET ET(R1, R2RN)
indicates equilibrium geometry.
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Approximations
Hartree Fock and Density Functional
Theories. Hartree Fock procedure Reduction
of the Many Body Problem to many One Body
problems (mean field approach).
Hi ?igt (Te,i V(ri) ) ?i
gt Ei ?i gt V(ri) Average potential for
electron i. No
inclusion of electron correlation! Density
Functional methods All ground state properties
of a system are expressed in terms of its
electronic density function ?. Energy E?
Energy functional. Electron correlation can
be taken into account through a correlation
functional Ec?. Density Functional Method
used in geometry optimizations B3LYP/6-311G.
Pseudopotential approach Subdivision of the
electronic system into core and valence
electrons.
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Test of Density Functional method by Quantum
Monte Carlo computation. Comparison of results
for CuSi4 from DFT with those from Fixed
Node Diffusion Monte Carlo (FNDMC) computation.
-gt -gt -gt
The order of the stabilities of three CuSi4
isomers as obtained by DFT is confirmed by the
Quantum Monte Carlo approach. From I.
Ovcharenko, W. A. Lester, C. Xiao, F. Hagelberg,
J. Chem. Phys. 114, 9028 (2001).
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Equilibrium geometry of Si6.
Cage like structure for CuSi6.
This geometry corresponds to a saddle point of
the potential energy Surface.
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CuSi6 Stable geometries from energy minimization.
Binding Energy
Adsorption site
2.68 eV
Substitutional site
2.80 eV
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MSi6 isomers analogous to Si7 (M Cu, Na).
Si7
CuSi6
NaSi6
From R.Kishi, A.Nakajima, K.Kaya, J. Chem. Phys.
107, 3056 (1997)
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Highest Occupied Molecular Orbitals of
Si7
CuSi6
NaSi6
in equatorial planes.
Antibonding interaction between Na and Si6 !
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NaSiN
Na acts as an electron donor in NaSiN.
NaSi6 Si6 adopts the equilibrium geometry of
Si6-.
Various isomers of NaSi6
NaSiN Zintl systems.
? unstable!
From R.Kishi, A.Nakajima, K.Kaya, J. Chem. Phys.
107, 3056 (1997)
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CuSi10
Substitutional sites of Cu.
CuSi10
Si11
Adsorption sites of Cu.
Si10
C.Xiao, F.Hagelberg, W.A.Lester, Jr., Phys. Rev.
B 66 75425 (2002).
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Endohedral sites of Cu in CuSi10.
CuSi12 Structure of lowest energy Cu occupies
endohedral site.
(A)
(B)
Structure (A) is by 0.44 eV higher in total
energy than structure (A).
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CuSiN with N ? 10 Cu prefers exohedral
sites. CuSiN with N 12 Cu prefers endohedral
sites. Si Si Bond lengths average in lowest
energy structures of Cu_at_SiN (N 10, 12).
D( Si Si) Å D(Si Si)/D(Si
Si)o 1 N 10 2.47
6.0 N 12 2.40
2.5 D(Si
Si) Si Si bond lengths average D(Si Si)o
Reference value of bond length for a conventional
Si Si single bond.
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Q(Cu) in CuSi12 0.48
CuSi12 CuSi12
Ionization Potentials of SiN and CuSiN.
Size dependence of the adiabatic ionization
potential for the most stable Isomers of SiN and
CuSiN clusters.
SiN and CuSiN (N 8 12) show opposite
tendencies
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W 5D0
WSi3
Binding Charge Energy eV on W
Spin
S 0
- 2.83 - 0.80
? ?
S 1
?
- 2.23
0.03
?
Alternating spin orientations.
? ?
- 1.92 0.26
?
?
S 2
Uniform spin orientations.
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WSi6 is stable in octahedral coordination.
Electronic levels
Molecular
orbital

Energies eV LUMO 1 T1u

-2.47 LUMO T2u

-3.01 HOMO T1u ?? ??
?? -5.66 HOMO
1 Eg ?? ??
-6.75
Shell closing effect
But Vanishing Si
Si interaction!
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Ground state geometry of WSi6 Substitutional
structure. WSi6
Si7 Substitutional
structure of WSi6 by 0.4 eV more stable than
octahedral structure.
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WSi12
CuSi12
Si12 (D6h)
Highest occupied molecular orbital for Si12
(D6h) HOMO Eg ?
? -gt Shell closing
through addition or subtraction of two electrons.
F. Hagelberg, C.Xiao, W.A.Lester, Jr., Phys. Rev.
B 67, 035426 (2003).
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WSi12 Natural Charge Q on W Q -1.74 e
HOMO of Si12
HOMO of WSi12
Strong ionic component in the bonding between the
W impurity and the Si12 cage.
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Energetic properties of MeSi12 (Me Cu, Mo, W)
MeSi12 Symmetry group ?Ee ?EHL
AIP CuSi12 C2h
- 3.84 2.09 6.59 MoSi12
D6h - 7.80 2.19
7.66 WSi12 D6h
- 9.96 2.59 7.79
?Ee Embedding energy
E(MeSi12) E(Me) E(Si12) ?EHL HOMO LUMO
energy difference. AIP Adiabatic Ionization
potential. All values are given in eV. High
values of the embedding energy and the HOMO
LUMO gap for Me Mo, W.
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Me2Si18 (Me Mo, W)
Experimentally detected W2Si18. (H. Hiura, T.
Miyazaki and T. Kanayama, Phys. Rev. Lett. 86,
1733 2001) Periodic change of Si Si bond
lengths in each Si6 layer ? Reduction of D6h to
D3h symmetry.
Charge density distribution of W2Si18
W2 is bonded to the two terminating Si6 layers
but does not interact with the intermediate one.
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Summary. Geometric
features W(Mo) impurities of MeSiN (Me Cu, W,
Mo) tend to stabilize in -
Adsorption - Substitution
- Center (endohedral) sites. At
a critical SiN cluster size (N ? 12) endohedral
sites have maximum stability. The W(Mo)Si12 unit
can be extended to yield W2(Mo2)Si18. Bonding
features Substitution sites Mostly covalent
bonding. Center sites Strong ionic bonding
components. Cluster internal charge transfer In
the ground states of MeSiN (Me W,Mo), W(Mo) act
as electron acceptors, Cu acts as electron
donor. Electron transfer determines the cage
structure of MeSi12 and Me2Si18. Stability. High
values of Binding Entergy, Embedding Energy and
HOMO-LUMO gap are found for MeSi12 (MeW,Mo).
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Polyhedral Oligomeric Silsesquioxane (POSS)
Monomers and analogous systems.
Species of the form (RSiO3/2)N
POSS core molecule Si8O12R8 , R organic group.
Spherosiloxane Si8O12H8

• Interest in POSS units motivated by
• A wide range of applications from polymer
• modifiers to lubricants.
• Addition of POSS compounds results in polymers
• with
• - extended temperature ranges,
• - reduced flammability,
• - lower thermal conductivity
• - lower viscosity.

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Study of geometry, stability and electronic
structure of - POSS monomers with atomic
impurities. - POSS analogous systems (X8O12R8
with X C, Ge)
POSS monomers with endohedral alkali and halogen
impurities. Impurities Li, Na, K, F-,
Cl-. Matrix Spherosiloxane.
Na_at_Si8O12H8
Li_at_Si8O12H8
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Energetic Parameters of A_at_Si8O12H8. Impurity
?E (HOMO LUMO) ?Eea
QAb Li 8.83
- 0.89 0.87 Na
8.73 0.47
0.88 K
8.59 3.14
0.94 F - 9.02
-4.22 - 0.79 Cl -
8.32 0.01
- 0.60 None
8.75 a
Embedding energy ? Ee E(A_at_Si8O12H8) - E(A)
- E(Si8O12H8) . b Natural charge of impurity A.
All energies in eV.
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Experimental data on POSS in combination with
atomic impurities?
Ion mobility measurements on various POSS species
cationized by attachment of Na.1 Use of
ToF
?, ToF Flight time of investigated species in
drift cell, ? scattering cross
section. Geometric information on POSS species
through comparison of measured ? with model
calculations.
1 J.Gidden et al., Int. J. Mass Spec. 222, 63
(2003)
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From ion mobility studies Na adopts an
exohedral position
Comparison between Si8O12H8 with endohedral and
with exohedral alkali impurities.
Example A Li. ? Ee (Li_at_Si8O12H8) - 1.74
eV ? Ee (Li Si8O12H8) 1.57 eV
The exohedral isomer of A X8O12H8 is found more
stable than the endohedral one for A Li, Na,
K, and X C, Si.
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Embedding and adsorption energies for
AX8O12H8 with A Li, Na, K and X C, Si, Ge.
Endohedral structures From X C to X Ge
Increase of stability From A Li to A K
Decrease of stability
At X Ge, A Li crossover between endohedral
and exohedral structures.
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Outlook

• Present projects
• Surface deposition of Silicon clusters.
• Pure SiN, as well as HMSiN and Me_at_SiN
  interacting with Si surfaces.
• Endohedral systems.
• Investigation of metallofullerenes with C68
  cages, also of HeN clusters
• enclosed in C60.

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With thanks to Dr. Chuanyun Xiao
Reginald Quinn Dr. Sung Soo Park
Ashley Abraham
Kendrick Walker
Special thanks to
NSF, NIH, AHPCRC
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