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AB Initio CI Investigation of Hydrogen Atom Adsorption on Li Clusters: Embedded Cluster Model.
Journal of Electron Spectroscopy and Related Phenomena, 29 (1983) 77-81 Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands
77
AB INITIO CI INVESTIGATION OF HYDROGEN ATOM ADSORPTION ON LI CLUSTERS: EMBEDDED CLUSTER MODEL. H.O. Beckmann Department of Chemistry State University of New York at Stony Brook, Stony Brook, New York 11794 Abstract The chemisorption of H on clusters representing the (100) surface of Li bee lattice has been studied with ab initio SCF and CI methods and an embedding theory based on orbital localization (Whitten and Pakkanen, Phys. Rev. B2l (1980) 4357). The results suggest that a convergence of the properties for adsorption on cluster models is almost reached when all metal atoms involved in the adsorption are surrounded by their neighbors.
Model calculations using a limited number of atoms to study the properties of a metal surface have been performed at various
levels
of approximations.
The
simplest and one of the most intensely studied systems is the interaction of a hydrogen atom with lithium clusters (1).
In this work we made the attempt to
compare these studies with results of embedded cluster calculations at the ab initio SCF and CI level.
Experimental data for this system is not available yet, but
experiments are planned (2). The theory for embedded cluster calculations using correlated configuration interaction (cO wave functions is described in detail in ref 3. brief description is given here. Li 24 and Li
25
Therefore. only a
A Li 4 cluster and a Li 5 cluster are embedded in a
cluster. respectively.
The basis set F l for the embedded cluster is
of STO-3G type and corresponds to the basis set F in ref. 1 (compare Table 1 in ref. 1).
For the embedded Li atoms in the cluster,all electrons are considered, while
for
the
boundary atoms only the valence electrons are
calculations. function.
included in the SCF
The basis set for the boundary atoms consists only of the Li2S
The basis set for hydrogen has been taken from ref. 4.
In the first step
of the SCF calculations only the minimal basis set is taken (p-polarization
0368-2048{83{0000-oOOO/$03.00 © 1983 Elsevier Scientific Publishing Company
78 functions are excluded).
A localization transformation based on electron exchange
maximization with the embedded cluster is carried out.
This gives two sets of
localized orbitals describing mainly the embedded cluster and the boundaries, respectively.
In the next step, SCF calculations employing the localized orbitals
and the p polarization functions are carried out followed by a second localization procedure to enhance the convergence of the subsequent configuration interaction (Cr)treatment.
CI calculations are performed by single and double excitations
from occupied localized orbitals to virtual localized orbitals of the embedded clus ter. The most important configurat ions, which contribute to an energy lowering greater than T=O.OOOI hartree with respect to the reference configuration, are retained for the diagonalization of the CI determinant. The following notation for the sections of the (100) plane of the Li bee lattice is used: Lie/Lin (nl' nZ) where e is the number of embedded Li atoms, Lin is the total number of Li atoms in the cluster, and nl and nZ are the total numbers of Li atoms in the first and second layers, respectively. clusters examined. Li
4/Li Z4
Li
5/Li Z5
Fig 1 shows the geometry of the two
The "bridge" absorption position of a H atom is studied on the
(1Z, lZ) cluster and the "on top" and the "open site" positions on the (9,16) and Li
0
V
\1 0
\1
'V 0
0
\1
• •V
0
0
(16,9) cluster, respectively.
\1
'V
0
T+T
0
V
5/Li Z5
0 0
\1
0
'V 0
T
\l
'V
\1
T
\1
'V
\1 0
\1
T
-+-... 0
0
'V
0
V
0 0
V V
Fig. 1. Li (1Z, rz) and Li 5/Li;15 (9,16) clusters modeling sections of the 4/Li Z4 (100) surface of Li-bcc lattice. C'ir c Les (0) represent the surface atoms, triangles the second layer and crosses the hydrogen atom. Filled symbols denote the embedded cluster.
79 The interaction energies of a hydrogen atom with the embedded Li clusters are given in Table 1.
The values for the binding energies have been corrected for the
basis superposition effect, which has been calculated by adding the H basis functions to the basis set in the calculations for the clean clusters.
The hydrogen
distances from the Li surface have not been optimized for the embedded clusters but have been taken from the H-Li 9(5,4), the H-Li and the H-Li cluster 9(4,5) 9(6,2) calculations
from
ref.
for
the
"on
top",
"open" and
"bridge" positions,
respectively. General tendencies for the interaction of a H atom with small Li clusters found in our previous work (1) are: I
It is energetically favorable for the hydrogen atom to have as many Li atoms
as possible as nearest neighbors. II
The interaction energies increase by enlarging the cluster for the "bridge"
absorption site. III
The interaction energies decrease if the Li atom to which the H-atom is
approaching in "on top" position, is surrounded by nearest neighbors. The binding energies decrease by enlarging the cluster to Li 25 for the "on top" adsorption position and increase for the "open site" and "bridge" positions (compare Table 1 and Table 5 in ref. 1).
The interaction energies for the "open
site" and "bridge" positions for the Li 25 and Li 24 clusters, respectively, are almost the same.
For the
L~4/Li24
02,12) cluster, the interact ion energy for the
hydrogen inside the cluster is 14 kcal/mole greater than that for H above the surface, in agreement with previous calculations of H-Li 4 and H-Li S clusters (ref.
1). The
opposing
trends
in H interaction energies
("on
top"
vs. "open" and
"bridge")on enlarging the cluster can be understood by analyzing the charge transfer from the Li to the H atom.
The larger net charges on H occur in the cases of
the "bridge" (-.S) and "open site"(-0.6) absorption top" position the net charge is slightly less (-0.5).
position
where as in the "on
The main difference between
the three adsorption sites, however, is that in the "on top" case the negative charge
3.3 0.5 0.5
"on top" position (9,16) Li
"open" position Li (16.9)
"bridge" position (12,12) Li
86.2
56.6
3.4
minimal basis
SCF
91.0
72.4
21.0
extended basis
SCF
(5.4). the H-Li
9
H-Li
78.9
77.7
27.9
CI
(4,5) and the
(6,2) (first minimum outside the cluster) for the "on top", "open" and "bridge" position, S respectively (compare ref 1 table 4).
bThe hydrogen distance R is not optimized and it was taken from the H-Li
9
4 and the Li 5 clusters are embedded in the Li 24 and Li 25 cluster, respectively.
The geometries are given in Fig. 1.
~e Li
4/Li24
5/Li 25
5/Li 25
(a.;u, )
Cluster
b R
Interaction energy (kcal/mole)
TABLE 1 Interaction energies of a H atom with embedded Li Clusters modelling the \.iuO) surface. a
o
00
81 on H comes mainly from the single Li atom below, creating an image charge of 0.4 electrons.
For the other two cases, the positive charge is spread over the cluster
and is not localized on those Li atoms nearest the H atom.
The greater availability
of electrons through enlarging the cluster seems to be the explanation of the increase in reactivity for the cases when the H atom has more than one nearest neighbor Li atom.
The third tendency, that Li atoms with a larger number of nearest
neighbors in the surface plane weaken bonds with the hydrogen atom,
can be
correlated with the relatively small change in the interaction energy between the RLi 9(5,4) and the H-Li 25(9,16) clusters (8 kcal/mole). This work was supported by the U. S. Department of Energy Contract No. DE-AC0277ER04387.
The author wishes to acknowledge a grant from the Alexander von
Rumbold t-Foundation and is indebted to Prof. J. L. Whitten and Dr. P. V. Madhavan for helpful discussions. REFERENCES 1 2 3 4
H. S. J. J.
O. M. L. L.
Beckmann and J. Koutecky, Surf. Sci. in press and references therein. Gates and R. C. Jornagin, private communication. Whitten and T. A. Pakkanen, Phys. Rev. B21 (1980) 4357. Whitten and M. Hackmeyer, J. Chern. Phys. 51(1969)5584.
77
AB INITIO CI INVESTIGATION OF HYDROGEN ATOM ADSORPTION ON LI CLUSTERS: EMBEDDED CLUSTER MODEL. H.O. Beckmann Department of Chemistry State University of New York at Stony Brook, Stony Brook, New York 11794 Abstract The chemisorption of H on clusters representing the (100) surface of Li bee lattice has been studied with ab initio SCF and CI methods and an embedding theory based on orbital localization (Whitten and Pakkanen, Phys. Rev. B2l (1980) 4357). The results suggest that a convergence of the properties for adsorption on cluster models is almost reached when all metal atoms involved in the adsorption are surrounded by their neighbors.
Model calculations using a limited number of atoms to study the properties of a metal surface have been performed at various
levels
of approximations.
The
simplest and one of the most intensely studied systems is the interaction of a hydrogen atom with lithium clusters (1).
In this work we made the attempt to
compare these studies with results of embedded cluster calculations at the ab initio SCF and CI level.
Experimental data for this system is not available yet, but
experiments are planned (2). The theory for embedded cluster calculations using correlated configuration interaction (cO wave functions is described in detail in ref 3. brief description is given here. Li 24 and Li
25
Therefore. only a
A Li 4 cluster and a Li 5 cluster are embedded in a
cluster. respectively.
The basis set F l for the embedded cluster is
of STO-3G type and corresponds to the basis set F in ref. 1 (compare Table 1 in ref. 1).
For the embedded Li atoms in the cluster,all electrons are considered, while
for
the
boundary atoms only the valence electrons are
calculations. function.
included in the SCF
The basis set for the boundary atoms consists only of the Li2S
The basis set for hydrogen has been taken from ref. 4.
In the first step
of the SCF calculations only the minimal basis set is taken (p-polarization
0368-2048{83{0000-oOOO/$03.00 © 1983 Elsevier Scientific Publishing Company
78 functions are excluded).
A localization transformation based on electron exchange
maximization with the embedded cluster is carried out.
This gives two sets of
localized orbitals describing mainly the embedded cluster and the boundaries, respectively.
In the next step, SCF calculations employing the localized orbitals
and the p polarization functions are carried out followed by a second localization procedure to enhance the convergence of the subsequent configuration interaction (Cr)treatment.
CI calculations are performed by single and double excitations
from occupied localized orbitals to virtual localized orbitals of the embedded clus ter. The most important configurat ions, which contribute to an energy lowering greater than T=O.OOOI hartree with respect to the reference configuration, are retained for the diagonalization of the CI determinant. The following notation for the sections of the (100) plane of the Li bee lattice is used: Lie/Lin (nl' nZ) where e is the number of embedded Li atoms, Lin is the total number of Li atoms in the cluster, and nl and nZ are the total numbers of Li atoms in the first and second layers, respectively. clusters examined. Li
4/Li Z4
Li
5/Li Z5
Fig 1 shows the geometry of the two
The "bridge" absorption position of a H atom is studied on the
(1Z, lZ) cluster and the "on top" and the "open site" positions on the (9,16) and Li
0
V
\1 0
\1
'V 0
0
\1
• •V
0
0
(16,9) cluster, respectively.
\1
'V
0
T+T
0
V
5/Li Z5
0 0
\1
0
'V 0
T
\l
'V
\1
T
\1
'V
\1 0
\1
T
-+-... 0
0
'V
0
V
0 0
V V
Fig. 1. Li (1Z, rz) and Li 5/Li;15 (9,16) clusters modeling sections of the 4/Li Z4 (100) surface of Li-bcc lattice. C'ir c Les (0) represent the surface atoms, triangles the second layer and crosses the hydrogen atom. Filled symbols denote the embedded cluster.
79 The interaction energies of a hydrogen atom with the embedded Li clusters are given in Table 1.
The values for the binding energies have been corrected for the
basis superposition effect, which has been calculated by adding the H basis functions to the basis set in the calculations for the clean clusters.
The hydrogen
distances from the Li surface have not been optimized for the embedded clusters but have been taken from the H-Li 9(5,4), the H-Li and the H-Li cluster 9(4,5) 9(6,2) calculations
from
ref.
for
the
"on
top",
"open" and
"bridge" positions,
respectively. General tendencies for the interaction of a H atom with small Li clusters found in our previous work (1) are: I
It is energetically favorable for the hydrogen atom to have as many Li atoms
as possible as nearest neighbors. II
The interaction energies increase by enlarging the cluster for the "bridge"
absorption site. III
The interaction energies decrease if the Li atom to which the H-atom is
approaching in "on top" position, is surrounded by nearest neighbors. The binding energies decrease by enlarging the cluster to Li 25 for the "on top" adsorption position and increase for the "open site" and "bridge" positions (compare Table 1 and Table 5 in ref. 1).
The interaction energies for the "open
site" and "bridge" positions for the Li 25 and Li 24 clusters, respectively, are almost the same.
For the
L~4/Li24
02,12) cluster, the interact ion energy for the
hydrogen inside the cluster is 14 kcal/mole greater than that for H above the surface, in agreement with previous calculations of H-Li 4 and H-Li S clusters (ref.
1). The
opposing
trends
in H interaction energies
("on
top"
vs. "open" and
"bridge")on enlarging the cluster can be understood by analyzing the charge transfer from the Li to the H atom.
The larger net charges on H occur in the cases of
the "bridge" (-.S) and "open site"(-0.6) absorption top" position the net charge is slightly less (-0.5).
position
where as in the "on
The main difference between
the three adsorption sites, however, is that in the "on top" case the negative charge
3.3 0.5 0.5
"on top" position (9,16) Li
"open" position Li (16.9)
"bridge" position (12,12) Li
86.2
56.6
3.4
minimal basis
SCF
91.0
72.4
21.0
extended basis
SCF
(5.4). the H-Li
9
H-Li
78.9
77.7
27.9
CI
(4,5) and the
(6,2) (first minimum outside the cluster) for the "on top", "open" and "bridge" position, S respectively (compare ref 1 table 4).
bThe hydrogen distance R is not optimized and it was taken from the H-Li
9
4 and the Li 5 clusters are embedded in the Li 24 and Li 25 cluster, respectively.
The geometries are given in Fig. 1.
~e Li
4/Li24
5/Li 25
5/Li 25
(a.;u, )
Cluster
b R
Interaction energy (kcal/mole)
TABLE 1 Interaction energies of a H atom with embedded Li Clusters modelling the \.iuO) surface. a
o
00
81 on H comes mainly from the single Li atom below, creating an image charge of 0.4 electrons.
For the other two cases, the positive charge is spread over the cluster
and is not localized on those Li atoms nearest the H atom.
The greater availability
of electrons through enlarging the cluster seems to be the explanation of the increase in reactivity for the cases when the H atom has more than one nearest neighbor Li atom.
The third tendency, that Li atoms with a larger number of nearest
neighbors in the surface plane weaken bonds with the hydrogen atom,
can be
correlated with the relatively small change in the interaction energy between the RLi 9(5,4) and the H-Li 25(9,16) clusters (8 kcal/mole). This work was supported by the U. S. Department of Energy Contract No. DE-AC0277ER04387.
The author wishes to acknowledge a grant from the Alexander von
Rumbold t-Foundation and is indebted to Prof. J. L. Whitten and Dr. P. V. Madhavan for helpful discussions. REFERENCES 1 2 3 4
H. S. J. J.
O. M. L. L.
Beckmann and J. Koutecky, Surf. Sci. in press and references therein. Gates and R. C. Jornagin, private communication. Whitten and T. A. Pakkanen, Phys. Rev. B21 (1980) 4357. Whitten and M. Hackmeyer, J. Chern. Phys. 51(1969)5584.