The system considered here is that of a single atom with one energy level chemisorbed on the (001) surface of a model bcc metal. We present the change in the density of electronic states Δn (E) due to chemisorption for two cases: one when the adatom is bound to a single substrate atom in the "on‐site" configuration and the other when it is bound to four substrate atoms in the "centered fourfold site." In principle, this change in the density of states Δn can be related to the results of photoemission measurements

Cunningham, S. L.

Ho, W.

Weinberg, W. H.

English

Caltech Authors - Main

Abstract: Chemisorption on a model bee metal*t 
W. Ho, S. L. Cunninghamt, and W. H. Weinberg 
Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125 
(Received 4 September 1975; in final form 2 October 1975) 
PACS numbers: 82.65.M, 73.20. 
The system considered here is that of a single atom 
with one energy level chemisorbed on the (001) surface 
of a model bee metal. We present the change in the 
density of electronic states D.n (E) due to chemisorp-
tion for two cases: one when the adatom is bound to 
a single substrate atom in the "on-site" configuration 
and the other when it is bound to four substrate atoms 
in the "centered fourfold site." In principle, this change 
in the density of states D.n can be related to the results 
of photoemission measurements. 1 
There are four reasons for this study: (I) By comparing 
with previous results2 of chemisorption on the (001) 
surface of a model simple-cubic metal, we can deter-
mine the sensitivity of D.n (E) to the substrate crystal 
structure. (2) We can investigate the sensitivity of 
D.n (E) to the binding site configuration. (3) The same 
model of the substrate can be easily extended to that 
of a two-band crystal with the CsCl structure. 3 There-
fore the results of this work will serve as a basis for 
comparison with the results of a chemisorption study 
on a model insulator surface.4 (4) Finally, a simple 
modification of the present theory can be used to study 
the adsorption of a monolayer of atoms on the same 
surface.4 A comparison of D.n (E) calculated for a 
single chemisorbed atom with D.n (E) for a monolayer 
will be important for understanding experimental 
photoemission results. 
To model the bee metal substrate, we use the linear 
combination of atomic orbitals (LCAO) method and 
the tight binding approximation (TBA) to generate the 
electronic energy levels and wave functions. Each atom 
is assumed to have one orbital at energy E 1, and only 
nearest-neighbor overlap integrals y are considered. A 
complete description of the Green's functions appropri-
ate for the (001) surface of this model metal has been 
presented elsewhere. 3 For the ada tom, we assume a 
single energy level of E a coupled to the surface with 
an interaction strength CJ'. The Green's function for 
this single level system is well known. 2 
To obtain the change in the electronic density of states 
due to chemisorption, we follow the procedures used 
before2•5 of determining the phase shift due to the 
perturbation potential associated with the formation of 
the chemisorption bond. This phase shift is the negative 
of the argument of the complex determinant of the 
matrix I-VG, where I is the unit matrix, V is the 
perturbation matrix, and G is a matrix containing the 
Green's functions for the adsorbed atom and the clean 
crystal surface. The change in the density of states 
D.n (E) is related simply to the derivative with respect 
to energy of this phase shift. 
1.0 
Ea= -I 
l:>n(E) <r' 1 
Centered 
fourfold-site 
0~8~--~-4~~~~~~4--L-~8 E 
1.0 y 
l:>n(E) On-s1te 
0~~~-=~~~--~--~~ 
-8 -4 4 8 ~ 
y 
-1.0 
FIG. 1. The change in the density of electronic states as a function 
of energy due to the chemisorption of a single atom of energy 
E0 = - 1 on the (001) surface of a model bee metal in two different 
binding sites. All energies are in units of -y, the metal nearest-
neighbor hopping integral. The case shown represents weak binding. 
In Fig. 1 we present a sample of the results. We plot 
the change in the density of states D.n as a function 
of energy E , where all energies are expressed in units 
of y. In these units the band width is 16. We have 
arbitrarily chosen the zero of energy to be at the 
middle of the band. In Fig. 1 we have set the adatom 
energy level E a= -1 as shown by the arrow. The 
binding strength is chosen to be CJ'= 1. (Note that CJ' 
is the overlap integral of the adatom orbital with the 
total surface wave function to which it binds. For 
on-site adsorption, this is the same as the nearest-
neighbor hopping integral, but for the centered four-
fold-site adsorption it is different. See Ref. 5.) 
For the on-site adsorption, D.n shows a bonding and 
antibonding resonance with a depletion of states near 
the middle of the band. This behavior occurs for all 
values of CJ' (even very small) and all values of Ea. 
As CJ' increases, the resonances move apart in energy 
and eventually become splitoff states below and above 
the band. This unexpected behavior for small CJ' is due 
to the fact that the surface Green's function appropri-
ate for on-site adsorption is singular at E =0. (This 
implies that there is a singularity in the density of 
states of the unperturbed surface.) 
For the centered-four-fold adsorption, the behavior is 
very similar to the results presented previously for the 
simple-cubic substrate.2 For small values of CJ' (CJ' < 2), 
the adatom level is a single broadened resonance. For 
stronger binding (CJ' > 2), the peak splits into a bonding 
and antibonding resonance and these move apart in 
349 J. Vac. Sci. Techno!., Vol. 13, No. 1, Jan./Feb. 1976 Copyright © 1976 by the American Vacuum Society 349 
energy as cr increases until one or both of the reso-
nances become splitoff states. The behavior of this 
adsorption site result differs from the on-site results for 
small cr because the Green's function appropriate for 
the four-fold-site adsorption does not contain any sin-
gularities. 
In conclusion, we have found that if the Green's 
function describing the substrate binding site contains 
a singularity, then the change in the density of states 
upon chemisorption shows a depletion of states at the 
energy of that singularity and this is independent of the 
strength of the coupling. For weak-binding chemisorp-
tion, this causes the change in the density of states to 
differ in a qualitative way depending on the substrate 
crystal structure (our on-site results differ from those 
for a simple cubic crystal substrate) or on the binding 
site geometry (our results differ for the two types of 
binding sites). Except for this one characteristic, 
however, the other features of the change in the density 
of states are not sensitive to either the substrate crystal 
structure or the binding site geometry, particularly for 
the case of strong chemisorption ( cr > 5). 
*Complete paper to appear in Surf. Sci. 
tWork supported by NSF Grant GK-43433. 
:j:IBM postdoctoral research fellow. 
1 See, for example, W.F. Egelhoff and D.L. Perry, Phys. Rev. Lett. 
34,93 (1975); D.E. Eastman and M.I. Nathan, Phys. Today 28, 
44 (1975). 
2 T.L. Einstein, Surf. Sci. 45, 713 (1974); J.W. Davenport, T.L. 
Einstein, and J.R. Schrieffer, Jpn. J. Appl. Phys. Suppl. 2, Pt. 2, 
691 (1974). 
3 W. Ho, S.L. Cunningham, W.H. Weinberg, and L. Dobrzynski, 
Phys. Rev. B 12, 3027 (1975). 
4 W. Ho, S.L. Cunningham, and W.H. Weinberg (unpublished). 
5 G. Allan, Ann. Phys. Paris 5, 12 (1970). 
Abstract: Hydrogen and transition metal adatom 
chemisorption on transition metals as a function of d 
bandfilling: Tenfold degenerate Hubbard and Anderson 
models 
Edward Siegel 
24 Fifth Avenue. New York, New York 10011 
(Received 16 September 197 5) 
PACS numbers: 82.65.M, 73.20. 
The Newns theory1 of the chemisorption of both hy-
drogen and transition metal adatoms via the Hubbard 
and Anderson models is reformulated in the true 
d -electron, tenfold spin-orbitally-degenerate Hubbard 
and Anderson models of Siegel and Kemeny. The 
theory is generally valid for chemisorption of hydrogen 
or any transition metal adatom on any transition metal 
surface, but we compare it for the Newns case of 5d 
adatom chemisorption on tungsten. The agreement is 
seen to be better. We also compare this treatment with 
that of chemisorption of Schrieffer and Gomer2 and 
conclude that this non-screened, intra-atomic Hubbard 
or Anderson model treatment is better than their inter-
atomic Hubbard or Anderson model treatment because 
intra-atomic coulomb and exchange interactions should 
dominate even without electron screening to decrease 
any interatomic electron interaction. The explicit inclu-
sion of Hunds rule in the Siegel-Kemeny theory also 
has profound consequences for transition metal sur-
faces. Lastly, the superiority of the perturbation theory 
treatment of the problem over the Hartree-Fock ap-
proximation or vice-versa is explored. It is shown that 
this is so for transition metal adatom chemisorption 
but the reverse is true for hydrogen chemisorption. 
1 D. M. Newns, Phys. Rev. Lett. 25, 22 (1970). 
2 J. R. Schrieffer and R. Gomer, Surf. Sci. 25,315 (1971). 
350 J. Vac. Sci. Technol., Vol. 13, No. 1, Jan./Feb. 1976 Copyright © 1976 by the American Vacuum Society 350 


Chemisorption on a model bcc metal

Abstract: Chemisorption on a model bee metal*t 
W. Ho, S. L. Cunninghamt, and W. H. Weinberg 
Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125 
(Received 4 September 1975; in final form 2 October 1975) 
PACS numbers: 82.65.M, 73.20. 
The system considered here is that of a single atom 
with one energy level chemisorbed on the (001) surface 
of a model bee metal. We present the change in the 
density of electronic states D.n (E) due to chemisorp-
tion for two cases: one when the adatom is bound to 
a single substrate atom in the "on-site" configuration 
and the other when it is bound to four substrate atoms 
in the "centered fourfold site." In principle, this change 
in the density of states D.n can be related to the results 
of photoemission measurements. 1 
There are four reasons for this study: (I) By comparing 
with previous results2 of chemisorption on the (001) 
surface of a model simple-cubic metal, we can deter-
mine the sensitivity of D.n (E) to the substrate crystal 
structure. (2) We can investigate the sensitivity of 
D.n (E) to the binding site configuration. (3) The same 
model of the substrate can be easily extended to that 
of a two-band crystal with the CsCl structure. 3 There-
fore the results of this work will serve as a basis for 
comparison with the results of a chemisorption study 
on a model insulator surface.4 (4) Finally, a simple 
modification of the present theory can be used to study 
the adsorption of a monolayer of atoms on the same 
surface.4 A comparison of D.n (E) calculated for a 
single chemisorbed atom with D.n (E) for a monolayer 
will be important for understanding experimental 
photoemission results. 
To model the bee metal substrate, we use the linear 
combination of atomic orbitals (LCAO) method and 
the tight binding approximation (TBA) to generate the 
electronic energy levels and wave functions. Each atom 
is assumed to have one orbital at energy E 1, and only 
nearest-neighbor overlap integrals y are considered. A 
complete description of the Green's functions appropri-
ate for the (001) surface of this model metal has been 
presented elsewhere. 3 For the ada tom, we assume a 
single energy level of E a coupled to the surface with 
an interaction strength CJ'. The Green's function for 
this single level system is well known. 2 
To obtain the change in the electronic density of states 
due to chemisorption, we follow the procedures used 
before2•5 of determining the phase shift due to the 
perturbation potential associated with the formation of 
the chemisorption bond. This phase shift is the negative 
of the argument of the complex determinant of the 
matrix I-VG, where I is the unit matrix, V is the 
perturbation matrix, and G is a matrix containing the 
Green's functions for the adsorbed atom and the clean 
crystal surface. The change in the density of states 
D.n (E) is related simply to the derivative with respect 
to energy of this phase shift. 
1.0 
Ea= -I 
l:>n(E) <r' 1 
Centered 
fourfold-site 
0~8~--~-4~~~~~~4--L-~8 E 
1.0 y 
l:>n(E) 
On-s1te 
0~~~-=~~~--~--~~ 
-8 -4 4 8 ~ 
y 
-1.0 
FIG. 1. The change in the density of electronic states as a function 
of energy due to the chemisorption of a single atom of energy 
E0 = - 1 on the (001) surface of a model bee metal in two different 
binding sites. All energies are in units of -y, the metal nearest-
neighbor hopping integral. The case shown represents weak binding. 
In Fig. 1 we present a sample of the results. We plot 
the change in the density of states D.n as a function 
of energy E , where all energies are expressed in units 
of y. In these units the band width is 16. We have 
arbitrarily chosen the zero of energy to be at the 
middle of the band. In Fig. 1 we have set the adatom 
energy level E a= -1 as shown by the arrow. The 
binding strength is chosen to be CJ'= 1. (Note that CJ' 
is the overlap integral of the adatom orbital with the 
total surface wave function to which it binds. For 
on-site adsorption, this is the same as the nearest-
neighbor hopping integral, but for the centered four-
fold-site adsorption it is different. See Ref. 5.) 
For the on-site adsorption, D.n shows a bonding and 
antibonding resonance with a depletion of states near 
the middle of the band. This behavior occurs for all 
values of CJ' (even very small) and all values of Ea. 
As CJ' increases, the resonances move apart in energy 
and eventually become splitoff states below and above 
the band. This unexpected behavior for small CJ' is due 
to the fact that the surface Green's function appropri-
ate for on-site adsorption is singular at E =0. (This 
implies that there is a singularity in the density of 
states of the unperturbed surface.) 
For the centered-four-fold adsorption, the behavior is 
very similar to the results presented previously for the 
simple-cubic substrate.2 For small values of CJ' (CJ' < 2), 
the adatom level is a single broadened resonance. For 
stronger binding (CJ' > 2), the peak splits into a bonding 
and antibonding resonance and these move apart in 
349 J. Vac. Sci. Techno!., Vol. 13, No. 1, Jan./Feb. 1976 Copyright © 1976 by the American Vacuum Society 349 
energy as cr increases until one or both of the reso-
nances become splitoff states. The behavior of this 
adsorption site result differs from the on-site results for 
small cr because the Green's function appropriate for 
the four-fold-site adsorption does not contain any sin-
gularities. 
In conclusion, we have found that if the Green's 
function describing the substrate binding site contains 
a singularity, then the change in the density of states 
upon chemisorption shows a depletion of states at the 
energy of that singularity and this is independent of the 
strength of the coupling. For weak-binding chemisorp-
tion, this causes the change in the density of states to 
differ in a qualitative way depending on the substrate 
crystal structure (our on-site results differ from those 
for a simple cubic crystal substrate) or on the binding 
site geometry (our results differ for the two types of 
binding sites). Except for this one characteristic, 
however, the other features of the change in the density 
of states are not sensitive to either the substrate crystal 
structure or the binding site geometry, particularly for 
the case of strong chemisorption ( cr > 5). 
*Complete paper to appear in Surf. Sci. 
tWork supported by NSF Grant GK-43433. 
:j:IBM postdoctoral research fellow. 
1 See, for example, W.F. Egelhoff and D.L. Perry, Phys. Rev. Lett. 
34,93 (1975); D.E. Eastman and M.I. Nathan, Phys. Today 28, 
44 (1975). 
2 T.L. Einstein, Surf. Sci. 45, 713 (1974); J.W. Davenport, T.L. 
Einstein, and J.R. Schrieffer, Jpn. J. Appl. Phys. Suppl. 2, Pt. 2, 
691 (1974). 
3 W. Ho, S.L. Cunningham, W.H. Weinberg, and L. Dobrzynski, 
Phys. Rev. B 12, 3027 (1975). 
4 W. Ho, S.L. Cunningham, and W.H. Weinberg (unpublished). 
5 G. Allan, Ann. Phys. Paris 5, 12 (1970). 
Abstract: Hydrogen and transition metal adatom 
chemisorption on transition metals as a function of d 
bandfilling: Tenfold degenerate Hubbard and Anderson 
models 
Edward Siegel 
24 Fifth Avenue. New York, New York 10011 
(Received 16 September 197 5) 
PACS numbers: 82.65.M, 73.20. 
The Newns theory1 of the chemisorption of both hy-
drogen and transition metal adatoms via the Hubbard 
and Anderson models is reformulated in the true 
d -electron, tenfold spin-orbitally-degenerate Hubbard 
and Anderson models of Siegel and Kemeny. The 
theory is generally valid for chemisorption of hydrogen 
or any transition metal adatom on any transition metal 
surface, but we compare it for the Newns case of 5d 
adatom chemisorption on tungsten. The agreement is 
seen to be better. We also compare this treatment with 
that of chemisorption of Schrieffer and Gomer2 and 
conclude that this non-screened, intra-atomic Hubbard 
or Anderson model treatment is better than their inter-
atomic Hubbard or Anderson model treatment because 
intra-atomic coulomb and exchange interactions should 
dominate even without electron screening to decrease 
any interatomic electron interaction. The explicit inclu-
sion of Hunds rule in the Siegel-Kemeny theory also 
has profound consequences for transition metal sur-
faces. Lastly, the superiority of the perturbation theory 
treatment of the problem over the Hartree-Fock ap-
proximation or vice-versa is explored. It is shown that 
this is so for transition metal adatom chemisorption 
but the reverse is true for hydrogen chemisorption. 
1 D. M. Newns, Phys. Rev. Lett. 25, 22 (1970). 
2 J. R. Schrieffer and R. Gomer, Surf. Sci. 25,315 (1971). 
350 J. Vac. Sci. Technol., Vol. 13, No. 1, Jan./Feb. 1976 Copyright © 1976 by the American Vacuum Society 350 


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Chemisorption on a model bcc metal

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