Chemisorption on a model transition metal : ordered overlayers with C(2 × 2) and (2 × 1) structures

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Chemisorption on a model transition metal : ordered overlayers with C(2 x 2) and (2 x 1) structures

K. Masuda

To cite this version:

K. Masuda. Chemisorption on a model transition metal : ordered overlayers with C(2 x 2) and (2 x 1) structures. Journal de Physique, 1979, 40 (3), pp.299-308. �10.1051/jphys:01979004003029900�.

�jpa-00209109�

299

Chemisorption ^{on a model} transition metal : ordered overlayers

with C(2 ^x 2) ^and (2 1) ^structures

K. Masuda

Department of Materials Science and Engineering, Tokyo Institute of Technology, Ookayama, Meguro, Tokyo 152, Japan (Reçu ^{le 9 octobre} 1978, accepté ^{le 20 novembre} 1978)

Résumé.

On étudie l’effet de la chimisorption de couches atomiques ordonnées, C(2

2) ^et (2 1)

^la

surface (001) de métaux de transition

utilisant le formalisme des fonctions de Green et la technique ^du déphasage.

La structure du substrat métallique ^{est décrite}

combinaison linéaire d’orbitales atomiques (LCAO) ^suivant

la méthode de Allan, Kalkstein et Soven. Les substrats sont soit cubique simple, ^soit cubique à corps centré.

Chaque ^{adatome est} représenté par

seul niveau d’énergie

dégénéré. Les adatomes sont placés

^{la surface,}

à la fois

le site et

centre de la configuration ^à quatre ^{sites. Le} changement de la densité d’états à la chimisorp-

tion est calculé suivant le modèle de Newns-Anderson. On montre que les effets d’ordre à longue distance dans la couche adsorbée, de géométrie d’adsorption ^{et de structure} de bandes du substrat

la structure électronique

des couches ordonnées sont importants. ^{On montre aussi} qu’il y

deux types ^d’états

liants pour les couches ordonnées.

Abstract.

The effect of chemisorption of ordered atomic layers ^with C(2

2) ^and (2 1) structures

the

(001) surface of model transition metals is investigated using the Green’s function formalism and the phase ^shift technique. The electronic structure of the metallic substrate is described by the Linear Combination of Atomic Orbital (LCAO) scheme and is obtained by the method developed by ^{Allan and} Kalkstein and Soven. For compa- rison, ^{both the} simple ^{cubic and} body centred cubic substrate models

used. Each adatom is represented by

a

single non-degenerate energy level. The adatoms

placed

^the surface in both the on-site and centred fourfold- site configurations. ^The change in the electronic density ^{of states} upon chemisorption is calculated within the Newns-Anderson model. It is shown that the effects of the long-range order of the adsorbate layer, adsorption geometries and the band structure of the substrate

of great importance for the electronic structure of the ordered overlayers. ^In addition, it is shown that there

two kinds of non-bonding ^states characteristic of the ordered overlayers.

LE JOURNAL DE

PHYSIQUE

40,

1979,

Classification

Physics ^Abstracts

73.20

1. Introduction.

There has been a great ^{deal of} theoretical and experimental ^work concerning ^the

electronic properties of chemisorbed systems Il, 2]. ^In

order to develop ^a qualitative picture ^{of the} complex chemisorption process, simple model calculations have been _very useful [3]. Using Green’s functions

coupled ^{with the} phase ^shift technique, several authors have investigated ^the electronic structure of chemi-

sorption systems. Allan, using ^this technique, ^has

obtained the binding energy of single transition metal atoms adsorbed on the (001) ^{surface of} tungsten, simulated by ^{a fivefold} degenerate ^s-band simple

cubic (sc) crystal [4]. ^Einstein [5] ^has calculated the

change in the electronic density ^{of states} (DOS) ^due

to single ^atom chemisorption ^{on the} (001) ^{s-band sc} crystal. Furthermore, Ho, Cunningham ^{and Wein-} berg [6] ^{have studied the} chemisorption ^behaviour

on the (001) surface of the s-band body centred cubic

(bcc) crystal.

Other simple ^{methods have} also been used to study

the chemisorption behaviour. Cyrot-Lackmann ^et

al. [7] ^{have used the moment method to calculate the}

local DOS for the adatom on the (001) ^{surface of the sc} crystal ^{in three different} adsorption geometries.

Haydock ^and Kelly [8], using ^{a similar method, have}

studied the adatom DOS for (001) surface of a bcc metal. More recently, Moràn-Lôpez, Kerker and Bennemann [9] ^have calculated the local DOS for the adatom on a disordered alloy surface, using ^the

continued fraction method.

In addition to the studies for the single ^atom adsorption, ^these approaches have further been

applied ^{to the various} chemisorption systems. ^Einstein and Schrieffer [10] ^{and Burke} [11] have studied the pair

interaction energies ^{between the adsorbate atoms. Ho,} Cunningham ^and Weinberg ^have investigated ^the change ^{in the} electronic DOS due to the adsorption ^of

a monolayer ^{of atoms} (0

1) ^{on the} (001) ^surface

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01979004003029900

both of a model bcc metal (one-band) ^{and of a model}

two-band crystal ^{with the CsCI structure} [12, 13].

The present ^author [14] ^{has studied the effect} of having

the monolayer ^{of atoms on the} tight-binding ^metal surface, using ^the two-peaked ^DOS model for the substrate.

So far, however, ^no theoretical calculations have been performed ^{for the} change in the electronic DOS due to the adsorption of ordered atomic layers ^with general coverage 0. Furthermore, in view of the fact that surface superstructures ^{are found in} many

chemisorption systems by ^low energy electron diffrac- tion (LEED) [15], e.g., C(2 ^x 2)-H ^{structure on} W(100) ^and Mo(100), C(2 ^x 2)-0 ^{structure on} Mo(100), (2 ^x 1)-0 ^{structure on} Mo(100), Mo(110)

and W(110) ^and (2 ^x 2)-0 ^and (4 ^x 1 )-0 ^structures

on W(100) ^surface (see also table I), it is desirable to

perform ^the chemisorption calculation for the ordered

overlayers ^with general coverage. It is the purpose of the present paper ^to investigate ^the changes ^{in the}

electronic DOS due to the adsorption ^{of the ordered}

atomic layers ^{with 0}

1/2, i.e., C(2 ^x 2) ^and (2 ^x 1) overlayers. However, the method presented ^{in this}

paper is quite general ^{and the ordered} overlayers

with 0=1/4, (2 ^x 2) ^and (4 x 1) structures, ^are treated in the Appendix.

Table I.

Ordered overlayers ^{with 0}

1 j2 ^and 1/4

on the transition metal surfaces. (From ^Somorjai, ref. [15].)

The present ^{method uses} the LCAO scheme and the tight-binding approximation ^to describe the semi- infinite crystal (1). ^For comparison, ^{both the sc and}

the bcc substrate models are used. Each adatom is

represented by ^a single nondegenerate energy level.

Two binding sites, ^the on-site and the centred fourfold- site, ^are considered. The Green’s function formalism and the phase-shift ^function approach ^{are used to}

calculate the change ^{in the} electronic DOS due to

(1) The d-bands of transition metals

well described by ^the tight-binding ^{model and}

good description ^{of the} properties (such

as

the chemisorption behaviour) of transition metals

be obtained from this model [Friedel ^{J., The} Physics of ^Metals (Cambridge University Press) 1969, p. 340].

chemisorption. ^These particular system ^{and method} have been chosen so that a direct comparison ^can

be made with the results of references [5, 6, 12]

and [14], ^{where the} single ^atom chemisorption ^and

the monolayer chemisorption ^are discussed under

same assumptions. ^{The main} advantage ^{of the} phase-

shift technique ^{is that it} gives directly ^the change ⁱⁿ

the electronic DOS due ^to chemisorption. ^This

information is quite important ^{since it is} directly applicable ^to photoemission. No other method gives

this same information in such a straightforward

manner.

The format of the present paper is as follows : In section 2, ^we present the formulation for obtaining

the phase-shift functions for the ordered overlayers.

It is also shown that the change in the electronic DOS due to chemisorption ^is easily calculated from the

phase-shift function. Results of the numerical calcula- tions and the related discussions are given in section 3.

The final section (section 4) is devoted to conclusions.

The extension of the theory ^{to the} chemisorbed systems ^{with 0}

1/4, (2 ^x 2) ^and (4x1) overlayers,

is given ^{in the} Appendix.

2. Phase-shift functions for the ordered overlayers

with 0

1/2.

^{The most} straightforward ^derivation

of the phase-shift functions for the ordered overlayers

with general coverage is first to obtain the phase-

shift function for a complete (1 x 1) ^{ordered over-} layer (0 = 1) ^{and then to} modify ^it taking ^{account of}

the structure of the ordered overlayers. Therefore, ^we first derive the phase-shift function for the (1 x 1)

ordered overlayer, commensurate monolayer. ^{In the}

case of the monolayer chemisorption, one can use the fact that the whole system has translational symmetry

parallel ^{to the surface.}

In order to derive the phase-shift ^function appro-

priate ^{for the} (1 x 1) ^ordered overlayer, ^{we need to}

know the Green’s functions for both the adatom in its free state and the clean substrate. When the direct interaction between the adatoms can be neglected,

the Green’s function for each adatom is given by

where E is the _energy and Ea is the orbital _energy of the adatom. The Green’s function for the semi-infinite clean substrate crystal ^{can be obtained, in a mixed}

Bloch-Wannier representation, ^{from the} previous

work of Kalkstein and Soven [16]. ^{For the} (001) ^sur-

face of the sc tight-binding ^metal,

where

301

and

Here, t ^{is the transfer} integral between the nearest-

neighbour ^{substrate atoms and} k Il (k,,, ky) ^{is the unitless}

two-dimensional wave vector (a

1 ; a is the lattice constant of the sc crystal) ^{within the} surface Brillouin

zone (SBZ). Furthermore, Eo ^{is the} energy of the middle of the band and the total bandwidth is 12 1 t f.

For the (001) surface of the bcc metal [17]

where

Here, ^T is the transfer integral ^{between the nearest-} neighbour ^substrate (bcc structure) ^{atoms and the}

bandwidth is 16 ! 1 T 1.

Following ^the phase-shift technique [4, 18-20], ^we

define the partial (kil dépendent) phase-shift ^function

for the chemisorption system ^as

where lis the identity matrix, V ^{and G are the} pertur- bation and the unperturbed ^{Green’s function matrices,} respectively, ^and x represents ^the adsorption geo- metry. ^{In the} following, ^{we consider the two} binding sites, ^the on-site and centred fourfold-site configura-

tions. For both binding ^{sites, the} unperturbed ^Green’s

function matrix is diagonal ^{and is} given by

The perturbation ^{matrix V describes the} hopping

interaction between the adatom and the substrate atoms and also describes the shifts of the orbital

energies of both the adsorbate and substrate atoms due to the formation of the chemisorption ^bonds [12, 18].

For the on-site adsorption ^{where the} adatom sits

directly ^over the substrate atom and is bonded only

to it, Vis expressed ^as

where Yt is the on-site binding strength, ^and bEa ^and bEe (2) ^{are the} changes ^{in the orbital} energies ^{of the}

e) Here, it is assumed that the perturbation is localized comple- tely ^{in the} monolayer of adatoms and the surface plane of substrate atoms.

adatom and the substrate atom directly ^{beneath it,} respectively. Both terms, âE. ^and BES, result from the redistribution of electrons _upon chemisorption ^and

their magnitudes ^{can be} determined to satisfy ^the

Friedel sum rule. The corresponding perturbation

matrix for the centred fourfold-site adsorption, ^where

the adatom is situated above the centre of four sub- strate atoms and is bonded to all four of them, ^is given by

where

and bEs ^and ôEf correspond ^to ôE., ^and bEa ^{for the}

on-site adsorption, respectively. Here, V,, ^{is the} binding strength of the adatom in the centred fourfold-site to each of the substrate atoms.

Using eqs. (9), (10), ^and (11), ^we obtain the partial phase-shift ^function per unit cell for the on-site

adsorption

For the centred fourfold-site adsorption, ^{we obtain a}

similar expression

Once the partial phase-shift function is known, ^the change ^{in the} electronic DOS, àp(E), ^{can be} given by [19, 20]

where the total phase-shift ^function 1Jx(E) is defined by

Here, Na ^{is the} number of adatoms and the Heaviside theta function is added so that Ap(E) directly gives ^the

difference in the DOS between the chemisorbed system and the clean substrate. _{In eq.} (16), ^{we find}

the sum rule

since we are adding ^{an electron state to the} system.

In addition, ^{it is} important ^{to realize that} àp(E) ⁱⁿ

eq. (16) ^{is the} quantity ^of experimental ^{interest since} photoemission difference spectra ^{are obtained} by

subtraction of the clean substrate spectrum ^{from the} chemisorbed system spectrum. ^The magnitudes ^{of the} diagonal ^{matrix elements,} bE., ^and bEa (ôEf ^and bE.’), ^{are in} principle ^obtained from the Friedel sum

rule under appropriate assumptions ^{such as}

For the adsorbate atoms with one valency, the Friedel

sum rule is expressed ^{in terms} of the total phase-shift

function as

where Ef ^{is the Fermi} energy of the substrate metal.

We now derive the phase-shift functions for the ordered overlayers ^{with 0}

1/2, C(2 ^x 2) ^and (2 x 1 ) overlayers, starting ^{from the} expressions ^{of the} partial phase-shift ^functions ?1,(k,,, ky ; ^{E) for the}

monolayer chemisorption. ^The modifications ^of eqs. (14), (15) ^and (17) ^are summarized as follows.

(1) ^{For the on-site} adsorption (eq. (14)), ^{the sub-}

strate Green’s function Gs(kl, ; ^{E) is replaced by}

where Kh("# ^(0, 0)) ^{is a} reciprocal lattice ^{vector for the}

ordered adsorbate lattice. This modification results from the physical considerations that an electron in the overlayer orbital ! 0, k Il > ^{can hop into the first} layer orbitals 11, kl, > ^and Il, kll ^{~ +} Kh > by ^the hopping interaction (off-diagonal ^{matrix elements of} P), ^{where 0 and 1} denote the adsorbate layer ^{and the}

first substrate layer, respectively [22, 23].

(2) ^{For the centred} fourfold-site adsorption (eq. ( 15)), a2(k ii ) Gr ,(k E) ^is replaced by

(3) ^The diagonal matrix element bE. ^is expected

to take the different values depending ^on whether the adatom is bonded directly ^to the substrate atom.

Note that in the first substrate layer, ^{there are atoms} directly coupled ^to the adatom and substrate atoms

coupled ^{to a} vacancy (vacant site). Therefore, it is

inadequate ^{to assume the uniform} values for bEs.

Since the rigorous ^{treatment of} ÔE, for the ordered

overlayers ^{with the} general coverage is complicated,

.we perform here the usual chemisorption calculation with the assumption bES

bEa

^0.

(4) ^{The summation over} kx ^and ky (eq. (17)) ^extends

over only ^a reduced SBZ with half the size (hereafter

referred to as the adsorbate Brillouin zone (ABZ)),

since the real _space unit cell area is doubled (see Fig. 1).

By the modifications (1) ’" (4), ^{one can obtain the} partial phase-shift functions for the ordered over-

layers ^{with 0}

1/2. ^{For the} C(2 ^x 2) structure,

Fig. ^1.

Two-dimensional Brillouin

appropriate ^for the

(001) ^surface (SBZ) ^{of the}

and bcc lattice and those for the adsor- bate lattice (ABZ) ^{with 0}

1/2 ; (2

1) ^and C(2

2) overlayers.

The lattice constant (a) ^{is set} equal ^to unity.

and

where t(c) ^{denotes the on-site} (centred fourfold-site) adsorption.

In addition, ^{for the} (2 x 1) type overlayers,

and

303

The method for obtaining ^the change ^{in the} DOS, àp(E), ^{due to} chemisorption ^{is similar to the case of}

the monolayer chemisorption except ^{that the summa-} tion over kll ^{extends over the ABZ} rather than the SBZ.

3. Results and discussi8lr.

In this section, ^we present the numerical results of the change ^{in the}

electronic DOS due to the adsorption of the ordered atomic layers ^with 0=1/2 (C(2

2) and (2 ^x 1) overlayers) ^{on the} (001) ^{surface of the sc and bcc} tight-binding ^metals (s-band approximation ^{for the}

d-band of the transition metals).

3.1 (001) SURFACE OF THE bcc METAL.

The elec- tronic structure of the clean surface of the bcc metal

are now well known [b,12]. ^In figure ^{2a we} present ^the

imaginary parts of the surface Green’s functions

appropriate for the on-site single ^atom adsorption (solid curve) and for the centred fourfold-site adsorp-

tion (dot-dashed) ^{on the} (001) surface of the bcc metal. The latter surface Green’s function is calcu- lated from

where Gs(kx, ky ; ^E) is defined by eq. (5). These Green’s function curves are helpful ^when discussing ^the chemisorption behaviours, Ap(F), ^{for the ordered} overlayers ^with 0=1/2.

Fig. ^2.

Imaginary part ^{of the Green’s} function for the single

atom adsorption

^the (001) surface of the bcc(a) ^{and the} sc(b) lattice ; ^on-site (solid curves) ^{and centred} fourfold-site (dot-dashed) adsorptions. ^The energies

in units of the half-bandwidth of the substrate band.

In figure 3, ^we present ^the changes in the electronic DOS, àp(E), ^{due to the on-site} adsorption ^{of the} C(2 ^x 2) ^and (2 x 1) overlayers ; ^all energies ^are expressed in units of 2 1 Tl. ^The corresponding

results (3) ^{for the centred} fourfold-site adsorption

are shown in figure ^{4. For} comparison, ^{we have also} presented ^the àp(E) ^{curves for the} single ^atom chemisorption ⁱⁿ figure ^{5. To relate our model} (s-band

(3) ^For comparison,

have chosen

Vc

Vt/2 [6, ^{12 and} 13].

Fig. ^3.

^The change in the electronic DOS, àp(E), per adatom for the (2 x 1) ^and C(2

2) overlayers

^the bcc(001) ^surface.

The adatoms (Ea

0.5)

situated in the on-site positions.

V,

^1.0 (dashed curves), ^2.0 (solid) ^{and 3.0} (dot-dashed).

1

Fig. ^4.

^The change in the electronic DOS, Ap(E), per adatom for the (2 x 1) ^and C(2

2) overlayers

^the bcc(001) ^surface.

The adatoms (E.

0.5)

situated in the centred fourfold-site

positions. Vc

^0.5 (dashed curves), ^1.0 (solid), ^{and 1.5} (dot- dashed).

tight-binding ^bcc metal) ^{to actual} crystals, ^{we assume}

2 1 T 1 1.2 eV. This gives ^a substrate bandwidth

of 10 eV, simulating ^the tungsten ^{d-band. We have}

chosen the adatom _energy level Ea ^{to be - 0.5} (in

units of 2 T 1) ^{as shown} by ^{the arrows in the} figures ;

this choice of Ea is useful when comparing ^{our results}

with those of reference [12], where the monolayer chemisorption is discussed using ^{the same substrate}

model.

Fig. ^5.

^The change ^{in the} electronic DOS, Ap(E), ^{due to the} single ^atom (Ea

0.5) adsorption

^the bcc(001) ^{surface :}

On-site and centred fourfold-site adsorptions. V,

1.0, 2.0 and 3.0

and V,,

0.5, 1.0 and 1.5.

The best rough estimate of Ea ^is the average of the ionization (I) ^{and the} affinity (A ) levels, ^which usually

sits around the centre of the d-band rather than near

the bottom (simple gas ^{atoms on} the transition metal

surface). Furthermore, for the on-site adsorption,

electron-hole symmetry gives self-consistency ^condi-

tion automatically ^{for a} half-filled band and Ea

^0.

Therefore, ^the position ^of Ea ^{near the band centre is}

reasonable. The magnitude ^{of the} binding strength

of the adatom Vt ^{is chosen from the} following ^conside-

rations. The value of Vt is often estimated from the

experimental binding energy. However, ^{as the} binding

energy is not a purely electronic property, it is difficult to obtain the magnitude ^{of the} binding strength accurately ^for specific chemisorption systems. ^There- fore, ^{it is desirable to} perform the numerical calcula- tions of àp(E) ^{for a wide} variety ^of Vt. ^{In the} present

investigation V, ^{is taken as} V, = 1 - 3. ^lThis para- meter range of Vt ^{is similar to that used} by ^Einstein

and Schrieffer [10] and Einstein [5] ^{for the sc} crystal.

The results presented ⁱⁿ figures 3-5 have the follow-

ing appealing ^features.

(a) ^{For the} coupling strength Vt

¹ (weak coupl- ing), the on-site Ap(E) ^curves (Fig. 3) ^for C(2 ^x 2) ^and (2 x 1) structures resemble the corresponding Ap(E)

curves for the single ^atom chemisorption (Fig. 5).

This indicates that the indirect interactions between the adatoms are not so important.

(b) However, ^{as the} coupling strength V, ^increases (Vt

^{2 -} 3), the on-site Ap(E) ^{curves for the} C(2 ^x 2)

and (2 x 1) overlayers ^{differ more} significantly ^from

the corresponding ^{curves for the} single ^atom adsorp-

tion : Note that the resonance peaks (both bonding

and anti-bonding) for the ordered overlayers ^are strongly skewed. This results from the fact that the localized electronic states (mentioned below) ^{for the} adsorption of the ordered overlayers ^{are wave vector}

kil dependent. Thus, ^{for the} stronger coupling ^the

indirect interactions between the adatoms become much more important.

(c) ^In contrast to the on-site adsorption, ^{the centred}

fourfold-site Ap(E) ^curves (Fig. 4) ^{for the ordered} overlayers ^differ dramatically ^{from the} corresponding

curves for the single ^atom adsorption ^even in the weak

coupling ^case (Vc

0. 5) . ^In particular, ^{for the} (2 ^x 1) overlayer ^{one can} observe the prominent peak ^at Ea (hereafter ^{referred to as} type ¹ non-bonding peak), irrespective ^{of the} strength ^of Vc. The appearance of this non-bonding peak ^is explained ^{as follows : For}

the (2 x 1) overlayer (centred fourfold-site adsorp- tion), ^the values both of a(k,l) ^and ex(k ~ + Kh) ^vanish

at the zone boundary ^{of the} ABZ, - n/2 kx n/2

and ky

^{± n.} Therefore, ^the electronic state with this

kll(kx’ ky) ^{has no} interaction between the adlayer ^and

the substrate layer ^{and thus has the} degenerate energy E

Ea. ^{From this, we see that the} type ¹ non-bonding

states do not occur for the on-site adsorption.

(d) Furthermore, in the centred fourfold-site ad-

sorption, ^the Ap(E) ^{curves for the} C(2 ^x 2) overlayer

differ greatly from those for the (2 x 1) overlayer.

This indicates that the long range order of the over-

layers strongly affects the electronic structure of the

overlayers. ^{In this} respect, ^{there is the} risk with the usual cluster model of loosing ^{some of the} important

features in the Ap(E) ^curves.

Finally, ^we discuss the behaviours of the localized electronic states for the ordered overlayers. ^{It is}

well known that the adsorption ^{of atoms to a surface}

can introduce electronic states which are localized outside the energy band. The localized ^states exist if there are solutions of the following equation

for values of E which lie outside the _energy bands

when plotted ⁱⁿ k ~ space. Here, ^{it is} important ^to

305

realize that for the ordered overlayers, ^{the indirect}

interaction between the adatoms gives ^{rise to wave}

vector (k,l) ^{dependent localized states which are}

outside the bands when plotted ⁱⁿ kll ^{space, but which}

can overlap the bands in energy. In contrast, ^{in the}

case of the single ^atom adsorption, ^{the localized}

states exist as a delta function outside the extrema of the band, i.e., ^the split-off ^states from the band

edges.

In figure 6, ^{we show the} positions of the localized electronic states with respect ^{to the} energy band along

the particular segments ^{in the} SBZ, ky

^{0, 0.3 n,}

0.5 n, and 0.8 n. The _upper curves, a, b, c, and d,

Fig. ^6.

^The positions of the localized electronic states for the ordered overlayers

^the bcc(001) ^surface along ^the segments;

(a) ^and (e) ky

^{0, (b) and} ( f ) ky

^{0.3 n, (c) and (g)} ky

^{0.5 n,}

and (d) ^and (h) ky

^0.8

^The

^below figures (a, e), (b, f), (c, g) ^and (d, h) indicate the boundary ^{of the ABZ.}

represent the on-site results with Ea

^{0.5 and} V,

^{3.0 and the lower} curves, e, f, g, and h, ^{do the} centred fourfold-site results with Ea

^{0.5 and} V,,

^1.5 (this gives ^{the same total} binding strength

for the two adsorption sites). ^{The solid curves and}

the dashed curves represent the results for the (2 x 1)

and C(2 ^x 2) overlayers, respectively. ^{For both} adsorption sites, the localized states exist both above and below the band. These states are derived from the

anti-bonding split-off-states ^and bonding split-off

states, respectively. ^{One can see that the localized}

states for the (2 x 1) overlayer ^are symmetric ^with

respect ^to kx

n/2 (ABZ boundary). This is in _agree-

ment with the view that the energy band associated with the adsorbate layer ^is periodic ^{in the} kll ^space.

In the segment ^of ky

^{7r/2, the localized states for the}

(2 ^x 1) overlayer ^{and those for the} C(2 ^x 2) overlayer overlap completely since sin (ky/2)

^cos (ky/2) ^for

this ky ^{value. As the total binding strength decreases,}

these localized states come closer to the energy band of the substrate.

3.2 (001) SURFACE OF THE SC LATTICE. - In order to investigate ^the effects of the crystal structure and the band structure on the chemisorption ^behaviour,

we have also performed the numerical calculations of Ap(E) ^{for the} C(2 ^x 2) ^and (2 x 1) overlayers using ^{the sc one-band} tight-binding model for the substrate. In view of the fact that the Green’s function

appropriate for the on-site single ^atom adsorption

on the sc(001) ^substrate quite resembles that for the centred fourfold-site adsorption ^{on the} bcc(OOl)

substrate (see Fig. 2), it is convenient and interesting

to consider the on-site adsorption ^{of the ordered}

atomic layers ^{on the} sc(001 ) ^surface.

In figure 7, ^we present the on-site Ap(E) ^{curves for}

the C(2 ^x 2) ^and (2 x 1) overlayers ^{on the} sc(001)

surface. For comparison, ^{we have also} presented ^the corresponding Ap(E) ^{curves for the} single ^atom adsorption ⁱⁿ figure ^{8. All} energies ^are expressed ⁱⁿ

units of 2 1 t 1. ^We have chosen the adatom _energy E.

to be - 0.375 (- 1/8 in units of the half-bandwidth, Wb/2) ^{and the} binding strength Vt ^{to be} 0.75, 1.5, and 2.25 (1/4,1/2, ^and 3/4 in units of Wb/2) ^{in order to}

facilitate the comparison of the results for the sc(001 )

Fig. ^7.

^The change in the electronic DOS, Ap(E), per adatom for the (2 x 1 ) and C(2

2) overlayers

^the sc(001 ) surface. The adatoms (E.

0.375)

situated in the on-site positions.

Vt

^0.75 (dashed curves), 1.5 (solid) ^{and 2.25} (dot-dashed).

Fig. ^8.

^The change in the electronic DOS, Ap(E) ^{due to the}

site single ^atom (E.

0.375) adsorption

^the sc(OOl) ^surface.

V,

0.75, 1.5 and 2.25.

surface with those for the bcc(001 ) ^{surface. One notices} in figure ^{8 that the on-site} àp(E) ^curves quite ^resemble

the centred fourfold-site Sp(E) ^{curves for the} single

atom adsorption ^{on the} bcc(001) ^surface (Fig. 5).

This is due to the similarity of the Green’s functions for the two adsorption ^sites (Fig. 2). ^{In this} respect, it has been believed that the most important ^{feature in} determining ^the àp(E) ^{is not the} geometrical ^structure

and not the band structure of the substrate but is the DOS of the _group orbital involved in the chemisorp-

tion bond [6]. ^{However, these ideas are} not correct for the ordered overlayers ^as mentioned below.

In the case of the ordered overlayers, ^the geometrical

structure and the substrate band structure are very

important ^{for the} chemisorption behaviour : The

general behaviour of the on-site àp(E) ^{curves in} figure ⁷ (ordered overlayers ^{on the} sc(OOl) surface)

differs almost completely from those of the centred fourfold-site Ap(E) ^{curves in} figure ⁴ (ordered° ^over- layers ^{on the} bcc(001) surface), ⁱⁿ contrast to the case

of the single ^atom chemisorption. ^This indicates that the indirect interactions between the adatoms depends strongly ^{on the} geometrical ^{structure of the} overlayer

and the substrate band structure.

Furthermore, ^{there are other} important features in the àp(E) ^{curves in} figure ^7. (1) ^The shapes ^{of the} bonding ^and anti-bonding resonances are skewed

compared ^{with the} resonances for the single ^atom adsorption (Fig. 8). (2) They depend strongly ^{on the} types ^{of the structure of the} overlayers, i.e., ^the long-range atomic environment of the adatoms.

(3) ^{For the} C(2 ^x 2) overlayer, ^{there is a} non-bonding

resonance peak ^near the adatom _energy level Ea (here-after ^{referred to as the} type ^II non-bonding states), in addition to the bonding ^and anti-bonding

resonance peaks. ^{It is clear that this} non-bonding

state does not belong ^{to the} type ¹ non-bonding ^states

since the adatoms are situated in the on-site positions.

In figure 9, ^{we show the} positions ^{of the localized}

electronic states with respect ^{to the} energy band along

the segments ^{in the} SBZ, ky

^{0, 0.3 x, 0.5 x, and}

0.8 ^x. The solid curves and the dashed curves repre- sent the results for the (2 x 1) ^and C(2 ^x 2) ^over- layers, respectively : Ea

^0.375 and Vt

^2.25.

For both overlayers, ^{there are states} derived from the

anti-bonding (above ^the band) ^{and the} bonding (below ^the band) split-off-states. ^{In addition, there are}

localized electronic states near the adatom _energy level Ea ^{for the} C(2 ^x 2) overlayers. ^{From this, one}

can see that the type ^II non-bonding ^{states are the wave}

vector (k,l) ^{dependent localized states and are not the} degenerate states at E = Ea (type ¹ non-bonding states). Furthermore, ^{if the} energy spectrum (localized

electronic states) ^{is drawn at a} given kll ^{in the ABZ,}

one can see that these localized states exist in a gap

(centred ^{on E}

0) between the two substrate bands for certain _ranges of kil. Therefore, ^the type ^{II non-} bonding (localized) ^states result from the existence of the gap between the ^two substrate bands, i.e., ^from

Fig. ^9.

^The positions of the localized electronic states for the ordered overlayers

^the sc(001) ^surface along ^the segments;

(a) ky ^{= 0, (b)} ky

^{0.3 1t,} (c) ky

^{0.5 1t, and (d )} ky

^0.8

Ea

^0.375 and V,

^{2.25. The}

^below figures (a), (b), (c)

and (d) indicate the boundary ^{of the ABZ.}

the lower translational symmetries of the ordered

overlayers. ^{From the} considerations mentioned above,

these non-bonding ^states (type ^{1 and} type II) ^are essentially different in nature from those for the single

atom chemisorption of references [24-26], ^{where the} non-bonding peak appears due to the minimum in the substrate DOS.

4. Conclusions.

We have obtained the change

in the electronic DOS, àp(E), ^{due to the} adsorption

of the ordered atomic layers ^{with 0}

1/2 ^{on the} (001)

surfaces of the model transition (one-band tight- binding model) metals. The calculations of the Ap(E)

have been performed ^{for the} C(2 ^x 2) ^and (2 x 1) overlayers and both for the sc and bcc substrate models. In addition, ^{the effects of the} adsorption

geometry ^{on the} chemisorption behaviours have been

extensively studied. To our knowledge, this is the first time that the change ^{in the} electronic DOS is calculated for the ordered overlayers ^{with 0 * 1.}

In general, ^{we have} found that the results of the

dp(E) ^{for the} C(2 ^x 2) ^{structure differ} significantly

from those for the (2 x 1) structure. Furthermore,

the àp(E) ^{curves for the ordered} overlayers ^with 6=1/2 ^differ dramatically ^{both from those for the} single ^atom adsorption (8 N 0), ^and from those for the

monolayer chemisorption (0

1), regarding ^the shape (the asymmetry increases with coverage) ^and positions

of the resonance peaks. ^{These features} (change ^{in the}

chemisorption behaviour with coverage) ^{are in fact}

307

seen in the photoemission spectra observed for the system ^{such as} HIW(100) [27].

The present work has also shown that two kinds

(type ^{I and} type II) ^{of the} non-bonding ^{states exist}

for the ordered overlayers ^{with 0}

1/2 : ^The type ¹ non-bonding ^states appear due to the symmetry ^{of the}

adlayer (centred fourfold-site adsorption) ^{while the} type ^II non-bonding ^states appear due to the lower translational symmetries of the ordered overlayers.

Upon comparing figures ^{4 and} 7, ^we have further demonstrated that the band structure of the substrate is _very important ^{for the} chemisorption behaviours of the ordered overlayers. The behaviour of the centred fourfold-site àp(E) ^{curves for the} overlayers ^{on the} bcc(001) surface differs almost completely ^from

that of the on-site Ap(E) ^{curves for the} overlayers ^on the sc(OOl) surface, ⁱⁿ spite ^{of the} similarity ^{of the}

Green’s functions for the single ^atom adsorptions.

This implies ^{that the} indirect interactions between the adatoms play ^the leading role in the chemisorption

of the ordered atomic layers.

Finally, ^{we note that the} present approach ^could

in a straightforward way be used to treat the ordered

overlayers with other adsorbate coverages. In the

Appendix, ^we present ^the formulation for treating

the overlayers ^with 0=1/4, ^i.e. (2 ^x 2) ^and (4 ^x 1) overlayers.

Acknowledgment.

The author is very grateful ^to

the Sakkokai Foundation for financial support.

Appendix.

^{In this} Appendix, ^we derive the partial phase-shift ^functions tl,(k Il ^{; E)} for the ordered over-

layers ^{with 0}

1/4, ^i.e. (2 ^x 2) ^and (4 ^x 1) overlayers (Fig. 10) ^{on the} (001) surface of the sc and bcc metals.

The method for obtaining ^the partial phase-shift functions and the change in the electronic DOS for the over-

layers ^{with 6}

1 /4 is similar to that for the overlayers ^{with 0}

1/2. ^{From the} physical considerations that an

electron in the overlayer orbital 0, kl, ^{E ABZ ) can hop} into the first layer ^substrate orbitals l, kl, > ^and

l 1, k ~ + Khi > (where k E ^{ABZ and} Khi (i

l, 2, ^and 3) denotes the three different reciprocal lattice ^{vectors for}

the overlayer ^{with 0}

1/4), ^{one can} obtain the following expressions ^for 1,(k Il ^{; E).}

Fig. ^{10. - ABZ for the} (2

2) and (4

1) overlayers

^the (001)

surface of the

and the bcc lattice. The lattice constant (a) ^{is set} equal ^to unity.

For the on-site adsorption,

and

In the case of the centred fourfold-site adsorption, ^these partial phase-shift ^{functions are} respectively given

by

and

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