The determination of energy-level shifts which accompany chemisorption

Surface Science 54 (1976) 197-209 0 North-Holland Publishing Company

THE DETERMINATION OF ENERGY-LEVEL SHIFTS WHICH ACCOMPANY CHEMISORPTION Homer D. HAGSTRUM Bell Laboratories, Murray Hi& New Jersey 0 79 74, II. S.A.

Received 21 July 1975; manuscript received in final form 15 October 1975 Considerable confusion exists concerning a reasonable procedure for determining energy shifts of atomic levels on adsorption of a free gas atom to a solid surface and concerning the basic concepts involved. This paper discusses the ionization limit with respect to which energy levels of the adsorbed complex should be referenced, how this limit may be defined and what the best method is for determining its energy level. It is also demonstrated that one cannot sidestep the determination of the ionizatron limit by measuring in the same apparatus the kinetic energies of electrons ejected from the free atom and from the adsorbed atom.

Several forms of electron spectroscopy are now providing the kinetic energy distributions of electrons ejected from the surfaces of solids to which foreign atoms are chemisorbed. These kinetic energy distributions, or functions obtained from them, show peaks which can be associated with the ionization of electrons initially in the orbitals of a surface complex or molecule. The energy levels of these orbitals depend upon the interplay of several factors such as the degree of hybridization of the orbitals of the adsorbate and adsorbent, the nature and degree of bonding, and image or relaxation effects. As has proven to be the case for free molecules [l-3] we expect the energy level changes which occur as a free atom is incorporated into a surface molecular structure to constitute important information that can help us to understand the nature of the chemical bonding within the surface structure. Recognizing this, most electron spectroscopists studying chemisorption have attempted to determine the energylevel shifts which accompany it. It seems to be generally recognized that the energy shift is the difference in ionization energies in the free and adsorbed state but no general agreement has been reached as to how to determine the ionization energy in the adsorbed state. What is more, there exists in the literature and in private communication and discussion considerable confusion as well as error concerning the basic concepts involved. As far as procedure is concerned some Investigators have added the work function, $c, of the clean substrate to the measured binding energy, Et, of the orbital in the adsorption complex [4,5], even though the adsorbate alters the work function by approximately an electron volt. In other papers, the work function with the

198

H.D. HagstrumlEnergy-level

shifts which accompany

chemisorption

adsorbate present has been used but no stipulation is made that this procedure is restricted to any particular coverage [6]. A number of investigators [5, 7-91 have pointed out that determination of an adsorbate ionization energy as the sum, Et t &, of the binding energy relative to the Fermi level and work function of the surface with adsorbate present is not unique and depends on surface coverage, 0. It has been pointed out by many that in a number of adsorption systems Et is the quantity that is essentially independent of 0. This has been shown to hold for core levels [5,7,8] as well as valence levels [IO]. This fact has led Carley, Joyner, and Roberts [7] to conclude that electron binding energies referred to the Fermi level have absolute significance and that the work function is, in fact, irrelevant. Becker and Hagstrum [lo], on the other hand, have taken the position that the value of the work function at saturation coverage, qsat, is for a certain class of simple adsorption systems the macroscopic variable that most closely reflects the variation in potential through the adsorbate complex. @satadded to Et should yield in these cases an energy that approximates the ionization energy, Ef, of the adsorbate complex which is the quantity to be compared with the ionization energy of the free atom orbital. As has been said, this prescription has by no means gained universal acceptance. The purpose of this paper is to present in detail the justification for simple adsorption systems of the prescription:

(1) In so doing it will be necessary to discuss the basic concepts underlying ionization at a surface and in free space. This should help to clarify the differences in point of view which, in my opinion, result from confusion concerning basic concepts and definitions. The paper also includes a discussion of the possibility of determining energy shifts by the measurement in the same apparatus of the kinetic energies of electrons photoejected from surface and free-atom orbitals. It is shown that this cannot be done. There can be little doubt that the energy shift we are seeking is a difference of ionization energies of electrons in the free atom and in the surface molecule. This will be made more evident in the later discussion of the measurement of kinetic energies of electrons ionized from free atoms and surface complexes. The ionization energy of the orbital in the free atom is readily defined, that of the surface orbital is not. In fig. la the potential well of a free atom is indicated with the energy level of the atomic orbital designated EC [ 111. We need consider only one vacuum level, here designated I!&. It is the energy of the ionized electron when it is sufficiently far from the atomic ion that there is no interaction between them. This level is reached at a separation of several hundred A. The vacuum level does not change if this separation is increased indefinitely, provided atom and electron are the only objects inside a sufficiently large field-free space enclosed by a metal of uniform work function. Thus in the gas phase we may write:

H.D. Hagstrum/Energy-level

shifts which accompany

chemisorption

199

Fig. 1. (a) Electron energy diagram of the levels of a free atom in field-free space. EG is the enerthe vacuum level at which electron-ion interaction has re- EG is the ionization energy of the orbital. (b) Schematic diagram of a crystal face iFr of fig. 2) with a single adsorbate forming a single surface complex or molecule. ‘Ihe face Fr is divided into equivalent sites. (c) Energy level diagram showing how the motive varies along the central line of the adsorption complex for the various situations discussed in the text. P& is the near-surface vacuum level at which electron-surface interaction has reached a negligrble value and P& is the vacuum level at infinity determined by the electrostatic effects of all the macroscopic faces of the crystal.

Ey =E,-

EG,

= E (ion, electron) - E (atom).

(2) (3)

The second of these equations emphasizes that E’i; is the difference in total energy between the system of relaxed ion and separated electron on the one hand and the

200

H.D. HagstrumlEnergy-level

pS

4’VAC

shifts which accompany

chemisorption

GAC

Fig. 2. Schematic of a crystal indicating Ps, the position at the surface of face F1 and PiK and

PGx where the near-surface vacuum level and the vacuum level at infinity are defined, respectively.

normal neutral atom on the other. In the case of gaseous atoms and small molecules it is evident that the vacuum level E,, in eq. (2) is entirely equivalent in concept to the ionization limit used in atomic and molecular spectroscopy [ 121. The situation is quite different in the case of a single surface molecule formed by the adsorption of a single foreign atom on the otherwise uniform face of a monocrystal (fig. lb). Let us assume a metallic crystal of dimensions of the order of i cm situated in a very large field-free space. In this case there are two vacuum levels which we must consider. As an electron is removed from an atom in a surface complex at position P, on face F, of the metal crystal (fig. 2) it feels a fictitious potential called the motive [13]. The motive is the actual electrostatic potential plus the term e/4x and accounts for the image force on the receding electron. When the electron is several hundred A from the surface the motive will reach a plateau as the electron is then beyond the range of the image interaction. The energy level here is the vacuum level, Ei,, j ust outside crystal face F, . This vacuum level at position PAc defines what Herring and Nichols [ 131 called the “true work function”, which we shall designate as 4’ : (4) We shall term the level E:M at P& the near-surface vacuum level. As the ionized electron is moved farther from the crystal the vacuum level will again change at separations from F, comparable to the crystal dimensions as the electrostatic effects of the other faces of the crystal are felt. This effect will saturate at a position P& which is separated from the crystal by, say, ten to a hundred times the linear dimensions of the crystal. Here the energy of an electron at rest is E& and the difference between E& and EF is the electrochemical potential ~1[ 131. Thus:

(5) E&is effectively the vacuum level at infinity which will be our term for it. Eiu: and E& are clearly separable when the crystal is of finite dimensions. For very small crystals such as those at the apex of a field-emission tip, however, these two vacuum levels cannot be so clearly distinguished and may, in fact, merge into one.

H.D. Hag-strum/Energy-level

shifts which accompany

chemisorption

201

It is readily shown that neither the vacuum level at infinity, Eza, nor the nearsurface vacuum level, E&, is appropriate as an ionization limit of a surface molecule. E:w is inappropriate because it depends on the electrostatic conditions prevailing on all the faces of a macroscopic crystal. Clearly the ionization energy of an orbital in an adsorption complex on one face of a crystal cannot be a function of the work function of another face of the crystal. E& depends on adsorbate coverage, 0, of the face of the crystal where the adsorbate is. This renders it inappropriate as an ionization limit because we know from the invariance of Et, the binding energy of electrons in the surface molecular orbital, that the variation of electrostatic potential through the surface molecule is essentially independent of coverage. In fact, we shall come to understand the significance of the important experimental observation that in many cases Et is independent of 0. And we shall see that only in the limiting case for which the work function & of the adsorbent face is independent of 19will the ionization limit of the surface molecule coincide with the nearsurface vacuum level E&. Thus we must rid ourselves of the notion that either of the definable vacuum levels of a crystal is per se to be identified as the ionization limit of the surface complex. The fact that the vacuum level outside a free atom or small molecule is always its ionization limit sheds no light on the problem of finding the ionization limit of an adsorbed complex. Thus we must face up to the problem of defining with a minimum of conceptual arbitrariness an ionization limit for a surface molecule and of specifying how its energy level can be approximated by the measurement of a macroscopic parameter. We shall do this for a simple adsorption system using the diagrams of figs. 1b and 1c. In fig. lb we show the molecule above a given site with all other sites on the surface, indicated by squares, empty. The variation of the motive along a line perpendicular to the crystal face is shown for various situations in fig. lc. In the absence of the adsorbate at position PA the surface barrier will vary as curve 1, becoming asymptotic to the near-surface vacuum level E,fM (13=0) at the position PvrX. The true work function of the clean surface is G1(f?=O). If the other faces of the macroscopic crystal are assumed to have work functions greater than $’ (0 =O) the motive will rise in the region between P,f,c and P& to the level E& yielding a chemical potential of the crystal p = G2 (0 =O). In this discussion we further assume, for simplicity, that only face F, will be subject to adsorption and that the coverage 0 refers to it only. Adsorption of a single atom or molecule, forming a surface molecule at position PA, produces a patch of different character which we shall call the “adsorption site”. Now consider the variation of the motive along the axis of the surface molecule normal to the surface. For a single adsorption site it will follow a curve such as curve 2 of fig. lc. In the outer portions of the surface molecule the motive will rise above E’vAc due to the short range potential variation of a dipole which will increase G1 of the face Fl . Farther out, the reverse field due to the dipole induced charges in the metal will take effect and the motive will fall to the value EvrK(O =0) at P&, as shown by curve 2 of fig. lc, since one surface molecule changes $1 by an infin-

202

H.D. HogstrumlEnergy-level

shifts which accompany

chemisorption

itesimal amount. As coverage 0 is increased EAc will rise to the saturation value at 0 = 1 where the motive follows curve 3 reaching E& (13= 1) at P&. At P& the variation of 19from 0 to 1 has a considerably smaller effect on E& and $2 since the electrostatic effect of face F, is diluted by averaging with that of all the other faces of the crystal which are assumed to be independent of 8. In order to come to a reasonable definition of the ionization limit of a surface molecule we seek the variation of the motive outside the surface molecule from which has been subtracted the effects of the reverse field produced by the surrounding surface. We expect this “component” of the total motive to vary as curve 4 of fig. lc. Its asymptote at large separation we shall define as the ionization limit of the surface molecule. We designate this limit as E& to differentiate it clearly from the near-surface vacuum level, E&,, of the entire face. The ionization energy of electrons in the surface orbital at EA is then

We define AI!, as AV,=E;9,

- EF.

(7)

Another conceptual procedure for determining the ionization limit Ek, suggested to me by C. Herring, is as follows: First determine the motive variation through the surface molecule to the point where the reverse field begins to exert its influence. This point should lie somewhere near the maximum of curve 2 of fig. lc between P, and PJK At this point we will have in all probability passed through essentially all of the short range potential changes produced by the surface molecule but will not have accounted for the entire image interaction with the solid. The ionization limit E& should lie above the motive at this point by the amount of image interaction there. This correction for the image interaction is thus the distance curve 2 at its maximum lies below the level Ek in fig. lc. In all of the above discussion it might have been more appropriate to talk about the average of the motive over the cross-section of the parallelepiped erected on the adsorption site (fg. lb) rather than the point value along the axis of the parallelepiped. It is crucial that we understand the concept of the ionization limit of the surface molecule and how it differs from the near-surface vacuum level E$m of the whole crystal face containing the surface molecule. The energy level of the ionization limit, Eh, relative to the electronic structure of the solid as specified by the Fermi level, E,, for example, is determined by the nature of the surface molecule formed and the bonding conditions which prevail within it. For low coverages we expect Et and AV, to be independent of 0, and at any coverage we expect AV, to deviate from its value at small 0 by virtue of interactions among neighboring surface molecules. The experimental observation for many orbitals in surface molecules that Et, the binding energy relative to the Fermi level, is independent of 0 is now to be taken as evidence that the electronic structure of the surface molecule and, in particular, the position of the ionization limit relative to bulk band structure features such as

H.D. HagstrumlEnergy-level shifts which accompany chemisorption

203

E, is not altered appreciably by neighboring adsorbates. It does not, in my opinion, confer any particular status on E, as a reference level for the comparison of ionization energies [7]. E, is a level in the bulk band structure to which the adsorbate

electronic structure is attached. It should not then be surprising that the quantity Et t c$’ should track exactly with I#J’ (6). This is translated into the paradoxical re-

sult that the energy shift tracks 9’ only by virtue of the erroneous assumption that the near-surface vacuum level, E:W, is the ionization limit of the surface molecule and thus Et t $I’ the ionization energy. As we have seen, it is equally erroneous to take the vacuum level at infinity, E,j&, as the ionization limit which makes the ionization energy Et t d2. AK may be looked upon as the “work function” of the single adsorption site. It is the smallness of the area of the adsorption site relative to the distance P&-PS over which the image interaction reduces to zero that makes it impossible for the motive to reach E& for low coverages. The adsorption site, viewed as a distinguishable face of the crystal, is completely swamped by the other sites of face F, . P.f,c for face F, plays a role with respect to the adsorption site much like that of PtX relative to the whole of the face F, . The question now arises as to whether there is any macroscopic parameter which approximates AL’, and thus locates the ionization limit E$_ at least approximately. It is now almost obvious that for uniform coverage (I?= 1) the motive variation of curve 3 should most closely approximate the desired curve 4. For clarity curves 3 and 4 in fig. lc are drawn as separated curves having easily distinguishable asymptotes, E$,(e = 1) and E$, . When every site contains a surface molecule there can be no reverse field between P, and PI due to parts of the face F, of lower work function. Any motive change, E~~--E,,,Yc between the near-surface vacuum level at P& and the vacuum level at infinity P& in no way enters the problem. These statements form the basis for the prescription given in eq. (1) which may be stated as follows: For simple adsorption systems the measurable macroscopic parameter which comes closest to giving the ionization energy of a surface orbital is the binding energy of the orbital with respect to the Fermi level plus the work function of the saturated, uniformly covered surface.

We turn now to illustrate these points with data taken from the work of ref. [lo]. In fig. 3a two kinetic energy distributions are shown for two coverages, 0, of CO on Ni(100). Curve 1 is for 8 = 8, at which $I= #,t near the knee of the Cpcurve of fig. 4. Curve 2 is for 0 R (l/3)8,. In fig. 3a the curves are plotted with a common fo;.Ey see that E,--EC0 is independent of 0 as is also seen in fig. 4. Three positions vAcand for EO, the low energy cutoff of the distributions, are shown. a and b correspond to curves 1 and 2, respectively and c is for the clean surface whose kinetic energy distribution is not shown. The ionization limit of the adsorbed CO corn lex is shown at Ek obtained by setting AI!, = $,t = Cp(0 =e,). Both Ef and E Bi are referenced to this common ionization limit. Ey is taken as 14.01 eV for the 50 orbital of gaseous CO [lo]. The

b

Fig. 3. (a) Experimental kinetic energy distributions of photoelectrons ejected by light of energy Aw = 21.2 eV from two surfaces of Ni with differing con~n~ations of adsorbed CO as described in the text. Here the curves are plotted on a scale which superposes their maxima at the Fermi level EF. (b) The same data plotted so that their minimum kinetic energies at the vacuum level cutoff coincide. This results in a common near-surface vacuum level, I?&, for all distributions. The curves of this figure are taken from the work of ref. [lo].

orbital at E - EF = -7.9 eV in adsorbed CO, whatever its character, lies 0.3 eV above the 50 orbital of gaseous CO. Had one used Gc = 5.1 eV rather than #sat ~5.9 eV in determining Ek, this shift would have been 1.1 eV. In fig. 3b the same curves are plotted with a common E. or vacuum level cutoff. This yields a common i?& for at1curves. It may be tempting to conclude that such a common vacuum level has universal significance, in particular that it coincides with the ionization limit of the surface molecule. It does not, as has been seen, except for that particular curve for which # = #%t = Av,. Another example of measured kinetic energy distributions is shown in fig. 5 1141. Here the distribution for clean Ni( 100) and Ni(100) with adsorbed Hg are shown. This is a special case in that $I(0 =0) = Cp(6 =B&. Thus A& = 9 for all 0 and one can be reasonably confident that one has determined the ionization limit of the adsorbed mercury atom. Ey is 14.842 and 16.707 eV for the .5d,/2 and Sd,jz Hg orbitals, respectively [IO]. The energy shift of +2 eV for both Hg orbitals is consistent with the image shift of essentially lone-pair orbitals.

H.D. HagstrumlEnergy-level shifts which accompany chemisorption

6.1

205

1 12

5.9

-40 57 ‘5: z 5.5

5.3

I 5.1 0 16

x EXPOSURE (TOrr

sea

Fig. 4. Work function, 0, and energy position of the higher-energy CO orbital, EF -EC-,, plotted as a function of exposure of the NitlOO) surface to CO. The saturation work function, asat, is indicated. These data come from the work of ref. [ 101 although these graphs were not specifically published there.

-2’;

I

-20

-16

-16

-14

-42

-10

-6

-6

Fig. 5. Kinetic energy distributions of photoelectrons ejected by light of energy ziw = 21.2 eV from a clean Ni(100) surface and this surface with a concentration of Hg atoms adsorbed to it. These data are from the work of ref. [ 141.

H.D. Hagstrum/Energy-level

206

shifts which accompany

chemisorption

The question now arises as to the general utility of the prescription of eq. (1). For the simple case of adsorption of a single species into one kind of site on a relatively perfect surface with little adsorbate-adsorbate interaction eq. (1) will produce a reasonable approximation since all elementary cells are essentially identical. The principal source of uncertainty then would appear to be the determination of the condition of saturation. In other words, where on the 4 versus 0 curve of fig. 4 should the &t level be placed? This problem does not arise when @does not vary with 0. If the surface is imperfect, if there are more than one type of adsorption site or more than one species of adsorbate, or if adsorbate-adsorbate interaction is appreciable, it is clear that we have departed from the “simple adsorption system” postulated and that eq. (1) is of lesser or no utility [9]. It is, nevertheless, the only prescription we have in terms of measurable quantities. The ionization limit of a surface molecule, which we can conceptually identify quite generally, can thus be experimentally identified with reasonable certainty only for a limited set of surfaces. Now let us consider the question as to whether one can determine the energy shift by measuring in the same apparatus the kinetic energies of electrons ejected photoelectrically from the orbitals at E, and EA in the free and adsorbed atom, respectively, thereby circumventing the necessity of locating the ionization limit of the adsorbed complex. We shall consider using the simple gridded retarding potential apparatus shown in fig. 6a. Here the gas or solid surface from which electrons are ejected is placed in the field-free space at the center of a spherical grid G, of uniform work function @cr. Grids G2 and G3 are connected together and constitute the retarding electrode. G, is at G, potential and the electrons passing G, are accelerated slightly to the electron collector C. As must be the case, it can be shown that the conclusions we shall draw do not depend on the type of electron energy analyzer employed nor do they depend on the exact nature of the environment chosen for the phase from which the electrons are photoemitted. In fig. 6b is shown the electron energy diagram appropriate to the ejection of electrons fromthe orbital at level EA and the retardation of these electrons to zero energy at the near-surface vacuum level of the retarding grids G2, G3 . This condition prevails when the final state of these electrons E,, = EA + fiio coincides with the near-surface vacuum level outside grids G2, G3. In fig. 6c the situation for gaseous atoms or_molecules analogous to that of fig. 6b is shown. Here the final state EFI --E G t fiiw coincides with the near-surface vacuum level outside the retarding grids G2, G,. The applied retarding voltages V$ and Vy are, respectively, the energy intervals between the Fermi level at G2, G, and the solid emitter in fig. 6b, and the Fermi level at G2, G, and the grid G, surrounding the gas in fig. 6c. We may now write down the following expressions:

I’*r

=ftw-$J

Eft

=fiw-g+E;t,

G2,3

-E* b,

(9)

H.D. H~gstmm/Energy-Ievel shifts which accompanychemisoption

207

Fig. 6. (a) Schematic diagram of a griddod retarding potential analyzer used in the discussion of a combined gas-phase and surface photo~iss~on experiment. (b) EIectron energy diagram for the surface photoemission experiment with the electrons ejected from the surface orbital at EA just retarded at the retarding grids Gz, G3. (c) Electron energy diagram for the gas-phase photoemission experiment in which the electrons photoejected from the atomic orbital at EG are just retarded at the retarding grids Gs , G3 .

From these we obtain the equations:

208

H.D. Hagstrum/Energy-level

shifts which accompany

EE-E$=V$Vt=E;-Ef. Using the relations of ionization

chemisorption

(12) and binding energies:

Ef=E;+Av,,

(13)

Ey =EE +GG,,

(14)

we determine

that the energy level shift on adsorption

Ef-Ey=E;-E;+AV,-&,.

Et

- E(f is expressed as: (15)

Thus the difference in measured electron kinetic energies is not equal to the energy level shift on adsorption, as might have been hoped, but must be corrected by the difference between the work function of the adsorption site AV, and the work function of the entrance aperture of the spectrometer. The binding energies in eq. (12) are not fundamental parameters of either the surface or free molecules. Knowledge of the work function of the electrode surrounding the gas and the position of the ionization limit of the surface molecule relative to the substrate Fermi level thus cannot be circumvented. Questions might be raised as to the appropriateness of the region within G, in which the photoejection from solid or gas atom occurs. In the case of the gas phase the size of the grid G, is immaterial since the gas is always to be found in a fieldfree space. Departure from a uniform inner surface of G, of constant work function to a composite surface of differing work functions complicates the problem but does not alter it in principle. In the solid-surface case one can ask whether the problem differs if G, is small enough to include P&but not P& on the one hand or is large enough to include P,/!? on the other hand. Incorporation within G, of the fields which exist between P& and P:, is the equivalent of adding another electrode between the solid T and the grid G,. It can be shown that the electrical effect of such an intermediate electrode will always cancel out provided its potential is such that it does not retard out the electrons ejected from the level at E,. Similarly, an acceleration or deceleration between T and G, accomplished by a battery VTGl inserted between them does not change things in principle. Eq. (8) remains unchanged provided V$ is measured between the Fermi levels of T and G,,LJ. In eqs. (9),(10),and(lS),‘J?i isreplacedbyE$t VTGl. One might also do the gas and surface experiments with the sample T present in both cases at the center of G, . Such comparative measurement of electrons ejected from adsorbed molecules and from gas-phase molecules present outside the influence of the adsorbent surface would only complicate matters without relieving one of the necessity of knowing AV, and $G1. If the sample T and grid G, had different work functions, for example, the gas-phase molecules would lie in a field gradient which would make a precise determination of even Et impossible. Finally, we address the question as to whether one can even determine by kinetic energy measurements the difference between energy shifts experienced by a given

H.D. Hagstrum/Energy-level shifts which accompany chemisorption

209

adsorbate level on different adsorbents. It is now readily shown that this also is not possible. Letting superscripts A and B differentiate adsorption on the two substrates, the analogue of eq. (12) may be written

Using eq. (13) for both the A and B substrate we find: (17) which from eq. (16) yields

the analogue of eq. (15). Since the difference in energy shifts from the gas phase to adsorption on each of the substrates must involve this difference in surface orbital ionization energies it cannot be determined without knowing the quantity AV, in each case. Assumption that the difference in energy shifts is obtainable as the difference in measured kinetic energies involves the dubious requirement that AVa is invariant from adsorbent to adsorbent. It is hardly likely that the electronic structure of the surface complex will adjust itself on all substrates relative to the band structure of the substrate so that AV, always has the same value. The author wishes to thank C. Herring, P.J. Estrup, J.J. Quinn, J.E. Rowe and G.E. Becker for helpful discussions and critical reading of the manuscript. References

III R.S. Mulliken, J. Cl-tern. Phys. 3 (1935) 564. I21 C.A. Coulson, Valence, 2nd ed. (Oxford, 1961). 131 D.W. Turner, Advan. Phys. Org. Chem. 4 (1966) 31. f41 D.E. Eastman and J.K. Cashion, Phys. Rev. Letters 27 (1971) 1520. ISI J.T. Yates, Jr., T.E. Madey and N.E. Erickson, Surface Sci. 43 (1974) 257,526. WI J.E. Demuth and D.E. Eastman, Phys. Rev. Letters 32 (1974) 1123. !71 A.F. Cariey, R.W. Joyner and M.W. Roberts, Chem. Phys. Letters 27 (1974) 580. PI P.R. Norton, Surface Sci. 47 (1975) 98. I91 D. Menzel, J. Vacuum Sci. Technoi. 12 (1975) 313. IlO1 G.E. Becker and H.D. Hagstrum, J. Vacuum Sci. Technol. 10 (1973) 31. I111 Energy levels and energy quantities are rigorously distinguished in this paper. Energy leveis, with which numbers are generally not associated, designate energy positions in an energy diagram. Symbols for levels have upper case subscripts (,lZF,EvN, etc.). Energy quantities are the differences between energy levels and are given numerical values. Their symbols have lower case subscripts (Ei, #,,Q. In space, one can also differentiate position (PS, P&c), the analogue of energy level, from separation or distance, which is the difference of two positions. 1121G. Herrberg, Molecular Spectra and Molecular Structure. I. Spectra of Diatomic Moiecules (Van Nostrand, 1950). [ 131 C. Herring and M.H. Nichols, Rev. Mod. Phys. 21 (1949) 185. [ 14 f H.D. Hagstrum and G-E. Becker, in: Proc. Battelle Colfoquium on The Physical Basis for Heterogeneous Catalysis, Gstaad, Switzerland, September 1974 (to be published).