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On the dipole moments of physisorbed rare gas atoms
CHEMICAL
Volume 61, number Z
PHYSICS
ON THE DlPOLE hlOMENTS OF PHYSISORBED Robert A_ KROMHOUT and Bruno LINDER = Chemical Ph_vsicsProgram. The Florida Stare Unit ersity.
LJZ-ITERS
15 February
1979
RARE GAS ATOMS”
Tallalrassee,
Florida 32306. USA
Received 30 August 1978 Revised manuscript received 3 Noxembcr 1978 Rare 9s ad&tom dipoles are shown to be small and uvxpnble of explaining observed uork function changes Three-body dispersion forces yield v;tlues consistent xrith the reduction in the adatom p.dr potentials; contrtbutions from adatom dipoles are negligible.
It is well known that the presence of a surface modifies the interaction between molecules adsorbed on it. There are two aspects to the problem: (1) a quantum mechanical treatment of the interaction energy between the admolecules and (2) a statistical mechanical treatment connecting the interaction energy to the thermodynamic and experimental results_ Three formulations have been advanced for the long-range forces and one for the short-range interaction between two admolecules. The long-range formulations predict that the perturbation by the solid reduces the interaction of the two molecules_ The short-range treatment [ 1] is based on the Gordon-Rim [2] local density method md is limited only to the region of strong electron overlap. In this note we confine our remarks to the long-range forces. The most frequentiy used form of the intermolecular potential between two adatoms has the form [3] u(r) = 4,s [(u/r)”
- (u/r)6 i- r&~/1-)3] _
(1)
This equation has the appearance of a modified Stockmayer potential in which q is a parameter generally chosen to give a best fit of the second virial coefficient of the two dimensional gas. The three longrange formulations predict potentials of the form (1) although they differ greatly in their derivation and interpretation of v_ Thus, McLachlan’s theory [4] is based on the image method, the MacRury-Linder [5] * Supported in p;ut by NSF _mt NIH grant No. GM-23223.
No. CHE-76-08541
and by
equations on reaction-field techniques, and the Sinanoglu-Pitzer [6] formulation on time-independent perturbation theory_ They all trace the inverse cube term to the three-body dispersion potential which results from the interaction of the two adatoms with the solid- The Sinanoglu-Pitzer theory assumes the existence of a permanent surface electric field which also contnbutes to the inverse cube term, along with the three-body dispersron term. Permanent electric fields also appear in the MacRury-Linder formalism. but only for a specialized model in which the electrons in the solid are free to move throughout the soiid and the nuclei are confined to oscrllatory motion about their lattice sites. The field contrrbution is exceedingly small and vanishes in the continuum model of the solid, which is the model assumed by Sinanoglu and Pitzer. The su=estion that permanent surface fields are present has led to much controversy and debate. Krizan and Crowell [7], and also Wolfe and Sams [S] have vigorously opposed the introduction of such fields in the theory of adsorption_ if such fields existed, they maintained these would be negligibly small. On the other hand, Everett [9] suggested that the contrrbution to the inverse cube term comes mainly from the permanent surface field and not from the three-body dispersion term. The esistence of permanent surface fields has also been inferred from an interpretation of the change of the work function of a met5 on which atoms are adsorbed- The solid distorts the wavefunction of the adsorbed atoms and this effect produces a “permrtnent“ 283
Volume 6 1. number 2
CHEMICAL
induced dipole nxxment in the perturbed atoms and hence a potential jump across the adsorbed layer. These “permznent” induced moments can be thought ofas being produced by “permanent surface fields’ and thus, it has been suggested that the e_xistence of permanent induced moments would be proof that surface fields e_xist_ Recently, Linder and Kromhout [IO] developed a general theory for determking the induced dipole moment which results from the van der Waals interaction of the adsorbed atom and the solid- in this theory no permanent (preesisting) surface fields are invoked- The production of permanent moments by the van der Wads interaction was suggested earlier by CrowelI [ 1 I! and Antoniewin [ I2J_ More recent studies of the moments induced by intermoiecutar forces were carried out by Zaremba [IS J and by Bruch and Ruijgrok [14] _There seems to be no doubt that the van der Nkds interaction gives rise to induced dipoies in the adsorbed atoms. The question is whether these dipoles xre sufficiently Iarge to have significant effects on the forces between adsorbed molecules or on the work functions. Table 1 lists the values for the induced dipole moments-for the noble gas atoms adsorbed on xenon and on pzdladium. The calcAtions are based on the appro_ximate formula: /l
=
- ; [G(O) CrrWJez;]
where %{O)
a/!J(w,
is the polarizability
f b) ,
15 Febroary 1979
PHYSICS LETTERS
(2)
of the adatQm, e is the
eiectronic charge, C a constant which has the value 912 for H, 914 for He and approximately 9125 for the other rare gases. For a crystalline solid made up of kumonic oscillators c = 25fN&O)wz and b2 = a$+ f Q, where NO is the number of oscillators per unit voiume, g(O) is the poIarizability at zero frequency, and ws the natural frequency ofan isolated oscillator_ For a metal, within random-phase approximation, a = b2 = i o$, where op is the plasma frequency. 2, is the perpendicular from the center of the atom to the surface- The parameters used in the calculations are also listed in table l_ The dipole moments were calcuhted for 2, equal to the gas phase collision diameter, It is seen that the dipole moments of the gases on Pd (carbon would be very similar) are considerably larger than on Xe, but in no case does the dipole moment exceed O-0065 D_ In table 2 are listed the dipole-dipole interaction energies, E$, arising from the action of the permanent induced dipoles, and the third order nonadditive dispersion energies, Eg$ arising from the correlations of the electron fluctuations within the solid and the two atoms_ The dipole-dipole interaction energies were calculated by the use of the equation:
(3 where r12 is the distance between the clusters of the two atoms- (it is noted that the dipoles point in the direction perpendicular to the surface.) The dispersion energies were obtained with the aid of
Table I Permanent kduced dipote moments Poluiz&iity~) cr X 10z4 (cm3)
Adsorbed
LF
-----_
-._--_ He
i\;r AI Kr
*xe
--. 0207 0.396 I.644 2.-?86 4.021
ionization potentidb) IW0
Col!ision diimeter d 0 X lO*(cm)
23.5
2.63 2.75 3-41 3.60 4.07
-__ 3153 IS-775 14.00 12.15
Induced moment JKx 102” (esu) on Xe
d)
2.00 093
6.00 957 15.60
Pd e) 8.72 4.02
25.2 39.8 64.2
a) Gkutted from ,gseous molar refraLtionsR, given in ref_ [241. b, Ret [25 I_ c, Ref. I16 j. p- 1: IO_ The Zo-values (i-e_ the drstance from the atom to the solid surface) \%eretaken fo be the same Y the collision dizmetrrs Q of the rare s atolns_ d, The density of Xe taken to be L24X 10z2 ato&cm3_ e, The palladium plasma frequency. fiwp = 25.5 eV. taken from ref. 1261_
284
Volume
61, number 2
CHEMICAL
PHYSICS
LETTERS
15 February 1979
Table 2
Interaction energiesbetueen adsorbedatoms =I_E(3) dis denotes the three-bodydispersioninteraction and dipoIe-dipoIe inreraction --Adsorbed &Is He Ne Ar Kr Xe
On Xe $2 0.14 0.72 2.88 3.88 5.07 _-__--~
E (3)_ denotes the
dlP
static
On Pd
X 1Or6(erg)
(3) Edip
--
X
lOa (erg)
0.22 0.042 0908 1.84 3.60
E$i
X lOI
(erg)
E$
---1.06 2.74 10 6 14.1 18.1
X 10zo
(er-)-_
4.18 0.78 15.9 31.8 61.0
‘) The Zo-vaiues acre taken to be the same as the inert gas s values.
(4)
where f(Q)=(L+3cos~~)sin~~,
and cr.J-ig) is the gas atom polarizability along the imaginary axis and e(-i5;) the dielectric constant of the solid, also along the imaginary axis. The function f(o) is close to one for all relevant values of 0 and, in the present calculations, is set equal to 1_ For a crystalline solid composed of harmonic osctiators of polarizability a,(O), eq. (4) reduces approximately to:
and for a metallic solid, eq. (4) reduces to
(-1 It is seen that, in general, the values of Egi are larger for metallic solids than for crystalline solids. The same holds true of @i_ Although the fractional contribution of Ei$ to the total three-body forces is slightly larger
for the metallic solid than for the crystalline, the contribution in either case is small, less than O-l%. Notice that this ratio would change only as Zc5, so that our conclusions apply for any reasonable choices of Z. _ Thus, the induced permanent moments play only a very minor, if not negligible, role in the long-range interaction between adsorbed molecules. A similar statement can be made regarding the change
in work function of the solid. Thus. the lxgest induced dipole moment calculated in our study is that of Xe at a distance of 2 A (less thari one-half the collision diameter above the surface). The value of this moment is 9.8 X 10-20esu, which is about 10% of the value needed to account for the observed change in the work function_ We emphasize that these results pertain only to the region of no overlap and are based on admittedly very crude calculations. One of the approximations made in the calculatrons of the dipole moments is the use of Slater orbitals in the estimation of C = (Z4> (22)-2. We recalculated the Cvalue for Xe using the tabulated Hartree-Fock-Slater wavefunctions of Herman and Skillman [15] _The C value so calculated is reduced by 43% from the “Slate? value C = 9/35. The fractional dipole-dipole energy is thus reduced by about d third to about 0.03%_ These results are consistent with the fmdings of Krizan and Crcwell [7], who concluded that an electrostatic dipole--dipole force makes negligible contribution to the interaction energy. It has been suggested [7-g]: as mentioned before, that the induced permanent dipole moment arising from van der Waals interaction might play an important role in the reduction of the work function of metals by adsorbed inert gas atoms. To effect the change observed a dipole moment of the order of one debye would be needed for Xe, for example. Antoniewicz [12] estimated a dipole of 0.7 debye for Xe on palladium which is about a factor of two smaller. One reason for the discrepancy is that Antoniewicz based his calculation on a Z, value of 2.09 A, tshich is the radius of the Xe atom, whereas our results are based on the collision diameter, (Y= 285
Volume 6 1, number 2
PHYSICS
CHEMICAL
407 _&_The true ZO-value undoubtedly lies somewhere inbetween, But if we had used ?heZO=2&our~cuhted JI would have been a faction (= +) of the one _&xtonitwicz
obtained,
We can recast our formula (3) in a form similar to
Antoniewicz-s formula (9) [ 121 by using the Kirkwood variational approximation to the polarizability 1161 and an effective number of electrons, treFf [i7] I
IQ where e is the electronic charge and ou the Bohr radius_ This formula when applied to I-I on a perfect metal (w, < 6) yields essentially Antonlewicz’s result _ Applied to Xe (tz&, = S-63) on Pd it gives an answer which is the same as that predicted by eq, (2)_ Antoniewicz’s Larger result comes from applying his hydrogen formula directly to Xe, The observed virial coefficient of the two-dimensional ,“a~ of adsorbed Xe on carbon [7,18] appears to be consistent with our calculations, A &pole of I D \voutd result in a repulsive inverse cube dependence which is perhaps an order of magnitude bigger than the data admitA common explanation of the origin of permanent induced dipoIes is the immersion of the adsorbed atoms in the electron cloud out,side the metal surf&z_ The range of this cloud outside the metal surface is about 1 A fcr metals [L9] _ These distances are considerably smaller than theZu values measured by LEED [Xl] [low energy electron dir’fraction) or estimated from collision data of inert gas atoms, The measured 20 t&es, Izirse compared to the range of the electron cloud, are consistent with the avoidance by the closed sheI atoms of the region of overlap. At these large Oistances the moments induced by this mcchanlsm shouid be neghgible. It has been suggested that “nonbondin$’ charge transfer from xenon to the metal might explain the large (z 1 V) changes in work function (for example, see ref. [Xl)_ A carding to the photoelectric data giLen by Landman and Kteiman 1201rthe ionization potential of xenon adsorbed on tungsten is reduced by 3 3 l __- 0_2v, presumably due to the stabllizatic;n of the ion by its interaction with its image_ (Apropos of the discussion abobe, this image potential corresponds to a Za of 34, ik-1 The pertinent point is that the same value is obtained for the removal of a core (3d) electron as fur an outer shell [Sp) electron, Taking the
286
LElTEIIS
15 February 1979
between the core and outer slreli shifts to be O-3 V (just within experimental error), and the difference between the ionization potenti& of Xei and XeII to be 9.1 V 122 J, it would appear that less than 0.03 electron was transferred from ~enorr to tungsten_ To produce the required one debye imageion dipole moment a transfer of about 0.15 electron is required_ it is difficult to make a good theoretical estimate of this charge transfer, but a very crude upper limit, estimated using the ion stabilization energy as a rough approximation to the matrix eIement, would sugest kss than O-06 electron would be transferred_ Furally it should be pointed out that the interaction between xenon atoms in this model would vary as the inverse j%zsl power at small distances, and would be quite inconsistent with the second virials, Strictly spetiing the oppositely directed induced dipole moments in the metal ought to be inciuded in form& (3); however these values are unknown_ The work function will depend on the vector sum of the adatom and metal dipoles, Kahn and tau 1331 have derived an expression for the long range interaction between the overaU (adatom-metal) moments which is of the same form as our eq_ (3) multiplied by 2. We are grateful to Professor L_W_ Bruch for drawing this point to our attention, although these considerations do not alter our general conchrsions_ In summary, it would appear that the observed change in the work function by adsorbed me gases cannor be explained by the induced dipoIe moments,
kwgest difference
References f 11 DL Z-reeman,J_ Chem_ Phys. 62 (1975) 4300, [2J R-G_Cordon arrd Y .S_ Kim, J, Chem- Phys, 56 (1972) 313’ ___ 131 T. Takaishi, Prosr- Surface Sci- 6 (1975) 43141 A-D- McLachkn, MO;, Phys- 7 (1964) 381, [S 1 T-B- MacRury and EL Lander, J_ Chem_ Phys_ 54 (197 L)
2056; 56 (1972) 4368_ [6l O_SinanoZjluad KS_ Pitzer, J_ Chem. Phys. 32 (1960) 1279_ [?l J-E. Krti ad A-D- CroweH, J_ Chem. Phys, 41 (1964)
1322; J-E_ Krizan, J_ Chem_ Phys. 42 (1965) 2923_ IS] R-Wolfe and J-R_ Sarns, J_ Chem, Phys. 44 (1966) 3,181, [9! D-H_Everett, DiscussionsFaradsy SOL 40 (1965) 177; J-R_ Sams, Pros_ Surface Membrarre Sci_ S (1974) I_
[IO j B_ tinder and R.A. Kromhout, Phys. Rev. B13 (1976) 1532_ [Xl ] A IL Crowell, J- Chem- Phys, 6 1 (1974) 3485,
Volume 61. number 2
CHEhIICAL
[lZ]
PHYSICS
P.R. Antoniewin, Phys. Rev. Letters 32 (1974) 1424_ E. Zaremba. Phys. Letters 57A (1976) 156. [141 L.W_ Bruch and Th.W_ Ruijsok. private communication. [15] F_ Herman and S- Skiian. Atomic structure calculations (Prentice-Hall, Englewood Cliffs, 1963). [IS]
[L6]
J-O_ Hirschfelder,
C-F_ Curtis
and R-B. Bird. XoIecular
theory of gases and Iiquids (Wiley. New York, 1954) p946. [ 171 E_A_ Moelwyn-Hughes, Physical chemistry (Pergamon Press, New York, 1961) p_ 389 and table 7. [IsI J.H. de Boer and S. Kruyer. Trans. Faraday Sot. 54 (1958) 540. 1191 N.H. March. Physics and contemporary needs (Plenum Press. New York. 1977) p_ 53.
LETTERS
15 February
1979
PO1 U- Lmdrnm and G.G. Klciman. Surface Defect Properties Solids 6 (1977) I. [211 B E. Nieuwnhuys, O.G. Aardennc and W.frf H. SachtIer, Chem. Phys. 5 (1974) 418. 1221 C.B. Moore, National Bureau of Standards Circular 447, Atomic Energy Levels, Vol. 3. 123 j W_ I;ohn and K.-H_ Lau. Solid State Commun. 18 (1976) 553. 1241 A.A. hkuyott and F. Buckle>, Natxonal Bureau of Standards Circular 537 (1953)_ [25 J EH. Field and J-L. franklin, Electron impact phenomena (Academic Press, New York, 1957) p_ 108. [26] N. Glickman, Solid State Phys. 26 (1971) 338.
Volume 61, number Z
PHYSICS
ON THE DlPOLE hlOMENTS OF PHYSISORBED Robert A_ KROMHOUT and Bruno LINDER = Chemical Ph_vsicsProgram. The Florida Stare Unit ersity.
LJZ-ITERS
15 February
1979
RARE GAS ATOMS”
Tallalrassee,
Florida 32306. USA
Received 30 August 1978 Revised manuscript received 3 Noxembcr 1978 Rare 9s ad&tom dipoles are shown to be small and uvxpnble of explaining observed uork function changes Three-body dispersion forces yield v;tlues consistent xrith the reduction in the adatom p.dr potentials; contrtbutions from adatom dipoles are negligible.
It is well known that the presence of a surface modifies the interaction between molecules adsorbed on it. There are two aspects to the problem: (1) a quantum mechanical treatment of the interaction energy between the admolecules and (2) a statistical mechanical treatment connecting the interaction energy to the thermodynamic and experimental results_ Three formulations have been advanced for the long-range forces and one for the short-range interaction between two admolecules. The long-range formulations predict that the perturbation by the solid reduces the interaction of the two molecules_ The short-range treatment [ 1] is based on the Gordon-Rim [2] local density method md is limited only to the region of strong electron overlap. In this note we confine our remarks to the long-range forces. The most frequentiy used form of the intermolecular potential between two adatoms has the form [3] u(r) = 4,s [(u/r)”
- (u/r)6 i- r&~/1-)3] _
(1)
This equation has the appearance of a modified Stockmayer potential in which q is a parameter generally chosen to give a best fit of the second virial coefficient of the two dimensional gas. The three longrange formulations predict potentials of the form (1) although they differ greatly in their derivation and interpretation of v_ Thus, McLachlan’s theory [4] is based on the image method, the MacRury-Linder [5] * Supported in p;ut by NSF _mt NIH grant No. GM-23223.
No. CHE-76-08541
and by
equations on reaction-field techniques, and the Sinanoglu-Pitzer [6] formulation on time-independent perturbation theory_ They all trace the inverse cube term to the three-body dispersion potential which results from the interaction of the two adatoms with the solid- The Sinanoglu-Pitzer theory assumes the existence of a permanent surface electric field which also contnbutes to the inverse cube term, along with the three-body dispersron term. Permanent electric fields also appear in the MacRury-Linder formalism. but only for a specialized model in which the electrons in the solid are free to move throughout the soiid and the nuclei are confined to oscrllatory motion about their lattice sites. The field contrrbution is exceedingly small and vanishes in the continuum model of the solid, which is the model assumed by Sinanoglu and Pitzer. The su=estion that permanent surface fields are present has led to much controversy and debate. Krizan and Crowell [7], and also Wolfe and Sams [S] have vigorously opposed the introduction of such fields in the theory of adsorption_ if such fields existed, they maintained these would be negligibly small. On the other hand, Everett [9] suggested that the contrrbution to the inverse cube term comes mainly from the permanent surface field and not from the three-body dispersion term. The esistence of permanent surface fields has also been inferred from an interpretation of the change of the work function of a met5 on which atoms are adsorbed- The solid distorts the wavefunction of the adsorbed atoms and this effect produces a “permrtnent“ 283
Volume 6 1. number 2
CHEMICAL
induced dipole nxxment in the perturbed atoms and hence a potential jump across the adsorbed layer. These “permznent” induced moments can be thought ofas being produced by “permanent surface fields’ and thus, it has been suggested that the e_xistence of permanent induced moments would be proof that surface fields e_xist_ Recently, Linder and Kromhout [IO] developed a general theory for determking the induced dipole moment which results from the van der Waals interaction of the adsorbed atom and the solid- in this theory no permanent (preesisting) surface fields are invoked- The production of permanent moments by the van der Wads interaction was suggested earlier by CrowelI [ 1 I! and Antoniewin [ I2J_ More recent studies of the moments induced by intermoiecutar forces were carried out by Zaremba [IS J and by Bruch and Ruijgrok [14] _There seems to be no doubt that the van der Nkds interaction gives rise to induced dipoies in the adsorbed atoms. The question is whether these dipoles xre sufficiently Iarge to have significant effects on the forces between adsorbed molecules or on the work functions. Table 1 lists the values for the induced dipole moments-for the noble gas atoms adsorbed on xenon and on pzdladium. The calcAtions are based on the appro_ximate formula: /l
=
- ; [G(O) CrrWJez;]
where %{O)
a/!J(w,
is the polarizability
f b) ,
15 Febroary 1979
PHYSICS LETTERS
(2)
of the adatQm, e is the
eiectronic charge, C a constant which has the value 912 for H, 914 for He and approximately 9125 for the other rare gases. For a crystalline solid made up of kumonic oscillators c = 25fN&O)wz and b2 = a$+ f Q, where NO is the number of oscillators per unit voiume, g(O) is the poIarizability at zero frequency, and ws the natural frequency ofan isolated oscillator_ For a metal, within random-phase approximation, a = b2 = i o$, where op is the plasma frequency. 2, is the perpendicular from the center of the atom to the surface- The parameters used in the calculations are also listed in table l_ The dipole moments were calcuhted for 2, equal to the gas phase collision diameter, It is seen that the dipole moments of the gases on Pd (carbon would be very similar) are considerably larger than on Xe, but in no case does the dipole moment exceed O-0065 D_ In table 2 are listed the dipole-dipole interaction energies, E$, arising from the action of the permanent induced dipoles, and the third order nonadditive dispersion energies, Eg$ arising from the correlations of the electron fluctuations within the solid and the two atoms_ The dipole-dipole interaction energies were calculated by the use of the equation:
(3 where r12 is the distance between the clusters of the two atoms- (it is noted that the dipoles point in the direction perpendicular to the surface.) The dispersion energies were obtained with the aid of
Table I Permanent kduced dipote moments Poluiz&iity~) cr X 10z4 (cm3)
Adsorbed
LF
-----_
-._--_ He
i\;r AI Kr
*xe
--. 0207 0.396 I.644 2.-?86 4.021
ionization potentidb) IW0
Col!ision diimeter d 0 X lO*(cm)
23.5
2.63 2.75 3-41 3.60 4.07
-__ 3153 IS-775 14.00 12.15
Induced moment JKx 102” (esu) on Xe
d)
2.00 093
6.00 957 15.60
Pd e) 8.72 4.02
25.2 39.8 64.2
a) Gkutted from ,gseous molar refraLtionsR, given in ref_ [241. b, Ret [25 I_ c, Ref. I16 j. p- 1: IO_ The Zo-values (i-e_ the drstance from the atom to the solid surface) \%eretaken fo be the same Y the collision dizmetrrs Q of the rare s atolns_ d, The density of Xe taken to be L24X 10z2 ato&cm3_ e, The palladium plasma frequency. fiwp = 25.5 eV. taken from ref. 1261_
284
Volume
61, number 2
CHEMICAL
PHYSICS
LETTERS
15 February 1979
Table 2
Interaction energiesbetueen adsorbedatoms =I_E(3) dis denotes the three-bodydispersioninteraction and dipoIe-dipoIe inreraction --Adsorbed &Is He Ne Ar Kr Xe
On Xe $2 0.14 0.72 2.88 3.88 5.07 _-__--~
E (3)_ denotes the
dlP
static
On Pd
X 1Or6(erg)
(3) Edip
--
X
lOa (erg)
0.22 0.042 0908 1.84 3.60
E$i
X lOI
(erg)
E$
---1.06 2.74 10 6 14.1 18.1
X 10zo
(er-)-_
4.18 0.78 15.9 31.8 61.0
‘) The Zo-vaiues acre taken to be the same as the inert gas s values.
(4)
where f(Q)=(L+3cos~~)sin~~,
and cr.J-ig) is the gas atom polarizability along the imaginary axis and e(-i5;) the dielectric constant of the solid, also along the imaginary axis. The function f(o) is close to one for all relevant values of 0 and, in the present calculations, is set equal to 1_ For a crystalline solid composed of harmonic osctiators of polarizability a,(O), eq. (4) reduces approximately to:
and for a metallic solid, eq. (4) reduces to
(-1 It is seen that, in general, the values of Egi are larger for metallic solids than for crystalline solids. The same holds true of @i_ Although the fractional contribution of Ei$ to the total three-body forces is slightly larger
for the metallic solid than for the crystalline, the contribution in either case is small, less than O-l%. Notice that this ratio would change only as Zc5, so that our conclusions apply for any reasonable choices of Z. _ Thus, the induced permanent moments play only a very minor, if not negligible, role in the long-range interaction between adsorbed molecules. A similar statement can be made regarding the change
in work function of the solid. Thus. the lxgest induced dipole moment calculated in our study is that of Xe at a distance of 2 A (less thari one-half the collision diameter above the surface). The value of this moment is 9.8 X 10-20esu, which is about 10% of the value needed to account for the observed change in the work function_ We emphasize that these results pertain only to the region of no overlap and are based on admittedly very crude calculations. One of the approximations made in the calculatrons of the dipole moments is the use of Slater orbitals in the estimation of C = (Z4> (22)-2. We recalculated the Cvalue for Xe using the tabulated Hartree-Fock-Slater wavefunctions of Herman and Skillman [15] _The C value so calculated is reduced by 43% from the “Slate? value C = 9/35. The fractional dipole-dipole energy is thus reduced by about d third to about 0.03%_ These results are consistent with the fmdings of Krizan and Crcwell [7], who concluded that an electrostatic dipole--dipole force makes negligible contribution to the interaction energy. It has been suggested [7-g]: as mentioned before, that the induced permanent dipole moment arising from van der Waals interaction might play an important role in the reduction of the work function of metals by adsorbed inert gas atoms. To effect the change observed a dipole moment of the order of one debye would be needed for Xe, for example. Antoniewicz [12] estimated a dipole of 0.7 debye for Xe on palladium which is about a factor of two smaller. One reason for the discrepancy is that Antoniewicz based his calculation on a Z, value of 2.09 A, tshich is the radius of the Xe atom, whereas our results are based on the collision diameter, (Y= 285
Volume 6 1, number 2
PHYSICS
CHEMICAL
407 _&_The true ZO-value undoubtedly lies somewhere inbetween, But if we had used ?heZO=2&our~cuhted JI would have been a faction (= +) of the one _&xtonitwicz
obtained,
We can recast our formula (3) in a form similar to
Antoniewicz-s formula (9) [ 121 by using the Kirkwood variational approximation to the polarizability 1161 and an effective number of electrons, treFf [i7] I
IQ where e is the electronic charge and ou the Bohr radius_ This formula when applied to I-I on a perfect metal (w, < 6) yields essentially Antonlewicz’s result _ Applied to Xe (tz&, = S-63) on Pd it gives an answer which is the same as that predicted by eq, (2)_ Antoniewicz’s Larger result comes from applying his hydrogen formula directly to Xe, The observed virial coefficient of the two-dimensional ,“a~ of adsorbed Xe on carbon [7,18] appears to be consistent with our calculations, A &pole of I D \voutd result in a repulsive inverse cube dependence which is perhaps an order of magnitude bigger than the data admitA common explanation of the origin of permanent induced dipoIes is the immersion of the adsorbed atoms in the electron cloud out,side the metal surf&z_ The range of this cloud outside the metal surface is about 1 A fcr metals [L9] _ These distances are considerably smaller than theZu values measured by LEED [Xl] [low energy electron dir’fraction) or estimated from collision data of inert gas atoms, The measured 20 t&es, Izirse compared to the range of the electron cloud, are consistent with the avoidance by the closed sheI atoms of the region of overlap. At these large Oistances the moments induced by this mcchanlsm shouid be neghgible. It has been suggested that “nonbondin$’ charge transfer from xenon to the metal might explain the large (z 1 V) changes in work function (for example, see ref. [Xl)_ A carding to the photoelectric data giLen by Landman and Kteiman 1201rthe ionization potential of xenon adsorbed on tungsten is reduced by 3 3 l __- 0_2v, presumably due to the stabllizatic;n of the ion by its interaction with its image_ (Apropos of the discussion abobe, this image potential corresponds to a Za of 34, ik-1 The pertinent point is that the same value is obtained for the removal of a core (3d) electron as fur an outer shell [Sp) electron, Taking the
286
LElTEIIS
15 February 1979
between the core and outer slreli shifts to be O-3 V (just within experimental error), and the difference between the ionization potenti& of Xei and XeII to be 9.1 V 122 J, it would appear that less than 0.03 electron was transferred from ~enorr to tungsten_ To produce the required one debye imageion dipole moment a transfer of about 0.15 electron is required_ it is difficult to make a good theoretical estimate of this charge transfer, but a very crude upper limit, estimated using the ion stabilization energy as a rough approximation to the matrix eIement, would sugest kss than O-06 electron would be transferred_ Furally it should be pointed out that the interaction between xenon atoms in this model would vary as the inverse j%zsl power at small distances, and would be quite inconsistent with the second virials, Strictly spetiing the oppositely directed induced dipole moments in the metal ought to be inciuded in form& (3); however these values are unknown_ The work function will depend on the vector sum of the adatom and metal dipoles, Kahn and tau 1331 have derived an expression for the long range interaction between the overaU (adatom-metal) moments which is of the same form as our eq_ (3) multiplied by 2. We are grateful to Professor L_W_ Bruch for drawing this point to our attention, although these considerations do not alter our general conchrsions_ In summary, it would appear that the observed change in the work function by adsorbed me gases cannor be explained by the induced dipoIe moments,
kwgest difference
References f 11 DL Z-reeman,J_ Chem_ Phys. 62 (1975) 4300, [2J R-G_Cordon arrd Y .S_ Kim, J, Chem- Phys, 56 (1972) 313’ ___ 131 T. Takaishi, Prosr- Surface Sci- 6 (1975) 43141 A-D- McLachkn, MO;, Phys- 7 (1964) 381, [S 1 T-B- MacRury and EL Lander, J_ Chem_ Phys_ 54 (197 L)
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1322; J-E_ Krizan, J_ Chem_ Phys. 42 (1965) 2923_ IS] R-Wolfe and J-R_ Sarns, J_ Chem, Phys. 44 (1966) 3,181, [9! D-H_Everett, DiscussionsFaradsy SOL 40 (1965) 177; J-R_ Sams, Pros_ Surface Membrarre Sci_ S (1974) I_
[IO j B_ tinder and R.A. Kromhout, Phys. Rev. B13 (1976) 1532_ [Xl ] A IL Crowell, J- Chem- Phys, 6 1 (1974) 3485,
Volume 61. number 2
CHEhIICAL
[lZ]
PHYSICS
P.R. Antoniewin, Phys. Rev. Letters 32 (1974) 1424_ E. Zaremba. Phys. Letters 57A (1976) 156. [141 L.W_ Bruch and Th.W_ Ruijsok. private communication. [15] F_ Herman and S- Skiian. Atomic structure calculations (Prentice-Hall, Englewood Cliffs, 1963). [IS]
[L6]
J-O_ Hirschfelder,
C-F_ Curtis
and R-B. Bird. XoIecular
theory of gases and Iiquids (Wiley. New York, 1954) p946. [ 171 E_A_ Moelwyn-Hughes, Physical chemistry (Pergamon Press, New York, 1961) p_ 389 and table 7. [IsI J.H. de Boer and S. Kruyer. Trans. Faraday Sot. 54 (1958) 540. 1191 N.H. March. Physics and contemporary needs (Plenum Press. New York. 1977) p_ 53.
LETTERS
15 February
1979
PO1 U- Lmdrnm and G.G. Klciman. Surface Defect Properties Solids 6 (1977) I. [211 B E. Nieuwnhuys, O.G. Aardennc and W.frf H. SachtIer, Chem. Phys. 5 (1974) 418. 1221 C.B. Moore, National Bureau of Standards Circular 447, Atomic Energy Levels, Vol. 3. 123 j W_ I;ohn and K.-H_ Lau. Solid State Commun. 18 (1976) 553. 1241 A.A. hkuyott and F. Buckle>, Natxonal Bureau of Standards Circular 537 (1953)_ [25 J EH. Field and J-L. franklin, Electron impact phenomena (Academic Press, New York, 1957) p_ 108. [26] N. Glickman, Solid State Phys. 26 (1971) 338.