Molecular Orbital Calculations of Atomic Hydrogen Chemisorption on

J. Phys. Chem. 1981, 85, 2037-2041. 2037. Molecular Orbital Calculations of Atomic Hydrogen Chemisorption on the Beryllium. (0001) Surface. Gar B. Hof...
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J. Phys. Chem. 1981, 85,2037-2041

2037

Molecular Orbital Calculations of Atomic Hydrogen Chemisorption on the Beryllium (0001) Surface Gar B. Hoflund hpaftment of Chemical Englneerlng, Unlverslty of FlorMe, Galnesville, FlorMe 326 11

and Robert

P. Merrill'

School of Chemical Engineering, Olin Hall, Cornel1 Unlverslty, Ithaca, New Yo& 14853 (Received: January 16, 1961)

Extended Huckel theory, Anderson's modification of extended Huckel theory, and the complete neglect of differential overlap method were used to study the chemisorption of atomic hydrogen on the (0001) surface of beryllium. The maximum cluster size used with each method is 5,73, and 10 beryllium atoms, respectively. Anderson's modification leads to improvement of the potential energy curves predicted by extended Huckel theory, and a fairly large cluster containing 73 atoms is necessary to attain convergence of chemisorption binding energies with respect to cluster size. CNDO predicts binding energies which are too large. When these energies are scaled by dividing by a constant for all sites, agreement is found with all other molecular orbital methods. General agreement also is found with results of Schaefer's ab initio calculations and Companion's CNDO with bicentric energy rescaling.

Introduction The theories of molecular chemistry currently present one of the most viable approaches for calculating the properties of an atom or molecule chemisorbed upon a solid surface. The semiempirical molecular orbital theories considered here include extended Huckel theory (EHT),' a modified form of the extended Huckel theory (MEHT) due to Anderson,2 and the complete neglect of differential overlap method (CND0).3 The results from calculations using these methods are compared with ab initio results (RHFT)4-7and the complete neglect of differential overlap with bicentric energy rescaling (CCNDO).g12 EHT, MEHT, and CNDO have been used in chemisorption along with several modifications to correct for (1)Hoffman, R.J. Chem. Phys. 1963,31,1397 (2)Anderson, A. B.; Hoffman, R. J. Chem. Phys. 1974,60,4271. (3)Pople, J. A.; Beveridge, D. L.; "Approximate Molecular Orbital Theory"; McGraw-Hill: New York, 1970. (4)Bauschlicher, C. W.; Liskow, D. H.; Bender, C. F.; Schaefer, 111, H. F. J. Chem. Phys. 1975,62,4815. (5)Brewington, R. B.; Bender, C. F.; Schaefer, 111, H. F. J. Chem. Phys. 1976,64,905. (6)Bender, C. F.;Schaefer, 111, H. F.; Bagus, P. S. Chem. Phys. 1976, 15,227. (7)(a) Bauschlicher, C. W., Ph.D. Dissertation, University of California, Berkeley, 1977. (b) Bauschlicher, C. W.; Bagus, P. S.; Schaefer, 111, H. F. IBM J . Res. Deu. 1978,22,213. (8) Companion, A. L. Theor. Chim. Acta (Berl.) 1972,25, 268. (9)Companion, A. L.; Hsia, Y. P. J . Mol. Struct. 1972,14,117. (10)Companion, A. L. J. Phys. Chem. 1973,77,3085. (11)Companion, A. L. Chem. Phys. 1976,14, 1. (12)Companion, A. L. Chem. Phys. 1976,14,7. (13)Lasarov, D.; Markov, P. Surf. Sci 1969,14,320. (14)Blyholder, G.; Coulson, C. A. Trans. Faraday SOC. 1967,63,1782. (15)Bennett, A. J.; McCarroll, B.; Messmer, R. P. Surf. Sci. 1971,24, 191. (16)Bennett, A. J.; McCarroll, B.; Messmer, R. P. Phys. Reu. B 1971, 3,1397. (17)Messmer, R.P.;McCarroll, R.; Singal, C. M. J. Vac. Sci. Technol. 1971,9,891. (18) Shopov, D.; Andrew, A.; Petkov, D. Surf. Sci. 1969, 13, 123. (19)Fassaert, D. J. M.; Verbeek, H.; Van Der Avoird, A. Surf. Sci. 1972,29,501.

some of the more obvious difficulties in their use for calculating surface properties. For the same chemisorption system different methods often do not give the same binding energy or even the same preferred binding site. Two examples are the discrepancies between E H T and CNDO calculations on the atomic hydrogen-graphite ~ y s t e m ' ~and J ~ the atomic hydrogen-nickel ~ y s t e r n . ' ~ ~ ~ Unfortunately experiments are not sensitive enough at this time to give potential energy surfaces and complete structural information about the chemisorption layer, and theory cannot predict this information exactly because the problem is so difficult. It is hoped that this study will serve as a basis for more comparisons and that other studies will be performed on this system using other important theoscattering3638 and pseudoretical techniques such as XCY potential t h e ~ r y . ~ ~ , ~ ~

(20)Anders, L. W.; Hansen, R. S.; Bartell, L. S. J. Chem. Phys. 1973, 59,5277. (21)Robertson, J. C.; Wilmsen, C. W. J Vac. Sci Technol. 1971,8,53. (22)Blyholder, G. J. Phys. Chem. 1964,68,2772. (23)Blyholder, G.; Allen, M. C. J. Am. Chem. SOC.1969,91,3158. (24)Robertson, J. C.; Wilmsen, C. W. J. Vac. Sci. Technol. 1972,9, 901. (25)Anderson, A. B.; Hoffman, R. J. Chem. Phys. 1974,61,4545. (26)Miyazaki, E.J. Catal. 1974,33,57. (27)Blyholder, G.Surf. Sci. 1974,42,249. (28)Blyholder, G. J. Chem. SOC.,Chem. Commun. 1973,625. (29)McCarroll, B.; Mesmer, R. P. Surf. Sci. 1971,27,451. (30)Baetzold, R. C. J. Chem. Phys. 1971,55,4355. (31)Baetzold, R. C. J. Chem. Phys. 1971,55,4363. (32)Baetzold, R.C. Surf. Sci. 1972,36,123. (33)Baetzold, R. C. J. Catal. 1973,29,129. (34)Baetzold, R. C. J. Solid State Chem. 1973,6,352. (35)Slater, J. C. J. Chem. Phys. 1965,43,5228. (36)Slater, J. C.; Johnson, K. Phys. Rev. E 1972,5,844. (37)Johnson, K.; Smith, F. C. Phys. Rev. B 1972,5,831. (38)Messner, R. P.;Knudson, S. K.; Johnson, K. H.; Diamond, J. B.; Yang, C. Y. Phys. Reu. B 1976,13, 1396. (39)Schluter, M.; Chelikowsky, J. R.; Louie, S. G.; Cohen, M. L. Phys. Reu. E 1975,12, 4200. (40)Chelikowsky, J. R.; Cohen, M. L. Phys. Rev. B 1976,14, 556.

0022-3654/8112085-2037$01.25/0 0 1981 American Chemical Society

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The Journal of Physical Chemistry, Vol. 85, No. 14, 1981

Hoflund and Merrill

TABLE I: Parameters Used in EHT and MEHT

I

Be (12,6)

I

Flgure 1. Be(12,6). The large dots represent beryllium atoms in the surface layer and the small dots represent beryllium atoms in the second layer.

One extremely important aspect of the cluster representation of a metal surface which is difficult to consider is the effect of the size of the cluster. Lasarov and Markov13 showed that a cluster containing at least 50 lithium atoms is required for stabilization of the atomic delocalization energy with cluster size using EHT. Baetzold also has considered cluster and has found that the cluster properties vary considerably as the number of atoms in the cluster increases. His clusters contained less than 20 atoms, and convergence of the cluster properties is not demonstrated. Until recently there has been no good standard of comparison for judging the reliability of the results given by these molecular orbital (MO) theories. But lately RHFT calculations have been undertaken for the chemisorption of a single hydrogen atom on beryllium clusters containing from 1 to 22 beryllium atoms by Schaefer and co-workem4-' RHFT calculation^^^ are very costly due to the enormous amount of computer time required and cannot be done on large clusters for the catalytically interesting transition metals. However, a comparison of these ab initio results with results from MO theories for atomic hydrogen on beryllium clusters should provide a good standard for accessing the utility of the simplified MO theories for chemisorption calculations. The RHFT chemisorption energy of hydrogen on a 22 beryllium atom cluster is estimated to be within 5.0 kcal/mol of the Hartree-Fock limit, and the equilibrium distances are within 0.01 nm.' Schaefer asserts that a cluster which contains all the second-order nearest neighbors to the metal atoms participating in the chemisorption bond adequately represents the metallic surface for chemisorption calculation^.^^ The conclusions drawn from this study are not dependent upon the assumption that the RHFT calculations give correct binding energies but rather support the RHFT results by the general agreement between all of the methods considered. Obviously, the most reliable comparison would be with experimental binding energies, but such measurements have not been made yet for this system. Methods of Calculation Clusters containing 1,3, 4, 5, 10, 19, 22, 25, 55, and 73 beryllium atoms were chosen to represent the surface. Be(12,6) containing 18 beryllium atoms is shown in Figure 1 as an example. Twelve is the number of beryllium atoms in the surface layers, and six is the number of beryllium atoms in the second layer. The geometrical configuration used is the same as that of bulk beryllium metal. This is (41) Dewar, M. J. S. "The Molecular Orbital Theory of Organic Chemistry"; McGraw-Hill: New York, 1969. (42) Schaefer, 111, H.F., personal communication.

Darameter

Be

H

shielding constant ionization potential, e V 1s 2s 2P,, 2P,, 2P*

0.956

1.2 13.6

9.32 5.96

reasonable since low-energy electron diffraction (LEED) experiments43-" have shown that the beryllium surface is not reconstructed. This must be considered because the results are sensitive to small displacements of the surface atoms. Beryllium is hexagonal close packed, and the (OOO1) surface is studied here. The nearest-neighbor distance within a layer is 2.2866 A, and the distance between similar (every other) layers is 3.5833 A, which means that the nearesbneighbor distance between adjacent layers is 2.2255

A.

All the calculations described in this paper except Schaefer's ab initio calculations were made by using a valence-basis set of Slater-type atomic orbitals (STO's) consisting of the 29, 2p,, 2p,, and 2p, orbitals for each beryllium atom and a 1s orbital for each hydrogen atom. EHT has been discussed e l s e ~ h e r e ' J ~and J ~ will ~ ~ not be reviewed here. The shielding constants for the STOs for the beryllium atoms were taken from the tables of Clementi and R a i r n ~ n d i . The ~ ~ shielding constant for the hydrogen 1s orbital was taken to be 1.2, which is slightly higher than Schaefer's value of 1.154 and lower than Hoffmann's recommended value of 1.3 for EHT.4g Changing the orbital exponents had only a very slight effect on the results. Ionization potentials were taken from the tables of Skinner and Prichard.& Table I summarizes the parameters used in EHT and MEHT in this study. The resonance integrals given by Hi, = $&H@j d r (1) were calculated by using the Wolfsberg-Helmholtz equation51

+

Hi, = Y2KSi,(Hii Hj,)

(2)

where K is a constant, Si, are overlap integrals, and Hii are Coulomb integrals (approximated by the valence state ionization potentials of the ith atomic orbital). In the past a value of K equal to 1.75 was commonly used because it worked well for hydrocarbon molecules. There is no a priori justification for this value nor for the thesis that K optimized for hydrocarbons will be suitable for other systems. In this study the value K was allowed to vary to match the binding energies predicted by RHFT on the 22 beryllium atom cluster. This is the only adjustable parameter used with MEHT in this study. An important criterion in this study is the use of only one adjustable parameter for any given cluster so that the calculations are not just a result of curve fitting with multiple parameters. The Anderson formulation of b ~ n d i n g , ~in. ~essence, ~-~ has justified the addition of a repulsive potential energy to the energy given by EHT in order to obtain the total potential energy curve and has provided a method for its (43) Baker, J. M.; Blakely, J. M. J. Vac. Sci. Technol. 1971, 8, 56. (44) Zimmer, R. S.; Robertson, W. D. Surf. Sci. 1974, 43, 61. (45) Clementi, E.;Raimondi, D. L. J. Chem. Phys. 1963, 38, 2686. (46) Skinner, H. A.; Pritchard, H. 0. Trans.Faraday SOC.1953, 49, 1254. (47) Anderson, A. B.; Parr, R. G. J. Chem. Phys. 1970,53, 3375. (48) Anderson, A. B. J. Chem. Phys. 1974, 60, 2477. (49) Anderson, A. B.; Hoffman, R. J. Chem. Phys. 1974, 61, 454. (50) Anderson, A. B. J . Chem. Phys. 1975, 62, 1187.

The Journal of Physical Chemistry, Vol. 85, No. 14, 198 1 2039

Atomic Hydrogen Chemisorption on Beryllium

TABLE 11: Binding Energies and Bond Lengths for BeH -125

-175 -1-200

-

9w

method

Re, A

D e , kcal/mol

RHFT minimum basis larger basis near Hartree-Fock' ( 5 3 ) large C I (~5 4 ) experiment

1.420 1.352 1.338 1.345 1.343c

46.4 44.5 50.3 48.8 49.8

Reference 53. Reference 56.

a

I I

0.08 0.10

I

I

1

I

Reference 54.

i t

0.1 0.2d

Reference 55.

I

I

I

I

I

I

I

I

0.12 0.14 0.16 0.18 Be-H Separation, nm

0.20

Flgure 2. Potential energy curves for beryllium hydride. The arrows locate the minima.

calculation. The importance of such an improvement can be demonstrated by considering what happens when EHT is used to describe the bonding of diatomic hydrogen. Repulsive effects in E H T are represented by decreasing overlap. As two Is orbitals approach one another there is no point where the overlap begins to decrease, and so the H2 molecule collapses to a single nucleus surrounded by two electrons in a 1s orbital. In MEHT the total curve for a diatomic molecule2 is given by W*(R) = W@) + W E H W (3)

1

1

012

008

020 0 2 4 Be-H Separation, nm 016

I

028

032

Figure 3. Potential energy cwves for BeH from a CI calculation, AHHT, and MEHT.

where W*(R)is the approximate total molecular energy, WEH(R) is the energy given by EHT, and WB(R)is given by A b I n i t i o Results

CI

for a period 1atom. N is the number of L-shell electrons, R is the distance in A, 5' is twice the exponent of the 2s and 2p functions for atom p, and 2 is the nuclear charge of atom a. Equation 4 gives the repulsive energy of superposing two rigid atoms.47 For the clusters studied in this paper, W&R)is replaced by the summation of the diatomic interactions. A later formulation of this theory49 does combine EHT and the repulsive terms together in a unified manner. This will be designated the Anderson-Hoffmann-Huckel theory (AHHT). CNDO also is described e l ~ e w h e r e . ~ J Standard ~~~'~~~ CNDOI2 parameterization3 was used. The binding energies predicted by CNDO are always too large by factors of 2-5 depending upon cluster size. To correct for this a scale factor was determined by dividing the CNDO binding energy for the eclipsed site by the RHFT binding energy for the same site. This same scale factor was then used for all the other sites on the cluster and at every point on the potential energy curve. This technique is essentially a one-parameter fit to the RHFT energy, and it gives a comparison of the shape of the potential energy curves but is not as well justified as Companion's bicentric energy rescaling method.8-12

Calculational Results and Discussion Figure 2 shows the potential energy curves for BeH calculated from MEHT and CNDO. MEHT yields a larger vibrational force constant, but both give approximately the same bond length. Table I1 gives the binding energy and

a

-iip)w 11 -50

0 . 0 2 0.06 0.10 0.14 0.18 0 . 2 2 Be (3,0)-H Separation, nrn

Flgure 4. CNDO and EHT potential energy curves for a hydrogen atom approaching a 88(3,0)cluster. The circle represents the chemisorption site on the cluster.

bond length for BeH from various sources. The bond lengths and energies agree quite well. E H T fails completely for BeH because the molecule collapses like H2. Figure 3 shows the potential energy curves for BeH calculated by using AHHT, MEHT, and a large configuration interaction c~mputation.~' It is obvious that MEHT represents the repulsive forces much better than EHT and that AHHT represents the repulsive forces better than MEHT. Unfortunately, CI potential energy curves are not available for larger clusters. The EHT and CNDO potential energy curves for a hydrogen atom approaching the triangular Be(3,O) cluster are shown in Figure 4. These curves are symmetrical about the energy axis. Again the bond lengths are in good agreement with RHFT results, and the CNDO result has smaller curvature. By using an energy adjustment pro(54) Bagus, P. s.;Moser, C. M.; Goethals, p.; Verhaegen, C. J. Chem. Phvs. 1973.58. 1886. ~-~ 755)Horne, R.; Colin, R. Bull. SOC.Chin. Belg. 1972, 81, 93. (56) Colin, R.; De Greef, D . Can. J . Phys. 1975, 53, 2142. (57) Chan, A. C. H.; Davidson, E. R. J . Chem. Phys. 1968, 49, 727. I

(51) Wolfsberg, M.; Helmholtz, L. J. Chem. Phys. 1952, 20,837. (52) Cadzuk, J. W. Surf. Sci. 1974, 43, 44. (53) Cade, P. E.; Huo, W. M. J . Chem. Phys. 1967, 47, 614.

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The Journal of Physical Chemistty, Vol. 85, No. 14, 1981

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90 7

I

0

I

I

I

I

I

I

I

Ab Initio Minima o Hole

R

L

8

30

0 Ecllpsed A hhdpoinl @ Overhead

;;;j,;)

-uverneaa,u

-I1

A b I n i t i o Results 0 Minimum Basis 0 Larger Basis

m

-30 -008.004 o Be(3,1)-H

0 0 4 o o a 0 1 2 0 1 6 020 S e p a r a t i o n , nm

i

Flgure 5. Potential energy curves for hydrogen approaching a Be(3,l) cluster.

70c

-'"r I1

\

Ab Initio Minima

I

I

-012 -008-004

I

1

1-4

ooa

I

I

I I

0 1 2 0 1 6 020 024 B e l 7 , 3 l - H Separation. nm

0

004

Figure 8. MEHT potential energy curves for a hydrogen atom approaching a Be(7,3) cluster at four sites. A different value of Kis used at each site to fit the binding energies given by RHFT on Be(14,8).

cedure, however, the RHFT minima are in agreement with the EHT and CNDO minima. No matter what value of K is used, the MEHT minima are not in agreement with the RHFT minima. This triangular cluster, however, is not a typical case since RHFT calculations show that the cluster itself is unstable with respect to three isolated beryllium atoms. The Be(3,l) cluster contains an atom in the second layer and is stable according to RHFT calculation^.^ The only site considered here is the eclipsed site (directly over the atom in the second layer). Here the hydrogen atom can penetrate through the surface. Figure 5 shows the potential energy curves calculated by all three methods. The RHFT bond length is 0.12 nm compared with 0.09 nm for EHT, 0.13 nm for MEHT, and 0.10 nm for CNDO. EHT predicts collapse of the hydrogen atom into the secondlayer beryllium atom, but the shapes of CNDO and MEHT are similar. Since EHT and MEHT differ mainly in the repulsive portion of the potential energy curve, only MEHT and CNDO results are presented for the larger clusters. The shapes of the potential energy curves do not vary significantly with cluster size so representative curves for the four sites considered on the Be(7,3) cluster are shown in Figure 6 for MEHT and in Figure 7 for CNDO. The Be(4,l) cluster is the smallest for which it is reasonable to consider several chemisorption sites. The three sites are the eclipsed site which is directly over a secondlayer beryllium atom, the hole site which is over the center of a triangle formed by three surface beryllium atoms, and the bond midpoint site which is above the center of a bond formed between two surface beryllium atoms. The use of these cluster calculations to model chemisorption on a large surface can be examined by assuming that the RHFT calculations for the 22 atom clusters4

Be(7,3)-H Separation, nm

Figure 7. CNDO potential energy curves for a hydrogen atom approaching a Be(7,3) cluster at four sites. All curves are scaled by the same ratio which set the binding energy of the eclipsed site to the RHFT result.

represent the semiinfinite surface. Support for such an assumption is found in the concept of the surface mole~ u l which e ~ ~assumes that the electronic structure of only a small number of metal atoms close to the chemisorbed species is changed significantly by adsorption. To determine if Be(4,l) could represent a large surface, a value of K was chosen for the eclipsed site so that MEHT would give the same binding energy as the eclipsed site in the RHFT 22 Be atom calculations. Then the potential energy curves for the hole and midpoint sites were calculated by using the same value of K , and it was found that the binding energies are too low by 14 kcal/mol for the hole site and 22 kcal/mol for the midpoint site. The CNDO potential energy curves for this cluster show the same features as the EHT curves, exhibiting energy maxima for the hole and midpoint sites and an inflection point in the repulsive portion for the eclipsed site. Like MEHT CNDO gives the correct relative order for the bond distances. The most noticeable differences are that the binding energy for the midpoint site, B, is 10.0 kcal/mol lower than the RHFT result and that the bond lengths are slightly larger than the RHFT results. On the Be(7,3) cluster the overhead site, which is directly above a surface Be atom, also can be considered. Figure 6 shows the potential energy curves from MEHT. As with Be(4,l)H the calculations predict the correct relative bond lengths, but they are about 0.02 nm longer than RHFT equilibrium bond lengths except for the overhead site. The curves for the hole, eclipsed, and midpoint sites are very similar in shape to the CNDO curves for Be(4,l). The CNDO curves predict a potential barrier to penetration of the surface at the eclipsed site that is 45 kcal/mol lower than that predicted by MEHT. With CNDO the binding energy of the hole site increases in going from the 5-atom cluster to the 10-atom cluster and is now only 5 kcal/mol less than the RHFT binding energy. The CNDO hole binding energy is in agreement with the RHFT results. Only MEHT calculations were performed for the larger clusters which include Be(12,7), Be(14,8), Be(14,8,3), Be(30,21,4) and Be(30,21,14,8). The shapes of the potential energy curves and the bond lengths have stabilized with cluster size. Also the bond lengths have the same increasing order predicted by RHFT: hole, eclipsed, midpoint, and overhead, but the magnitudes are 0.01-0.02 nm larger than RHFT values. Another point of comparison is the electron population of the chemisorbed hydrogen atom. RHFT predicts that the hydrogen-beryllium interaction is basically covalent in nature with populations of 0.96 at the overhead site, 1.01 at the midpoint site, and 1.02 at both the hole and eclipsed sites. The MEHT re-

The Journal of Physical Chemistry, Vol. 85,No. 14, 1981 2041

Atomic Hydrogen Chemisorption on Beryllium

TABLE 111: Binding Energies (in kcal/mol) Predicted by MEHT Using a Constant K for Each Cluster cluster 0 E M H Be( 14,8,3) Be(30,21,4) Be(30,21,14,8)

41.0 34.5 30.1

50.4 52.4 52.9

41.0 49.6 55.3

54.4 54.0 53.5

- 10

TABLE IV: Comparison of Binding Energies at Different Sites on the Largest Cluster Used with Each Method site E M 0 H

RHFT (22) 51.9 53.4 31.4 55.1

CCNDO

CNDO

(10) 53.5 49.7 46.0 56.0

(10) 51.9 48.4 29.9 52.7

MEHT (73) 51.9 52.8 30.9 54.9

sults on the Be(30,21,14,8) cluster are 1.04 at the overhead site and 1.00 at the midpoint, hole, and eclipsed sites which are consistent with the RHFT values. When an appropriately chosen energy scaling technique is used, all three simplified molecular orbital methods are able to give minima that are in agreement with RHFT minima. The overall potential energy curves show the same general features except where EHT obviously fails due to its inability to treat the repulsive forces properly. The variation in MEHT binding energies at the different sites are shown in Table I11 for the three largest clusters, and the binding energies predicted by RHFT, CCNDO, CNDO, and MEHT on the largest cluster considered with each method are given in Table IV. It is clear that with MEHT and CNDO all sites have converged to the RHFT results. Companion uses a scaling method in which one ratios each bicentric energy by the factor CNDO binding energy for diatomic xy (5) R x y = actual binding energy for diatomic xy and then computes the CNDO energy in the normal manner. This has a firmer theoretical basis and eliminates the need for our rescaling. Figure 8 is a reproduction of Companion’s results. The curves are qualitatively very similar to those presented here. The binding energies of these sites from CCNDO are also in very close agreement with RHFT, CNDO, and MEHT. Only the overhead site shows any discrepancy. RHFT, MEHT, and CNDO predict about 30 kcal/mol, and CCNDO predicts 46 kcal/mol. The RHFT value is 30 kcal/mol as shown by RHFT calculations on the larger Be(14,8,14) cluster.42 This is the only site which has been calculated on this large cluster, and it clearly has converged. CCNDO predicts a binding energy of 46.0 kcal/mol which is the binding energy of beryllium hydride, so that the hydrogen atom is just interacting with the Be atom directly below it. In essence this Be atom has been decoupled from the cluster. It is believed that a t high symmetry positions on certain clusters, Bloch wave functions are formed which cancel out leaving just one beryllium atom. This was found to be the case with MEHT a t the center Be atom of some clusters also. This problem is being investigated further by using

-60

t

U

0.10 0 0.10 0.20 B e ( 7 , 3 ) - H S e p a r a t i o n , nm

iJ

1-250

Flgure 8. Companion’s reparameterized CNDO with bicentric energy rescaiing calculations showing potential energy curves for the chemisorption of atomic hydrogen at four sites on Be(7,3).

clusters which are infinite in two dimensions and will be discussed in another study.

Conclusion It has been demonstrated that agreement can be achieved in the results of cluster chemisorption calculations by using different techniques varying in complexity from extended Huckel theory to ab initio Roothaan-HartreeFock theory. This lends confidence to the cluster approach and to the computational techniques. I t must be emphasized that the cluster size is an important consideration and that different size clusters are required to adequately model the surface for different theories. The cluster symmetry can influence the results as seen in the case of the overhead site. It also has been shown that Anderson’s modification of extended Huckel theory is an important improvement. The comparison thus far has been based on the potential energy surfaces calculated from the different methods. Unfortunately, no experimental data are available on the hydrogen-beryllium chemisorption system, but an experimental UPS study of this system has begun. All of the calculational methods yield electronic structure information which can be compared with the experimental data to give another assessment of the performance of the theories. Acknowledgment. We thank H. F. Schaefer, 111, and R. Baetzold for many helpful discussions. We are grateful to the AFOSR (research sponsored by the Air Force Office of Scientific Research, Air Force Systems Command, under AFOSR Contract/Grant No. 76-2926) and the Chevron Research Corporation for financial support. The computations were performed at the University of California, Berkeley, Computer Center and on Lawrence Berkeley Laboratory’s CDC 7600.