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A cluster model study of multiple H adsorption on Be(0001)
Surface Science 245 (1991) 439-451 North-Holland
439
A cluster model study of multiple H adsorption
on Be(OOO1)
Ian P. Dillon and John D. Head Department
of Chemistry,
University of Hawaii, Honolulu, HI 96822, USA
Received 15 August 1990; accepted for publication 14 November 1990
The different results obtained from slab and cluster ~culations are compared. In the clusters we model various H coverages on the Be(0001) surface using a single-layer Be,, cluster interacting with different numbers of H atoms. With a single H atom the on-top structure is the most stable. Two H atoms are computed to preferentially adsorb at an open site above 3 Be atoms. Caution always needs to be exercised when comparing slab and cluster calculations owing to the different adsorbate coverages being modelled. However, by increasing the number of H atoms in the cluster to simulate a monolayer of H atoms on the Be@OO1)surface we obtain results similar to slab calculations with the open and bridging structures close in energy and the on-top structure being least stable. These calculations with H monolayer coverage are noteworthy because they also enable the definition of a desorption energy Eda corresponding to the energy of removal for a single H atom from the monolayer. Edcs differs in value from the average H binding energy D, often used to evaluate the stability of different adsorbate structures on a surface. By using Ed._, an explanation for the experimentally observed bridging structure for H on the Be@OO1)surface is suggested. A similar computation of Ed_ is not possible in a slab calculation owing to limitations on the allowed unit cell size.
Theoretical studies of the electronic properties of adsorbates interacting with surfaces typically make use of either cluster models and the techniques of quantum chemistry [l-3], or extended two-dimensional slabs and the techniques of solid-state physics [4-71. Both procedures have strong advantages. Cluster models, for example, allow in principle, the treatment of low symmetry features such as those which must occur in a chemical reaction. On the other hand, slab calculations facilitate the analysis of ordered adsorbate overlayers. The range of application of both methods is largely determined by the available computer power. An important concern in a cluster calculation is the size of the cluster needed to circumvent edge effects. Choosing a large cluster with high symmetry is one common trick for easing the computational requirements [8]. Similarly, the slab calculations are restricted to considering relatively high overlayer coverages, where the lowest surface coverage treated is determined by the largest unit cell dimension tractable in the 0039-6028/91/$03.50
calculation. Thus, the high s~et~ clusters often treat only a single adsorbing species, while slabs model the intermediate and high coverage regimes of chemisorption. Furthermore, the extended slab c~c~ations automatic~ly include adsorbate-adsorbate interactions which are absent in the lowcoverage cluster calculations. Caution should be used when comparing the results from the two different methods. There is, however, no inherent restriction on the cluster model to prevent multiple adsorption studies. It is this difference in surface coverage modeled by cluster and slab calculations which we consider here. We use cluster models to examine multiple H adsorption on the Be(OO01) surface. There have been a number of cluster Es-151 and slab [16-U] calculations reported previously and a summary of the various results are given in table 1. Many of these calculations were performed before the recent experimental data, which finds the bridge site to be preferred at sub-monolayer coverage [19], became available. Table 1 show the calculations to predict many differing stable geometries for the chemisorbed H. The possible different H atom
0 1991 - Elsevier Science Publishers KY. (North-Holland)
I.P. DiNon, J.D. Head / Cluster model stu& of mulripleH adsorption on Be(OtWij
440
Table 1 Comparison of theoretical Be-H bond distance, RaeH, binding energy, DC, from cluster and slab calculations Authors
Adsorption
and
site type
OS
BS ‘)
TS
R BcH
9
Reek
4
G‘%
W4’
(A,
fkcW
mol)
R BeH s (4
mol)
0,
(kcal/ mol)
Cb4ster.s 1LDH 1MDH
1.72 1.59
57.2 32.4
1.64 1.50 ’
54.4 34.9 ’
1.40 1.38
60.1 25.3
1L BBS 21, BBS 3L BBS
1.72 1.62 1.60
56.1 55.1 57.7
1.64 1.55 1.52
53.1 53.4 43.7
1.41 1.39 1.38
59.0 31.4 31.6
1.58
1.2
SL METS 1L PPK SCF Cl
1.78 1.74
11.7 41.4
1.65 1.58
35.1 42.7
1.43 1.44
48.3 51.4
Slabs IL WTB 4LYL
1.62 1.61
47.7 53.3
1.56 1.51
37.6 55.2
1.48 1.41
25.1 38.3
is as follows:
(1) DH:
‘) The ES result is for Be,,HlO. Abbreviation
of the authors
Dillon and
Head from the present work; (2) BBS: Bauschlicher,
Bagus and Schaefer [9,10]; (3) METS: Marino, Ermler, Tompa and Siedl 11.51; (4) PPK: Pacchioni, Pewestorf amd Koutecky [13]; (5) WTB: Wu, Trickey and Boettger [16]; (6) YL: Yu and Lam [17]. lL, ZL, etc. indicates the number of layers in the calculation. 1M represents cluster which simulates the H monolayer coverage.
sites include: the on-top site (TS) with H vertically above a Be atom; the bridging site (BS) where H bridges 2 adjacent Be atoms; the open site (OS) where the H is on the 3-fold axis above the center of a triangle of 3 Be atoms both in the first and second layers of the Be(~l~ surface; and the eclipsed site (ES) where H is again at a 3-fold position, but with a Be directly below the H in the second surface layer. In single Be layers the OS and ES structures are equivalent. An overview of the previous H with Be calculations has already been given by Wu, Trickey and Boettger (WTB) and we only mention features relevant to the present work. Bagus, Bauschlicher and Schaeffer (BBS) have performed an extensive series of calculations with clusters composed of 3 adsorption
to 36 Be atoms and one H atom using HartreeFock and correlated treatments [9,10]. In ref. [lo], BBS report HF results for single H adsorption on a single-layer Be,, (14, O), a double-layer Be,, (14, S), and a triple-layer Be,, (14, 8, 14) cluster and conclude that such properties as H to surface bond distances and vibrations converge reasonably rapidly with cluster size, while others, such as dissociation energies converge more slowly. In the single-layer cluster, BBS find the TS to be the most stable, while in the 2 and 3 layer clusters the TS becomes the least stable relative to the OS and BS. In going from the single-layer cluster to the multi-layers the TS Be-H distance changes only slightly, whereas there is appreciable reduction of R, for the other sites. WTB report heterogeneous 2 layer slab calculations with Be one layer and H the other layer [16]. Likewise, Yu and Lam (YL) have performed calculations on a slab of 4 Be layers with 1 H layer adsorbed on either side [17]. Both sets of slab calculations use the local density functional method. The H to Be surface distance at the different sites are quite similar for the two different slab calculations. However, analogous to the BBS observations the H-to-Be binding energy differs in going from the 1 Be layer to 4 Be layer slab. It is interesting that the 4 Be layer YL binding energies mimic fairly well the 2 and 3 layer BBS results, with the TS site being less stable than the OS and BS sites. However, differences from the 3 layer BBS calculations are also evident. The 1 layer BBS TS site is the most stable contrasting sharply with the WTB result where the TS site is the most unstable. The aim of this present study is to examine whether multiple H adsorption on a cluster could result in different preferred adsorption geometries. Our result “1M’” DH, given in table 1, for the case of multiple H adsorption indeed shows different adsorption energies are obtained. We have performed calculations with one and several H atoms located at different positions on the same single-layer Be,, cluster as originally used by BBS. To enable a direct comparison with the previous BBS one, and two- and three-layer Be cluster results all calculations are performed at the Hartree-Fock level using the same minimal basis set as BBS. Even with this relatively simple ap-
f.P. Dillon, J.D. Head / Cluster model study of multiple H adsorption on Be(ikWi)
preach some of the calculations are computationally demoing owing to the lower point group symmetries resulting from the new cluster geometries investigated. In table 1 we include for comparison the results obtained by Pacchioni et al. for Be,H clusters using a (4s4p)/[2slp] valence basis at the SCF and correlated level [133. These Be,H calculations demonstrate some of the errors which should be expected when using Hartree-Fock calculations. The CI calculations give slightly larger H binding energies along with changes in the ground-state symmetry, owing to the close spacing of states, of the TS and OS wavefunction. Comparing the SCF Be,H results with BBS Be,,H results suggest the minimal basis set overestimates the H binding energy, although cluster edge effects may also be playing a role especially for the OS in Be,. However, we feel such minimal basis set Hartree-Fock calculations are useful for investigating trends to be expected for multiple H adsorption on a B~~l) monolayer. Further details on the method of calculation and the geometries of the clusters are presented in the next section. Comparison of the single H atom adsorption sites with the previous BBS calculations are given in section 3. The results of double H atom adsorption on Be,, are presented in section 4. Section 5 considers the simulation of a monolayer of H atoms on the Be,, cluster. Section 6 examines the energetics of removal of single H atoms from monolayer covered Be,,. The final section contains concluding remarks.
2. Computational procedure. The naked Be,, cluster is illustrated in fig. 1. A nearest-neighbor distance of 2.2866 A was taken from the bulk metal structure [20], and kept fixed for all clusters studied. Since Be metal is known to be non-magnetic only closed shell Hartree-Fock calculations were performed on the bare Be,, cluster. For the Be,, interacting with one or more H atoms both restricted closed and open shell calculations were performed. To keep the calculations tractable we use the minimal STO-3G basis IIb previously described by BBS [9]. BBS also list this basis set in ref. [lo] but note there is a typographi-
441
Be5
Fig. 1. Bare Be,., cluster. The Be atomic labels are used to describe the different locations of the adsorbing H atoms.
cal error. BBS selected basis IIb by minimizing the energy of a Be,, cluster while allowing the 2s and 2p orbital exponents to be different so as to facilitate a more realistic treatment of the Be2p orbitals. For small clusters BBS found the IIb basis set binding energies to be within 20% of their double-zeta basis set results [9]. Both BBS’s reported and our SCF energies for the Be and H atom are - 14.38918 and -0.48388 hartree, respectively. An important concern in any c~culation on a cluster composed of metal atoms is the determination of the correct ground state. The very nature of a metal implies there will be very many low-lying excited states thus making elucidation of the clusters ground state difficult. In all the calculations we used the charge build-up procedure recomended by BBS. We start the calculation by initially filling the Bels core orbitals in the SCF calculation. We then restarted the calculation occupying now a few of the low-energy valence molecular orbitals determined in the previous step. The gradual filling of the valence orbitals is repeated until the molecular orbitals for the neutral cluster are obtained. At this stage further SCF calculations are performed by swapping some of the higher occupied molecular orbitals with low unoccupied molecular orbitals. A different cluster energy is usually obtained when molecular orbitals belonging to different irreducible representations
442
I.P. Dillon, J.D. Head / Cluster model study of multiple H aakorption on Be(OOO1)
are interchanged. For the naked Be,, cluster we only consider closed shell configurations because the previous work of BBS indicates the open shells are associated with cluster edge effects. A brief comparison of the results from our Be,, calculations and BBS is given in the next section. The optimum H-to-Be surface distance at the different adsorption sites is determined from the minimum SCF energy obtained at different H-toBe distances. In the region of the energy minimum, the H-to-Be surface distance and SCF energy were fitted to a quadratic function to provide an accurate estimate of the optimum geometry R,. The SCF energy Escf(R,) was then recalculated at the optimum geometry and used to determine the H-to-Be,, binding energy De per H atom 0, = [ Esct(%
1 - Escr@edL)
- n&f
(H)] /n, (1)
where n is the number of H atoms in the cluster. De is positive when Be14H, is more stable than the
separate naked cluster and H atoms. All calculations were performed on a VAX 8650 computer using the HONDO program (211.
3. Be,, and single H atom adsorption Some of the difficulties in converging to the correct ground state are perhaps illustrated by the difference between the BBS and our Be cohesive energy calculated for the naked Be,, cluster. We obtain 16.04 kcal/mol versus the BBS 14.44 kcal/mol. Some of this discrepancy may be due to us finding an electronic configuration with lower total energy for Be,, although the similarity between the BBS and our single H atom binding energies, given below, suggest there may be a systematic error in the total energy calculations. The Be,, cluster has D,, point group symmetry, but with respect to the C, subgroup with the u plane pe~endi~ular to the Be,, short axis we find a ground-state wavefunction with 17a’ and lla” orbitals occupied. The Be,, ground-state configuration differs from 16a’ and 12a” expected if the Be Is2 2s2 atomic configuration is maintained, and reflects changes due to hybridization of the
Be2s and 2p orbitals. Indeed, the second-highest occupied molecular orbital is an a’ orbital consisting entirely of p, orbitals perpendicular to the Be,, plane with no s components. A similar p,, molecular orbital was found and discussed by Pacchioni et al. [13] for planar Be,, and Be,,. Table 2 presents a Mulliken population analysis and net charges for the symmetrical ineq~v~ent atoms in Be,,. The 4 central atoms, 11, 12, 13 and 14, are the Be,,‘s closest approximation to the environment of a surface like atom. The p-orbital population on each Be increases as the number of nearest neighbors increases, with the central atoms having the largest p-orbital populations. It is interesting how a large p, orbital population develops on the central Be atoms even though the cluster consists of only a single-atom layer. Thus from Be,, we can already see the Be2p orbitals playing a role in the bonding, confirming the need to use the BBS basis IIb in the calculations. The small Be net charges, also given in table 2, provide some support for using Be,, as an adequate cluster model of the Be(OOO1)surface. The calculated H atom equilibrium perpendicular distances above the Be cluster plane R, and the H binding energies De for the three different types of binding sites are given in table 3. For comparison the previous BBS results are also given in table 3. Both series of calculations give the on-top site (TS,,) as the most stable, followed by the open site (OS) and finally the bridging site (BS). We attribute the smaI1 numerical differences between the BBS and our results to using different computer programs. As noted in the introduction, BBS find the single-layer Be,, cluster to be unusual relative to the larger multi-layer clusters in Table 2 Mulliken Unique s
population Be atoms ‘)
PI! PW
analysis 7 2.957 0.984 0.035
Net charge
0.023
Number of near Be neigbbours
3
‘) Atomic
positions
for Be,4 3 2.876 1.072 0.085 -0.033 5
5 3.028 0.892 0.044 0.035 3
are given in fig. 1.
11 2.744 0.869 0.403 -0.019 6
13 2.730 0.953 0.314 0.003 6
I.P. Dillon, 3.13. Head / Chster model stu& of mtdtiple H portion Table 3 Optimized vertical distances R, and binding energies D, for a single H atom on Be,, computed by Bauschlicher, Bagus and Schaefer and the present work Site
TS,, TS,, OS BS
Present work
~u~~ch~-Bags-~haefer
R, (A)
DC(kcal/mol)
R, (A)
D, (kcal/mol)
1.40 1.40 1.11 1.18
55.4 60.1 57.2 54.4
1.40 1.11 1.17
59.0 56.1 53.1
favoring the TS adsorption site. For example in Be,, and Be,, BBS find the OS slightly more stable than the BS, which in turn is slightly more stable than the eclipsed site; all three sites are much more stable than the TS. In Be,, the OS and eclipsed sites are equivalent. We have computed the equilibrium geometry R, and binding energy
cm Rails
443
D, for H above the Be atom 13 at the TS,,. The R, for TS,, is essentially unchanged from the TS,, value but now the 0, value is between the OS and BS binding energies. The TS,, calculation gives some indication of the accuracy of R, and De value to be expected in a cluster calculation and suggests small perturbations to the cluster may alter the preferred adsorption site. Examination of the Hartree-Fock eigenvectors and eigenvalues reveal striking differences in the bonding at the different adsorption sites. The BS and OS have very similar eigenvalue spectra even though the H atom is moved 0.67 A horizontally in going from the BS to the OS. Essentially the OS and BS Hartree-Fock determinants both have the same molecular orbital occupancy and hence similar bonding. The TS12 geometry can also be obtained from the BS geometry by moving the H
Table 4 The two major H-containing molecular orbitah and M&liken population analysis for H adsorbed on Be,,
T&2
-63
OS
BS
Be,4
MO energy a)
- 0.563
- 0.563
- 0.612
- 0.601
-0.540
H s population
0.137
0.139
0.285
0.249
Nearest Be populations bt
0.216 s 12 0.089 s l&13,14
0.215 s 13 0.102 s 11,12
0.116 s 11, 12 0.136 s 13
0.145 s II, 12
MO energy ‘)
- 0.319
- 0.326
- 0.282
- 0.281
H s population
0.170
0.180
0.080
0.092
Nearest Be populations ‘)
0.212 p, 12
0.227 p,, 13
0.076 p,, 11,12 0.089 p, 13
0.100 p* II,12
Net H population
0.994
0.995
1.038
1.026
Net Be pq population b, 0.096 11 0.764 12 0.112 13 0.112 14
0.077 0.077 0.752 0.010
0.319 0.319 0.401 0.038
0.364 0.364 0.118 0.118
Net Be-H bond order b, 0.025 H-11 0.821 H-12 0.032 H-13 0.032 H-14
0.031 0.031 0.829 0.001
0.306 0.306 0.347 0.008
0.417 0.417 0.070 0.070
0.130 s 11,12 0.122 s 13,14 - 0.191
0.201 p, 11,12 0.156 p, 13,14
0.403 0.403 0.314 0.314
‘) Energy is in atomic units. b, s and p, give the orbital type and 11, 12, 13 and 14 correspond to the Be central atom numbers given in fig. 1.
444
I.P. Dillon, J. D. Head / CIuster model study of muliiple Ii adwrption
atom both 1.14 A horizontally and 0.3 A vertically. This larger displacement results in markedly different bonding for the on-top sites versus the BS and the OS. Taking into consideration the changes in cluster symmetries we also find the TS,, and TS,,, H to cluster bonding interactions to be very similar. In each of the four Be,,H clusters we find two molecular orbitals with large H orbital components. Table 4 summarizes these molecular orbitals and presents the major features of the Mull&en population and bonding analysis for the different adsorption sites. The lowest molecular orbital in the valence band for each Be,,H cluster correlates with the H orbital interacting with lowest energy level in the valence band of the naked Be,, cluster. This valence lowest energy level in the naked cluster has 50% of the electrons localized on the central 4 atoms with the remaining electrons fairly evenly distributed over the outer atoms. Table 4 shows for the Be,,H clusters that after the H interaction the Be electrons become localized closer to the position of the H atom. For this lowest valence band level both the OS and the BS have much lower orbital energies and larger H s orbital populations than for both TSs. The second molecular orbital with large H atom population occurs approximately a third of the way from the top of the Be,,H valence band and correlates with the H atom interacting with the second-crest occupied molecular orbital of the naked Be,, cluster. This Be,, orbital is entirely p,, in nature with 70% of the Be p, electron localized on the clusters central atoms. Table 4 indicates the larger H s and Be p,, populations are occurring for the TSs relative to the BS and OS, suggesting that the TS have a strong bonding with the Be p, orbital. BBS have previously argued the unusual stability for the TS,, for the Be,,H is due to formation of a sp hybrid on the Be atom 12, while in the larger Be,, and Be,, clusters the TS H binding interaction has to compete with Be atom 12 bonding to Be atoms in the cluster’s second and third layers. Our present study does not present any new evidence for this interpretation. However, it is interesting to note that for all the Be,,H clusters the H adsorption does result in a reduced net pfl population on the Be atoms 11-14 relative to the naked clusters. The
on Betel)
TSs approximately double the p, population on the Be atom nearest to the H atom relative to the naked Be,, cluster p, orbitals; while the next nearest neighbor atoms p,, populations are small. The BS and OS also show similar trends in that the Be atoms nearest to adsorbed H atom have the larger p,, populations, with the next-nearest neighbor Be atoms having smaller p, populations. Differences in the bonding are also indicated by the net charges on the H. The total Mulliken populations in table 4 show the H at TS to be essentially neutral or slightly positive while the BS and OS H are slightly negatively charged. Unfortunately the above results does not offer a simple chemical insight into why one adsorption site is to be preferred over another. From consideration of the Hartree-Fock eigenvalues for the two molecular orbitals with large H populations we conclude that the BS and the OS geometries are largely stabilized by bonding interactions with the lowest valence energy level in Be,,, while in the TS clusters the major bonding interactions occur with the Be,, p, level. Based on these observations we anticipate for those naked Be clusters which allow large H-to-Be p, interactions relative to H-to-Be s interactions to preferenti~ly adsorb hydrogen at the TS. Differences in the bonding interactions for the OS and BS are harder to distinguish. We only notice that OS lowest valence energy level is slightly below the corresponding BS level and the H s population is larger for OS. It might be argued that OS should be favored over BS because the H orbital can overlap with three Be atoms versus two for the BS site. Table 4 gives the Mu&ken bond order between H and the four central BI: atoms on the Be,, cluster. The TSs clusters have the largest single bond orders between the H and the nearest Be atom. The BS and OS clusters show lower bond orders as the H atom interacts with 2 and 3 nearest Be atoms. Summing the bond order over the nearestneighbor Be atoms gives the OS cluster the largest bond order of 0.95 versus 0.83 for BS and TS,,. We also find the bond orders between the central Be atoms on the Be,,H clusters to be reduced relative to the bond orders for the same atoms in the naked Be,, cluster. As one might expect, we also observe the optimized H to nearest Be atom
I.P. Dillon, J.D. Head / Cluster model study of multiple H ahorption on Be(OOOl,l
distance to increase with decreasing Be-H bond orders. The above discussion is somewhat lengthy, but we felt it was needed because when there are multiple H adsorbed on Be,, we find that the same basic bonding picture persists. The details of these multiple H interactions are given in the next two sections.
4. Double H atom adsorption In this section we present results for several different ~angements of 2 H atoms on the Be,, cluster. In all cases both H are placed at the same adsorption site type and we have not considered the effect of mixing sites. In finding the optimum H-to-Be surface vertical distance R, we always keep the two H atoms parallel to the surface, even in situations where because of the low Bei4H, cluster symmetry one might expect differing R, distances for the two H atoms. Table 5 summarizes the geometries for the different clusters investigated, with the “nearest Be atoms” column specifying where each H atom is located. The optimized R, and binding energies r>, per H atom along with internuclear separation between the two II atoms RH2 are also given in table 5. The OS, BS and TS clusters all have AH2 the same distance at the Be-Be nearest-neighbor separation and we regard these clusters as the two H atom
Table 5 Optimized vertical distances R, and binding energies De for two H atoms adsorbed on BeI Site
RHI (A)
R,(A)
De (kcal,/mol)
Nearest Be atoms a)
OS OS’ OS”
2.287 2.281 1.320
0.94 1.00 1.04
56.9 46.6 26.1
7-12-14 8-11-14 7-12-1411-12-13 11-12-1311-12-14
BS BS’ BS”
2.287 1.980 1.143
1.17 1.04 1.10
40.6 46.3 35.6
11-14 12-13 12-1312-14 11-1312-13
TS TS’ TS”
2.287 2.287 3.961
1.38 1.39 1.38
35.6 46.2 48.8
1112 11 13 13 14
a) Atom positions are given in fig. 1.
445
analog for the monolayer coverage of a Be surface. The H atoms in both the BS and TS clusters have newest-nei~bor Be atoms all belon~g to the 4 central atoms of the Be,, cluster, whereas the OS site has two Be,, edge atoms, 7 and 8, close to the H atoms. To test whether the edge atoms affect the OS R, and 0, we examined the OS’ cluster where there is now only one edge Be atom close to the H atom. However, the OS’ cluster has no symmetry and since this may influence the results we also performed the no symmetry TS’ calculation. Each of these BS, OS’ and TS’ clusters are related to each other by horizontal translations of the two H atoms in much the same manner as for the single H atom clusters discussed in the previous section. Unfortunately the OS’ and TS’ results do not enable a clear distinction between the role of symmetry or edge atoms in computing the preferred adsorbate site. The 0, values suggest that two H atoms at OS is the most stable geometry followed by the BS and TS both being close in stability. The Be,,H, De energy separation between the OS and other two sites is larger than obtained in the single H atom clusters and is more in line with BBS Be, and Be,, results and WTB’s slab calculations. The De per H atom is generally reduced for the two H atom cluster relatively to the single H atom adsorption case indicating that perhaps the two H atoms are now sharing bonding electrons from the Be; for clusters with even more H atoms we should anticipate further reduction in the D, per H atom and we find this to be the case as shown below. The Bet4H, R, distance for the OS is reduced by 0.17 A from the single H atom cluster value and has an R, equal to the BBS Bezz result. The Be,,H, TS R, decreases slightly, BBS find the TS R, to change the least with Be cluster size. The Be,,H, BS R, also only changes slightly, although the BS R, varies dramatically with the R H2 distance while BBS find the BS R, ‘to decrease with increasing cluster size. The molecular orbitals for Be,,H, exhibit very similar bonding interactions to the Be,,H clusters, only now the number of molecular orbitals with large H components are essentially doubled. For example, the OS cluster has two energy levels at the bottom of the Be,,H, valence band with large H s orbital populations. In the lowest level, the
446
I.P. Dillon, J. D. Head / Cluster model study of multiple H adsorption on Be(OOO1)
two H s otbitals are in phase and have a bonding u overlap, and this orbital correlates with a H, u orbital interacting with the lowest valence Be,, molecular orbital. The second level has the two H s orbitals out of phase with an anti-bonding cr* overlap and correlates with a valence Be,, molecular orbital at higher energy which also contains some Be p, character. Essentially the same pair of molecular orbitals with H-to-Be interactions also occur for the OS’ and BS clusters. The sum of the H populations for both of the u and u* orbitals are much larger than single H orbital population in the corresponding Be,,H clusters. Whilst the bonding between H and Be,, in OS and BS remains basically unchanged from the Be,,H clusters, the H 0, value is significantly reduced for the BS geometry. We can only attribute the extra stability of the OS to the larger differences between the OS and BS two lowest valence band eigenvalues than obtained in the Be,,H cluster. In the TS clusters the low-lying H, u and u* also occur at the bottom of the Be,,H, valence band but now the H populations are much smaller than for the OS and BS geometries. Analogous to the Be,,H cluster the Be,,H, TS H atoms interact with a Be,, p, orbital only now this interaction is spread over two molecular orbitals with H, u and u * components giving a total H population approximately the same as in the single-atom TS cluster. It is interesting to notice the net H populations for the Be,,H, clusters OS, OS’, BS and TS are very close to values for the corresponding Be,,H clusters and this again illustrates the small changes
in bonding features for the two types of clusters. The net p, population on the Be,, central atoms show some variation from the single H atom adsorption but this can be traced to some of the Be atoms now being coordinated by two H atoms. The bond orders between H and the central Be atoms in Be,,H, are essentially identical with the Be,,H values. Caution is always needed when comparing extended and cluster calculations because clusters with single H atoms do not include the H-H interactions which are automatically included in the extended systems. Obviously some H-H interaction must be taking place in the Be,,H, clusters or else the R, and L$ would be the same as for the Be,,H clusters. However, we find no evidence for a direct interaction in the Be,,H, clusters when RH, = 2.287 A if one uses the H-H bond order, listed in table 6, as a guide. Decomposing the Be,,H, net H orbital population into u and u* con~butions we find the H orbital populations split equally between the two symmetry types for the OS and BS geometries while the TS H population is 56% u symmetry. This slightly larger H u population for TS may be a result of some indirect H-H interactions via the Be surface atoms taking place. However, any socalled “H-H indirect interaction” may simply be a reflection of the two H atoms competing for the same bonding electrons from the Be. An altemative perspective is that the Be surface is weakening the H-H interactions. By performing a two-configuration MCSCF calculation on an isolated H, with internuclear separation of the Be-Be nearest-neighbor distance we find 66% of the H,
Table 6 Mulliken population and bond-order analysis for two H atoms adsorbed on Be,, OS
OS’
OS”
BS
BS’
BS”
TS
TS’
TS”
Net H population
1.066
1.046, 1.049
0.973
1.027
1.036
0.985
0.969
0.999,0.993
0.997
Net central Be p,, 11 12 13 14
0.269 0.269 0.024 0.533
0.478 0.284 0.311 0.261
0.345 0.345 0.167 0.167
0.357 0.357 0.467 0.467
0.136 0.614 0.323 0.323
0.262 0.262 0.262 0.019
0.649 0.649 0.084 0.084
0.753 0.103 0.793 0.144
0.069 0.069 0.792 0.792
H-H bond order
0.000
0.000
0.125
0.001
0.0203
0.191
0.000
0.001
0.001
I.P. Dillon, J.D. Head / Chter
model study of multiple H aakorption on Be(OOO1)
electrons in the a2 configuration and a binding of 4.7 kcal/mol relative to the two separate H atoms. In table 6 we have also included some Be,,H, clusters with RH, different from the Be-Be nearest-neighbor distances. For example, the clusters OS”, BS’ and BS” all have RH, shorter than 2.287 A. The bonding in these Be,,H, clusters still resembles the OS and BS clusters except now the two H atoms are close enough to interact with each other. Thus in table 6 the energy splitting between the two lowest Be,,H, valence band molecular orbitals, with large H (I and u * components, are greater for the OS” and BS” relative to the OS and BS. We also find larger percentage H (I populations of 68%, 52% and 72% for OS”, BS’ and BS”, respectively, and these populations correlate with the H-H bond orders given in table 6. As one might expect table 5 shows the H-to-Be,, binding energies De per H atom generally decrease with increasing H-H interactions. This illustrates there is a large barrier preventing recombination of two H atoms adsorbed on the surface, although the BS’ De value suggests the possibility that a small H-H interaction may initially be favorable in H adsorption. The TS” cluster has the two H atoms well separated and might be expected to approximate two independent H atoms on the Be surface. Indeed as the TS” molecular orbitals with large H components are much closer in energy than in the TS and TS’ clusters. However, the TS” cluster does have a small non-zero H-H bond order suggesting some H-H interaction is taking place. The TS” H binding energy De is also 11 kcal/mol smaller than the Be,,H TS,, De and we must conclude the Be,, cluster is simply not large enough to allow the computation of binding energies for two independent non-interacting H atoms. Thus in this section we have demonstrated that the interaction between two H atoms adsorbed on a cluster does influence the stability of different adsorption sites. The final geometry, however, as in the clusters with a single H atom, is still a result of a balance between two effects; H bonding with the Be s orbitals or H bonding with the Be p, orbitals. In the Be,, cluster the largest binding energy De is obtained when the two H atoms are adsorbed at the open sites.
447
5. H monolayer adsorption
The clusters used to model a monolayer of H atoms adsorbed on the Be,, cluster are shown in fig. 2. We define the monolayer of H atoms to be a planar cluster of H atoms held at the Be-Be internuclear separation with close to one H atom per Be atom. In the on-top cluster TS,, there are an equal number of Be and H atoms. To avoid H atoms being outside the Be,, cluster boundary we model the H monolayer for the other clusters with less than 14 H atoms, so that for open-site monolayer OS, there are 8 H atoms, while for the bridging-site clusters there are two possible arrangements of the H atoms to give the BS, and BS,, clusters composed of 9 and 10 H atoms, respectively. An important feature of these clusters is that now the H atoms at the center of the cluster have the same nearest-neighbor environment as an H atom in an extended calculation. Table 7 summarizes the optimized vertical distances R, for the H atom above the Be,, plane. This R, value has been computed from the minimum of the total Hartree-Fock energy for parallel planes of the H monolayer and Be,,. An important concern is whether the Hartree-Fock
Fig. 2. Clusters used to simulate the monolayer coverage of H atoms: (a) on-top TS,,; (b) bridging B$; (c) bridging BS,,; (d) open 3-fold OSs.
448
I. P. Dillon, J. D. Head / Cluster model study of multiple H adsorption on Be(0001)
energy is dominated by interactions between the cluster edge H and edge Be atoms. To check this, once we had determined the R, value, we reoptimized the H-to-Be distance for those H atoms above the central 11-14 Be atoms and found, somewhat surprisingly, no change in the H-to-Be distance. It should be no surprise that the T&, R, value is 1.38 A when one considers the results for the TS Be,,H and Be,,H* clusters. On the other hand, the R, for OS,, BS, and BS,e are reduced significantly from the single and double H atom clusters. Consistency amongst the different cluster calculations is suggested by the similar R, for the BS, and BS,, clusters. The H binding energies De for the monolayer clusters are, as expected, reduced relative to the 0, for Be,,H and Be,,H, clusters. However, it is interesting that now in these monolayer calculations the OS and BS geometries are difficult to distinguish in stability and that both structural types are appreciably more stable than the TS geometry. Apart from WTB finding the OS geometry to be 10 kcal/mol more stable than the BS, our monolayer R, and D, values are also in reasonable agreement with the WTB slab calculations. This suggests cluster and slab calculation will give comparable results providing the same adsorbate coverage is used. The monolayer BeH distances in both the OS and BS clusters are reduced by over 0.1 A from the geometry obtained with the Be,,H clusters. These monolayer BeH distances are also slightly shorter than the WTB monolayer results but are close to the 4 layer YL slab values and the 2 and 3 layer BBS bond length. The bonding picture for these H monolayer clusters can still be described in terms of the bonding interactions used for the Be,,H and Be,,H, clusters. Thus the OS and BS clusters still have H atoms interacting with Be s orbitals at the bottom of the valence band with little H-to-Be p, interaction, while the TS monolayer prefers the H-to-Be p, interaction. The difference between the OS and the BS interaction versus the TS interaction is also evident from the valence molecular orbital energies computed for Be,, and the monolayer clusters. The H-to-Be interactions for the OS and BS clusters result in the Be,, valence band splitting into two parts. The lower part con-
tains the molecular orbitals where the H electrons bind with the Be s electrons and consists of one molecular orbital for each H atom in the cluster. The OS, cluster is found to have the largest valence band splitting perhaps suggesting the OS geometry should have the lowest energy; however, because the BS, and BS,, clusters contain more H atoms than the OS, cluster we may be obtaining larger De for the BS geometries even though the Q is calculated as a per H atom quantity. The larger De value for BS,, versus BS, may also reflect the difficulty with the 0, equation. The splitting for the TS,, valence band is much smaller than for the other clusters and the lower half of the valence band consists of only eight molecular orbitals as expected if H s to Be p, interactions become important. The Mulliken populations for the monolayer clusters are consistent with the results from the Be,,H and Be,,H, clusters. The net H atom populations, given in table 7, show the same trends as obtained previously with the OS and BS H atoms being slightly negatively charged and the TS H atoms being slightly positive. However, the OS and BS net Be p_ populations are somewhat larger than in the corresponding Be,,H and Be,,H, clusters, but this must be due to the H monolayer being able to more effectively polarize the Be atoms. In the TS,, cluster the Be p,, population is reduced relatively to the single and double H atom clusters reflecting the competition between H atoms to attract Be p, electrons. It is interesting to note that the bond order for an H atom above a Be atom is still 0.82 and unchanged from the Be,,H value. Summarizing, the bonding picture for a H monolayer on the Be,, cluster is basically unchanged from the clusters containing only one or two H atoms. The BS,, cluster is found to give the largest De but the closeness of the OS De prevents a firm conclusion on the preferred structure.
6. H atom removal clusters
from H monolayer
covered
In the previous section we used clusters model the H atom monolayer coverage regime
to of
I.P. Dillon, J.D. Head / Cluster model siu& of multiple H adsorption on 3eQWO~)
449
Table 7 Optimized vertical distance R,, binding energies D,, and M&liken population analysis for H monolayers on Bell Site R,
BS9 1.02 31.7
BS,, 0.99 34.9
0.989 11-12 1.043 5-12 1.022 3-13 1.078 1-2
1.009 12-13 1.035 7-12 1.073 2-13 1.046 1-3 1.051 3-5
OS,
ch
0.90
0, (kcal/mol)
32.4
Net H population a>
1.053 1.057 1.075 1.015
Net central Be pw population 11 12 13 14
11-12-13 1-3-13 3-5-12 7-12-14
0.558 0.558 0.433 0.623
0.595 0.595 0.572 0.572
34
1.38 25.1 0.928 11,12 0.923 13, 14 0.964 1,2,9, 10 0.960 3,4, 7, 8 0.956 5,6
0.581 0.581 0.506 0.506
0.611 0.611 0.641 0.641
‘) H positions are referenced to the nearest-neighbor Be atom numbers given in fig. 1.
surface. We define the desorption removal of a single H atom by
the Be(OO01) surface. In this section we go one stage further and use clusters to compute the desorption energy of a single H atom from the surface monolayer. This calculation is very simple to perform using a cluster model. The limitations on the allowed unit cell size prevent a similar calculation being performed using slab models. To calculate the desorption energy we start with the optimum monolayer described in the previous section and remove a single H atom from one of the positions above the central Be atoms, 11, 12, 13 and 14, on Be,, and recalculate the cluster total SCF energy. We choose a H above a central Be cluster atom and simulate the removal of a H atom which has the same number of Be and H nearest neighbors as on the extended monolayer
Edes = EBe,,H,_,
+ EH -
= nl),(Be,,H,)
-
energy for the
EBe,,H, (n
-
(24
1)Q+(Be14%,-l), cw
where n is the number of H atoms on the Be14Hn cluster. Edes should not be confused with the energy needed to desorb H,. Ekl. (2a) shows Edes to be positive when Bei4H, is more stable than the separate Bei4H,_i cluster and H atom, while eq. (2b) indicates how Edes is related to the H binding energy De on the different clusters. The E des values are presented in table 8 along with binding energies De for the n H atom monolayers
Table 8 Binding energies D, and desorption energies Edes for H monolayers on Be,, N
TS,, (13) ‘)
Site
OS,
=9
BSIO
0, (kcal/mol) BeI& Be@,-1
32.4 35.1
31.7 33.0
34.9 36.7
25.1 28.2
25.1 28.3
13.3
21.4
18.6
- 15.8
- 16.6
7314
(12)
Edes (kcal/mol)
a) The number in parentheses indicates the Be atom from above which the H was removed.
450
I.P. Dillon, J. D. Head / Clmter model study of multiple H adsorption on Be(0001)
and n - 1 H atom clusters, in all calculations the optimum monolayer H-to-Be surface distance has been kept at their values listed in table 7. It is interesting how all the Be14Hn_i De’s have increased from there corresponding Bei4H, values. This is not really surprising because the H surface coverage is being reduced when the H atom desorbs resulting in stronger Be-to-H adsorbate interactions, essentially in the same manner as the reduction in De was found in going from Be,,H to Be,,H,. Again like the monolayer calculations, the De for the (n - 1) H atom cluster suggest close stability for both the BS and OS structures while the TS is considerably less stable. are very striking, not only by their The &es range of values, but also because they are very different from the average H binding energy De. The two BS clusters have an average Ed_ of 20 kcal/mol. This is the energy needed to remove a single H atom from the BS monolayer. In contrast, the TS monolayer with negative Ed_ is more stable after desorbing H suggesting the TS structure can never be formed. Finally the OS Ed_ is positive but much smaller than the BS value. Some of this difference between the Ed_ for the OS and BS sites might be due to the OS monolayer having only 8 H atoms although Edes reduces on going from BS, to BS,,. The Edes represent also an estimate of the energy gain for adsorbing a single H on a partly covered surface. More energy is to be gained by adsorbing at a BS implying a BS monolayer would be formed even though the binding energies De indicate little energetic difference between the OS and BS structures. In many of the calculations listed in table 1, especially those of YL and our monolayer results, the De values for the OS and BS are sufficiently close to imply that both structures could occur as different domains on the Be(OOO1) surface. Thus in a TDS experiment, two major peaks might be observed, the low-temperature peak coming from the OS structure, at higher temperatures the BS domain would start to desorb. Ray and Plummer only report peaks occurring at about 450 K in their TDS experiments [19]. However, we make the above comments with reservations because upon going to larger multi-layered clusters changes in the Edes should be expected.
7. Conclusion We have examined using cluster models different adsorbate coverages on surfaces. We find slab and cluster calculations to be generally consistent with each other providing the substrate is modeled by the same number of surface layers and the adsorbate coverages are similar. For the Be,, cluster the binding energies De decrease with increasing H coverage indicating interactions between the H atoms do occur although the essentially zero H-H bond orders suggest an indirect mechanism. The type of H-to-Be bonding varies only slightly with surface coverage. At the open 3-fold (OS) and bridging (BS) sites the H atoms largely bond with Be2s orbitals at the bottom of the valence band. While at the on-top (TS) site the H interacts mostly with the Be p, orbitals. Thus the bonding of H with Be(OOO1) could simply be modeled by a cluster corresponding to low surface coverage. In other systems the chemisorption bond may be more sensitive to the surface coverage and this needs to be investigated further using cluster calculations. The average H binding energies De from the clusters simulating a H monolayer surface coverage predict the OS and BS structures to be close in energy. However, by computing the single H atom desorption energy Edes from the monolayer we predict the BS structure to be the most resistant to desorbing a H atom. This work demonstrates another strong advantage of using cluster models in that Ed_ is a straightforward calculation. A similar calculation of Edes is not possible using a slab model.
Acknowledgements We are grateful to the University of Hawaii Computer Center for providing the facilities which enabled us to perform these calculations. We also appreciate the preprint of ref. [16] from J. Wu, S.B. Trickey and J.C. Boettger. References [l] J. Sauer, Chem. Rev. 89 (1989) 199. [2] J. Koutecky and P. Fantucci, Chem. Rev. 86 (1986) 539.
I.P. Dillon, J.D. Head / Cluster model sturdy of multiple H Aotption [3] G.M. Zhidomirov
[4] [5]
[6] [7]
[8]
[9]
and V.B. Kazansky, Adv. Catal. 34 (1986) 131. M.L. Cohen and S.G. Louie, Amm. Rev. Phys. Chem. 35 (1984) 537. C. Pisani and R. Dovesi, Int. J. Quantum Chem. 17 (1980) 501; C. Pisani and R. Dovesi, Theor. Chim. Acta 72 (1987) 277; C. Pisani, R. Dovesi and C. Roetti, in: Hartree-Fock Ab Initio Treatment of Crystalhne Systems, Vol. 48 of Lecture Notes in Chemistry (Springer, Heidelberg, 1988). J.C. Boettger and S.B. T&key, J. Phys. F (Met. Phys.) 16 (1986) 693. M.-H. Whangbo and R. Hoffmann, J. Am. Chem. Sot. 100 (1978) 6093; M.-H. Whangbo, R. Hoffmann and R.B. Woodward, Proc. R. Sot. London A 366 (1979) 23; R. Hoffmann, Angew. Chem. Int. Ed. EngI. 26 (1987) 846; R. Hoffmann, Rev. Mod. Phys. 60 (1988) 601. R.B. Ross, W.C. ErmIer, R.M. Pitzer and C.W. Kern, Chem. Phys. Lett. 134 (1987) 115; W.C. ErmIer, R.B. Ross, C.W. Kern, R.M. Pitzer and N.W. Winter, J. Phys. Chem. 92 (1988) 3042. C.W. Bauschlicher, Jr., P.S. Bagus and H.F. Schaeffer III, IBM J. Res. Dev. 22 (1978) 213.
on Be(ObO1)
451
[lo] P.S. Bagus, H.F. Schaeffer and C.W. Bauschlicher, Jr., J. Chem. Phys. 78 (1983) 1390. [ll] B.N. Cox and C.W. Bauschlicher, Jr., Surf. Sci. 102 (1981) 295. [12] C.W. Bauschlicher, Jr. and P.S. Bagus, Chem. Phys. Lett. 90 (1982) 355. [13] G. Pacchioni, W. Pewestorf and J. Koutecky, Chem. Phys. 83 (1984) 261. [14] J. Rubio, F. IlIas and J.M. Ricart, J. Chem. Phys. 84 (1986) 3311. [15] M.M. Marino, W.C. ErmIer, G.S. Tompa and M. Seidl, Surf. Sci. 208 (1989) 189. [16] J.Z. Wu, S.B. Trickey and J.C. Boettger, Phys. Rev. B 42 (1990) 1633. [17] R. Yu and P.K. Lam, Phys. Rev. B 39 (1989) 5035. [18] G. Angonoa, J. Koutecky, A.N. Ermoshkin and C. Pisani, Surf. Sci. 138 (1984) 51. [19] K.B. Ray and E.W. Plummer, Bull. Am. Phys. Sot. 33 (1988) 655. [20] J. Donohue, T’he structure bf the Elements (Wiley, New York, 1974). [21] HONDO, M. Dupuis, J.D. Watts, H.O. Vi&r and G.J.B. Hurst, Version 7.0, IBM, Scientific and Engineering Computations, Kingston, NY, 1987.
439
A cluster model study of multiple H adsorption
on Be(OOO1)
Ian P. Dillon and John D. Head Department
of Chemistry,
University of Hawaii, Honolulu, HI 96822, USA
Received 15 August 1990; accepted for publication 14 November 1990
The different results obtained from slab and cluster ~culations are compared. In the clusters we model various H coverages on the Be(0001) surface using a single-layer Be,, cluster interacting with different numbers of H atoms. With a single H atom the on-top structure is the most stable. Two H atoms are computed to preferentially adsorb at an open site above 3 Be atoms. Caution always needs to be exercised when comparing slab and cluster calculations owing to the different adsorbate coverages being modelled. However, by increasing the number of H atoms in the cluster to simulate a monolayer of H atoms on the Be@OO1)surface we obtain results similar to slab calculations with the open and bridging structures close in energy and the on-top structure being least stable. These calculations with H monolayer coverage are noteworthy because they also enable the definition of a desorption energy Eda corresponding to the energy of removal for a single H atom from the monolayer. Edcs differs in value from the average H binding energy D, often used to evaluate the stability of different adsorbate structures on a surface. By using Ed._, an explanation for the experimentally observed bridging structure for H on the Be@OO1)surface is suggested. A similar computation of Ed_ is not possible in a slab calculation owing to limitations on the allowed unit cell size.
Theoretical studies of the electronic properties of adsorbates interacting with surfaces typically make use of either cluster models and the techniques of quantum chemistry [l-3], or extended two-dimensional slabs and the techniques of solid-state physics [4-71. Both procedures have strong advantages. Cluster models, for example, allow in principle, the treatment of low symmetry features such as those which must occur in a chemical reaction. On the other hand, slab calculations facilitate the analysis of ordered adsorbate overlayers. The range of application of both methods is largely determined by the available computer power. An important concern in a cluster calculation is the size of the cluster needed to circumvent edge effects. Choosing a large cluster with high symmetry is one common trick for easing the computational requirements [8]. Similarly, the slab calculations are restricted to considering relatively high overlayer coverages, where the lowest surface coverage treated is determined by the largest unit cell dimension tractable in the 0039-6028/91/$03.50
calculation. Thus, the high s~et~ clusters often treat only a single adsorbing species, while slabs model the intermediate and high coverage regimes of chemisorption. Furthermore, the extended slab c~c~ations automatic~ly include adsorbate-adsorbate interactions which are absent in the lowcoverage cluster calculations. Caution should be used when comparing the results from the two different methods. There is, however, no inherent restriction on the cluster model to prevent multiple adsorption studies. It is this difference in surface coverage modeled by cluster and slab calculations which we consider here. We use cluster models to examine multiple H adsorption on the Be(OO01) surface. There have been a number of cluster Es-151 and slab [16-U] calculations reported previously and a summary of the various results are given in table 1. Many of these calculations were performed before the recent experimental data, which finds the bridge site to be preferred at sub-monolayer coverage [19], became available. Table 1 show the calculations to predict many differing stable geometries for the chemisorbed H. The possible different H atom
0 1991 - Elsevier Science Publishers KY. (North-Holland)
I.P. DiNon, J.D. Head / Cluster model stu& of mulripleH adsorption on Be(OtWij
440
Table 1 Comparison of theoretical Be-H bond distance, RaeH, binding energy, DC, from cluster and slab calculations Authors
Adsorption
and
site type
OS
BS ‘)
TS
R BcH
9
Reek
4
G‘%
W4’
(A,
fkcW
mol)
R BeH s (4
mol)
0,
(kcal/ mol)
Cb4ster.s 1LDH 1MDH
1.72 1.59
57.2 32.4
1.64 1.50 ’
54.4 34.9 ’
1.40 1.38
60.1 25.3
1L BBS 21, BBS 3L BBS
1.72 1.62 1.60
56.1 55.1 57.7
1.64 1.55 1.52
53.1 53.4 43.7
1.41 1.39 1.38
59.0 31.4 31.6
1.58
1.2
SL METS 1L PPK SCF Cl
1.78 1.74
11.7 41.4
1.65 1.58
35.1 42.7
1.43 1.44
48.3 51.4
Slabs IL WTB 4LYL
1.62 1.61
47.7 53.3
1.56 1.51
37.6 55.2
1.48 1.41
25.1 38.3
is as follows:
(1) DH:
‘) The ES result is for Be,,HlO. Abbreviation
of the authors
Dillon and
Head from the present work; (2) BBS: Bauschlicher,
Bagus and Schaefer [9,10]; (3) METS: Marino, Ermler, Tompa and Siedl 11.51; (4) PPK: Pacchioni, Pewestorf amd Koutecky [13]; (5) WTB: Wu, Trickey and Boettger [16]; (6) YL: Yu and Lam [17]. lL, ZL, etc. indicates the number of layers in the calculation. 1M represents cluster which simulates the H monolayer coverage.
sites include: the on-top site (TS) with H vertically above a Be atom; the bridging site (BS) where H bridges 2 adjacent Be atoms; the open site (OS) where the H is on the 3-fold axis above the center of a triangle of 3 Be atoms both in the first and second layers of the Be(~l~ surface; and the eclipsed site (ES) where H is again at a 3-fold position, but with a Be directly below the H in the second surface layer. In single Be layers the OS and ES structures are equivalent. An overview of the previous H with Be calculations has already been given by Wu, Trickey and Boettger (WTB) and we only mention features relevant to the present work. Bagus, Bauschlicher and Schaeffer (BBS) have performed an extensive series of calculations with clusters composed of 3 adsorption
to 36 Be atoms and one H atom using HartreeFock and correlated treatments [9,10]. In ref. [lo], BBS report HF results for single H adsorption on a single-layer Be,, (14, O), a double-layer Be,, (14, S), and a triple-layer Be,, (14, 8, 14) cluster and conclude that such properties as H to surface bond distances and vibrations converge reasonably rapidly with cluster size, while others, such as dissociation energies converge more slowly. In the single-layer cluster, BBS find the TS to be the most stable, while in the 2 and 3 layer clusters the TS becomes the least stable relative to the OS and BS. In going from the single-layer cluster to the multi-layers the TS Be-H distance changes only slightly, whereas there is appreciable reduction of R, for the other sites. WTB report heterogeneous 2 layer slab calculations with Be one layer and H the other layer [16]. Likewise, Yu and Lam (YL) have performed calculations on a slab of 4 Be layers with 1 H layer adsorbed on either side [17]. Both sets of slab calculations use the local density functional method. The H to Be surface distance at the different sites are quite similar for the two different slab calculations. However, analogous to the BBS observations the H-to-Be binding energy differs in going from the 1 Be layer to 4 Be layer slab. It is interesting that the 4 Be layer YL binding energies mimic fairly well the 2 and 3 layer BBS results, with the TS site being less stable than the OS and BS sites. However, differences from the 3 layer BBS calculations are also evident. The 1 layer BBS TS site is the most stable contrasting sharply with the WTB result where the TS site is the most unstable. The aim of this present study is to examine whether multiple H adsorption on a cluster could result in different preferred adsorption geometries. Our result “1M’” DH, given in table 1, for the case of multiple H adsorption indeed shows different adsorption energies are obtained. We have performed calculations with one and several H atoms located at different positions on the same single-layer Be,, cluster as originally used by BBS. To enable a direct comparison with the previous BBS one, and two- and three-layer Be cluster results all calculations are performed at the Hartree-Fock level using the same minimal basis set as BBS. Even with this relatively simple ap-
f.P. Dillon, J.D. Head / Cluster model study of multiple H adsorption on Be(ikWi)
preach some of the calculations are computationally demoing owing to the lower point group symmetries resulting from the new cluster geometries investigated. In table 1 we include for comparison the results obtained by Pacchioni et al. for Be,H clusters using a (4s4p)/[2slp] valence basis at the SCF and correlated level [133. These Be,H calculations demonstrate some of the errors which should be expected when using Hartree-Fock calculations. The CI calculations give slightly larger H binding energies along with changes in the ground-state symmetry, owing to the close spacing of states, of the TS and OS wavefunction. Comparing the SCF Be,H results with BBS Be,,H results suggest the minimal basis set overestimates the H binding energy, although cluster edge effects may also be playing a role especially for the OS in Be,. However, we feel such minimal basis set Hartree-Fock calculations are useful for investigating trends to be expected for multiple H adsorption on a B~~l) monolayer. Further details on the method of calculation and the geometries of the clusters are presented in the next section. Comparison of the single H atom adsorption sites with the previous BBS calculations are given in section 3. The results of double H atom adsorption on Be,, are presented in section 4. Section 5 considers the simulation of a monolayer of H atoms on the Be,, cluster. Section 6 examines the energetics of removal of single H atoms from monolayer covered Be,,. The final section contains concluding remarks.
2. Computational procedure. The naked Be,, cluster is illustrated in fig. 1. A nearest-neighbor distance of 2.2866 A was taken from the bulk metal structure [20], and kept fixed for all clusters studied. Since Be metal is known to be non-magnetic only closed shell Hartree-Fock calculations were performed on the bare Be,, cluster. For the Be,, interacting with one or more H atoms both restricted closed and open shell calculations were performed. To keep the calculations tractable we use the minimal STO-3G basis IIb previously described by BBS [9]. BBS also list this basis set in ref. [lo] but note there is a typographi-
441
Be5
Fig. 1. Bare Be,., cluster. The Be atomic labels are used to describe the different locations of the adsorbing H atoms.
cal error. BBS selected basis IIb by minimizing the energy of a Be,, cluster while allowing the 2s and 2p orbital exponents to be different so as to facilitate a more realistic treatment of the Be2p orbitals. For small clusters BBS found the IIb basis set binding energies to be within 20% of their double-zeta basis set results [9]. Both BBS’s reported and our SCF energies for the Be and H atom are - 14.38918 and -0.48388 hartree, respectively. An important concern in any c~culation on a cluster composed of metal atoms is the determination of the correct ground state. The very nature of a metal implies there will be very many low-lying excited states thus making elucidation of the clusters ground state difficult. In all the calculations we used the charge build-up procedure recomended by BBS. We start the calculation by initially filling the Bels core orbitals in the SCF calculation. We then restarted the calculation occupying now a few of the low-energy valence molecular orbitals determined in the previous step. The gradual filling of the valence orbitals is repeated until the molecular orbitals for the neutral cluster are obtained. At this stage further SCF calculations are performed by swapping some of the higher occupied molecular orbitals with low unoccupied molecular orbitals. A different cluster energy is usually obtained when molecular orbitals belonging to different irreducible representations
442
I.P. Dillon, J.D. Head / Cluster model study of multiple H aakorption on Be(OOO1)
are interchanged. For the naked Be,, cluster we only consider closed shell configurations because the previous work of BBS indicates the open shells are associated with cluster edge effects. A brief comparison of the results from our Be,, calculations and BBS is given in the next section. The optimum H-to-Be surface distance at the different adsorption sites is determined from the minimum SCF energy obtained at different H-toBe distances. In the region of the energy minimum, the H-to-Be surface distance and SCF energy were fitted to a quadratic function to provide an accurate estimate of the optimum geometry R,. The SCF energy Escf(R,) was then recalculated at the optimum geometry and used to determine the H-to-Be,, binding energy De per H atom 0, = [ Esct(%
1 - Escr@edL)
- n&f
(H)] /n, (1)
where n is the number of H atoms in the cluster. De is positive when Be14H, is more stable than the
separate naked cluster and H atoms. All calculations were performed on a VAX 8650 computer using the HONDO program (211.
3. Be,, and single H atom adsorption Some of the difficulties in converging to the correct ground state are perhaps illustrated by the difference between the BBS and our Be cohesive energy calculated for the naked Be,, cluster. We obtain 16.04 kcal/mol versus the BBS 14.44 kcal/mol. Some of this discrepancy may be due to us finding an electronic configuration with lower total energy for Be,, although the similarity between the BBS and our single H atom binding energies, given below, suggest there may be a systematic error in the total energy calculations. The Be,, cluster has D,, point group symmetry, but with respect to the C, subgroup with the u plane pe~endi~ular to the Be,, short axis we find a ground-state wavefunction with 17a’ and lla” orbitals occupied. The Be,, ground-state configuration differs from 16a’ and 12a” expected if the Be Is2 2s2 atomic configuration is maintained, and reflects changes due to hybridization of the
Be2s and 2p orbitals. Indeed, the second-highest occupied molecular orbital is an a’ orbital consisting entirely of p, orbitals perpendicular to the Be,, plane with no s components. A similar p,, molecular orbital was found and discussed by Pacchioni et al. [13] for planar Be,, and Be,,. Table 2 presents a Mulliken population analysis and net charges for the symmetrical ineq~v~ent atoms in Be,,. The 4 central atoms, 11, 12, 13 and 14, are the Be,,‘s closest approximation to the environment of a surface like atom. The p-orbital population on each Be increases as the number of nearest neighbors increases, with the central atoms having the largest p-orbital populations. It is interesting how a large p, orbital population develops on the central Be atoms even though the cluster consists of only a single-atom layer. Thus from Be,, we can already see the Be2p orbitals playing a role in the bonding, confirming the need to use the BBS basis IIb in the calculations. The small Be net charges, also given in table 2, provide some support for using Be,, as an adequate cluster model of the Be(OOO1)surface. The calculated H atom equilibrium perpendicular distances above the Be cluster plane R, and the H binding energies De for the three different types of binding sites are given in table 3. For comparison the previous BBS results are also given in table 3. Both series of calculations give the on-top site (TS,,) as the most stable, followed by the open site (OS) and finally the bridging site (BS). We attribute the smaI1 numerical differences between the BBS and our results to using different computer programs. As noted in the introduction, BBS find the single-layer Be,, cluster to be unusual relative to the larger multi-layer clusters in Table 2 Mulliken Unique s
population Be atoms ‘)
PI! PW
analysis 7 2.957 0.984 0.035
Net charge
0.023
Number of near Be neigbbours
3
‘) Atomic
positions
for Be,4 3 2.876 1.072 0.085 -0.033 5
5 3.028 0.892 0.044 0.035 3
are given in fig. 1.
11 2.744 0.869 0.403 -0.019 6
13 2.730 0.953 0.314 0.003 6
I.P. Dillon, 3.13. Head / Chster model stu& of mtdtiple H portion Table 3 Optimized vertical distances R, and binding energies D, for a single H atom on Be,, computed by Bauschlicher, Bagus and Schaefer and the present work Site
TS,, TS,, OS BS
Present work
~u~~ch~-Bags-~haefer
R, (A)
DC(kcal/mol)
R, (A)
D, (kcal/mol)
1.40 1.40 1.11 1.18
55.4 60.1 57.2 54.4
1.40 1.11 1.17
59.0 56.1 53.1
favoring the TS adsorption site. For example in Be,, and Be,, BBS find the OS slightly more stable than the BS, which in turn is slightly more stable than the eclipsed site; all three sites are much more stable than the TS. In Be,, the OS and eclipsed sites are equivalent. We have computed the equilibrium geometry R, and binding energy
cm Rails
443
D, for H above the Be atom 13 at the TS,,. The R, for TS,, is essentially unchanged from the TS,, value but now the 0, value is between the OS and BS binding energies. The TS,, calculation gives some indication of the accuracy of R, and De value to be expected in a cluster calculation and suggests small perturbations to the cluster may alter the preferred adsorption site. Examination of the Hartree-Fock eigenvectors and eigenvalues reveal striking differences in the bonding at the different adsorption sites. The BS and OS have very similar eigenvalue spectra even though the H atom is moved 0.67 A horizontally in going from the BS to the OS. Essentially the OS and BS Hartree-Fock determinants both have the same molecular orbital occupancy and hence similar bonding. The TS12 geometry can also be obtained from the BS geometry by moving the H
Table 4 The two major H-containing molecular orbitah and M&liken population analysis for H adsorbed on Be,,
T&2
-63
OS
BS
Be,4
MO energy a)
- 0.563
- 0.563
- 0.612
- 0.601
-0.540
H s population
0.137
0.139
0.285
0.249
Nearest Be populations bt
0.216 s 12 0.089 s l&13,14
0.215 s 13 0.102 s 11,12
0.116 s 11, 12 0.136 s 13
0.145 s II, 12
MO energy ‘)
- 0.319
- 0.326
- 0.282
- 0.281
H s population
0.170
0.180
0.080
0.092
Nearest Be populations ‘)
0.212 p, 12
0.227 p,, 13
0.076 p,, 11,12 0.089 p, 13
0.100 p* II,12
Net H population
0.994
0.995
1.038
1.026
Net Be pq population b, 0.096 11 0.764 12 0.112 13 0.112 14
0.077 0.077 0.752 0.010
0.319 0.319 0.401 0.038
0.364 0.364 0.118 0.118
Net Be-H bond order b, 0.025 H-11 0.821 H-12 0.032 H-13 0.032 H-14
0.031 0.031 0.829 0.001
0.306 0.306 0.347 0.008
0.417 0.417 0.070 0.070
0.130 s 11,12 0.122 s 13,14 - 0.191
0.201 p, 11,12 0.156 p, 13,14
0.403 0.403 0.314 0.314
‘) Energy is in atomic units. b, s and p, give the orbital type and 11, 12, 13 and 14 correspond to the Be central atom numbers given in fig. 1.
444
I.P. Dillon, J. D. Head / CIuster model study of muliiple Ii adwrption
atom both 1.14 A horizontally and 0.3 A vertically. This larger displacement results in markedly different bonding for the on-top sites versus the BS and the OS. Taking into consideration the changes in cluster symmetries we also find the TS,, and TS,,, H to cluster bonding interactions to be very similar. In each of the four Be,,H clusters we find two molecular orbitals with large H orbital components. Table 4 summarizes these molecular orbitals and presents the major features of the Mull&en population and bonding analysis for the different adsorption sites. The lowest molecular orbital in the valence band for each Be,,H cluster correlates with the H orbital interacting with lowest energy level in the valence band of the naked Be,, cluster. This valence lowest energy level in the naked cluster has 50% of the electrons localized on the central 4 atoms with the remaining electrons fairly evenly distributed over the outer atoms. Table 4 shows for the Be,,H clusters that after the H interaction the Be electrons become localized closer to the position of the H atom. For this lowest valence band level both the OS and the BS have much lower orbital energies and larger H s orbital populations than for both TSs. The second molecular orbital with large H atom population occurs approximately a third of the way from the top of the Be,,H valence band and correlates with the H atom interacting with the second-crest occupied molecular orbital of the naked Be,, cluster. This Be,, orbital is entirely p,, in nature with 70% of the Be p, electron localized on the clusters central atoms. Table 4 indicates the larger H s and Be p,, populations are occurring for the TSs relative to the BS and OS, suggesting that the TS have a strong bonding with the Be p, orbital. BBS have previously argued the unusual stability for the TS,, for the Be,,H is due to formation of a sp hybrid on the Be atom 12, while in the larger Be,, and Be,, clusters the TS H binding interaction has to compete with Be atom 12 bonding to Be atoms in the cluster’s second and third layers. Our present study does not present any new evidence for this interpretation. However, it is interesting to note that for all the Be,,H clusters the H adsorption does result in a reduced net pfl population on the Be atoms 11-14 relative to the naked clusters. The
on Betel)
TSs approximately double the p, population on the Be atom nearest to the H atom relative to the naked Be,, cluster p, orbitals; while the next nearest neighbor atoms p,, populations are small. The BS and OS also show similar trends in that the Be atoms nearest to adsorbed H atom have the larger p,, populations, with the next-nearest neighbor Be atoms having smaller p, populations. Differences in the bonding are also indicated by the net charges on the H. The total Mulliken populations in table 4 show the H at TS to be essentially neutral or slightly positive while the BS and OS H are slightly negatively charged. Unfortunately the above results does not offer a simple chemical insight into why one adsorption site is to be preferred over another. From consideration of the Hartree-Fock eigenvalues for the two molecular orbitals with large H populations we conclude that the BS and the OS geometries are largely stabilized by bonding interactions with the lowest valence energy level in Be,,, while in the TS clusters the major bonding interactions occur with the Be,, p, level. Based on these observations we anticipate for those naked Be clusters which allow large H-to-Be p, interactions relative to H-to-Be s interactions to preferenti~ly adsorb hydrogen at the TS. Differences in the bonding interactions for the OS and BS are harder to distinguish. We only notice that OS lowest valence energy level is slightly below the corresponding BS level and the H s population is larger for OS. It might be argued that OS should be favored over BS because the H orbital can overlap with three Be atoms versus two for the BS site. Table 4 gives the Mu&ken bond order between H and the four central BI: atoms on the Be,, cluster. The TSs clusters have the largest single bond orders between the H and the nearest Be atom. The BS and OS clusters show lower bond orders as the H atom interacts with 2 and 3 nearest Be atoms. Summing the bond order over the nearestneighbor Be atoms gives the OS cluster the largest bond order of 0.95 versus 0.83 for BS and TS,,. We also find the bond orders between the central Be atoms on the Be,,H clusters to be reduced relative to the bond orders for the same atoms in the naked Be,, cluster. As one might expect, we also observe the optimized H to nearest Be atom
I.P. Dillon, J.D. Head / Cluster model study of multiple H ahorption on Be(OOOl,l
distance to increase with decreasing Be-H bond orders. The above discussion is somewhat lengthy, but we felt it was needed because when there are multiple H adsorbed on Be,, we find that the same basic bonding picture persists. The details of these multiple H interactions are given in the next two sections.
4. Double H atom adsorption In this section we present results for several different ~angements of 2 H atoms on the Be,, cluster. In all cases both H are placed at the same adsorption site type and we have not considered the effect of mixing sites. In finding the optimum H-to-Be surface vertical distance R, we always keep the two H atoms parallel to the surface, even in situations where because of the low Bei4H, cluster symmetry one might expect differing R, distances for the two H atoms. Table 5 summarizes the geometries for the different clusters investigated, with the “nearest Be atoms” column specifying where each H atom is located. The optimized R, and binding energies r>, per H atom along with internuclear separation between the two II atoms RH2 are also given in table 5. The OS, BS and TS clusters all have AH2 the same distance at the Be-Be nearest-neighbor separation and we regard these clusters as the two H atom
Table 5 Optimized vertical distances R, and binding energies De for two H atoms adsorbed on BeI Site
RHI (A)
R,(A)
De (kcal,/mol)
Nearest Be atoms a)
OS OS’ OS”
2.287 2.281 1.320
0.94 1.00 1.04
56.9 46.6 26.1
7-12-14 8-11-14 7-12-1411-12-13 11-12-1311-12-14
BS BS’ BS”
2.287 1.980 1.143
1.17 1.04 1.10
40.6 46.3 35.6
11-14 12-13 12-1312-14 11-1312-13
TS TS’ TS”
2.287 2.287 3.961
1.38 1.39 1.38
35.6 46.2 48.8
1112 11 13 13 14
a) Atom positions are given in fig. 1.
445
analog for the monolayer coverage of a Be surface. The H atoms in both the BS and TS clusters have newest-nei~bor Be atoms all belon~g to the 4 central atoms of the Be,, cluster, whereas the OS site has two Be,, edge atoms, 7 and 8, close to the H atoms. To test whether the edge atoms affect the OS R, and 0, we examined the OS’ cluster where there is now only one edge Be atom close to the H atom. However, the OS’ cluster has no symmetry and since this may influence the results we also performed the no symmetry TS’ calculation. Each of these BS, OS’ and TS’ clusters are related to each other by horizontal translations of the two H atoms in much the same manner as for the single H atom clusters discussed in the previous section. Unfortunately the OS’ and TS’ results do not enable a clear distinction between the role of symmetry or edge atoms in computing the preferred adsorbate site. The 0, values suggest that two H atoms at OS is the most stable geometry followed by the BS and TS both being close in stability. The Be,,H, De energy separation between the OS and other two sites is larger than obtained in the single H atom clusters and is more in line with BBS Be, and Be,, results and WTB’s slab calculations. The De per H atom is generally reduced for the two H atom cluster relatively to the single H atom adsorption case indicating that perhaps the two H atoms are now sharing bonding electrons from the Be; for clusters with even more H atoms we should anticipate further reduction in the D, per H atom and we find this to be the case as shown below. The Bet4H, R, distance for the OS is reduced by 0.17 A from the single H atom cluster value and has an R, equal to the BBS Bezz result. The Be,,H, TS R, decreases slightly, BBS find the TS R, to change the least with Be cluster size. The Be,,H, BS R, also only changes slightly, although the BS R, varies dramatically with the R H2 distance while BBS find the BS R, ‘to decrease with increasing cluster size. The molecular orbitals for Be,,H, exhibit very similar bonding interactions to the Be,,H clusters, only now the number of molecular orbitals with large H components are essentially doubled. For example, the OS cluster has two energy levels at the bottom of the Be,,H, valence band with large H s orbital populations. In the lowest level, the
446
I.P. Dillon, J. D. Head / Cluster model study of multiple H adsorption on Be(OOO1)
two H s otbitals are in phase and have a bonding u overlap, and this orbital correlates with a H, u orbital interacting with the lowest valence Be,, molecular orbital. The second level has the two H s orbitals out of phase with an anti-bonding cr* overlap and correlates with a valence Be,, molecular orbital at higher energy which also contains some Be p, character. Essentially the same pair of molecular orbitals with H-to-Be interactions also occur for the OS’ and BS clusters. The sum of the H populations for both of the u and u* orbitals are much larger than single H orbital population in the corresponding Be,,H clusters. Whilst the bonding between H and Be,, in OS and BS remains basically unchanged from the Be,,H clusters, the H 0, value is significantly reduced for the BS geometry. We can only attribute the extra stability of the OS to the larger differences between the OS and BS two lowest valence band eigenvalues than obtained in the Be,,H cluster. In the TS clusters the low-lying H, u and u* also occur at the bottom of the Be,,H, valence band but now the H populations are much smaller than for the OS and BS geometries. Analogous to the Be,,H cluster the Be,,H, TS H atoms interact with a Be,, p, orbital only now this interaction is spread over two molecular orbitals with H, u and u * components giving a total H population approximately the same as in the single-atom TS cluster. It is interesting to notice the net H populations for the Be,,H, clusters OS, OS’, BS and TS are very close to values for the corresponding Be,,H clusters and this again illustrates the small changes
in bonding features for the two types of clusters. The net p, population on the Be,, central atoms show some variation from the single H atom adsorption but this can be traced to some of the Be atoms now being coordinated by two H atoms. The bond orders between H and the central Be atoms in Be,,H, are essentially identical with the Be,,H values. Caution is always needed when comparing extended and cluster calculations because clusters with single H atoms do not include the H-H interactions which are automatically included in the extended systems. Obviously some H-H interaction must be taking place in the Be,,H, clusters or else the R, and L$ would be the same as for the Be,,H clusters. However, we find no evidence for a direct interaction in the Be,,H, clusters when RH, = 2.287 A if one uses the H-H bond order, listed in table 6, as a guide. Decomposing the Be,,H, net H orbital population into u and u* con~butions we find the H orbital populations split equally between the two symmetry types for the OS and BS geometries while the TS H population is 56% u symmetry. This slightly larger H u population for TS may be a result of some indirect H-H interactions via the Be surface atoms taking place. However, any socalled “H-H indirect interaction” may simply be a reflection of the two H atoms competing for the same bonding electrons from the Be. An altemative perspective is that the Be surface is weakening the H-H interactions. By performing a two-configuration MCSCF calculation on an isolated H, with internuclear separation of the Be-Be nearest-neighbor distance we find 66% of the H,
Table 6 Mulliken population and bond-order analysis for two H atoms adsorbed on Be,, OS
OS’
OS”
BS
BS’
BS”
TS
TS’
TS”
Net H population
1.066
1.046, 1.049
0.973
1.027
1.036
0.985
0.969
0.999,0.993
0.997
Net central Be p,, 11 12 13 14
0.269 0.269 0.024 0.533
0.478 0.284 0.311 0.261
0.345 0.345 0.167 0.167
0.357 0.357 0.467 0.467
0.136 0.614 0.323 0.323
0.262 0.262 0.262 0.019
0.649 0.649 0.084 0.084
0.753 0.103 0.793 0.144
0.069 0.069 0.792 0.792
H-H bond order
0.000
0.000
0.125
0.001
0.0203
0.191
0.000
0.001
0.001
I.P. Dillon, J.D. Head / Chter
model study of multiple H aakorption on Be(OOO1)
electrons in the a2 configuration and a binding of 4.7 kcal/mol relative to the two separate H atoms. In table 6 we have also included some Be,,H, clusters with RH, different from the Be-Be nearest-neighbor distances. For example, the clusters OS”, BS’ and BS” all have RH, shorter than 2.287 A. The bonding in these Be,,H, clusters still resembles the OS and BS clusters except now the two H atoms are close enough to interact with each other. Thus in table 6 the energy splitting between the two lowest Be,,H, valence band molecular orbitals, with large H (I and u * components, are greater for the OS” and BS” relative to the OS and BS. We also find larger percentage H (I populations of 68%, 52% and 72% for OS”, BS’ and BS”, respectively, and these populations correlate with the H-H bond orders given in table 6. As one might expect table 5 shows the H-to-Be,, binding energies De per H atom generally decrease with increasing H-H interactions. This illustrates there is a large barrier preventing recombination of two H atoms adsorbed on the surface, although the BS’ De value suggests the possibility that a small H-H interaction may initially be favorable in H adsorption. The TS” cluster has the two H atoms well separated and might be expected to approximate two independent H atoms on the Be surface. Indeed as the TS” molecular orbitals with large H components are much closer in energy than in the TS and TS’ clusters. However, the TS” cluster does have a small non-zero H-H bond order suggesting some H-H interaction is taking place. The TS” H binding energy De is also 11 kcal/mol smaller than the Be,,H TS,, De and we must conclude the Be,, cluster is simply not large enough to allow the computation of binding energies for two independent non-interacting H atoms. Thus in this section we have demonstrated that the interaction between two H atoms adsorbed on a cluster does influence the stability of different adsorption sites. The final geometry, however, as in the clusters with a single H atom, is still a result of a balance between two effects; H bonding with the Be s orbitals or H bonding with the Be p, orbitals. In the Be,, cluster the largest binding energy De is obtained when the two H atoms are adsorbed at the open sites.
447
5. H monolayer adsorption
The clusters used to model a monolayer of H atoms adsorbed on the Be,, cluster are shown in fig. 2. We define the monolayer of H atoms to be a planar cluster of H atoms held at the Be-Be internuclear separation with close to one H atom per Be atom. In the on-top cluster TS,, there are an equal number of Be and H atoms. To avoid H atoms being outside the Be,, cluster boundary we model the H monolayer for the other clusters with less than 14 H atoms, so that for open-site monolayer OS, there are 8 H atoms, while for the bridging-site clusters there are two possible arrangements of the H atoms to give the BS, and BS,, clusters composed of 9 and 10 H atoms, respectively. An important feature of these clusters is that now the H atoms at the center of the cluster have the same nearest-neighbor environment as an H atom in an extended calculation. Table 7 summarizes the optimized vertical distances R, for the H atom above the Be,, plane. This R, value has been computed from the minimum of the total Hartree-Fock energy for parallel planes of the H monolayer and Be,,. An important concern is whether the Hartree-Fock
Fig. 2. Clusters used to simulate the monolayer coverage of H atoms: (a) on-top TS,,; (b) bridging B$; (c) bridging BS,,; (d) open 3-fold OSs.
448
I. P. Dillon, J. D. Head / Cluster model study of multiple H adsorption on Be(0001)
energy is dominated by interactions between the cluster edge H and edge Be atoms. To check this, once we had determined the R, value, we reoptimized the H-to-Be distance for those H atoms above the central 11-14 Be atoms and found, somewhat surprisingly, no change in the H-to-Be distance. It should be no surprise that the T&, R, value is 1.38 A when one considers the results for the TS Be,,H and Be,,H* clusters. On the other hand, the R, for OS,, BS, and BS,e are reduced significantly from the single and double H atom clusters. Consistency amongst the different cluster calculations is suggested by the similar R, for the BS, and BS,, clusters. The H binding energies De for the monolayer clusters are, as expected, reduced relative to the 0, for Be,,H and Be,,H, clusters. However, it is interesting that now in these monolayer calculations the OS and BS geometries are difficult to distinguish in stability and that both structural types are appreciably more stable than the TS geometry. Apart from WTB finding the OS geometry to be 10 kcal/mol more stable than the BS, our monolayer R, and D, values are also in reasonable agreement with the WTB slab calculations. This suggests cluster and slab calculation will give comparable results providing the same adsorbate coverage is used. The monolayer BeH distances in both the OS and BS clusters are reduced by over 0.1 A from the geometry obtained with the Be,,H clusters. These monolayer BeH distances are also slightly shorter than the WTB monolayer results but are close to the 4 layer YL slab values and the 2 and 3 layer BBS bond length. The bonding picture for these H monolayer clusters can still be described in terms of the bonding interactions used for the Be,,H and Be,,H, clusters. Thus the OS and BS clusters still have H atoms interacting with Be s orbitals at the bottom of the valence band with little H-to-Be p, interaction, while the TS monolayer prefers the H-to-Be p, interaction. The difference between the OS and the BS interaction versus the TS interaction is also evident from the valence molecular orbital energies computed for Be,, and the monolayer clusters. The H-to-Be interactions for the OS and BS clusters result in the Be,, valence band splitting into two parts. The lower part con-
tains the molecular orbitals where the H electrons bind with the Be s electrons and consists of one molecular orbital for each H atom in the cluster. The OS, cluster is found to have the largest valence band splitting perhaps suggesting the OS geometry should have the lowest energy; however, because the BS, and BS,, clusters contain more H atoms than the OS, cluster we may be obtaining larger De for the BS geometries even though the Q is calculated as a per H atom quantity. The larger De value for BS,, versus BS, may also reflect the difficulty with the 0, equation. The splitting for the TS,, valence band is much smaller than for the other clusters and the lower half of the valence band consists of only eight molecular orbitals as expected if H s to Be p, interactions become important. The Mulliken populations for the monolayer clusters are consistent with the results from the Be,,H and Be,,H, clusters. The net H atom populations, given in table 7, show the same trends as obtained previously with the OS and BS H atoms being slightly negatively charged and the TS H atoms being slightly positive. However, the OS and BS net Be p_ populations are somewhat larger than in the corresponding Be,,H and Be,,H, clusters, but this must be due to the H monolayer being able to more effectively polarize the Be atoms. In the TS,, cluster the Be p,, population is reduced relatively to the single and double H atom clusters reflecting the competition between H atoms to attract Be p, electrons. It is interesting to note that the bond order for an H atom above a Be atom is still 0.82 and unchanged from the Be,,H value. Summarizing, the bonding picture for a H monolayer on the Be,, cluster is basically unchanged from the clusters containing only one or two H atoms. The BS,, cluster is found to give the largest De but the closeness of the OS De prevents a firm conclusion on the preferred structure.
6. H atom removal clusters
from H monolayer
covered
In the previous section we used clusters model the H atom monolayer coverage regime
to of
I.P. Dillon, J.D. Head / Cluster model siu& of multiple H adsorption on 3eQWO~)
449
Table 7 Optimized vertical distance R,, binding energies D,, and M&liken population analysis for H monolayers on Bell Site R,
BS9 1.02 31.7
BS,, 0.99 34.9
0.989 11-12 1.043 5-12 1.022 3-13 1.078 1-2
1.009 12-13 1.035 7-12 1.073 2-13 1.046 1-3 1.051 3-5
OS,
ch
0.90
0, (kcal/mol)
32.4
Net H population a>
1.053 1.057 1.075 1.015
Net central Be pw population 11 12 13 14
11-12-13 1-3-13 3-5-12 7-12-14
0.558 0.558 0.433 0.623
0.595 0.595 0.572 0.572
34
1.38 25.1 0.928 11,12 0.923 13, 14 0.964 1,2,9, 10 0.960 3,4, 7, 8 0.956 5,6
0.581 0.581 0.506 0.506
0.611 0.611 0.641 0.641
‘) H positions are referenced to the nearest-neighbor Be atom numbers given in fig. 1.
surface. We define the desorption removal of a single H atom by
the Be(OO01) surface. In this section we go one stage further and use clusters to compute the desorption energy of a single H atom from the surface monolayer. This calculation is very simple to perform using a cluster model. The limitations on the allowed unit cell size prevent a similar calculation being performed using slab models. To calculate the desorption energy we start with the optimum monolayer described in the previous section and remove a single H atom from one of the positions above the central Be atoms, 11, 12, 13 and 14, on Be,, and recalculate the cluster total SCF energy. We choose a H above a central Be cluster atom and simulate the removal of a H atom which has the same number of Be and H nearest neighbors as on the extended monolayer
Edes = EBe,,H,_,
+ EH -
= nl),(Be,,H,)
-
energy for the
EBe,,H, (n
-
(24
1)Q+(Be14%,-l), cw
where n is the number of H atoms on the Be14Hn cluster. Edes should not be confused with the energy needed to desorb H,. Ekl. (2a) shows Edes to be positive when Bei4H, is more stable than the separate Bei4H,_i cluster and H atom, while eq. (2b) indicates how Edes is related to the H binding energy De on the different clusters. The E des values are presented in table 8 along with binding energies De for the n H atom monolayers
Table 8 Binding energies D, and desorption energies Edes for H monolayers on Be,, N
TS,, (13) ‘)
Site
OS,
=9
BSIO
0, (kcal/mol) BeI& Be@,-1
32.4 35.1
31.7 33.0
34.9 36.7
25.1 28.2
25.1 28.3
13.3
21.4
18.6
- 15.8
- 16.6
7314
(12)
Edes (kcal/mol)
a) The number in parentheses indicates the Be atom from above which the H was removed.
450
I.P. Dillon, J. D. Head / Clmter model study of multiple H adsorption on Be(0001)
and n - 1 H atom clusters, in all calculations the optimum monolayer H-to-Be surface distance has been kept at their values listed in table 7. It is interesting how all the Be14Hn_i De’s have increased from there corresponding Bei4H, values. This is not really surprising because the H surface coverage is being reduced when the H atom desorbs resulting in stronger Be-to-H adsorbate interactions, essentially in the same manner as the reduction in De was found in going from Be,,H to Be,,H,. Again like the monolayer calculations, the De for the (n - 1) H atom cluster suggest close stability for both the BS and OS structures while the TS is considerably less stable. are very striking, not only by their The &es range of values, but also because they are very different from the average H binding energy De. The two BS clusters have an average Ed_ of 20 kcal/mol. This is the energy needed to remove a single H atom from the BS monolayer. In contrast, the TS monolayer with negative Ed_ is more stable after desorbing H suggesting the TS structure can never be formed. Finally the OS Ed_ is positive but much smaller than the BS value. Some of this difference between the Ed_ for the OS and BS sites might be due to the OS monolayer having only 8 H atoms although Edes reduces on going from BS, to BS,,. The Edes represent also an estimate of the energy gain for adsorbing a single H on a partly covered surface. More energy is to be gained by adsorbing at a BS implying a BS monolayer would be formed even though the binding energies De indicate little energetic difference between the OS and BS structures. In many of the calculations listed in table 1, especially those of YL and our monolayer results, the De values for the OS and BS are sufficiently close to imply that both structures could occur as different domains on the Be(OOO1) surface. Thus in a TDS experiment, two major peaks might be observed, the low-temperature peak coming from the OS structure, at higher temperatures the BS domain would start to desorb. Ray and Plummer only report peaks occurring at about 450 K in their TDS experiments [19]. However, we make the above comments with reservations because upon going to larger multi-layered clusters changes in the Edes should be expected.
7. Conclusion We have examined using cluster models different adsorbate coverages on surfaces. We find slab and cluster calculations to be generally consistent with each other providing the substrate is modeled by the same number of surface layers and the adsorbate coverages are similar. For the Be,, cluster the binding energies De decrease with increasing H coverage indicating interactions between the H atoms do occur although the essentially zero H-H bond orders suggest an indirect mechanism. The type of H-to-Be bonding varies only slightly with surface coverage. At the open 3-fold (OS) and bridging (BS) sites the H atoms largely bond with Be2s orbitals at the bottom of the valence band. While at the on-top (TS) site the H interacts mostly with the Be p, orbitals. Thus the bonding of H with Be(OOO1) could simply be modeled by a cluster corresponding to low surface coverage. In other systems the chemisorption bond may be more sensitive to the surface coverage and this needs to be investigated further using cluster calculations. The average H binding energies De from the clusters simulating a H monolayer surface coverage predict the OS and BS structures to be close in energy. However, by computing the single H atom desorption energy Edes from the monolayer we predict the BS structure to be the most resistant to desorbing a H atom. This work demonstrates another strong advantage of using cluster models in that Ed_ is a straightforward calculation. A similar calculation of Edes is not possible using a slab model.
Acknowledgements We are grateful to the University of Hawaii Computer Center for providing the facilities which enabled us to perform these calculations. We also appreciate the preprint of ref. [16] from J. Wu, S.B. Trickey and J.C. Boettger. References [l] J. Sauer, Chem. Rev. 89 (1989) 199. [2] J. Koutecky and P. Fantucci, Chem. Rev. 86 (1986) 539.
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