


R^{a}  DFT  DE 
5.0  351.08155  0.1 
4.0  351.08060  0.7 
3.0  351.05959  13.8 
2.75  351.03903  26.7 
2.5  351.00352  49.0 
2.25  351.17777  60.3 
2.0  351.23220  94.5 
^{a} R is the perpendicular distance from the second layer of the cluster. Column 2 gives the density functional theory (DFT) energy in atomic units (Hartree). Column 3 gives the relative energy in kcal/mol (one kcal/mol = 0.00695 aJ). The same conventions are used in the remaining tables.
Reaction (2) should have a low barrier since it is a carbene insertion process. As a first model a small cluster (See Fig. 4) was used which had one surface carbon and two second layer carbon atoms. (With the second layer carbon atoms fixed at bulk values and tied off with H atoms.) The barrier for reaction (2) was found to be 0.01 aJ (1.4 kcal/mol) and the exothermicity for this reaction is 0.79 aJ (113.3 kcal/mol). (See Table II.)
Several other processes were also studied for this cluster. The inversion barrier for a H atom bonded to the carbene atom is less than 0.0007 aJ (0.1 kcal/mol). The HCC_{2} moiety is only 10 deg. from planar, which is reasonable by analogy to CH_{3}, and consistent with the small computed barrier. The barrier to abstraction of an H atom from a surface CH_{2} by H atom was found to be to be 0.07 aJ (9.6 kcal/mol) and the heat of reaction is 0.03 aJ (4.4 kcal/mol) (endothermic). The final question was the barrier for adding H atom to a surface CH. No barrier was found for this ( doublet + doublet reaction) and the bond strength is found to be 0.73 aJ(105.4 kcal/mol).
Fig. 4. Cluster model for a carbene site on diamond 100 plus H/H_{2}. There is one surface C atom and two subsurface C atoms. Cluster1 is the bare cluster., cluster1+H is the monohydrogenated cluster, cluster1 + H2 SP is the saddle point for addition of H_{2} via a carbene process, and cluster1 + H3 abs sp is the saddle point for H atom abstraction from the dihydrogenated cluster.
Table II. Energetics for cluster1(100) + nH.
structure  DFT  DE 
cluster1  117.75947  
H  0.50027  
118.25974  0.0  
cluster1 + H  118.44733  117.7 
cluster1 + H SP  118.44732  117.7 
cluster1  117.75947  
H2  1.17548  
118.93495  0.0  
cluster1+H_{2} sp  118.93265  1.4 
cluster1 + H_{2}  119.11556  113.3 
cluster1 + H  118.44733  
H2  1.17548  
119.62281  0.0  
cluster1+H + H_{2} abs sp  119.60751  9.6 
cluster1 + H_{2}  119.11556  
H  0.50027  
119.61583  4.4  
cluster1 + H  118.44733  
H  0.50027  
118.94760  0.0  
cluster1 + H_{2}  119.11556  105.4 
Fig. 5 and Table III show energetics for reaction (2b). (The cluster is shown in Fig. 1.) This process is assuming an entrance channel saddle point that leads to the structure labeled by min2 in Table III. This structure has two H atoms bonded to one C and the other carbon is a carbene site. An interesting feature of Fig. 5 is the low barrier for migration of a H onto a carbene center. This process is well known in gas phase chemistry (e.g. the isomerization of vinylidene to acetylene). (Walch and Taylor, 1995)
Table III. Energetics for reaction (2b).
structure  DFT  DE 
dimer singlet  349.90617  
H2  1.17548  
351.08165  0.0  
cluster100+h2.min2  351.14608  40.4 
cluster100+h2.sp1  351.14157  37.6 
cluster100+h2.min1  351.24082  99.9 
^{a} Note that cluster100 is shown in Fig. 1.
Fig. 5. Energetics for reaction (2b).
Another issue which was considered is the formation of a dihydride phase (i.e. two H atoms per surface C atom).
The structures which were considered here are shown in Fig. 7 and the energetics are shown in Table IVa. One question that hadn’t been considered before is the structure of the two minima for three and four H atoms on the 100 surface dimer. One speculation was that these structures would twist outofplane to minimize repulsions. However, calculations that were started with twisted geometries reverted to planar geometries when optimized. From the structure of the 4 H atom minimum it is clear that there would be significant interactions with an adjacent dimer site with 4 H atoms. Thus, for the extended surface with 2H per surface carbon there would be large nonbonded repulsions with the CH bonds of adjacent monohydrogenated dimers. The main effects of this nonbonded repulsion were included by placing CH_{2} groups in the locations of the nearer carbon of the adjacent surface dimers. (Here one CH bond is oriented along the CC bond of the adjacent dimer and the other CH bond is in the location of the CH bond of the adjacent surface dimer. See Fig. 6.) This is similar to what was done earlier in our studies of the monofluorinated silicon surface (Walch and Halicioglu, to be published). Table IVa gives computed energetics for the case without adjacent CH_{2} groups. Here it is seen that the binding energy for a third H atom to the mono hydrogenated dimer is 0.35 aJ (50.3 kcal/mol) or about half a CH bond strength. This is due to disruption of the CC p bond of the dimer. The barrier to H migration is only 0.10 aJ (13.7 kcal/mol), which is much less than the barrier of 0.44 aJ (63.8 kcal/mol) for H atom migration of a single H atom on a surface dimer. Adding another H atom to the dimer plus three H atoms leads to a CH bond strength of 0.68 aJ (98.4 kcal/mol) in the dimer plus 4 H atom cluster.
Fig. 6. Cluster for a surface dimer plus two adjacent CH_{2} groups to simulate the nonbonded repulsions with adjacent surface dimers.
A number of other results are also summarized in Table IVa. These include the barrier for carbene insertion of H_{2} into the structure (2b) of Fig. 2. This barrier is 0.04 aJ (6.3 kcal/mol), which is ~0.03 aJ (5 kcal/mol) larger than for reaction (2a).
From Table IVb it is seen that the presence of adjacent CH_{2} groups reduces the binding energies of H atoms to a surface dimer. The reductions are 0.01 aJ (2.0 kcal/mol), 0.09 aJ (12.4 kcal/mol), and 0.13 aJ (18.1 kcal/mol) for 2H, 3H, and 4H, respectively.
Fig. 7. Clusters for a surface dimer on diamond 100 plus three and four H atoms. The structure in the upper left is the minimum energy configuration for a dimer plus 3 H atoms. The structure in the upper right is the exchange saddle point for a dimer plus 3 H atoms. The structure in the lower left is the saddle point for H2 addition to an activated dihydrogenated surface dimer. The structure in the lower right is the minimum energy configuration for a surface dimer plus 4 H atoms.
Table IVa. Energetics for cluster100 + nH.
structure  DFT  DE 
cluster100  349.90617  
H  0.50027  
350.40644  0.0  
cluster100 + H  350.56623  100.3 
dimer singlet  349.90617  
H2  1.17548  
351.08165  0.0  
cluster100+H2.min2  351.14608  40.4 
cluster100+H2.sp1  351.14157  37.6 
cluster100+H2.min1  351.24082  99.9 
cluster100 +H  350.56623  
H  0.50027  
351.06650  0.0  
cluster100+H2.min1  351.24082  109.4 
cluster100+H2.min1  351.24082  
H  0.50027  
351.74109  0.0  
cluster100+H3, exc sp  351.79945  36.6 
cluster100+H3  351.82120  50.3 
cluster100+H2.min1  351.24082  
H2  1.17548  
352.32156  0.0  
cluster 100+H4 sp  352.31146  6.3 
cluster100+H4  352.47834  98.4 
cluster100+H3  351.82120  
H  0.50027  
352.32147  0.0  
cluster100+H4  352.47834  98.4 
Table IVb.
structure  DFT  DE 
cluster100+2ch2  428.12925  
H2  1.17548  
429.30473  0.0  
cluster100+2ch2 + H_{2}  429.46072  97.9 
cluster100+2ch2 + H_{2}  429.46072  
H  0.50027  
429.96099  0.0  
cluster100+2ch2 + H_{3 }SP  430.01735  35.4 
cluster100+2ch2 + H_{3}  430.02139  37.9 
cluster100+2ch2 + H_{3}  430.02139  
H  0.50027  
430.52166  0.0  
cluster100+2ch2 + H_{4}  430.64957  80.3 
Table V and Fig. 8 show the reaction of H_{2} with a surface dimer along an abstraction pathway. From Fig. 8 it is seen that the abstraction reaction is nearly thermoneutral and has a small barrier. The calculations were carried out for the triplet spin state. Fig. 8 also shows a singlet pathway. This pathway is constructed assuming that the barrier is comparable on the singlet surface. Note that for the reverse reaction either singlet or triplet spin is possible, and the saddle point region on the singlet surface is assumed to be an open shell singlet. Here it is seen that on the singlet surface, the barrier including the endothermicity is about 0.10 aJ (15 kcal/mol).
Table V. Energetics for abstraction of a H from cluster100+h.
structure  DFT  DE 
cluster100+h  350.56623  
H  0.50027  
351.06650  0.0  
cluster100+h2.abs  351.05537  7.0 
dimer triplet  349.88903  
H2  1.17548  
351.06451  1.2  
dimer singlet  349.90617  
H2  1.17548  
351.08165  9.0 
Fig. 8. Abstraction pathway for H_{2} reacting with a surface dimer on diamond (100). The singlet and triplet pathways are indicated.
Table VI and Fig. 9 show the process of adding a second H atom to the surface dimer via the abstraction pathway. This process occurs only on a doublet surface and has a small (about 0.04 aJ (6 kcal/mol) ) barrier.
Table VI. Energetics for abstraction of a H from min1.
structure  DFT  DE 
cluster100+h2.min1  351.24082  
H  0.50027  
351.74109  0.0  
cluster100+h3.sp1  351.73166  5.9 
cluster100+h  350.56623  
H2  1.17548  
351.74171  0.4 
Fig. 9. Energetics for adding a second H atom to a dimer on diamond (100) via an abstraction process.
Table VII and Fig. 10 show energetics for adding an H atom to a dimer on diamond (100). DFT calculations show no barrier to addition of H to the singlet state of the dimer. Addition of a second H atom should also be a barrierless process. The exchange of an H atom between the two C atoms is also shown. This process has a barrier of 0.44 aJ (63.8 kcal/mol).
Table VII. Energetics for H atom plus dimer on diamond 100.
structure  DFT  DE 
cluster100  349.90617  
H  0.50027  
350.40644  0.0  
cluster100 +h  350.56623  100.3 
exchange sp  350.46461  36.5 
Fig. 10. Energetics for adding an H atom to a dimer on diamond (100).
We now consider reactions on the diamond 110 surface. Fig. 11 shows the clusters that were used for this surface. This cluster has 4 surface and 6 second layer C atoms with the dangling bonds tied of with H atoms. Here the position of the 4 surface atoms was partially optimized (with the constraint that the three CC bond lengths remain the same). ( Calculations in which the CC bond lengths were allowed to be different indicated a slight energetic preference for an alternating structure.) The center two surface atoms of this cluster will be considered as a dimer pair. The computed energetics are given in Table VIII. From Table VIII it is seen that the CH bond strength for adding one H atom to the dimer pair (cluster110b+h3) is 0.76 aJ (109.6 kcal/mol) and the exchange barrier is 0.50 aJ (72.0 kcal/mol) as compared to 0.44 aJ (63.8 kcal/mol) for the 100 surface. This larger barrier probably results from more hydridization of the radical orbitals away from each other as compared to the 100 surface. The overlap of adjacent singlet coupled radical orbitals is 0.292 in a GVB(pp) calculation and the singlet to triplet excitation energy is 0.05 aJ (7.3 kcal/mol) for the diamond110 surface, compared to 0.462 and 0.22 aJ (32 kcal/mol) for the diamond100 surface. The abstraction barriers were also computed for abstracting an H atom from the mono and dihydrogenated dimer (cluster110b+h2+h2.abs and cluster110b+h3+h2.abs, respectively). The abstraction barriers are 0.04 aJ (5.2 kcal/mol) and 0.05 aJ (6.8 kcal/mol) and the heats of reaction are 0.0007 aJ (0.1 kcal/mol) and 0.01 aJ (1.9 kcal/mol) for the mono and dihydrogenated dimer, respectively.
Calculations were also carried out for a symmetry constrained addition of H_{2} across the dimer. These results are given in Table IX. Here it is seen that the barrier for the symmetry constrained approach is ~0.30 aJ (43 kcal/mol). For diamond 100 the barrier was ~0.34 aJ (49 kcal/mol). This is consistent with the smaller overlap of the p bond for the 110 surface compared to the 100 surface.
Table IX. Energetics for cluster110b+h2 + H_{2}. (C_{2v})
structure  R  DFT  DE 
cluster110b+h2  390.47045  
H2  1.17548  
391.64593  0.0  
3.5  391.62828  11.1  
3.25  391.61083  22.0  
3.0  391.57688  43.3  
2.75  391.66756  13.6  
2.5  391.73221  54.1 
Fig. 11. Cluster model for the diamond 110 surface plus 14 H atoms.
Table VIII. Energetics for cluster110b + nH.
structure  DFT  DE 
cluster110b  389.15909  
H  0.50027  
389.65936  0.0  
cluster110b+h2  390.47045  
H  0.50027  
390.97072  0.0  
cluster110b+h3  391.14543  109.6 
cluster110b+h3,exc.  391.03057  37.6 
cluster110b+h3  391.14543  
H  0.50027  
391.64570  0.0  
cluster110b+h4  391.81757  107.9 
cluster110b+h2  390.47045  
H2  1.17548  
391.64593  0.0  
cluster110b+h3.abs  391.63764  5.2 
cluster110b+h3  391.14543  
H  0.50027  
391.64570  0.1  
cluster110b+h3  391.14543  
H2  1.17548  
392.32091  0.0  
cluster110b+h4 abs  392.31004  6.8 
cluster110b+h4  391.81757  
H  0.50027  
392.31784  1.9 
Table IX. Energetics for cluster110b+h2 + H_{2}. (C_{2v})
structure  R  DFT  DE 
cluster110b+h2  390.47045  
H2  1.17548  
391.64593  0.0  
3.5  391.62828  11.1  
3.25  391.61083  22.0  
3.0  391.57688  43.3  
2.75  391.66756  13.6  
2.5  391.73221  54.1 
Calculations were also carried out for several processes on the diamond 111 surface. The cluster used here has two surface carbons and one second layer carbon. (See Fig. 12 and Table X) The two surface dangling bonds are separated by second nearest neighbor distances and interact only very weakly. This weak interaction is evident in the first and second CH bond energies which are 0.81 aJ (116.1 kcal/mol) and 0.81 aJ (115.9 kcal/mol), respectively. Also these binding energies are significantly larger than on the 100 and 110 surfaces, which also is expected from the free radical character of the surface dangling bond on the 111 surface, compared to the other surfaces, where there is some p bonding. The barrier for abstraction is calculated to be 0.03 aJ (4.0 kcal/mol) and the reaction is exothermic by 0.04 aJ (6.1 kcal/mol). The exothermic nature of the abstraction reaction is due to the greater CH bond strength for the 111 surface.
Fig. 12. Cluster model for diamond 111 + Hn.
Table X. Energetics for cluster2(111)+h2 + H_{2}.
structure  DFT  DE 
cluster2  117.74505  
H  0.50027  
118.24532  0.0  
cluster2+h  118.43039  116.1 
cluster2+h  118.43039  
H  0.50027  
118.93066  0.0  
cluster2+h2  119.11536  115.9 
cluster2+h  118.43039  
H_{2}  1.17548  
119.60587  0.0  
cluster2+h+h2, abs  119.59943  4.0 
cluster2+h2  119.11536  
H  0.50027  
119.61563  6.1 
Fig. 13 and Table XI show results for a dimer on the reconstructed Si100 surface plus one to four H atoms. The binding energies shown in Fig. 13 are for the processes: Si100+H > Si100H, Si100+H_{2}> HSiSiH, HSiSiH+H> HSiSiH_{2}, and HSiSiH+H_{2}> SiH_{2}SiH_{2}, respectively. Table XI also gives the individual bond strengths for HSiSiH. Here it is seen that the bond strengths for the first and second SiH bonds are 0.60 aJ (86.1 kcal/mol) and 0.58 aJ (83.4 kcal/mol), respectively. Note that these are D_{e}’s (i.e they do not include an estimate of vibrational zeropoint effects). An estimate of these effects may be taken from earlier work ( Wu and Carter, 1991), which leads to D_{0}’s of 0.54 aJ (78.1 kcal/mol) and 0.57 aJ (81.4 kcal/mol) for the first and second SiH bond strengths. This suggests a significant preference for adding a second H atom to the same dimer. From Fig. 13 it is also seen that the DE’s for Si100+H_{2}> HSiSiH and HSiSiH+H_{2}> SiH_{2}SiH_{2 }are 0.40 aJ (57.8 kcal/mol) and 0.10 aJ (15.0 kcal/mol), respectively. This compares to 0.69 aJ (99.9 kcal/mol) and 0.68 aJ (98.4 kcal/mol) for the analagous structures on the diamond 100 surface. Thus, the formation of a dihydride phase is less likely on silicon as compared to diamond.
Fig. 13. Structures for a dimer on the silicon 100 surface plus one to four H atoms. The numbers are binding energies in kcal/mol for the processes Si100+H > Si100H, Si100+H_{2}> HSiSiH, HSiSiH+H> HSiSiH_{2}, and HSiSiH+H_{2}> SiH_{2}SiH_{2}, respectively
Table XI. Si100+nH (medium basis)
Si100 (singlet)  42.00983  
H  0.50027  
42.51010  0.0  
Si100 + H  42.64727  86.1 
Si100 + H  42.64727  
H  0.50027  
43.14754  0.0  
Si100+H_{2}  43.28041  83.4 
Si100 (singlet)  42.00983  
H_{2}  1.17854  
43.18837  0.0  
Si100+H_{2}  43.28041  57.8 
Si100+H_{2}  43.28041  
H  0.50027  
43.78068  0.0  
Si100+2H+H  43.84346  39.4 
Si100+H_{2}  43.28041  
H_{2}  1.17854  
Si100+H_{2}+H_{2}  44.45895  0.0 
Si100+2H+2H  44.48278  15.0 
Table XII and Fig. 14 show the energetics for adding H_{2} to a dimer on the silicon (100) surface. This is a C_{2v} constrained minimum energy pathway obtained in the same way as for the results for diamond 100 + H_{2} shown in Table I. Here it is seen that the barrier is only about 0.10 aJ (14 kcal/mol) (using the small basis set) as compared to 0.35 aJ (50 kcal/mol) for diamond. Table XIII and Fig. 14 show energetics for the abstraction process analagous to reaction (3) for the diamond 100 surface. Here it is seen that abstraction of one H from H_{2,} to give a single H bonded to the surface dimer plus H atom, is uphill by 0.15 aJ (22 kcal/mol) (using the small basis set), but there is no barrier other than the endothermicity. Thus, for Si100 it is more favorable to add an H_{2} via the C_{2v} constrained approach leading to the Si100 + H_{2} structure than to transfer a single H to the surface (abstraction pathway). ( See Fig. 14.) Table XIII and Fig. 15 show a non C_{2v} constrained addition pathway. Here it is seen that the addition barrier is 0.16 (23.5 kcal/mol) (using the small basis set) and subsequent steps are all below the reactants energy. The structures for min1, sp1, min2, and sp3 are given in Fig. 16. Details of the pathways are given in Fig. 17 for sp3, which is the non C_{2v} addition pathway, and in Fig. 18 for sp1, which is the second barrier shown in Fig. 15.
The nonsymmetry constrained addition of H_{2} to the surface dimer (reaction (2)) differs for diamond and silicon. In the diamond case, this reaction can happen in two ways. One occurs by activation of the surface dimer by moving both H atoms onto one dimer carbon atom (reaction (2b) ). (CHCH > CH_{2}C) This process is endothermic by 0.41 aJ (59.5 kcal/mol) and requires 0.43 aJ (62.3 kcal/mol) to surmount the barrier. The resulting CH_{2}C structure is 0.28aJ (40.4 kcal/mol) below the surface dimer plus H_{2}. The resulting localized carbene center can add an H_{2} by a carbene insertion process with a low barrier ( about 0.04 aJ (6 kcal/mol) ) leading to a dihydride structure. The other mechanism involves a competition between the dimerization energy per dimer and the low barrier to carbene insertion into H_{2} for a localized carbene site. However the dimerization energy for diamond 100 is computed to be 0.48 aJ (69.3 kcal/mol) per dimer and therefore the barrier to addition would be a predicted to be greater than 0.49 aJ (70 kcal/mol). (This saddle point has not been located.) In the silicon case, all the saddle point structures for this reaction have been located. The first step is addition of H_{2} to a surface dimer leading to a SiH_{2}Si structure. In the silicon case the dimerization energy per surface dimer is 0.12 aJ (17.4 kcal/mol) which is consistent with the barrier for nonsymmetry constrained addition of H_{2} which is 0.16 aJ (23.4 kcal/mol) with the largest basis set. Thus, for the silicon case symmetry constrained and nonsymmetry constrained addition of H_{2 }have comparable barriers. In the silicon case the nonsymmetry constrained addition is followed by rearrangement to a SiHSiH structure, which is analagous to reaction (2b) in the diamond case.
Table XIIIb gives energetics with the large basis set for the processes dicussed above. Here it is seen that the best estimates of the barrier heights are 0.17 aJ (24.7 kcal/mol) for abstraction, 0.13 aJ (19.4 kcal/mol) for symmetry constrained addition, and 0.13 aJ (23.4 kcal/mol) for nonsymmetry constrained addition. This leads to a bottomofwell to bottomofwell estimate of 0.58 aJ (82.9 kcal/mol) for the barrier to desorption of H_{2}. (via the nonsymmetryconstrained pathway). The experimental estimates of this quantity are 0.31 aJ (45 kcal/mol) to 0.46 aJ (66 kcal/mol). However, the computed quantity does not include vibrational zeropoint effects or the destabilization of the HSiSiH structure by interaction with adjacent monohydrogenated dimers. Both of these effects would be expected to significantly reduce the computed activation energy for desorption of H_{2}. Therefore, we can not say how well the present results agree with the experimental activation energy until estimates of these quantities are obtained. An important result in the present work is that the nonsymmetryconstrained and symmetryconstrained pathways have very similar barrier heights. Thus, both pathways may be occuring simultaneously.
Table XIV and Fig. 19 show energetics for a single H atom bonded to a surface dimer and for the exchange of this atom between the two si atoms of the dimer. Here it is seen that the most reliable estimate of the barrier to exchange (large basis set results) is 0.30 aJ (43.6 kcal/mol) for silicon 100 as compared to 0.44 aJ (63.8 kcal/mol) for diamond 100.
Fig. 14. Energetics for Si100 + H_{2 }(symmetry constrained approach and abstraction pathway).
Table XII. Si100 plus H_{2}, C_{2v} addition pathway (small basis).
R^{a}  DFT  DE 
5.0  42.98212  0.9 
4.0  42.96978  8.7 
3.75  42.96341  12.7 
3.5  42.96195  13.6 
3.25  42.96182  13.6 
3.0  43.06702  52.4 
^{a} R is the perpendicular distance from the second layer of the cluster.
Table XIIIa. Si100 plus H_{2 }(small basis).
Si100 (singlet)  41.80809  
H_{2}  1.17548  
42.98357  0.0  
Si100 + H_{2} abstr. sp  42.94918  21.6 
Si100 + H min.  42.44862  
H  0.50027  
42.94862  21.9  
Si100 + H_{2} min1  43.07823  59.4 
Si100 + H_{2 } sp1  43.01594  20.3 
Si100 + H_{2} min2  43.03474  32.1 
Si100 + H_{2 } sp3  42.94617  23.5 
Table XIIIb. Si100 plus H_{2 }(large basis).
Si100 (singlet)  42.02589  
H_{2}  1.17854  
43.20443  0.0  
Si100 + H_{2} abstr. sp  43.16502  24.7 
Si100 + H min.  
H  
Si100 + H_{2}, C_{2v} , 3.75  43.17375  19.3 
Si100 + H_{2}, C_{2v} , 3.625  43.17358  19.4 
Si100 + H_{2}, C_{2v} , 3.5  43.17351  19.4 
Si100 + H_{2}, C_{2v} , 3.25  43.17500  18.4 
Si100 + H_{2}, C_{2v} , 3.0  43.28242  48.9 
Si100 + H_{2} min1  43.29922  59.5 
Si100 + H_{2 } sp1  43.23628  20.0 
Si100 + H_{2} min2  43.25019  28.7 
Si100 + H_{2 } sp3  43.16714  23.4 
Fig. 15. Energetics for Si100 + H_{2}( non C_{2v} approach).
Fig. 16. Stationary point structures for Si100 + H_{2} (non C_{2v} approach).
Fig. 17. Minimum energy path for the reaction Si100 + H_{2} > sp3 > min2.
Fig. 18. Minimum energy path for the reaction min2 > sp1 > min1.
Fig. 19. Energetics for Si100 + H.
Table XIVa. Si100 +H (small basis).
Si100 (singlet)  41.80809  
H  0.50027  
42.30836  0.0  
Si100 + H exchange  42.37274  40.4 
Si100 + H min.  42.44862  88.0 
Table XIVb. Si100 +H (large basis).
Si100 (singlet)  42.02589  
H  0.50027  
42.52616  0.0  
Si100 + H exchange  42.59533  43.4 
Si100 + H min.  42.66474  87.0 
We have looked at the reaction of H_{2} with the diamond 100, 110, and 111 and silicon 100 surfaces using a cluster model and DFT with the B3LYP functional. For each of the four surfaces we have studied the symmetry constrained and nonsymmetry constrained addition of H_{2}, the addition of H atom, and abstraction of an H atom from a surface CH by a gas phase H atom.
For the dimer reconstructed 100 surfaces we considered the reactions shown in Fig. 2. The symmetry constrained addition of H_{2} to the surface dimer (reaction (1)) is found to have barriers of 0.35 aJ (50 kcal/mol) and 0.10 aJ (14 kcal) for diamond and silicon 100 surfaces, respectively. (Using comparable doublezeta like basis sets.) For the silicon surface the barrier increases to 0.13 aJ (19.4 kcal/mol) with addition of polarization functions to both Si and H.
The nonsymmetry constrained addition of H_{2} to the surface dimer (reaction (2)) differs for diamond and silicon. In the diamond case, one possibility is activation of the surface dimer by moving both H atoms onto one dimer carbon atom (reaction (2b) ). (CHCH > CH_{2}C) This process is endothermic by 0.41 aJ (59.5 kcal/mol) and requires 0.43 aJ (62.3 kcal/mol) to surmount the barrier. The resulting CH_{2}C structure is 0.28 aJ (40.4 kcal/mol) below the surface dimer plus H_{2} and there is a small barrier ( about 0.04 aJ (6 kcal/mol) ) to addition of H_{2} to the localized carbene center to give a dihydride structure. The other possibility involves a competition between the dimerization energy per surface dimer and the small barrier for addition of H_{2} to a localized carbene center. However the dimerization energy for diamond 100 is computed to be 0.48 aJ (69.3 kcal/mol) per dimer and therefore the barrier to addition would be predicted to be greater than 0.49 aJ (70 kcal/mol). (This saddle point has not been located.) In the silicon case, all the saddle point structures for this reaction have been located. The first step is nonsymmetry constrained addition of H_{2} to a surface dimer leading to a SiH_{2}Si structure. Here the dimerization energy per surface dimer is 0.12 aJ (17.4 kcal/mol). This is consistent with the barrier for nonsymmetry constrained addition of H_{2} which is 0.16 aJ (23.4 kcal/mo)l with the largest basis set. Thus, for the silicon case, symmetry constrained and nonsymmetry constrained addition of H_{2 }have comparable barriers. The nonsymmetry constrained addition is followed by rearrangement to a SiHSiH structure.
For hydrogen abstraction by a gas phase H atom (reaction(3) ), there is a barrier of about 0.04 aJ (6 kcal/mol) with respect to H atom and the surface CHC species. For the process H_{2} + CC > H + HCC the reaction is approximately thermoneutral on the triplet surface, but is uphill by about 0.07 aJ (10 kcal/mol) on the singlet surface in addition to the 0.04 aJ (6 kcal/mol) barrier. For the silicon triplet surface, this reaction is uphill by 0.15 aJ (22 kcal/mol), but there is no barrier other than the endothermicity. For the reaction H_{2} + CCH > H + HCCH, the reaction is exothermic by 0.003 aJ (0.4 kcal/mol) and has an approximately 0.04 aJ (6 kcal/mol) barrier.
For the addition of a H atom to a surface dimer, there is no barrier for either the diamond or silicon surfaces.
Another process which was studied for the 100 surface is the barrier to exchange of an H atom ( HCC > CCH or HSiSi > SiSiH). The barriers here are 0.44 aJ (63.8 kcal/mol) and 0.30 aJ (43.6 kcal/mol) for diamond and silicon, respectively.
Important differences are seen between diamond and silicon with respect to the abstraction process. For the diamond surface, the abstraction process has the lowest barrier (other than the H atom addition, which is barrierless on both surfaces) but the C_{2v} constrained addition of H_{2 }has a large barrier. On the silicon surface, this ordering is reversed and the symmetry constrained addition of H_{2 }has a lower barrier than the abstraction reaction. These differences are related to the properties of the surface dimer, especially the lower amount of p bonding for the silicon surface as compared to the diamond surface.
Calculations were also carried out for the analagous reactions on diamond 110 and 111 surfaces. For the diamond 110 surface the exchange barrier is larger 0.50 aJ (72.0 kcal/mol) than the 0.44 aJ (63.8 kcal/mol) barrier obtained for the 100 surface. The barrier to symmetry constrained addition of H_{2} is 0.30 aJ (43 kcal/mol) as compared to 0.34 aJ (49 kcal/mol) for the 100 surface. Both of these results are related to the lower overlap of the two orbitals of the dimer pair p bond for the 110 surface as compared to the 100 surface. Abstraction barriers were also computed. These are 0.04 aJ (5.2 kcal/mol) and 0.04 aJ (5.8 kcal/mol) for the reactions H + CHC > H_{2} + CC and H + CHCH > H_{2} + CCH, respectively, and the reactions are approximately thermoneutral. For the 110 surface the nonsymmetry constrained addition of H_{2} would be expected to be unfavorable, since breaking the dimer bond involves breaking at least 3 CC bonds.
For the 111 surface of diamond, the surface dangling bonds are only very weakly interacting, and the only reaction that was considered likely on this surface is abstraction of a H atom by a gas phase H atom. If the reaction is written in the direction H_{2} + CCH > H + HCCH the barrier is 4.0 kcal/mol and the reaction is exothemic by 0.04 aJ (6.1 kcal/mol). Note that for the diamond 100 surface the analogous reaction is endothermic by 0.07 aJ (10 kcal/mol) in addition to the 0.04 aJ (6 kcal/mol) barrier (on the singlet surface), while for the 110 surface there is a 0.30.4 aJ (56 kcal/mol) barrier and the reaction is essentially thermoneutral, and for the 111 surface the barrier is reduced to 0.03 aJ (4 kcal/mol) and the reaction is exothermic. These differences relate to the increase in CH bond strength with 111 > 110 > 100, and these differences in turn relate to the differences in overlap of the dangling bonds of a dimer pair.
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