J . Phys. Chem. 1991, 95, 9167-9169
9167
Jahn-Teller Distortions in the Octahedral Ni, Cluster Zhengtian Yu and Jan Almlof* Department of Chemistry, University of Minnesota, Minneapolis, Minnesota 55455 (Received: May 31, 1991)
The Jahn-Teller effect on the geometry of Ni, has been studied using ab initio CASSCF calculations. Jahn-Teller stabilization and 3Tlg).Wave energies (Em) are in the range 0.6-4.8 kcal/mol for the two electronic states that have been studied (qzu functions where the degeneracy is only due to the 3d part are not inert to Jahn-Teller effects, even though the d orbitals do not contribute to the metal-metal bonding. The ionization potential (IP) of Ni6 has been evaluated and compares favorably with recent experimental measurement.
Introduction The electronic structure of small clusters of the "late" transition metals has been subject to considerable interest, partly due to the close relation between these clusters and cluster models used for studying metal-catalyzed chemical reactions on surfaces.' The study of such clusters provides information about metal-metal bonding, especially on the question of d-orbital participation2 Jahn-Teller distortions often occur in these clusters as a consequence of degenerate electronic states, arising from (potentially) highly symmetric geometries. In the present work, Jahn-Teller effects on the geometry of the Ni6 cluster have been investigated. The purpose of the work is in particular to determine how crucial the Jahn-Teller effect is when the degeneracy is due to the 3d part of wave function, as compared with the 4s part. Clusters of Ni atoms have recently been generated using laser photoionization techniq~e.~Riley and co-workers have estimated the ionization potential (IP) of Nis to be 6.78 f 0.36 eV.4 Theoretically, the electronic energy for the ground state of Ni, has been calculated at the S C F leveL5 The IP was estimated based on either Koopmans' theorem or on ASCF calculations. All low-lying states of Ni6 can be derived from atomic states of the (3d)9(4s)1 configuration. The energetically most favorable orientation for the d-hole in the cluster is in orbitals of &type with the lobes pointing between the neighboring atoms: as illustrated in Figure 1. The ground-state configuration of octahedral Ni, can be understood with the partly filled 3d part and the valence (4s) part considered separately. The 4s part is intermediate-spin coupled (3Tlg)of occupation (a18)2(tlu)4(e,)0, while the 3d part is high-spin coupled (7A2u)of occupation (a2,)'(t2J3(eJ2. These partial wave functions couple to a total wave function of 9T2u symmetry. (A state of 'Tlu symmetry, with the same orbital occupancy, has recently been found to be competitive or even lower in energy, but the difference in structure and total energy is insignificant for the present p ~ r p o s e . ~With ) a triply degenerate ground state, the octahedral geometry is distorted as a result of the Jahn-Teller effect. Since the degeneracy is due to the 4s part (3T18)involving the mainly bonding orbitals,* the Jahn-Teller distortion is expected to be significant. In order to see what Jahn-Teller distortion may arise from degeneracies in the 3d part, we have also studied other electronic states, e.g., one in which the 3d orbitals are coupled to (3Tlg),whereas the 4s part of the wave function is nondegenerate (\Alg). Although this state is formally a candidate for Jahn-Teller distortion, one might expect the
TABLE I: Total Energies for Ni, total energy, state hartree 9T~P -9040.111 17 9T~P -9040.097 41 'TZP -9040.097 40 %g -9040.090 78 'Tlg -9039.209 9 1
2875. (6) Basch, H.;Newton, M. D.; Moskowitz. J. W.J . Chem. Phys. 1980, 73. 4492. (7) Gropcn, 0.;Almlof, J., to be published. (8) Shim, 1.: Gingerich, K. A. In Physics ond chemistry of smoll clusters; Jena. P., Rao. B. K..Khanna, S.N., Eds.; Plenum: New York. 1987; p 523.
cm,o
12/12
12/10
0.97 0.99
1019 12/10
0.23
816
0.99
1 .oo
" Coefficient of the leading configuration. bThe electronic energy is -9032.458 94 hartree at the SCF level (ref 5). TABLE 11: Summarv of Ionization Potentials for Ni, author method IP, eV Bl yholderO CNDO 6.3 Adachi et aL6 Xa 5.1 Basch et a].' SCF (Koopman's) 4.9 Tomonari et a1.d SCH (Koopman's) 5.7 ASCF 4.4 Pastor et aLc tight-binding/UHF 5.6 this work ACASSCF 6.1 Riley et al! experiment 6.78 i 0.36 "See ref 13. *See ref 14. CSeeref 6. dSee ref 5. CSeeref 15. fSee refs 3 and 4. ~
geometry to be insignificantly affected if the 3d orbitals largely play the role of an outer atomic core. Furthermore, we have also focused on a situation in which both the 4s part and the 3d part are degenerate ()TI8) but where they couple to a nondegenerate total wave function of symmetry. This excited state is formally not a candidate for Sahn-Teller distortion. Nevertheless, one may still expect its geometry to be distorted since it has the same 4s wave function as the ground state. The octahedral geometry of Ni, and the distortion parameters are shown in Figure 2. The distorted cluster is of either D4,,or DZhsymmetry resulting from e8 and tZ8Jahn-Teller active modes, whereas the reference structure of NI, is an optimized geometry of Ohsymmetry. In this work, the Jahn-Teller energy EJThas been calculated for the following different electronic states: 9T2U
@ eg:
9TZu @ t2g:
9T2U
-
-
(Oh)
9TZu (oh)
3T1g@ eg:
3T1g
[9EU
[9Blu
5A18 @ e8
( I ) Kunz, B..A. In Theory of Chemisorption; Smith, R. J., Ed.; Springer-Verlan: Berlin. 1980. (2) Hiutecky, J.; Fantucci, P. Chem. Reu. 1986, 86, 539. (3) Knickelbein, M.; Yang, S.;Riley, S.J . Chem. fhys. 1990, 93, 94. (4) Parks, E.: Klots, T.; Riley, S.J. Chem. fhys. 1990, 92, 3813. (5) Tomonari, M.:Tatewaki, H.; Nakamura, T. J. Chem. fhys. 1986,85,
active space
(oh)
-
+ 9B2U1(D4h)
+ 9B2u + 9B3u1(D2h)
f3A2g
+ 'Egl(D4h)
Computational Details The basis set used is based on the ( I 3s,7p,Sd) GTO basis optimized by Hyla-Kryspin et aL9 The basis was contracted to a minimal [4s,2p,ld] using a general contraction scheme.I0 Since (9) Hyla-Kryspin, L.; Demuynck, J.; Strich, A.; Benard, M. J . Chem. Phys. 1981, 75, 3955.
(IO) Raffenetti, R. C. J . Chem. f h y s . 1973, 58, 4452.
0022-365419112095-9167%02.50/0 0 1991 American Chemical Society
Yu and Almlof
9168 The Journal of Physical Chemistry, Vol, 95, No. 23, 1991 TABLE 111: Jshn-Teller Distortions of Nis case state
9T2u@ en
AB, deg
9B2u ( 0 4 1 )
9E, ( D 4 h ) 9T2u @ t2p0 9T2u@ (eB+ t2g) 5Alg @ eg
9B3u (D2h) 9B3u (DZh)
lT18 @ e8
'E8 (D4h)
ALi, A 0.09
-0.10
4.00 4.00
3A2g (O46)
0.00 -0.10
0.05 -0.03 0.03 -0.06
A -0.16
0.25 0.10 0.41 -0.03 0.05 -0.05 0.13
EJT,kcal/mol
-4.80 -4.39 -4.38 -2.47 -2.31 -2.31
-2.56 -6.17 -1.75 -0.55 -0.55 -2.84
CAS 12/12
12/10 1019 12/12
12/10 10/9 1019 1019 12/10
816 816
'Optimization on the B3, state failed, and the results shown here are obtained by optimizing average orbitals for three states of BSU,B,,, and B,, symmetry. bThis state is not subject to FOJT. The distortion shown here is formally a SOJT effect.
3d,, hole
Figure 1. Schematic representation of three different 3d-hole configurations for Ni, in the oh point group. Each set of 3d holes spans six symmetry orbitals, with only one out of each degenerate set displayed here. The 3d, hole forms the ground state of Ni,. The irreducible representations spanned by the 3d, holes are a,,,, e,, and t28.
Z
t
Figure 2. Geometry of the Ni, cluster.
the orbital exponents were optimized for the 3d94s1configuration of the Ni atom, the 4p orbital is not represented with the basis, and the outermost p-type function is quite contracted. The basis set was therefore augmented with a single pfunction with exponent of 0.092. Furthermore, the most diffuse s- and d-type functions were added uncontracted to the basis, giving a final basis denoted (13~,8p,Sd)/[5~,3p,2d].Since there is no loss of energy due to contraction if a general contraction scheme is used, the energy with this basis is actually 5 mH lower than the energy with the original primitive basis, the difference being due to the extra p-function in our basis. As a comparison, the atomic energy obtained with the segmented basis used in ref 5 is more than 1.2 hartree higher than ours. Our final set has a total of 24 functions per atom or 144 for the Ni6 cluster, after the totally symmetric d-component has been eliminated.
The active space used in the CASSCF calculations had 12 electrons distributed in 12 active orbitals (12/12). The orbitals in the active space are essentially the 4s orbitals and the open d,(~3~) orbitals. For the qzu state we also performed 12/10 CAS calculations with the e, type orbitals excluded, as well as a 10/9 CAS where in addition the (al,)z orbital is kept inactive (Le. doubly occupied). The results are shown in Table I. Since the 10/9 CAS is essentially a Hartree-Fock calculation (the leading configuration has a coefficient of 1.OO) and since there is no difference between 10/9 and 12/10 in terms of total energy, the near-degeneracy correlation effect on the (a1J2 orbital appears to be unimportant. On the other hand, the energy lowering on going to the 12/ 12 CAS suggests that near-degeneracy correlation involving the e, type orbitals is of some importance. As we will see later, however, this will not significantly affect the relative energy or the calculated Jahn-Teller distortions, since the magnitudes of near-degeneracy effects are almost same both for the undistorted and the distorted structure. Therefore, we may conclude that the size of active space is not quite crucial, and for the low-lying excited states SAl, and 3Tls, we have limited our active space to 12/10 and 8/6, respectively. All calculation presented here were performed using the MOLECULE-SWEDEN code."
Results and Discussion The IP of Nib has been calculated at the 12/12 CAS level. Table I1 lists our result and compared them with those of other theoretical investigations and with experimental results. Our result compares quite favorably with experiment. The difference in calculated IP of 1.7 eV between our result and the ASCF value from ref 4 indicates that accounting for near-degeneracy correlation (and to some extent our use of a better basis set) improves the results significantly. The calculated Jahn-Teller distortions for three different electronic states are shown in Table 111. As expected, both the distortion parameters and EJTshow that the distortion of the ground state is stronger than for the excited states. In other words, the degeneracy of the 4s part of the wave function is more crucial for geometry-related properties than the 3d part. All low-lying states have the 4s configuration (al,)*(t1J4, whereas the choice among the many different possible couplings of the open d-orbitals is energetically unimportant. In other words, the 'd-band" is quite narrow, consistent with previous SCF calculation6 or experiment.'* As a result, the distortion for the state can be accounted for as mainly due to the degeneracy of the 4s part. Because of the formal nondegeneracy of the total wave function for this state, (1 1) MOLECULE-SWEDEN is a vectorized SCF-MCSCF-MRCI program, written by: Siegbahn, P. E. M.; Bauschlicher, C. W.; Roos, B. 0.; Taylor, P. R.; Heiberg, A,; AlmlBf, J.; Langhoff, S.R.; and Chong, D. P. (12) Hufner, S.; Wertheim, G. K.; Smith, N . V.;Traum, M. M. Solid State Commun. 1972, 11, 329. (13) Blyholder, G. Surf. Sci. 1974, 42, 249. (14) Adachi, H.; Tsukada, N.; Satoko, C. J. Phys. Soc. Jpn. 1978,45,875. (15) Pastor, G. M.; Dorantes-Davila, J.; Bennemann, K. H. Chem. Phys. Lett. 1988, 148, 459
9169
J . Phys. Chem. 1991, 95,9169-9175
state E,, which stems from an e, type distortion, can be further distorted by the t2, mode; this combined (e, t2J leads to the equilibrium geometry for the ground-state of the Ni6 cluster.
+
0
-
h
0
-1
E
: Lo -2 u
A
Y
-3
D4h
-5 -0.3
0.2
-0.1
O.Oo
0.1
0.2
0.3
ALz (A) Figure 3. Jahn-Teller stabilization energies (EJr) for three different states, due to distortions along the e* mode. The symmetriesof states in D,* symmetry are shown in italics. it only shows a slight SOJT distortion (0.55-1.75 kcal/mol) as compared with the other excited state considered here, 3Tlg (0.55-2.84 kcal/mol) as shown in Figure 3. Distortion along the t,, mode results in a smaller Jahn-Teller distortion than for the e, mode in terms of EJT.The degenerate
Conclusions The IP of Ni6 has been calculated to be 6.1 eV using CASSCF calculations and a CGTO basis set. The result compares favorably with recent experimental measurements. Jahn-Teller effects on the geometry of the Ni6 cluster have been studied for several electronic states. The Jahn-Teller distortion energy Em has been calculated to about 2.3-4.8 kcal/mol for the ground electronic state and 0.6-2.8 kcal/mol for excited states. The origin of the Jahn-Teller distortion is mainly the degenerate 4s part of the wave function. Other states also show small "Jahn-Teller" type distortions if the 4s part of the wave function is degenerate. Degenerate states where the degeneracy stems from the 3d part of the wave function also show a nonnegligible FOJT effect on the geometry. This is not to be interpreted as a d-orbital participation in the cluster binding, but rather this shows the effect of the nonsymmetric field, resulting from the 3d part of the wave function. Acknowledgment. This work was supported by the National Science Foundation, grant no. CHE-8915629, and by the Minnesota Supercomputer Institute.
"Mixed" Metallic-Ionic Clusters of Sllver/Silver Iodide Clifton K. Fagerquist, Dilip K. Sensharma, and Mostafa A. El-Say&* Department of Chemistry and Biochemistry, University of California, Los Angeles, Los Angeles, California 90024 (Received: June 7 , 1991)
We have sputtered isotopically enriched silver foil IwAg in the source of a double-focusingmass spectrometer (reverse geometry) in the presence of methyl iodide vapor. We have detected the formation of a range of positively and negatively charged iodinated silver clusters of formula [AgxIYlkalong with purely metallic silver clusters. The important observations are as follows: ( I ) The cluster mass peak intensities, in accord with the spherical jellium model, showed n-oddln-even alternation in intensity and in some cases closed-shell behavior when plotted against the number of delocalized electrons, n, where n = X - Y- k and k is the overall charge on the cluster. This suggests that as the iodine atoms are added to the cluster, equal numbers of Agl ionic bonds are formed which localizes an equal number of previously delocalized silver valence electrons on the iodine atoms. (2) The n-oddln-even intensity oscillation is more pronounced at lower X than at higher X. (3) Cluster species of unusually low intensity either have one delocalized electron in excess of that necessary to complete a jellium shell closing or are one delocalized electron deficient of a shell closing. (4) The purely metallic positively charged Ag clusters are formed with greater intensity in the presence of CH31, suggesting that their formation and stability are enhanced by the reaction. (5) Although the positively charged iodinated clusters are stronger in intensity than the negatively charged iodinated clusters, the maximum number of iodines that are added is higher for the negatively charged metallic clusters than for the positively charged clusters which suggests the importance of a charge-transfer mechanism in the iodine addition process. (6) The intensity of all clusters decreases quasiexponentially with cluster size and with the number of halogens contained, suggesting that these clusters are formed from smaller ones in the gas phase by multiple collisions.
Introduction Recent attention has been given to metal clusters whose relative stability is dependent not on the packing or structure of the cluster but on the number of delocalized valence electrons that a particular metal cluster possesses. The spherical jellium model' predicted enhanced stabilities for metallic clusters possessing a specific number of delocalized valence electrons corresponding to a "closed" shell of configurations: 1s2,1 p6.ldlo,2s2,1fI4,2p6,etc. Metal clusters (charged or neutral) with 8, 18,20, 34, and 40 delocalized electrons showed enhanced stability and thus strong peaks in the mass spectrum. These are called magic numbers. Metal clusters
possessing 9, 19, 21, 35, 41, etc., delocalized electrons showed relative instability as confirmed by the mass spectral ion peak intensity distribution of the clusters. Along with these "shell" closing effects there is observed odd/even alternation in the intensity where clusters with an even number of delocalized electrons clusters show greater intensity over their odd-delocalized electron neighbors. Experimental verification of the spherical jellium model was first observed for sodium clusters by Knight and co-workers.2 Subsequent experiments revealed that other alkali metals showed similar patterns of enhanced stability and instability' in accordance
(1) Martins, J. L.;Car, R.;Buttet, J. Surf. Sci. 1981, 106, 265. Ekardt, W. f h y s . Rev. B 1984, 29, 1558.
(2) Knight, W. D.; Clemenger, K.;de Heer, W. A.; Saunders, W. A.; Chou, M. Y.;Cohen, M. L . f h y s . Rev. Lerr. 1984, 52, 2141.
0022-3654/91/2095-9169$02.50/0
0 1991 American Chemical Society
