1096
J. Phys. Chem. 1983, 87, 1096-1097
Structure and Stability of Li,, and Lis Clusters Dejan PlavEile,+ Jaroslav Kouteckg, Glanfranco Pacchlonl,$ and Vlasta BonaEb-Kouteckf Institut fur Physikalische Chemie, Freie Universitat Berlin, 1000 Berlin 33, Germany (Received December 2 1, 1982; I n Final Form: February 7, 1983)
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The results of ab initio CI calculations on Lig and Lis clusters are compared with those recently obtained by Richtsmeier et al. (J.Phys. Chem., 86,3942 (1982)) with the DIM method. The planar sections of the fccub Li crystal lattice exhibiting singlet ground state are the most stable Li clusters. More compact structures such as Lid ( T d )and Lis (0,) are less favored and have a triplet ground state.
Recent widespread interest in the theoretical investigation of clusters necessitates a critical comparison of the applicability and reliability of various theoretical approaches employed to handle the difficult problem of chemical binding in small clusters. For studies of lithium clusters rather sophisticated quantum chemical methods can be employed for evident reasons, and consequently these clusters with a small number of electrons are suitable for testing the reliability and efficiency of theoretical methods. Until now the ab initio SCF,’ CI,2and CEPA3 as well as DIM4 studies of Li clusters have been published but the obtained results are not in complete agreement with each other as has been already pointed out elsewhere.2a The conclusions drawn in the recent work of Richtsmeier, Dixon, and Gole5 differ from some of our current results obtained employing the ab initio all-electron multireference double excitations CI method (MRD CI).2a,cpdTherefore, in the present contribution the discrepancies among the results on Li4clusters are elucidated and relevant unpublished work on Li6 is presented. The Li4 cluster with minimal energy in its singlet state has a planar rhombic geometry with an angle of 127’ and a side length of 5.82 au.% The similarity with the rhombus which is a part of the Li fccub lattice is evident. The square form of Li, exhibiting biradical features is substantially less stable than the rhombus, with the energies of the singlet and triplet states almost equal to the energy of two Liz molecules. Consequently, square Li4 cannot be considered as a stable form in contrast with the rhombic arrangement. An even less stable form than the square Li, is the tetrahedral Lid cluster which exhibits the triplet ground state lying energetically essentially below the singlet state.% These well-established results contradict the conclusions of the investigation employing the DIM method by Richtsmeier et aL5that among several energetically close lying forms of Li4the tetrahedral cluster is the most stable arrangement. The majority of very stable Li6 clusters can be considered as part of the fccub lattice. Their average interatomic distances do not deviate substantially from the experimental ones in the fccub Li crystalzd (see also Table I). The spin properties are strongly dependent on the changes in cluster geometry. For example, the deformation of the cluster from the DZhto C% (Figure 1) causes only a small energy increase but the “closed shell” D% clusters go over in the biradical Ca species with nearly degenerate lowest singlet and triplet states (cf. Figure 3 of ref 2d). The MRD-CI energies and binding energies per atom (BE/n) are given in the Table I (see also Figure 1) for Present address: “Ruder BoikoviE” Institute, 41001 Zagreb, Yugoslavia. *On leave from Istituto di Chimica Generale e Inorganica, Universit6 di Milano, 1-20133 Milano, Italy.
TABLE I: Binding Energies of Li, Clustersa
cluster:
spin multiplicityC
1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1
3 1 3 1 3 1 3
theor treatmen td kcal/mol n M / c i c i z
BE / n ,
E,,,
au
-44.402 -44.361 -44.400 -44.355 -44.398 -44.311 -44.395 -44.377 -44.386 -44.390 -44.390 -44.388 -44.388 -44.389 -44.380 -44.384 -44.382 -44.362 -44.373 -44.381 -44.360 -44.381 -44.318 -44.358 -44.368 -44.356
59 89 95 35
81 07
41 54 02 13 69 75 92 42 03 21 56 59 96 21 95 18 29 92 81 18
14.02 9.16 13.85 9.08 13.62 10.12 13.28 11.40 12.28 12.78 12.77 12.57 12.59 12.64 11.66 12.10 11.92 9.83 11.02 11.79 9.61 11.18 11.48 9.45 10.50 9.17
4M/0.85 3M/0.83 1M/0.83 1M/0.83 3M/0.83 2M/0.84 1M/0.83 1M/0.83 5Ml0.85 4Ml0.85 4M/0.85 1M/0.84 3M/0.81 2M/0.83 3M/0.82 1M/0.82 6M/0.84 9M/0.83 lMi0.82 1M/0.84 2Ml0.80 1M/0.83 8M/0.86 5M10.84 2M/0.81 1M/0.80
Results obtained with basis set F of ref 2c. If not mentioned otherwise, the Li-Li distance has been fixed to the value of the nearest-neighbor distance in a fccub Li crystal 1= singlet, (5.8654 au). See Figure 1 for definitions. 3 = triplet. nM indicates the number of reference configurations from which all single and double excitations are generated. All configurations which contribute more than 1%to the CI expansion are choosen as leading configurations. c ici’ gives the total weight of the main configurations in the final CI wave function. e The geometry optimization for this structure gives the following results: Re = 5.905 au, EcI = -44.40101 au, BE/n = 13.86 kcal/mol. The geometry optimization for this structure gives the following results: Re = 5.876; E C I = -44.39882; BEIn = 13.62 kcal/mol. g The geometrical parameters for this bipyramidal Li, cluster have been taken from ref 3b. The geometry optimization for the triplet state of this structure gives the following results: Re = 5.895 au; E,, = -44.39018 au, BE/n = 12.18 kcal/mol.
selected Li6 clusters with fixed interatomic distances6 which are either rather stable (large BE/n) or related to (1) (a) R. Janoschek, J.Mol. Struct., 6 , 283 (1970); (b) F. Marinelli, A. Julg, and G. Abbate, Surf. Sci., 59, 319 (1976);(c) R. F. Marshall, R. J. Blint, and A. B. Kunz, Phys. Reu. B , 13,3333 (1976);(d) P. Fantucci and P. Balzarini, J. Mol. Catal., 4, 337 (1978); (e) G. Del Conde, J. Garcia-Prieto, and 0. Novaro, Mol. Phys., 44,477 (1981);(0 R. Car and J. L. Martins, Surf. Sci., 106, 280 (1981).
0022-3654/83/2087-1096$01.50/0 0 1983 American Chemical Society
The Journal of Physical Chemistry, Vol. 87, No. 7, 1983
Letters
1097
(fj c2:
c5v
D4h
Oh
4@ ...
-'
D2 l-l
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C1
6.
D3h
D2h
c2v
60
90
150
120
180
aio)
Figure 1. Geometries of the Li, clusters reported in Table I. The C, structure is obtained by changing the dihedral angle between the two rhombus of the planar C2"'structure. The analogous deformation of the D, cluster gives the C l v (a= 120') and the D, structures (see also Figure 2).
Figure 2. Dependence of the binding energy per atom (BEln) on the angle between the Liz-Li, and Li,-LI, "bond": (-) deformation from C2"'to C,;(.-e) deformation from D, to D W ;s means singlet state, t triplet. The dotted line (. -) indicates the avoided crossing of the two triplet states of the C, cluster.
the clusters investigated by DIM approach in the work of Richtsmeier et al.5 These results have been obtained by employing the all-electron MRD-CI procedure with A 0 basis set F, described in the ref 2c. The methodical details are given in Table I. The sequence of L&clusters in Table I is chosen according to cluster stability. The most stable Lis arrangement belonging to the CBvpoint group (cf. Figure 1) which can be considered as a step in the pentagonal crystal grow' is followed by two planar clusters D%' and C%'. The square bipyramidal DBhis slightly less stable than the planar structures representing sections of the fccub lattice. All these structures have a singlet ground state. The highly symmetrical and compact o h structure is an even less stable form with the triplet state energy 3 kcal/mol below the lowest singlet state. This contradicts the DIM results of ref 5. The triplets are also ground states of less stable C,, C2h, C1,and D3hgeometries. The characteristic changes of the binding energy per atom (BE/n) for several low-lying states of two Li6 structures as functions of the angle a between the planes of the two squares or two rhombus in the interval 60'
