1066-3622/03/4503-0233$25.00�2003 MAIK �Nauka/Interperiodica�
Radiochemistry, Vol. 45, No. 3, 2003, pp. 233�236. From Radiokhimiya, Vol. 45, No. 3, 2003, pp. 213�216.Original English Text Copyright � 2003 by Sekine, Kondo, Yamamoto, Onoe.
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Geometric and Electronic Structures of Tc and Mn Clustersby Density Functional Calculations1, 2
R. Sekine*, R. Kondo*, T. Yamamoto*, and J. Onoe*** Department of Chemistry, Faculty of Science, Shizuoka University, Shizuoka, Japan
** Materials Science Division, Research Laboratory for Nuclear Reactors,Tokyo Institute of Technology, Tokyo, Japan
Received December 26, 2002
Abstract�The geometric structures of Tc2�Tc5 and Mn2�Mn8 clusters were optimized by the Amsterdamdensity functional method. The trimeric, tetrameric, and pentameric Tc clusters exhibit the equilibrium struc-tures of isosceles triangle, tetrahedron, and square pyramid, respectively. The structures of the Mn clusters upto Mn4 are similar to those of the respective Tc clusters, while the Mn5, Mn6, Mn7, and Mn8 clusters havethe distorted trigonal bipyramidal, distorted octahedral, pentagonal bipyramidal, and C2v structures, respec-tively. The Tc clusters are paramagnetic, while the Mn clusters are basically ferromagnetic.
Many properties of metal clusters differ from thoseof bulk metals, in particular, the bond length [1], ioni-zation energy [2], magnetic moment [3, 4], and chemi-cal behavior [5, 6]. Transition metal clusters are ofspecial interest owing to a large number of electronicstates of different spin multiplicities and complexityof the metal bond (participation of the metal s, p, andd orbitals). Here we focus on the similarity and dis-similarity between the Mn and Tc clusters. The elec-tronic configurations of these atoms are different: thatof Mn is [Ar]3d 54s2, while that of Tc is [Kr]4d65s1,although Mn and Tc belong to the same group of theperiodic table.
Manganese clusters show some interesting charac-teristics that distinguish then from the other 3d-transi-tion metal clusters. For example, certain experimentalresults suggest that the Mn atom in small clustersbehaves like a rare-gas atom. In particular, the bondenergy in neutral Mn2 is less than 0.1 eV [7]. Thisvalue is one or more orders of magnitude lower thanthe bond energy in the other 3d-metal dimers. Theinteratomic distance in Mn2 is 3.4 �, which is 130%of that in the bulk crystal [8]. These facts show thatmetallic 4s�4s and 3d�4s interactions in Mn2 areweak.
These peculiar characteristics mainly originatefrom the electronic configuration of the isolated Mnatoms, 3d 54s2. The 3d orbital is half-filled, and the4s orbital, fully filled; both have a spherical sym-������������
1 This article was submitted by the authors in English.2 Reported at the Third Russian�Japanese Seminar on Techne-
tium (Dubna, June 23�July 1, 2002).
metry. It is an interesting configuration, maybe evenmore interesting than that of bivalent metals, from thepoint of view of how the fully or half-filled orbitalsare broadened to form the band structure. Fujima andYamaguchi reported that, as the cluster size increasesfrom 2 to 7, the number of electrons on the s orbitaldecreases while that on the p orbital grows. This in-dicates that s�p hybridization occurs when the clustersize increases [9]. Nayak and Jena have optimized theequilibrium geometries of Mnn for n � 5 at two levelsof approximation: LSD and the generalized gradientapproximation (GGA). The calculated bond lengthand bond energy in Mn2 are very sensitive to the treat-ment of exchange and correlation, and only the GGAcalculations at the B3LYP level are able to explainsome of the experimental results (the calculated bondlength is 3.53 A, and the bond energy, 0.06 eV [10]).As for the spin state, ferromagnetic and antiferromag-netic or frustrated antiferromagnetic solutions havebeen reported by Pederson et al. [11].
As compared to the Mn clusters, there are onlya few reports on the electronic, geometric, or spinstructures of Tc clusters. Klyagina et al. calculated thespin states of Tc dimers and concluded that the Tcelectronic structure is 4d65s1. However, they have notoptimized the dimer bond length, and it is quite prob-able that the spin state of the Tc dimer will stronglycorrelate with the bond length.
In this study we obtained the geometry of smallMn and Tc clusters by the density functional methodand examined a correlation between the spin state ofthese metal clusters and their geometry.
RADIOCHEMISTRY Vol. 45 No. 3 2003
234 SEKINE et al.
Fig. 1. The most stable structures of Mnn clusters (n =2�8). (Eb) Binding energy. The bond length (�), total spinS, equal to the half of the difference between the number of�- and �-spins, magnetic moment per atom (�B), and sym-metry are indicated; the same for Figs. 3�5.
Fig. 2. Spin magnetic moments per atom of Mnn clusters(n = 2�8).
COMPUTATIONAL METHOD
We have performed geometry optimization for Mnn(n = 2�8) and Tcn (n = 2�5) clusters using the pro-gram package of the Amsterdam density functional(ADF) method [13]. The basis set for the cluster wasconstructed by triple-� Slater-type orbitals (STO). ForMn [Tc], the 1s, 2s, and 2p [1s, 2s, 2p, 3s, 3p, and 3d]
atomic orbitals were treated in the frozen core ap-proximation, while the 3s, 3p, 3d, 4s, and 4p [4s, 4p,4d, 5s, and 5p] orbitals were treated as valence func-tions. We used the VWN potential as a local part ofthe exchange and correlation potentials [14], and thePW91 potential, as gradient correction [15]. For Tcclusters, the relativistic effects were considered. Inthis calculation, the first-order relativistic PauliHamiltonian was used [16, 17]. That is, the singlepoint group symmetry and the scalar relativistic cor-rections (Darwin and mass�velocity terms) were in-cluded. The relativistic core potentials were obtainedusing four-component Dirac�Slater Hamiltonian forisolated atoms. We performed spin-unrestricted calcu-lations for all the clusters because the Mn and Tcatoms have a magnetic moment. We assumed the pos-sible spin state N to be in the range 0 � N � 7 �(number of atoms). Here, N is the difference betweenthe numbers of �-spin (up-spin) and �-spin (down-spin) electrons. The multiplier 7 corresponds to thenumber of valence electrons of Tc (4d65s1) and Mn(3d 54s2). We examined not only highly symmetricbut also distorted structures in order to provide thefreedom of spin states.
RESULTS AND DISCUSSION
Optimized Structures and Magnetic Momentsof Mn Clusters
The most stable structures of Mnn (n = 2�8), ob-tained by ADF calculations, are shown in Fig. 1. Theequilibrium bond lengths, total spins (S, equal to thehalf of the difference between the number of �- and�-spins), magnetic moments per atom (�B), sym-metries, and binding energies (Eb) are also given. Forall the clusters, the variety of isomers with differentmagnetic moments were examined. The most stablestructures are equilateral triangle, tetrahedron, dis-torted trigonal bipyramid, distorted octahedron, penta-gonal bipyramid, and the C2v structure for the trimer,tetramer, pentamer, hexamer, heptamer, and octamer,respectively. Up to hexamer, these structures arealmost the same as those obtained by Nayak et al. [10]and Pederson et al. [11]. As for the heptamer andoctamer, the structures are different from those de-scribed by Pederson et al. [11]. They reported twoeclipsed triangles with a single atom cap for theheptamer and a distorted cube for the octamer.
The spin moments of the Mn clusters are sum-marized in Fig. 2. The spin moment is 5 �B for theclusters up to the tetramer, and for higher clusters itslightly decreases to 4 �B. Since the isolated Mn atomhas the spin moment of 5 �B, it can be concluded that
RADIOCHEMISTRY Vol. 45 No. 3 2003
GEOMETRIC AND ELECTRONIC STRUCTURES OF Tc AND Mn CLUSTERS 235
Fig. 3. Optimized geometries of Tc2 and Tc3.
Mn clusters have ferromagnetic properties. This con-clusion is consistent with the results obtained in[10, 11].
Optimized Structures of Tc Clusters
The optimized geometries of the Tc dimer and tri-mers are shown in Fig. 3. The bond length in Tc2 wascalculated to be 2.014 �, which is much shorter thanthe value of 2.710 � for Tc metal [18]. The extremelyshort bond in Tc2 is a common characteristic of s1
elements such as Na, K, and Cu [1]. We examinedthree types of geometry of Tc3. The most stable struc-ture was found to be the C2v structure (isosceles tri-angle). However, the second most stable structure ofD3h symmetry (equilateral triangle) has almost thesame binding energy as the C2v structure. The leaststable is the linear (Dh) structure.
The Tc4 isomers examined in this study are shownin Fig. 4. The most stable is the tetrahedral structure(Td symmetry). The distorted structure (C3v sym-metry) has approximately the same Eb, bond length,and spin states as does the Td structure. The secondmost stable isomer of Tc4 is distorted square (Cs sym-metry). The more symmetrical structure, D4h square,was found to be less stable (Eb = �6.215 eV). Theleast stable tetramer has the linear (Dh) structure.
The optimized geometries of Tc5 isomers are sum-marized in Fig. 5. The most stable structure is thesquare pyramid (C4v symmetry). The second, the
Fig. 4. Optimized geometries of Tc4.
Fig. 5. Optimized geometries of Tc5.
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236 SEKINE et al.
Fig. 6. Correlation between the optimized bond length (r)in Tc2 and Mn2, bond energies (Eb, per atom), and spinstates S.
third, and the least stable structures are trigonal bi-pyramid (D3h), planar pentagon (D5h), and linearstructure (Dh), respectively.
Comparison of the geometries of the Tc clusterswith those of the Mn clusters shows that the trimerand the tetramer structures are the same, whereas themost stable structures of Tc5 and Mn5 are different.The former is a square pyramid (C4v), and the latter,a distorted trigonal bipyramid. In the case of the Tcpentamer, the trigonal bipyramid (D3h) is the secondmost stable structure, and the calculated difference inEb between the C4v and the D3h structures is as smallas 0.078 eV (Fig. 5). Furthermore, the distorted tri-gonal bipyramid for Mn5 can easily transform intothe distorted square pyramid. Therefore, the differencein the geometries of these clusters should not be con-sidered as significant.
Spin Moment of Tc Clusters
The spin moments per atom of all the Tc clustersup to Tc5, except Tc4, are calculated to be 1.00 �B.The Tc4 cluster has the moment of 2.00 �B. Thus, theTc clusters are essentially paramagnetic, stronglydiffering from the Mn clusters. As mentioned above,the Mn clusters have the ferromagnetic character. Inorder to elucidate the difference in spin interactionbetween the Tc and Mn clusters, we examined the cor-relation of the spin states with the bond lengths fordimer and bond angles in the trimer.
Figure 6 shows the correlation between the op-
timized bond length (r, �) in Mn2 and Tc2, the totalspin S, and the binding energies (Eb) at the optimizedbond lengths. For both Tc2 and Mn2, as the spinmoment increases, the bond lengths also increase.This means that strong spin interaction causes repul-sion of the atoms. Contrary to the bond lengths, thecorrelations of Eb with the spin states are opposite.In the case of Tc2, as the spin moment increases, Ebgrows also, whereas in Mn2 Eb decreases with in-crease in the bond length. This difference may be dueto the difference in the interaction between 3d and4d electrons. Systematic comparison of the spinstates of 4d and 3d metals may be a subject of furtherstudies.
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