Tight-binding molecular dynamics study of transition metal carbide clusters

A minimal-parameters basis is used to obtain a transferable tight-binding parametrization of the Ni–C interactions applicable to binary Ni C clusters. The data base for fitting the parameters is obtained from ab initio results for small m n Ni C , nqm(4, clusters obtained using the density functional method and the single, double and triple coupled-clusters m n method. The parametrization is incorporated into the tight-binding molecular dynamics scheme to study Ni C clusters of m n arbitrary sizes and the interaction of Ni with graphite. Our results are in very good agreement with experiment. q 1999 Elsevier Science B.V. All rights reserved. w x Recent experimental works 1–7 confirmed by w x parallel theoretical investigations 8–10 have shown that graphite interacts strongly with transition metal Ž . TM atoms and that this interaction exhibits a strong variation of the hybridization strength between carbon p and the TM d-orbitals. As a result, the z strength of the magnetic moment of a TM atom on the surface of the graphite was found to depend strongly on the adsorption site and the height of the w x TM atom above the graphite surface 8–10 . From the series of the 3d TM atoms, Fe, Co and Ni Ž . monolayers ML were found to be ferromagnetic on ) Corresponding author. E-mail: [email protected] 1 E-mail: [email protected] graphite, while V and Cr MLs were found non-magw x netic 8 . Similarly, from the 4d TM series, Rh and Ru overlayers of small coverage can sustain small magnetic moments on graphite, while Pd monolayers w x were found non-magnetic 9 . One characteristic feature of the adsorption of TM Ž atoms on graphite is the change increase or de. crease in their magnetic moments upon adsorption w x when compared to the isolated TM atoms 10 . In the case of Ni, the adsorption on graphite results in a pronounced reduction in the magnetic moment. The magnetic moment is found to vanish for the single Ni atoms as well as for the Ni dimers on graphite 2 w x 10 . The question can be raised whether an incipient 3-dimensional structure is a necessary condition for the appearance of a finite spin of Ni on graphite. In 0009-2614r99r$ see front matter q 1999 Elsevier Science B.V. All rights reserved. Ž . PII: S0009-2614 99 00059-7 ( ) A.N. Andriotis et al.rChemical Physics Letters 301 1999 503–508 504 the case of a Ni ML adsorbed on graphite, however, the reduction in the value of the magnetic moment of the Ni atoms has been reported to be 25% of the value found for the corresponding unsupported w x monolayer 8 ; the latter measured to be 0.4 m per B w x Ni atom 8 . Thus, results for Ni MLs supported on graphite, in contradistinction with those for single Ni atom andror Ni on graphite, confirm that small 2 magnetic moment can be sustained by adsorbed Ni atoms on graphite. Therefore, the chief question that needs to be answered is whether one can identify the factors affecting the delicate interplay between the geometric and the magnetic ordering of the Ni adatoms on graphite. The recent experimental results on the interactions w x of TM atoms with C clusters 4–7 provide another 60 interesting area for the study of the hybridization strength between carbon p and the TM d-orbitals. z Some of these experiments report results of the adsorptionrdesorption of TM atom clusters on C60 w x molecules 5–7 , while others deal with the effects of substitutional replacement of one or more C atoms on the C and C clusters with one or more TM 60 70 w x atoms 4 . These experiments have left open the structural information, so intimately related to the magnetic state of these complex hetero-systems. These results pose a challenge to the theoretical investigations to determine realistic structures of Ž . M C , MsNi,Co,V,Sc,Cr. Similarly, the mechn 60 m anism responsible for the production of the cluster series C Ni and C Ni; ns0,1,2, . . . , has 59y2 n 69y2 n also not been understood. Furthermore, the measured resistivity and the thermo-electronic power of single-walled carbon nanotubes interacting with TM w x atoms 3 indicate a different behavior when compared with the corresponding graphite–TM systems and, therefore, pose even more challenging problems for a theoretical investigation. From the theoretical point of view, the understanding of these experimental results requires a series of systematic computations which, however, due to the size of the systems, their low symmetry and the presence of the TM atoms, are beyond the reach of the present day ab initio methods. The need exists, therefore, for a simpler semi-empirical computational approach which allows one to perform spin and geometry unrestricted calculations. To this end, our newly developed tight-binding molecular Ž . w x dynamics TBMD method 11,12 , as generalized recently to treat hetero-nuclear magnetic systems w x 13 , appears very promising for the study of complex systems such as the ones described earlier. In this work, we present results from applications of our TBMD method to the Ni C clusters and the m n interaction of Ni atoms with graphite. The details of our TBMD method has been described in our recent Ž w x papers see, e.g., Refs. 11–13 and references . therein and, therefore, will not be repeated here. For the purpose of completeness, however, it should be noted that in our method we make use of Harrison’s w x w x 14 universal Slater–Koster-type 15 parameters appropriately scaled with respect to the inter-atomic distance. In the case of clusters consisting of only single species, a minimal set of five parameters is required as an input to the TBMD method. These parameters include the strength F i j of the pair repulsive interac0 tion between atoms i and j; the scaling factor a i j which is used to describe the variation of the Slater–Koster parameters as well as the pair repulsive interaction with the inter-atomic distance, r ; i j the strength s of the intra-site exchange interaction 0 for the atoms i; and, finally, two other parameters, namely the a and b , used to define the calibration i j i j w x energy term U 11,12 . For a hetero-nuclear sysbond tems the set of the input parameters described above Ž is required for each species and with the exception i . of s for each pair ij of different atoms i and j. All 0 these parameters are obtained by fitting the results of the TBMD method to the experimental data or to reliable ab initio results if the experimental information is not available. The input data, necessary for our fitting process in the case of the hetero-nuclear Ž clusters A B consisting of n atoms of type A and n m . w x m atoms of type B , includes 13 the bond lengths, r , the vibrational frequencies v , the charge ab a b states Q , asA, B, and the binding energies, E, a B asA, B; bsA, B, of the dimers A , B and AB. 2 2 Also, a knowledge of the cohesive energies of the bulk phase of the species A and B as well as the energy difference between the ground state and the Ž . lowest-lying magnetic states if any of the trimers A , B andror the tetramers A , B is needed. 3 3 4 4 Thus, for the Ni C system, which is of interest in m n Ž the present work, we need the experimental or ab . initio derived information for the dimers Ni , C 2 2 ( ) A.N. Andriotis et al.rChemical Physics Letters 301 1999 503–508 505