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COMMENTS Reply to “Comment on ‘Tuning Magnetic Moments by 3d Transition-Metal-Doped Au6 Clusters’” Meng Zhang,* Li-Ming He, Li-Xia Zhao, Xiao-Juan Feng, and You-Hua Luo*
Department of Physics, East China UniVersity of Science and Technology, Shanghai 200237, China
Figure 1. The symmetry type (at 0.01 Å tolerance) and the bond lengths (Å) of the ground-state Sc@Au6 cluster optimized with PW91/VPSR (DMOL3), PBE/VPSR (DMOL3), and B3PW91/SDD (G03), respectively. The center gray sphere represents vanadium atom.
ReceiVed: October 21, 2009 In a recent paper entitled “Tuning Magnetic Moments by 3d Transition-Metal-Doped Au6 Clusters”,1 we performed a relativistic all-electron density functional theory computation implemented in the DMOL3 package2 using PW91 functional3 and DND basis4 to investigate the geometries, electronic, and magnetic properties of the 3d transition-metal-doped gold cluster, M@Au6 clusters (M ) Sc, Ti, V, Cr, Mn, Fe, Co, Ni). It is found that the d orbitals of these transition metal atoms can stabilize the Au6 ring structure. Furthermore, the magnetic moments of these clusters vary from 0µB to 4µB by doping different transition metal atoms with open d shells into Au6 ring. We found the number of the valence electrons of M@Au6 clusters were responsible for the total magnetic moments. Ho¨ltzl et al.5 reported the phenomenological shell model of metal clusters (PSM) in their comment on our recent paper1 to provide a consistent rationalization for the observed variation of the geometries and magnetic properties of M@Au6. The main assumption of the PSM is that molecular orbitals corresponding to the itinerant electrons have shapes similar to that of the atomic orbitals which can be denoted by capital S, P, D. With the model of PSM, the total magnetic moment of the high D6h symmetry Mn@Au6 cluster and the local magnetic moment of the Mn atom, which were indeed found in our work,1 are simply explained by the closed electronic shell. The results of other M@Au6 clusters obtained in our work can also be explained by PSM.5 For the case of Sc@Au6, we reported the lowest energy structure of this cluster had a D6h symmetry computed at PW91/VPSR level of theory.1 However, Ho¨ltzl et al.5 pointed out the D6h symmetry was unexpected since this compound had 9 shell electrons with a 1S21Px21Py21Dxy21Dx2 - y21 electron configuration according to the PSM model. It should be noted that Sc@Au6 has D6h symmetry at 0.1 Å tolerance in our previous work,1 if the tolerance is set at 0.01 Å, this cluster shows D2h symmetry (see Figure 1a). In addition, we have reperformed quantum chemical calculations of the Sc@Au6 cluster at the DFT level using the DMOL3 program. Allelectron spin-unrestricted calculations with scalar relativity * To whom correspondence should be addressed. E-mail: (Y.-H.L.)
[email protected]; (M.Z.)
[email protected].
(via VPSR tag) and double-numerical basis set that included d polarization functions (DND) are employed in this work. Generalized gradient approximation in the Perdue-BurkeErnzerhof (PBE)6 functional form is chosen. The quality of self-consistent field (SCF) convergence tolerance is set as “fine” with a convergence criterion of 1 × 10-5 Hartree on total energy and electron density, 2 × 10-3 Hartree/Å on the gradient, and 5 × 10-3 Å on the displacement in our calculation. The atomic distance cutoff in real space is set as fine. This structure is reoptimized using the PW91 functional (B3PW91 key word) with a scalar relativistic effective core potential Stuttgart/Dresden (SDD) basis set,7 implemented in the Gaussian03 package.8 Both PBE/VPSR (DMOL3) and B3PW91/SDD (G03) computations show the ring structure of Sc@Au6 prefers the D2h symmetry at 0.01 Å tolerance (see Figure 1b,c), even the cluster is performed in its D6h symmetry, the geometry optimizations will still lead to the D2h symmetry owing to the Jahn-Teller effect, in agreement with the computations of Ho¨ltzl et al.5 This indicates that the PSM model presented by Ho¨ltzl et al.5 can be used to describe and predict the electronic structure of the M@Au6 system.
References and Notes (1) Zhang, M.; He, L.-M.; Zhao, L.-X.; Feng, X.-J.; Luo, Y.-H. J. Phys. Chem. C 2009, 113, 6491. (2) DMOL3 is a density functional theory program distributed by Accelrys, Inc. See also: Delley, B. J. Chem. Phys. 1990, 92, 508. (3) Perdew, J. P.; Wang, Y. Phys. ReV. B 1992, 45, 13244. (4) Pulay, P. Chem. Phys. Lett. 1980, 73, 393. (5) Ho¨ltzl, T.; Lievens, P.; Veszpre´mi, T.; Nguyen, M. T. J. Phys. Chem. C, submitted for publication. (6) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. ReV. Lett. 1996, 77, 3865. (7) Dolg, M.; Wedig, U.; Stoll, H.; Preuss, H. J. Chem. Phys. 1987, 86, 866. (8) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.;
10.1021/jp910051s CCC: $40.75 2009 American Chemical Society Published on Web 11/17/2009
Comments Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz,
J. Phys. Chem. C, Vol. 113, No. 49, 2009 21015 P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, revision D.01; Gaussian, Inc.: Wallingford, CT, 2004.
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