Voltar
Artigo Revisado por pares
BIBTEX RIS

Calcium d States: Chemical Bonding of CaC 6

2008; Wiley; Volume: 47; Issue: 35 Linguagem: Inglês

10.1002/anie.200801985

ISSN

1521-3773

Autores

Shuiquan Deng, Arndt Simon, Jürgen Köhler,

Tópico(s)

Rare-earth and actinide compounds

Resumo

Angewandte Chemie International EditionVolume 47, Issue 35 p. 6703-6706 Communication Calcium d States: Chemical Bonding of CaC6 Shuiquan Deng Dr., Shuiquan Deng Dr. [email protected] Max-Planck-Institut für Festkörperforschung, Heisenbergstrasse 1, 70569 Stuttgart (Germany), Fax: (+49) 711-689-1091Search for more papers by this authorArndt Simon Prof. Dr., Arndt Simon Prof. Dr. Max-Planck-Institut für Festkörperforschung, Heisenbergstrasse 1, 70569 Stuttgart (Germany), Fax: (+49) 711-689-1091Search for more papers by this authorJürgen Köhler Prof. Dr., Jürgen Köhler Prof. Dr. Max-Planck-Institut für Festkörperforschung, Heisenbergstrasse 1, 70569 Stuttgart (Germany), Fax: (+49) 711-689-1091Search for more papers by this author Shuiquan Deng Dr., Shuiquan Deng Dr. [email protected] Max-Planck-Institut für Festkörperforschung, Heisenbergstrasse 1, 70569 Stuttgart (Germany), Fax: (+49) 711-689-1091Search for more papers by this authorArndt Simon Prof. Dr., Arndt Simon Prof. Dr. Max-Planck-Institut für Festkörperforschung, Heisenbergstrasse 1, 70569 Stuttgart (Germany), Fax: (+49) 711-689-1091Search for more papers by this authorJürgen Köhler Prof. Dr., Jürgen Köhler Prof. Dr. Max-Planck-Institut für Festkörperforschung, Heisenbergstrasse 1, 70569 Stuttgart (Germany), Fax: (+49) 711-689-1091Search for more papers by this author First published: 11 August 2008 https://doi.org/10.1002/anie.200801985Citations: 17Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Graphical Abstract The Ca 3d state is a necessary and sufficient condition to produce an interlayer band in CaC6 according to model and first-principles studies, and this band cannot be considered to be a free-electron band. Involvement of the Ca 3d state in the chemical bonding and its tight-binding character explain the unusual Ca isotope effect in CaC6. The picture shows the orbital topology of one of the Fermi states of CaC6. References 1 1aK. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, A. A. Firsov, Nature 2005, 438, 197; 1bA. Bostwick, T. Ohta, T. Seyller, K. Horn, E. Rotenberg, Nat. Phys. 2007, 3, 36. 2 2aT. E. Weller, M. Ellerby, S. S. Saxena, R. P. Smith, A. N. T. Skipper, Nat. Phys. 2005, 1, 39; 2bN. Emery, C. Hérold, M. d'Astuto, V. Garcia, C. Bellin, J. F. Marêché, P. Lagrange, G. Loupias, Phys. Rev. Lett. 2005, 95, 087003; 2cN. Emery, C. Hérold, P. Lagrange, J. Solid State Chem. 2005, 178, 2947. 3M. Posternak, A. Baldereschi, A. J. Freeman, E. Wimmer, M. Weinert, Phys. Rev. Lett. 1983, 50, 761. 4T. Fauster, F. J. Himpsel, J. E. Fischer, E. W. Plummer, Phys. Rev. Lett. 1983, 51, 430. 5G. Csányi, P. B. Littlewood, A. H. Nevidomskyy, C. J. Pickard, B. D. Simons, Nat. Phys. 2005, 1, 42. 6 6aS. L. Molodtsov, C. Laubschat, M. Richter, Th. Gantz, A. M. Shikin, Phys. Rev. B 1996, 53, 16621; 6bG. Lamura, M. Aurino, G. Gufariello, E. Di Gennaro, A. Andreone, N. Emery, C. Hérold, J. F. Marêché, P. Lagrange, Phys. Rev. Lett. 2006, 96, 107008; 6cJ. S. Kim, L. Boeri, R. K. Kremer, F. S. Razavi, Phys. Rev. B 2006, 74, 214513. 7D. G. Hinks, D. Rosenmann, H. Claus, M. S. Bailey, J. D. Jorgensen, Phys. Rev. B 2007, 75, 014509. 8aI. I. Mazin, Phys. Rev. Lett. 2005, 95, 227001; 8bM. Calandra, F. Mauri, Phys. Rev. Lett. 2005, 95, 237002. 9 9aS. Y. Savrasov, Phys. Rev. B 1996, 54, 16470; 9bF. Janak, V. L. Moruzzi, A. R. Williams, Phys. Rev. B 1975, 12, 1257; 9cJ. P. Perdew, Y. Wang, Phys. Rev. B 1992, 45, 13244. 10 10aR. Hoffmann, J. Chem. Phys. 1963, 39, 1397; 10bG. A. Landrum, YaeHMOP: Yet Another extended Hückel Molecular Orbital Package. 11The experimental structural data for CaC6 from Ref. [2c] were used throughout this work. 2κ 4s, 4p, 3d and 2s, 2p basis sets for Ca and C, respectively, were used for the expansion of valence states, while the Ca 3s, 3p states were treated as semicore states. In the interstitial region, the pseudo-LMTOs were expanded in plane waves up to 75.64, 109.5, and 156.5 eV for the Ca 4s, 4p, and 3d shells, and 533.3, 776.8 eV for C 2s and 2p shells, respectively, while the potential and charge density in the interstitial region were expanded in plane waves up to 2250.9 eV, corresponding to 17 752 plane waves. 4237 and 13 independent k points for the valence and semicore states, respectively, were used in the self-consistent calculations. 12Orbital compositions for some representative Fermi states: Ψ(pd,1)=15.1 % Eg (Ca dxy+Ca d)+14.7 % Eg (Ca dxz+Ca dyz)+64.9 % A2u C pz; Ψ(sd,2)=60.9 % A1g Ca s+15.6 % A1g Ca d); Ψ(pd,3)=30.0 % Eg (Ca dxz+Ca dyz)+68.9 % A2u C pz; Ψ(sd,4)=22.7 % A1g Ca s+66.3 % A1g Ca d); Ψ(sd,5)=37.1 % A1g Ca s+51.2 % A1g Ca d); Ψ(sd,6)=63.4 % A1g Ca s+32.2 % A1g Ca d; Ψ(sd,7)=49.9 % A1g Ca s+23.9 % A1g Ca d+11.3 % A2u C pz; Ψ(pd,8)=30.4 % Eg (Ca dxy+Ca d)+56.6 % A2u C pz; Ψ(pp,9)=15.5 % A2u Ca pz+77.3 % A2u C pz. The contributions below 10 % are omitted for brevity. The orbitals are grouped according to their symmetry in the corresponding point group of R̄m. 13O. K. Andersen, O. Jepsen, Physica B 1977, 91, 317. 14Tight-binding dispersion relation of the sd hybrid band: EΓ–L(x)=α+2β+4γ+(4β+2γ+6δ)cos(2πx); EL–Z(x)=α+2β−2γ−4δ+4βcos[(2 x−1)π]+4γcos(2πx)+2δcos[(4x−1)π]; EZ–Γ(x)=α+6β+(6γ+6δ)cos(2πx); EΓ–F(x)=α+2β+2γ+4δ+(4β+4γ) cos(2πx)+2δcos(4πx), where α is the on-site energy of the sd hybrid, β, γ, δ are the hopping integrals for 1st , 2nd, and 3rd nearest neighbors for a sd hybrid, respectively, and x is a parameter ranging between 0 and 1/2. In deriving the above formula, it is assumed that there is no hybridization between the sd hybrids and other states, and a cutoff for such interactions to the 3rd nearest neighbors is taken. Global fitting to the first-principles sd band was not attempted; instead, the parameters α, β, γ, δ are extracted with the eigenvalues at the special points Γ, L, Z, and F. The obtained values are 27.651, −0.2655, −0.0555, and −0.0747 eV for α, β, γ, δ, respectively. 15Simulation of free-electron behavior: The formula for the quasi-free electron E=k2+V(0) is given in the Rydberg atomic unit. Along the Γ–Z direction, k=α(g1+g2+g3), with 0≤α≤1/2, while along the Γ–F direction, k=α(g1+g2), with 0≤α≤1/2, where gi are the reciprocal lattice vectors corresponding to the primitive basis vectors of the direct lattice. By choosing k in this way, the anisotropy of the structure is implicitly considered. 16R. A. Dunlap, The Golden Ratio and Fibonacci Numbers, World Scientific Publishing, Singapore, 1997. 17A. S. Hedayat, N. J. A. Sloane, J. Stufken, Orthogonal Arrays: Theory and Applications, Springer, New York, 1999. 18Optimized EH parameters for Ca in this work: H4s (eV): −9.5, ζs: 1.6; H4p: −2.5, ζp: 1.6, H3d: −7.0, ζ1,3d: 2.74, c1:0.413, ζ2,3d: 1.13, c2: 0.7228; standard parameters: H4s (eV): −7.0, ζs: 1.2; H4p: −4.0, ζp: 1.2. 19L. Boeri, G. B. Bachelet, M. Giantomassi, O. K. Andersen, Phys. Rev. B 2007, 76, 064510. 20P. Hohenberg, W. Kohn, Phys. Rev. B 1964, 136, 864. 21Terms contained in the Coulomb potential energy, where ZR is the nuclear charge at R, Eee is the static Coulomb interaction between electrons, ENe is the nuclear electron interaction, and ENN is the nuclear–nuclear interaction [ΔM=M[ρ]with d−M[ρ]without d (M=E, T, U, Exc,…︁)]: 22S. Deng, A. Simon, J. Köhler, A. Bussmann-Holder, J. Supercond. 2003, 16, 919. In this work, the real-space hopping integrals and orbital coefficients are all extracted from FP-LMTO calculations. 23R. Dronskowski, P. E. Blöchl, J. Phys. Chem. 1993, 97, 8617. 24 24aA. D. Becke, K. E. Edgecombe, J. Chem. Phys. 1990, 92, 5397; 24bA. Savin, O. Jepsen, O. K. Andersen, H. Preuss, H. G. von Schnering, Angew. Chem. 1992, 31, 187; 24cB. Silvi, A. Savin, Nature 1994, 371, 683. 25R. Tank, O. Jepsen, A. Burkhardt, O. K. Andersen, TB-LMTO-ASA (version 4.7) 1998, MPI für Festkörperforschung, Stuttgart, Germany. 26 26aK. A. Yee, T. Hughbanks, Inorg. Chem. 1991, 30, 2321; 26bM.-H. Whangbo, E. Canadell, J. Am. Chem. Soc. 1992, 114, 9587. 27 27aM. Springborg, R. C. Albers, Synth. Met. 1993, 56, 3383; 27bC.-M. Fang, J. Bauer, J. Y. Saillard, J. F. Halet, Z. Naturforsch. B 2007, 62, 971. 28 28aS. Deng, A. Simon, J. Köhler, Solid State Sci. 2000, 2, 31; 28bJ. P. Jan, H. L. Skriver, J. Phys. F 1981, 11, 805. 29 29aA. Simon, Angew. Chem. 1997, 109, 1873; Angew. Chem. Int. Ed. Engl. 1997, 36, 1788; 29bS. Deng, A. Simon, J. Köhler, Struct. Bonding (Berlin) 2005, 114, 103. Citing Literature Volume47, Issue35August 18, 2008Pages 6703-6706 ReferencesRelatedInformation

Referência(s)