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Electronic structure calculations for molecule based magnets and metals with the CRYSTAL code Klaus Doll Max-Planck-Institute for Solid State Research, Stuttgart

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Contents Introduction CRYSTAL-Code Metallic surfaces Molecule based magnetism CRYSTAL06: New features Conclusion

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Motivation: Interpretation and possibly prediction of experimental results: magnetism (Institut für Physik der Kondensierten Materie, Institut für Technische Physik, TU Braunschweig; Hahn-Meitner-Institut, Berlin) surfaces (synchrotron at Daresbury, UK) Test new features of the code (~1998: code worked well for insulators and had just been improved for metals)

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Methods used: Hartree-Fock: Etotal= mathematically clear, but too crude (correlations are missing, more than 1 Slaterdeterminant) Density functional theory: Etotal=E( ) Hybrid functionals: mix Hartree-Fock and standard functionals e.g. B3LYP, highly successful for molecules

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CRYSTAL-Code 1975 Turin: Begin of the code development Idea: Use methods of molecular quantum chemistry for periodic systems C. Pisani, R. Dovesi, C. Roetti, „Hartree-Fock Ab initio treatment of Crystalline Systems“, Springer, 1988 Coulomb-theory: V. R. Saunders et al, Mol. Phys. 77, 629 (1992) first release: CRYSTAL88 present release: CRYSTAL2006 R. Dovesi, V. R. Saunders, C. Roetti, R. Orlando, C. M. Zicovich-Wilson, F. Pascale, B. Civalleri, K. Doll, N. M. Harrison, I. J. Bush, Ph. D‘Arco, M. Llunell, CRYSTAL2006

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Systems with any periodicity (3d: solids, 2d: surfaces, 1d: polymers, 0d: molecules) all symmetry operations total energy, forces, band structure …. simple magnetic states unit cells with ~100 atoms depending on system, symmetry… Hartree-Fock, standard functionals, hybrid functionals (e.g. B3LYP) no f-elements yet Features:

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Alternative: plane waves (WIEN, VASP, CASTEP, S/Phi/nX …) Molecule: periodic system: H F Na Cl Na Cl Na H-atom: factorizes: Basis functions: Gaussians

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Modelling of Surfaces finite number of layers, not repeated in the third dimension CPU time for single point calculation: ~1 day on single CPU

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Cl/Cu(111) Coverage: 1/3 of monolayer, exp.: P. J. Goddard and R. M. Lambert, Surf.Sci. 67. 180 (1977) bond length binding energy fcc 2.40 Å 3.696 eV hcp 2.41 Å 3.691 eV bridge 2.33 Å 3.609 eV top 2.17 Å 3.235 eV exp. 2.39 Å 2.59 eV fcc site, M.D. Crapper et al, Europhys. Lett. 2, 857 (1986) Rules: low coordination number=> low binding energy low coordination number=> short “bond” length (few “bonds”, but strong) K. Doll, N. M. Harrison, Chem. Phys. Lett. 317, 282 (2000)

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2.64 Å 3.12 eV 2.64 Å 3.12 eV 2.56 Å 3.04 eV 2.39 Å 2.68 eV VASP: L. Jia, Y. Wang and K. Fan, J. Phys. Chem. B 107, 3813 (2003) N.H. deLeeuw et al, Phys. Rev. B 69, 045419 (2004) Cl/Ag(111) two controversial experiments! bond length binding energy fcc 2.62 Å 3.04 eV hcp 2.62 Å 3.03 eV bridge 2.54 Å 2.96 eV top 2.38 Å 2.58 eV exp. 2.48 Åa; 2.70 Åb a: A. G. Shard and V. R. Dhanak, J. Phys. Chem. B 104, 2743 (2000) b: G. M. Lamble et al, Phys. Rev. B 34, 2975 (1986) CRYSTAL: K. Doll and N.M.Harrison, Phys. Rev. B 63, 165410 (2001)

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Effective Cl radius subtract radius of metal: substrate a rCl Cu 3.63 Å 1.12 Å Ag 4.10 Å 1.17 Å Ni 3.53 Å 1.09 Å compare with data from Kittel, Solid State Physics: Cl: r=0.99 Å Cl-: r=1.81 Å radius consistent with Mulliken charge: ~ -0.1 … -0.3 |e|

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Charge on chlorine Cl/Ag(111) site charge 3s level (a.u.) fcc -0.198 -0.563 hcp -0.204 -0.562 bridge -0.218 -0.555 top -0.252 -0.532 Mulliken charge increases => 3s level destabilized (nuclear charge less well screened)


K/Cu(111) pioneering work: Na, K on Al(111): J. Neugebauer and M. Scheffler, Phys. Rev. B 46, 16067 (1992) K/Cu(111): top site occupied S. Å. Lindgren et al, Phys. Rev. B 28, 6707 (1983) simulations prove: Cu atom under K is pushed into substrate, atoms 1,2,3 upwards, rumpling crucial (K on top site generates overlap with more neighbors) without rumpling with rumpling fcc 1.249 eV 1.265 eV hcp 1.243 eV 1.263 eV bridge 1.243 eV 1.265 eV top 1.227 eV 1.287 eV K. Doll, Eur. Phys. J. B 22, 389 (2001)

Coverage dependence: K/Ag(111): 

Coverage dependence: K/Ag(111) structure 2x2 coverage 0.25 0.33 => K-K closer => stronger repulsion K Mulliken charge 0.24 0.16 => depolarization bond length (Å) 3.20 3.27 => larger K radius exp.a 3.27±0.03 3.29±0.02 => larger bond length binding energy (eV) 1.11 1.14 K 3s level, relative to EF (eV) -32.5 -32.2 core levels 3p -16.3 -16.1 destabilied a: G. S. Leatherman, R. D. Diehl, P. Kaukosoina and M. Lindroos, Phys. Rev. B 53, 10254 (1996) b: K. Doll, Phys. Rev. B 66, 155421 (2002)

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CO/Pt(111) Standard functionals give wrong site: „The CO/Pt(111) puzzle“ P.J. Feibelman, B. Hammer, J. K. Nørskov, F. Wagner, M. Scheffler, R. Watwe, R. Dumesic, J. Phys. Chem. 105, 4018 (2001) possible explanation: energy for back donation incorrectly described by standard functionals back donation varies for the sites A. Gil et al, Surf. Sci. 530, 71 (2003)

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CO charge ~ -0.05 ~ -0.35 LDA+U: G. Kresse et al, Phys. Rev. B 68, 073401 (2003) periodic B3LYP: CO/Pt(111): K. Doll, Surf. Sci. 573, 464 (2004) CO/Cu(111): M. Neef und K. Doll, Surf. Sci. 600, 1085 (2006) cluster-extrapolated B3LYP and MP2: Q.-M. Hu, K. Reuter, M. Scheffler, submitted to Phys. Rev. Lett.

Work function: tricky with a local basis set: 

Work function: tricky with a local basis set compute work function: electrostatic potential at infinity, minus Fermi energy But: Cu(111), reasonable basis set on copper atoms: Φ=3.86 eV experimental: Φ=4.98 eV strongly basis set dependent: tiny variation of Cu basis causes huge change in work function, little change for other properties

Solution: use basis functions in the vacuum region: 

Solution: use basis functions in the vacuum region analogous to strategy to compute basis set superposition error 1-2 „ghost“ layers are sufficient: without „ghosts“: 3.86 eV 1 „ghost“ layer on each side: 5.14 eV 2 „ghost“ layers on each side: 5.17 eV 3 „ghost“ layers on each side: 5.17 eV experiment: 4.98 eV K. Doll, Surf. Sci. 600, L321 (2006) see also: P. J. Feibelman, Phys. Rev. B 51, 17867 (1995) ← 2 „ghost“ layers ← 6 Cu layers ←2 „ghost“ layers

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Magnetism Questions: „Strength“: exchange interaction J magnetic moments, spin and charge densities, electrical field gradient dependence on pressure

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Exchange interaction J from energy difference Triplet: Singlet:

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magn. moment J Ni O Hartree-Fock 1.9 0.1 -5.4 meV B3LYP 1.8 0.2 -29 meV LDA 1.6 0.4 -94 meV Spin density at selected point difficult (e.g. Fermi contact coupling), integrated spin density easier exp.: -20 meV Example: NiO

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Examples for J Hartree-Fock B3LYP LDA exp. NiO -5.4 meV -29 meV -94 meV -20 meV KNiF3 -2.6 meV -15 meV -9 meV La2CuO4 -36 meV -130 meV MnF2 J1 0.2 meV 0.05 meV J2 -0.07 meV -0.3 meV systematic deviation prediction possible for 180º angle technically: good energy resolution calculations with CRYSTAL code from 1994 on

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ferric wheel full molecule: Hartree-Fock: B3LYP: LDA: exp.: J +0.7 meV -2.6 meV -10.3 meV -1.8 meV 2 iron-cluster: MRPT2 (Molpro): J = -0.5 meV when Fe d, bridging oxygen correlated -1.2 meV when all valence orbitals correlated exp.: G. L. Abbati et al, Inorg. Chem. 36, 6443 (1997) H. Nieber, K. Doll, G. Zwicknagl, Eur. Phys. J. B 44, 209 (2005); 51,215 (2006)

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Fe(pyrimidine)2Cl2 Orientation of the magnetic moment from Mössbauer spectroscopy and calculation (electrical field gradient) R. Feyerherm, A. Loose, T. Ishida, T. Nogami, J. Kreitlow, D. Baabe, F. J. Litterst, S. Süllow, H.-H. Klauss, K. Doll, Phys. Rev. B 69,134427 (2004) canted =>weakly ferromagnetic

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Exchange interaction J exp. th. (B3LYP) FePM2Cl2 -0.03 meV -0.08 meV NiPM2Cl2 -0.25 meV -0.6 meV Increase of J when compressing by 5%: ~15% (Experiment and theory) technically: good energy resolution necessary, good error cancellation helps

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Bulk modulus exp.: very soft: 15 GPa calculated: 1) use experimental values for cell as a function of pressure, keep fractional coordinates fixed: 122 GPa !!! 2) use experimental values for cell, optimize fractional coordinates: 18 GPa What happens under pressure? a;c Fe-N Fe-Cl N-C C-H C-C (Å) 7.0972; 19.840 2.14 2.46 1.34 1.08 1.38 7.5331; 20.623 2.26 2.45 1.35 1.09 1.38 A. U. B. Wolter, H.-H. Klauss, F. J. Litterst, T. Burghardt, A. Eichler, R. Feyerherm, S. Süllow, Polyhedron 22, 2139 (2003) J. Kreitlow, D. Menzel, A. U. B. Wolter, J. Schoenes, S. Süllow, K. Doll, Phys. Rev. B 72, 134418 (2005)

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New in CRYSTAL03: analytical first derivative: K. Doll, V. R. Saunders, N. M. Harrison, Int. J. Quant. Chem. 82, 1 (2001) K. Doll, Comp. Phys. Comm. 137, 74 (2001) Why faster than numerical gradient? N Atoms: 3N derivatives to be computed analytical gradient by factor N faster FePM2Cl2, 14 independent derivatives analytical gradient: 35 h CPU numerical gradient: 396 h CPU ->factor 11! 2nd derivative would be even better (properties) Code development „The task of programming derivatives can become so demanding that the corresponding implementations are missing.“ J. Gauss, „Molecular properties“ (2000)

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CRYSTAL06: gradient with respect to cell parameters: 3D: K. Doll, R. Dovesi, R. Orlando, Theor. Chem. Acc. 112, 394 (2004) 1D, 2D: K. Doll, R. Dovesi, R. Orlando, Theor. Chem. Acc., 115, 354 (2006)

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Tests: compare with numerical derivative: examples: analytical numerical Al2O3 -0.19630 -0.19625 urea -0.01501 -0.01475 NiO, AF 0.01111 0.01234 „ITOL“ higher 0.01094 0.01109 MgO: lattice constant energy gradient 4.18 Å -274.664192 0.00085 4.19 Å -274.664222 0.00008 4.20 Å -274.664209 -0.00067

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Applications and further developments: Turin: A. Damin, S. Bordiga, A. Zecchina, K. Doll, C. Lamberti : Ti-Zeolite JCP 2003 London: I. Saadoune, C. R. A. Catlow, K. Doll, F. Corà : Water on HAlPO, Mol. Sim. 2004 Pau, Turin: M. Mérawa, P. Labeguerie, P. Ugliengo, K. Doll, R. Dovesi: LiOH und NaOH; structure and vibrations, CPL 2004 Turin, Paris: S. Casassa, M. Calatayud, K. Doll, C. Minot, C. Pisani: Ice CPL 2005 Turin: S. Tosoni, K. Doll, P. Ugliengo: Kaolinite; structure and vibrations Chem. Mat. 2006

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Example for Vibrations: CaCO3 first derivative analytical, second derivative numerical: vibrational frequencies for only frequencies: frequencies and infrared intensities: Experiment: Hellwege et al (1970) experimentally computed experimentally computed

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220 cm-1 286 cm-1 299 cm-1 711 cm-1 874 cm-1 1400 cm-1 125 cm-1 126 cm-1 L. Valenzano, J. Torres, K. Doll, F. Pascale, C. Zicovich-Wilson, R. Dovesi, Z. Phys. Chem. (2005)

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Conclusion ab initio calculations for solids, surfaces, molecules with Gaussian basis sets reasonable agreement for geometries, energetics … with data from experiment and plane wave codes magnetism: systematic deviation for exchange interaction J, good energy resolution; hyperfine interaction (Fermi contact) very difficult work function: a bit tricky all electron calculations pose no problems (-> core levels) Mulliken population surprisingly reliable hybrid functionals available => LDA,GGA vs. B3LYP vs. HF

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