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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
2
Contents

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

3
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)

4
Methods used

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

5
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. DArco, M. Llunell, CRYSTAL2006
6
Features

• 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

7
Basis functions Gaussians
Molecule
periodic system
H F
Na Cl Na
Cl Na
factorizes
H-atom
Alternative plane waves
(WIEN, VASP, CASTEP, S/Phi/nX )
8
Modelling of Surfaces
finite number of layers, not repeated in the
third dimension CPU time for single point
calculation 1 day on single CPU
9
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 numbergt low
binding energy low coordination
numbergt short bond length
(few bonds, but
strong)
K. Doll, N. M. Harrison, Chem. Phys. Lett. 317,
282 (2000)
10
Cl/Ag(111)
two controversial experiments!
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)
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)
11
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 r0.99
Å Cl- r1.81 Å radius consistent with Mulliken
charge -0.1 -0.3 e
12
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 gt 3s level
destabilized
(nuclear charge less well
screened)
13
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

14
Coverage dependence K/Ag(111)
structure
2x2 coverage
0.25 0.33 gt K-K closer


gt stronger repulsion K Mulliken
charge 0.24 0.16
gt depolarization bond length (Å)
3.20 3.27 gt
larger K radius exp.a
3.270.03 3.290.02 gt 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)
15
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)

16

CO
charge

-0.05

-0.35 LDAU 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.
17
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 F3.86
eV experimental
F4.98
eV strongly basis set dependent tiny variation
of Cu basis causes huge change
in work function,
little change for other properties
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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
19
Magnetism

• Questions
• Strength exchange interaction J
• magnetic moments, spin and charge densities,
  electrical field gradient
• dependence on pressure

20
Exchange interaction
Triplet Singlet
J from energy difference
21
Example NiO


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
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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 calculat
ions 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
canted gtweakly ferromagnetic
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)
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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
26
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?
ac 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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Code development
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 -gtfactor 11! 2nd
derivative would be even better (properties)
The task of programming derivatives can become
so demanding that the corresponding
implementations are missing. J. Gauss,
Molecular properties (2000)
28
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)
29
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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125 cm-1
126 cm-1
220 cm-1
286 cm-1
299 cm-1
711 cm-1
874 cm-1 1400
cm-1
L. Valenzano, J. Torres, K. Doll, F. Pascale, C.
Zicovich-Wilson, R. Dovesi, Z. Phys. Chem. (2005)
33
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 (-gt
  core levels)
• Mulliken population surprisingly reliable
• hybrid functionals available
• gt LDA,GGA vs. B3LYP vs.
  HF