VASP_tutorial

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					Modeling materials and processes with VASP:
       From spintronics to catalysis
                     Overview I

• The prehistory of VASP
• Getting started
• From pseudopotentials to all-electron calculations
• Current developements:
   Towards post-DFT approaches
                  Overview II
A quantum perspective to materials science

    A – DFT applied to materials science
   • Complex intermetallic alloys
   • Vibrational spectroscopy of DNA bases
   • Nanostructured magnetic materials for spintronics
   • Bimetallic catalysts for selective hydrogenation
   • Nanoporous materials: molecular reactions in zeolites

              B -- Post-DFT studies
   • Strongly correlated transition-metal oxides – DFT +U
   • Hybrid functionals applied to molecules and solids
               The prehistory of VASP

Car-Parrinello ab-initio MD - 1985
  - Total energy minimization via dynamical simulated annealing
  - Adiabatic propagation of electronic orbitals via pseudo-Newtonian
    dynamics
  - Control of adiabaticity for metallic systems ?


Conjugate gradient minimization of total energy - 1989
  - Dynamics on the Born-Oppenheimer surface
  - Slow convergence or even instability for metallic systems
    (``charge sloshing´´)
            Getting started: 1991-1993
Learning from precursors
  - Remain on the Born-Oppenheimer surface
 - Improve stability and convergence for metals
 - Iterative diagonalization
    - Conjugate gradient minimization of eigenvalues or residuum
      minimization
    - Optimized charge- and spin-mixing


Improve basis-set convergence
   - Optimized ultrasoft pseudopotentials
   - Data-base of potentials for all elements
Making a high-performance code 1995-99

 Migration to F90 and Parallelization
   -   MPI-based, highly transportable code

 Spin-polarized version for magnetic systems

 Avoid limitations due to pseudopotentials
  - Full-potential version based on projector–augmented waves
G.Kresse and J. Hafner, Phys. Rev. B 47,558 (1993)
G. Kresse and J. Furthmüller, Phys. Rev. B 54, 111969 (1996);
                              Comput. Mater. Sci. 6, 15 (1996)
G. Kresse and D. Joubert, Phys. Rev. B 59, 1758 (1999).
         Principal features of VASP - I
• (Spin)-Density Functional Theory (and beyond)
 - The ‚Jacobs ladder‘ of DFT
  - Local (spin-)density approximation (L(S)DA)
  - Generalized gradient approximation (GGA) – PW91, (R)PBE
  - Meta-GGA
  - Hybrid functionals (HSE03, PBE0)
- Exact and screened exchange
- LDA+U for strongly correlated systems
- Scalar-relativistic + spin-orbit coupling
- Unconstrained noncollinear magnetism
- Orbital polarization
           Principal features of VASP - II

• Plane-wave basis set
 - Norm-conserving (NC) and ultrasoft (US) pseudopotentials
 - Projector-augmented-wave (PAW) full-potential treatment
 - PP and PAW data base for all elements (including lanthanides
  and actinides)
• Efficient iterative diagonalization of the Hamiltonian
 - Minimization of norm of residual vector to each eigenstate or
   conjugate-gradient minimization of eigenvalues
 - Optimized charge- and spin-density mixing
• Exact calculation of Hellmann-Feynman forces and stresses
 - Static optimization of unit cell and atomic positions
 - Molecular dynamics in the microcanonical and canonical
   ensembles (Nose dynamics)
• Graphical user interface and visualization tools
        Principal features of VASP - III
• Tool-box
   Electronic band structure and density of states, partial DOS
   Charge- and spin-densities
   Photoelectron spectroscopy (incl. core levels)
   Optical spectroscopy
   Polarizability
   STM simulations
   Phonons in solids
   Molecular vibrational spectroscopy
   Transition-state search, calculation of reaction rates

• Limitations
   Electronic structure and static structure optimization for systems
   with up to 10000 valence electrons)
   Ab-initio MD for systems with up to about 3000 valence electrons )
   extending over 50 – 80 ps
         VASP – Current developments
• Exact exchange and hybrid functionals
    Hybrid functionals (HSE0, PBE0)
    Exact and screened exchange
    New functionals
• All-electron (valence plus core) PAW approach
• Transformation to most localized Wannier orbitals
• Approximate treatment of vdW forces within DFT
• Many-body perturbation theory (GW)
• Additions to tool box
   Polarizability, dielectric constant, Born effective charges
   Many-body perturbation theory (GW)
   Electric field gradients, NMR spectra
   Electronic transport
   Magnetic anisotropy
... and the next generation of codes beyond VASP !
Current applications of                within the CMS group

Complex magnetism
 Nanostructured magnets, noncollinear magnetism
Intermetallic compounds and alloys
 Mechanical properties, embrittlement, quasicrystals
Molten metals and alloys
 Chemical order in Zintl alloys
Surface science, catalysis and corrosion
 Metals and alloys, oxides, sulfides
Zeolites and related materials
 Acid-based catalysis: Bronsted- and Lewis sites
Nanotubes and related materials
Current status of                     usership throughout the world

• Cooperation with Material Design SA
• No maintenance, no support licences from Univ. Wien

• About 50 industrial site-licences

• More than 500 academic site-licences (universities and public
  non-profit research laboratories)
Current applications of               worldwide:

 Materials:
  Semiconductors and insulators
  Ferrolelectrics
  Glasses, ceramics and minerals
  Metals, alloys and intermetallic compounds
  Magnetic materials
  Molecular crystals
  Fullerenes and nanotubes
  ...........................
 Properties and processes:
   Mechanical properties: elasticity and plasicity
  Phonons and thermodynamics
  Theoretical crystallography, mineralogy
  Heterogeneous catalysis: oxidation, hydrogenation,
    hydrodesulfurization, isomerization cracking
  Electrochemistry and electrocatalysis
  .............................
          Case studies based on
          I. DFT calculations
• Complex intermetallic compounds
     Components of Al-rich high-strength alloys
• Surfaces of quasicrystals
    STM studies of fivefold surfaces of icosahedral AlPdMn
• Vibrational spectroscopy of molecules and solids
    Crystalline DNA bases
• An old problem and computational tour de force:
    Crystalline and magnetic structure of Mn
• Nanostructured magnetic materials:
    Ultrathin films, nanowires and clusters
• Selective hydrogenation on bimetallic catalysts:
    Conversion of unsaturated aldehydes to unsaturated alcohols
• Molecular reactions in zeolites:
    Beckmann rearrangement of cyclohexanone to caprolactam
    Al-rich nanocrystalline high-strength alloys
  Nanocrystalline Al94V4Fe2 has a tensile strength of 1300 MPa,
   exceeding the strength of usual technical steels
  The alloys consist of crystalline Al-rich compounds in a partially amorphous
   matrix – here we analyze the bonding properties of Al10V

                                       3D-Kagome-network with V atoms at vertices,
cF176 crystal structure of Al10V        Al2 atoms in the centers of V-V links
Space group Fd3m (No 227)              Large voids occupied by Friauf polyhedra
                                        of 4 Al1 and 12 Al3 atoms




                              Al10V-structure = ´´super-Laves phase´´ of MgCu2 type:
                              Mg atoms are replaced by Friauf clusters of Al1 and Al3,
                              Cu atoms by V atoms linked by Al2 atoms
Covalent bonding in Al10V: ...V-Al-V-Al-... chains




    Total electron density (left) and difference-electron density (right)
    along the .....–V-Al2-V-Al2-.... chains in the Al10V structure
Covalent bonding in Al10V: Friauf-polyhedra




Total electron density (left) and difference-electron density (right)
In a plane cutting across the Friauf-polyhedra. Maxima in the
difference-electron density mark covalent bonds between Al3 atoms
        Phase stability of Al-rich Al-V compounds




Heat of formation of Al-rich Al-V compounds (the solid line connects pure Al and Al3V):
- Filling the center of the Friauf polyhedra with Al is energetically unfavorable
- Other Al-rich compounds have comparable heats of formation
                            Quasicrystals



• Quasicrystals are ordered structures without translational periodicity
  and non-crystallographic (icosahedral, decagonal, ....) symmetry
• Quasicrystalline structures may be constructed by a cut-and-
  projection techniques from higher dimensions, e.g. projecting a
  hypercube in 6D onto the vertices of an icosahedron
• A hierarchy of periodic structures („rational approximants“)
  systematically approaching the quasiperiodic limit may be
  constructed by replacing in the vectors defining the icosahedral
  vertices the Golden Mean t by a ratio of Fibonacci numbers:
     Fn+1/Fn= 1/1, 2/1, 3/2, 5/3, ................. t ~ 1.6180...
  Icosahedral AlPdMn: 1/1 approximant                 128 atoms/cell
                          2/1 approximant             542 atoms/cell
       Structure of icosahedral quasicrystals
Structure model for face-centred icosahedral Al-Pd-Re(Mn) in 6D:
quasiperiodic structure determined by projection of 6D acceptance
domains on physical space, chemical order determined by shell-structure
of atomic surfaces.




  Structure in real space: Interpenetrating Mackay- and Friauf-
  clusters – imaging by scanning tunneling microscopy ?
Structure of quasicrystals and quasicrystalline surfaces




Tiling model (left) and electron-density map (right) of a fivefold surface of
               a stable icosahedral AlPdMn quasicrystal
Structure of quasicrystals and quasicrystalline surfaces
Modeling of quasicrystalline surface: Low-order (2/1) approximant,
             periodic slab model >> ~ 540 atoms/cell




 Simulated STM images of characteristic structural features observed
 on the 5-fold surfaces of i-AlPdMn: the ‚white flower‘ and the ‚dark hole‘,
 together with the underlying tiling model

 M. Krajci and J.H., Phys. Rev. B 71 (2005) 054202
 M. Krajci, J.H., J. Ledieu and R. McGrath, Phys. Rev. B (submitted)
Structure and vibrational spectra of molecular crystals

• Understanding the vibrational spectra of crystalline DNA
  bases
• Influence of intermolecular bonding based on hydrogen
  bonds
• Positions of protons not very well determined by diffraction
  experiment
  >>>> Optimization of crystal structure using VASP
  >>>> Calculation of vibrational eigenfrequencies and
         eigenvectors using ab-initio force constants

   M.Plazanet, N. Fukushima and M. Johnson, Chem. Phys.
   280(2002) 53
Structure and vibrational spectra of molecular crystals




                                Calculated and measured INS spectra:
                                (a) experiment, (b) calculated with fully
                                relaxed cell geometry and internal
                                coordinates, (c) and (d) calculated for
                                LT and HT structures after coordinate
                                optimization only
 Crystal structure of thymine
Structure and vibrational spectra of molecular crystals




   Eigenvectors of characteristic vibrational eigenmodes of thymine
   Crystalline and magnetic structure of Mn
                            a-Mn
T>TN : PM, cubic A12 – cI58 – I43m, isostructural to g-Mg17Al12
T<TN : noncollinear AFM, tetragonal I42m,
       magnetic space-group PI43m or subgroup




    D. Hobbs, J. Hafner, and D. Spisak, Phys. Rev. B 68, 014407 (2003)
Complex reconstructions of ultrathin g-Fe films on Cu(100)




                                               Atomically resolved STM images of 2 – 4 ML films
 STM images of films grown at 300K
 (A) 3ML film with (1x4) stripes and
     (1x1) domains
                                       STM : A.Biedermann et al., PRL 86, 464 (2001)
 (B) 4ML film with (1x6) domains                                   PRL 87,086103 (2001)
                                       LEED: S. Müller et al., PRL 74, 765 (1995)
Complex reconstructions of ultrathin g-Fe films on Cu(100)



   Computational strategy:

   • Model system by thick slabs (up to 15 monolayers) with large
     surface cells

   • Use generalized gradient approximation (mandatory for
     magnetic systems)

   • Simultaneous optimization of all structural and magnetic
     degrees of freedom
Complex reconstruction of ultrathin g-Fe films on Cu(100)
            Shear instability of fct Fe along the Bain path




     a=3.40 A (minimizing the total energy of ferromagnetic fct Fe)

             Epitaxial constraint: a=aCu=3.637 Angstr.
     Ferromagnetic        c/a=1.0, d=0.259 Angstr., a=14.5°
     Bilayer antiferrom. c/a=0.99, d=0.128 Angstr., a=7.3°
     Antiferromagnetic c/a=0.97, d=0.077 Angstr., a=4.4°
     Paramagnetic         c/a=0.90, d=0.045 Angstr., a=2.6°

     Strong correlation between lattice distortion and magnetism !
Complex reconstruction of ultrathin g-Fe films on Cu(100)

                                       (1x4) reconstruction of the Fe surface




Total energy of 1-, 3-ML films (FM),
and of a 6-ML film (bilayer AFM) as a
function of the shearing of the surface
layer

Layer-resolved lateral displacements
in a (1x4) reconstructed FM 3ML
Fe/Cu(100) film
Shear angle 13° (calc.), 14° (STM)
Vertical buckling Dz =0.18 Angst.
(calculation and LEED)
Complex reconstruction of ultrathin g-Fe films on Cu(100)
 (1x2) reconstruction of a bilayer-antiferromagnetic 6ML Fe/Cu(100) film:
          - Only surface layer reconstructs, shear angle 13.5°
          - Deeper layers are rigidly shifted along x direction




  .

  • All g-Fe films on Cu(100) are instable against monoclinic shear
  • Shearing increases with increasing ferromagnetic character
  • 3ML: Shearing reduced in deeper layers due to epitaxial constraint
  • 6ML: Deeper layers only rigidly shifted
                                        D. Spisak and J.H., PRL 88,056101 (2002)
Complex reconstruction of ultrathin g-Fe films on Cu(111)

         • Stable fcc films up to 6 ML by pulsed laser deposition
         • High-spin ferromagnetism up to 3 ML
         • Low-spin ferrimagnetic state for 4 to 6 ML



• Bilayer antiferromagnetic order
with [100] stacking sequence is
also the magnetic ground-state in
4ML Fe/Cu(111) films
• Magnetic energy difference
relative to FM state 223 meV/atom
    .
• BAFM[100] ordering reduces
geometric distortions




                                     D. Spisak and J.H., PRB 67, 1334434 (2003)
                        Transition-metal clusters I
•   Determine cluster geometry
•   Determine magnetic ground-state
•   Role of orbital moments
     Fully relativistic calculation: spin-orbit coupling and non-collinearity


                                 Spin-moment                 Orbital moment
Pt5-cluster
Magnetic moments

-perp. to 3-fold axis
 S=5.6 mB, L=1.0 mB

-parallel 3-fold axis
 S=5.6 mB, L=1.2 mB

MAE = 5 meV/atom
                        Transition-metal clusters II


Pt6-                             Spin-moment      Orbital moment
cluster

Magnetic moments

 S=6.9 mB, L=1.3 mB




 S=6.4 mB, L=1.7 mB

MAE = 4 meV/atom

Local spin- and orbital moments noncollinear, but cluster moments aligned
 T. Futschek, M. Marsman, J.H., to be published
     Nanostructured magnetic materials for spintronics


• Ab-initio simulations allow access to locally resolved magnetic
information not available from experiment

• Exploration of structure/property relationship

• Modelling of complex reconstructions

• Fast exploration of novel materials: nanostripes, nanowires, clusters
           Surface science and catalysis

Bimetallic catalysts:

Selective hydrogenation of unsaturated aldehydes to unsaturated
alcohols on Pt-Fe – origin of selectivity ?

Acid-based catalysis in zeolites:
Beckmann rearrangement of cyclohexanone to e-caprolactam –
nature of the active sites ?

Computational strategy:
• Use slab-models with large surface cells for the surfaces of metallic
  catalysts and periodic models for zeolites
• Explore possible all adsorption configurations of reactants, perform
  transition-state, use harmonic transition-state theory for reaction rates
• Theoretical ‚in-situ‘ spectroscopy for comparison with experiment
 Selective hydrogenation on bimetallic catalysts
                           a,b-unsaturated aldehydes


                                                          (a) acrolein (2-propenal)
                                                          (b) crotonaldehyde (2-butenal)
                                                          (c) Prenal (3-methyl-2-butenal)




Hydrogenation of C=O double-bond: unsaturated alcohols
Hydrogenation of C=C double-bond: saturated aldehydes
Pt-catalysts: low selectivity
Bimetallic Pt-Fe and Pt-Sn: improved selectivity
R. Hirschl, F. Delbecq, Ph. Sautet, J.H., J. Catal., 217, 354 (2003).
 Selective hydrogenation on bimetallic catalysts
                   Surface of Pt-Fe catalysts




UHV studies and DFT calculations: Pt segregates at surface:
Origin of selectivity ????
Adsorption studies: strong Fe-O interaction partially reverses
segregation, creates active Fe-sites in surface
      Selective hydrogenation on bimetallic catalysts
Adsorption modes of a,b-unsaturated aldehydes on a metal surface

           disCC                                           disCO
 Pt        1.042                                          Pt        0.248
 Pt/PtFe   0.584                                          Pt/PtFe   0.004   -0.077
 Fe/PtFe 0.482                                            Fe/PtFe 0.681      0.688


           h4-trans                                        top
                                                          Pt
 Pt        1.134    0.671
 Pt/PtFe 0.628      0.180                                 Pt/PtFe 0.126

 Fe/PtFe 1.247      0.788                                 Fe/PtFe 0.558     0.383

           h3-cis                                          dis-14
                                                          Pt
 Pt
                                                          Pt/PtFe 0.425
 Pt/PtFe 0.768     0.155

 Fe/PtFe 1.476     0.971                                  Fe/PtFe 1.090     0.679



Adsorption energies at 1/12 coverage: Acrolein / Prenal
        Selective hydrogenation on bimetallic catalysts

• Strong differences in adsorption energies on Pt/PtFe and Fe/PtFe
surfaces partially reverses surface segration: Quasichemical model




      • Strong Fe-O interaction activates C=O double bond
       Selective hydrogenation on bimetallic catalysts

   • Strong Fe-O interaction activates C=O double bond




Prenal adsorbed in h3-configuration on a segregated Pt/PtFe surface (left)
and at a Fe atom in a Fe/PtFe surface. Difference electron densities: dark
– charge influx, bright – charge depletion
   Selective hydrogenation on bimetallic catalysts

   • Vibrational spectroscopy of reactants (prenal)




Reaction scenario can be verified by in-situ spectroscopy
    Selective hydrogenation on bimetallic catalysts



• Strong interaction with reactant modifies surface of
catalyst

• Strong Fe-O interaction activates C=O double bond

• Fe in surface provides a strong attractive potential for
Hydrogen (not shown here)

• Ab-initio process simulation combined with theoretical
spectroscopy establishes a strong link between theory
and experiment
                   Acid-based catalysis in zeolites
            Structure and nature of the catalytically active sites




                                                   Surface-silanol groups (top-view)

Structure of mordenite, looking
down the main channel



       Si-Al-OH Bronsted sites
       in the main channel
       (a,b,d) and in the side-
       pocket (c)
                    Beckmann rearrangement

• Transformation of oximes to amides:




• Transition-state optimization
 - maximize potential energy along one direction (reaction coordinate),
    minimized with respect to all other degrees of freedom
  - exact reaction coordinate is not known in advance
  - basis set for ionic relaxation: internal coordinates (bonds, angles,
    torsions,.... )
  - constrained relaxation – drag method: invert gradient corresponding
    to estimated reaction coordinate
• Calculation of reaction rate: Harmonic transition-state theory
               Beckmann rearrangement


Conventional process
• catalyzed by a sulfuric acid
• problems with corrosion
• large amount of by-products (ammonium
sulfate, 4.0 t per t e-caprolactam)



         Heterogeneously catalyzed reaction
         • environmentally friendly alternative to conventional process
         • catalyzed by solid acids such as zeolites
         • cyclohexanone oxime in the vapor phase – T~350C
         • problems short life-time of catalyst
         • what are the active centers?
    BR catalyzed by Brønsted acid sites




                                 ΔEads=139.4 kJ/mol




due to its size, cyclohexanone
oxime can enter only into
large pores (12 MR)

                                 ΔEads=53.9 kJ/mol
         Beckmann rearrangement at BA sites      1,2-H-shift
E (kJ/mol)




                            95.8


                                              85.5

                 R_1          TS_1             R_2
      Beckmann rearrangement at BA sites N-insertion

E (kJ/mol)




                           79.1




                    50.0


              R_2           TS_2         R_3
      Beckmann rearrangement at BA sites   Hydrolysis




                            47.6
E (kJ/mol)




                    172.0




              R_3            TS_3          P
BA site vs. gas-phase reaction

                                                  BA site




  Adsorption   1,2-H-shift N-insertion    Hydrolysis   Desorption



                                         Gas phase
Beckmann rearrangement – alternative reaction scenarios
   • Reaction at external silanol groups
   • Reaction at silanol nests within the framework

                                   Summary
   • weak acid sites are active in the chemical reactions
   • reaction catalyzed by zeolitic BA sites follows similar pattern
     as the reaction in the gas phase, interaction with the conjugated
     basis (zeolite framework) changes significantly the potential
     energy profile of reaction.
   • hydrogen bonding plays a crucial role in the reactivity of
     silanol groups, the activation energy for the rate-determining
     step (N-insertion) decreases in order: isolated SiOH > H-bonded
     SiOH > silanol nests, but remains substantially higher than at
     BA sites
   • Solvent effect, side reactions?
 T. Bucko, L. Benco, J.H., J. Phys. Chem. A 108, 11 388 (2004)
        Case studies based on
        II. Post-DFT calculations


• Strongly correlated transition-metal oxides:
   Bulk Nickel oxide and hematite
   Hematite surfaces – DFT+U
   Bulk MnO – DFT+U vs. hybrid functionals

• Hybrid functionals:
   Molecules
   Solids
      Strongly correlated transition-metal oxides


• Strong on-site correlation are underestimated in DFT
  calculations >>
    - too narrow energy-gaps
    - too small magnetic moments
• Treat in a DFT+U approximation, adding an on-site Coulomb-
  interaction to increase the exchange-splitting of the 3d-states
• Influence on surface structure and stability ?


       - Properties of NiO and Fe2O3
       - Surface phase-diagram of Fe2O3 (0001)
       - Electronic properties of MnO
Strongly correlated transition-metal oxides - NiO




Adding an on-site Coulomb repulsion to a spin-
polarized GGA calculation
- Increases magnetic moment and band-gap
- Increases Ni-d-O-p hybridization
- Changes the character of the band-gap to a mixed
  charge-transfer/Mott d-d-type
Strongly correlated transition-metal oxides –Fe2O3




Structure of hematite
     Surface properties of hematite and chromia




Structure models for O-, Fe-, and FeO terminated hematite surfaces
       Surface phase-diagram for Fe2O3(0001)




  Results from GGA calculations (left) and from GGA+U (right)
   >> On-site Hubbard correction necessary to correct gap-
      width and to produce correct AF ground-state
   >> Hubbard-corrections stabilize Fe-terminated surface
      even under high O partial pressures

A. Rohrbach, G. Kresse and J.H., Phys. Rev. B 70 (2004) 135426/1-17
                     Electronic structure of MnO




Although DFT+U corrects the width of the
Gap and the magnitude of the magnetic moment,
considerable differences exists in the Mn/O
hybridization and band dispersion




      C.Franchini, V. Bayer, G. Kresse et al., Phys. Rev. B 72, 045132 (2005)
             Hybrid functionals – Test for molecules

• VASP vs. GAUSSIAN03
• PBE vs. PBE0                               Test of basis set convergence:
                                             Quintuple-zeta basis set required
                                             to match plane-wave results !




J. Paier, R. Hirschl, M. Marsman, G. Kresse, J. Chem.Phys. 122,234102(2005)
                Hybrid functionals – Test for solids
• PBE vs. HSE03 functionals
• VASP vs. GAUSSIAN03




            Lattice constants                       Bulk modulus

J.Paier, M. Marsman, K. Hummer, G. Kresse, I. Gerber, J.G. Angyan,
                               J. Chem. Phys. 124, 154709(2006)
         Materials simulations using VASP:
              Properties and processes
• VASP is an extremely efficient DFT code, its limitations are
  beyond the break-even point with O(N) methods

• VASP meets industrial programming standards concerning
  stability, transferability etc.

• VASP provides a carefully tested data-base for all elements
  of the Periodic Table

• VASP offers a continuously expanded tool-box for many
  applications and a choice of GUI´s

• Post-DFT corrections (DFT+U, hybrid functionals, GW, ....)
  available in newest version
The CMS group at the Institute for Materials Physics


   Georg Kresse                Tomas Bucko
   Martijn Marsman             Mihal Jahnatek
   Lubomir Benco               Joachim Paier
   Daniel Spisak               Lukas Köhler
   Florian Mittendorfer        Orest Dubay
   Doris Vogtenhuber           K.Termentzidis
   Kerstin Hummer              Judith Harl
   Maxim Shishkin              David Karhanek
   Ellie Uzunova

				
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