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 Al 94 V 4 Fe 2 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 Al 10 V cF176 crystal structure of Al10V Space group Fd3m (No 227)

 

3D-Kagome-network with V atoms at vertices, Al2 atoms in the centers of V-V links Large voids occupied by Friauf polyhedra of 4 Al1 and 12 Al3 atoms Al 10 V-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 Al 10 V: ...V-Al-V-Al-... chains Total electron density (left) and difference-electron density (right) along the .....–V-Al2-V-Al2-.... chains in the Al 10 V structure

Covalent bonding in Al 10 V: 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 Al 3 V):

- 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: F n+1 /F n = 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

Crystal structure of thymine 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

Structure and vibrational spectra of molecular crystals

Eigenvectors of characteristic vibrational eigenmodes of thymine

Crystalline and magnetic structure of Mn

a

-Mn

T>T N : PM, cubic A12 – cI58 – I43m, isostructural to g -Mg 17 Al 12 T

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 (B) 4ML film with (1x6) domains

STM : A.Biedermann et al., PRL 86, 464 (2001) 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=a Cu =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 D z =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 • 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 Pt

5

-cluster Magnetic moments -perp. to 3-fold axis S=5.6 m

B

, L=1.0 m

B

-parallel 3-fold axis S=5.6 m

B

, L=1.2 m

B

MAE = 5 meV/atom

Pt

6

cluster Magnetic moments S=6.9 m

B

, L=1.3 m

B

Transition-metal clusters II Spin-moment Orbital moment S=6.4 m

B

, L=1.7 m

B

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 di s CC Pt 1.042 Pt/PtFe 0.584

Fe/PtFe 0.482

h 4 -trans Pt 1.134 Pt/PtFe 0.628 Fe/PtFe 1.247 0.671

0.180

0.788

h 3 -cis Pt Pt/PtFe 0.768

0.155

Fe/PtFe 1.476 0.971

di s CO Pt 0.248

Pt/PtFe 0.004 -0.077

Fe/PtFe 0.681 0.688

top Pt Pt/PtFe 0.126

Fe/PtFe 0.558 0.383

Pt di s -14 Pt/PtFe 0.425

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

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) Surface-silanol groups (top-view)

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 Br ønsted acid sites

ΔE ads =139.4 kJ/mol due to its size, cyclohexanone oxime can enter only into large pores (12 MR) ΔE ads =53.9 kJ/mol

Beckmann rearrangement at BA sites

1,2-H-shift

R_1 95.8

TS_1 85.5

R_2

Beckmann rearrangement at BA sites

N-insertion

79.1

R_2 50.0

TS_2 R_3

Beckmann rearrangement at BA sites

Hydrolysis

R_3 172.0

47.6

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 Fe

2

O

3

- Surface phase-diagram of Fe 2 O

3

- Electronic properties of MnO (0001)

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 –Fe

2

O

3

Structure of hematite

Surface properties of hematite and chromia Structure models for O-, Fe-, and FeO terminated hematite surfaces

Surface phase-diagram for Fe 2 O 3 (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 Martijn Marsman Lubomir Benco Daniel Spisak Florian Mittendorfer Doris Vogtenhuber Kerstin Hummer Maxim Shishkin Ellie Uzunova Tomas Bucko Mihal Jahnatek Joachim Paier Lukas Köhler Orest Dubay K.Termentzidis Judith Harl David Karhanek