Modelling Interatomic Forces Progress and Challenges

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Modelling Interatomic Forces Progress and
Challenges

• Mike Finnis
• Atomistic Simulation Centre
• School of Mathematics and Physics
• Queens University Belfast
• Belfast BT7 1NN
• Northern Ireland, UK

http//titus.phy.qub.ac.uk
CECAM 17 October 2005
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Keep it simple
Why make simple models at all when you have
ABINIT, CASTEP, CONQUEST, NEWTEP, SIESTA, VASP,
WIEN2K .
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Keep it simple
Crack blunting in copper35 million atoms
Courtesy of Brad Holian and Peter Lomdahl
http//bifrost.lanl.gov/
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Keep it simple
Size is less important to some people.
You may want statistical sampling for time gt 1ns
to find equilibrium free energy Kinetic
Monte-Carlo
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Keep it simple
SCTB, Thermodynamic integration
ZrO2 Free energy
Fabris, S. Paxton, A. T. Finnis, M. W., Free
energy and molecular dynamics calculations for
the cubic-tetragonal phase transition in
zirconia. Physical Review B 2001, 63
094101-1-13.
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Keep it simple

• Simple models can be more accurate than DFT LDA
• Band gaps
• Correlated systems van der Waals interaction,
  thin films of water

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Keep it simple
The too-big carpet problem

• Give me n parameters

Medieval Renaissance Baroque Romantic
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But not too simple!
Look after the baby

• Morse and Lennard-Jones fail on defect energies
  and elastic constants
• Non-self-consistent tight-binding fails at
  defects due to neglect of charge equilibration
  and three-centre integrals
• Rigid ion/shell models fail on structural
  energies and defects

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Models

• Hybrid schemes
• MGPT
• - EMT
• - EAM

Depending on the structure of the DOS

• Pair potentials
• - empirical
• ab initio

DFT 2nd order
The physics is in the functions

• Ionic Models
• Born
• - shell
• - variable charge

• Tight-binding
• empirical
• self-consistent
• BOPs

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Variable Charge models

• Rappe, A. K. Goddard, W. A.,
• Charge Equilibration for Molecular Dynamics
  Simulations.
• Journal of Physical Chemistry 1991, 95, (8),
  3358-3363.
• Streitz, F. H. Mintmire, J. W.,
• Electrostatic Potentials for Metal-Oxide Surfaces
  and Interfaces.
• Physical Review B 1994, 50, (16), 11996-12003.
• Campbell, T. J. Aral, G. Ogata, S. Kalia, R.
  K. Nakano, A. Vashishta, P.,
• Oxidation of aluminum nanoclusters.
• Physical Review B 2005, 71, (20), art.
  no.-205413.0

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Bond Order Potentials
Pettifor, D. G., New Many-Body Potential for the
Bond Order. Physical Review Letters 1989, 63,
(22), 2480-2483.
Density matrix
Partial bond order
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Pair potentials for Al and Ga
Ga
Al
Hafner, J. Heine, V., Theory of the Atomic
Interactions in (s,p)-bonded Metals. Journal of
Physics F Metal Physics 1986, 16, (10),
1429-1458.
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Ingredients for DFT
Free atom or ion densities
LDA,GGA,
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The second-order functional
Standard Kohn-Sham
Expand to second order about input charge
density
Elstner, M. Porezag, D. Jungnickel, G. Elsner,
J. Haugk, M. Frauenheim, T. Suhai, S.
Seifert, G., Self-consistent-charge
density-functional tight-binding method for
simulations of complex materials properties.
Physical Review B 1998, 58, 7260-7268.
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Kernel
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Variable charge ionic models
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TB BOPs and all that
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TB BOPs and all that
Atomic charge neutrality
Assume on-site repulsion keeps charge neutral on
atoms
Enforce by iteration
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TB BOPs and all that
Enforced neutral atoms
Approximate the trace difference
Inter-site
On-site
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TB BOPs and all that
Enforced neutral atoms
The repulsive terms
(also dustbin for any other small terms)
Bonding energy model
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The covalent energy
For orthogonal orbitals this reduces to
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Environment-dependent BOPs
Haas, H. Wang, C. Z. Fahnle, M. Elsasser, C.
Ho, K. M., Environment-dependent tight-binding
model for molybdenum. Physical Review B 1998,
57, (3), 1461-1470.
Mrovec, M. Nguyen-Manh, D. Pettifor, D. G.
Vitek, V., Bond-order potential for molybdenum
Application to dislocation behavior. Physical
Review B 2004, 69, (9), art. no.-094115.
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Environment-dependent BOPs
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Environment-dependent BOPs
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Environment-dependent BOPs

• Cawkwell, M. J. Nguyen-Manh, D. Woodward, C.
  Pettifor, D. G. Vitek, V.,
• Origin of Brittle Cleavage in Iridium.
• Science 2005, 309, (5737), 1059-1062.

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Where pair potentials come from
jellium
Non-local XC!
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Conclusions

• It is advantageous to define a functional both
  for understanding the ingredients (eg to avoid
  double counting) and to get consistent forces.
• The second-order DFT functional is a universal
  starting point for most existing models.

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Challenges

• Is there a reliable universal recipe for oxides?
• Include spin DFT - up and down spin density.
• Build good non-local model functionals for
  correlated systems with variable valence
• Weld-on non-local terms in C (Van der Waals)
• Include self-consistency and excited electrons

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Thank you!
Youve heard the talk
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Thank you!
Youve heard the talk