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Introduction to the SIESTA method

SUMMER SCHOOL ON COMPUTATIONAL MATERIALS SCIENCE University of Illinois at Urbana-Champaign, June 13-23, 2005 . Introduction to the SIESTA method. Some technicalities. Born-Oppenheimer DFT Pseudopotentials Numerical atomic orbitals Numerical evaluation of matrix elements.

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Introduction to the SIESTA method

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  1. SUMMER SCHOOL ON COMPUTATIONAL MATERIALS SCIENCE University of Illinois at Urbana-Champaign, June 13-23, 2005 Introduction to the SIESTA method Some technicalities

  2. Born-Oppenheimer DFT Pseudopotentials Numerical atomic orbitals Numerical evaluation of matrix elements relaxations, MD, phonons. LDA, GGA norm conserving, factorised. finite range SUMMER SCHOOL ON COMPUTATIONAL MATERIALS SCIENCE University of Illinois at Urbana-Champaign, June 13-23, 2005 Linear-scaling DFT based on Numerical Atomic Orbitals (NAOs) P. Ordejon, E. Artacho & J. M. Soler , Phys. Rev. B 53, R10441 (1996) J. M.Soler et al, J. Phys.: Condens. Matter 14, 2745 (2002)

  3. SUMMER SCHOOL ON COMPUTATIONAL MATERIALS SCIENCE University of Illinois at Urbana-Champaign, June 13-23, 2005 unknown Def. and HCn=ɛnSCn ~ - ~- Matrix equations: Expand in terms of a finite set of known wave-functions

  4. Initial guess Mixing Total energy Charge density Forces Self-consistent iterations

  5. SUMMER SCHOOL ON COMPUTATIONAL MATERIALS SCIENCE University of Illinois at Urbana-Champaign, June 13-23, 2005 s p d f Basis Set: Atomic Orbitals Strictly localised (zero beyond a cut-off radius)

  6. SUMMER SCHOOL ON COMPUTATIONAL MATERIALS SCIENCE University of Illinois at Urbana-Champaign, June 13-23, 2005 H = T + Vion(r) + Vnl+ VH(r) + Vxc(r) Long range Vna(r) = Vion(r) + VH[ratoms(r)]Neutral-atom potential dVH(r) = VH[rSCF(r)] - VH[ratoms(r)] Two-center integrals Grid integrals H = T + Vnl + Vna(r) + dVH (r)+ Vxc(r) Long-range potentials

  7. SUMMER SCHOOL ON COMPUTATIONAL MATERIALS SCIENCE University of Illinois at Urbana-Champaign, June 13-23, 2005 5 4 1 2 3 Non-overlap interactions Basis orbitals KB pseudopotential projector Sparsity 1 with 1 and 2 2 with 1,2,3, and 5 3 with 2,3,4, and 5 4 with 3,4 and 5 5 with 2,3,4, and 5 SandHare sparse is not strictly sparse but only a sparse subset is needed

  8. SUMMER SCHOOL ON COMPUTATIONAL MATERIALS SCIENCE University of Illinois at Urbana-Champaign, June 13-23, 2005 Two-center integrals Convolution theorem

  9. SUMMER SCHOOL ON COMPUTATIONAL MATERIALS SCIENCE University of Illinois at Urbana-Champaign, June 13-23, 2005 FFT Grid work

  10. SUMMER SCHOOL ON COMPUTATIONAL MATERIALS SCIENCE University of Illinois at Urbana-Champaign, June 13-23, 2005 Grid points Orbital/atom E x Egg-box effect • Affects more to forces than to energy • Grid-cell sampling

  11. SUMMER SCHOOL ON COMPUTATIONAL MATERIALS SCIENCE University of Illinois at Urbana-Champaign, June 13-23, 2005 x  kc=/x  Ecut=h2kc2/2me Grid smoothness: energy cutoff

  12. SUMMER SCHOOL ON COMPUTATIONAL MATERIALS SCIENCE University of Illinois at Urbana-Champaign, June 13-23, 2005 Grid smoothness: convergence

  13. SUMMER SCHOOL ON COMPUTATIONAL MATERIALS SCIENCE University of Illinois at Urbana-Champaign, June 13-23, 2005 Boundary conditions • Isolated object (atom, molecule, cluster): • Open boundary conditions (defined at infinity) • 3D Periodic object (crystal): • Periodic Boundary Conditions • Mixed: • 1D periodic (chains) • 2D periodic (slabs) Unit cell

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