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The Plane-Wave Pseudopotential Method

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The Plane-Wave Pseudopotential Method The Plane-wave Pseudopotential Method i(G+k) r k(r)= ck,Ge · XG Chris J Pickard Electrons in a Solid Nearly Free Electrons Nearly Free Electrons Nearly Free Electrons Electronic Structures Methods Empirical Pseudopotentials Ab Initio Pseudopotentials Ab Initio Pseudopotentials Ab Initio Pseudopotentials Ab Initio Pseudopotentials Ultrasoft Pseudopotentials (Vanderbilt, 1990) Projector Augmented Waves Deriving the Pseudo Hamiltonian PAW vs PAW C. G. van de Walle and P. E. Bloechl 1993 (I) PAW to calculate all electron properties from PSP calculations" P. E. Bloechl 1994 (II)! The PAW electronic structure method" " The two are linked, but should not be confused References David Vanderbilt, Soft self-consistent pseudopotentials in a generalised eigenvalue formalism, PRB 1990 41 7892" Kari Laasonen et al, Car-Parinello molecular dynamics with Vanderbilt ultrasoft pseudopotentials, PRB 1993 47 10142" P.E. Bloechl, Projector augmented-wave method, PRB 1994 50 17953" G. Kresse and D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, PRB 1999 59 1758 On-the-fly Pseudopotentials - All quantities for PAW (I) reconstruction available" - Allows automatic consistency of the potentials with functionals" - Even fewer input files required" - The code in CASTEP is a cut down (fast) pseudopotential code" - There are internal databases" - Other generation codes (Vanderbilt’s original, OPIUM, LD1) exist It all works! Kohn-Sham Equations Being (Self) Consistent Eigenproblem in a Basis Just a Few Atoms In a Crystal Plane-waves Represent the orbital in Fourier space" ig r 3 (r)= ˜(g)e · d r Z For a periodic system we have Bloch’s Theorem" i(G+k) r k(r)= ck,Ge · XG Where the Gs are reciprocal lattice vectors and k is a symmetry label in the 1st Brillouin zone" Cutoff Energy Limit the number of plane wave components to those such that (G + k)2 E 2 cut This defines a length scale ⇡ λ = pEcut Cutoff Energy "" - The minimum length scale depends on the elements in the system through PSPs" "" - Variational principle -> energy monotonically decreases to ground state energy as Ecut increases (not strictly for USP/PAW)" "" - Converge required property with respect to cut- off energy " Cutoff Energy "" - The minimum length scale depends on the elements in the system through PSPs" "" - Variational principle -> energy monotonically decreases to ground state energy as Ecut increases (not strictly for USP/PAW)" "" - Converge required property with respect to cut- off energy " Cutoff Energy "" - The minimum length scale depends on the elements in the system through PSPs" "" - Variational principle -> energy monotonically decreases to ground state energy as Ecut increases (not strictly for USP/PAW)" "" - Converge required property with respect to cut- off energy " Why Plane-waves? - Systematic convergence with respect to single parameter" - Non-local. Cover all space equally" - Cheap forces (no Pulay term)" - No basis-set superposition error " - Numerically efficient " - Use FFTs to transform between real and reciprocal space" - The obvious choice for periodic and works well for aperiodic systems" - Rapid development of new functionality Progress, but … The Total Energy Applying H Evaluating the Energy Iterative Diagonalisation Minimisation Plane-wave Codes CASTEP PEtot VASP PARATEC PWscf Da Capo Abinit CPMD Qbox fhi98md PWPAW SFHIngX DOD-PW NWchem Octopus JDFTx CASTEP Original code due to Mike Payne rewritten by CDG, starting 1999, unveiled at 2001 CASTEP Workshop " Modern modular design, using best features of Fortran90 " Focus on robustness, ease of use, and core functionality " Particular strength in spectroscopy (NMR/IR/Raman/EELS) " Marketed commercially by Biovia (formerly Accelrys) " Low cost European Academic licence available The CDG Matthew Segall Main author of the code specification, and responsible for all the low-level communications and basis set coding. Also the population analysis algorithms. " Matt Probert Responsible for the geometry optimisation and molecular dynamics coding, and keeper of the parameters module. " Stewart Clark Responsible for the band structure and exchange-correlation functional coding and keeper of the cell module. Also co-author of the linear response code. " Chris Pickard Responsible all pseudopotential coding, amongst other things. Also co-author of the NMR code. " Phil Hasnip Responsible for the electronic energy minimisation coding (including density mixing and ensemble DFT), band-parallelism, run-time profiling and parallel efficiency report, and wavefunction subroutines. Also works on optimisation and parallel performance. " Keith Refson Responsible for phonon and E-field calculations and co-author of the linear response code. " Jonathan Yates Co-author of the NMR code, responsible for spectral module (dos, optics, eels). " Mike Payne CASTEP creator and general overseer of the whole project..
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