Comparison of various abinitio codes used in periodic calculations
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1 Comparison of various abinitio codes used in periodic calculations 1 Prof.P. Ravindran, Department of Physics, Central University of Tamil Nadu, India & Center for Materials Science and Nanotechnology, University of Oslo, Norway
2 How to choose the code? 2
3 The Three Basic Methods for Modern Electronic Structure Calculations 3 Plane waves The simplicity of Fourier Expansions The speed of Fast Fourier Transforms Requires smooth pseudopotentials Localized orbitals The intuitive appeal of atomic-like states Simplest interpretation in tight-binding form Gaussian basis widely used in chemistry Numerical orbitals used in SIESTA Augmented methods Best of both worlds also most demanding Requires matching inside and outside functions Most general form (L)APW Key Point - All methods agree when done carefully!
4 Plane wave based codes 4 APW Match all-electron wave function at sphere boundary Atomic functions PAW Smooth function plus added function only inside sphere Pseudopotential Cast theory in terms of only the smooth functions that are solutions of pseudopotential equations
5 CRYSTAL (Torino) 5 Periodic ab-initio program in 0D (molecular calculation), 1D, 2D (surfaces) or 3D. Atomic orbital basis sets (gaussians). We benefit from the usual information for the molecules: Mulliken charges and overlap populations. Usual Hamiltonians are available (HF, hybrid methods B3LYP) beyond DFT One should optimize the basis set for each system. VASP program (Vienna) Periodic DFT program in three dimensions. A calculation for adsorption necessitates to simulate a 2D calculation by a 3D calculation. Plane waves basis sets. Convergence is fast and Optimization methods are very efficient. No «basis set superposition error». It is difficult to have accurate reference energies for atoms. information for the molecules: Mulliken charges and overlap populations is not available. Empty space costs. LDA, GGA, Hybrid functionals, GW available.
6 Basis set 6 (L)APW method Augmentation: represent the wave function inside each sphere in spherical harmonics & plane waves in interstitial. Best of both worlds But requires matching inside and outside functions Most general form can approach arbitrarily precision
7 Basis set: Planewaves 7 Pseudopotential Method replace each potential solid 2 Pseudopotential atom Generate Pseudopotential in atom (spherical) use in solid Pseudopotential can be constructed to be weak Can be chosen to be smooth Solve Kohn-Sham equations in solid directly in Fourier space
8 8
9 9
10 Comparisons LAPW PAW - - Pseudopotentials (VASP code) 10 a lattice constant; B bulk modulus; m magnetization a Holzwarth, et al.; b Kresse & Joubert; c Cho & Scheffler; d Stizrude, et al.
11 VASP-PAW,WIEN2k-LAPW, RSPt-FLMTO 11
12 RSPt and VASP results: Lattice Constants 12
13 RSPt and VASP results: Bulk Moduli 13
14 Taken from Mathias Scheffler, FHI-WS Compared
15 Aluminum: Free Atom 15
16 Aluminum Bulk 16
17 Aluminum Bulk 17
18 18
19 (1x1) Oxygen adlayer on a 7-layer slab of aluminum 19
20 (2x2) Oxygen adlayer on a 7-layer slab of aluminum 20
21 (2x2) Oxygen adlayer on a 7-layer slab of aluminum 21
22 Remarks 22
23 Comparison of Results 23
24 Conclusions 24
25 Overview of Popular Codes 25
26 26
27 27
28 28
29 29
30 Other Codes 30
31 Other Codes 31
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