Comparison of various abinitio codes used in periodic...

P.Ravindran, FME-course on Comparison of various abinitio codes used in periodic calculations

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Comparison of various abinitio codes used in periodic calculations

23 February 2011; V172


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The Three Basic Methods for Modern Electronic Structure Calculations

• 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

• Plane waves– The simplicity of Fourier Expansions– The speed of Fast Fourier Transforms– Requires smooth pseudopotentials

Key Point -All methods agree when done carefully!


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Plane wave based codes

r (a.u.)

RC = 0.9

5P

4d

Rc = 2.0

RC = 2.0

5s

−zv /r

0.8

0.6

0.4

0.2

0.0

−0.2

−0.2

−0.2

−2.0

−4.0

−6.0

−8.0

−10.00.4 1.2 2.0 2.8 3.6 4.4

0.4

0.4

0.2

0.0

0.2

0.0

0.0

φ(r

) . r

φ(r

) . r

φ(r

) . r

VlP

S (

r) (

a.u.

)

l = 2

l = 1

l = 0

l = 0

l = 1

l = 2

≈

≈

≈

• APW Match all-electron wave function at sphere boundary

• 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

Atomic functions


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• CRYSTAL (Torino)• 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.


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Basis set

• 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

• (L)APW method


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Basis set: Planewaves

• 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

• Pseudopotential Method – replace each potential

Pseudopotential atom

solid

1

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1 2


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Comparisons – LAPW – PAW - - Pseudopotentials (VASP code)

• a – lattice constant; B – bulk modulus; m – magnetization

• aHolzwarth , et al.; bKresse & Joubert; cCho & Scheffler; dStizrude, et al.


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VASP-PAW,WIEN2k-LAPW, RSPt-FLMTO


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Taken from Mathias Scheffler, FHI-WS 2003.

Compared


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Overview of Popular Codes


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Comparison of various abinitio codes used in periodic...

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