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GW

This page gives hints on how to perform a GW calculation, including self-consistency with the ABINIT package.

Introduction

DFT performs reasonably well for the determination of structural properties, but fails to predict accurate band gaps. A more rigorous framework for the description of excited states is provided by many-body perturbation theory (MBPT) [Fetter1971], [Abrikosov1975], based on the Green’s functions formalism and the concept of quasi-particles [Onida2002].

Within MBPT, one can calculate the quasi-particle (QP) energies, E, and amplitudes, Ψ, by solving a nonlinear equation involving the non-Hermitian, nonlocal and frequency dependent self-energy operator Σ.

This equation goes beyond the mean-field approximation of independent KS particles as it accounts for the dynamic many-body effects in the electron- electron interaction.

Details about the GW implementation in ABINIT can be found here

A typical GW calculation consists of two different steps (following a DFT calculation): first the screened interaction ε-1 is calculated and stored on disk (optdriver=3), then the KS band structure and W are used to evaluate the matrix elements of Σ, finally obtaining the QP corrections (optdriver=4).

The computation of the screened interaction is described in topic_Susceptibility, while the computation of the self-energy is described in topic_SelfEnergy. The frequency meshes, used e.g. for integration along the real and imaginary axes are described in topic_FrequencyMeshMBPT.

Related Input Variables

compulsory:

• optdriver OPTions for the DRIVER

basic:

• bdgw BanDs for GW calculation
• gw_nstep GW Number of self-consistent STEPs
• gw_sctype GW, Self-Consistency TYPE
• gw_toldfeig GW TOLerance on the DiFference of the EIGenvalues
• gwcalctyp GW CALCulation TYPe
• gwpara GW PARAllelization level
• nband Number of BANDs

useful:

• getqps GET QuasiParticle Structure
• getscr GET SCReening (the inverse dielectric matrix) from…
• getsuscep GET SUSCEPtibility (the irreducible polarizability) from…
• irdqps Integer that governs the ReaDing of QuasiParticle Structure
• irdscr Integer that governs the ReaDing of the SCReening
• irdsuscep Integer that governs the ReaDing of the SUSCEPtibility
• mbpt_sciss Many Body Perturbation Theory SCISSor operator
• nbandkss Number of BANDs in the KSS file
• nsym Number of SYMmetry operations
• rhoqpmix RHO QuasiParticle MIXing
• symmorphi SYMMORPHIc symmetry operation selection
• usepawu USE PAW+U (spherical part)

expert:

• fftgw FFT for GW calculation
• gw_nqlwl GW, Number of Q-points for the Long Wave-Length Limit

Selected Input Files

v3:

• tests/v3/Input/t30.in
• tests/v3/Input/t31.in

v4:

• tests/v4/Input/t84.in
• tests/v4/Input/t85.in

v5:

• tests/v5/Input/t65.in
• tests/v5/Input/t66.in
• tests/v5/Input/t69.in

Tutorials

• gw1 tutorial The first tutorial on GW (GW1) deals with the computation of the quasi-particle band gap of Silicon (semiconductor), in the GW approximation (much better than the Kohn-Sham LDA band structure), with a plasmon-pole model.
• gw2 tutorial The second tutorial on GW (GW2) deals with the computation of the quasi-particle band structure of Aluminum, in the GW approximation (so, much better than the Kohn-Sham LDA band structure) without using the plasmon-pole model.
• Parallelism of Many-Body Perturbation calculations (GW) allows to speed up the calculation of accurate electronic structures (quasi-particle band structure, including many-body effects).