Calculate Electronic Band Gap with GW Approximation¶
This tutorial page explains how to calculate the electronic band gap of a semiconducting material based on Density Functional Theory. We consider crystalline silicon in its standard equilibrium cubicdiamond crystal structure, and use VASP as our main simulation engine during this tutorial.
What sets the present tutorial apart from the other tutorial on band gap calculations is the employment of the "GW Approximation", which is reviewed in the subsequent paragraph. This method is more computeintensive, however similarly to the HSE method it yields more accurate results closer to experimental values, thus rectifying the tendency of the GGA to underestimate the size of the band gap. More information on this approximation, together with a demonstration of its application and results on a sample set of materials, can be found in Ref. ^{1}.
The GW Approximation¶
A comprehensive theoretical review of the GW Approximation can be found in Refs. ^{2},^{3} and ^{4}.
For the sake of this short introduction, it suffices to know that the GWapproximation is obtained using a systematic algebraic approach on the basis of Green function techniques, the most suitable approach for studying excitedstate properties of extended systems. It constitutes an approximate expansion of the selfenergy up to linear order in the screened Coulomb potential, which describes the interaction between the crystalline atoms. The implementation of theapproximation relies on a perturbative treatment starting from Density Functional Theory.
Workflow Structure¶
We shall now describe the computational implementation of the GW Approximation for computing electronic band gaps on our platform, illustrating the various steps constituting the overall Workflow. For the present explanation, we consider the example case of the VASP modeling engine. Further information on how the GW method is supported by VASP can be retrieved in Refs. ^{5} and ^{6}.
Workflows performing GW calculations follow a threestep procedure:
1. Preliminary Ground State SCF Calculation¶
The first subworkflow step in the overall GW Workflow is a standard selfconsistent field (scf) total ground state energy calculation, providing the ensuing steps of the workflow with the wavefunctions of the material structure under investigation (GW calculations always require a oneelectron basis set).
For the sake of the present example, we can set the grid of special kpoints to 10 x 10 x 10, under Important Settings.
2. Many Bands SCF Calculation¶
A significant number of empty bands is required for GW calculations, such that it is typically better to perform the calculations in two steps, as two separate subworkflows: first the abovementioned standard groundstate SCF calculation with only a few unoccupied orbitals, and secondly a calculation over a large number of unoccupied orbitals (bands), by setting the NBANDS
VASP tag to a large value.
3. GW Step¶
The actual GW calculation is done in this final subworkflow step. Here different GW flavors are possible and are selected with the ALGO
VASP tag.
The "Single Shot" quasiparticle energies method, often referred to as G0W0, is the simplest GW calculation, and computationally the most efficient one. A singleshot calculation calculates the quasiparticle energies from a single GW iteration by neglecting all offdiagonal matrix elements of the selfenergy, and employing a Taylor expansion of the selfenergy around the DFT energies.
After a successful G0W0 run, VASP will write the quasiparticle energies into the main "OUTCAR" output file for every kpoint in the Brillouin zone of the crystal structure under investigation.
In the present example we calculate quasiparticle energies on the grid of kpoints. This might not be the most accurate approach, as points on the grid might not fall exactly onto the band extrema for conduction and valence band, however, it is robust and can provide a very reasonable approximation. An intelligent interpolation technique might be used to further extract band dispersions along symmetry paths.
Creating and Executing Job¶
GWbased band gap calculation workflows can readily be imported into the accountowned collection from the Workflows Bank, for example under the name "D1GW0BG".
Apart from this, the same procedural instructions as in the other band gap calculation tutorial should be followed for creating and launching the corresponding GWbased electronic band gap Job through our Web Interface, and for inspecting the associated results.
Animation¶
In the video animation below, we outline the procedure for creating and executing an electronic band gap calculation job via the GW Approximation, considering crystalline silicon as our example material and employing VASP as the main simulation engine. We conclude by inspecting the corresponding results displayed under the Results Tab of Job Viewer.
Computational cost of GW calculations
GW calculations are in general quite computationally demanding. We therefore recommend the employment of at least 8 computing cores. For larger calculations, OF queues will have faster turnaround than the OR queues considered in the video.
Comparison with Experimental Value¶
The calculated value of 1.094 eV for the indirect band gap of silicon is in better agreement with the experimental value for this material (1.17 eV ^{7}) than the alternative case of standard band gap calculations performed with the Generalized Gradient Approximation (GGA), whose shortcomings are assessed in another tutorial page.
This provides an example of how the GW Approximation can result in improved precision in the estimation of important material properties than more traditional approaches within DFT.
Links¶

P. Das, M. Mohammadi, T. Bazhirov: "Accessible computational materials design with high fidelity and high throughput"; arXiv:1807.05623, 15 Jul 2018 ↩

C. Friedrich and A. Schindlmayr: "ManyBody Perturbation Theory: The GW Approximation"; John von Neumann Institute for Computing, Document ↩

F. Aryasetiawan and O. Gunnarsson: "The GW method"; arXiv:condmat/9712013v1, 1 Dec 1997 ↩

Accessible computational materials design with high fidelity and high throughput, P. Das, M. Mohammadi, and T.Bazhirov, Arxiv preprint, 2017 ↩