GW

Parameters needed to set up a GW calculation for electronic level energies \(\varepsilon_{n\mathbf{k}}^{G_0W_0}\) of molecules and the band structure of materials: \(\varepsilon_{n\mathbf{k}}^{G_0W_0}= \varepsilon_{n\mathbf{k}}^\text{DFT}+\Sigma_{n\mathbf{k}} -v^\text{xc}_{n\mathbf{k}}\). For the GW algorithm for molecules, see https://doi.org/10.1021/acs.jctc.0c01282. For 2D materials, see https://doi.org/10.1021/acs.jctc.3c01230. [Edit on GitHub]

Subsections

Keywords

Keyword descriptions

SECTION_PARAMETERS: logical = F

Lone keyword: T

Controls the activation of the GW calculation. [Edit on GitHub]

APPROX_KP_EXTRAPOL: logical = F

Lone keyword: T

Usage: APPROX_KP_EXTRAPOL

If true, use only a 4x4 kpoint mesh for frequency points \(\omega_j, j \ge 2\) (instead of a 4x4 and 6x6 k-point mesh). The k-point extrapolation of \(W_{PQ}(i\omega_j,\mathbf{q})\) is done approximately from \(W_{PQ}(i\omega_1,\mathbf{q})\). [Edit on GitHub]

CUTOFF_RADIUS_RI: real = 3.00000000E+000 [angstrom]

Usage: CUTOFF_RADIUS_RI 3.0

Mentions: ⭐Band structure from GW

The cutoff radius (in Angstrom) for the truncated Coulomb operator. The larger the cutoff radius, the faster converges the resolution of the identity (RI) with respect to the RI basis set size. Larger cutoff radius means higher computational cost. [Edit on GitHub]

CUTOFF_RADIUS_RI_RS: real = -1.00000000E+000 [angstrom]

Usage: CUTOFF_RADIUS_RI_RS 15.0

Override (in Angstrom) of the truncated-Coulomb cutoff radius Rc used to size the per-atom RI-RS integration domain B^P = {r : |r - R_P| < Rc + r_AO(P)}, where r_AO(P) is the spatial extent of the most diffuse AO Gaussian on atom P. By default (-1.0) Rc falls back to CUTOFF_RADIUS_RI from the GW section (the same Rc used to build the RI metric integrals). Useful for convergence sweeps. [Edit on GitHub]

EPS_FILTER: real = 1.00000000E-008

Usage: EPS_FILTER 1.0E-6

Mentions: ⭐Band structure from GW

Determines a threshold for the DBCSR based sparse multiplications. Normally, EPS_FILTER determines accuracy and timing of low-scaling GW calculations. (Lower filter means higher numerical precision, but higher computational cost.) [Edit on GitHub]

FREQ_MAX_FIT: real = 1.00000000E+001 [eV]

Usage: FREQ_MAX_FIT 20.0

For analytic continuation, a fit on Σ(iω) is performed. This fit is then evaluated at a real frequency, Σ(ω), which is used in the quasiparticle equation \(\varepsilon_{n\mathbf{k}}^{G_0W_0}= \varepsilon_{n\mathbf{k}}^\text{DFT}+\Sigma_{n\mathbf{k}} -v^\text{xc}_{n\mathbf{k}}\). The keyword FREQ_MAX_FIT determines fitting range for the self-energy Σ(iω) on imaginary axis: i*[0, ω_max] for empty orbitals/bands, i*[-ω_max,0] for occ orbitals. A smaller ω_max might lead to better numerical stability (i.e., if you observe clearly wrong GW eigenvalues/bands around HOMO/LUMO, decreasing ω_max might fix this issue). A small benchmark of ω_max is contained in Fig. 5 of J. Wilhelm et al., JCTC 12, 3623-3635 (2016). Note that we used ω_max = 1 Ha = 27.211 eV in the benchmark M. Azizi et al., PRB 109, 245101 (2024). [Edit on GitHub]

GRID_SELECT: integer = 1

Usage: GRID_SELECT 1

Selection of the atom-centeredgrid type used in RI-RS optimized by Duchemin and Blase. (1) def2-TZVPP: Grid optimized by Duchemin and Blase, available for elements up to the fourth row of the periodic table (see https://doi.org/10.1021/acs.jctc.1c00101). (2) cc-pVTZ: Optimized grids available for H, C, N, and O atoms (see https://doi.org/10.1063/1.5090605). [Edit on GitHub]

HEDIN_SHIFT: logical = F

Lone keyword: T

Usage: HEDIN_SHIFT

If true, use Hedin’s shift in G0W0, evGW and evGW0. Details see in Li et al. JCTC 18, 7570 (2022), Figure 1. G0W0 with Hedin’s shift should give similar GW eigenvalues as evGW0; at a lower computational cost. [Edit on GitHub]

KPOINTS_W: integer[3] = -1 -1 -1

Usage: KPOINTS_W N_x N_y N_z

Monkhorst-Pack k-point mesh of size N_x, N_y, N_z for calculating \(W_{PQ}^\mathbf{R}=\int_\text{BZ}\frac{d\mathbf{k}}{\Omega_\text{BZ}}\, e^{-i\mathbf{k}\cdot\mathbf{R}}\,W_{PQ}(\mathbf{k})\). For non-periodic directions α, choose N_α = 1. Automatic choice of the k-point mesh for negative values, i.e. KPOINTS_W -1 -1 -1. K-point extrapolation of W is automatically switched on. [Edit on GitHub]

MEMORY_PER_PROC: real = 2.00000000E+000

Usage: MEMORY_PER_PROC 16

Mentions: ⭐Band structure from GW

Specify the available memory per MPI process. Set MEMORY_PER_PROC as accurately as possible for good performance. If MEMORY_PER_PROC is set lower as the actually available memory per MPI process, the performance will be bad; if MEMORY_PER_PROC is set higher as the actually available memory per MPI process, the program might run out of memory. You can calculate MEMORY_PER_PROC as follows: Get the memory per node on your machine, mem_per_node (for example, from a supercomputer website, typically between 100 GB and 2 TB), get the number of MPI processes per node, n_MPI_proc_per_node (for example from your run-script; if you use slurm, the number behind ‘–ntasks-per-node’ is the number of MPI processes per node). Then calculate MEMORY_PER_PROC = mem_per_node / n_MPI_proc_per_node (typically between 2 GB and 50 GB). Unit of keyword: Gigabyte (GB). [Edit on GitHub]

NUM_TIME_FREQ_POINTS: integer = 30

Usage: NUM_TIME_FREQ_POINTS 30

Mentions: ⭐Band structure from GW

Number of discrete points for the imaginary-time grid and the imaginary-frequency grid. The more points, the more precise is the calculation. Typically, 10 points are good for 0.1 eV precision of band structures and molecular energy levels, 20 points for 0.03 eV precision, and 30 points for 0.01 eV precision, see Table I in https://doi.org/10.1021/acs.jctc.0c01282. GW computation time increases linearly with NUM_TIME_FREQ_POINTS. [Edit on GitHub]

N_PROCS_PER_ATOM_Z_LP: integer = 1

Usage: N_PROCS_PER_ATOM_Z_LP 16

Number of MPI ranks that cooperate on one atom’s Cholesky factorisation in compute_coeff_Z_lP. Default 1 keeps the single-rank LAPACK dpotrf path (BLAS, fastest when D_local fits per rank). Setting > 1 enables a ScaLAPACK pdpotrf path: ranks are split into atom-groups of this size, D_local is block-cyclic distributed across each group (per-rank memory ~1/G), the compute_d_lp build is also distributed across the subgroup, and multiple groups process different atoms in parallel. Use for systems where n_local_grid is large enough that the dense (n_local_grid)^2 D_local does not fit in a single rank’s memory. [Edit on GitHub]

REGULARIZATION_MINIMAX: real = -1.00000000E+000

Usage: REGULARIZATION_MINIMAX 1.0E-4

Parameter to regularize the Fourier transformation with minimax grids. In case the parameter 0.0 is chosen, no regularization is performed. [Edit on GitHub]

REGULARIZATION_RI: real = -1.00000000E+000

Usage: REGULARIZATION_RI 1.0E-4

Mentions: ⭐Band structure from GW

Parameter for RI regularization, setting a negative value triggers the default value. Affects RI basis set convergence but in any case large RI basis will give RI basis set convergence. [Edit on GitHub]

RI_RS: logical = F

Lone keyword: T

Usage: RI_RS

Real-Space Resolution of Identity (RI-RS) method. This approximation replaces the conventional 3-center RI integrals (μν|P) by a factorized representation on an atom-centered real-space grid {r_ℓ}: (μν|P) ≈ ∑_ℓ φ_μ(r_ℓ) φ_ν(r_ℓ) Z_ℓP. The coefficients Z_ℓP combine the numerical integration weights and the Coulomb potential of the auxiliary basis function P evaluated at grid point r_ℓ. To reduce the computational cost, only grid points within the sphere B^P are included, where B^P = {r : |r - R_P| < Rc + r_P}. Here, r_P is the effective Gaussian basis radius for atom P at which the basis function magnitude falls below a threshold δ (currently controlled through EPS_FILTER). This locality approximation yields a sparse representation of the 3-center integrals enables reduced computational cost. See details in https://doi.org/10.1063/1.5090605. [Edit on GitHub]

SIZE_LATTICE_SUM: integer = 3

Usage: SIZE_LATTICE_SUM 4

Parameter determines how many neighbor cells \(\mathbf{R}\) are used for computing \(V_{PQ}(\mathbf{k}) = \sum_{\mathbf{R}} e^{i\mathbf{k}\cdot\mathbf{R}}\,\langle P, \text{cell}{=}\mathbf{0}|1/r|Q,\text{cell}{=}\mathbf{R}\rangle\). Normally, parameter does not need to be touched. [Edit on GitHub]

TIKHONOV: real = 1.00000000E-008

Usage: TIKHONOV 1.0E-8

Regularization parameter (α) used to stabilize the inversion of the grid-overlap matrix D in the Real-Space RI (RI-RS) method. See Equation (9) in https://doi.org/10.1063/1.5090605. [Edit on GitHub]