`Sigma`

code input keywords (`sigma.inp`

)

## Required keywords

## Optional keywords

`avgpot [float]`

`avgpot_outer [float]`

`bare_coulomb_cutoff [float]`

`bare_exchange_fraction [float]`

`cd_integration_method [integer]`

`cell_average_cutoff [float]`

`cell_box_truncation`

`cell_slab_truncation`

`cell_wire_truncation`

`coulomb_truncation_radius [float]`

`cvfit [array of integers]`

`cvfit_outer [array of integers]`

`degeneracy_check_override`

`delta_frequency_eval [float]`

`begin diag ... end`

`die_outside_sphere`

`dont_symmetrize`

`dont_use_hdf5`

`dont_use_vxcdat`

`ec0 [float]`

`ec0_outer [float]`

`ecdel [float]`

`ecdel_outer [float]`

`ecs [float]`

`ecs_outer [float]`

`eqp_corrections`

`eqp_outer_corrections`

`ev0 [float]`

`ev0_outer [float]`

`evdel [float]`

`evdel_outer [float]`

`evs [float]`

`evs_outer [float]`

`exact_static_ch [integer]`

`fermi_level [float]`

`fermi_level_absolute`

`fermi_level_relative`

`finite_difference_form [integer]`

`finite_difference_spacing [float]`

`frequency_dependence [integer]`

`frequency_dependence_method [integer]`

`frequency_grid_shift [integer]`

`full_ch_conv_log [integer]`

`fullbz_replace`

`fullbz_write`

`gpp_broadening [float]`

`gpp_sexcutoff [float]`

`ignore_outside_sphere`

`init_frequency_eval [float]`

`invalid_gpp_mode [integer]`

`max_frequency_eval [float]`

`no_symmetries_offdiagonals`

`no_symmetries_q_grid`

`number_bands [integer]`

`number_diag`

`number_frequency_eval [integer]`

`number_offdiag`

`number_sigma_pools [integer]`

`begin offdiag ... end`

`qgrid [array of integers]`

`begin qpoints ... end`

`screened_coulomb_cutoff [float]`

`sigma_matrix [array of integers]`

`skip_averagew`

`spherical_truncation`

`spin_index_max [integer]`

`spin_index_min [integer]`

`subsample`

`tol_degeneracy`

`use_epsilon_remainder`

`use_symmetries_q_grid`

`use_xdat`

`verbosity [integer]`

`write_vcoul`

## Keyword documentation

### Specification of self-energy matrix elements to compute

The flags below control which matrix elements \langle \psi_n | \Sigma(E_l) | \psi_m \rangle
will be computed, where n and m are band indices, and E_l is the energy at
which to evaluate the self-energy operator. Note that E_l is irrelevant for
Hatree-Fock and static COHSEX calculations, i.e., if `frequency_dependence`

== -1 or 0.

In typical cases, you just want to compute diagonal (n=m) matrix elements
of \Sigma between a lower and an uper bound. In this case, you can simply
use the flags `band_index_min`

and `band_index_max`

to specify these bounds.
Advanced users can also use the flags `diag`

, `offdiag`

and `sigma_matrix`

in order to compute arbitrary diagonal and off-diagonal matrix elements.

`band_index_min [integer]`

Minimum band index for diagonal matrix elements (n=m) of \Sigma to be computed.

`band_index_max [integer]`

Maximum band index for diagonal matrix elements (n=m) of \Sigma to be computed.

`number_diag`

Number or diagonal matrix elements, i.e., for n=m.

`begin diag ... end`

Band indices for the diagonal matrix elements of Sigma (n=m=l)

`number_offdiag`

Number of off-diagonal matrix elements

`begin offdiag ... end`

The off-diagonal matrix elements of Sigma
`band_index_min`

<= n <= `band_index_max`

`band_index_min`

<= m <= `band_index_max`

`band_index_min`

<= l <= `band_index_max`

NOTE: the offdiag utility only works with the sigma_matrix syntax, below.

`sigma_matrix [array of integers]`

Alternatively, select a specific value of l and let n and m vary in the range from band_index_min to band_index_max Set l to 0 to skip the off-diagonal calculation (default) If l = -1 then l_i is set to n_i (i = 1 ... noffdiag) i.e. each row is computed at different eigenvalue If l = -2 then l_i is set to m_i (i = 1 ... noffdiag) i.e. each column is computed at different eigenvalue For l > 0, all elements are computed at eigenvalue of band l. Set t to 0 for the full matrix (default) or to -1/+1 for the lower/upper triangle

### Frequency grid used to evaluate the self-energy

In order to evaluate \Sigma(\omega), you have to specify a frequency grid for the frequencies \omega. You can control where to center/shift the grid.

`frequency_grid_shift [integer]`

Use this flag to control where the center of the frequency grid is. The options are:

- 0 if you don't want any shift, i.e., \omega is an absolute energy
- 1 if you want to shift the first frequency \omega=0 to the Fermi energy
(this was the default behavior in
`BerkeleyGW-1.0`

) - 2 if you want to center the frequency grid around each mean-field QP energy (default)

`delta_frequency_eval [float]`

If `frequency_grid_shift`

is 2 (default), specify the frequency spacing
`delta_frequency_eval`

in eV (default=0.2) and the width, in eV, of the
evaluation grid centered around each QP state (default=2.0). The code
will generate a frequency grid from -`max_frequency_eval`

to `max_frequency_eval`

.
You should increase the value of `max_frequency_eval`

if you expect the
absolute QP corrections to be large, such as when dealing with molecules
(the code will warn if the frequency grid is too small).
Note for advanced users: the grids are actually centered around the outer
mean-field energies, so you can use `WFN_outer`

and eqp_outer_corrections or
outer scissors parameters to fine-tune the frequency grid.

`max_frequency_eval [float]`

`init_frequency_eval [float]`

If `frequency_grid_shift`

is 0 or 1, specify the initial frequency
`init_frequency_eval`

(before the shift), in eV, the frequency spacing
`delta_frequency_eval`

, in eV, and the number of frequency points
`number_frequency_eval`

.

`delta_frequency_eval [float]`

`number_frequency_eval [integer]`

### Options for the generalized plasmon-pole (GPP) calculations

The matrix element of the self-energy operator is expanded to first order in the energy around Ecor.

`finite_difference_form [integer]`

This flag controls the finite difference form for numerical derivative of \Sigma(\omega):

- grid = -3 : Calculate Sigma(w) on a grid, using the same frequency grid as in full-frequency calculations.
- none = -2 : dSigma/dE = 0 [skip the expansion].
- backward = -1 : dSigma/dE = (Sigma(Ecor) - Sigma(Ecor-dE)) / dE
- central = 0 : dSigma/dE = (Sigma(Ecor+dE) - Sigma(Ecor-dE)) / (2dE)
- forward = 1 : dSigma/dE = (Sigma(Ecor+dE) - Sigma(Ecor)) / dE
- default = 2 : forward for diagonal and none for off-diagonal

`finite_difference_spacing [float]`

Finite difference spacing given in eV (defaults to 1.0)

### Options for Hartree-Fock & hybrid calculations

For Hartree-Fock/hybrid functional, no `epsmat`

/`eps0mat`

files are needed.
Instead provide a list of q-points and the grid size.
The list of q-points should not be reduced with time
reversal symmetry - because BerkeleyGW never uses time
reversal symmetry to unfold the q/k-points. Instead,
inversion symmetry does the job in the real version of
the code.
You can generate this list with kgrid.x: just set the shifts to zero and use
same grid numbers as for WFN_inner.

`begin qpoints ... end`

qx qy qz 1/scale_factor is_q0

Reduced coordinates of q-points. scale_factor is for specifying values such as 1/3 is_q0 indicated whether a q-point is Gamma (1) or not (0)

`qgrid [array of integers]`

The regular grid of q-points corresponding to the list.

### Scissors operator

Scissors operator (linear fit of the quasiparticle
energy corrections) for the bands in `WFN`

and `WFNq`

.
For valence-band energies:

`ev_cor = ev_in + evs + evdel * (ev_in - ev0)`

For conduction-band energies:

`ec_cor = ec_in + ecs + ecdel * (ec_in - ec0)`

Defaults is zero for all entries, i.e., no scissors corrections.
`evs`

, `ev0`

, `ecs`

, `ec0`

are in eV.
If you have `eqp.dat`

and `eqp_q.dat`

files
this information is ignored in favor of the eigenvalues
in eqp.dat and eqp_q.dat.
One can specify all parameters for scissors operator
in a single line with `cvfit evs ev0 evdel ecs ec0 ecdel`

`evs [float]`

`ev0 [float]`

`evdel [float]`

`ecs [float]`

`ec0 [float]`

`ecdel [float]`

`cvfit [array of integers]`

### Truncation schemes for the Coulomb potential

Since BerkerleyGW is a plane-wave-based code, one must truncate the Coulomb potential to avoid spurious interactions between repeated supercells when dealing with systems with reduced dimensionality. Make sure you understand how to setup your mean-field calculation so that the supercell is large enough to perform a truncation of the Coulomb potential.

`cell_box_truncation`

Truncate the Coulomb potential based on the Wigner-Seitz cell. This is the recommended truncation for 0D systems.

`cell_wire_truncation`

Truncation scheme for 1D systems, such as carbon nanotubes. The z direction is assumed to be periodic, and x and y confined.

`cell_slab_truncation`

Truncation scheme for 2D systems, such as graphene or monolayer MoS2. The z direction is assumed to be confined, and x and y periodic.

`spherical_truncation`

Truncate the Coulomb potential based on an analytical scheme.
This is ok for quasi-spherical systems, such as CH4 molecule or C60,
but the `cell_box_truncation`

is the most general and recommended
scheme. When using spherical truncation, you must also specify the
radius for the truncation in `spherical_truncation`

.

`coulomb_truncation_radius [float]`

This specifies the radius of for spherical truncation, in Bohr,
so that the Coulomb potential v(r) is zero for r larger than
these values. This flag is to be used together with `spherical_truncation`

.

### Misc. parameters

`screened_coulomb_cutoff [float]`

Energy cutoff for the screened Coulomb interaction, in Ry. The screened Coulomb interaction W_{GG'}(q) will contain all G-vectors with kinetic energy |q+G|^2 up to this cutoff. Default is the epsilon_cutoff used in the epsilon code. This value cannot be larger than the epsilon_cutoff or the bare_coulomb_cutoff.

`bare_coulomb_cutoff [float]`

Energy cutoff for the bare Coulomb interaction, in Ry. The bare Coulomb interaction v(G+q) will contain all G-vectors with kinetic energy |q+G|^2 up to this cutoff. Default is the WFN cutoff.

`number_bands [integer]`

Total number of bands (valence+conduction) to sum over. Defaults to the number of bands in the WFN file minus 1.

The range of spin indices for which Sigma is calculated The default is the first spin component

`spin_index_min [integer]`

`spin_index_max [integer]`

`cell_average_cutoff [float]`

Cutoff energy (in Ry) for averaging the Coulomb Interaction in the mini-Brillouin Zones around the Gamma-point without Truncation or for Cell Wire or Cell Slab Truncation.

`frequency_dependence [integer]`

Frequency dependence of the inverse dielectric matrix.

- Set to -1 for the Hartree-Fock and hybrid functional approximation.
- Set to 0 for the static COHSEX approximation.
- Set to 1 for the Generalized Plasmon Pole model (default).
- Set to 2 for the full frequency dependence.
- Set to 3 for the Generalized Plasmon Pole model in the Godby-Needs flavor. Note: does not work with parallelization in frequencies.

`frequency_dependence_method [integer]`

Full frequency dependence method for the polarizability. set to 0 for the real-axis integration method. set to 2 for the contour-deformation method (default).

`cd_integration_method [integer]`

For contour deformation calculations, specify the integration method on the imaginary axis (default is 0). Options are:

- 0 for piecewise constant matrix elements centered at each imaginary frequency
- 2 for piecewise quadratic matrix elements over each integration segment
- 3 for cubic Hermite matrix elements over each integration segment

`invalid_gpp_mode [integer]`

What should we do when we perform a HL-GPP or a GN-GPP calculations and we find an invalid mode frequency with \omega_{GG'}^2 < 0 Options are: -1: Default, same as 3. 0: Skip invalid mode and ignore its contribution to the self energy. 1: "Find" a purely complex mode frequency. This was the default behavior in BGW-1.x. 2: Set the mode frequency to a fixed value of 2 Ry. 3: Treat that mode within the static COHSEX approximation (move frequency to infinity).

`use_epsilon_remainder`

Add remainder from tail of epsilon for full frequency.

`full_ch_conv_log [integer]`

Logging the convergence of the CH term with respect to the number of bands in the output file "ch_converge.dat". Options are:

- 0 to log only the real part of VBM, CBM and the gap (default).
- 1 to log the real and imag. parts of all bands for which we compute Sigma.

`use_xdat`

Use precalculated matrix elements of bare exchange from x.dat. The default is not to use them.

`dont_use_vxcdat`

The default behavior is to load the precalculated exchange-correlation
matrix elements \langle n | \hat{V}_{xc} | m \rangle from file `vxc.dat`

.
Use this flag to load the whole exchange-correlation matrix
in reciprocal space, V_{xc}(G), which should be provided in the file
`VXC`

.

`bare_exchange_fraction [float]`

Fraction of bare exchange. Set to 1.0 if you use the exchange-correlation matrix elements read from file vxc.dat. Set to 1.0 for local density functional, 0.0 for HF, 0.75 for PBE0, 0.80 for B3LYP if you use the local part of the exchange-correlation potential read from file VXC. For functionals such as HSE whose nonlocal part is not some fraction of bare exchange, use vxc.dat and not this option. This is set to 1.0 by default.

`gpp_broadening [float]`

Broadening for the energy denominator in CH and SX within GPP. If it is less than this value, the sum is better conditioned than either CH or SX directly, and will be assigned to SX while CH = 0. This is given in eV, the default value is 0.5

`gpp_sexcutoff [float]`

Cutoff for the poles in SX within GPP. Divergent contributions that are supposed to sum to zero are removed. This is dimensionless, the default value is 4.0

`begin kpoints ... end`

kx ky kz 1/scale_factor

scale_factor is for specifying values such as 1/3

`fermi_level [float]`

Specify the Fermi level (in eV), if you want implicit doping
Note that value refers to energies *after* scissor shift or eqp corrections.
See also `fermi_level_absolute`

and `fermi_level_relative`

to control
the meaning of the Fermi level.

The Fermi level in keyword `fermi_level`

can be treated as an absolute
value or relative to that found from the mean field (default)

`fermi_level_absolute`

`fermi_level_relative`

`dont_use_hdf5`

Read from traditional simple binary format for epsmat/eps0mat instead of HDF5 file format. Relevant only if code is compiled with HDF5 support.

`verbosity [integer]`

Verbosity level, options are:

- 1: default
- 2: medium - info about k-points, symmetries, and eqp corrections.
- 3: high - full dump of the reduced and unfolded k-points.
- 4: log - log of various function calls. Use to debug code.
- 5: debug - extra debug statements. Use to debug code.
- 6: max - only use if instructed to, severe performance downgrade. Note that verbosity levels are cumulative. Most users will want to stick with level 1 and, at most, level 3. Only use level 4+ if debugging the code.

Scissors operator (linear fit of the quasiparticle energy corrections) for the bands in WFN_outer. Has no effect if WFN_outer is not supplied. For valence-band energies: ev_cor = ev_in + evs_outer + evdel_outer (ev_in - ev0_outer) For conduction-band energies: ec_cor = ec_in + ecs_outer + ecdel_outer (ec_in - ec0_outer) Defaults below. evs_outer, ev0_outer, ecs_outer, ec0_outer are in eV

`evs_outer [float]`

`ev0_outer [float]`

`evdel_outer [float]`

`ecs_outer [float]`

`ec0_outer [float]`

`ecdel_outer [float]`

`cvfit_outer [array of integers]`

One can specify these parameters in a single line as (evs_outer ev0_outer evdel_outer ecs_outer ec0_outer ecdel_outer)

`eqp_corrections`

Set this to use eigenvalues in eqp.dat If not set, this file will be ignored.

`eqp_outer_corrections`

Set this to use eigenvalues in eqp_outer.dat If not set, this file will be ignored. Has no effect if WFN_outer is not supplied.

`avgpot [float]`

The average potential on the faces of the unit cell in the non-periodic directions for the bands in WFN_inner This is used to correct for the vacuum level The default is zero, avgpot is in eV

`avgpot_outer [float]`

The average potential on the faces of the unit cell in the non-periodic directions for the bands in WFN_outer This is used to correct for the vacuum level. Has no effect if WFN_outer is not supplied. The default is zero, avgpot_outer is in eV

`write_vcoul`

Write the bare Coulomb potential v(q+G) to file

`number_sigma_pools [integer]`

Number of pools for parallel sigma calculations The default is chosen to minimize memory in calculation

`tol_degeneracy`

Threshold for considering bands degenerate, for purpose of making sure all of degenerate subspaces are included, for band-averaging, and for setting offdiagonals to zero by symmetry. (Ry)

'unfolded BZ' is from the kpoints in the WFN_inner file 'full BZ' is generated from the kgrid parameters in the WFN_inner file See comments in Common/checkbz.f90 for more details

`fullbz_replace`

Replace unfolded BZ with full BZ

`fullbz_write`

Write unfolded BZ and full BZ to files

`degeneracy_check_override`

The requested number of bands cannot break degenerate subspace Use the following keyword to suppress this check Note that you must still provide one more band in wavefunction file in order to assess degeneracy

The sum over q-points runs over the full Brillouin zone. For diagonal matrix elements between non-degenerate bands and for spherically symmetric Coulomb potential (no truncation or spherical truncation), the sum over q-points runs over the irreducible wedge folded with the symmetries of a subgroup of the k-point. The latter is the default. In both cases, WFN_inner should have the reduced k-points from an unshifted grid, i.e. same as q-points in Epsilon. With no_symmetries_q_grid, any calculation can be done; use_symmetries_q_grid is faster but only diagonal matrix elements of non-degenerate or band-averaged states can be done.

`no_symmetries_q_grid`

`use_symmetries_q_grid`

`dont_symmetrize`

If no_symmetries_q_grid is used, this flag skips the averaging of the degenerate subspace. This might be useful for treating accidental degeneracies.

`no_symmetries_offdiagonals`

Off-diagonal elements are zero if the two states belong to different irreducible representations. As a simple proxy, we use the size of the degenerate subspaces of the two states: if the sizes are different, the irreps are different, and the matrix element is set to zero without calculation. Turn off this behavior for testing by setting flag below. Using WFN_outer effectively sets no_symmetries_offdiagonals.

Rotation of the k-points may bring G-vectors outside of the sphere. Use the following keywords to specify whether to die if some of the G-vectors fall outside of the sphere. The default is to die. Set to die in case screened_coulomb_cutoff = epsilon_cutoff. Set to ignore in case screened_coulomb_cutoff < epsilon_cutoff.

`die_outside_sphere`

`ignore_outside_sphere`

`exact_static_ch [integer]`

Dealing with the convergence of the CH term. Set to 0 to compute a partial sum over empty bands. Set to 1 to compute the exact static CH. In case of exact_static_ch = 1 and frequency_dependence = 1 (GPP) or 2 (FF), the partial sum over empty bands is corrected with the static remainder which is equal to 1/2 (exact static CH - partial sum static CH), additional columns in sigma_hp.log labeled ch', sig', eqp0', eqp1' are computed with the partial sum without the static remainder, and ch_converge.dat contains the static limit of the partial sum. In case of exact_static_ch = 0 and frequency_dependence = 0 (COHSEX), columns ch, sig, eqp0, eqp1 contain the exact static CH, columns ch', sig', eqp0', eqp1' contain the partial sum static CH, and ch_converge.dat contains the static limit of the partial sum. For exact_static_ch = 1 and frequency_dependence = 0 (COHSEX), columns ch', sig', eqp0', eqp1' are not printed and file ch_converge.dat is not written. Default is 0 for frequency_dependence = 1 and 2; 1 for frequency_dependence = 0; has no effect for frequency_dependence = -1. It is important to note that the exact static CH answer depends not only on the screened Coulomb cutoff but also on the bare Coulomb cutoff because G-G' for G's within the screened Coulomb cutoff can be outside the screened Coulomb cutoff sphere. And, therefore, the bare Coulomb cutoff sphere is used.

`skip_averagew`

Do not average W over the minibz, and do not replace the head of eps0mat with averaged value. Only use this option for debugging purposes.

`subsample`

By default, the code reads the dielectric matrix for a single q->0 q-point. The following flag enables the subsampling of Voronoi cell containing Gamma. Your eps0mat file should contain a list of radial q-points (which will not be unfolded by symmetries) instead of a single q->0 point. You should provide a file subweights.dat containing the weights w(q) associated to each subsampled q-point (which will be renormalized so that \sum w(q)=1). Using this subsampling allows one to accelerate the convergence with respect to the number of q-points, and is especially helpful when dealing with large unit cells, truncated Coulomb potential and birefringent materials.