`Absorption`

code input keywords (`absorption.inp`

)

## Required keywords

`energy_resolution [float]`

`number_cond_bands_coarse [integer]`

`number_cond_bands_fine [integer]`

`number_val_bands_coarse [integer]`

`number_val_bands_fine [integer]`

## Optional keywords

`average_w`

`avgpot [float]`

`cell_average_cutoff [float]`

`cell_box_truncation`

`cell_slab_truncation`

`cell_wire_truncation`

`coulomb_truncation_radius [float]`

`cvfit [array of integers]`

`degeneracy_check_override`

`delaunay_interpolation`

`delta_frequency [float]`

`diagonalization`

`dont_use_hdf5`

`ec0 [float]`

`ecdel [float]`

`ecs [float]`

`energy_resolution_gamma [float]`

`energy_resolution_sigma [float]`

`eqp_co_corrections`

`eqp_corrections`

`ev0 [float]`

`evdel [float]`

`evs [float]`

`extended_kernel`

`fermi_level [float]`

`fermi_level_absolute`

`fermi_level_relative`

`full_bse`

`fullbz_replace`

`fullbz_write`

`gaussian_broadening`

`greedy_interpolation`

`haydock`

`highest_occupied_band`

`kernel_scaling [float]`

`lanczos`

`lanczos_gauss_quadrature`

`local_fields`

`lorentzian_broadening`

`lowest_occupied_band`

`no_lanczos_gauss_quadrature`

`no_symmetries_coarse_grid`

`no_symmetries_fine_grid`

`no_symmetries_shifted_grid`

`noeh_only`

`number_eigenvalues`

`number_iterations [integer]`

`polarization [array of integers]`

`q_shift [array of integers]`

`read_dtmat`

`read_eigenvalues`

`read_eps2_moments`

`read_epsdiag`

`read_kpoints`

`read_vmtxel`

`regular_grid [array of integers]`

`screening_graphene`

`screening_metal`

`screening_semiconductor`

`skip_interpolation`

`spherical_truncation`

`spin_singlet`

`spin_triplet`

`spinor`

`subsample_line`

`unrestricted_transformation`

`use_dos`

`use_momentum`

`use_symmetries_coarse_grid`

`use_symmetries_fine_grid`

`use_symmetries_shifted_grid`

`use_velocity`

`verbosity [integer]`

`voigt_broadening`

`write_eigenvectors`

`write_vcoul`

`zero_coupling_block`

`zero_q0_element`

`zero_unrestricted_contribution`

## Keyword documentation

### Band occupation

In metallic systems, PARATEC often outputs incorrect occupation levels in wavefunctions. Use this to override these values. lowest_occupied_band should be 1 unless you have some very exotic situation.

`lowest_occupied_band`

`highest_occupied_band`

### Screening type

How does the screening of the system behaves? (default=`screening_semiconductor`

)
BerkeleyGW uses this information to apply a different numerical
procedure to computing the diverging q\rightarrow 0 contribution
to the screened Coulomb potential W_{GG'}(q).
These models are not used in Hartree-Fock calculations.

`screening_semiconductor`

Use this flag on gapped system (**default**).

`screening_metal`

Use this flag on metallic system, i.e., constant DOS at the Fermi energy.

`screening_graphene`

Use this flag on systems with vanishing linear DOS at the Fermi level, such as graphene.

### 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`

.

### K-point unfolding and symmetries

These flags define whether to use symmetries to unfold the Brillouin zone or not in files. The following files are read by BerkleyGW depending on which flags you use:

`WFN_fi`

:`use_symmetries_fine_grid`

,`no_symmetries_fine_grid`

;`WFNq_fi`

:`use_symmetries_shifted_grid`

,`no_symmetries_shifted_grid`

; and`WFN_co`

:`use_symmetries_coarse_grid`

,`no_symmetries_coarse_grid`

.

Warning

**Default is always not to unfold!**
You probably want to use symmetries to unfold the grid in
`WFN_co`

, i.e., `use_symmetries_coarse_grid`

, but not to use symmetries
when unfolding files `WFN_fi`

and `WFNq_fi`

when they are randomly shifted,
i.e., `no_symmetries_fine_grid`

and `no_symmetries_shifted_grid`

.
The idea is that, if apply a random shift to `WFN_fi`

or
`WFNq_fi`

, these files will contain the full Monkhorst-Pack
grid. If you apply symmetry elements on top of that,
you will get a non-uniform grid.

Warning

Make sure that you pick either `no_symmetries_coarse_grid`

or
`use_symmetries_coarse_grid`

consistently with your
`kernel`

calculation!

`no_symmetries_fine_grid`

Don't use symmetries to unfold the k-points from `WFN_fi`

. This is
a good idea when you use a random shift in your fine grid.

`use_symmetries_fine_grid`

Use symmetries to unfold the k-points from `WFN_fi`

. Use this whenever
your `WFN_fi`

contains a full, unshifted k-point grid.

`no_symmetries_shifted_grid`

Don't use symmetries to unfold the k-points from `WFNq_fi`

. This is a
good idea when you use a random shift in your q-shifted fine grid and in your
`WFN_fi`

files.

`use_symmetries_shifted_grid`

Use symmetries to unfold the k-points from `WFNq_fi`

. Use this whenever
both your `WFN_fi`

and `WFNq_fi`

contain a full, unshifted k-point grid. In
this case, you will need to generate the shifted grid using the same
procedure as generating the shifted grid for an epsilon calculation. i.e.
use non-zero small q-shift in `kgrid.inp`

.

`no_symmetries_coarse_grid`

Don't use symmetries to unfold the coarse k-points from `WFN_co`

.
Make sure to use the same parameter that you used in `kernel`

!

`use_symmetries_coarse_grid`

Use symmetries to unfold the coarse k-points from `WFN_co`

.
Make sure to use the same parameter that you used in `kernel`

!

### Dipole transition matrix elements

How to calculate optical transition probabilities?

- For absorption, there is no default, one must be specified.
- For inteqp, default is
`use_momentum`

.

Note: for `use_momentum`

and `use_dos`

, only `WFN_fi`

is used.
For `use_velocity`

, the valence bands come from `WFNq_fi`

.

`use_velocity`

Recommended option for absorption calculations. The dipole matrix
elements are rigorously computed using two wave function files,
`WFN_fi`

, and `WFNq_fi`

, which includes effects such as the non-local
part of the pseudopotential in the transition matrix elements.

`use_momentum`

When you use the momentum operator, you are throwing away the contribution
from the non-local part of the pseudopotential to the dipole transition matrix
elements. However, you won't need to specify a `WFNq_fi`

file. This option
is very useful to debug calculations, but use it with caution!

`use_dos`

For Haydock there is also a third option to calculate Joint density of states. Diagonalization computes this for free. This is equivalent to setting the dipole transition matrix elements to a constant.

### BZ unfolding (experimental)

The 'unfolded BZ' refers to symmetry-unfolded set of k-points in the `WFN*`

files, while 'full BZ' is generated from the k-grid parameters in the WFN
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

### Numerical broadening

Numerical broadening width and type for generating absorption spectrum.
Haydock only does Lorentzian broadening, and \varepsilon_1(\omega) is always broadened with a Lorentzian profile.
The width is controlled by the `energy_resolution`

flag, and \varepsilon_2(\omega)
can be broadened with the diagonalization algorithm with either a Gaussian or Lorentzian curve.

`energy_resolution [float]`

By how much each peak in \varepsilon_2(\omega) should be broadened, in eV.

`lorentzian_broadening`

Use a Lorentzian curve to broaden \varepsilon_2(\omega). This is the only option with the Haydock algorithm.

`gaussian_broadening`

Use a Gaussian curve to broaden \varepsilon_2(\omega). This is the default with the diagonalization algorithm.

`voigt_broadening`

Use a Voigt profile to broaden \varepsilon_2(\omega), i.e., a convolution
of a Lorentzian with a Gaussian curve. This is only available with the
diagonalization algorithm. See parameters `energy_resolution_sigma`

and
`energy_resolution_gamma`

. Note that the Voigt profile becomes Lorentzian
as `energy_resolution_sigma`

approaches 0, and a Gaussian as
`energy_resolution_gamma`

approaches 0. However, the parametrization
of the Voigt function diverges at `energy_resolution_sigma`

= 0.

`energy_resolution_sigma [float]`

Broadening of the Gaussian contribution to the Voigt profile, in eV.

`energy_resolution_gamma [float]`

Broadening of the Lorentzian contribution to the Voigt profile, in eV.

### Spin transition to compute

Options are:

`spin_triplet`

: direct kernel only, appropriate only for spin-unpolarized calculations (no exchange).`spin_singlet`

(default): direct + exchange, appropriate for spin-polarized too.`local_fields`

: local-fields + RPA (exchange only)

Warning

Triplet transition matrix elements would be exactly zero for electric-dipole transitions, so we give instead the spin part of a magnetic-dipole interaction.

Note that triplet kernel only applies to a spin-unpolarized system; for a spin-polarized system, the solutions naturally include both singlets and triplets (or other multiplicities for a magnetic system).

`spin_triplet`

`spin_singlet`

`local_fields`

### K-point interpolation scheme

`delaunay_interpolation`

The interpolation algorithm is based on the Delaunay tessellation of the k-points. This guarantees that the interpolant is a continuous function, and that we are always interpolating, and never extrapolating. (default)

`greedy_interpolation`

You can also use the previous interpolation method, which might give interpolants that are not continuous.

### Misc. parameters

`number_val_bands_fine [integer]`

Number of occupied bands on fine (interpolated) k-point grid, `WFNq_fi`

.

`number_val_bands_coarse [integer]`

Number of occupied bands on coarse (input) k-point grid, `WFN_co`

.

`number_cond_bands_fine [integer]`

Number of unoccupied bands on fine (interpolated) k-point grid, `WFN_fi`

.

`number_cond_bands_coarse [integer]`

Number of unoccupied bands on coarse (input) k-point grid, `WFN_co`

.

`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.

`regular_grid [array of integers]`

Regular grid used to calculate qpt_averages.
Default is the kgrid in the `WFN_fi`

file.
It matters only if you want to perform minicell averages.

`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

`read_kpoints`

Advanced flag: read k-points from the `kpoints`

file.
The default is to read k-points from the wfn file.

`q_shift [array of integers]`

This is needed only with `read_kpoints`

and if you selected velocity operator above.
This should match the shift between `WFN_fi`

and `WFNq_fi`

.

`degeneracy_check_override`

The requested number of valence or conduction 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. For inteqp, only the coarse grid is checked.

`spinor`

Request calculation of the fully-relativistic form of the BSE, using spinor wavefunctions

Which algorithm do we use to solve the BSE? We can either do a full
diagonalization with ScaLAPACK or LAPACK) or use the Haydock iterative
solver. Note that the `lanczos`

solver below also requires you to
specify `diagonalization`

here.

`diagonalization`

`haydock`

`lanczos`

In adittion to the solver above, you can also use the Lanczos iterative
solver, which requires ScaLAPACK, but works with both TDA and full BSE.
If you want to use the `lanczos`

solver, you also need to set the
`diagonalization`

flag.

For the `lanczos`

scheme, you can specify whether you can do use the average
Gaussian quadrature, which typically speeds up convergence with respect
to the number of iterations by a factor of 2. The default is to use it.

`lanczos_gauss_quadrature`

`no_lanczos_gauss_quadrature`

`number_eigenvalues`

Compute only the lowest neig eigenvalues/eigenvectors.
The default is to calculate all n_v n_c n_k of them.
Only for `diagonalization`

, not for `haydock`

.

`number_iterations [integer]`

If you are not performing full diagonalization (eg: if using `haydock`

or
`diagonalization`

+ `lanczos`

), you must specify the number of
iterations.

`eqp_corrections`

Set this to use eigenvalues in `eqp.dat`

and `eqp_q.dat`

If not set, these files will be ignored.

`eqp_co_corrections`

Set this to use eigenvalues in `eqp_co.dat`

These quasiparticle corrections will be interpolated to
the shifted and unshifted fine grids and written to `eqp.dat`

,
eqp_q.dat, and bandstructure.dat. If not set, this file will be ignored.

`cell_average_cutoff [float]`

Cutoff energy for averaging the Coulomb Interaction
in the Mini Brillouin Zones around the Gamma-point
without Truncation or for Cell Wire or Cell Slab Truncation.
The value is in Rydbergs, the default is `1.0d-12`

.

`polarization [array of integers]`

This is needed if you selected momentum operator above. This vector will be normalized in the code.

`read_vmtxel`

If we have already calculated the optical matrix elements, do we read them from file to save time?

`read_eps2_moments`

Read `eps2_moments`

generated during previous run. Only for `haydock`

calculations.

`read_eigenvalues`

Reduce cost of calculation if we've already computed
the eigensolutions. This reads the eigenvalues and
transition matrix elements from the file `eigenvalues.dat`

.

`noeh_only`

If we only want the non-interacting spectra (i.e. no electron-
hole interaction, RPA). Only `WFN_fi`

and `WFNq_fi`

are needed as inputs.
With the `read_eigenvalues`

flag, both `absorption_eh.dat`

and
`absorption_noeh.dat`

will be created.

`read_dtmat`

If already calculated, read the interpolation matrices `dvv`

and `dcc`

from file `dtmat`

.

`delta_frequency [float]`

Frequency step, in eV, for generating absorption spectrum.

`read_epsdiag`

This specifies what kind of epsilon we read. Default is to read epsmat and eps0mat, but if this flag is present we read file epsdiag.dat instead. epsdiag.dat contains only the diagonal part of eps(0)mat which is all that is needed by absorption. It is always created by an absorption run for use in future runs, to save time reading.

`write_eigenvectors`

Determines output of eigenvectors (eigenvectors).

- eig = 0 : do not write eigenvectors (default)
- eig < 0 : write all eigenvectors
- eig > 0 : write eig eigenvectors

`write_vcoul`

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

`skip_interpolation`

Warning

Do not use this if you have a different fine grid from the coarse grid, as for velocity operator.

`average_w`

Average the head of W in addition to the head of V using a model for the inverse dielectric matrix. This is done for insulators for all truncation schemes. The W average is limited only to the first minibz even if cell_average_cutoff != 0. Currently it is always done regardless whether average_w is included in the input file or not.

`kernel_scaling [float]`

Multiply kernel by arbitrary factor. Default is 1.0 of course.

`extended_kernel`

Use the same flag as in `kernel.inp`

.

`full_bse`

Solve the full Bethe-Salpeter equation without using the Tamm-Dancoff
approximation. This flag automatically turns on the `extended_kernel`

flag.

`zero_coupling_block`

Zero the coupling (H_B) block in the full Bethe-Salpeter equation. This is useful to test the diagonalization routine.

`unrestricted_transformation`

Perform the coarse-fine WFN transformation and eqp interpolation without restricting the character of the coefficients.

## Details

Without this flag, we would otherwise restrict the character of the states when computing transformation coefficients. For instance, in the default approach, we approximate a valence state v in the fine grid as $$ |v\rangle \approx \sum_{v'} d_{vv'} |v'\rangle, $$ where |v'\rangle is a valence state in the coarse grid for a fixed k-point.

With the `unrestricted_transformation`

flag, we instead approximate a
valence state in the fine grid as
$$
|v\rangle \approx \sum_n d_{vn'} |n'\rangle,
$$
where n' now runs over all valence *and* conduction states in the coarse
grid for a fixed k-point.

The `unrestricted_transformation`

flag is a very good idea for metallic
systems, but it does not work so well for semiconductors because of the
inherit approximation used in the interpolation. Notes:

- If
`extended_kernel`

is not set, we restrict the d_{vn'} and d_{cn'} coefficients to the subspaces of d_{cc'} and d_{vv'} after the eqp interpolation. - If
`extended_kernel`

is set, this flag is automatically turned on, and we keep the unrestricted d_{vn'} and d_{cn'} coefficients for the kernel interpolation. - See also:
`zero_unrestricted_contribution`

Warning

Don't use the `unrestricted_transformation`

flag with semiconducting
systems!

`zero_unrestricted_contribution`

Zero out all d_{vc'}/d_{cv'} coefficients. Use this flag together with
extended_kernel to reproduce the result of a restricted kernel calculation.
See also: `unrestricted_transformation`

.

`zero_q0_element`

The averaging scheme performed for the q=0 term of the BSE Hamiltonian yields exciton binding energies that do not converge variationally. One can fix this issue by zeroing out the q=0 term of the interaction, either before or after the interpolation of the kernel of the BSE. See Figure 7 of PRB 93, 235435 (2016).

Possible values for `n`

are:

- 0: don't zero the W(q=0) term (default).
- 1: zero W(q=0) term after interpolation.
- 2: zero W(q=0) before interpolation (not recommended)

`subsample_line`

This option turns on the clustered sampled interpolation (CSI) method.

For 1D and 2D systems, kernel interpolation may not work well if the coarse
k-grid is too coarse to capture fast variations in screening at small q.
The `subsample_line`

flag lets you replace the interpolated matrix elements with
matrix elements from a different (subsampled) `bsemat`

file for |q| < cutoff.
The subsampled bsemat can be calculated on a small patch around each coarse point,
thus allowing for very fine effective k-point sampling.

When this flag is present, during kernel interpolation, a fine k-point,
|k_\mathrm{fi}\rangle, is expanded over the closest coarse point,
|k_\mathrm{co}\rangle, while |k_\mathrm{fi}'\rangle is expanded over
over a k-point, |k_\mathrm{sub}\rangle, in the subsampled `bsemat`

file
such that |k_\mathrm{co}-k_\mathrm{sub}| is as close as possible
to |k_\mathrm{fi}-k_\mathrm{fi}'|. The current implementation assumes
that the BSE kernel is isotropic in the Voronoi cell around each coarse point.
Use of this flag requires a `subsample.inp`

file in the same directory.
The cutoff is in a.u.