Calculators

class rhodent.calculators.DensityCalculator(gpw_file, density_matrices, filter_occ=[], filter_unocc=[])

Obtain induced density from frequency or pulse response density matrices.

The induced density (i.e. the density minus the ground state density) is to first order given by

\[\delta n(\boldsymbol{r}) = -2 \sum_{ia}^\text{eh} n_{ia}(\boldsymbol{r}) \mathrm{Re}\:\delta\rho_{ia}\]

plus PAW corrections, where \(n_{ia}(\boldsymbol{r})\) is the density of ground state Kohn-Sham pair \(ia\)

\[n_{ia}(\boldsymbol{r}) = \psi^{(0)}_i(\boldsymbol{r}) \psi^{(0)}_a(\boldsymbol{r}).\]

Parameters:

• gpw_file (str) – Filename of GPAW ground state file

• density_matrices (BaseDensityMatrices) – Object that gives the density matrix in the time or freqency domain

• filter_occ (Sequence[tuple[float, float]]) – Filters for occupied states (holes). Provide a list of tuples (low, high) to compute the density of holes with energies within the interval low-high.

• filter_unocc (Sequence[tuple[float, float]]) – Filters for unoccupied states (electrons). Provide a list of tuples (low, high) to compute the density of excited electrons with energies within the interval low-high.

property N_c: ndarray[Any, dtype[int64]]

Number of points in each Cartesian direction of the grid

property calc: gpaw.GPAW

GPAW calculator instance

property cell_cv: ndarray[Any, dtype[float64]]

Cell vectors

property gd: GridDescriptor

Real space grid

property gdshape: tuple[int, int, int]

Shape of the real space grid

get_density(rho_ia, n1, n2, fltn1=slice(None, None, None), fltn2=slice(None, None, None), u=0)

Calculate a real space density from a density matrix in the Kohn-Sham basis.

Return type:

Distributed array with the density in real space on the root rank

get_result_keys()

Get the keys that each result will contain, and dimensions thereof.

Return type:

Object representing the data that will be present in the result objects.

icalculate()

Iteratively calculate results. The results include the total induced density, and the densities of electrons and holes, optionally decomposed by filter_occ and filter_unocc.

Yields:

• Tuple (work, result) on the root rank of the calculation communicator

• work – An object representing the metadata (time, frequency or pulse) for the work done

• result – Object containg the calculation results for this time, frequency or pulse

• Yields nothing on non-root ranks of the calculation communicator.

Return type:

Generator[tuple[WorkMetadata, Result], None, None]

property occ_filters: list[slice]

List of energy filters for occupied states

property unocc_filters: list[slice]

List of energy filters for unoccupied states

property voronoi: VoronoiWeights

Voronoi weights object

class rhodent.calculators.DipoleCalculator(density_matrices, voronoi, energies_occ, energies_unocc, sigma=None)

Obtain contributions to induced dipole moment from density matrices

The induced dipole moment (i.e. the dipole moment minus the permanent component) is to first order given by

\[\delta\boldsymbol{\mu} = -2 \sum_{ia}^\text{eh} \boldsymbol{\mu}_{ia} \mathrm{Re}\:\delta\rho_{ia},\]

where \(\boldsymbol{\mu}_{ia}\) is the dipole matrix element of ground state Kohn-Sham pair \(ia\)

\[\boldsymbol{\mu}_{ia} = \int \psi^{(0)}_i(\boldsymbol{r}) \boldsymbol{r} \psi^{(0)}_a(\boldsymbol{r}) \mathrm{d}\boldsymbol{r}.\]

This class can also compute projections of the above on Voronoi weights \(w_{ia}\).

Parameters:

• density_matrices (BaseDensityMatrices) – Object that gives the density matrix in the time or freqency domain

• voronoi (VoronoiWeights | None) – Voronoi weights object

• energies_occ (list[float] | ndarray[Any, dtype[float64]]) – Energy grid (in eV) for occupied levels (hot holes)

• energies_unocc (list[float] | ndarray[Any, dtype[float64]]) – Energy grid (in eV) for unoccupied levels (hot electrons)

• sigma (Optional[float]) – Gaussian broadening width in eV

get_result_keys(yield_total_ia=False, yield_proj_ia=False, yield_total_ou=False, yield_proj_ou=False, decompose_v=True, v=None)

Get the keys that each result will contain, and dimensions thereof.

Parameters:

• yield_total_ia (bool) – The results should include the total dipole contributions in the electron-hole basis \(-2 \boldsymbol{\mu}_{ia} \mathrm{Re}\:\delta\rho_{ia}\).

• yield_proj_ia (bool) – The results should include projections of the dipole contributions in the electron-hole basis \(-2 \boldsymbol{\mu}_{ia} \mathrm{Re}\:\delta\rho_{ia} w_{ia}\).

• yield_total_ou (bool) – The results should include the total dipole contributions on the energy grid

• yield_proj_ou (bool) – The results should include projections of the dipole contributions on the energy grid

• decompose_v (bool) – The results should include the dipole moment and/or its contributions decomposed by Cartesian direction.

• v (Optional[int]) – If not None, then the results should include the v:th Cartesian component of the dipole moment and its contributions.

Return type:

ResultKeys

icalculate(yield_total_ia=False, yield_proj_ia=False, yield_total_ou=False, yield_proj_ou=False, decompose_v=True, v=None)

Iteratively calculate dipole contributions.

Parameters:

• yield_total_ia (bool) – The results should include the total dipole contributions in the electron-hole basis \(-2 \boldsymbol{\mu}_{ia} \mathrm{Re}\:\delta\rho_{ia}\).

• yield_proj_ia (bool) – The results should include projections of the dipole contributions in the electron-hole basis \(-2 \boldsymbol{\mu}_{ia} \mathrm{Re}\:\delta\rho_{ia} w_{ia}\).

• yield_total_ou (bool) – The results should include the total dipole contributions on the energy grid

• yield_proj_ou (bool) – The results should include projections of the dipole contributions on the energy grid

• decompose_v (bool) – The results should include the dipole moment and/or its contributions decomposed by Cartesian direction.

• v (Optional[int]) – If not None, then the results should include the v:th Cartesian component of the dipole moment and its contributions.

Yields:

• Tuple (work, result) on the root rank of the calculation communicator

• work – An object representing the metadata (time, frequency or pulse) for the work done

• result – Object containg the calculation results for this time, frequency or pulse

• Yields nothing on non-root ranks of the calculation communicator.

Return type:

Generator[tuple[WorkMetadata, Result], None, None]

class rhodent.calculators.EnergyCalculator(density_matrices, voronoi, energies_occ, energies_unocc, sigma=None)

Obtain energy contributions from pulse response density matrices.

The total energy can be written

\[E_\text{tot}(t) = E^{(0)}_\text{tot} + \sum_{ia}^\text{eh} E_{ia}(t) + E_\text{pulse}(t).\]

The contributions to the total energy are

\[E_{ia} = \frac{1}{2} \left[ p_{ia}\dot{q}_{ia} - q_{ia} \dot{p}_{ia} - v_{ia} q_{ia} \right],\]

the contributions to the Hartree energy are

\[E_{ia}^\text{c} = -\frac{1}{2} \left[ \omega_{ia} q_{ia}^2 - q_{ia} \dot{p}_{ia} - v_{ia} q_{ia} \right],\]

and the rate of energy change is

\[\dot{E}_{ia} = \frac{1}{2} \left[ p_{ia}\ddot{q}_{ia} - q_{ia} \ddot{p}_{ia} - v_{ia} \dot{q}_{ia} - \dot{v}_{ia} q_{ia} \right],\]

where

\[v_{ia} = \sqrt{2 f_{ia}} \int \psi^{(0)}_i(\boldsymbol{r}) \left(\boldsymbol{r}\cdot\hat{\boldsymbol{e}}_\text{pulse}\right) \psi^{(0)}_a(\boldsymbol{r}) \mathrm{d}\boldsymbol{r}.\]

Parameters:

• density_matrices (BaseDensityMatrices) – Object that gives the density matrix in the time or freqency domain

• voronoi (VoronoiWeights | None) – Voronoi weights object

• energies_occ (list[float] | ndarray[Any, dtype[float64]]) – Energy grid (in eV) for occupied levels (hot holes)

• energies_unocc (list[float] | ndarray[Any, dtype[float64]]) – Energy grid (in eV) for unoccupied levels (hot electrons)

• sigma (Optional[float]) – Gaussian broadening width in eV

get_result_keys(yield_total_E_ia=False, yield_proj_E_ia=False, yield_total_E_ou=False, yield_total_dists=False, direction=2)

Get the keys that each result will contain, and dimensions thereof.

Parameters:

• yield_total_E_ia (bool) – The results should include the contributions in the electron-hole basis to the total energy \(E_{ia}\) and Coulomb energy \(E_{ia}^\text{c}\)

• yield_proj_E_ia (bool) – The results should include the contributions in the electron-hole basis to the total energy projected on the occupied and unoccupied Voronoi weights \(E_{ia} w_i\) and \(E_{ia} w_a\).

• yield_total_E_ou (bool) – The results should include the contributions the total energy broadened on the occupied and unoccupied energy grids \(\sum_{ia} E_{ia}\delta(\varepsilon_\text{occ}-\varepsilon_{i}) \delta(\varepsilon_\text{unocc}-\varepsilon_{a})\) and

• yield_total_dists (bool) – The results should include the contributions the total energy and Coulomb energy broadened by electronic transition energy onto the unoccupied energies grid \(\sum_{ia} E_{ia} \delta(\varepsilon-\omega_{ia})\) and \(\sum_{ia} E_{ia}^\text{C} \delta(\varepsilon-\omega_{ia})\)

• direction (int | Sequence[int]) – Direction \(\hat{\boldsymbol{e}}_\text{pulse}\) of the polarization of the pulse. Integer 0, 1 or 2 to specify x, y or z, or the direction vector specified as a list of three values. Default: polarization along z.

Return type:

ResultKeys

icalculate(yield_total_E_ia=False, yield_proj_E_ia=False, yield_total_E_ou=False, yield_total_dists=False, direction=2)

Iteratively calculate energies.

Parameters:

• yield_total_E_ia (bool) – The results should include the contributions in the electron-hole basis to the total energy \(E_{ia}\) and Coulomb energy \(E_{ia}^\text{c}\)

• yield_proj_E_ia (bool) – The results should include the contributions in the electron-hole basis to the total energy projected on the occupied and unoccupied Voronoi weights \(E_{ia} w_i\) and \(E_{ia} w_a\).

• yield_total_E_ou (bool) – The results should include the contributions the total energy broadened on the occupied and unoccupied energy grids \(\sum_{ia} E_{ia}\delta(\varepsilon_\text{occ}-\varepsilon_{i}) \delta(\varepsilon_\text{unocc}-\varepsilon_{a})\) and

• yield_total_dists (bool) – The results should include the contributions the total energy and Coulomb energy broadened by electronic transition energy onto the unoccupied energies grid \(\sum_{ia} E_{ia} \delta(\varepsilon-\omega_{ia})\) and \(\sum_{ia} E_{ia}^\text{C} \delta(\varepsilon-\omega_{ia})\)

• direction (int | Sequence[int]) – Direction \(\hat{\boldsymbol{e}}_\text{pulse}\) of the polarization of the pulse. Integer 0, 1 or 2 to specify x, y or z, or the direction vector specified as a list of three values. Default: polarization along z.

Yields:

• Tuple (work, result) on the root rank of the calculation communicator

• work – An object representing the metadata (time, frequency or pulse) for the work done

• result – Object containg the calculation results for this time, frequency or pulse

• Yields nothing on non-root ranks of the calculation communicator.

Return type:

Generator[tuple[WorkMetadata, Result], None, None]

class rhodent.calculators.HotCarriersCalculator(density_matrices, voronoi, energies_occ, energies_unocc, sigma=None)

Obtain hot-carrier distributions, by calculating the second order response of the density matrix.

For weak perturbations, the response of the density matrix is to first order non-zero only in the occupied-unoccupied space, i.e. the block off-diagonals

\[\begin{split}\delta\rho = \begin{bmatrix} 0 & [\delta\rho_{ai}^*] \\ [\delta\rho_{ia}] & 0 \end{bmatrix}.\end{split}\]

The unoccupied-occupied, or electron-hole, part of the density matrix is thus linear in perturbation and can by transformed using Fourier transforms.

From the first-order response, the second order response, i.e. the hole-hole (\(\delta\rho_{ii'}\)) and electron-electron (\(\delta\rho_{aa}\)) parts can be obtained.

The hole-hole part is

\[\delta\rho_{ii'} = - \frac{1}{2} \sum_n^{f_n > f_i, f_n > f_{i'}} P_{ni} P_{ni'} + Q_{ni} Q_{ni'}\]

and the electron-hole part

\[\delta\rho_{aa'} = \frac{1}{2} \sum_n^{f_n < f_a, f_n < f_a'} P_{ia} P_{ia'} + Q_{ia} Q_{ia'}\]

where

\[\begin{split}\begin{align} P_{ia} &= \frac{2 \mathrm{Im}\:\delta\rho_{ia}}{\sqrt{2 f_{ia}}} \\ Q_{ia} &= \frac{2 \mathrm{Re}\:\delta\rho_{ia}}{\sqrt{2 f_{ia}}} , \end{align}\end{split}\]

where \(f_{ia}\) is the occupation number difference of pair \(ia\).

Parameters:

• density_matrices (BaseDensityMatrices) – Object that gives the density matrix in the time or freqency domain

• voronoi (VoronoiWeights | None) – Voronoi weights object

• energies_occ (list[float] | ndarray[Any, dtype[float64]]) – Energy grid (in eV) for occupied levels (hot holes)

• energies_unocc (list[float] | ndarray[Any, dtype[float64]]) – Energy grid (in eV) for unoccupied levels (hot electrons)

• sigma (Optional[float]) – Gaussian broadening width in eV

get_result_keys(yield_total_hcdists=False, yield_proj_hcdists=False, yield_total_P=False, yield_proj_P=False, yield_total_P_ou=False)

Get the keys that each result will contain, and dimensions thereof.

Parameters:

• yield_total_hcdists (bool) – The results should include the total hot-carrier distributions on the energy grid

• yield_proj_hcdists (bool) – The results should include the projections of the hot-carrier distributions on the energy grid

• yield_total_P (bool) – The results should include the total hot-carrier distributions in the electron-hole basis

• yield_proj_P (bool) – The results should include the projections of the hot-carrier distributions in the electron-hole basis

• yield_total_P_ou (bool) – The results should include the transition matrix broadened on the energy grid

icalculate(yield_total_hcdists=False, yield_proj_hcdists=False, yield_total_P=False, yield_proj_P=False, yield_total_P_ou=False)

Iteratively calculate second order density matrices and hot-carrier distributions.

Parameters:

• yield_total_hcdists (bool) – The results should include the total hot-carrier distributions on the energy grid

• yield_proj_hcdists (bool) – The results should include the projections of the hot-carrier distributions on the energy grid

• yield_total_P (bool) – The results should include the total hot-carrier distributions in the electron-hole basis

• yield_proj_P (bool) – The results should include the projections of the hot-carrier distributions in the electron-hole basis

• yield_total_P_ou (bool) – The results should include the transition matrix broadened on the energy grid

Yields:

• Tuple (work, result) on the root rank of the calculation communicator

• work – An object representing the metadata (time, frequency or pulse) for the work done

• result – Object containg the calculation results for this time, frequency or pulse

• Yields nothing on non-root ranks of the calculation communicator.

Return type:

Generator[tuple[WorkMetadata, Result], None, None]