Voronoi
- class rhodent.voronoi.VoronoiWeights(comm=None, log=None)[source]
Abstract base class for Voronoi weights in Kohn-Sham basis.
- property root: bool
Whether this rank is the root rank.
- abstract property atom_projections: Sequence[list[int] | ndarray[tuple[int, ...], dtype[float64]]]
Atom projections.
- abstract property nn: int
Number of bands.
- property nproj: int
Number of projections.
- property comm: gpaw.mpi.Communicator
MPI Communicator.
- abstract property saved_fields: dict[str, Any]
Saved data fields associated with the object.
If this object is read from a ULM file there might be some extra data in that file. Return that data, or an empty dict if there is none.
- class rhodent.voronoi.VoronoiWeightCalculator(voronoi_lcao)[source]
Calculate Voronoi weights in the basis of ground state Kohn-Sham orbitals.
For each atomic projection, calculates
\[W_{nn'} = \left<\psi_n | \hat{w} | \psi_{n'}\right> = \left<\tilde{\psi}_n | \hat{w} | \tilde{\psi}_{n'}\right> + \sum_{aij} \left<\tilde{\psi}_n | \tilde{p}_i^a\right> \Delta S_{ij}^a \left<\tilde{p}_i^a | \tilde{\psi}_{n'}\right>\]where the operator \(\hat{w} = w(\vec{r})\) is 1 in the Voronoi region of atoms and 0 outside. The sum over atoms is restricted to atoms in the region \(w(\vec{r}) = 1\).
The PAW projectors
\[P_{ni}^a = \left<\tilde{p}_i^a | \tilde{\psi}_n \right>\]and overlap matrix
\[\Delta S_{ij}^a = \left<\phi_i^a|\phi_j^a\right> - \left<\tilde{\phi}_i^a|\tilde{\phi}_j^a\right>\]are obtained from the GPAW calculator and the smooth weight matrix is obtained by a basis change of the smooth LCAO weights
\[\left<\tilde{\psi}_n | \hat{w} | \tilde{\psi}_{n'}\right> = \sum_{\mu\nu} C_{n\mu} C_{n'\nu} \left<\tilde{\phi}_\mu | \hat{w} | \tilde{\phi}_{\nu}\right>.\]- Parameters:
voronoi_lcao (
VoronoiLCAOWeights) – Object that calculates or loads the LCAO weights from file.
- property atom_projections: Sequence[list[int] | ndarray[tuple[int, ...], dtype[float64]]]
Atom projections.
- property nn: int
Number of bands.
- property comm: gpaw.mpi.Communicator
MPI Communicator.
- property saved_fields: dict[str, Any]
Saved data fields associated with the object.
If this object is read from a ULM file there might be some extra data in that file. Return that data, or an empty dict if there is none.
- calculate_and_write(out_fname, write_extra={})[source]
Calculate the Voronoi weights in the Kohn-Sham basis and write to file.
The weights are saved in a numpy archive if the file extension is
.npzor in a ULM file if the file extension is.ulm.- Parameters:
out_fname (
str) – File name of the resulting data file.write_extra (
dict[str,Any]) – Dictionary of additional data written to the file.
- classmethod from_gpw(atom_projections, gpw_file, voronoi_grid=None, comm=None)[source]
Set up calculation from GPAW file.
- Parameters:
atom_projections (AtomProjectionsType) – List of atom groups. Each atom group is a list of integers (of any length).
gpw_file (str) – Filename of GPAW ground state file.
voronoi_grid (VoronoiGrid | None | str) – Voronoi grid, or
Noneto calculate it, or a filename to read it from file.comm (Communicator | None) – Communicator.
- Return type:
VoronoiWeightCalculator
- classmethod from_lcao_file(voronoi_lcao_file, comm=None)[source]
Set up calculation from file of already computed weights in LCAO basis.
- Parameters:
voronoi_lcao_file (str) – Filename of file with Voronoi weights in LCAO basis.
comm (Communicator | None) – Communicator.
- Return type:
VoronoiWeightCalculator
- class rhodent.voronoi.VoronoiReader(ulm_fname, comm=None)[source]
Read Voronoi weights from ulm file.
- Parameters:
ulm_fname (str) – Filename.
comm (Communicator | None) – GPAW MPI communicator object. Defaults to world.
- property atom_projections: Sequence[list[int] | ndarray[tuple[int, ...], dtype[float64]]]
Atom projections.
- property nn: int
Number of bands.
- property saved_fields: dict[str, Any]
Saved data fields associated with the object
If this object is read from a ULM file there might be some extra data in that file. Return that data, or an empty dict if there is none.
- class rhodent.voronoi.EmptyVoronoiWeights(comm=None, log=None)[source]
Object representing a lack of weights.
- property atom_projections
Atom projections.
- property nn
Number of bands.
- property saved_fields
Saved data fields associated with the object.
If this object is read from a ULM file there might be some extra data in that file. Return that data, or an empty dict if there is none.
- class rhodent.voronoi.VoronoiLCAOWeights[source]
Abstract base class for Voronoi weights in LCAO basis.
- abstract property nn: int
Number of bands.
- abstract property nM: int
Number of basis functions.
- property nproj: int
Number of atomic projections
- property atom_projections: Sequence[list[int] | ndarray[tuple[int, ...], dtype[float64]]]
List of atom projections.
- property calc: GPAWCalculator | None
GPAW calculator instance.
- property comm: gpaw.mpi.Communicator
MPI Communicator.
- property root: bool
Whether this rank is the root rank.
- property C_nM: ndarray[tuple[int, ...], dtype[float64]] | None
LCAO wave function coefficients on root rank,
Noneon other ranks.
- property P_ani: dict[int, ndarray[tuple[int, ...], dtype[float64]]] | None
PAW projectors \(P_{ni}^a\) on the root rank,
Noneon other ranks.\[P_{ni}^a = \left<\tilde{p}_i^a | \tilde{\psi}_n \right>\]
- property dS_aii: dict[int, ndarray[tuple[int, ...], dtype[float64]]] | None
Overlap matrix PAW corrections \(\Delta S_{ij}^a\) on the root rank,
Noneon other ranks.\[\Delta S_{ij}^a = \left<\phi_i^a|\phi_j^a\right> - \left<\tilde{\phi}_i^a|\tilde{\phi}_j^a\right>\]
- abstract property saved_fields: dict[str, Any]
Saved data fields associated with the object.
If this object is read from a ULM file there might be some extra data in that file. Return that data, or an empty dict if there is none.
- class rhodent.voronoi.VoronoiLCAOReader(ulm_fname, comm=None)[source]
Read Voronoi weights in the LCAO basis from ULM file.
- Parameters:
ulm_fname (
str) – Filename.comm – GPAW MPI communicator object. Defaults to world.
- property nn: int
Number of bands.
- property nM: int
Number of basis functions.
- property saved_fields: dict[str, Any]
Saved data fields associated with the object.
If this object is read from a ULM file there might be some extra data in that file. Return that data, or an empty dict if there is none.
- class rhodent.voronoi.VoronoiLCAOWeightCalculator(atom_projections, gpw_file, voronoi_grid=None, domain=-1, comm=None)[source]
Calculate Voronoi weights in LCAO basis.
For each atomic projection, calculates
\[\tilde{v}_{\mu\nu} = \left<\tilde{\phi}_{\mu} | \hat{w} | \tilde{\phi}_{\nu}\right> = \int w(\vec{r}) \tilde{\phi}_{\mu}^*(\vec{r}) \tilde{\phi}_{\nu}(\vec{r}) d\vec{r}\]where the operator \(\hat{w} = w(\vec{r})\) is 1 in the Voronoi region of the atomic projections and 0 outside, and \(\tilde{\phi}_{\nu}\) are the smooth LCAO basis functions.
- Parameters:
atom_projections (AtomProjectionsType) – List of atom groups. Each atom group is a list of integers (of any length).
gpw_file (str) – Filename of GPAW ground state file.
voronoi_grid (VoronoiGrid | None | str) – Voronoi grid, or
Noneto calculate it, or a filename to read it from file.domain (int) – Domain size.
comm (Communicator | None) – Communicator.
- property nn: int
Number of bands.
- property nM: int
Number of basis functions.
- property saved_fields: dict[str, Any]
Saved data fields associated with the object.
If this object is read from a ULM file there might be some extra data in that file. Return that data, or an empty dict if there is none.
- calculate_and_write(out_fname, write_extra={})[source]
Calculate the Voronoi weights in the LCAO basis and write to file.
The weights are saved in a numpy archive if the file extension is
.npzor in a ULM file if the file extension is.ulm.- Parameters:
out_fname (
str) – File name of the resulting data file.write_extra (
dict[str,Any]) – Dictionary of additional data written to the file.
- class rhodent.voronoi.VoronoiGrid[source]