Voronoi

class rhodent.voronoi.EmptyVoronoiWeights

property atom_projections

Atom projections

property dtype

dtype of wave functions

property nn

Global 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.VoronoiLCAOReader(ulm_fname, comm_is_domain=False, comm=None)

Read Voronoi weights in LCAO basis from ulm file.

Parameters:

• ulm_fname (str) – filename

• broadcast_weights – If true, the array of weights is broadcasted and yielded on all ranks

• comm – GPAW MPI communicator object. Defaults to world

property C_nM

LCAO wave function coefficients. Distributed over bands.

property P_ani: ArrayDict

PAW projectors. Distributed over domains and bands.

\[P_{ni}^a = \left<\tilde{p}_i^a | \tilde{\psi}_n \right>\]

property dtype: dtype

dtype of the wave functions

property nM: int

Global number of bands

property nn: int

Global 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.VoronoiLCAOWeightCalculator(atom_projections, gpw_file, voronoi_grid_file=None, recalculate_grid=False, domain=-1, use_pblas=False, comm=None)

Loads Voronoi grid and calculates Voronoi weights from ground state file using LCAO basis function overlaps and PAW corrections.

\[W_{nn'} = \left<\psi_n|\hat{w}|\psi_{n'}\right> = \int w(\vec{r}) \psi_n^*(\vec{r}) \psi_{n'}(\vec{r}) d\vec{r}\]

where the operator \(\hat{w} = w(\vec{r})\) is 1 in the Voronoi region of the atomic projections and 0 outside.

Parameters:

• atom_projections (Sequence[Union[list[int], ndarray[Any, dtype[float64]]]]) – List of atom groups (length Ni). Each atom group is a list of integers (of any length)

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

property C_nM

LCAO wave function coefficients. Distributed over bands.

property P_ani

PAW projectors. Distributed over domains and bands.

\[P_{ni}^a = \left<\tilde{p}_i^a | \tilde{\psi}_n \right>\]

property a_G

Returns the voronoi decomposition on the coarse grid, distributed over domain_comm

If this quantity is not stored, the voronoi decomposition on the master rank is distributed

distribute_a_G()

Distribute the voronoi decomposition on the coarse grid over domain_comm

Afterwards delete the non-distributed array

property dtype: dtype

Global number of bands

property nM: int

Global number of bands

property nn: int

Global 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.VoronoiLCAOWeights

abstract property C_nM

LCAO wave function coefficients. Distributed over bands.

abstract property P_ani: ArrayDict

PAW projectors. Distributed over domains and bands.

\[P_{ni}^a = \left<\tilde{p}_i^a | \tilde{\psi}_n \right>\]

property comm: gpaw.mpi.Communicator

Communicator

property dS_aii

Overlap matrix PAW corrections. Same data on all ranks

\[\Delta S_{ij}^a= = \left<\phi_i^a|\phi_j^a\right> - \left<\tilde{\phi}_i^a|\tilde{\phi}_j^a\right>\]

property dist_C_nM

LCAO wave function coefficients. Distributed in block cyclic form.

abstract property dtype: dtype

dtype of the wave functions

property gather_P_ani: ArrayDict

PAW projectors. Gathered to band comm rank 0. None on all other band comm ranks.

abstract property nM: int

Global number of bands

abstract property nn: int

Global number of bands

property nproj: int

Number of atomic projections

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.VoronoiReader(ulm_fname, broadcast_weights=False, comm=None)

Read Voronoi weights from ulm file.

Parameters:

• ulm_fname (str) – filename

• broadcast_weights (bool) – If true, the array of weights is broadcasted and yielded on all ranks

• comm – GPAW MPI communicator object. Defaults to world

property atom_projections: Sequence[list[int] | ndarray[Any, dtype[float64]]]

Atom projections

property dtype: dtype

dtype of wave functions

property nn: int

Global 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.VoronoiWeightCalculator(voronoi_lcao_gen, use_pblas=False)

Calculates KS wave function overlaps under operator \(\hat{w}\) using LCAO basis function overlaps and PAW corrections.

\[W_{nn'} = \left<\psi_n | \hat{w} | \psi_{n'}\right> = \left<\tilde{\psi}_n | \hat{T}^\dagger \hat{w} \hat{T} | \tilde{\psi}_{n'}\right> = \left<\tilde{\psi}_n | \hat{w} | \tilde{\psi}_{n'}\right> + \sum_{aij} \left<\tilde{\psi}_n | \tilde{p}_i^a\right> \Delta S_{ij}^a \left<\tilde{p}_i^a | \tilde{\psi}_{n'}\right>\]

where the operator \(\hat{w} = w(\vec{r})\) is 1 in the Voronoi region of atoms proj_atoms and 0 outside.

The sum over atoms is restricted to atoms in the region \(w(\vec{r}) = 1\).

\(\hat{T}\) is the PAW transformation operator.

Parameters:

• voronoi_lcao_gen (VoronoiLCAOWeights) – Object that calculates or loads the LCAO weights from file

• use_pblas (bool) – Whether PBLAS/ScaLAPACK should be used (more efficient parallelization)

property atom_projections: Sequence[list[int] | ndarray[Any, dtype[float64]]]

Atom projections

calculate_weight_nn(proj_atoms, weight_MM, out=None)

Calculates weights.

Parameters:

• proj_atoms (list[int] | ndarray[Any, dtype[float64]]) – Do the Voronoi decomposition for these atoms

• weight_MM (ndarray[Any, dtype[float64]] | None) – The weights in LCAO without PAW corrections

• out (Optional[ndarray[Any, dtype[float64]]]) – If this is specified the result is written to here on rank 0

Return type:

ndarray[Any, dtype[float64]] | None

Returns:

The matrix elements \(W_{nn'}\) on root and None on other ranks

calculate_weight_nn_pblas(proj_atoms, weight_MM, out=None)

Calculates weights using PBLAS.

Parameters:

• proj_atoms (list[int] | ndarray[Any, dtype[float64]]) – Do the Voronoi decomposition for these atoms

• weight_MM (ndarray[Any, dtype[float64]] | None) –

  The weights in LCAO without PAW corrections.

  The weights should be summed to the rank 0 of the domain communicator The weights on other ranks than 0 on the band communicator are ignored (they should be identical on all ranks)

• out (Optional[ndarray[Any, dtype[float64]]]) – If this is specified the result is written to here on rank 0

Return type:

ndarray[Any, dtype[float64]] | None

Returns:

The matrix elements \(W_{nn'}\) on root and None on other ranks

property comm: gpaw.mpi.Communicator

Communicator

property dtype: dtype

dtype of wave functions

property nn: int

Global 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.VoronoiWeights

abstract property atom_projections: Sequence[list[int] | ndarray[Any, dtype[float64]]]

Atom projections

property comm: gpaw.mpi.Communicator

Communicator

abstract property dtype: dtype

dtype of wave functions

abstract property nn: int

Global number of bands

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.

rhodent.voronoi.calc_correction(correction_on_atoms, P_ani, dS_aii, Nn, out=None)

Calculate the PAW correction to KS wave function overlaps on this domain.

\[c_{nn'} = \sum_a \left<\tilde{\psi}_n | \tilde{p}_i^a\right> \Delta S_{ij}^a \left<\tilde{p}_j^a | \tilde{\psi}_{n'}\right>,\]

where the sum over atoms only includes a selection of atoms.

Parameters:

• correction_on_atoms (list[int] | ndarray[Any, dtype[float64]]) – Which atoms to loop over

• P_ani (dict[int, ndarray[Any, dtype[float64]]] | ArrayDict) – The matrix of projectors \(\left<\tilde{p}_i^a | \tilde{\psi}_{n}\right>\)

• dS_aii (dict[int, ndarray[Any, dtype[float64]]]) – \(\Delta S_{ij}^a\)

• Nn (int) – Global number of bands

• out (Optional[ndarray[Any, dtype[float64]]]) – If this is specified the result is appended to here

Return type:

ndarray[Any, dtype[float64]]

Returns:

\(c_{nn'}'\)

rhodent.voronoi.calc_vt_MM(calc, w_G)

Calculate LCAO basis function overlaps.

\[\tilde{v}_{\mu\nu} = \left<\tilde{\phi}_{\mu} | \hat{w} | \tilde{\phi}_{\nu}\right> = \int w(\vec{r}) \tilde{\phi}_{\mu}^*(\vec{r}) \tilde{\phi}_{\nu}(\vec{r}) d\vec{r}\]

Parameters:

• calc (gpaw.GPAW) – GPAW calculator object.

• w_G (ndarray[Any, dtype[float64]]) – Operator w in real space (distributed on the domain of each rank). Should be 0 or 1 in each grid point.

Return type:

ndarray[Any, dtype[float64]]

Returns:

The contribution to \(\tilde{v}_{\mu\nu}\) from this domain

rhodent.voronoi.calc_vt_nn(C_nM, vt_MM)

Calculate pseudo KS wave function overlaps from LCAO overlaps.

\[\widetilde{W}_{nn'} = \left<\tilde{\psi}_n | \hat{w} | \tilde{\psi}_{n'}\right> = \sum_{\mu\nu} C_{\mu n}^* C_{\nu n'} \left<\tilde{\phi}_{\mu} | \hat{w} | \tilde{\phi}_{\nu}\right> = \sum_{\mu\nu} C_{\mu n}^* C_{\nu n'} \tilde{v}_{\mu\nu}\]

Parameters:

• C_nM (ndarray[Any, dtype[float64]]) – The (transposed) LCAO coefficients \(C_{\mu n}\)

• vt_MM (ndarray[Any, dtype[float64]]) – The contribution to \(\tilde{v}_{\mu\nu}\) on domain

Return type:

The contribution to \(\widetilde{W}_{nn'}\) on this domain

rhodent.voronoi.calc_vt_nn_pblas(dist_C_nM, dist_vt_MM, dist_vt_nn)

See calc_vt_nn().

Parameters:

• dist_C_nM – LCAO coefficients, in block cyclic form

• dist_vt_MM – The contribution to :math:tilde{v}_{munu}` on domain, in block cyclic form

• dist_vt_nn – Buffer in block cyclic form, into which the contribution to \(\widetilde{W}_{nn}\) on this domain will be written

rhodent.voronoi.calculate_a_g(gpw_file=None, fine_grid=True, calc=None)

Calculate Voronoi grid

Parameters:

• gpw_file (str | None) – Filename of ground state file. Ignored if calc is not None

• calc (GPAWCalculator | None) – Initialized GPAW calculator

• fine_grid (bool) – True if Voronoi grid on fine grid should be calculated, False if on coarse

Return type:

Voronoi grid as nx,ny,nz array