3.7.5. horton.meanfield.gridgroup
– Container for observables involving numerical integration¶

class
horton.meanfield.gridgroup.
GridGroup
(obasis, grid, grid_terms, label=’grid_group’, density_cutoff=1e09)¶ Bases:
horton.meanfield.observable.Observable
Initialize a GridGroup instance.
Parameters:  obasis (GOBasis) – The orbital basis.
 grid (IntGrid) – A numerical integration grid. (must have
points
attribute andintegrate
method.)  grid_terms (list of GridObservable instances.) – The contributions to the effective Hamiltonian.
 label (str) – A label for the group.
 density_cutoff (float) – Whenever the density on a grid point falls below this threshold, all data for that grid point is set to zero. This is mainly relevant for functionals that use derivatives of the density or the orbitals, i.e. GGA and MGGA functionals.

__init__
(obasis, grid, grid_terms, label=’grid_group’, density_cutoff=1e09)¶ Initialize a GridGroup instance.
Parameters:  obasis (GOBasis) – The orbital basis.
 grid (IntGrid) – A numerical integration grid. (must have
points
attribute andintegrate
method.)  grid_terms (list of GridObservable instances.) – The contributions to the effective Hamiltonian.
 label (str) – A label for the group.
 density_cutoff (float) – Whenever the density on a grid point falls below this threshold, all data for that grid point is set to zero. This is mainly relevant for functionals that use derivatives of the density or the orbitals, i.e. GGA and MGGA functionals.

add_dot_hessian
(cache, *outputs)¶ Add contribution to the dot product of the Hessian with the trial delta DM.
The Hessian in this method is the second derivative of the observable towards the matrix elements of the density matrix or matrices. The
dms
anddelta dms
are stored in the cache.Parameters:  cache – A cache object used to store intermediate results that can be reused or inspected later. All results specific for the detla_dm are stored with the tag ‘d’ in the cache object.
 output2, .. (output1,) – Output objects, to which contributions from the dot product of the Hessian with the delta density matrices is added.

add_fock
(cache, *focks)¶ Add contributions to the Fock matrix.
This method basically dispatches the work to all
GridObservable
instances inself.grid_terms
.Parameters:  cache (Cache) – Used to store intermediate results.
 focks (list of TwoIndex) – A list of Fock matrices.

compute_energy
(cache)¶ Compute the sum of the expectation values.
This method basically dispatches the work to all
GridObservable
instances inself.grid_terms
.Parameters: cache (Cache) – Used to store intermediate results.

df_level
¶ The densityfunctional level of this grid group.
Returns: df_level – This can be any of the following: DF_LEVEL_LDA
: only LDA functionals are used.DF_LEVEL_GGA
: GGA (and LDA) functionals are used.DF_LEVEL_MGGA
: MGGA (and LDA and/or GGA) functionals are used.
Return type: int

class
horton.meanfield.gridgroup.
RGridGroup
(obasis, grid, grid_terms, label=’grid_group’, density_cutoff=1e09)¶ Bases:
horton.meanfield.gridgroup.GridGroup
Initialize a GridGroup instance.
Parameters:  obasis (GOBasis) – The orbital basis.
 grid (IntGrid) – A numerical integration grid. (must have
points
attribute andintegrate
method.)  grid_terms (list of GridObservable instances.) – The contributions to the effective Hamiltonian.
 label (str) – A label for the group.
 density_cutoff (float) – Whenever the density on a grid point falls below this threshold, all data for that grid point is set to zero. This is mainly relevant for functionals that use derivatives of the density or the orbitals, i.e. GGA and MGGA functionals.

__init__
(obasis, grid, grid_terms, label=’grid_group’, density_cutoff=1e09)¶ Initialize a GridGroup instance.
Parameters:  obasis (GOBasis) – The orbital basis.
 grid (IntGrid) – A numerical integration grid. (must have
points
attribute andintegrate
method.)  grid_terms (list of GridObservable instances.) – The contributions to the effective Hamiltonian.
 label (str) – A label for the group.
 density_cutoff (float) – Whenever the density on a grid point falls below this threshold, all data for that grid point is set to zero. This is mainly relevant for functionals that use derivatives of the density or the orbitals, i.e. GGA and MGGA functionals.

add_dot_hessian
(cache, output_alpha)¶ Add contribution to the dot product of the Hessian with the trial delta DM.
The Hessian in this method is the second derivative of the observable towards the matrix elements of the density matrix or matrices. The
dms
anddelta dms
are stored in the cache.Parameters:  cache – A cache object used to store intermediate results that can be reused or inspected later. All results specific for the detla_dm are stored with the tag ‘d’ in the cache object.
 output2, .. (output1,) – Output objects, to which contributions from the dot product of the Hessian with the delta density matrices is added.

add_fock
(cache, *focks)¶ Add contributions to the Fock matrix.
This method basically dispatches the work to all
GridObservable
instances inself.grid_terms
.Parameters:  cache (Cache) – Used to store intermediate results.
 focks (list of TwoIndex) – A list of Fock matrices.

compute_energy
(cache)¶ Compute the sum of the expectation values.
This method basically dispatches the work to all
GridObservable
instances inself.grid_terms
.Parameters: cache (Cache) – Used to store intermediate results.

df_level
¶ The densityfunctional level of this grid group.
Returns: df_level – This can be any of the following: DF_LEVEL_LDA
: only LDA functionals are used.DF_LEVEL_GGA
: GGA (and LDA) functionals are used.DF_LEVEL_MGGA
: MGGA (and LDA and/or GGA) functionals are used.
Return type: int

class
horton.meanfield.gridgroup.
UGridGroup
(obasis, grid, grid_terms, label=’grid_group’, density_cutoff=1e09)¶ Bases:
horton.meanfield.gridgroup.GridGroup
Initialize a GridGroup instance.
Parameters:  obasis (GOBasis) – The orbital basis.
 grid (IntGrid) – A numerical integration grid. (must have
points
attribute andintegrate
method.)  grid_terms (list of GridObservable instances.) – The contributions to the effective Hamiltonian.
 label (str) – A label for the group.
 density_cutoff (float) – Whenever the density on a grid point falls below this threshold, all data for that grid point is set to zero. This is mainly relevant for functionals that use derivatives of the density or the orbitals, i.e. GGA and MGGA functionals.

__init__
(obasis, grid, grid_terms, label=’grid_group’, density_cutoff=1e09)¶ Initialize a GridGroup instance.
Parameters:  obasis (GOBasis) – The orbital basis.
 grid (IntGrid) – A numerical integration grid. (must have
points
attribute andintegrate
method.)  grid_terms (list of GridObservable instances.) – The contributions to the effective Hamiltonian.
 label (str) – A label for the group.
 density_cutoff (float) – Whenever the density on a grid point falls below this threshold, all data for that grid point is set to zero. This is mainly relevant for functionals that use derivatives of the density or the orbitals, i.e. GGA and MGGA functionals.

add_dot_hessian
(cache, *outputs)¶ Add contribution to the dot product of the Hessian with the trial delta DM.
The Hessian in this method is the second derivative of the observable towards the matrix elements of the density matrix or matrices. The
dms
anddelta dms
are stored in the cache.Parameters:  cache – A cache object used to store intermediate results that can be reused or inspected later. All results specific for the detla_dm are stored with the tag ‘d’ in the cache object.
 output2, .. (output1,) – Output objects, to which contributions from the dot product of the Hessian with the delta density matrices is added.

add_fock
(cache, *focks)¶ Add contributions to the Fock matrix.
This method basically dispatches the work to all
GridObservable
instances inself.grid_terms
.Parameters:  cache (Cache) – Used to store intermediate results.
 focks (list of TwoIndex) – A list of Fock matrices.

compute_energy
(cache)¶ Compute the sum of the expectation values.
This method basically dispatches the work to all
GridObservable
instances inself.grid_terms
.Parameters: cache (Cache) – Used to store intermediate results.

df_level
¶ The densityfunctional level of this grid group.
Returns: df_level – This can be any of the following: DF_LEVEL_LDA
: only LDA functionals are used.DF_LEVEL_GGA
: GGA (and LDA) functionals are used.DF_LEVEL_MGGA
: MGGA (and LDA and/or GGA) functionals are used.
Return type: int

class
horton.meanfield.gridgroup.
GridObservable
(label)¶ Bases:
object
Initialize a GridObservable.
Parameters: label (str) – A unique label for this contribution. 
__init__
(label)¶ Initialize a GridObservable.
Parameters: label (str) – A unique label for this contribution.

add_dot
(cache, grid, *args)¶ Add a dot product with the kernel to the output arguments.
Parameters:  cache (Cache) – Used to share intermediate results between the
compute
andadd_pot
methods. This cache will also contain precomputed functions evaluate on the grid. SeeRGridGroup
andUGridGroup
for more details.  grid (IntGrid) – A numerical integration grid.
 args (list of [np.ndarray, shape=(npoint, npot), dtype=float]) – The result of this method is added to these output arguments. They are a list of dot arrays. (Only one array for the alpha density in case of restricted. Two arrays, one for alpha and one for beta electrons, in case of unrestricted.) To each array dot data will be added, e.g. the dot product of the density kernel with a change in density, the dot product of the gradient kernel with a change in gradient, etc.
 cache (Cache) – Used to share intermediate results between the

add_pot
(cache, grid, *args)¶ Add the potential to the output arguments.
Parameters:  cache (Cache) – Used to share intermediate results between the
compute
andadd_pot
methods. This cache will also contain precomputed functions evaluate on the grid. SeeRGridGroup
andUGridGroup
for more details.  grid (IntGrid) – A numerical integration grid.
 args (list of [np.ndarray, shape=(npoint, npot), dtype=float]) –
A list of potential arrays. (Only one array for the alpha density in case of restricted. Two arrays, one for alpha and one for beta electrons, in case of unrestricted.) Each array contains potential data, e.g. derivatives of a density functional toward:
 column 0: the density
 columns 1,2,3: gradient (x, y, z)
 column 4: Laplacian
 column 5: kinetic energy density
Later columns may not be present if the functional does not need them. They could be present when other terms in the effective Hamiltonian need them.
 cache (Cache) – Used to share intermediate results between the

compute_energy
(cache, grid)¶ Compute the expectation value using numerical integration.
Parameters:  cache (Cache) – Used to share intermediate results between the
compute
andadd_pot
methods. This cache will also contain precomputed functions evaluate on the grid. SeeRGridGroup
andUGridGroup
for more details.  grid (IntGrid) – A numerical integration grid.
 cache (Cache) – Used to share intermediate results between the

df_level
= None¶
