# 3.9.2. horton.meanfield.builtin – Built-in energy terms¶

class horton.meanfield.builtin.RBeckeHartree(lmax, label='hartree_becke')

Bases: horton.meanfield.builtin.BeckeHartree

add_pot(cache, grid, dpot_alpha)

Add the potential to the output arguments

Arguments:

cache
A Cache instance used to share intermediate results between the compute and add_pot methods. This cache will also contain pre-computed functions evaluate on the grid. See RGridGroup and UGridGroup for more details.
grid
A numerical integration grid

Possible arguments: depending on the subclass some of these may not be applicable.

dpot_alpha
The functional derivative of the expectation value toward the density of the alpha electron density. Shape = (grid.size,)
dpot_beta
The functional derivative of the expectation value toward the density of the beta electron density. Shape = (grid.size,)
gpot_alpha
The functional derivative of the expectation value toward the gradient of the alpha electron density. Shape = (grid.size, 3)
gpot_beta
The functional derivative of the expectation value toward the gradient of the beta electron density. Shape = (grid.size, 3)
compute_energy(cache, grid)

Compute the expectation value using numerical integration

Arguments:

cache
A Cache instance used to share intermediate results between the compute and add_pot methods. This cache will also contain pre-computed functions evaluate on the grid. See RGridGroup and UGridGroup for more details.
grid
A numerical integration grid
gga = False
class horton.meanfield.builtin.UBeckeHartree(lmax, label='hartree_becke')

Bases: horton.meanfield.builtin.BeckeHartree

add_pot(cache, grid, dpot_alpha, dpot_beta)

Add the potential to the output arguments

Arguments:

cache
A Cache instance used to share intermediate results between the compute and add_pot methods. This cache will also contain pre-computed functions evaluate on the grid. See RGridGroup and UGridGroup for more details.
grid
A numerical integration grid

Possible arguments: depending on the subclass some of these may not be applicable.

dpot_alpha
The functional derivative of the expectation value toward the density of the alpha electron density. Shape = (grid.size,)
dpot_beta
The functional derivative of the expectation value toward the density of the beta electron density. Shape = (grid.size,)
gpot_alpha
The functional derivative of the expectation value toward the gradient of the alpha electron density. Shape = (grid.size, 3)
gpot_beta
The functional derivative of the expectation value toward the gradient of the beta electron density. Shape = (grid.size, 3)
compute_energy(cache, grid)

Compute the expectation value using numerical integration

Arguments:

cache
A Cache instance used to share intermediate results between the compute and add_pot methods. This cache will also contain pre-computed functions evaluate on the grid. See RGridGroup and UGridGroup for more details.
grid
A numerical integration grid
gga = False
class horton.meanfield.builtin.RDiracExchange(label='x_dirac', coeff=None)

Bases: horton.meanfield.builtin.DiracExchange

Optional arguments:

label
A label for this observable.
coeff
The coefficient Cx in front of the Dirac exchange energy. It defaults to the uniform electron gas value, i.e. $$C_x = \frac{3}{4} \left(\frac{3}{\pi}\right)^{1/3}$$.
add_pot(cache, grid, dpot_alpha)

Add the potential to the output arguments

Arguments:

cache
A Cache instance used to share intermediate results between the compute and add_pot methods. This cache will also contain pre-computed functions evaluate on the grid. See RGridGroup and UGridGroup for more details.
grid
A numerical integration grid

Possible arguments: depending on the subclass some of these may not be applicable.

dpot_alpha
The functional derivative of the expectation value toward the density of the alpha electron density. Shape = (grid.size,)
dpot_beta
The functional derivative of the expectation value toward the density of the beta electron density. Shape = (grid.size,)
gpot_alpha
The functional derivative of the expectation value toward the gradient of the alpha electron density. Shape = (grid.size, 3)
gpot_beta
The functional derivative of the expectation value toward the gradient of the beta electron density. Shape = (grid.size, 3)
compute_energy(cache, grid)

Compute the expectation value using numerical integration

Arguments:

cache
A Cache instance used to share intermediate results between the compute and add_pot methods. This cache will also contain pre-computed functions evaluate on the grid. See RGridGroup and UGridGroup for more details.
grid
A numerical integration grid
gga = False
class horton.meanfield.builtin.UDiracExchange(label='x_dirac', coeff=None)

Bases: horton.meanfield.builtin.DiracExchange

Optional arguments:

label
A label for this observable.
coeff
The coefficient Cx in front of the Dirac exchange energy. It defaults to the uniform electron gas value, i.e. $$C_x = \frac{3}{4} \left(\frac{3}{\pi}\right)^{1/3}$$.
add_pot(cache, grid, dpot_alpha, dpot_beta)

Add the potential to the output arguments

Arguments:

cache
A Cache instance used to share intermediate results between the compute and add_pot methods. This cache will also contain pre-computed functions evaluate on the grid. See RGridGroup and UGridGroup for more details.
grid
A numerical integration grid

Possible arguments: depending on the subclass some of these may not be applicable.

dpot_alpha
The functional derivative of the expectation value toward the density of the alpha electron density. Shape = (grid.size,)
dpot_beta
The functional derivative of the expectation value toward the density of the beta electron density. Shape = (grid.size,)
gpot_alpha
The functional derivative of the expectation value toward the gradient of the alpha electron density. Shape = (grid.size, 3)
gpot_beta
The functional derivative of the expectation value toward the gradient of the beta electron density. Shape = (grid.size, 3)
compute_energy(cache, grid)

Compute the expectation value using numerical integration

Arguments:

cache
A Cache instance used to share intermediate results between the compute and add_pot methods. This cache will also contain pre-computed functions evaluate on the grid. See RGridGroup and UGridGroup for more details.
grid
A numerical integration grid
gga = False