"""Contains all Hartree functionality and solvers."""
from collections.abc import Callable
import numpy as np
import iDEA.system
import iDEA.state
import iDEA.observables
import iDEA.methods.non_interacting
name = "hartree"
kinetic_energy_operator = iDEA.methods.non_interacting.kinetic_energy_operator
external_potential_operator = iDEA.methods.non_interacting.external_potential_operator
[docs]def hartree_potential_operator(s: iDEA.system.System, n: np.ndarray) -> np.ndarray:
r"""
Compute the Hartree potential operator.
| Args:
| s: iDEA.system.System, System object.
| n: np.ndarray, Charge density.
| Returns:
| Vh: np.ndarray, Hartree potential energy operator.
"""
v_h = iDEA.observables.hartree_potential(s, n)
Vh = np.diag(v_h)
return Vh
[docs]def hamiltonian(
s: iDEA.system.System,
up_n: np.ndarray,
down_n: np.ndarray,
up_p: np.ndarray,
down_p: np.ndarray,
K: np.ndarray = None,
Vext: np.ndarray = None,
) -> np.ndarray:
r"""
Compute the Hamiltonian from the kinetic and potential terms.
| Args:
| s: iDEA.system.System, System object.
| up_n: np.ndarray, Charge density of up electrons.
| down_n: np.ndarray, Charge density of down electrons.
| up_p: np.ndarray, Charge density matrix of up electrons.
| down_p: np.ndarray, Charge density matrix of down electrons.
| K: np.ndarray, Single-particle kinetic energy operator [If None this will be computed from s]. (default = None)
| Vext: np.ndarray, Potential energy operator [If None this will be computed from s]. (default = None)
| Returns:
| H: np.ndarray, Hamiltonian, up Hamiltonian, down Hamiltonian.
"""
if K is None:
K = kinetic_energy_operator(s)
if Vext is None:
Vext = external_potential_operator(s)
Vh = hartree_potential_operator(s, up_n + down_n)
H = K + Vext + Vh
return H, H, H
[docs]def total_energy(s: iDEA.system.System, state: iDEA.state.SingleBodyState) -> float:
r"""
Compute the total energy.
| Args:
| s: iDEA.system.System, System object.
| state: iDEA.state.SingleBodyState, State. (default = None)
| Returns:
| E: float, Total energy.
"""
E = iDEA.observables.single_particle_energy(s, state)
n = iDEA.observables.density(s, state)
v_h = iDEA.observables.hartree_potential(s, n)
E -= 0.5 * iDEA.observables.hartree_energy(s, n, v_h)
return E
[docs]def solve(
s: iDEA.system.System,
k: int = 0,
restricted: bool = False,
mixing: float = 0.5,
tol: float = 1e-10,
initial: tuple = None,
silent: bool = False,
) -> iDEA.state.SingleBodyState:
r"""
Solves the Schrodinger equation for the given system.
| Args:
| s: iDEA.system.System, System object.
| k: int, Energy state to solve for. (default = 0, the ground-state)
| restricted: bool, Is the calculation restricted (r) on unrestricted (u). (default=False)
| mixing: float, Mixing parameter. (default = 0.5)
| tol: float, Tollerance of convergence. (default = 1e-10)
| initial: tuple. Tuple of initial values used to begin the self-consistency (n, up_n, down_n, p, up_p, down_p). (default = None)
| silent: bool, Set to true to prevent printing. (default = False)
| Returns:
| state: iDEA.state.SingleBodyState, Solved state.
"""
return iDEA.methods.non_interacting.solve(
s, hamiltonian, k, restricted, mixing, tol, initial, name, silent
)
[docs]def propagate(
s: iDEA.system.System,
state: iDEA.state.SingleBodyState,
v_ptrb: np.ndarray,
t: np.ndarray,
hamiltonian_function: Callable = None,
restricted: bool = False,
) -> iDEA.state.SingleBodyEvolution:
r"""
Propagate a set of orbitals forward in time due to a dynamic local pertubation.
| Args:
| s: iDEA.system.System, System object.
| state: iDEA.state.SingleBodyState, State to be propigated.
| v_ptrb: np.ndarray, Local perturbing potential on the grid of t and x values, indexed as v_ptrb[time,space].
| t: np.ndarray, Grid of time values.
| hamiltonian_function: Callable, Hamiltonian function [If None this will be the non_interacting function]. (default = None)
| restricted: bool, Is the calculation restricted (r) on unrestricted (u). (default=False)
| Returns:
| evolution: iDEA.state.SingleBodyEvolution, Solved time-dependent evolution.
"""
return iDEA.methods.non_interacting.propagate(
s, state, v_ptrb, t, hamiltonian, restricted, name
)