mirror of https://github.com/triqs/dft_tools
Added 2 new methods to find chemical potential, refactored DC calculation with stateless function while keeping legacy code
This commit is contained in:
alberto-carta
Alexander Hampel
parent
d68d6d8974
commit
d4f3c48784
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@ -36,7 +36,85 @@ from .block_structure import BlockStructure
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from itertools import product
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from warnings import warn
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from scipy import compress
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from scipy.optimize import minimize, newton, brenth, brentq
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from scipy.optimize import minimize, newton, brenth
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def compute_DC_from_density(N_tot, U, J, N_spin = None, n_orbitals=5, method='cFLL'):
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"""
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Computes the double counting correction in terms using various methods
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Parameters
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----------
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N_tot : float
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Total density of the impurity
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N_spin : float , default = None
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Spin density, defaults to N_tot*0.5 if not specified
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U : float
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U value
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J : float
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J value
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n_orbitals : int, default = 5
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Total number of orbitals
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method : string, default = 'cFLL'
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possibilities:
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- cFLL: DC potential from Ryee for spin unpolarized DFT: (DOI: 10.1038/s41598-018-27731-4)
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- sFLL: same as above for spin polarized DFT
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- cAMF: around mean field
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- sAMF: spin polarized around mean field
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- cHeld: unpolarized Held's formula as reported in (DOI: 10.1103/PhysRevResearch.2.03308)
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- sHeld: NOT IMPLEMENTED
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Returns
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-------
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List of floats:
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- DC_val: double counting potential
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- E_val: double counting energy
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"""
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if N_spin is not None:
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N_spin2 = N_tot-N_spin
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Mag = N_spin - N_spin2
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L_orbit = (n_orbitals-1)/2
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match method:
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case 'cFLL':
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E_val = 0.5 * U * N_tot * (N_tot-1) - 0.5 * J * N_tot * (N_tot*0.5-1)
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DC_val = U * (N_tot-0.5) - J *(N_tot*0.5-0.5)
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case 'sFLL':
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assert N_spin is not None, "Spin density not given"
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E_val = 0.5 * U * N_tot * (N_tot-1) - 0.5 * J * N_tot * (N_tot*0.5-1) - 0.25 * J * Mag**2
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DC_val = U * (N_tot-0.5) - J *(N_spin-0.5)
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case 'cAMF':
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E_val = +0.5 * U * N_tot **2
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E_val -= 0.25*(U+2*L_orbit*J)/(2*L_orbit+1)*N_tot**2
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DC_val = U * N_tot - 0.5*(U+2*L_orbit*J)/(2*L_orbit+1)*N_tot
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case 'sAMF':
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assert N_spin is not None, "Spin density not given"
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E_val = 0.5 * U * N_tot **2
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E_val -= 0.25*(U+2*L_orbit*J)/(2*L_orbit+1)*N_tot**2
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E_val -= 0.25*(U+2*L_orbit*J)/(2*L_orbit+1)*Mag**2
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DC_val = U * N_tot - (U+2*L_orbit*J)/(2*L_orbit+1)*N_spin
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case 'cHeld':
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U_mean = (U + (n_orbitals-1)*(U-2*J)+(n_orbitals-1)*(U-3*J))/(2*n_orbitals-1)
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E_val = 0.5 * U_mean * N_tot * (N_tot - 1)
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DC_val = U_mean * (N_tot-0.5)
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case 'sHeld':
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raise ValueError(f"Method sHeld not yet implemented")
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case _:
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raise ValueError(f"DC type {method} not supported")
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mpi.report(f"DC potential computed using the {method} method, V_DC = {DC_val:.6f} eV")
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mpi.report(f"E_DC using the {method} method, E_DC = {E_val:.6f} eV")
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if 'Held' in method:
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mpi.report(f"Held method for {n_orbitals} orbitals, computed U_mean={U_mean:.6f} eV")
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return DC_val, E_val
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class SumkDFT(object):
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@ -1657,7 +1735,7 @@ class SumkDFT(object):
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self.dc_energ = dc_energ
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def calc_dc(self, dens_mat, orb=0, U_interact=None, J_hund=None,
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use_dc_formula=0, use_dc_value=None, transform=True):
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use_dc_formula=0, use_dc_value=None, transform=True, legacy=True):
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r"""
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Calculate and set the double counting corrections.
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@ -1727,51 +1805,73 @@ class SumkDFT(object):
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if self.SP == 1 and self.SO == 1:
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assert dim % 2 == 0
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dim //= 2
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if use_dc_value is None:
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if legacy:
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if U_interact is None and J_hund is None:
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raise ValueError("set_dc: either provide U_interact and J_hund or set use_dc_value to dc value.")
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if U_interact is None and J_hund is None:
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raise ValueError("set_dc: either provide U_interact and J_hund or set use_dc_value to dc value.")
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if use_dc_formula == 0: # FLL
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if use_dc_formula == 0: # FLL
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self.dc_energ[icrsh] = U_interact / \
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2.0 * Ncrtot * (Ncrtot - 1.0)
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self.dc_energ[icrsh] = U_interact / \
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2.0 * Ncrtot * (Ncrtot - 1.0)
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for sp in spn:
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Uav = U_interact * (Ncrtot - 0.5) - \
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J_hund * (Ncr[sp] - 0.5)
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self.dc_imp[icrsh][sp] *= Uav
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self.dc_energ[icrsh] -= J_hund / \
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len(spn) * (Ncr[sp]) * (Ncr[sp] - 1.0)
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mpi.report(
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"DC for shell %(icrsh)i and block %(sp)s = %(Uav)f" % locals())
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elif use_dc_formula == 1: # Held's formula, with U_interact the interorbital onsite interaction
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self.dc_energ[icrsh] = (U_interact + (dim - 1) * (U_interact - 2.0 * J_hund) + (
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dim - 1) * (U_interact - 3.0 * J_hund)) / (2 * dim - 1) / 2.0 * Ncrtot * (Ncrtot - 1.0)
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for sp in spn:
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Uav = (U_interact + (dim - 1) * (U_interact - 2.0 * J_hund) + (dim - 1)
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* (U_interact - 3.0 * J_hund)) / (2 * dim - 1) * (Ncrtot - 0.5)
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self.dc_imp[icrsh][sp] *= Uav
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mpi.report(
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"DC for shell %(icrsh)i and block %(sp)s = %(Uav)f" % locals())
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elif use_dc_formula == 2: # AMF
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self.dc_energ[icrsh] = 0.5 * U_interact * Ncrtot * Ncrtot
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for sp in spn:
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Uav = U_interact * \
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(Ncrtot - Ncr[sp] / dim) - \
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J_hund * (Ncr[sp] - Ncr[sp] / dim)
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self.dc_imp[icrsh][sp] *= Uav
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self.dc_energ[
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icrsh] -= (U_interact + (dim - 1) * J_hund) / dim / len(spn) * Ncr[sp] * Ncr[sp]
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mpi.report(
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"DC for shell %(icrsh)i and block %(sp)s = %(Uav)f" % locals())
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mpi.report("DC energy for shell %s = %s" %
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(icrsh, self.dc_energ[icrsh]))
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else:
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#For legacy compatibility
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match use_dc_formula:
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case 0:
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mpi.report(f"Detected {use_dc_formula=}, changing to sFLL")
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use_dc_formula = "sFLL"
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case 1:
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mpi.report(f"Detected {use_dc_formula=}, changing to cHeld")
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use_dc_formula = "cHeld"
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case 2:
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mpi.report(f"Detected {use_dc_formula=}, changing to sAMF")
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use_dc_formula = "sAMF"
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for sp in spn:
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Uav = U_interact * (Ncrtot - 0.5) - \
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J_hund * (Ncr[sp] - 0.5)
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self.dc_imp[icrsh][sp] *= Uav
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self.dc_energ[icrsh] -= J_hund / \
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len(spn) * (Ncr[sp]) * (Ncr[sp] - 1.0)
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mpi.report(
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"DC for shell %(icrsh)i and block %(sp)s = %(Uav)f" % locals())
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DC_val, E_val = compute_DC_from_density(N_tot=Ncrtot,U=U_interact, J=J_hund, n_orbitals=dim, N_spin=Ncr[sp], method=use_dc_formula)
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self.dc_imp[icrsh][sp] *= DC_val
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self.dc_energ[icrsh] -= E_val
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elif use_dc_formula == 1: # Held's formula, with U_interact the interorbital onsite interaction
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self.dc_energ[icrsh] = (U_interact + (dim - 1) * (U_interact - 2.0 * J_hund) + (
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dim - 1) * (U_interact - 3.0 * J_hund)) / (2 * dim - 1) / 2.0 * Ncrtot * (Ncrtot - 1.0)
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for sp in spn:
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Uav = (U_interact + (dim - 1) * (U_interact - 2.0 * J_hund) + (dim - 1)
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* (U_interact - 3.0 * J_hund)) / (2 * dim - 1) * (Ncrtot - 0.5)
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self.dc_imp[icrsh][sp] *= Uav
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mpi.report(
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"DC for shell %(icrsh)i and block %(sp)s = %(Uav)f" % locals())
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elif use_dc_formula == 2: # AMF
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self.dc_energ[icrsh] = 0.5 * U_interact * Ncrtot * Ncrtot
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for sp in spn:
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Uav = U_interact * \
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(Ncrtot - Ncr[sp] / dim) - \
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J_hund * (Ncr[sp] - Ncr[sp] / dim)
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self.dc_imp[icrsh][sp] *= Uav
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self.dc_energ[
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icrsh] -= (U_interact + (dim - 1) * J_hund) / dim / len(spn) * Ncr[sp] * Ncr[sp]
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mpi.report(
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"DC for shell %(icrsh)i and block %(sp)s = %(Uav)f" % locals())
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mpi.report("DC energy for shell %s = %s" %
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(icrsh, self.dc_energ[icrsh]))
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else: # use value provided for user to determine dc_energ and dc_imp
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