Editing Self-consistent U determination (section)

==Determining the U parameter by a linear response approach==

The Hubbard U parameter can be determined self-consistently by applying first order perturbation theory (i.e. linear response theory), following the approach of Coccoccioni and de Gironcoli ([[Image:Cococcioni,_De_Gironcoli_-_2005_-_Linear_response_approach_to_the_calculation_of_the_effective_interaction_parameters_in_the_LDAU_method.pdf‎]])[https://journals.aps.org/prb/abstract/10.1103/PhysRevB.71.035105], and later modified by Kulik et al.[https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.97.103001]

This approach is based on a rotationally invariant scheme. The main idea is to apply a small perturbation on the occupation number of the atom i in a lattice (i is the atom to which U shall be added) and to calculate the (linear) response of the system.

One of the main drawbacks of this method is that U is dependent on the supercell size; in other words, you need to have a large supercell to avoid any spurious interaction due to periodic boundaries. One way to circumvent this is the reciprocal space formulation of DFPT.[https://journals.aps.org/prb/abstract/10.1103/PhysRevB.98.085127] 




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