Self-consistent U determination

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 (File:Cococcioni, De Gironcoli - 2005 - Linear response approach to the calculation of the effective interaction parameters in the LDAU method.pdf)

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.

An example:

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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 ([1])

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