Self-consistent U determination: Difference between revisions
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==Determining the U parameter by a linear response approach== | ==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]]) | 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. | 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. | ||
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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 | 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] | ||
Revision as of 11:05, 18 April 2020
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)[1], and later modified by Kulik et al.[2]
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:
... tbd ...
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.[3]
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