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New page: ==Determining the U parameter by a linear response approach== The Hubbard U parameter can be determined self-consistently by applying first order density functional perturbation theory (i...
 
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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 density functional perturbation theory (i.e. linear response theory), following the approach of Coccoccioni and de Gironcoli (''here add reference'')
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]


  LDAU    = T              # Switch on LDA+U
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.
  LDAUTYPE = 2              # LSDA + U Dudarev's approach = type 2 in .vasp


You will need to add the U and J term for each atom type. For example to put an effective U=1 for the second type of atom, you will put LDAUU=2 and LDAUJ=1 as follow:
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]
  # Add on-site interaction for the respective atoms (same order as in POSCAR)
 
  LDAUL =  -1  2    -1      # 2 for d-orbital interactions, -1 no on-site interaction
 
  LDAUU =  0.0  2.0  0      # Define U-parameters for on-site Coulomb interaction
 
  LDAUJ =  0.0  1.0  0      # Define J-parameters for on-site Exchange interaction
 
  LDAUPRINT = 0              # 0 to ignore, 1 to print occupation matrix in OUTC
Back to [[Núria López and Group]].
Finally, this flag is used to speed up DFT+U calculation:
  LMAXMIX = 4  #DFT+U calculations may require LMAXMIX to 4 for d-electrons (or 6 for f-elements) for faster convergence to the groundstate
Back to [[Núria López and Group]] / [[Scripts_for_VASP]].

Latest revision as of 19:03, 24 August 2021

Determining the U parameter by a linear response approach[edit]

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.

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]



Back to Núria López and Group.

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