# Tag Info

16

You can calculate U in an ab initio way via linear response theory, for instance. See an example here. However, there is no guarantee that a linear response U value is empirically ideal. That is part of the reason why, in practice, many people invoke some empirical U term and hope that it holds reasonably well for their system (especially compared to U = 0 ...

16

Unfortunately, I don't believe such a resource exists. One should keep in mind that it's not just a matter of a single U value for every metal, of course. The "best" empirical U value will depend on the property of interest. Perhaps more problematic, not every metal environment is made equal. Different oxidation states, coordination environments, and overall ...

16

This is a bit late, but I would say the short answer to your direct question is: technically no, there is no "standard" reliable way, since there are several approaches to determining U self-consistently from first principles. By self-consistently I mean a first-principles U is calculated, which when applied changes the electronic structure, so a new U is ...

14

The answer is based on Chapter 1 - The DFT+U: Approaches, Accuracy, and Applications from the book Density Functional Calculations: Recent Progresses of Theory and Application For practical implementation of DFT+U, the strength of the on-site interactions is described by a couple of parameters: the on-site Coulomb term U and the site exchange term J. These ...

12

When I first read your question, I found it somewhat puzzling. I have to admit, I still do in part. Why? Well, even your link defines $J$ as a sum of matrix elements $\langle m,m'|V_{ee}|m',m\rangle$. Mathematically, each of these matrix elements is an integral involving wave functions in the system. If we know these wave functions or know how to approximate ...

3

The Hubbard Model is already manifestly SU(2) spin-rotation invariant because there are no terms that connect the $\uparrow$ and $\downarrow$ sectors (here by connect, I mean change a $\uparrow$ to a $\downarrow$ or vice versa. The full Hamiltonian in terms of fermion annihilation/creation operators is:  H = - t \sum \limits_{t,\sigma} \left( c^\dagger_{i,\...

2

I assume you mean including a Hubbard U potential within a Kohn-Sham density functional theory (DFT) calculation. The main reason why you might wish to do this is because you are studying a material for which you expect a significant self-interaction error. The self-interaction error arises because the Hartree term in the DFT energy functional is the Coulomb ...

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