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SOC Matrix Element in DFT
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SOC in DFT
We start from this formula of SOC expression in DFT: \(H_{SOC}=\sum_i\xi_i(r)\vec{L}_i\cdot\vec{S}_i\)
notes on Large Deviation Principle
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Large Deviation Principle
Definition:
The large deviation principle defines a rate function $I(\mathbf{x})$ that: \(\lim_{n\to\infty}-\frac{1}{n}\ln p(\mathbf{x})=I(\mathbf{x})\)
notes on Wannier Tight-Binding Method
1 minute read
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The Wannier Function is the Fourier transform of the bloch functions. Since bloch function have a gauge freedom, that one can choose a phase function that is periodic in K space and won’t change the bloch function’s functionality, so the wanneir function can be formed in varies ways.
notes on Density Functional Theory (DFT)
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About local and non-local functional: https://physics.stackexchange.com/questions/121816/local-versus-non-local-functionals variation of functionals: Mathematical Physics p.1051 deduction from many body electronic potential to hatree potential and exchange energy. https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Advanced_Theoretical_Chemistry_(Simons)/06%3A_Electronic_Structure/6.03%3A_The_Hartree-Fock_Approximation