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| description | authors |
|---|---|
| How to perform calculation within constrained DFT | EB and XG |
This page gives hints on how to perform calculation with constrained DFT (atomic charge, atomic magnetic moments) with the ABINIT package.
Introduction
Constrained Density Functional Theory (cDFT) imposes constraints on the charge density and magnetic moments. Usually integrals of the charge density and magnetization (real-space functions) inside spheres are constrained to user-defined values. This is described in e.g. cite:Kaduk2012 or cite:Ma2015.
The algorithm implemented in ABINIT (to be published in 2021) is a clear improvement of the algorithm reported in both papers. The algorithm in cite:Kaduk2012, initially reported in cite:Wu2005, implements a double-loop cycle, which is avoided in the present implementation. It is also an improvement on the algorithm presented in cite:Ma2015, based on a penalty function (it is NOT a Lagrange multiplier approach, unlike claimed by these authors) also implemented in ABINIT, see topic:MagMom, in that it imposes to arbitrary numerical precision the constraint, instead of an approximate one with a tunable accuracy under the control of magcon_lambda. The present algorithm is also not subject to instabilities that have been observed when magcon_lambda becomes larger and larger in the cite:Wu2005 algorithm.
ABINIT implements forces as well as stresses in cDFT. Also, derivatives of the total energy with respect to the constraint are delivered. For the charge constraint, vector magnetization constraint, magnetization length constraint and magnetization axis constraint, the derivative is determind with respect to the value of the constraint defined directly by the user, while for the magnetization direction constraint, the derivative is evaluated with respect to the change of angle.
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