This page gives hints on how to perform calculation with constrained DFT (atomic charge, atomic magnetic moments) with the ABINIT package.
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. [Kaduk2012] or [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 [Kaduk2012], initially reported in [Wu2005], implements a double-loop cycle, which is avoided in the present implementation. It is also an improvement on the algorithm presented in [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 [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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