mirror of https://github.com/abinit/abinit.git
36 lines
2.0 KiB
Markdown
36 lines
2.0 KiB
Markdown
---
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description: How to perform calculation within constrained DFT
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authors: EB and XG
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---
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<!--- This is the source file for this topics. Can be edited. -->
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This page gives hints on how to perform calculation with constrained DFT (atomic charge, atomic magnetic moments) with the ABINIT package.
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## Introduction
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Constrained Density Functional Theory (cDFT) imposes constraints on the charge density and magnetic moments. Usually
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integrals of the charge density and magnetization (real-space functions) inside spheres are constrained to user-defined
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values. This is described in e.g. [[cite:Kaduk2012]] or [[cite:Ma2015]].
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The algorithm implemented in ABINIT (to be published in 2021) is a clear improvement of the algorithm reported in both papers.
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The algorithm in [[cite:Kaduk2012]],
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initially reported in [[cite:Wu2005]], implements a double-loop cycle, which is avoided in the present implementation.
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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,
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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
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[[magcon_lambda]].
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The present algorithm is also not subject to instabilities that have been observed when [[magcon_lambda]] becomes larger and larger
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in the [[cite:Wu2005]] algorithm.
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ABINIT implements forces as well as stresses in cDFT. Also, derivatives of the total energy with respect to the constraint are delivered.
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For the charge constraint, vector magnetization constraint, magnetization length constraint and magnetization axis constraint, the derivative
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is determind with respect to the value of the constraint defined directly by the user, while for the magnetization direction constraint,
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the derivative is evaluated with respect to the change of angle.
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## Related Input Variables
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{{ related_variables }}
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## Selected Input Files
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{{ selected_input_files }}
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