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This page gives hints on how to use Van der Waals functionals with the ABINIT package.

Introduction

It is well known that long range correlations responsible of van der Waals interactions are out of reach for both LDA and GGA approximations to the exchange-correlation energy in DFT. In recent years several methods have been devised to include such interactions, which can be grouped into two strategies, namely ad hoc methods and self-consistent approaches. Currently ABINIT can perform calculations based on either the DFT-D methods or the vdW- WF methods, as described later, both belonging to the first group.

A fully customizable implementation of the vdW-DF method [[cite:Dion2004]], a self-consistent approach, and an adaptation of the strategy followed by G.Roman-Perez et al. [[cite:Romanperez2009]] to the case of ABINIT are under development. It will offer around 25 ajustable parameters and be delivered with graphical tools to help users assess the quality of their kernels. It does not only aim at performing production calculations with vdW-DF, but also at helping researchers who develop new density functionals optimised for systems requiring van-der-Waals interactions.

The DFT-D methods have been implemented inside ABINIT, namely DFT-D2 [[cite:Grimme2006]], DFT-D3 [[cite:Grimme2010]] and DFT-D3(BJ) [[cite:Grimme2011]]. In these cases, pair-wise terms (and 3-body corrections for DFT-D3 and DFT-D3(BJ)) are added to the DFT energy, which are independent of the electronic density, in order to mimic the vdW interactions. The implementation includes the contributions of these methods to forces and stresses, in view of geometry optimization, as well as to first-order response functions like dynamical matrices, clamped elastic constants and internal strain coupling parameters.

To activate DFT-D dispersion correction, two keywords are in use: [[vdw_xc]] = 5/6/7 to choose between DFT-D2, DFT-D3 and DFT-D3(BJ), and [[vdw_tol]], to control the inclusion of largely distant pairs (those giving a contribution below [[vdw_tol]] are ignored). It is also possible to include 3-body corrections [[cite:Grimme2010]] (for ground-state only) with the keyword [[vdw_tol_3bt]], which also controls the tolerance over this term.

Methods based on maximally localized Wannier functions (MLWFs) to calculate vdW energy corrections have also been implemented in ABINIT. In this case the pair-wise terms come from contributions of pairs of MLWFs rather than from atoms. Among the implemented methods in ABINIT it is found vdW-WF1 [[cite:Silvestrelli2008]], [[cite:Silvestrelli2009]] vdW-WF2 [[cite:Ambrosetti2012]] and vdW-QHO-WF [[cite:Silvestrelli2013]]. A full description of the implementation of vdW-WF1 is reported in [[cite:Espejo2012]].

Selection of one of these 3 methods is achieved by using [[vdw_xc]]=10/11/14 respectivelly. Since vdW-WF1 and vdW-WF2 methods are approximations for the dispersion energy of non overlapping electronic densities, it is necessary to define the interacting fragments of the system whose dispersion energy is going to be calculated. The latter is achieved by using the input variables [[vdw_nfrag]] and [[vdw_typfrag]] to define the number of interacting fragments in the unit cell and to assign each atom to a fragment. A given MLWF belongs to the same fragment as its closer atom. The need for defining the interacting fragments is overridden in the vdW-QHO-WF, for which these input variables are not used. When dealing with periodic systems the input variable [[vdw_supercell]] controls the number of neighbor unit cells that will be included in the calculation. Each one of the 3 components of [[vdw_supercell]] indicates the maximum number of cells along both positive or negative directions of the corresponding primitive vector. This is useful for studying the spacial convergency of the vdW energy. It should be noticed that the user must set the variables associated to the calculation of MLWFs and that the resulting vdW energies strongly depend on the obtained Wannier functions.

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Selected Input Files

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