# Van der Waals functionals

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

##### Copyright (C) 2016-2017 ABINIT group (YPouillon, BVanTroeye)

Mentioned in help_features#2.2.

### Table of content:

- 1. Introduction.
- 2. Related input variables.
- 3. Selected input files.
- 4. References.

### 1. 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 [Dion2004], a self-consistent approach, and an adaptation of the strategy followed by G.Roman-Perez et al. [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 [Grimme2006], DFT-D3 [Grimme2010] and DFT-D3(BJ) [Grimme2010a]. 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 [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 [Silvestrelli2008],[Silvestrelli2009] vdW-WF2 [Ambrosetti2012] and vdW-QHO-WF [Silvestrelli2013]. A full description of the implementation of vdW-WF1 is reported in [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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### 2. Related input variables.

Compulsory input variables:

... vdw_tol [Van Der Waals TOLerance]
... vdw_xc [Van Der Waals eXchange-Correlation functional]

Basic input variables:

... vdw_nfrag [Van Der Waals Number of interacting FRAGments]
... vdw_supercell [Van Der Waals correction from Wannier functions in SUPERCELL]
... vdw_tol_3bt [Van Der Waals TOLerance for 3-Body Term]
... vdw_typfrag [Van Der Waals TYPe of FRAGment]

Useful input variables:

... irdvdw [Integer that governs the ReaDing of _VDW files]
... prtwf [PRinT the WaveFunction]

Input variables for experts:

... vdw_df_acutmin [vdW-DF MINimum Angular CUT-off]
... vdw_df_aratio [vdW-DF Angle RATIO between the highest and lowest angles.]
... vdw_df_damax [vdW-DF Delta for Angles, MAXimum ]
... vdw_df_damin [vdW-DF Delta for Angles, MINimum]
... vdw_df_dcut [vdW-DF D-mesh CUT-off]
... vdw_df_dratio [vdW-DF, between the highest and lowest D, RATIO.]
... vdw_df_dsoft [vdW-DF Distance for SOFTening.]
... vdw_df_gcut [vdW-DF G-space CUT-off]
... vdw_df_ndpts [vdW-DF Number of D-mesh PoinTS]
... vdw_df_ngpts [vdW-DF Number of G-mesh PoinTS]
... vdw_df_nqpts [vdW-DF Number of Q-mesh PoinTS]
... vdw_df_nrpts [vdW-DF Number of R-PoinTS]
... vdw_df_nsmooth [vdW-DF Number of SMOOTHening iterations]
... vdw_df_phisoft [vdW-DF PHI value SOFTening.]
... vdw_df_qcut [vdW-DF Q-mesh CUT-off]
... vdw_df_qratio [vdW-DF, between highest and lowest Q, RATIO .]
... vdw_df_rcut [vdW-DF Real-space CUT-off]
... vdw_df_rsoft [vdW-DF radius SOFTening.]
... vdw_df_threshold [vdW-DF energy calculation THRESHOLD]
... vdw_df_tolerance [vdW-DF global TOLERANCE.]
... vdw_df_tweaks [vdW-DF TWEAKS.]
... vdw_df_zab [vdW-DF ZAB parameter]
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### 3. Selected input files.

WARNING : as of ABINITv8.6.x, the list of input files provided in the specific section of the topics Web pages is still to be reviewed/tuned. In some cases, it will be adequate, and in other cases, it might be incomplete, or perhaps even useless.
The user can find some related example input files in the ABINIT package in the directory /tests, or on the Web:

tests/wannier90/Input: t11.in t12.in t13.in

tests/vdwxc/Input: t10.in

tests/v7/Input: t97.in t98.in t99.in
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### 4. References.

[Ambrosetti2012] A. Ambrosetti and P. L. Silvestrelli, "van der Waals interactions in density functional theory using Wannier functions: Improved C6 and C3 coefficients by a different approach", Phys. Rev. B 85, 073101 (2012).
[Dion2004] M. Dion, H. Rydberg, E. Schröder, D. C. Langreth and B. I. Lundqvist, "Van der Waals Density Functional for General Geometries", Phys. Rev. Lett. 92, 246401 (2004).
DOI: 10.1103/PhysRevLett.92.246401.
[Espejo2012] C. Espejo, T. Rangel, Y. Pouillon, A. H. Romero and X. Gonze, "Wannier functions approach to van der Waals} interactions in ABINIT", Comp. Phys. Comm. 183, 480 (2012).
[Grimme2006] S. Grimme, "Semiempirical GGA-Type Density Functional Constructed with a Long-Range Dispersion Correction", J. Comput. Chem. 27, 1787 (2006).
[Grimme2010] S. Grimme, J. Anthony, S. Ehrlich and H. Krieg, "A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D)} for the 94 elements H-Pu", J. Chem. Phys. 132, 154104 (2010).
[Grimme2010a] S. Grimme, S. Ehrlich and L. Goerigk, "Effect of the Damping Function in Dispersion Corrected Density Functional Theory", J. Comput. Chem. 32, 1456-1465 (2011).
[Romanperez2009] G. Román-Pérez and J.M. Soler, "Efficient Implementation of a Van der Waals Density Functional: Application to Double-Wall Carbon Nanotubes", Phys. Rev. Lett. 103, 096102 (2009).
DOI: 10.1103/PhysRevLett.103.096102.
[Silvestrelli2008] P. L. Silvestrelli, "van der Waals Interactions in DFT Made Easy by Wannier Functions", Phys. Rev. Lett. 100, 053002 (2008).
[Silvestrelli2009] P. L. Silvestrelli, "van der Waals Interactions in Density Functional Theory Using Wannier Functions", J. Phys. Chem. A 113, 5224 (2009).
[Silvestrelli2013] P. L. Silvestrelli, "van der Waals interactions in density functional theory by combining the quantum harmonic oscillator-model with localized Wannier functions", J. Chem. Phys. 139, 054106 (2013).

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