Interface to DFTD3 by S. Grimme¶
Code author: Lori A. Burns
Section author: Lori A. Burns
Module: Samples
Installation¶
Binary
DFTD3 is available as a conda package for Linux and macOS (and Windows, through the Ubuntu shell).
If using the PSI4 binary, DFTD3 has already been installed alongside.
If using PSI4 built from source, and anaconda or miniconda has already been installed (instructions at Quick Installation), the dftd3 executable can be obtained through
conda install dftd3
.To remove a conda installation,
conda remove dftd3
.
Source
If using PSI4 built from source and you want to build DFTD3 from from source also, follow the instructions provided with the source (essentially, download the freely available tarball, unpack the source, edit the Makefile to select a Fortran compiler, and run make). From version 3.1.0 onwards, DFTD3 can be used asis; for earlier versions, patches are available: psi4/psi4/share/psi4/scripts/patch_grimme_dftd3.3.0.2.
To be used by PSI4, the program binary (dftd3
) must be
found in your PSIPATH
or PATH
(in that order). If
PSI4 is unable to execute the binary, an error will be reported.
To preferentially use a particular dftd3 compilation, simply adjust its
position in the path environment variables.
Theory¶
The local or semilocal character of conventional density functionals necessarily leads to neglect of the longrange correlation interactions which capture attractive van der Waals forces. Initially proposed by Yang [Wu:2002:515] and assiduously developed by Grimme, [Grimme:2004:1463] [Grimme:2006:1787] [Grimme:2010:154104] the DFT+Dispersion method appends to the base functional a scaled, damped, and fitted leading term to the wellknown dispersion energy series, \(E_{disp} = C_6/R^6 C_8/R^8 C_{10}/R^{10}\cdots\). The DFTD2 [Grimme:2006:1787] variant takes the explicit form below. Here, dispersion coefficients, \(C_6^{ij}\), obtained from the geometric mean of tabulated elemental values, are summed over interatomic distances, \(R_{ij}\), modulated by a damping function, \(f_{damp}(R_{ij})\), that gradually activates the dispersion correction (at a rate characterized by \(\alpha_6\)) over a distance characterized by the sum of the two atomic vdW radii, \(R_{vdW}\), while an overall scaling term, \(s_6\), is optimized to be unique to each \(E_{xc}\) functional. (\(\alpha_6\) is sometimes allowed to vary as well.)
Grimme recently presented a refined method, DFTD3, [Grimme:2010:154104] which incorporates an additional \(R^{8}\) term in the dispersion series and adjusts the \(C_{6}^{ij}\) combination formula and damping function. The individual atomic \(C_6^i\) are interpolated from several reference values based upon coordination numbers extracted from the molecular structure, rather than assigned solely by atomic identity as in DFTD2, and thereby incorporate some awareness of the chemical environment into an otherwise largely heuristic correction. The D3 dispersion has the following form, where \(s_{r,6}\) and \(s_8\) are the customary nonunity parameters fitted for individual functionals.
A modified damping scheme for DFTD3 using the rational damping form of Becke and Johnson was introduced in [Grimme:2011:1456]. The parameters fit for individual functionals are now \(s_6\), \(s_8\), \(a_1\), and \(a_2\).
All parameters characterizing the dispersion correction are taken from http://toc.unimuenster.de/DFTD3/ or else from the literature.
Running DFTD3¶
A number of a posteriori dispersion corrections are available in
PSI4. While most are computed within PSI4’s codebase (D1, D2,
CHG, DAS2009, DAS2010), the D3 correction and its variants are
available only through the DFTD3
program. Once installed, the
dftd3
/PSI4 interface is transparent, and all corrections are
interfaced exactly alike.
Dispersion corrections are built into DFT functionals, so appending an a
posteriori correction to a computation is as simple as
energy('b2plypd')
vs. energy('b2plyp')
. For example, the
following input file computes (with much redundant work) for water a
B3LYP, a B3LYPD2, and a B3LYPD3 (zerodamping) energy.
1 2 3 4 5 6 7 8 9 10 11  molecule h2o {
O
H 1 1.0
H 1 1.0 2 104.5
}
set {
basis ccpVDZ
}
energy('b3lyp')
energy('b3lypd')
energy('b3lypd3')

Consult the table D Functionals to see for each
functional what corrections are available and what default parameters
define them. The dispersion correction is available after a calculation in
the PSI variable DISPERSION CORRECTION ENERGY
.
By default, the output from the dftd3
program is suppressed; to see it in the output file, set print > 2.
Extension [1]  Variant and Computing Program  DFT_DISPERSION_PARAMETERS 

D  alias to D2P4  
D1  D1 [2] within PSI4  
D2  alias to D2P4  
D2P4  D2 [3] within PSI4  [\(s_6\)] 
D2GR  D2 [3] through dftd3 
[\(s_6\), \(\alpha_6\)] 
D3  alias to D3ZERO  
D3ZERO  D3 [4] w/ original zerodamping through dftd3 
[\(s_6\), \(s_8\), \(s_{r,6}\), \(\alpha_6\)] 
D3BJ  D3 [5] w/ newer BeckeJohnson rational damping through dftd3 
[\(s_6\), \(s_8\), \(a_1\), \(a_2\)] 
D3M  alias to D3MZERO  
D3MZERO  D3 [6] w/ reparameterized and more flexible original zerodamping through dftd3 
[\(s_6\), \(s_8\), \(s_{r,6}\), \(\beta\)] 
D3MBJ  D3 [6] w/ reparameterized newer BeckeJohnson rational damping through dftd3 
[\(s_6\), \(s_8\), \(a_1\), \(a_2\)] 
Footnotes
[1]  Note that there are functionals with these extensions (e.g., wB97XD) that, not being Grimme corrections, have nothing to do with this table. 
[2]  [Grimme:2004:1463] 
[3]  (1, 2) [Grimme:2006:1787] 
[4]  [Grimme:2010:154104] 
[5]  [Grimme:2011:1456] 
[6]  (1, 2) [Smith:2016:2197] 
A few practical examples:
DFTD2 single point with default parameters (
dftd3
not called)1
energy('bp86d')
DFTD3BJ optimization with default parameters
1
optimize('pbed3bj')
DFTD2 optimization with custom s6 parameter
1 2
set dft_dispersion_parameters [1.20] optimize('b3lypd2')
DFTD3ZERO single point (b3lyp) with custom s8 parameter (reset all four values)
1 2
set dft_dispersion_parameters [1.0, 2.0, 1.261, 14.0] energy('b3lypd3')
If only dispersion corrections (rather than total energies) are of
interest, the dftd3
program can be run independently of the scf
through the python function run_dftd3()
. (This function
is the same PSI4/dftd3
interface that is called during an scf job.)
This route is much faster than running a DFTD energy.
Some setup:
1 2 3 4 5 6
molecule nene { Ne Ne 1 2.0 } nene.update_geometry()
The same four dispersion corrections/gradients as the section above:
1 2 3 4 5 6 7 8 9 10 11 12 13 14
>>> print nene.run_dftd3('bp86', 'd', dertype=0) 7.735e05 >>> E, G = nene.run_dftd3('pbe', 'd3bj') >>> print G [[0.0, 0.0, 1.1809087569358e05], [0.0, 0.0, 1.1809087569358e05]] >>> E, G = nene.run_dftd3('b3lyp', 'd2', {'s6': 1.20}) >>> print E 8.84e05 >>> E, G = nene.run_dftd3(dashlvl='d3', dashparam={'s8': 2.0, 'alpha6': 14.0, 'sr6': 1.261, 's6': 1.0}) >>> print E 0.00024762

qcdb.interface_dftd3.
run_dftd3
(self, func=None, dashlvl=None, dashparam=None, dertype=None, verbose=False)[source]¶ Function to call Grimme’s dftd3 program (http://toc.unimuenster.de/DFTD3/) to compute the D correction of level dashlvl using parameters for the functional func. The dictionary dashparam can be used to supply a full set of dispersion parameters in the absense of func or to supply individual overrides in the presence of func. Returns energy if dertype is 0, gradient if dertype is 1, else tuple of energy and gradient if dertype unspecified. The dftd3 executable must be independently compiled and found in
PATH
orPSIPATH
. self may be either a qcdb.Molecule (sensibly) or a psi4.Molecule (works b/c psi4.Molecule has been extended by this method pyside and only public interface fns used) or a string that can be instantiated into a qcdb.Molecule.func  functional alias or None dashlvl  functional type d2gr/d3zero/d3bj/d3mzero/d3mbj dashparam  dictionary dertype = derivative level