# 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 Psi4conda installer, DFTD3 has already been installed alongside.

• If using the PSI4 conda package, the dftd3 conda package can be obtained through conda install dftd3 -c psi4 or conda install psi4-rt -c psi4.

• 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 -c psi4.

• 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 as-is; 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 long-range 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 well-known dispersion energy series, $$E_{disp} = -C_6/R^6 -C_8/R^8 -C_{10}/R^{10}-\cdots$$. The DFT-D2 [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.)

(1)$E_{disp}^{\text{D2}}=-s_6 \sum_{i,j>i}^{N_{at}} \frac{C_6^{ij}}{(R_{ij})^6} f_{damp}(R_{ij})$
$f_{damp}(R_{ij}) = \frac{1}{1 + e^{- \alpha_6 (R_{ij}/R_{vdW} - 1)}}$

Grimme recently presented a refined method, DFT-D3, [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 DFT-D2, 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.

(2)$E_{disp}^{\text{D3ZERO}}=-\sum_{n=6,8} s_n \sum_{i,j>i}^{N_{at}} \frac{C_n^{ij}}{(R_{ij})^n} f_{damp}(R_{ij})$
$f_{damp}(R_{ij}) = \frac{1}{1 + 6 (R_{ij}/(s_{r,n} R_0^{ij}))^{- \alpha_n}}$

A modified damping scheme for DFT-D3 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 $$a_2$$.

$E_{disp}^{\text{D3BJ}}=-\sum_{n=6,8} s_n \sum_{i,j>i}^{N_{at}} \frac{C_n^{ij}}{(R_{ij})^n + (f_{damp})^n}$
$f_{damp} = a_1 \sqrt{\frac{C_8^{ij}}{C_6^{ij}}} + a_2$

All parameters characterizing the dispersion correction are taken from Grimme’s website 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('b2plyp-d') vs. energy('b2plyp'). For example, the following input file computes (with much redundant work) for water a B3LYP, a B3LYP-D2, and a B3LYP-D3 (zero-damping) 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 cc-pVDZ } energy('b3lyp') energy('b3lyp-d') energy('b3lyp-d3') 

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.

Variants of S. Grimme’s -D correction
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 zero-damping through dftd3 [$$s_6$$, $$s_8$$, $$s_{r,6}$$, $$\alpha_6$$]
-D3BJ -D3 [5] w/ newer Becke-Johnson 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 zero-damping through dftd3 [$$s_6$$, $$s_8$$, $$s_{r,6}$$, $$\beta$$]
-D3MBJ -D3 [6] w/ reparameterized newer Becke-Johnson rational damping through dftd3 [$$s_6$$, $$s_8$$, $$a_1$$, $$a_2$$]

Footnotes

 [1] Note that there are functionals with these extensions (e.g., wB97X-D) that, not being Grimme corrections, have nothing to do with this table.
 [3] (1, 2) [Grimme:2006:1787]
 [6] (1, 2) [Smith:2016:2197]

A few practical examples:

• DFT-D2 single point with default parameters (dftd3 not called)

 1 energy('bp86-d') 
• DFT-D3BJ optimization with default parameters

 1 optimize('pbe-d3bj') 
• DFT-D2 optimization with custom s6 parameter

 1 2 set dft_dispersion_parameters [1.20] optimize('b3lyp-d2') 
• DFT-D3ZERO 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('b3lyp-d3') 

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 DFT-D energy.

• Some set-up:

 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) -7.735e-05 >>> E, G = nene.run_dftd3('pbe', 'd3bj') >>> print G [[0.0, 0.0, -1.1809087569358e-05], [0.0, 0.0, 1.1809087569358e-05]] >>> E, G = nene.run_dftd3('b3lyp', 'd2', {'s6': 1.20}) >>> print E -8.84e-05 >>> 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(mol, func=None, dashlvl=None, dashparam=None, dertype=None, verbose=False)[source]

Compute dispersion correction using Grimme’s DFTD3 executable.

Function to call Grimme’s dftd3 program to compute the -D correction of level dashlvl using parameters for the functional func. dashparam can supply a full set of dispersion parameters in the absence of func or individual overrides in the presence of func.

The DFTD3 executable must be independently compiled and found in PATH or PSIPATH.

Parameters: mol (qcdb.Molecule or psi4.core.Molecule or str) – Molecule on which to run dispersion calculation. Both qcdb and psi4.core Molecule classes have been extended by this method, so either allowed. Alternately, a string that can be instantiated into a qcdb.Molecule. func (str or None) – Density functional (Psi4, not Turbomole, names) for which to load parameters from dashcoeff[dashlvl][func]. This is not passed to DFTD3 and thus may be a dummy or None. Any or all parameters initialized can be overwritten via dashparam. dashlvl ({'d2p4', 'd2gr', 'd3zero', 'd3bj', 'd3mzero', d3mbj', 'd', 'd2', 'd3', 'd3m'}) – Flavor of a posteriori dispersion correction for which to load parameters and call procedure in DFTD3. Must be a keys in dashcoeff dict (or a key in dashalias that resolves to one). dashparam (dict, optional) – Dictionary of the same keys as dashcoeff[dashlvl] used to override any or all values initialized by dashcoeff[dashlvl][func]. dertype ({None, 0, 'none', 'energy', 1, 'first', 'gradient'}, optional) – Maximum derivative level at which to run DFTD3. For large mol, energy-only calculations can be significantly more efficient. Also controls return values, see below. verbose (bool, optional) – When True, additionally include DFTD3 output in output. energy (float, optional) – When dertype is 0, energy [Eh]. gradient (list of lists of floats or psi4.core.Matrix, optional) – When dertype is 1, (nat, 3) gradient [Eh/a0]. (energy, gradient) (float and list of lists of floats or psi4.core.Matrix, optional) – When dertype is unspecified, both energy [Eh] and (nat, 3) gradient [Eh/a0].

Notes

research site: https://www.chemie.uni-bonn.de/pctc/mulliken-center/software/dft-d3 Psi4 mode: When psi4 the python module is importable at import qcdb

time, Psi4 mode is activated, with the following alterations: * output goes to output file * gradient returned as psi4.core.Matrix, not list o’lists * scratch is written to randomly named subdirectory of psi scratch * psivar “DISPERSION CORRECTION ENERGY” is set * verbose triggered when PRINT keywork of SCF module >=3