Density Functional Tight Binding in ONETEP

Author:

Arihant Bhandari, University of Southampton, United Kingdom

Author:

Jacek Dziedzic, University of Southampton, United Kingdom

Author:

Chris-Kriton Skylaris, University of Southampton, United Kingdom

Date:

December 2022

Introduction to Density Functional Tight Binding (DFTB)

Density Functional Tight binding models have been derived by a Taylor expansion of the DFT energy functional in terms of the electron density and truncation up to a certain order in the expansion [Foulkes1989]. Within DFTB, the following eigenvalue equations are solved via diagonalization:

(113)\[ \begin{aligned} H_{\alpha\beta}M^{\beta}_{\,i} = S_{\alpha\beta} M^{\beta}_{\,i} \epsilon_i, \end{aligned}\]

where \(H_{\alpha\beta}\) is the hamiltonian matrix, \(S_{\alpha\beta}\) is the overlap matrix, \(M^{\beta}_{\,i}\) are the orbital coefficients, and \(\epsilon_i\) are energy eigenvalues. The Hamiltonian is built from parameters. [Elstner1998] proposed a self consistent charge (SCC) extension to the traditional DFTB approach, which optmizes the atomic charges self consistently. Henceforth, a series of SCC DFTB methods have been developed [Gaus2014]. Recently, non-SCC methods have undergone a revival because of their speed and applicability to large systems [Bannwarth2020]. E.g. GFN0 is one such method where atomic charges are found using a charge equilibriation scheme [Pracht2019]. The total energy in GFN0 also includes zeroth order terms such as dispersion, repulsion, electrostatic interactions and short range basis correction.

We have implemented the GFN0 method taking the advantage of linear-scaling capabilities of ONETEP. Here we include D2 dispersion correction [Grimme2006] instead of D4 [Caldeweyher2019]. The standard ensemble-DFT subroutines are used for diagonalization and calculation of electronic energies and forces. The parameter files are available in [utils-devel].

Keywords

  • dftb: T/F

[Boolean, default dftb: F].
If true, it enables DFTB calculations.

  • dftb_method: GFN0

[Text, default dftb_method: GFN0].
Variant of the DFTB method, only GFN0 has been implemented at the moment.

  • dftb_method_param_file: file address

[Text, default dftb_method_param_file: param_gfn0-xtb.txt].
Path to the parameter file. A specimen file is supplied in utils-devel/dftb folder.

  • dftb_common_param_file: file address

[Text, default dftb_common_param_file: param_gfn_common.txt].
Path to the file for common GFN parameters. A specimen file is supplied in utils-devel/dftb folder.

  • dftb_bc: O O O / P P P

[Boolean, default dftb_bc: P P P].
Boundary conditions. Only fully open (O O O) or full periodic (P P P) are implemented.

  • dftb_coord_cutoff: 50.0 ang

[Real Physical, default dftb_coord_cutoff: 40.0 bohr].
Cutoff distance for truncating interactions for calculating coordination numbers. Refer to eq. (10) of [Pracht2019].

  • dftb_rep_cutoff: 50.0 ang

[Real Physical, default dftb_rep_cutoff: 40.0 bohr].
Cutoff distance for truncating interactions for calculating repulsion energy. Refer to eq. (3) of [Pracht2019].

  • dftb_srb_cutoff: 20.0 ang

[Real Physical, default dftb_srb_cutoff: 14.14 bohr].
Cutoff distance for truncating interactions for calculating short-range basis correction energy. Refer to eq. (4) of [Pracht2019].

  • dftb_ewald_parameter: 5.0 ang-1

[Real Physical, default dftb_ewald_parameter: -1.0 bohr-1].
If positive, this value is used as the parameter for Ewald summation for periodic electrostatic interactions. Otherwise, the optimum parameter for ewald summation is calculated on the fly.

  • dftb_cartesian_ngwfs: T/F

[Boolean, default dftb_cartesian_ngwfs: F].
If true, the program uses Cartesian Gaussian orbitals, otherwise the program uses spherical orbitals as basis. Note that the currently implemented GFN0 method has been developed for a basis of spherical orbitals and may give incorrect results with Cartesian orbitals.

  • dftb_overlap_analytical: T/F

[Boolean, default dftb_overlap_analytical: T].
If false, elements of the overlap are calculated via integrals on grid, otherwise analytically. Note that the gradients of overlap matrix on grid are not yet implemented.

Acknowledgement

We would like to thank Loukas Kollias, Denis Kramer and John R. Owen for useful discussions.

[Foulkes1989]

W. Matthew C. Foulkes, Roger Haydock, Phys. Rev. B 1989, 39, 12520, https://doi.org/10.1103/PhysRevB.39.12520

[Elstner1998]

Marcus Elstner et. al., Phys. Rev. B 1998, 58, 7260, https://doi.org/10.1103/PhysRevB.58.7260

[Gaus2014]

Michael Gaus, Qiang Cui, Marcus Elstner, “Density functional tight binding: application to organic biological molecules”, WIREs Comput. Mol. Sci. 2014, 4, 49, https://doi.org/10.1002/wcms.1156

[Bannwarth2020]

Christoph Bannwarth et. al., “Extended tight-binding quantum chemistry methods”, WIREs Comput. Mol. Sci. 2021, 11, 1, https://doi.org/10.1002/wcms.1493

[Pracht2019] (1,2,3,4)

Philipp Pracht, Eike Caldeweyher, Sebastian Ehlert, Stefan Grimme, “A robust non-self-consistent tight-binding quantum chemistry method for large molecules”, ChemRxiv 2019, https://doi.org/10.26434/chemrxiv.8326202.v1

[Grimme2006]

Stefan Grimme, “Semi-empirical GGA-type density functional constructed with a long-range dispersion correction”, J. Comput. Chem. 2006, 27, 1787, https://doi.org/10.1002/jcc.20495

[Caldeweyher2019]

Eike Caldeweyher et. al., “A generally applicable atomic-charge dependent London dispersion correction”, J. Chem. Phys. 2019, 150, 154122, https://doi.org/10.1063/1.5090222