It is approximately 10^{2} – 10^{3} times faster than DFT but can match its results to *chemical accuracy*. Its main applications are in simulating the ground, excited and transport properties of molecules, nano-structures and materials, but also recently it has been used in several new machine learning schemes for quantum chemistry.

Recent publications show the range of new extensions [2] that are available, its application to real-time quantum dynamics in molecular and nano-strucutured systems [3] and its capabilities on petaflop scale supercomputers [4].

## References

[1] B. Aradi, B. Hourahine, and T. Frauenheim, “DFTB+, a sparse matrix-based implementation of the DFTB method,” Journal of Physical Chemistry A, vol. 111, iss. 26, p. 5678–5684, 2007.

[Bibtex]

[Bibtex]

```
@Article{strathprints31166,
author = {B. Aradi and B. Hourahine and Th. Frauenheim},
journal = {Journal of Physical Chemistry A},
title = {DFTB+, a sparse matrix-based implementation of the DFTB method},
year = {2007},
month = {July},
number = {26},
pages = {5678--5684},
volume = {111},
abstract = {A new Fortran 95 implementation of the DFTB (density functional-based tight binding) method has been developed, where the sparsity of the DFTB system of equations has been exploited. Conventional dense algebra is used only to evaluate the eigenproblems of the system and long-range Coulombic terms, but drop-in O(N) or O(N-2) modules are planned to replace the small code sections that these entail. The developed sparse storage structure is discussed in detail, and a short overview of other features of the new code is given.},
doi = {10.1021/jp070186p},
keywords = {electronic structur calculations, density functional theory, tight binding method, ewald sums, convergence, simulations, potentials, molecules, Physics, Physical and Theoretical Chemistry},
url = {https://strathprints.strath.ac.uk/31166/},
}
```

[2] B. Hourahine, B. Aradi, V. Blum, F. Bonafé, A. Buccheri, C. Camacho, C. Cevallos, M. Y. Deshaye, T. Dumitriča, A. Dominguez, S. Ehlert, M. Elstner, T. van der Heide, J. Hermann, S. Irle, J. J. Kranz, C. Kohler, T. Kowalczyk, T. Kubař, I. S. Lee, V. Lutsker, R. J. Maurer, S. K. Min, I. Mitchell, C. Negre, T. A. Niehaus, A. M. N. Niklasson, A. J. Page, A. Pecchia, G. Penazzi, M. P. Persson, J. Řezáč, C. G. Sánchez, M. Sternberg, M. Stöhr, F. Stuckenberg, A. Tkatchenko, V. W. -z. Yu, and T. Frauenheim, “DFTB+, a software package for efficient approximate density functional theory based atomistic simulations,” Journal of Chemical Physics, vol. 152, iss. 12, p. 124101, 2020.

[Bibtex]

[Bibtex]

```
@Article{strathprints71868,
author = {B. Hourahine and B. Aradi and V. Blum and F. Bonaf{\'e} and A. Buccheri and C. Camacho and C. Cevallos and M.Y. Deshaye and T. Dumitri{\v c}a and A. Dominguez and S. Ehlert and M. Elstner and van der Heide, T. and J. Hermann and S. Irle and J. J. Kranz and C. Kohler and T. Kowalczyk and T. Kuba{\v r} and I. S. Lee and V. Lutsker and R. J. Maurer and S. K. Min and I. Mitchell and C. Negre and T. A. Niehaus and A. M. N. Niklasson and A. J. Page and A. Pecchia and G. Penazzi and M. P. Persson and J. {\v R}ez{\'a}{\v c} and C. G. S{\'a}nchez and M. Sternberg and M. St{\"o}hr and F. Stuckenberg and Alexandre Tkatchenko and V. W.-z. Yu and T. Frauenheim},
journal = {Journal of Chemical Physics},
title = {{DFTB+}, a software package for efficient approximate density functional theory based atomistic simulations},
year = {2020},
month = {March},
number = {12},
pages = {124101},
volume = {152},
abstract = {DFTB+ is a versatile community developed open source software package offering fast and efficient methods for carrying out atomistic quantum mechanical simulations. By implementing various methods approximating density functional theory (DFT), like the density functional based tight binding (DFTB) and the extended tight binding (xTB) method, it enables simulations of large systems and long timescales with reasonable accuracy while being considerably faster for typical simulations than respective ab initio methods. Based on the DFTB framework it additionally offers approximated versions of various DFT extensions including hybrid functionals, time dependent formalism for treating excited systems, electron transport using non-equilibrium Green?s functions and many more. DFTB+ can be used as a user-friendly standalone application as well as being embedded into other software packages as a library or acting as a calculation-server accessed by socket communication. We give an overview of the recently developed capabilities of the DFTB+ code, demonstrating with a few use case examples, discuss the strengths and weaknesses of the various features and discuss on-going developments and possible future perspectives.},
doi = {10.1063/1.5143190},
keywords = {electronic structure theory, software engineering, open quantum systems, excited states, dispersion interactions, nanotube modeling, molecular dynamics method, correlated systems, GPU acceleration, parallel algorithms, Physics, Physics and Astronomy(all), Physical and Theoretical Chemistry},
url = {https://strathprints.strath.ac.uk/71868/},
}
```

[3] F. P. Bonafé, B. Aradi, B. Hourahine, C. R. Medrano, F. J. Hernández, T. Frauenheim, and C. G. Sánchez, “A real-time time-dependent density functional tight-binding implementation for semiclassical excited state electron-nuclear dynamics and pump-probe spectroscopy simulations,” Journal of Chemical Theory and Computation, vol. 16, p. 4454–4469, 2020.

[Bibtex]

[Bibtex]

```
@Article{strathprints72639,
author = {Franco P. Bonaf{\'e} and B{\'a}lint Aradi and Ben Hourahine and Carlos R. Medrano and Federico J. Hern{\'a}ndez and Thomas Frauenheim and Cristi{\'a}n G. S{\'a}nchez},
journal = {Journal of Chemical Theory and Computation},
title = {A real-time time-dependent density functional tight-binding implementation for semiclassical excited state electron-nuclear dynamics and pump-probe spectroscopy simulations},
year = {2020},
month = {June},
note = {Manuscript includes supplementary information.},
pages = {4454--4469},
volume = {16},
abstract = {The increasing need to simulate the dynamics of photoexcited molecular and nanosystems in the sub-picosecond regime demands new efficient tools able to describe the quantum nature of matter at a low computational cost. By combining the power of the approximate DFTB method with the semiclassical Ehrenfest method for nuclear-electron dynamics we have achieved a real-time time-dependent DFTB (TD-DFTB) implementation that fits such requierements. In addition to enabling the study of nuclear motion effects in photoinduced charge transfer processes, our code adds novel features to the realm of static and time-resolved computational spectroscopies. In particular, the optical properties of periodic materials such as graphene nanoribbons or the use of corrections such as the "LDA+U" and "pseudo SIC" methods to improve the optical properties in some systems, can now be handled at the TD-DFTB level. Moreover, the simulation of fully-atomistic time-resolved transient absorption spectra and impulsive vibrational spectra can now be achieved within reasonable computing time, owing to the good performance of the implementation and a parallel simulation protocol. Its application to the study of UV/visible light-induced vibrational coherences in molecules is demonstrated and opens a new door into the mechanisms of non-equilibrium ultrafast phenomena in countless materials with relevant applications.},
doi = {10.1021/acs.jctc.9b01217},
keywords = {nanosystems, photoexcited molecular systems, DFTB, graphene nanoribbons, time-resolved computational spectroscopies, Solid state physics. Nanoscience, Physical and Theoretical Chemistry, Computer Science Applications},
url = {https://strathprints.strath.ac.uk/72639/},
}
```

[4] V. W. Yu, C. Campos, W. Dawson, A. García, V. Havu, B. Hourahine, W. P. Huhn, M. Jacquelin, W. Jia, M. Keçeli, R. Laasner, Y. Li, L. Lin, J. Lu, J. Moussa, J. E. Roman, Á. Vázquez-Mayagoitia, C. Yang, and V. Blum, “ELSI – An open infrastructure for electronic structure solvers,” Computer Physics Communications, vol. 256, p. 107459, 2020.

[Bibtex]

[Bibtex]

```
@Article{strathprints71182,
author = {Victor Wen-zhe Yu and Carmen Campos and William Dawson and Alberto Garc{\'i}a and Ville Havu and Ben Hourahine and William P. Huhn and Mathias Jacquelin and Weile Jia and Murat Ke{\c c}eli and Raul Laasner and Yingzhou Li and Lin Lin and Jianfeng Lu and Jonathan Moussa and Jose E. Roman and {\'A}lvaro V{\'a}zquez-Mayagoitia and Chao Yang and Volker Blum},
journal = {Computer Physics Communications},
title = {{ELSI} -- {A}n open infrastructure for electronic structure solvers},
year = {2020},
month = {December},
pages = {107459},
volume = {256},
abstract = {Routine applications of electronic structure theory to molecules and periodic systems need to compute the electron density from given Hamiltonian and, in case of non-orthogonal basis sets, overlap matrices. System sizes can range from few to thousands or, in some examples, millions of atoms. Different discretization schemes (basis sets) and different system geometries (finite non-periodic vs. infinite periodic boundary conditions) yield matrices with different structures. The ELectronic Structure Infrastructure (ELSI) project provides an open-source software interface to facilitate the implementation and optimal use of high-performance solver libraries covering cubic scaling eigensolvers, linear scaling density-matrix-based algorithms, and other reduced scaling methods in between. In this paper, we present recent improvements and developments inside ELSI, mainly covering (1) new solvers connected to the interface, (2) matrix layout and communication adapted for parallel calculations of periodic and/or spin-polarized systems, (3) routines for density matrix extrapolation in geometry optimization and molecular dynamics calculations, and (4) general utilities such as parallel matrix I/O and JSON output. The ELSI interface has been integrated into four electronic structure code projects (DFTB+, DGDFT, FHI-aims, SIESTA), allowing us to rigorously benchmark the performance of the solvers on an equal footing. Based on results of a systematic set of large-scale benchmarks performed with Kohn-Sham density-functional theory and density-functional tight-binding theory, we identify factors that strongly affect the efficiency of the solvers, and propose a decision layer that assists with the solver selection process. Finally, we describe a reverse communication interface encoding matrix-free iterative solver strategies that are amenable, e.g., for use with planewave basis sets.},
doi = {10.1016/j.cpc.2020.107459},
keywords = {electronic structure theory, density-functional theory, density-functional tight binding, parallel computing, eigensolver, density matrix, Physics, Hardware and Architecture, Physics and Astronomy(all)},
url = {https://strathprints.strath.ac.uk/71182/},
}
```