• 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. doi:10.1021/acs.jctc.9b01217

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.

@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/},
}

• 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.

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.

@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.},
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/},
}

• H. Xu, G. Drozdov, B. Hourahine, P. J. Gyu, R. Sweat, T. Frauenheim, and T. Dumitrică, “Collapsed carbon nanotubes: from nano to mesoscale via density functional-based tight-binding objective molecular modeling,” Carbon, vol. 143, p. 786–792, 2019.

Due to the inherent spatial and temporal limitations of atomistic modeling and the lack of mesoscale models, mesoscopic simulation methods for guiding the development of super strong lightweight material systems comprising collapsed carbon nanotubes (CNTs) are missing. Here we establish a path for deriving ultra-coarse-grained mesoscopic distinct element method (mDEM) models directly from the quantum mechanical representation of a collapsed CNT. Atomistic calculations based on density functional theory-based tight-binding (DFTB) extended with Lennard-Jones interactions allow for the identification of the cross-section and elastic constants of an elastic beam idealization of a collapsed CNT. Application of the quantum treatment is possible due to the simplification in the number of atoms introduced by accounting for the helical and angular symmetries exhibited by twisted and bent CNTs. The modeling chain established here is suitable for deriving mesoscopic models for a variety of microscopic filaments with bending anisotropy.

@Article{strathprints66672,
author = {Hao Xu and Grigorii Drozdov and Benjamin Hourahine and Park Jin Gyu and Rebekah Sweat and Thomas Frauenheim and Traian Dumitrică},
title = {Collapsed carbon nanotubes: from nano to mesoscale via density functional-based tight-binding objective molecular modeling},
journal = {Carbon},
year = {2019},
volume = {143},
pages = {786--792},
month = {March},
abstract = {Due to the inherent spatial and temporal limitations of atomistic modeling and the lack of mesoscale models, mesoscopic simulation methods for guiding the development of super strong lightweight material systems comprising collapsed carbon nanotubes (CNTs) are missing. Here we establish a path for deriving ultra-coarse-grained mesoscopic distinct element method (mDEM) models directly from the quantum mechanical representation of a collapsed CNT. Atomistic calculations based on density functional theory-based tight-binding (DFTB) extended with Lennard-Jones interactions allow for the identification of the cross-section and elastic constants of an elastic beam idealization of a collapsed CNT. Application of the quantum treatment is possible due to the simplification in the number of atoms introduced by accounting for the helical and angular symmetries exhibited by twisted and bent CNTs. The modeling chain established here is suitable for deriving mesoscopic models for a variety of microscopic filaments with bending anisotropy.},
keywords = {coarse-grained model, carbon nanotube, density functional based tight binding, Physics, Chemistry(all), Physics and Astronomy(all)},
url = {https://strathprints.strath.ac.uk/66672/}
}

• D. Verma, B. Hourahine, T. Frauenheim, R. D. James, and T. Dumitrică, “Directional-dependent thickness and bending rigidity of phosphorene,” Physical Review B (Condensed Matter), vol. 94, iss. 12, p. 121404(R), 2016.

The strong mechanical anisotropy of phosphorene combined with the atomic-scale thickness challenges the commonly employed elastic continuum idealizations. Using objective boundary conditions and a density functional-based potential, we directly uncover the flexibility of individual {\ensuremath{\alpha}}, {\ensuremath{\beta}} and {\ensuremath{\gamma}} phosphorene allotrope layers along an arbitrary bending direction. A correlation analysis with the in-plane elasticity finds that although a monolayer thickness cannot be defined in the classical continuum sense, an unusual orthotropic plate with a directional-dependent thickness can unambiguously describe the out-of-plane deformation of {\ensuremath{\alpha}} and {\ensuremath{\gamma}} allotropes. Such decoupling of the in-plane and out-of-plane nanomechanics might be generic for two-dimensional materials beyond graphene.

@Article{strathprints57606,
author = {Deepti Verma and Benjamin Hourahine and Thomas Frauenheim and Richard D. James and Traian Dumitrică},
title = {Directional-dependent thickness and bending rigidity of phosphorene},
journal = {Physical Review B (Condensed Matter)},
year = {2016},
volume = {94},
number = {12},
pages = {121404(R)},
month = {September},
note = {{\copyright} 2016 American Physical Society.},
abstract = {The strong mechanical anisotropy of phosphorene combined with the atomic-scale thickness challenges the commonly employed elastic continuum idealizations. Using objective boundary conditions and a density functional-based potential, we directly uncover the flexibility of individual {\ensuremath{\alpha}}, {\ensuremath{\beta}} and {\ensuremath{\gamma}} phosphorene allotrope layers along an arbitrary bending direction. A correlation analysis with the in-plane elasticity finds that although a monolayer thickness cannot be defined in the classical continuum sense, an unusual orthotropic plate with a directional-dependent thickness can unambiguously describe the out-of-plane deformation of {\ensuremath{\alpha}} and {\ensuremath{\gamma}} allotropes. Such decoupling of the in-plane and out-of-plane nanomechanics might be generic for two-dimensional materials beyond graphene.},
keywords = {phosphorene, atomic-scale thickness, nanomechanics, Physics, Condensed Matter Physics},
url = {http://strathprints.strath.ac.uk/57606/}
}

• I. Nikiforov, B. Hourahine, T. Frauenheim, and T. D. u a, “Formation of helices in graphene nanoribbons under torsion,” Journal of Physical Chemistry Letters, vol. 5, iss. 23, p. 4083–4087, 2014.

We use objective boundary conditions and self-consistent charge density-functional-based tight-binding to simulate at the atomistic scale the formation of helices in narrow graphene nanoribbons with armchair edges terminated with fluorine and hydrogen. We interpret the microscopic data using an inextensible, unshearable elastic rod model, which considers both bending and torsional strains. When fitted to the atomistic data, the simple rod model uses closed-form solutions for a cubic equation to predict the strain energy and morphology at a given twist angle and the crossover point between pure torsion and a helix. Our modeling and simulation bring key insights into the origin of the helical graphene morphologies stored inside of carbon nanotubes. They can be useful for designing chiral nanoribbons with tailored properties.

@Article{strathprints50426,
author = {Ilia Nikiforov and Benjamin Hourahine and Thomas Frauenheim and Traian Dumitric{\u a}},
title = {Formation of helices in graphene nanoribbons under torsion},
journal = {Journal of Physical Chemistry Letters},
year = {2014},
volume = {5},
number = {23},
pages = {4083--4087},
month = {December},
abstract = {We use objective boundary conditions and self-consistent charge density-functional-based tight-binding to simulate at the atomistic scale the formation of helices in narrow graphene nanoribbons with armchair edges terminated with fluorine and hydrogen. We interpret the microscopic data using an inextensible, unshearable elastic rod model, which considers both bending and torsional strains. When fitted to the atomistic data, the simple rod model uses closed-form solutions for a cubic equation to predict the strain energy and morphology at a given twist angle and the crossover point between pure torsion and a helix. Our modeling and simulation bring key insights into the origin of the helical graphene morphologies stored inside of carbon nanotubes. They can be useful for designing chiral nanoribbons with tailored properties.},
keywords = {objective boundary conditions, graphene nanoribbons, strain energy, morphology, Physics, Materials Science(all)},
url = {http://strathprints.strath.ac.uk/50426/}
}

• I. Nikiforov, B. Hourahine, B. Aradi, T. Frauenheim, and T. D. u a, “Ewald summation on a helix : a route to self-consistent charge density-functional based tight-binding objective molecular dynamics,” Journal of Chemical Physics, vol. 139, p. 94110, 2013.

We explore the generalization to the helical case of the classical Ewald method, the harbinger of all modern self-consistent treatments of waves in crystals, including ab initio electronic structure methods. Ewald-like formulas that do not rely on a unit cell with translational symmetry prove to be numerically tractable and able to provide the crucial component needed for coupling objective molecular dynamics with the self-consistent charge density-functional based tight-binding treatment of the inter-atomic interactions. The robustness of the method in addressing complex hetero-nuclear nano- and bio-systems is demonstrated with illustrative simulations on a helical boron nitride nanotube, a screw dislocated zinc oxide nanowire, and an ideal DNA molecule.

@Article{strathprints44729,
author = {Ilia Nikiforov and Benjamin Hourahine and B. Aradi and Th. Frauenheim and Traian Dumitric{\u a}},
title = {Ewald summation on a helix : a route to self-consistent charge density-functional based tight-binding objective molecular dynamics},
journal = {Journal of Chemical Physics},
year = {2013},
volume = {139},
pages = {094110},
month = {September},
abstract = {We explore the generalization to the helical case of the classical Ewald method, the harbinger of all modern self-consistent treatments of waves in crystals, including ab initio electronic structure methods. Ewald-like formulas that do not rely on a unit cell with translational symmetry prove to be numerically tractable and able to provide the crucial component needed for coupling objective molecular dynamics with the self-consistent charge density-functional based tight-binding treatment of the inter-atomic interactions. The robustness of the method in addressing complex hetero-nuclear nano- and bio-systems is demonstrated with illustrative simulations on a helical boron nitride nanotube, a screw dislocated zinc oxide nanowire, and an ideal DNA molecule.},
keywords = {helical electrostratics dispersion electronic structure, ewald summation, tight-binding objective, molecular dynamics, Physics, Physical and Theoretical Chemistry, Condensed Matter Physics, Materials Science (miscellaneous)},
url = {http://strathprints.strath.ac.uk/44729/}
}

• B. Hourahine, B. Aradi, and T. Frauenheim, “DFTB+ and lanthanides,” Journal of Physics Conference Series, vol. 242, iss. 1, p. 12005, 2010.

DFTB+ is a recent general purpose implementation of density-functional based tight binding. One of the early motivators to develop this code was to investigate lanthanide impurities in nitride semiconductors, leading to a series of successful studies into structure and electrical properties of these systems. Here we describe our general framework to treat the physical effects needed for these problematic impurities within a tight-binding formalism, additionally discussing forces and stresses in DFTB. We also present an approach to evaluate the general case of Slater-Koster transforms and all of their derivatives in Cartesian coordinates. These developments are illustrated by simulating isolated Gd impurities in GaN.

@Article{strathprints34306,
author = {B. Hourahine and B Aradi and T. Frauenheim},
title = {DFTB+ and lanthanides},
journal = {Journal of Physics Conference Series},
year = {2010},
volume = {242},
number = {1},
pages = {012005},
abstract = {DFTB+ is a recent general purpose implementation of density-functional based tight binding. One of the early motivators to develop this code was to investigate lanthanide impurities in nitride semiconductors, leading to a series of successful studies into structure and electrical properties of these systems. Here we describe our general framework to treat the physical effects needed for these problematic impurities within a tight-binding formalism, additionally discussing forces and stresses in DFTB. We also present an approach to evaluate the general case of Slater-Koster transforms and all of their derivatives in Cartesian coordinates. These developments are illustrated by simulating isolated Gd impurities in GaN.},
keywords = {crystals, semiconductors, crystal impurities, condensed matter, tight-binding approach, Physics, Physics and Astronomy(all)},
url = {http://strathprints.strath.ac.uk/34306/}
}

• S. Sanna, B. Hourahine, T. Frauenheim, and U. Gerstmann, “Theoretical study of rare earth point defects in GaN,” Physica Status Solidi C, vol. 5, iss. 6, p. 2358–2360, 2008.

The behavior of rare earth dopants in GaN was investigated by means of theoretical techniques. The Density Functional based Tight-Binding method (DFTB) has been extended to include orbital dependent potentials (LDA+U and SIC-like) in attempt to model. the 4f states of lanthanide impurities within a realistic crystal model. We present results of an investigation into the structural and and energetic Properties of rare earth (Eu, Er and Tm) point defects in GaN. Lanthanide ions (either isolated or complexed with GaN native defects) prefer the Ga-site. Among the investigated defects the REGa V-N pairs are the most promising candidates as luminescent centers, while, interstitial lauthanides are found not to be compatible with the observed luminescence. Differences in the behavior of the single lanthanide ions are explained in term of different 4f-shell occupation and ion size.

@article{strathprints35316,
volume = {5},
number = {6},
month = {May},
author = {Simone Sanna and Benjamin Hourahine and Thomas Frauenheim and U. Gerstmann},
title = {Theoretical study of rare earth point defects in GaN},
journal = {Physica Status Solidi C},
pages = {2358--2360},
year = {2008},
keywords = {earth point defects , GaN , lanthanide impurities , crystals, interstitial lauthanides, Physics, Condensed Matter Physics},
url = {http://strathprints.strath.ac.uk/35316/},
abstract = {The behavior of rare earth dopants in GaN was investigated by means of theoretical techniques. The Density Functional based Tight-Binding method (DFTB) has been extended to include orbital dependent potentials (LDA+U and SIC-like) in attempt to model. the 4f states of lanthanide impurities within a realistic crystal model. We present results of an investigation into the structural and and energetic Properties of rare earth (Eu, Er and Tm) point defects in GaN. Lanthanide ions (either isolated or complexed with GaN native defects) prefer the Ga-site. Among the investigated defects the REGa V-N pairs are the most promising candidates as luminescent centers, while, interstitial lauthanides are found not to be compatible with the observed luminescence. Differences in the behavior of the single lanthanide ions are explained in term of different 4f-shell occupation and ion size.}
}

• S. Sanna, B. Hourahine, U. Gerstmann, and T. Frauenheim, “Efficient tight-binding approach for the study of strongly correlated systems,” Physical Review B, vol. 76, iss. 15, p. 155128, 2007.

In this work, we present results from self-consistent charge density functional based tight-binding (DFTB) calculational scheme, including local-density approximation +U (LDA+U) and simplified self-interaction-corrected-like potentials for the simulation of systems with localized strongly correlated electrons. This approach attempts to combine the efficiency of tight binding with the accuracy of more sophisticated ab initio methods and allows treatment of highly correlated electrons for very large systems. This is particularly interesting for the case of rare earths in GaN, where dilute amount of rare earth ions is used. In this work, we show the results of test calculations on bulk ErN and on the substitutional Er-Ga in wurtzite GaN, which we choose as representatives of bulk and point defects in solids with strongly correlated electrons. We find that ErN is a half metal in the ferromagnetic phase and that the substitutional Er-Ga in wurtzite GaN has C-3v symmetry. These examples show that the DFTB approach reproduces well the results of more demanding calculation schemes with a very low computational cost, making it suitable for the study of extended systems beyond the capabilities of density functional theory.

@Article{strathprints31163,
author = {Simone Sanna and B. Hourahine and U. Gerstmann and Th. Frauenheim},
title = {Efficient tight-binding approach for the study of strongly correlated systems},
journal = {Physical Review B},
year = {2007},
volume = {76},
number = {15},
pages = {155128},
month = {October},
abstract = {In this work, we present results from self-consistent charge density functional based tight-binding (DFTB) calculational scheme, including local-density approximation +U (LDA+U) and simplified self-interaction-corrected-like potentials for the simulation of systems with localized strongly correlated electrons. This approach attempts to combine the efficiency of tight binding with the accuracy of more sophisticated ab initio methods and allows treatment of highly correlated electrons for very large systems. This is particularly interesting for the case of rare earths in GaN, where dilute amount of rare earth ions is used. In this work, we show the results of test calculations on bulk ErN and on the substitutional Er-Ga in wurtzite GaN, which we choose as representatives of bulk and point defects in solids with strongly correlated electrons. We find that ErN is a half metal in the ferromagnetic phase and that the substitutional Er-Ga in wurtzite GaN has C-3v symmetry. These examples show that the DFTB approach reproduces well the results of more demanding calculation schemes with a very low computational cost, making it suitable for the study of extended systems beyond the capabilities of density functional theory.},
keywords = {density functional theory, electronic structure, self interaction, complex materials, Gallium Nitride, III-Nitrides, GaN, erbium, ER, simulations, Physics, Electronic, Optical and Magnetic Materials, Condensed Matter Physics},
url = {http://strathprints.strath.ac.uk/31163/}
}

• B. Hourahine, S. Sanna, B. Aradi, C. Kohler, T. Niehaus, and T. Frauenheim, “Self-interaction and strong correlation in DFTB,” Journal of Physical Chemistry A, vol. 111, iss. 26, p. 5671–5677, 2007.

The density functional based tight-binding (DFTB) method can benefit substantially from a number of developments in density functional theory (DFT) while also providing a simple analytical proving ground for new extensions. This contribution begins by demonstrating the variational nature of charge-self-consistent DFTB (SCC-DFTB), proving the presence of a defined ground-state in this class of methods. Because the ground state of the SCC-DFTB method itself can be qualitatively incorrect for some systems, suitable forms of the recent LDA+U functionals for SCC-DFTB are also presented. This leads to both a new semilocal self-interaction correction scheme and a new physical argument for the choice of parameters in the LDA+U method. The locality of these corrections can only partly repair the HOMO-LUMO gap and chemical potential discontinuity, hence a novel method for introducing this further physics into the method is also presented, leading to exact derivative discontinuities in this theory at low computational cost. The prototypical system NiO is used as an illustration for these developments.

@Article{strathprints5105,
author = {B. Hourahine and S. Sanna and B. Aradi and C. Kohler and T. Niehaus and T. Frauenheim},
title = {Self-interaction and strong correlation in DFTB},
journal = {Journal of Physical Chemistry A},
year = {2007},
volume = {111},
number = {26},
pages = {5671--5677},
month = {July},
abstract = {The density functional based tight-binding (DFTB) method can benefit substantially from a number of developments in density functional theory (DFT) while also providing a simple analytical proving ground for new extensions. This contribution begins by demonstrating the variational nature of charge-self-consistent DFTB (SCC-DFTB), proving the presence of a defined ground-state in this class of methods. Because the ground state of the SCC-DFTB method itself can be qualitatively incorrect for some systems, suitable forms of the recent LDA+U functionals for SCC-DFTB are also presented. This leads to both a new semilocal self-interaction correction scheme and a new physical argument for the choice of parameters in the LDA+U method. The locality of these corrections can only partly repair the HOMO-LUMO gap and chemical potential discontinuity, hence a novel method for introducing this further physics into the method is also presented, leading to exact derivative discontinuities in this theory at low computational cost. The prototypical system NiO is used as an illustration for these developments.},
keywords = {density, tight-binding, DFTB, nanoscience, applied physics, Solid state physics. Nanoscience, Physical and Theoretical Chemistry},
url = {http://strathprints.strath.ac.uk/5105/}
}

• J. M. Knaup, B. Hourahine, and T. Frauenheim, “Initial steps toward automating the fitting of DFTB E-rep(r),” Journal of Physical Chemistry A, vol. 111, iss. 26, p. 5637–5641, 2007.

The most time-consuming part of developing new parametrizations for the density functional based tight-binding (DFTB) method consists of producing accurate and transferable repulsive pair potentials. In the conventional approach to repulsive parametrization, every possible diatomic combination of the elements covered by the parametrization must be individually hand-constructed. We present an initial attempt to automate some of this time-consuming process. We consider a simple genetic algorithm-based approach to the fitting problem.

@article{strathprints31169,
volume = {111},
number = {26},
month = {July},
author = {J.M. Knaup and B. Hourahine and Th. Frauenheim},
title = {Initial steps toward automating the fitting of DFTB E-rep(r)},
journal = {Journal of Physical Chemistry A},
pages = {5637--5641},
year = {2007},
keywords = {density functional theory, tight binding method, scheme, energy, Physics, Physical and Theoretical Chemistry},
url = {http://strathprints.strath.ac.uk/31169/},
abstract = {The most time-consuming part of developing new parametrizations for the density functional based tight-binding (DFTB) method consists of producing accurate and transferable repulsive pair potentials. In the conventional approach to repulsive parametrization, every possible diatomic combination of the elements covered by the parametrization must be individually hand-constructed. We present an initial attempt to automate some of this time-consuming process. We consider a simple genetic algorithm-based approach to the fitting problem.}
}

• C. Kohler, T. Frauenheim, B. Hourahine, G. Seifert, and M. Sternberg, “Treatment of collinear and noncollinear electron spin within an approximate density functional based method,” Journal of Physical Chemistry A, vol. 111, iss. 26, p. 5622–5629, 2007.

We report benchmark calculations of the density functional based tight-binding method concerning the magnetic properties of small iron clusters (Fe-2 to Fe-5) and the Fe-13 icosahedron. Energetics and stability with respect to changes of cluster geometry of collinear and noncollinear spin configurations are in good agreement with ab initio results. The inclusion of spin-orbit coupling has been tested for the iron dimer.

@article{strathprints31168,
volume = {111},
number = {26},
month = {July},
author = {Christof Kohler and Thomas Frauenheim and Ben Hourahine and Gotthard Seifert and Michael Sternberg},
title = {Treatment of collinear and noncollinear electron spin within an approximate density functional based method},
journal = {Journal of Physical Chemistry A},
pages = {5622--5629},
year = {2007},
keywords = {complex materials, ground state, magnetism, clusters, simulations, systems, iron, Physics, Physical and Theoretical Chemistry},
url = {http://strathprints.strath.ac.uk/31168/},
abstract = {We report benchmark calculations of the density functional based tight-binding method concerning the magnetic properties of small iron clusters (Fe-2 to Fe-5) and the Fe-13 icosahedron. Energetics and stability with respect to changes of cluster geometry of collinear and noncollinear spin configurations are in good agreement with ab initio results. The inclusion of spin-orbit coupling has been tested for the iron dimer.}
}

• S. Sanna, B. Hourahine, T. Gallauner, and T. Frauenheim, “An efficient LDA+U based tight binding approach,” Journal of Physical Chemistry A, vol. 111, iss. 26, p. 5665–5670, 2007.

The functionals usually applied in DFT calculations have deficiencies in describing systems with strongly localized electrons such as transition metals or rare earth (RE) compounds. In this work, we present the self-consistent charge density based functional tight binding (SCC-DFTB) calculation scheme including LDA+U like potentials and apply it for the simulation of RE-doped GaN. DFTB parameters for the simulation of GaN and a selection of rare earth ions, where the f electrons were explicitly included in the valence, have been created. The results of the simulations were tested against experimental data (where present) and against various more sophisticated but computationally more costly DFT calculations. Our approach is found to correctly reproduce the geometry and the energetic of the studied systems.

@article{strathprints31167,
volume = {111},
number = {26},
month = {July},
author = {Simone Sanna and B. Hourahine and Th. Gallauner and Th. Frauenheim},
title = {An efficient LDA+U based tight binding approach},
journal = {Journal of Physical Chemistry A},
pages = {5665--5670},
year = {2007},
keywords = {self interaction correction, density functional theory, absorption fine structure, doped GaN, electronic structure, complex materials, lattice location, Gallium Nitride , implanted GaN, erbium, Physics, Physical and Theoretical Chemistry},
url = {http://strathprints.strath.ac.uk/31167/},
abstract = {The functionals usually applied in DFT calculations have deficiencies in describing systems with strongly localized electrons such as transition metals or rare earth (RE) compounds. In this work, we present the self-consistent charge density based functional tight binding (SCC-DFTB) calculation scheme including LDA+U like potentials and apply it for the simulation of RE-doped GaN. DFTB parameters for the simulation of GaN and a selection of rare earth ions, where the f electrons were explicitly included in the valence, have been created. The results of the simulations were tested against experimental data (where present) and against various more sophisticated but computationally more costly DFT calculations. Our approach is found to correctly reproduce the geometry and the energetic of the studied systems.}
}

• 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.

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.

@article{strathprints31166,
volume = {111},
number = {26},
month = {July},
author = {B. Aradi and B. Hourahine and Th. Frauenheim},
title = {DFTB+, a sparse matrix-based implementation of the DFTB method},
journal = {Journal of Physical Chemistry A},
pages = {5678--5684},
year = {2007},
keywords = {electronic structur calculations, density functional theory, tight binding method, ewald sums, convergence, simulations, potentials, molecules, Physics, Physical and Theoretical Chemistry},
url = {http://strathprints.strath.ac.uk/31166/},
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.}
}

• B. Hourahine, S. Sanna, B. Aradi, C. Kohler, and T. Frauenheim, “A theoretical study of erbium in GaN,” Physica B: Condensed Matter, vol. 376-377, p. 512–515, 2006.

Electroluminescence from rare earth-doped nitride semiconductors shows promise for a variety of applications since strong room temperature luminescence can be observed in these materials for a variety of lanthanide dopants. Modelling of the microscopic structure and properties of the defects involved in the luminescence presents a substantial challenge to current theoretical methods. While it is possible to investigate issues of defect stability using pseudopotential-based approaches, which avoid the problems of modelling strongly correlated f-electron systems, this cannot address luminescence from these centres. Explicitly treating 4f electrons is beyond the reach of the usual mean-field methods normally employed in density-functional theory. In an attempt to improve the theoretical description of these systems while extending the size of models used, we present the results using density-functional -based tight-binding calculations on the properties of erbium in wurtzite GaN. Both substitutional defects and complexes with nitrogen vacancies are considered. We account for strong correlation of the 4f shell using a variant of the LDA+ U method. (c) 2005 Elsevier B.V. All rights reserved.

@article{strathprints31164,
volume = {376-377},
month = {April},
title = {A theoretical study of erbium in GaN},
author = {B. Hourahine and S. Sanna and B. Aradi and C. Kohler and Th. Frauenheim},
year = {2006},
pages = {512--515},
journal = {Physica B: Condensed Matter},
keywords = {GaN, erbium, theory, TB-Doped GaN, ER, films, EU, MBE, Physics, Electronic, Optical and Magnetic Materials, Electrical and Electronic Engineering, Condensed Matter Physics},
url = {http://strathprints.strath.ac.uk/31164/},
abstract = {Electroluminescence from rare earth-doped nitride semiconductors shows promise for a variety of applications since strong room temperature luminescence can be observed in these materials for a variety of lanthanide dopants. Modelling of the microscopic structure and properties of the defects involved in the luminescence presents a substantial challenge to current theoretical methods. While it is possible to investigate issues of defect stability using pseudopotential-based approaches, which avoid the problems of modelling strongly correlated f-electron systems, this cannot address luminescence from these centres. Explicitly treating 4f electrons is beyond the reach of the usual mean-field methods normally employed in density-functional theory. In an attempt to improve the theoretical description of these systems while extending the size of models used, we present the results using density-functional -based tight-binding calculations on the properties of erbium in wurtzite GaN. Both substitutional defects and complexes with nitrogen vacancies are considered. We account for strong correlation of the 4f shell using a variant of the LDA+ U method. (c) 2005 Elsevier B.V. All rights reserved.}
}

• S. Petit, R. Jones, M. J. Shaw, P. R. Briddon, B. Hourahine, and T. Frauenheim, “Electronic behavior of rare-earth dopants in AlN: A density-functional study,” Physical Review B: Condensed Matter and Materials Physics, vol. 72, p. 73205, 2005.

Local density functional calculations are carried out on Er, Eu, and Tm rare-earth (RE) dopants in hexagonal AlN. We find that the isolated impurities prefer to substitute for Al and, in contrast with isolated RE dopants in GaAs and GaN, REAl defects are electrically active and introduce deep donor levels around Ev+0.5 eV. RE complexes with oxygen and vacancies are discussed; some of these have deep levels in the upper third of the gap and could account for a threshold excitation energy around 4 eV observed for intra-f transitions at 465 and 478 nm in AlN:Tm.

@Article{strathprints2953,
author = {S. Petit and R. Jones and M.J. Shaw and P.R. Briddon and B. Hourahine and T. Frauenheim},
title = {Electronic behavior of rare-earth dopants in AlN: A density-functional study},
journal = {Physical Review B: Condensed Matter and Materials Physics},
year = {2005},
volume = {72},
pages = {073205},
month = {August},
abstract = {Local density functional calculations are carried out on Er, Eu, and Tm rare-earth (RE) dopants in hexagonal AlN. We find that the isolated impurities prefer to substitute for Al and, in contrast with isolated RE dopants in GaAs and GaN, REAl defects are electrically active and introduce deep donor levels around Ev+0.5 eV. RE complexes with oxygen and vacancies are discussed; some of these have deep levels in the upper third of the gap and could account for a threshold excitation energy around 4 eV observed for intra-f transitions at 465 and 478 nm in AlN:Tm.},
keywords = {local density functional calculations, rare-earth dopants, nanoscience, Solid state physics. Nanoscience, Electronic, Optical and Magnetic Materials, Condensed Matter Physics},
url = {http://strathprints.strath.ac.uk/2953/}
}