TBMaLT, a flexible toolkit for combining tight-binding and machine learning.

Tight-binding approaches, especially the Density Functional Tight-Binding (DFTB) and the extended tight-binding schemes, allow for efficient quantum mechanical simulations of large systems and long-time scales. They are derived from ab initio density functional theory using pragmatic approximations and some empirical terms, ensuring a fine balance between speed and accuracy. Their accuracy can be improved by tuning the empirical parameters using machine learning techniques, especially when information about the local environment of the atoms is incorporated. As the significant quantum mechanical contributions are still provided by the tight-binding models, and only short-ranged corrections are fitted, the learning procedure is typically shorter and more transferable as it were with predicting the quantum mechanical properties directly with machine learning without an underlying physically motivated model. As a further advantage, derived quantum mechanical quantities can be calculated based on the tight-binding model without the need for additional learning. We have developed the open-source framework-Tight-Binding Machine Learning Toolkit-which allows the easy implementation of such combined approaches. The toolkit currently contains layers for the DFTB method and an interface to the GFN1-xTB Hamiltonian, but due to its modular structure and its well-defined interfaces, additional atom-based schemes can be implemented easily. We are discussing the general structure of the framework, some essential implementation details, and several proof-of-concept applications demonstrating the perspectives of the combined methods and the functionality of the toolkit.

DFTB+, a software package for efficient approximate density functional theory based atomistic simulations.

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), such as the density functional based tight binding (DFTB) and the extended tight binding method, it enables simulations of large systems and long timescales with reasonable accuracy while being considerably faster for typical simulations than the 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 in addition to 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 also discuss on-going developments and possible future perspectives.

Accurate hydrogen bond energies within the density functional tight binding method.

The density-functional-based tight-binding (DFTB) approach has been recently extended by incorporating one-center exchange-like terms in the expansion of the multicenter integrals. This goes beyond the Mulliken approximation and leads to a scheme which treats in a self-consistent way the fluctuations of the whole dual density matrix and not only its diagonal elements (Mulliken charges). To date, only the performance of this new formalism to reproduce excited-state properties has been assessed (Domínguez et al. J. Chem. Theory Comput., 2013, 9, 4901-4914). Here we study the effect of our corrections on the computation of hydrogen bond energies for water clusters and water-containing systems. The limitations of traditional DFTB to reproduce hydrogen bonds has been acknowledged often. We compare our results for a set of 22 small water clusters and water-containing systems as well as for five water hexadecamers to those obtained with the DFTB3 method. Additionally, we combine our extension with a third-order energy expansion in the charge fluctuations. Our results show that the new formalisms significantly improve upon original DFTB.

Phthalocyanine adsorption to graphene on Ir(111): evidence for decoupling from vibrational spectroscopy.

Phthalocyanine molecules have been adsorbed to Ir(111) and to graphene on Ir(111). From a comparison of scanning tunneling microscopy images of individual molecules adsorbed to the different surfaces alone it is difficult to discern potential differences in the molecular adsorption geometry. In contrast, vibrational spectroscopy using inelastic electron scattering unequivocally hints at strong molecule deformations on Ir(111) and at a planar adsorption geometry on graphene. The spectroscopic evidence for the different adsorption configurations is supported by density functional calculations.

The atomic structure of ternary amorphous TixSi1-xO2 hybrid oxides.

Atomic length-scale order characteristics of binary and ternary amorphous oxides are presented within the framework of ab initio theory. A combined numerically efficient density functional based tight-binding molecular dynamics and density functional theory approach is applied to model the amorphous (a) phases of SiO2 and TiO2 as well as the amorphous phase of atomically mixed TixSi1-xO2 hybrid-oxide alloys over the entire composition range. Short and mid-range order in the disordered material phases are characterized by bond length and bond-angle statistics, pair distribution function analysis, coordination number and coordination polyhedra statistics, as well as ring statistics. The present study provides fundamental insights into the order characteristics of the amorphous hybrid-oxide frameworks formed by versatile types of TiOn and SiOm coordination polyhedra. In a-SiO2 the fourfold crystal coordination of Si ions is almost completely preserved and the atomic structure is widely dominated by ring-like mid-range order characteristics. In contrast, the structural disorder of a-TiO2 arises from short-range disorder in the local coordination environment of the Ti ion. The coordination number analysis indicates a large amount of over and under-coordinated Ti ions (coordination defects) in a-TiO2. Aside from the ubiquitous distortions of the crystal-like coordinated polyhedra, even the basic coordination-polyhedra geometry type changes for a significant fraction of TiO6 units (geometry defects). The combined effects of topological and chemical disorder in a-TixSi1-xO2 alloys lead to a continuos increase in both the Si as well as the Ti coordination number with the chemical composition x. The important roles of intermediate fivefold coordination states of Ti and Si cations are highlighted for ternary a-TixSi1-xO2 as well as for binary a-TiO2. The continuous decrease in ring size with increasing Ti content reflects the progressive loss of mid-range order structure characteristics and the competing roles of network forming and network modifying SiOm and TiOn units in the mixed hybrid oxides.

Extensions of the Time-Dependent Density Functional Based Tight-Binding Approach.

The time-dependent density functional based tight-binding (TD-DFTB) approach is generalized to account for fractional occupations. In addition, an on-site correction leads to marked qualitative and quantitative improvements over the original method. Especially, the known failure of TD-DFTB for the description of σ → π* and n → π* excitations is overcome. Benchmark calculations on a large set of organic molecules also indicate a better description of triplet states. The accuracy of the revised TD-DFTB method is found to be similar to first principles TD-DFT calculations at a highly reduced computational cost. As a side issue, we also discuss the generalization of the TD-DFTB method to spin-polarized systems. In contrast to an earlier study, we obtain a formalism that is fully consistent with the use of local exchange-correlation functionals in the ground state DFTB method.

Controllable magnetic doping of the surface state of a topological insulator.

A combined experimental and theoretical study of doping individual Fe atoms into Bi(2)Se(3) is presented. It is shown through a scanning tunneling microscopy study that single Fe atoms initially located at hollow sites on top of the surface (adatoms) can be incorporated into subsurface layers by thermally activated diffusion. Angle-resolved photoemission spectroscopy in combination with ab initio calculations suggest that the doping behavior changes from electron donation for the Fe adatom to neutral or electron acceptance for Fe incorporated into substitutional Bi sites. According to first principles calculations within density functional theory, these Fe substitutional impurities retain a large magnetic moment, thus presenting an alternative scheme for magnetically doping the topological surface state. For both types of Fe doping, we see no indication of a gap at the Dirac point.

Electron Transport Suppression from Tip-π State Interaction on Si(100)-2 × 1 Surfaces.

We investigate the electron transport between a scanning tunneling microscope tip and Si(100)-2 × 1 surfaces with four distinct configurations by performing calculations using density functional theory and the nonequilibrium Green's function method. Interestingly, we find that the conducting mechanism is altered when the tip-surface distance varies from large to small. At a distance larger than the critical value of 4.06 Å, the conductance is increased with a reduction in distance owing to the π state arising from the silicon dimers immediately under the tip; this in turn plays a key role in facilitating a large transmission probability. In contrast, when the tip is closer to the substrate, the conductance is substantially decreased because the π state is suppressed by the interaction with the tip, and its contribution in the tunneling channels is considerably reduced.

Calculating absorption shifts for retinal proteins: computational challenges.

Rhodopsins can modulate the optical properties of their chromophores over a wide range of wavelengths. The mechanism for this spectral tuning is based on the response of the retinal chromophore to external stress and the interaction with the charged, polar, and polarizable amino acids of the protein environment and is connected to its large change in dipole moment upon excitation, its large electronic polarizability, and its structural flexibility. In this work, we investigate the accuracy of computational approaches for modeling changes in absorption energies with respect to changes in geometry and applied external electric fields. We illustrate the high sensitivity of absorption energies on the ground-state structure of retinal, which varies significantly with the computational method used for geometry optimization. The response to external fields, in particular to point charges which model the protein environment in combined quantum mechanical/molecular mechanical (QM/MM) applications, is a crucial feature, which is not properly represented by previously used methods, such as time-dependent density functional theory (TDDFT), complete active space self-consistent field (CASSCF), and Hartree-Fock (HF) or semiempirical configuration interaction singles (CIS). This is discussed in detail for bacteriorhodopsin (bR), a protein which blue-shifts retinal gas-phase excitation energy by about 0.5 eV. As a result of this study, we propose a procedure which combines structure optimization or molecular dynamics simulation using DFT methods with a semiempirical or ab initio multireference configuration interaction treatment of the excitation energies. Using a conventional QM/MM point charge representation of the protein environment, we obtain an absorption energy for bR of 2.34 eV. This result is already close to the experimental value of 2.18 eV, even without considering the effects of protein polarization, differential dispersion, and conformational sampling.

A global investigation of excited state surfaces within time-dependent density-functional response theory.

This work investigates the capability of time-dependent density functional response theory to describe excited state potential energy surfaces of conjugated organic molecules. Applications to linear polyenes, aromatic systems, and the protonated Schiff base of retinal demonstrate the scope of currently used exchange-correlation functionals as local, adiabatic approximations to time-dependent Kohn-Sham theory. The results are compared to experimental and ab initio data of various kinds to attain a critical analysis of common problems concerning charge transfer and long range (nondynamic) correlation effects. This analysis goes beyond a local investigation of electronic properties and incorporates a global view of the excited state potential energy surfaces.

The mechanism of diamond nucleation from energetic species.

A model for diamond nucleation by energetic species (for example, bias-enhanced nucleation) is proposed. It involves spontaneous bulk nucleation of a diamond embryo cluster in a dense, amorphous carbon hydrogenated matrix; stabilization of the cluster by favorable boundary conditions of nucleation sites and hydrogen termination; and ion bombardment-induced growth through a preferential displacement mechanism. The model is substantiated by density functional tight-binding molecular dynamics simulations and an experimental study of the structure of bias-enhanced and ion beam-nucleated films. The model is also applicable to the nucleation of other materials by energetic species, such as cubic boron nitride.

Quantum mechanics simulation of protein dynamics on long timescale.

Protein structure and dynamics are the keys to a wide range of problems in biology. In principle, both can be fully understood by using quantum mechanics as the ultimate tool to unveil the molecular interactions involved. Indeed, quantum mechanics of atoms and molecules have come to play a central role in chemistry and physics. In practice, however, direct application of quantum mechanics to protein systems has been prohibited by the large molecular size of proteins. As a consequence, there is no general quantum mechanical treatment that not only exceeds the accuracy of state-of-the-art empirical models for proteins but also maintains the efficiency needed for extensive sampling in the conformational space, a requirement mandated by the complexity of protein systems. Here we show that, given recent developments in methods, a general quantum mechanical-based treatment can be constructed. We report a molecular dynamics simulation of a protein, crambin, in solution for 350 ps in which we combine a semiempirical quantum-mechanical description of the entire protein with a description of the surrounding solvent, and solvent-protein interactions based on a molecular mechanics force field. Comparison with a recent very high-resolution crystal structure of crambin (Jelsch et al., Proc Natl Acad Sci USA 2000;102:2246-2251) shows that geometrical detail is better reproduced in this simulation than when several alternate molecular mechanics force fields are used to describe the entire system of protein and solvent, even though the structure is no less flexible. Individual atomic charges deviate in both directions from "canonical" values, and some charge transfer is found between the N and C-termini. The capability of simulating protein dynamics on and beyond the few hundred ps timescale with a demonstrably accurate quantum mechanical model will bring new opportunities to extend our understanding of a range of basic processes in biology such as molecular recognition and enzyme catalysis.

A hydrogen storage mechanism in single-walled carbon nanotubes.

We have carried out systematic calculations for hydrogen-adsorption and -storage mechanism in carbon nanotubes at zero temperature. Hydrogen atoms first adsorb on the tube wall in an arch-type and zigzag-type up to a coverage of theta = 1.0 and are stored in the capillary as a form of H(2) molecule at higher coverages. Hydrogen atoms can be stored dominantly through the tube wall by breaking the C--C midbond, while preserving the wall stability of a nanotube after complete hydrogen insertion, rather than by the capillarity effect through the ends of nanotubes. In the hydrogen-extraction processes, H(2) molecule in the capillary of nanotubes first dissociates and adsorbs onto the inner wall and is further extracted to the outer wall by the flip-out mechanism. Our calculations describe suitably an electrochemical storage process of hydrogen, which is applicable for the secondary hydrogen battery.

Do arsenic interstitials really exist in As-rich GaAs?

To investigate the lattice distortion caused by point defects in As-rich GaAs, we make use of a self-consistent-charge density-functional based tight-binding method. Both relevant defects, the As antisite and the As interstitial, cause significant lattice distortion. In contrast to As interstitials, isolated As antisites lead to lattice strain as well as displacement of nearest neighbor As lattice atoms into the <110> channels, in excellent agreement with experiments. Therefore, our result gives powerful evidence for As antisites being the dominating defect in as-grown As-rich GaAs.

Coherent external and internal phonons in quasi-one-dimensional organic molecular crystals.

We have directly time resolved coherent phonon oscillations in quasi-one-dimensional organic crystals of MePTCDI ( N-N'-dimethylperylene-3,4,9,10-dicarboximide), using femtosecond pump-probe experiments. We observe both higher-energy oscillations caused by intramolecular vibrations (internal phonons) and, for the first time in a quasi-one-dimensional organic system, lower-energy modulations which are related to coherent lattice phonons (external phonons). For internal A(g) vibrations, the coherence decay time of about 2 ps is almost independent of the mode. In contrast, the damping time of the external phonons increases strongly with decreasing energy.

Tetragonal crystalline carbon nitrides: theoretical predictions.

New tetragonal phases of crystalline carbon nitride (CN) and their atomic structures have been identified using a self-consistent-charge density-functional tight-binding method. A tetragonal rocksalt structure provides theoretical support to recent experimental evidence for a stoichiometric CN phase with tetragonal symmetry. A body-centered tetragonal CN phase with 1:1 stoichiometry is predicted to be highly stable and of interesting atomic structure with complicated C-C and N-N dimerizations along the c axis. The cubic-to-tetragonal transitions are carefully examined to understand the underlying mechanism.

Observation of "Stick" and "Handle" intermediates along the fullerene road

The hypothesis that fullerenes grow in a carbon plasma by the addition of C2 units (the "fullerene road") has been widely acclaimed as the most plausible mechanism for formation of larger fullerenes including C60 and C70. Calculations suggest that the association of C2 with fullerenes proceeds through two classes of intermediates, "sticks" and "handles." Here we report the observation of these species using high-resolution ion-mobility measurements for C(n) cations generated by laser vaporization of graphite and laser desorption of C60. Sticks with up to eight-atom chains have also been found.

Structure and electronic properties of MoS2 nanotubes

Structural and electronic properties as well as the stability of MoS2 nanotubes are studied using the density-functional-based tight-binding method. It is found that MoS2 zigzag ( n,0) nanotubes exhibit a narrow direct band gap and MoS2 armchair ( n,n) possess a nonzero moderate direct gap. Interestingly, the ( n,n) tubes show a small indirect gap similar to the direct gap of ( n,0) nanotubes. Simulated electron diffraction patterns confirm the existence of armchair and zigzag disulphide nanotubes. The structure of the MoS2 nanotube tips is explained by introducing topological defects which produce positive and negative curvature.

Adsorption and desorption of an O2 molecule on carbon nanotubes

Adsorption and desorption of an oxygen molecule on carbon nanotubes are investigated using density functional calculations. Several precursor states exist at the edge of armchair nanotubes, whereas an exothermic adsorption takes place at the edge of zigzag nanotubes. We also estimate desorption barriers of a CO molecule from nanotubes as well as fullerenes and amorphous phases. Our calculations suggest that carbon nanotubes can survive selectively during the oxidative etching process with a precise control of annealing temperature, in good agreement with experimental results of purification process of carbon nanotubes.