Time-dependent Density Functional Tight Binding Research Articles

Two excited-state datasets for quantum chemical UV-vis spectra of organic molecules

We present two open-source datasets that provide time-dependent density-functional tight-binding (TD-DFTB) electronic excitation spectra of organic molecules. These datasets represent predictions of UV-vis absorption spectra performed on optimized geometries of the molecules in their electronic ground state. The GDB-9-Ex dataset contains a subset of 96,766 organic molecules from the original open-source GDB-9 dataset. The ORNL_AISD-Ex dataset consists of 10,502,904 organic molecules that contain between 5 and 71 non-hydrogen atoms. The data reveals the close correlation between the magnitude of the gaps between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), and the excitation energy of the lowest singlet excited state energies quantitatively. The chemical variability of the large number of molecules was examined with a topological fingerprint estimation based on extended-connectivity fingerprints (ECFPs) followed by uniform manifold approximation and projection (UMAP) for dimension reduction. Both datasets were generated using the DFTB+ software on the “Andes” cluster of the Oak Ridge Leadership Computing Facility (OLCF).

Analytical excited state gradients for time-dependent density functional theory plus tight binding (TDDFT + TB).

Understanding photoluminescent mechanisms has become essential for photocatalytic, biological, and electronic applications. Unfortunately, analyzing excited state potential energy surfaces (PESs) in large systems is computationally expensive, and hence limited with electronic structure methods such as time-dependent density functional theory (TDDFT). Inspired by the sTDDFT and sTDA methods, time-dependent density functional theory plus tight binding (TDDFT + TB) has been shown to reproduce linear response TDDFT results much faster than TDDFT, particularly in large nanoparticles. For photochemical processes, however, methods must go beyond the calculation of excitation energies. Herein, this work outlines an analytical approach to obtain the derivative of the vertical excitation energy in TDDFT + TB for more efficient excited state PES exploration. The gradient derivation is based on the Z vector method, which utilizes an auxiliary Lagrangian to characterize the excitation energy. The gradient is obtained when the derivatives of the Fock matrix, the coupling matrix, and the overlap matrix are all plugged into the auxiliary Lagrangian, and the Lagrange multipliers are solved. This article outlines the derivation of the analytical gradient, discusses the implementation in Amsterdam Modeling Suite, and provides proof of concept by analyzing the emission energy and optimized excited state geometry calculated by TDDFT and TDDFT + TB for small organic molecules and noble metal nanoclusters.

Nonadiabatic molecular dynamics simulations based on time-dependent density functional tight-binding method.

Nonadiabatic excited state molecular dynamics underpin many photophysical and photochemical phenomena, such as exciton dynamics, and charge separation and transport. In this work, we present an efficient nonadiabatic molecular dynamics (NAMD) simulation method based on time-dependent density functional tight-binding (TDDFTB) theory. Specifically, the adiabatic electronic structure, an essential NAMD input, is described at the TDDFTB level. The nonadiabatic effects originating from the coupled motions of electrons and nuclei are treated by the trajectory surface hopping algorithm. To improve the computational efficiency, nonadiabatic couplings between excited states within the TDDFTB method are derived and implemented using an analytical approach. Furthermore, the time-dependent nonadiabatic coupling scalars are calculated based on the overlap between molecular orbitals rather than the Slater determinants to speed up the simulations. In addition, the electronic decoherence scheme and a state reassigned unavoided crossings algorithm, which has been implemented in the NEXMD software, are used to improve the accuracy of the simulated dynamics and handle trivial unavoided crossings. Finally, the photoinduced nonadiabatic dynamics of a benzene molecule are simulated to demonstrate our implementation. The results for excited state NAMD simulations of benzene molecule based on TDDFTB method compare well to those obtained with numerically expensive time-dependent density functional theory. The proposed methodology provides an attractive theoretical simulation tool for predicting the photophysical and photochemical properties of complex materials.

Hybrid Carbon Nanotubes–Graphene Nanostructures: Modeling, Formation, Characterization

A technology for the formation and bonding with a substrate of hybrid carbon nanostructures from single-walled carbon nanotubes (SWCNT) and reduced graphene oxide (rGO) by laser radiation is proposed. Molecular dynamics modeling by the real-time time-dependent density functional tight-binding (TD-DFTB) method made it possible to reveal the mechanism of field emission centers formation in carbon nanostructures layers. Laser radiation stimulates the formation of graphene-nanotube covalent contacts and also induces a dipole moment of hybrid nanostructures, which ensures their orientation along the force lines of the radiation field. The main mechanical and emission characteristics of the formed hybrid nanostructures were determined. By Raman spectroscopy, the effect of laser radiation energy on the defectiveness of all types of layers formed from nanostructures was determined. Laser exposure increased the hardness of all samples more than twice. Maximum hardness was obtained for hybrid nanostructure with a buffer layer (bl) of rGO and the main layer of SWCNT—rGO(bl)-SWCNT and was 54.4 GPa. In addition, the adhesion of rGO to the substrate and electron transport between the substrate and rGO(bl)-SWCNT increased. The rGO(bl)-SWCNT cathode with an area of ~1 mm2 showed a field emission current density of 562 mA/cm2 and stability for 9 h at a current of 1 mA. The developed technology for the formation of hybrid nanostructures can be used both to create high-performance and stable field emission cathodes and in other applications where nanomaterials coating with good adhesion, strength, and electrical conductivity is required.

On application of deep learning to simplified quantum-classical dynamics in electronically excited states

Deep learning (DL) is applied to simulate non-adiabatic molecular dynamics of phenanthrene, using the time-dependent density functional based tight binding (TD-DFTB) approach for excited states combined with mixed quantum–classical propagation. Reference calculations rely on Tully’s fewest-switches surface hopping (FSSH) algorithm coupled to TD-DFTB, which provides electronic relaxation dynamics in fair agreement with various available experimental results. Aiming at describing the coupled electron-nuclei dynamics in large molecular systems, we then examine the combination of DL for excited-state potential energy surfaces (PESs) with a simplified trajectory surface hopping propagation based on the Belyaev–Lebedev (BL) scheme. We start to assess the accuracy of the TD-DFTB approach upon comparison of the optical spectrum with experimental and higher-level theoretical results. Using the recently developed SchNetPack (Schütt et al 2019 J. Chem. Theory Comput. 15 448–55) for DL applications, we train several models and evaluate their performance in predicting excited-state energies and forces. Then, the main focus is given to the analysis of the electronic population of low-lying excited states computed with the aforementioned methods. We determine the relaxation timescales and compare them with experimental data. Our results show that DL demonstrates its ability to describe the excited-state PESs. When coupled to the simplified BL scheme considered in this study, it provides reliable description of the electronic relaxation in phenanthrene as compared with either the experimental data or the higher-level FSSH/TD-DFTB theoretical results. Furthermore, the DL performance allows high-throughput analysis at a negligible cost.

Trajectory Surface Hopping Approach to Condensed-Phase Nonradiative Relaxation Dynamics Using Divide-and-Conquer Spin-Flip Time-Dependent Density-Functional Tight Binding.

Nonradiative relaxation of excited molecules is central to many crucial issues in photochemistry. Condensed phases are typical contexts in which such problems are considered, and the nonradiative relaxation dynamics are expected to be significantly affected by interactions with the environment, for example, a solvent. We developed a nonadiabatic molecular dynamics simulation technique that can treat the nonradiative relaxation and explicitly include the environment in the calculations without a heavy computational burden. Specifically, we combined trajectory surface hopping with Tully's fewest-switches algorithm, a tight-binding approximated version of spin-flip time-dependent density-functional theory, and divide-and-conquer (DC) spatial fragmentation scheme. Numerical results showed that this method can treat systems with thousands of atoms within reasonable computational resources, and the error arising from DC fragmentation is negligibly small. Using this method, we obtained molecular insights into the solvent dependence of the photoexcited-state dynamics of trans-azobenzene, which demonstrate the importance of the environment for condensed-phase nonradiative relaxation.

Photoinduced charge-transfer in chromophore-labeled gold nanoclusters: quantum evidence of the critical role of ligands and vibronic couplings.

The electron flow between a metallic aggregate and an organic molecule after excitation with light is a crucial step on which hybrid photovoltaic nanomaterials are based. So far, designing such devices with the help of theoretical approaches has been heavily limited by the computational cost of quantum dynamics models able to track the evolution of the excited states over time. In this article, we present the first application of the time-dependent density functional tight-binding (TD-DFTB) method for an experimental nanometer-sized gold-organic system consisting of a hexyl-protected Au25 cluster labelled with a pyrene fluorophore, in which the fluorescence quenching of the pyrene is attributed to the electron transfer from the metallic cluster to the dye. The full quantum rationalization of the electron transfer is attained through quantum dynamics simulations, highlighting the crucial role of the protecting ligand shell in electron transfer, as well as the coupling with nuclear movement. This work paves the way towards the fast and accurate theoretical design of optoelectronic nanodevices.

Fast Nonadiabatic Molecular Dynamics via Spin-Flip Time-Dependent Density-Functional Tight-Binding Approach: Application to Nonradiative Relaxation of Tetraphenylethylene with Locked Aromatic Rings.

Nonadiabatic dynamics around conical intersections between ground and excited states are crucial to understand excited-state phenomena in complex chemical systems. With this background in mind, we present an approach combining fewest-switches trajectory surface hopping and spin-flip (SF) time-dependent (TD) density-functional tight binding (DFTB), which is a simplified version of SF-TD density functional theory (DFT) with semiempirical parametrizations, for computationally efficient nonadiabatic molecular dynamics simulations. The estimated computational time of the SF-TD-DFTB approach is several orders of magnitude lower than that of SF-TD-DFT. In addition, the proposed method reproduces the time scales and quantum yields in photoisomerization reactions of azobenzene at a level comparable with conventional ab initio approaches, demonstrating reasonable accuracy. Finally, we report a practical application of the developed technique to explore the nonradiative relaxation processes of tetraphenylethylene and its derivative with torsionally locked aromatic rings and discuss the effect of locking the rings on the excited-state lifetime.

Simulation of Structural Evolution Using Time-Dependent Density-Functional Based Tight-Binding Method.

A faster and more efficient quantum mechanical simulation method for application to complicated issues of real systems beyond model cases has long been sought after. The density-functional based tight-binding (DFTB) method has successfully explained the atomistic and electronic properties of semiconductors, surfaces, and nanostructures. In addition, the time-dependent formalism implemented in DFTB showed high efficiency in terms of computational cost. In this study, we demonstrated the structural and electronic evolution of small molecules induced by a laser pulse using the time-dependent DFTB (TD-DFTB) method. We identified the critical fluence of the input laser for structural dissociations in carbon chains and fullerenes, which related to the structural stability. The excitation energies of several molecules calculated by TD-DFTB agreed with the experimental values.

TD-DFTB study of optical properties of silver nanoparticle homodimers and heterodimers.

The absorption spectra for face-centered cubic nanoparticle dimers at various interparticle distances are investigated using time-dependent density functional tight binding. Both homodimers and heterodimers are investigated in this work. By studying nanoparticles at various interparticle distances and analyzing their vertical excitations, we found that as the interparticle distance decreases, a red shift arises from contributions of the transition dipole moment that are aligned along the z-axis with nondegenerate features; blue shifts occur for peaks that originate from transition dipole moment components in the x and y directions with double degeneracy. When the nanoparticles are similar in size, the features in the absorption spectra become more sensitive to the interparticle distances. The best-fit curves from vertical excitation energy in the form of AR-b for ΔEredshift/ΔEblueshift vs R are determined. In this way, we determined trends for absorption peak shifts and how these depend on the interparticle distance.

DFTB/MM Molecular Dynamics Simulations of the FMO Light-Harvesting Complex

Because of the size of light-harvesting complexes and the involvement of electronic degrees of freedom, computationally these systems need to be treated with a combined quantum-classical description. To this end, Born-Oppenheimer molecular dynamics simulations have been employed in a quantum mechanics/molecular mechanics (QM/MM) fashion for the ground state followed by excitation energy calculations again in a QM/MM scheme for the Fenna-Matthews-Olson (FMO) complex. The self-consistent-charge density functional tight-binding (DFTB) method electrostatically coupled to a classical description of the environment was applied to perform the ground-state dynamics. Subsequently, long-range-corrected time-dependent DFTB calculations were performed to determine the excitation energy fluctuations of the individual bacteriochlorophyll a molecules. The spectral densities obtained using this approach show an excellent agreement with experimental findings. In addition, the fluctuating site energies and couplings were used to estimate the exciton transfer dynamics.

Finite-temperature-based time-dependent density-functional theory method for static electron correlation systems.

In this study, we developed a time-dependent density-functional theory (TDDFT) with a finite-temperature (FT) scheme, denoted as FT-TDDFT. We introduced the concept of fractional occupation numbers for random phase approximation equation and evaluated the excited-state electronic entropy terms with excited-state occupation number. The orbital occupation numbers for the excited state were evaluated from the change in the ground-state electron configuration with excitation and deexcitation coefficients. Furthermore, we extended the FT formulation to the time-dependent density-functional tight-binding (TDDFTB) method for larger systems, denoted as FT-TDDFTB. Numerical assessment for the FT-(TD)DFT method showed smooth potential curves for double-bond rotation of ethylene in both ground and excited states. Excited-state calculations based on the FT-TDDFTB method were applied to the uniform π-stacking columns composed of trioxotriangulene, possessing neutral radicals in strong correlation systems.

Theoretical investigation of the electronic relaxation in highly excited chrysene and tetracene: The effect of armchair vs zigzag edge.

Non-adiabatic molecular dynamics of neutral chrysene and tetracene molecules is investigated using Tully's fewest switches surface hopping algorithm coupled to the time-dependent density functional based tight-binding (TD-DFTB) method for electronic structure calculations. We first assess the performance of two DFTB parameter sets based on the computed TD-DFTB absorption spectra. The main focus is given to the analysis of the electronic relaxation from the brightest excited state following absorption of a UV photon. We determine the dynamical relaxation times and discuss the underlying mechanisms. Our results show that the electronic population of the brightest excited singlet state in armchair-edge chrysene decays an order-of-magnitude faster than the one in zigzag-edge tetracene. This is correlated with a qualitatively similar difference of energy gaps between the brightest state and the state lying just below in energy, which is also consistent with our previous study on polyacenes.

Performance study of the electronic and optical parameters of thermally activated delayed fluorescence nanosized emitters (CCX-I and CCX-II) via DFT, SCC-DFTB and B97-3c approaches

Conventional density functional theory (DFT) is the common choice of researchers. However, recently the density functional tight binding (DFTB) methods and composite B97-3c methods have been used as a faster and accurate DFT alternative. Moreover, the B97-3c based time-dependent DFT, simplified Tamm–Dancoff (sTDA) and simplified TDDFT (sTDDFT) calculations have expanded the domain of state of art excited state calculations. Here, the recently developed organic nanosized emitters 3-(9H-[3,9′-bicarbazol]-9-yl)-9H-xanthen-9-one (CCX-I) and 3-(9′H-[9,3′:6′,9″-tercarbazol]-9′-yl)-9H-xanthen-9-one (CCX-II) have been used as samples to study the performance of the above mentioned methods at the ground and excited levels in gas and solvent conditions, both with and without the dispersion corrections respectively. Bond lengths calculated by DFTB and B97-3c approaches are in excellent agreement with the DFT results. Root mean square deviation (RMSD) values suggest that the DFTB approach provides better band gap values than B97-3c. But, B97-3c results in better torsion angles. Optical properties are found to be closest to the DFT values when calculated by time-dependent DFTB (TD-DFTB) approach with the lowest RMSDs for excitation energies (0.75 eV) and oscillator strengths (~0.08). The computational speed boosts of the B97-3c based sTDDFT and sTDA approaches are ~ 4 and ~33 times faster than the TDDFT counterpart.

Large-Scale Molecular Dynamics Simulation for Ground and Excited States Based on Divide-and-Conquer Long-Range Corrected Density-Functional Tight-Binding Method.

In this study, divide-and-conquer (DC) based density-functional tight-binding (DFTB) and time-dependent density-functional tight-binding (TD-DFTB) methods were developed using long-range correction (LC), which resolved the underestimation of energy gaps between the highest occupied molecular orbital and lowest unoccupied molecular orbital. We implemented the LC term by the entrywise product for the effective utilization of the math kernel library. Test calculations of formaldehyde in explicit water molecules demonstrate the efficiency of the developed method. Furthermore, the DC-TD-LCDFTB method was applied to 2,2'-bipyridine-3,3'-diol (BP(OH)2), which exhibits excited-state intramolecular proton transfer in polar solvents.

Excited State Relaxation Dynamics of Silicon Nanosheets using Time-dependent Density Functional Tight Binding Theory

By combining time-dependent density functional tight binding (TD-DFTB) calculations for electrons with molecular dynamics simulations, time evolution of excited state relaxation and single electron self-trapping of silicon nanosheets (SinHm) are investigated. We identify the atoms and bonds contributing to the excitations and observe the time evolution of charge density, indicating the migration of exciton from initial position to neighboring bonds. Different temperature 50K and 100K are attempted in the MD simulations, and the temperature is found to affect the electronic localization. Our simulations reveal the formation of exciton trapping and localization on certain bonds upon excitation within the timescale about 200-300fs. In summary, TD-DFTB excited state MD simulations can provide interesting insights into photoreactions and have crucial implications in modulating the exciton transport efficiency in strongly confined low-dimensional systems.

Benchmark and performance of long-range corrected time-dependent density functional tight binding (LC-TD-DFTB) on rhodopsins and light-harvesting complexes.

The chromophores of rhodopsins (Rh) and light-harvesting (LH) complexes still represent a major challenge for a quantum chemical description due to their size and complex electronic structure. Since gradient corrected and hybrid density functional approaches have been shown to fail for these systems, only range-separated functionals seem to be a promising alternative to the more time consuming post-Hartree-Fock approaches. For extended sampling of optical properties, however, even more approximate approaches are required. Recently, a long-range corrected (LC) functional has been implemented into the efficient density functional tight binding (DFTB) method, allowing to sample the excited states properties of chromophores embedded into proteins using quantum mechanical/molecular mechanical (QM/MM) with the time-dependent (TD) DFTB approach. In the present study, we assess the accuracy of LC-TD-DFT and LC-TD-DFTB for rhodopsins (bacteriorhodopsin (bR) and pharaonis phoborhodopsin (ppR)) and LH complexes (light-harvesting complex II (LH2) and Fenna-Matthews-Olson (FMO) complex). This benchmark study shows the improved description of the color tuning parameters compared to standard DFT functionals. In general, LC-TD-DFTB can exhibit a similar performance as the corresponding LC functionals, allowing a reliable description of excited states properties at significantly reduced cost. The two chromophores investigated here pose complementary challenges: while huge sensitivity to external field perturbation (color tuning) and charge transfer excitations are characteristic for the retinal chromophore, the multi-chromophoric character of the LH complexes emphasizes a correct description of inter-chromophore couplings, giving less importance to color tuning. None of the investigated functionals masters both systems simultaneously with satisfactory accuracy. LC-TD-DFTB, at the current stage, although showing a systematic improvement compared to TD-DFTB cannot be recommended for studying color tuning in retinal proteins, similar to some of the LC-DFT functionals, because the response to external fields is still too weak. For sampling of LH-spectra, however, LC-TD-DFTB is a viable tool, allowing to efficiently sample absorption energies, as shown for three different LH complexes. As the calculations indicate, geometry optimization may overestimate the importance of local minima, which may be averaged over when using trajectories. Fast quantum chemical approaches therefore may allow for a direct sampling of spectra in the near future.

Attaching titania clusters of various size to reduced graphene oxide and its impact on the conceivable photocatalytic behavior of the junctions—a DFT/D + U and TD DFTB modeling

DFT/D + U and density functional based tight binding (DFTB) molecular modeling was used to investigate the role of the structural, electronic and optical properties of reduced graphene oxide surface (r-GO), hybridized with hydrated TiO2 moieties of various size, ranging from small molecular Ti2O4 clusters into extended Ti43O86 rutile type nanocrystals of ~5 nm diameter. The calculated adhesion energies, varying from −5.048 eV (r-GO|Ti2O4), −12.159 eV (r-GO|Ti5O10), −18.499 eV (r-GO|Ti15O30) to −42.484 eV (r-GO|Ti43O86), indicate high stability of these composites. It was shown that electronic interactions at the r-GO|(1 1 0)TiO2 interface give rise to net charge flow from the r-GO substrate towards the TiO2 moieties, analyzed in terms of the partial charge density 3D plots and an interfacial dipole moment formation. The DOS structure of the composites was calculated by means of the time dependent DFTB approach, and the position and composition of the VB and CB edges, along with the presence of weak mid-gap 2p C states originating from the intact graphene-like patches in the r-GO substrate were discussed in detail in the context of conceivable photocatalytic activity of the composites. The constructed band alignment diagram implies formation of the staggered type II scheme, with the electric field offset that is sensitive to the titania cluster size. In the case of the nano-reticular TiO2, where only a fraction of the Ti atoms is engaged in the Ti–O–C linkers formation, recombination of the photogenerated charges is inhibited owing to favorable spatial separation effect. For small molecular TiO2 clusters with all Ti cations anchored to the r-GO layer fast cross-relaxation quenches the beneficial interfacial charge separation effect, since the strong hybridization of the oxygen and carbon states provides a convenient pathway for the efficient electronic coupling between the CB edge states of r-GO and the VB edge states of the TiO2 moieties. A phenomenological model of the molecular r-GO|Ti2O4 and the reticular r-GO|Ti43O86 composites was constructed in account for different photocatalytic behavior of both junctions.

Davydov-type excitonic effects on the absorption spectra of parallel-stacked and herringbone aggregates of pentacene: Time-dependent density-functional theory and time-dependent density-functional tight binding.

Exciton formation leads to J-bands in solid pentacene. Describing these exciton bands represents a challenge for both time-dependent (TD) density-functional theory (DFT) and for its semi-empirical analog, namely, for TD density-functional tight binding (DFTB) for three reasons: (i) solid pentacene and pentacene aggregates are bound only by van der Waals forces which are notoriously difficult to describe with DFT and DFTB, (ii) the proper description of the long-range coupling between molecules, needed to describe Davydov splitting, is not easy to include in TD-DFT with traditional functionals and in TD-DFTB, and (iii) mixing may occur between local and charge transfer excitons, which may, in turn, require special functionals. We assess how far TD-DFTB has progressed toward a correct description of this type of exciton by including both a dispersion correction for the ground state and a range-separated hybrid functional for the excited state and comparing the results against corresponding TD-CAM-B3LYP/CAM-B3LYP+D3 results. Analytic results for parallel-stacked ethylene are derived which go beyond Kasha's exciton model [M. Kasha, H. R. Rawls, and A. El-Bayoumi, Pure Appl. Chem. 11, 371 (1965)] in that we are able to make a clear distinction between charge transfer and energy transfer excitons. This is further confirmed when it is shown that range-separated hybrids have a markedly greater effect on charge-transfer excitons than on energy-transfer excitons in the case of parallel-stacked pentacenes. TD-DFT calculations with the CAM-B3LYP functional and TD-lc-DFT calculations lead to negligible excitonic corrections for the herringbone crystal structure, possibly because of an overcorrection of charge-transfer effects (CAM refers to Coulomb attenuated method). In this case, TD-DFT calculations with the B3LYP functional or TD-DFTB calculations parameterized to B3LYP give the best results for excitonic corrections for the herringbone crystal structure as judged from comparison with experimental spectra and with Bethe-Salpeter equation calculations from the literature.

New candidates for the global minimum of medium-sized silicon clusters: A hybrid DFTB/DFT genetic algorithm applied to Sin, n = 8-80

In this study, we perform a systematic search to find the possible lowest energy structure of silicon nanoclusters Sin (n = 8-80) by means of an evolutionary algorithm. The fitness function for this search is the total energy of density functional tight binding (DFTB). To be on firm ground, we take several low energy structures of DFTB and perform further geometrical optimization by density functional theory (DFT). Then we choose structures with the lowest DFT total energy and compare them with the reported lowest energy structures in the literature. In our search, we found several lowest energy structures that were previously unreported. We further observe a geometrical transition at n = 27 from elongated to globular structures. In addition, the optical gap of the lowest energy structures is investigated by time-dependent DFTB (TD-DFTB) and time-dependent DFT (TD-DFT). The results show the same trend in TD-DFTB and TD-DFT for the optical gap. We also find a sudden drop in the optical gap at n = 27, precisely where the geometrical transition occurs.