Parametrization and Benchmark of Long-Range Corrected DFTB2 for Organic Molecules

Nonadiabatic Exciton Dynamics and Energy Gradients in the Framework of FMO-LC-TDDFTB

We introduce a novel methodology for simulating the excited-state dynamics of extensive molecular aggregates in the framework of the long-range corrected time-dependent density-functional tight-binding fragment molecular orbital method (FMO-LC-TDDFTB) combined with the mean-field Ehrenfest method. The electronic structure of the system is described in a quasi-diabatic basis composed of locally excited and charge-transfer states of all fragments. In order to carry out nonadiabatic molecular dynamics simulations, we derive and implement the excited-state gradients of the locally excited and charge-transfer states. Subsequently, the accuracy of the analytical excited-state gradients is evaluated. The applicability to the simulation of exciton transport in organic semiconductors is illustrated on a large cluster of anthracene molecules. Additionally, nonadiabatic molecular dynamics simulations of a model system of benzothieno-benzothiophene molecules highlight the method's utility in studying charge-transfer dynamics in organic materials. Our new methodology will facilitate the investigation of excitonic transfer in extensive biological systems, nanomaterials, and other complex molecular systems consisting of thousands of atoms.

Nonadiabatic Simulation of Exciton Dynamics in Organic Semiconductors Using Neural Network-Based Frenkel Hamiltonian and Gradients

In this study, we present a multiscale method to simulate the propagation of Frenkel singlet excitons in organic semiconductors (OSCs). The approach uses neural network models to train a Frenkel-type Hamiltonian and its gradient, obtained by the long-range correction version of density functional tight-binding with self-consistent charges. Our models accurately predict site energies, excitonic couplings, and corresponding gradients, essential for the nonadiabatic molecular dynamics simulations. Combined with the fewest switches surface hopping algorithm, the method was applied to four representative OSCs: anthracene, pentacene, perylenediimide, and diindenoperylene. The simulated exciton diffusion constants align well with experimental and reported theoretical values and offer valuable insights into exciton dynamics in OSCs.

CHARMM-GUI QM/MM Interfacer for a Quantum Mechanical and Molecular Mechanical (QM/MM) Simulation Setup: 1. Semiempirical Methods

Quantum mechanical (QM) treatments, when combined with molecular mechanical (MM) force fields, can effectively handle enzyme-catalyzed reactions without significantly increasing the computational cost. In this context, we present CHARMM-GUI QM/MM Interfacer, a web-based cyberinfrastructure designed to streamline the preparation of various QM/MM simulation inputs with ligand modification. The development of QM/MM Interfacer has been achieved through integration with existing CHARMM-GUI modules, such as PDB Reader and Manipulator, Solution Builder, and Membrane Builder. In addition, new functionalities have been developed to facilitate the one-stop preparation of QM/MM systems and enable interactive and intuitive ligand modifications and QM atom selections. QM/MM Interfacer offers support for a range of semiempirical QM methods, including AM1(+/d), PM3(+/PDDG), MNDO(+/d, +/PDDG), PM6, RM1, and SCC-DFTB, tailored for both AMBER and CHARMM. A nontrivial setup related to ligand modification, link-atom insertion, and charge distribution is automatized through intuitive user interfaces. To illustrate the robustness of QM/MM Interfacer, we conducted QM/MM simulations of three enzyme-substrate systems: dihydrofolate reductase, insulin receptor kinase, and oligosaccharyltransferase. In addition, we have created three tutorial videos about building these systems, which can be found at https://www.charmm-gui.org/demo/qmi. QM/MM Interfacer is expected to be a valuable and accessible web-based tool that simplifies and accelerates the setup process for hybrid QM/MM simulations.

Obtaining Robust Density Functional Tight-Binding Parameters for Solids across the Periodic Table

The density functional tight-binding (DFTB) approach allows electronic structure-based simulations at length and time scales far beyond what is possible with first-principles methods. This is achieved by using minimal basis sets and empirical approximations. Unfortunately, the sparse availability of parameters across the periodic table is a significant barrier to the use of DFTB in many cases. We therefore propose a workflow that allows the robust and consistent parametrization of DFTB across the periodic table. Importantly, our approach requires no element-pairwise parameters so that the parameters can be used for all element combinations and are readily extendable. This is achieved by parametrizing all elements on a consistent set of artificial homoelemental crystals, spanning a wide range of coordination environments. The transferability of the resulting periodic table baseline parameters to multielement systems and unknown structures is explored and the model is extensively benchmarked against previous specialized and general DFTB parametrizations.

Polarity profiling of porous architectures: solvatochromic dye encapsulation in metal-organic frameworks

Metal-organic frameworks (MOFs) have gathered significant interest due to their tunable porosity leading to diverse potential applications. In this study, we investigate the incorporation of the fluorosolvatochromic dye 2-butyl-5,6-dimethoxyisoindoline-1,3-dione ([double bond, length as m-dash]Phth) into various MOF structures as a means to assess the polarity of these porous materials. As a purely inorganic compound, zeolite Y was tested for comparison. The fluorosolvatochromic behavior of Phth, which manifests as changes in its emission spectra in response to solvent polarity, provides a sensitive probe for characterizing the local environment within the MOF pores. Through systematic variation of the MOF frameworks, we demonstrate the feasibility of using (fluoro-)solvatochromic dyes as probes for assessing the polarity gradients within MOF structures. Additionally, the fluorosolvatochromic response was studied as a function of loading amount. Our findings not only offer insights into the interplay between MOF architecture and guest molecule interactions but also present a promising approach for the rational design and classification of porous materials based on their polarity properties.

Exploring the Mechanisms behind Non-aromatic Fluorescence with the Density Functional Tight Binding Method

Recent experimental findings reveal nonconventional fluorescence emission in biological systems devoid of conjugated bonds or aromatic compounds, termed non-aromatic fluorescence (NAF). This phenomenon is exclusive to aggregated or solid states and remains absent in monomeric solutions. Previous studies focused on small model systems in vacuum show that the carbonyl stretching mode along with strong interaction of short hydrogen bonds (SHBs) remains the primary vibrational mode explaining NAF in these systems. In order to simulate larger model systems taking into account the effects of the surrounding environment, in this work we propose using the density functional tight-binding (DFTB) method in combination with non-adiabatic molecular dynamics (NAMD) and the mixed quantum/molecular mechanics (QM/MM) approach. We investigate the mechanism behind NAF in the crystal structure of l-pyroglutamine-ammonium, comparing it with the related nonfluorescent amino acid l-glutamine. Our results extend our previous findings to more realistic systems, demonstrating the efficiency and robustness of the proposed DFTB method in the context of NAMD in biological systems. Furthermore, due to its inherent low computational cost, this method allows for a better sampling of the nonradiative events at the conical intersection which is crucial for a complete understanding of this phenomenon. Beyond contributing to the ongoing exploration of NAF, this work paves the way for future application of this method in more complex biological systems such as amyloid aggregates, biomaterials, and non-aromatic proteins.

Excited state properties of an A-D-A non-fullerene electron acceptor: a LC-TD-DFTB study

Understanding charge transfer processes is essential to estimate the performance of organic photovoltaic technologies. Although experimental production is on the rise, predictability strongly relies on theoretical modeling, which is limited to the size of semiconductors. As a computationally favorable approach, we benchmarked the long-range corrected (LC) time-dependent (TD) formulation of the semi-empirical density functional-based tight-binding method (DFTB) for three polycyclic aromatic hydrocarbons (PAHs) and studied the DTP-IC-4Ph molecule, a PAH-based non-fullerene electron acceptor (NFA) with an A-D-A backbone structure. After a thorough investigation into the long-range parameter (ω) tuning for naphthalene, anthracene and pyrene, the excitation energies, oscillator strengths and Natural Transition Orbitals (NTOs) were compared with the standard ωB97X-D/6-31G(d,p) level of theory and the ADC2/6-31G(d,p) multiconfigurational method. We estimated mobility-related properties of the NFA and considered 1000 thermally accessible configurations to qualitatively reproduce the experimental absorption profile and investigate the energetic disorder. Finally, we conducted a fragment-based analysis using the one-electron transition density matrix (1TDM) to determine the character of the excited states and investigate the effect of side chains on exciton formation. Our results are sensitive to the level of theory and highly dependent on the long-range parameter but suggest that the presence of alkyl chains promotes a higher average charge delocalization and allows for additional hopping mechanisms, favoring the charge transfer dynamics.

Formulation of transition dipole gradients for non-adiabatic dynamics with polaritonic states

A general formulation of the strong coupling between photons confined in a cavity and molecular electronic states is developed for the state-interaction state-average spin-restricted ensemble-referenced Kohn-Sham method. The light-matter interaction is included in the Jaynes-Cummings model, which requires the derivation and implementation of the analytical derivatives of the transition dipole moments between the molecular electronic states. The developed formalism is tested in the simulations of the nonadiabatic dynamics in the polaritonic states resulting from the strong coupling between the cavity photon mode and the ground and excited states of the penta-2,4-dieniminium cation, also known as PSB3. Comparison with the field-free simulations of the excited-state decay dynamics in PSB3 reveals that the light-matter coupling can considerably alter the decay dynamics by increasing the excited state lifetime and hindering photochemically induced torsion about the C=C double bonds of PSB3. The necessity of obtaining analytical transition dipole gradients for the accurate propagation of the dynamics is underlined.

Developing semi-empirical water model for efficiently simulating temperature-dependent chemisorption of CO2 in amine solvents

Classical molecular dynamics (MD) simulations without bond forming/breaking cannot be used to model chemical reactions (CRs) among small molecules. Although the first-principle MD simulation can adequately describe CRs with explicit water molecules, such simulation is normally too costly for most researchers to afford. Generally, water molecules in a solvent can exert hydrophobic forces on reacting molecules, which yields a so-called caging effect that cannot be ignored when constructing a free energy landscape for reacting molecules. Many recently developed semi-empirical methods (such as DFTB, PM6 and xTB) are highly efficient for modeling CRs, however none of them can be directly used to model bulk water properly. Here, we developed a modified xTB approach that enables the simulation of CRs in explicit water. Using the chemisorption of CO2 by amines in water as an example application, we demonstrate that our approach yielded results comparable with the first-principle ones, while only using a limited computing resource. Potentially, our proposed semi-empirical water model can be utilized for the computational study of any CR in water.

Quantum mechanical assessment on the optical properties of capsanthin conformers

As optical properties, the ultraviolet-visible (UV-Vis) absorption spectra of capsanthin-based red natural dye are a decisive parameter for their usage in various applications. Thus, accurately predicting the maximum UV-Vis wavelength (λ max ) values is critical in designing dye-conjugated material. Extensive metadynamics simulations were carried out to generate capsanthin conformers at various levels of the extended tight-binding method. Benchmarking the time-dependent density-functional theory (TD-DFT) methods help understand the results of a particular functional and allows a comparison between results obtained with different functional. The long-range correction (LC) scheme in LC-TD-DFT-D4/ωB97X/def2-SVP has been found to reproduce the experimentalλ max , and exhibited the effect of conformational changes to the calculated wavelengths. On the other hand, an inexpensive yet efficient LC-TD-DFTB method reproduced the experimentalλ max insensitive to conformational changes.

Multipole Expansion of Atomic Electron Density Fluctuation Interactions in the Density-Functional Tight-Binding Method

The accuracy of the density-functional tight-binding (DFTB) method in describing noncovalent interactions is limited due to its reliance on monopole-based spherical charge densities. In this study, we present a multipole-extended second-order DFTB (mDFTB2) method that takes into account atomic dipole and quadrupole interactions. Furthermore, we combine the multipole expansion with the monopole-based third-order contribution, resulting in the mDFTB3 method. To assess the accuracy of mDFTB2 and mDFTB3, we evaluate their performance in describing noncovalent interactions, proton transfer barriers, and dipole moments. Our benchmark results show promising improvements even when using the existing electronic parameters optimized for the original DFTB3 model. Both mDFTB2 and mDFTB3 outperform their monopole-based counterparts, DFTB2 and DFTB3, in terms of accuracy. While mDFTB2 and mDFTB3 perform comparably for neutral and positively charged systems, mDFTB3 exhibits superior performance over mDFTB2 when dealing with negatively charged systems and proton transfers. Overall, the incorporation of the multipole expansion significantly enhances the accuracy of the DFTB method in describing noncovalent interactions and proton transfers.

Toward Quantum Chemical Free Energy Simulations of Platinum Nanoparticles on Titania Support

Platinum nanoparticles (Pt-NPs) supported on titania surfaces are costly but indispensable heterogeneous catalysts because of their highly effective and selective catalytic properties. Therefore, it is vital to understand their physicochemical processes during catalysis to optimize their use and to further develop better catalysts. However, simulating these dynamic processes is challenging due to the need for a reliable quantum chemical method to describe chemical bond breaking and bond formation during the processes but, at the same time, fast enough to sample a large number of configurations required to compute the corresponding free energy surfaces. Density functional theory (DFT) is often used to explore Pt-NPs; nonetheless, it is usually limited to some minimum-energy reaction pathways on static potential energy surfaces because of its high computational cost. We report here a combination of the density functional tight binding (DFTB) method as a fast but reliable approximation to DFT, the steered molecular dynamics (SMD) technique, and the Jarzynski equality to construct free energy surfaces of the temperature-dependent diffusion and growth of platinum particles on a titania surface. In particular, we present the parametrization for Pt-X (X = Pt, Ti, or O) interactions in the framework of the second-order DFTB method, using a previous parametrization for titania as a basis. The optimized parameter set was used to simulate the surface diffusion of a single platinum atom (Pt1) and the growth of Pt6 from Pt5 and Pt1 on the rutile (110) surface at three different temperatures (T = 400, 600, 800 K). The free energy profile was constructed by using over a hundred SMD trajectories for each process. We found that increasing the temperature has a minimal effect on the formation free energy; nevertheless, it significantly reduces the free energy barrier of Pt atom migration on the TiO2 surface and the transition state (TS) of its deposition. In a concluding remark, the methodology opens the pathway to quantum chemical free energy simulations of Pt-NPs' temperature-dependent growth and other transformation processes on the titania support.

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).

Evaluation of tight-binding DFT performance for the description of organic photochromes properties

Photochromic molecules are widely studied and developed for their many potential applications. To optimize the required properties through theoretical models, a considerable chemical space is to be explored, and their environment in devices is to be accounted for.. To this end, cheap and reliable computational methods can be powerful tools to steer synthetic developments. As ab initio methods remain costly for extensive studies (in terms of the size of the system and/or number of molecules), semiempirical methods such as density functional tight-binding (TB) could offer a good compromise between accuracy computational cost. However, these approaches necessitate benchmarking on the families of compounds of interest. Thus, the aim of the present study is to evaluate the accuracy of several key features calculated with TB methods (DFTB2, DFTB3, GFN2-xTB, and LC-DFTB2) for three sets of photochromic organic molecules: azobenzene (AZO), norbornadiene/quadricyclane (NBD/QC), and dithienylethene (DTE) derivatives. The features considered here are the optimized geometries, the difference in energy between the two isomers (ΔE), and of the energies of the first relevant excited states. All the TB results are compared to those obtained with DFT methods and state-of-the-art electronic structure calculation methods: DLPNO-CCSD(T) for ground states and DLPNO-STEOM-CCSD for excited states. Our results show that, overall, DFTB3 is the TB method leading to the best results for the geometries and the ΔE values and can be used alone for these purposes for NBD/QC and DTE derivatives. Single point calculations at the r2SCAN-3c level using TB geometries allow circumventing the deficiencies of the TB methods in the AZO series. For electronic transition calculations, the range separated LC-DFTB2 method is the most accurate TB method tested for AZO and NBD/QC derivatives, in close agreement with the reference.

Long-range corrected fragment molecular orbital density functional tight-binding method for excited states in large molecular systems

Herein, we present a new method to efficiently calculate electronically excited states in large molecular assemblies, consisting of hundreds of molecules. For this purpose, we combine the long-range corrected tight-binding density functional fragment molecular orbital method (FMO-LC-DFTB) with an excitonic Hamiltonian, which is constructed in the basis of locally excited and charge-transfer configuration state functions calculated for embedded monomers and dimers and accounts explicitly for the electronic coupling between all types of excitons. We first evaluate both the accuracy and efficiency of our fragmentation approach for molecular dimers and aggregates by comparing it with the full LC-TD-DFTB method. The comparison of the calculated spectra of an anthracene cluster shows a very good agreement between our method and the LC-TD-DFTB reference. The effective computational scaling of our method has been explored for anthracene clusters and for perylene bisimide aggregates. We demonstrate the applicability of our method by the calculation of the excited state properties of pentacene crystal models consisting of up to 319 molecules. Furthermore, the participation ratio of the monomer fragments to the excited states is analyzed by the calculation of natural transition orbital participation numbers, which are verified by the hole and particle density for a chosen pentacene cluster. The use of our FMO-LC-TDDFTB method will allow for future studies of excitonic dynamics and charge transport to be performed on complex molecular systems consisting of thousands of atoms.

Calculation of exciton couplings based on density functional tight-binding coupled to state-interaction state-averaged ensemble-referenced Kohn-Sham approach

We introduce the combination of the density functional tight binding (DFTB) approach, including onsite correction (OC) and long-range corrected (LC) functional and the state-interaction state-averaged spin-restricted ensemble-referenced Kohn-Sham (SI-SA-REKS or SSR) method with extended active space involving four electrons and four orbitals [LC-OC-DFTB/SSR(4,4)], to investigate exciton couplings in multichromophoric systems, such as organic crystals and molecular aggregates. We employ the LC-OC-DFTB/SSR(4,4) method to calculate the excitonic coupling in anthracene and tetracene. As a result, the LC-OC-DFTB/SSR(4,4) method provides a reliable description of the locally excited (LE) state in a single chromophore and the excitonic couplings between chromophores with reasonable accuracy compared to the experiment and the conventional SSR(4,4) method. In addition, the thermal fluctuation of excitonic couplings from dynamic nuclear motion in an anthracene crystal with LC-OC-DFTB/SSR(4,4) shows a similar fluctuation of excitonic coupling and spectral density with those of first-principle calculations. We conclude that LC-OC-DFTB/SSR(4,4) is capable of providing reasonable features related to LE states, such as Frenkel exciton with efficient computational cost.

Divide-and-Conquer Linear-Scaling Quantum Chemical Computations

Fragmentation and embedding schemes are of great importance when applying quantum-chemical calculations to more complex and attractive targets. The divide-and-conquer (DC)-based quantum-chemical model is a fragmentation scheme that can be connected to embedding schemes. This feature article explains several DC-based schemes developed by the authors over the last two decades, which was inspired by the pioneering study of DC self-consistent field (SCF) method by Yang and Lee (J. Chem. Phys. 1995, 103, 5674-5678). First, the theoretical aspects of the DC-based SCF, electron correlation, excited-state, and nuclear orbital methods are described, followed by the two-component relativistic theory, quantum-mechanical molecular dynamics simulation, and the introduction of three programs, including DC-based schemes. Illustrative applications confirmed the accuracy and feasibility of the DC-based schemes.

Hydrogen Bonding and Infrared Spectra of Ethyl-3-methylimidazolium Bis(trifluoromethylsulfonyl)imide/Water Mixtures: A View from Molecular Dynamics Simulations

Simulations of ab initio molecular dynamics have been performed for mixtures of ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide (EMIM-TFSI) ionic liquid and water. Statistics of donors and acceptors of hydrogen bonds has revealed that with increasing water content, hydrogen bonds between EMIM cations and TFSI anions are replaced by bonds to water molecules. In the mixture of liquids, the total number of bonds (from EMIM cations or water molecules) formed by TFSI acceptors increases. IR spectra obtained from ab initio molecular dynamics trajectories are in good agreement with literature data for ionic liquid/water systems. Analysis of oscillations of individual C-H and O-H bonds has shown correlations between vibrational frequencies and hydrogen bonds formed by an EMIM cation or water molecule and has indicated that the changes in the IR spectrum result from the decreased number of water-water hydrogen bonds in the mixture. The tests of DFTB methodology with tailored parameterizations have yielded reasonably good description of the IR spectrum of bulk water, whereas available parameterizations have failed in satisfactory reproduction of the IR spectrum of EMIM-TFSI/water mixtures in the region above 3000 cm^-1.

Conformational Energy Benchmark for Longer n-Alkane Chains

We present the first benchmark set focusing on the conformational energies of highly flexible, long n-alkane chains, termed ACONFL. Unbranched alkanes are ubiquitous building blocks in nature, so the goal is to be able to calculate their properties most accurately to improve the modeling of, e.g., complex (biological) systems. Very accurate DLPNO-CCSD(T1)/CBS reference values are provided, which allow for a statistical meaningful evaluation of even the best available density functional methods. The performance of established and modern (dispersion corrected) density functionals is comprehensively assessed. The recently introduced r²SCAN-V functional shows excellent performance, similar to efficient composite DFT methods like B97-3c and r²SCAN-3c, which provide an even better cost-accuracy ratio, while almost reaching the accuracy of much more computationally demanding hybrid or double hybrid functionals with large QZ AO basis sets. In addition, we investigated the performance of common wave function methods, where MP2/CBS surprisingly performs worse compared to the simple D4 dispersion corrected Hartree-Fock. Furthermore, we investigate the performance of several semiempirical and force field methods, which are commonly used for the generation of conformational ensembles in multilevel workflows or in large scale molecular dynamics studies. Outstanding performance is obtained by the recently introduced general force field, GFN-FF, while other commonly applied methods like the universal force field yield large errors. We recommend the ACONFL as a helpful benchmark set for parametrization of new semiempirical or force field methods and machine learning potentials as well as a meaningful validation set for newly developed DFT or dispersion methods.

Generalized Formulation of the Density Functional Tight Binding-Based Restricted Ensemble Kohn-Sham Method with Onsite Correction to Long-Range Correction

We present a generalized formulation for the combination of the density functional tight binding (DFTB) approach and the state-interaction state-average spin-restricted ensemble-referenced Kohn-Sham (SI-SA-REKS or SSR) method by considering onsite correction (OC) as well as the long-range corrected (LC) functional. The OC contribution provides more accurate energies and analytic gradients for individual microstates, while the multireference character of the SSR provides the correct description for conical intersections. We benchmark the LC-OC-DFTB/SSR method against various DFTB calculation methods for excitation energies and conical intersection structures with π/π* or n/π* characters. Furthermore, we perform excited-state molecular dynamics simulations with a molecular rotary motor with variations of LC-OC-DFTB/SSR approaches. We show that the OC contribution to the LC functional is crucial to obtain the correct geometry of conical intersections.

Pathways to fluorescence via restriction of intramolecular motion in substituted tetraphenylethylenes

The design of materials with enhanced luminescence properties is a fast-developing field due to the potential applicability of these materials as light-emitting diodes or for bioimaging. A transparent way to enhance the emission properties of interesting molecular candidates is blocking competing and unproductive non-radiative relaxation pathways by the restriction of intramolecular motions. Rationalized functionalization is an important possibility to achieve such restrictions. Using time-dependent density functional theory (TD-DFT) based on the ωB97XD functional and the semiempirical tight-binding method including long-range corrections (TD-LC-DFTB), this work investigates the effect of functionalization of the paradigmatic tetraphenylethylene (TPE) on achieving restricted access to conical intersections (RACI). Photodynamical surface hopping simulations have been performed on a larger set of compounds including TPE and ten functionalized TPE compounds. Functionalization has been achieved by means of electron-withdrawing groups, bulky groups which block the relaxation channels via steric hindrance and groups capable of forming strong hydrogen bonds, which restrict the motion via the formation of hydrogen bond channels. Most of the investigated functionalized TPE candidates show ultrafast deactivation to the ground state due to their still existing structural flexibility, but two examples, one containing -CN and -CF₃ groups and a second characterized by a network of hydrogen bonds, have been identified as interesting candidates for creating efficient luminescence properties in solution.

BENCHMARKS OF THE DENSITY FUNCTIONAL TIGHT-BINDING METHOD FOR REDOX, PROTONATION AND ELECTRONIC PROPERTIES OF QUINONES

Organic materials with controllable molecular design and sustainable resources are promising electrode materials. Crystalline quinones have been investigated in a variety of rechargeable battery chemistries due to their ubiquitous nature,...

Exploring the similarity of single-layer covalent organic frameworks using electronic structure calculations

Exploiting a similarity metric to classify COFs according to the degree of π-electron conjugation of their bridges.

Understanding excited state properties of host materials in OLEDs: simulation of absorption spectrum of amorphous 4,4-bis(carbazol-9-yl)-2,2-biphenyl (CBP)

4,4-bis(carbazol-9-yl)-2,2-biphenyl (CBP) is widely used as a host material in phosphorescent organic light-emitting diodes (PhOLEDs). In the present study, we simulate the absorption spectra of CBP in gas and condensed...

Understanding intermolecular interactions of large systems in ground state and excited state by using density functional based tight binding methods

A novel energy decomposition analysis scheme, named DFTB-EDA, is proposed based on the density functional based tight-binding method (DFTB/TD-DFTB), which is a semi-empirical quantum mechanical method based on Kohn-Sham-DFT for large-scale calculations. In DFTB-EDA, the total interaction energy is divided into three terms: frozen density, polarization, and dispersion. Owing to the small cost of DFTB/TD-DFTB, DFTB-EDA is capable of analyzing intermolecular interactions in large molecular systems containing several thousand atoms with high computational efficiency. It can be used not only for ground states but also for excited states. Test calculations, involving the S66 and L7 databases, several large molecules, and non-covalent bonding complexes in their lowest excited states, demonstrate the efficiency, usefulness, and capabilities of DFTB-EDA. Finally, the limits of DFTB-EDA are pointed out.

PyUNIxMD: A Python-based excited state molecular dynamics package

Theoretical/computational description of excited state molecular dynamics is nowadays a crucial tool for understanding light-matter interactions in many materials. Here we present an open-source Python-based nonadiabatic molecular dynamics program package, namely PyUNIxMD, to deal with mixed quantum-classical dynamics for correlated electron-nuclear propagation. The PyUNIxMD provides many interfaces for quantum chemical calculation methods with commercial and noncommercial ab initio and semiempirical quantum chemistry programs. In addition, the PyUNIxMD offers many nonadiabatic molecular dynamics algorithms such as fewest-switch surface hopping and its derivatives as well as decoherence-induced surface hopping based on the exact factorization (DISH-XF) and coupled-trajectory mixed quantum-classical dynamics (CTMQC) for general purposes. Detailed structures and flows of PyUNIxMD are explained for the further implementations by developers. We perform a nonadiabatic molecular dynamics simulation for a molecular motor system as a simple demonstration.

Robust and Efficient Implicit Solvation Model for Fast Semiempirical Methods

We present a robust and efficient method to implicitly account for solvation effects in modern semiempirical quantum mechanics and force fields. A computationally efficient yet accurate solvation model based on the analytical linearized Poisson-Boltzmann (ALPB) model is parameterized for the extended tight binding (xTB) and density functional tight binding (DFTB) methods as well as for the recently proposed GFN-FF general force field. The proposed methods perform well over a broad range of systems and applications, from conformational energies over transition-metal complexes to large supramolecular association reactions of charged species. For hydration free energies of small molecules, GFN1-xTB(ALPB) is reaching the accuracy of sophisticated explicitly solvated approaches, with a mean absolute deviation of only 1.4 kcal/mol compared to the experiment. Logarithmic octanol-water partition coefficients (log K_ow) are computed with a mean absolute deviation of about 0.65 using GFN2-xTB(ALPB) compared to experimental values indicating a consistent description of differential solvent effects. Overall, more than twenty solvents for each of the six semiempirical methods are parameterized and tested. They are readily available in the xtb and dftb+ programs for diverse computational applications.

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.

Analytical Time-Dependent Long-Range Corrected Density Functional Tight Binding (TD-LC-DFTB) Gradients in DFTB+: Implementation and Benchmark for Excited-State Geometries and Transition Energies

The absorption and emission of light is a ubiquitous process in chemical and biological processes, making a theoretical description inevitable for understanding and predicting such properties. Although ab initio and DFT methods are capable of describing excited states with good accuracy in many cases, the investigation of dynamical processes and the need to sample the phase space in complex systems often requires methods with reduced computational costs but still sufficient accuracy. In the present work, we report the derivation and implementation of analytical nuclear gradients for time-dependent long-range corrected density functional tight binding (TD-LC-DFTB) in the DFTB+ program. The accuracy of the TD-LC-DFTB potential-energy surfaces is benchmarked for excited-state geometries and adiabatic as well as vertical transition energies. The benchmark set consists of more than 100 organic molecules taken as subsets from available benchmark sets. The reported method yields a mean deviation of 0.31 eV for adiabatic excitation energies with respect to CC2. In order to study more subtle effects, seminumerical second derivatives based on the analytical gradients are employed to simulate vibrationally resolved UV/vis spectra. This extensive test exhibits few problematic cases, which can be traced back to the parametrization of the repulsive potential.

Effect of varying the TD-lc-DFTB range-separation parameter on charge and energy transfer in a model pentacene/buckminsterfullerene heterojunction

Atomistic modeling of energy and charge transfer at the heterojunction of organic solar cells is an active field with many remaining outstanding questions owing, in part, to the difficulties in performing reliable photodynamics calculations on very large systems. One approach to being able to overcome these difficulties is to design and apply an appropriate simplified method. Density-functional tight binding (DFTB) has become a popular form of approximate density-functional theory based on a minimal valence basis set and neglect of all but two center integrals. We report the results of our tests of a recent long-range correction (lc) [A. Humeniuk and R. Mitrić, J. Chem. Phys. 143, 134120 (2015)] for time-dependent (TD) lc-DFTB by carrying out TD-lc-DFTB fewest switches surface hopping calculations of energy and charge transfer times using the relatively new DFTBABY [A. Humeniuk and R. Mitrić, Comput. Phys. Commun. 221, 174 (2017)] program. An advantage of this method is the ability to run enough trajectories to get meaningful ensemble averages. Our interest in the present work is less in determining exact energy and charge transfer rates than in understanding how the results of these calculations vary with the value of the range-separation parameter (R_lc = 1/μ) for a model organic solar cell heterojunction consisting of a gas-phase van der Waals complex P/F made up of a single pentacene (P) molecule together with a single buckminsterfullerene (F) molecule. The default value of R_lc = 3.03 a₀ is found to be much too small as neither energy nor charge transfer is observed until R_lc ≈ 10 a₀. Tests at a single geometry show that the best agreement with high-quality ab initio spectra is obtained in the limit of no lc (i.e., very large R_lc). A plot of energy and charge transfer rates as a function of R_lc is provided, which suggests that a value of R_lc ≈ 15 a₀ yields the typical literature (condensed-phase) charge transfer time of about 100 fs. However, energy and charge transfer times become as high as ∼300 fs for R_lc ≈ 25 a₀. A closer examination of the charge transfer process P^*/F → P⁺/F^- shows that the initial electron transfer is accompanied by a partial delocalization of the P hole onto F, which then relocalizes back onto P, consistent with a polaron-like picture in which the nuclei relax to stabilize the resultant redistribution of charges.

Ab-initio search for efficient red thermally activated delayed fluorescence molecules for organic light emitting diodes

In this work, we present a computational study on 105 selected organic molecules in order to find suitable candidates for using as thermally activated delayed fluorescent (TADF) emitters in organic light emitting diodes (OLEDs), in the emission range of red light. Based on time-dependent density functional theory (TD-DFT) computations, three promising candidates were found, predicted to have low singlet-triplet splittings, lower than 0.06 eV, and TADF rates of 0.124, 0.154 and 0.231 1/μs. Then, using an experimental-theory calibration approach, the emission wavelength of the molecules were estimated to be 570, 476, and 623 nm, respectively. For the molecule whose emission wavelength (623 nm) is predicted to be in our desired range, we measured the photoluminescence (PL) spectrum and find out that its emission peak is within the predicted accuracy of the employed method. Moreover, we benchmarked the performance of density functional based tight-binding (DFTB) method for future screening works and find out that, this method is an efficient pre-screening tool, useful in searching for molecules with desired emission wavelengths.

Excitonic and charge transfer interactions in tetracene stacked and T-shaped dimers

Extended quantum chemical calculations were performed for the tetracene dimer to provide benchmark results, analyze the excimer survival process, and explore the possibility of using long-range-corrected (LC) time-dependent second-order density functional tight-biding (DFTB2) for this system. Ground- and first-excited-state optimized geometries, vertical excitations at relevant minima, and intermonomer displacement potential energy curves (PECs) were calculated for these purposes. Ground-state geometries were optimized with the scaled-opposite-spin (SOS) second-order Møller-Plesset perturbation (MP2) theory and LC-DFT (density functional theory) and LC-DFTB2 levels. Excited-state geometries were optimized with SOS-ADC(2) (algebraic diagrammatic construction to second-order) and the time-dependent approaches for the latter two methods. Vertical excitations and PECs were compared to multireference configuration interaction DFT (DFT/MRCI). All methods predict the lowest-energy S₀ conformer to have monomers parallel and rotated relative to each other and the lowest S₁ conformer to be of a displaced-stacked type. LC-DFTB2, however, presents some relevant differences regarding other conformers for S₀. Despite some state-order inversions, overall good agreement between methods was observed in the spectral shape, state character, and PECs. Nevertheless, DFT/MRCI predicts that the S₁ state should acquire a doubly excited-state character relevant to the excimer survival process and, therefore, cannot be completely described by the single reference methods used in this work. PECs also revealed an interesting relation between dissociation energies and the intermonomer charge-transfer interactions for some states.

Predicting the bulk modulus of single-layer covalent organic frameworks with square-lattice topology from molecular building-block properties

Two-dimensional Covalent Organic Frameworks (2D COFs) have attracted a lot of interest because of their potential for a broad range of applications. Different combinations of their molecular building blocks can lead to new materials with different physical and chemical properties. In this study, the elasticity of different single-layer tetrabenzoporphyrin (H2-TBPor) and phthalocyanine (H2-Pc) based 2D COFs is numerically investigated using a density-functional based tight-binding approach. Specifically, we calculate the 2D bulk modulus and the equivalent spring constants of the respective molecular building-blocks. Using a spring network model we are able to predict the 2D bulk modulus based on the properties of the isolated molecules. This provides a path to optimize elastic properties of 2D COFs.

Multicolor polymeric carbon dots: synthesis, separation and polyamide-supported molecular fluorescence

Multicolor carbon dots (CDs) have been developed recently and demonstrate great potential in bio-imaging, sensing, and LEDs. However, the fluorescence mechanism of their tunable colors is still under debate, and efficient separation methods are still challenging. Herein, we synthesized multicolor polymeric CDs through solvothermal treatment of citric acid and urea in formamide. Automated reversed-phase column separation was used to achieve fractions with distinct colors, including blue, cyan, green, yellow, orange and red. This work explores the physicochemical properties and fluorescence origins of the red, green, and blue fractions in depth with combined experimental and computational methods. Three dominant fluorescence mechanism hypotheses were evaluated by comparing time-dependent density functional theory and molecular dynamics calculation results to measured characteristics. We find that blue fluorescence likely comes from embedded small molecules trapped in carbonaceous cages, while pyrene analogs are the most likely origin for emission at other wavelengths, especially in the red. Also important, upon interaction with live cells, different CD color fractions are trafficked to different sub-cellular locations. Super-resolution imaging shows that the blue CDs were found in a variety of organelles, such as mitochondria and lysosomes, while the red CDs were primarily localized in lysosomes. These findings significantly advance our understanding of the photoluminescence mechanism of multicolor CDs and help to guide future design and applications of these promising nanomaterials.

Density-functional tight-binding for phosphine-stabilized nanoscale gold clusters

We report a parameterization of the second-order density-functional tight-binding (DFTB2) method for the quantum chemical simulation of phosphine-ligated nanoscale gold clusters, metalloids, and gold surfaces. Our parameterization extends the previously released DFTB2 "auorg" parameter set by connecting it to the electronic parameter of phosphorus in the "mio" parameter set. Although this connection could technically simply be accomplished by creating only the required additional Au-P repulsive potential, we found that the Au 6p and P 3d virtual atomic orbital energy levels exert a strong influence on the overall performance of the combined parameter set. Our optimized parameters are validated against density functional theory (DFT) geometries, ligand binding and cluster isomerization energies, ligand dissociation potential energy curves, and molecular orbital energies for relevant phosphine-ligated Au n clusters (n = 2-70), as well as selected experimental X-ray structures from the Cambridge Structural Database. In addition, we validate DFTB simulated far-IR spectra for several phosphine- and thiolate-ligated gold clusters against experimental and DFT spectra. The transferability of the parameter set is evaluated using DFT and DFTB potential energy surfaces resulting from the chemisorption of a PH3 molecule on the gold (111) surface. To demonstrate the potential of the DFTB method for quantum chemical simulations of metalloid gold clusters that are challenging for traditional DFT calculations, we report the predicted molecular geometry, electronic structure, ligand binding energy, and IR spectrum of Au108S24(PPh3)16.

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.

Recent developments in the general atomic and molecular electronic structure system

A discussion of many of the recently implemented features of GAMESS (General Atomic and Molecular Electronic Structure System) and LibCChem (the C++ CPU/GPU library associated with GAMESS) is presented. These features include fragmentation methods such as the fragment molecular orbital, effective fragment potential and effective fragment molecular orbital methods, hybrid MPI/OpenMP approaches to Hartree-Fock, and resolution of the identity second order perturbation theory. Many new coupled cluster theory methods have been implemented in GAMESS, as have multiple levels of density functional/tight binding theory. The role of accelerators, especially graphical processing units, is discussed in the context of the new features of LibCChem, as it is the associated problem of power consumption as the power of computers increases dramatically. The process by which a complex program suite such as GAMESS is maintained and developed is considered. Future developments are briefly summarized.

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.

Density-functional tight-binding: basic concepts and applications to molecules and clusters

The scope of this article is to present an overview of the Density Functional based Tight Binding (DFTB) method and its applications. The paper introduces the basics of DFTB and its standard formulation up to second order. It also addresses methodological developments such as third order expansion, inclusion of non-covalent interactions, schemes to solve the self-interaction error, implementation of long-range short-range separation, treatment of excited states via the time-dependent DFTB scheme, inclusion of DFTB in hybrid high-level/low level schemes (DFT/DFTB or DFTB/MM), fragment decomposition of large systems, large scale potential energy landscape exploration with molecular dynamics in ground or excited states, non-adiabatic dynamics. A number of applications are reviewed, focusing on -(i)- the variety of systems that have been studied such as small molecules, large molecules and biomolecules, bare orfunctionalized clusters, supported or embedded systems, and -(ii)- properties and processes, such as vibrational spectroscopy, collisions, fragmentation, thermodynamics or non-adiabatic dynamics. Finally outlines and perspectives are given.

Synergistic Approach of Ultrafast Spectroscopy and Molecular Simulations in the Characterization of Intramolecular Charge Transfer in Push-Pull Molecules

The comprehensive characterization of Intramolecular Charge Transfer (ICT) stemming in push-pull molecules with a delocalized π-system of electrons is noteworthy for a bespoke design of organic materials, spanning widespread applications from photovoltaics to nanomedicine imaging devices. Photo-induced ICT is characterized by structural reorganizations, which allows the molecule to adapt to the new electronic density distribution. Herein, we discuss recent photophysical advances combined with recent progresses in the computational chemistry of photoactive molecular ensembles. We focus the discussion on femtosecond Transient Absorption Spectroscopy (TAS) enabling us to follow the transition from a Locally Excited (LE) state to the ICT and to understand how the environment polarity influences radiative and non-radiative decay mechanisms. In many cases, the charge transfer transition is accompanied by structural rearrangements, such as the twisting or molecule planarization. The possibility of an accurate prediction of the charge-transfer occurring in complex molecules and molecular materials represents an enormous advantage in guiding new molecular and materials design. We briefly report on recent advances in ultrafast multidimensional spectroscopy, in particular, Two-Dimensional Electronic Spectroscopy (2DES), in unraveling the ICT nature of push-pull molecular systems. A theoretical description at the atomistic level of photo-induced molecular transitions can predict with reasonable accuracy the properties of photoactive molecules. In this framework, the review includes a discussion on the advances from simulation and modeling, which have provided, over the years, significant information on photoexcitation, emission, charge-transport, and decay pathways. Density Functional Theory (DFT) coupled with the Time-Dependent (TD) framework can describe electronic properties and dynamics for a limited system size. More recently, Machine Learning (ML) or deep learning approaches, as well as free-energy simulations containing excited state potentials, can speed up the calculations with transferable accuracy to more complex molecules with extended system size. A perspective on combining ultrafast spectroscopy with molecular simulations is foreseen for optimizing the design of photoactive compounds with tunable properties.

SCC-DFTB-PIMD Method To Evaluate a Multidimensional Quantum Free-Energy Surface for a Proton-Transfer Reaction

The self-consistent charge density functional tight binding method was combined with the path-integral molecular dynamics method for the first time to evaluate the two-dimensional free-energy surface including nuclear quantum effects of a proton-transfer reaction in a 2,4-dichlorophenol-trimethylamine complex. A statistically converged two-dimensional quantum free-energy surface was evaluated by the multidimensional blue moon ensemble method. The accuracy was guaranteed by optimizing the repulsive potential between the sp³-hybridized nitrogen and hydrogen atoms in a SCC-DFTB3 parameter set for the system to reproduce high-level quantum chemical calculations. The present study illustrates the usefulness of this new approach to investigate nuclear quantum effects in various realistic proton-transfer reactions.

Time-Dependent Long-Range-Corrected Density-Functional Tight-Binding Method Combined with the Polarizable Continuum Model

In this study, excited-state free energies and geometries were efficiently evaluated using a linear-response time-dependent long-range-corrected density-functional tight-binding method integrated with the polarizable continuum model (TD-LC-DFTB2/PCM). Although the LC-DFTB method required the evaluation of the exchange-type term, which was moderately computationally expensive, a single evaluation of the excited-state gradient for a system consisting of more than 1000 atoms in a vacuum was completed within 30 min using one CPU core. Benchmark calculations were conducted for 3-hydroxyflavone, which exhibits dual emission: the absorption and enol-form emission wavelengths calculated by TD-LC-DFTB2/PCM agreed well with those predicted based on the density functional theory using a long-range corrected functional; however, there was a large error in the predicted keto-form emission wavelength. Further benchmark calculations for more than 20 molecules indicated that the conventional TD-DFTB method underestimated the absorption and 0-0 transition energies compared with those which were measured experimentally, whereas the TD-LC-DFTB2 method systematically overestimated these metrics. Nevertheless, the agreement of the results of the TD-LC-DFTB2 method with those obtained by the CAM-B3LYP method demonstrates the potential of the TD-LC-DFTB2/PCM method. Moreover, changing the range separation parameter to 0.15 minimized this deviation.