Vibrationally resolved UV/Vis spectroscopy with time-dependent density functional based tight binding

Addressing electronic and dynamical evolution of molecules and molecular clusters: DFTB simulations of energy relaxation in polycyclic aromatic hydrocarbons

We present a review of the capabilities of the density functional based Tight Binding (DFTB) scheme to address the electronic relaxation and dynamical evolution of molecules and molecular clusters following energy deposition via either collision or photoabsorption. The basics and extensions of DFTB for addressing these systems and in particular their electronic states and their dynamical evolution are reviewed. Applications to PAH molecules and clusters, carbonaceous systems of major interest in astrochemical/astrophysical context, are reported. A variety of processes are examined and discussed such as collisional hydrogenation, fast collisional processes and induced electronic and charge dynamics, collision-induced fragmentation, photo-induced fragmentation, relaxation in high electronic states, electronic-to-vibrational energy conversion and statistical versus non-statistical fragmentation. This review illustrates how simulations may help to unravel different relaxation mechanisms depending on various factors such as the system size, specific electronic structure or excitation conditions, in close connection with experiments.

Effects of Endohedral Gd-Containing Fullerenols with a Different Number of Oxygen Substituents on Bacterial Bioluminescence

Gadolinium (Gd)-containing fullerenols are perspective agents for magnetic resonance imaging and cancer research. They combine the unique paramagnetic properties of Gd with solubility in water, low toxicity and antiradical activity of fullerenols. We compared the bioeffects of two Gd-containing fullerenols with a different number of oxygen groups-20 and 42: Gd@C82O20H14 and Gd@C82O42H32. The bioluminescent bacteria-based assay was applied to monitor the toxicity of fullerenols, bioluminescence was applied as a signal physiological parameter, and bacterial enzyme-based assay was used to evaluate the fullerenol effects on enzymatic intracellular processes. Chemiluminescence luminol assay was applied to monitor the content of reactive oxygen species (ROS) in bacterial and enzymatic media. It was shown that Gd@C82O42H32 and Gd@C82O20H14 inhibited bacterial bioluminescence at >10-1 and >10-2 gL-1, respectively, revealing a lower toxicity of Gd@C82O42H32. Low-concentration (10-3-10-1 gL-1) bacterial bioluminescence activation by Gd@C82O42H32 was observed, while this activation was not found under exposure to Gd@C82O20H14. Additional carboxyl groups in the structure of Gd@C82O42H32 were determined by infrared spectroscopy and confirmed by quantum chemical calculations. The groups were supposed to endow Gd@C82O42H32 with higher penetration ability through the cellular membrane, activation ability, lower toxicity, balancing of the ROS content in the bacterial suspensions, and lower aggregation in aqueous media.

Isolated Dimers Versus Solid-State Dimers of N-Heteropolycycles: Matrix-Isolation Spectroscopy in Concert with Quantum Chemistry

In this work, matrix-isolation spectroscopy and quantum-chemical calculations are used together to analyse the structure and properties of weakly bound dimers of the two isomers benzo[a]acridine and benzo[c]acridine. Our measured experimental electronic absorbance spectra agree with simulated spectra calculated for the equilibrium structures of the dimers in gas-phase, but in contrast, disagree with the simulated spectra calculated for the structures obtained by optimising the experimental solid-state structures. This highlights the sensitivity of the electronic excitations with respect to the dimer structures. The comparison between the solid-state and gas-phase dimers shows how far the intermolecular interactions could change the geometric and electronic structure in a disordered bulk material or at device interfaces, imposing consequences for exciton and charge mobility and other material properties.

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.

Structure and Vibrational Spectroscopy of C82 Fullerenol Valent Isomers: An Experimental and Theoretical Joint Study

Gd@C₈₂O_xH_y endohedral complexes for advanced biomedical applications (computer tomography, cancer treatment, etc.) were synthesized using high-frequency arc plasma discharge through a mixture of graphite and Gd₂O₃ oxide. The Gd@C₈₂ endohedral complex was isolated by high-efficiency liquid chromatography and consequently oxidized with the formation of a family of Gd endohedral fullerenols with gross formula Gd@C₈₂O₈(OH)₂₀. Fourier-transformed infrared (FTIR) spectroscopy was used to study the structure and spectroscopic properties of the complexes in combination with the DFTB3 electronic structure calculations and infrared spectra simulations. It was shown that the main IR spectral features are formed by a fullerenole C₈₂ cage that allows one to consider the force constants at the DFTB3 level of theory without consideration of gadolinium endohedral ions inside the carbon cage. Based on the comparison of experimental FTIR and theoretical DFTB3 IR spectra, it was found that oxidation of the C₈₂ cage causes the formation of Gd@C₈₂O₂₈H₂₀, with a breakdown of the integrity of the parent C₈₂ cage with the formation of pores between neighboring carbonyl and carboxyl groups. The Gd@C₈₂O₆(OOH)₂(OH)₁₈ endohedral complex with epoxy, carbonyl and carboxyl groups was considered the most reliable fullerenole structural model.

The dominant nature of Herzberg-Teller terms in the photophysical description of naphthalene compared to anthracene and tetracene

The first order and second order corrected photoluminescence quantum yields are computed and compared to experiment for naphthalene in this manuscript discussing negative results. Results for anthracene and tetracene are recalled from previous work (Manian et al. in J Chem Phys 155:054108, 2021), and the results for all three polyacenes are juxtaposed to each other. While at the Franck-Condon point, each of the three noted polyacenes were found to possess a quantum yield near unity. Following the consideration of Herzberg-Teller effects, quantum yields stabilised for anthracene and tetracene to 0.19 and 0.08, respectively. Conversely, the second order corrected quantum yield for naphthalene was found to be 0.91. Analysis of this result showed that while the predicted non-radiative pathways correlate well with what should be expected, the approximation used to calculate second order corrected fluorescence, which yielded very positive results for many other molecular systems, here is unable to account for strong second order contributions, resulting in a grossly overestimated rate of fluorescence. However, substitution of an experimental radiative rate results in a quantum yield of 0.33. This work extols the importance of Herzberg-Teller terms in photophysical descriptions of chromophores, and highlights those cases in which a treatment beyond the above approximation is required.

Modeling radiative and non-radiative pathways at both the Franck-Condon and Herzberg-Teller approximation level

Here, we present a concise model that can predict the photoluminescent properties of a given compound from first principles, both within and beyond the Franck-Condon approximation. The formalism required to compute fluorescence, Internal Conversion (IC), and Inter-System Crossing (ISC) is discussed. The IC mechanism, in particular, is a difficult pathway to compute due to difficulties associated with the computation of required bosonic configurations and non-adiabatic coupling elements. Here, we offer a discussion and breakdown on how to model these pathways at the Density Functional Theory (DFT) level with respect to its computational implementation, strengths, and current limitations. The model is then used to compute the photoluminescent quantum yield (PLQY) of a number of small but important compounds: anthracene, tetracene, pentacene, diketo-pyrrolo-pyrrole (DPP), and Perylene Diimide (PDI) within a polarizable continuum model. Rate constants for fluorescence, IC, and ISC compare well for the most part with respect to experiment, despite triplet energies being overestimated to a degree. The resulting PLQYs are promising with respect to the level of theory being DFT. While we obtained a positive result for PDI within the Franck-Condon limit, the other systems require a second order correction. Recomputing quantum yields with Herzberg-Teller terms yields PLQYs of 0.19, 0.08, 0.04, 0.70, and 0.99 for anthracene, tetracene, pentacene, DPP, and PDI, respectively. Based on these results, we are confident that the presented methodology is sound with respect to the level of quantum chemistry and presents an important stepping stone in the search for a tool to predict the properties of larger coupled systems.

Symmetry-Breaking Enhanced Herzberg-Teller Effect with Brominated Polyacenes

Molecular symmetry is vital to the selection rule of vibrationally resolved electronic transition, particularly when the nuclear dependence of electronic wave function is explicitly treated by including Franck-Condon (FC) factor, Franck-Condon/Herzberg-Teller (FC/HT) interference, and Herzberg-Teller (HT) coupling. Our present study investigated the light absorption spectra of highly symmetric tetracene, pentacene, and hexacene molecules of point-group D_2h, as well as their monobrominated derivatives with a lower C_s symmetry. It was found that the symmetry-breaking monobromination allows more vibrational normal modes and their pairs to contribute to FC/HT interference and HT coupling, respectively. Through a projection of a molecule's vibrational normal modes to its irreducible representations, a linear relationship between the FC/HT intensity to the polyacene's size was deduced alongside a quadratic dependence of the HT intensity. Both theoretically derived correlations were well justified by our numerical simulations, which also demonstrated an approximately 20% improvement on the agreement with experimental line shape if the HT theory is adopted to replace the FC approximation. Moreover, for these low-symmetry monobrominated polyacenes, the FC intensity was even weaker than its FC/HT and HT counterparts at some excitation energies, making the HT theory imperative to decipher vibronic coupling, a fundamental driving force behind numerous chemical, biological, and photophysical processes.

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.

Electronic Structure Modeling of Metal-Organic Frameworks

Owing to their molecular building blocks, yet highly crystalline nature, metal-organic frameworks (MOFs) sit at the interface between molecule and material. Their diverse structures and compositions enable them to be useful materials as catalysts in heterogeneous reactions, electrical conductors in energy storage and transfer applications, chromophores in photoenabled chemical transformations, and beyond. In all cases, density functional theory (DFT) and higher-level methods for electronic structure determination provide valuable quantitative information about the electronic properties that underpin the functions of these frameworks. However, there are only two general modeling approaches in conventional electronic structure software packages: those that treat materials as extended, periodic solids, and those that treat materials as discrete molecules. Each approach has features and benefits; both have been widely employed to understand the emergent chemistry that arises from the formation of the metal-organic interface. This Review canvases these approaches to date, with emphasis placed on the application of electronic structure theory to explore reactivity and electron transfer using periodic, molecular, and embedded models. This includes (i) computational chemistry considerations such as how functional, k-grid, and other model variables are selected to enable insights into MOF properties, (ii) extended solid models that treat MOFs as materials rather than molecules, (iii) the mechanics of cluster extraction and subsequent chemistry enabled by these molecular models, (iv) catalytic studies using both solids and clusters thereof, and (v) embedded, mixed-method approaches, which simulate a fraction of the material using one level of theory and the remainder of the material using another dissimilar theoretical implementation.

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.

Calculation of vibrationally resolved absorption spectra of acenes and pyrene

Absorption spectra of polycyclic aromatic hydrocarbons have been simulated by using a real-time generating function method that combines adiabatic electronic excitation energies with vibrational energies of the excited states.

Non-adiabatic molecular dynamics investigation of the size dependence of the electronic relaxation in polyacenes

Electronic relaxation from the brightest excited state has been investigated for neutral polyacenes ranging in size from naphthalene to heptacene.