Long-range Corrected Time-dependent Density Research Articles

Singlet Fission as the Gateway to Triplet Generation in Heavy Atom-Free Organic Molecules.

Triplet generations in heavy atom-free organic molecules are primarily revealed to proceed through singlet fissions (SFs) by investigating the contributions of SFs and intersystem crossings to the generation rates. The spin-flip long-range corrected time-dependent density functional theory calculations on 11 organic molecules known for triplet generation under photoirradiation are performed. The correlation between the descriptors for SF and the experimental singlet-to-triplet conversion rates strongly supports the predominance of SF progressions in all these molecules, corroborated by experimental observations of their triplet-triplet annihilations. Based on these findings, we propose updated conditions for SF progression: There is a high-absorption singlet state just above the triplet-triplet excitation of the chromophore dimer, or the singlet (triplet-triplet) excitation itself is responsible for photoabsorption. To the best of our knowledge, all organic molecules known for rapid triplet state generation fulfill these conditions.

Singlet fission initiating organic photosensitizations

The feasibility of singlet fission (SF) in organic photosensitizers is investigated through spin-flip long-range corrected time-dependent density functional theory. This study focuses on four major organic photosensitizer molecules: benzophenone, boron-dipyrromethene, methylene blue, and rose bengal. Calculations demonstrate that all these molecules possess moderate pi-stacking energies and closely-lying singlet (S) and quintet (triplet–triplet, TT) excitations, satisfying the essential conditions for SF: (1) Near-degenerate low-lying S and (TT) excitations with a significant S–T energy gap, and (2) Moderate pi-stacking energy of chromophores, slightly higher than solvation energy, enabling dissociation for triplet-state chromophore generation. Moreover, based on the El-Sayed rule, intersystem crossing is found to simultaneously proceed at very slow rates in all these photosensitizers. This is attributed to the fact that the lowest singlet excitation of the monomers partly involves npi ^* transitions alongside the main pi pi ^* transitions. The proposed mechanisms are strongly substantiated by comparisons with experimental studies.

Roles of Singlet Fission in the Photosensitization of Silicon Phthalocyanine.

The roles of singlet fission in the triplet generation of silicon phthalocyanine (SiPc), a compound analogous to the IRDye700DX photosensitizer used in near-infrared photoimmunotherapy, are investigated by considering the energetical relation between the excitations of this compound. These excitations are obtained through spin-flip long-range corrected time-dependent density functional theory calculations. To initiate singlet fission, chromophores must meet two conditions: (1) near-degenerate low-lying singlet and quintet (triplet-triplet) excitations with a considerable energy gap of the lowest singlet and triplet excited states and (2) moderate π-stacking energy of chromophores, which is higher than but not far from the solvation energy, to facilitate the dissociation and generation of triplet-state chromophores. The present calculations demonstrate that SiPc satisfies both of these conditions after the formation of π-stacking irrespective of the presence of an axial ligand(s), suggesting that singlet fission plays a crucial role in the triplet generation process, although intersystem crossing occurs simultaneously at a very slow rate.

Singlet fission initiating triplet generations of BODIPY derivatives through pi -stacking: a theoretical study

The role of singlet fission (SF) in the triplet-state generation mechanism of 1,3,5,7-tetramethyl-boron-dipyrromethene derivatives is revealed by exploring the cause for the solvent dependence of the generation rate. Comparing the adsorption energy calculations of solvent molecules, i.e., cyclohexane, chloroform and acetonitrile molecules, to the derivatives with the pi -stacking energies of these derivatives surprisingly show that the hierarchy of the solvation energies and pi -stacking energies strongly correlates with the experimentally-suggested solvent dependence of the triplet-state generation of these derivatives for five and more adsorbing solvent molecules. Following this finding, the excitation spectra of these derivatives in acetonitrile solvent are explored using the proprietary spin-flip long-range corrected time-dependent density functional theory. It is, consequently, confirmed that the pi -stacking activates the second lowest singlet excitation to trigger the spin-allowed transition to the singlet doubly-excited tetraradical (TT)_1 state, which generates the long-lived quintet (TT)_1 state causing the SF. However, it is also found that the pi -stacking also get a slow intersystem crossing active around the intersections of the lowest singlet excitations with the lowest triplet T_1 excitations in parallel with the SF due to the charge transfer characters of the lowest singlet excitations. These results suggest that SF initiates the triplet-state generations through near-degenerate low-lying singlet and (TT) excitations with a considerable singlet-triplet energy gap after the pi -stacking of chromophores stronger than but not far from the solvation. Since these derivatives are organic photosensitizers, this study proposes that SF should be taken into consideration in developing novel heavy atom-free organic photosensitizers, which will contribute to a variety of research fields such as medical care, photobiology, energy science, and synthetic chemistry.

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.

Solvent effects and charge transfer states in organic photovoltaics: a time-dependent density functional theory study on the PCPDTBT:PCBM low band gap system

Long-range corrected time-dependent density functional theory has been used to study the solvent effect on excited state properties of PCPDTBT:PCBM (Poly[2,6-(4,4-dimethyl-4H-cyclopenta[2,1-b:3,4-b′]-dithiophene)-alt-4,7-(2,1,3-benzothiadiazole)]:[6,6]-Phenyl-C61-butyric acid methyl ester) molecular system. A polarizable continuum model has been applied within the linear response (LR) and state-specific (SS) approaches to account for the dielectric environment. The results show that the influence of the solvent depends on the nature of the excitations. For neutral excitonic states that are essentially localized on a single molecule, the solvent has little or no effects on the excitation energies according to both solvent schemes. On the other hand, for states with a significant amount of charge transfer (CT), the SS approach predicts a sufficient decline in the excitation energy as the dielectric constant increases so that the CT state can be stabilized to the lowest excited state, whereas the LR counterpart shows almost no change. The comparison of two solvent approaches is discussed.

Exciton localization in excited-state dynamics of a tetracene trimer: a surface hopping LC-TDDFTB study.

Excitons in the molecular aggregates of chromophores are key participants in important processes such as photosynthesis or the functioning of organic photovoltaic devices. Therefore, the exploration of exciton dynamics is crucial. Here we report on exciton localization during excited-state dynamics of the recently synthesized tetracene trimer [Liu et al., Org. Lett., 2017, 19, 580]. We employ the surface hopping approach to nonadiabatic molecular dynamics in conjunction with the long-range corrected time-dependent density functional tight binding (LC-TDDFTB) method [Humeniuk and Mitrić, Comput. Phys. Commun., 2017, 221, 174]. Utilizing a set of descriptors based on the transition density matrix, we perform comprehensive analysis of exciton dynamics. The obtained results reveal an ultrafast exciton localization to a single tetracene unit of the trimer during excited-state dynamics, along with exciton transfer between units.

Optical Absorption Spectra and Electronic Properties of Symmetric and Asymmetric Squaraine Dyes for Use in DSSC Solar Cells: DFT and TD-DFT Studies.

The electronic absorption spectra, ground-state geometries and electronic structures of symmetric and asymmetric squaraine dyes (SQD1–SQD4) were investigated using density functional theory (DFT) and time-dependent (TD-DFT) density functional theory at the B3LYP/6-311++G** level. The calculated ground-state geometries reveal pronounced conjugation in these dyes. Long-range corrected time dependent density functionals Perdew, Burke and Ernzerhof (PBE, PBE1PBE (PBE0)), and the exchange functional of Tao, Perdew, Staroverov, and Scuseria (TPSSh) with 6-311++G** basis set were employed to examine optical absorption properties. In an extensive comparison between the optical data and DFT benchmark calculations, the BEP functional with 6-311++G** basis set was found to be the most appropriate in describing the electronic absorption spectra. The calculated energy values of lowest unoccupied molecular orbitals (LUMO) were 3.41, 3.19, 3.38 and 3.23 eV for SQD1, SQD2, SQD3, and SQD4, respectively. These values lie above the LUMO energy (−4.26 eV) of the conduction band of TiO2 nanoparticles indicating possible electron injection from the excited dyes to the conduction band of the TiO2 in dye-sensitized solar cells (DSSCs). Also, aromaticity computation for these dyes are in good agreement with the data obtained optically and geometrically with SQD4 as the highest aromatic structure. Based on the optimized molecular geometries, relative positions of the frontier orbitals, and the absorption maxima, we propose that these dyes are suitable components of photovoltaic DSSC devices.

Photodissociation spectrum and structure of Au4+·H2O clusters

The gold–water interaction is essential for a fundamental understanding of the coordination chemistry of gold as well as applied materials sciences. Here isolated Au4+ and Au4+·H2O clusters are characterized with electronic photodissociation spectroscopy and long-range corrected time-dependent density functional theory. Structural information of these clusters is obtained by comparing their photodissociation spectra with the optical absorption spectra calculated for low-energy isomers, which are found with a genetic algorithm coupled to electronic structure methods. For Au4+, the most stable structure is found to be a D2h rhomboid, while a remarkable contribution of the higher-energy Y-shaped C2v isomer is also observed in the experimental spectrum. For Au4+·H2O, the most stable Cs (2A′) structure is formed through an AuO bond of H2O to the Au4+ (D2h) structure with a binding energy of 1.15eV. The Au4+·H2O structure exhibits Cs instead of C2v symmetry, which suggests substantial covalent contributions to the bonding between H2O and Au4+. The natural bond orbital charge analysis shows that a net positive charge of about 0.1e is transferred to H2O. The long-range corrected CAM-B3LYP* (ω=0.33) functional has proven reliable in predicting optical spectra of Au4+ and Au4+·H2O clusters close to experimental observation.

Theoretical investigations of the perylene electronic structure: Monomer, dimers, and excimers

The structural and electronic properties of perylene molecule, dimers, and excimers have been computationally studied. The present work represents the first systematic study of perylene molecule and dimer forms by means of long-range corrected time-dependent density functional theory (TDDFT) approaches. Initially, the study explores the photophysical properties of the molecular species. Vertical transitions to many excited singlet states have been computed and rationalized with different exchange-correlation functionals. Differences between excitation energies are discussed and compared to the absorption spectrum of perylene in gas phase and diluted solution. De-excitation energy from the relaxed geometry of the lowest excited singlet is in good agreement with the experimental fluorescence emission. Optimization of several coplanar forms of the perylene pair prove that, contrary to generalized gradient approximation (GGA) and hybrid exchange-correlation functionals, corrected TDDFT is able to bind the perylene dimer in the ground state. Excitation energies from different dimer conformers point to dimer formation prior to photoexcitation. The fully relaxed excimer geometry belongs to the perfectly eclipsed conformation with D2h symmetry. The excimer equilibrium intermolecular distance is shorter than the separation found for the ground state, which is an indication of stronger interchromophore interaction in the excimer state. Excimer de-excitation energy is in rather good agreement with the excimer band of perylene in concentrated solution. The study also scans the energy profiles of the ground and lowest excited states along several geometrical distortions. The nature of the interactions responsible for the excimer stabilization is explored in terms of excitonic and charge resonance contributions. © 2015 Wiley Periodicals, Inc.

Comparison of LC-TDDFT and ADC(2) Methods in Computations of Bright and Charge Transfer States in Stacked Oligothiophenes.

Long-range corrected time-dependent density functional theory (LC-TDDFT) has been applied to compute singlet vertical electronic excitations of oligothiophene molecules and their dimers and compared with the algebraic diagrammatic construction method to second order [ADC(2)], a wave function-based polarization propagator method. The excitation energies obtained from both methods agree to each other excellently. In particular, energetics of charge transfer states is concertedly reproduced. The linear response (LR) and the state specific (SS) approaches have been evaluated to appraise solvent effect on excited states. Benchmarked by the reference wave function method, the necessity of the SS treatment is justified in the prediction of charge transfer (CT) states under the TDDFT framework.

Optical and electronic properties of mixed Ag-Au tetramer cations

We present experimental and theoretical studies of the optical response of mixed Ag(n)Au(+)(4-n) (n=1-3) clusters in the photon energy range ℏω = 1.9-3.5 eV. Absorption spectra are recorded by a newly built longitudinal molecular beam depletion spectroscopy apparatus providing lower limits to absolute photodissociation cross sections. The experimental data are compared to optical response calculations in the framework of long-range corrected time-dependent density functional theory with initial cluster geometries obtained by the unbiased Birmingham Cluster Genetic Algorithm coupled with density functional theory. Experiments and excited state calculations shed light on the structural and electronic properties of the mixed Ag-Au tetramer cations.

Diradical Character Based Design for Singlet Fission of Condensed-Ring Systems with 4nπ Electrons

By applying the diradical character based molecular design guideline for singlet fission (SF), we investigate the feasibility of efficient SF in condensed-ring π-conjugated molecules with 4nπ electrons (n = 4, 5, ...), i.e., antiaromatic polycyclic hydrocarbons composed of five- and six-membered rings. The multiple diradical character (yi), which takes a value between 0 (closed shell) and 1 (pure open shell), is defined as the occupation number of the lowest unoccupied natural orbital (LUNO) + i (i = 0, 1, ...) calculated using the approximately spin-projected spin-unrestricted Hartree–Fock method. The excitation energies are also evaluated using the tuned long-range corrected time-dependent density functional theory method with the Tamm–Dancoff approximation to examine the energy level matching conditions for SF: (i) 2E(T1) – E(S1) ∼ 0 or ≤ 0 and (ii) 2E(T1) – E(T2) < 0, where S1, T1 and T2 represent singlet first, triplet first, and triplet second excited states, respectively. It turns out that the ener...

Theoretical study of the excited‐state double proton transfer in the (3‐methyl‐7‐azaindole)‐(7‐azaindole) heterodimer

Excited-state double proton transfer (ESDPT) in the (3-methyl-7-azaindole)-(7-azaindole) heterodimer is theoretically investigated by the long-range corrected time-dependent density functional theory method and the complete-active-space second-order perturbation theory method. The calculated potential energy profiles exhibit a lower barrier for the concerted mechanism in the locally excited state than for the stepwise mechanism through the charge-transfer state. This result suggests that the ESDPT in the isolated heterodimer is likely to follow the former mechanism, as has been exhibited for the ESDPT in the homodimer of 7-azaindole.

Spin-orbit relativistic long-range corrected time-dependent density functional theory for investigating spin-forbidden transitions in photochemical reactions

A long-range corrected (LC) time-dependent density functional theory (TDDFT) incorporating relativistic effects with spin-orbit couplings is presented. The relativistic effects are based on the two-component zeroth-order regular approximation Hamiltonian. Before calculating the electronic excitations, we calculated the ionization potentials (IPs) of alkaline metal, alkaline-earth metal, group 12 transition metal, and rare gas atoms as the minus orbital (spinor) energies on the basis of Koopmans' theorem. We found that both long-range exchange and spin-orbit coupling effects are required to obtain Koopmans' IPs, i.e., the orbital (spinor) energies, quantitatively in DFT calculations even for first-row transition metals and systems containing large short-range exchange effects. We then calculated the valence excitations of group 12 transition metal atoms and the Rydberg excitations of rare gas atoms using spin-orbit relativistic LC-TDDFT. We found that the long-range exchange and spin-orbit coupling effects significantly contribute to the electronic spectra of even light atoms if the atoms have low-lying excitations between orbital spinors of quite different electron distributions.

Theoretical Investigations on the Photoinduced Phase Transition Mechanism of Tetrathiafulvalene-p-chloranil

The photoinduced phase transition (PIPT) mechanism of tetrathiafulvalene-p-chloranil (TTF-CA) molecular crystal was theoretically investigated using the long-range corrected time-dependent density functional theory (LC-TDDFT) combined with a local response dispersion (LRD) method, which enables us to quantitatively reproduce charge transfer (CT) excitations of van der Waals clusters. By calculating the excitation spectrum and potential energy surface, we found that the PIPT of TTF-CA crystal may proceed through the angle change of the molecular planes. We also found that the CT excitation of one TTF-CA pair helps other neighboring TTF-CA pairs to become excited. Consequently, we theoretically proposed the initial structural change in the neutral-to-ionic PIPT of TTF-CA crystal, which is consistent with experiments.

Exciton Dissociation at Thiophene/Fullerene Interfaces: The Electronic Structures and Quantum Dynamics

Exciton dissociation at donor–acceptor heterojunctions is one of the key processes that determine the energy conversion efficiency of organic solar cells. Here, we theoretically investigate the exciton dissociations at oligothiophene/C60 donor–acceptor heterojunctions by using the long-range corrected time-dependent density functional theory and quantum dynamics calculations. We analyze the absorption spectra, electronic structures in adiabatic and diabatic representations, vibronic coupling, and dynamics of the exciton dissociations. The coupling strength and relative energy between the exciton and charge transfer (CT) states depend sensitively on the donor–acceptor distance and the stacking structure, which in turn affects the absorption spectra and the dynamics of exciton dissociations. Our quantum dynamics calculations exhibit ultrafast exciton dissociations owing to the strong coupling between the exciton and CT states, as observed in the time-resolved spectroscopies of the donor–acceptor interfaces of conjugated polymers and fullerenes.

Concerted or Stepwise Mechanism? CASPT2 and LC-TDDFT Study of the Excited-State Double Proton Transfer in the 7-Azaindole Dimer.

Excited-state double proton transfer (ESDPT) in the 7-azaindole dimer is investigated using the complete active space second-order perturbation theory (CASPT2) method and the long-range corrected time-dependent density functional theory (LC-TDDFT) method. These methods are employed for geometry optimizations as well as single-point energy calculations of the excited-state potential energy profiles along the reaction paths. It is shown that three main reaction routes involving double proton transfer exist. In the first route, the ESDPT reaction takes place in the locally excited state through a single transition state following the concerted mechanism in which each proton-transfer process occurs simultaneously without forming any stable zwitterionic intermediate. The concerted ESDPT reaction is found to proceed asynchronously in Cs symmetry rather than synchronously in C2h symmetry. In the second and third routes, on the other hand, the ESDPT reaction takes place following the stepwise mechanism in which each proton-transfer process occurs sequentially forming a neutral intermediate in the charge-transfer state. The calculated energy profiles of the three routes exhibit a lower barrier in the first route than in the other routes, suggesting that the ESDPT in the gas phase is likely to follow the asynchronous concerted mechanism at the lowest excitation energy.

Long-range corrected time-dependent density functional study on fluorescence of 4,4′-dimethylaminobenzonitrile

Dual fluorescence of 4,4(')-dimethylaminobenzonitrile (DMABN) was theoretically investigated on the basis of long-range corrected time-dependent density functional theory. Excited-state geometry optimization states and single-point energy calculations with and without solvent effect were carried out. It has been explained that DMABN emits dual fluorescence only in polar solvents through locally excited (LE) and charge transfer (CT) states. It was, however, concluded from this study that although the main spectrum of dual fluorescence in acetonitrile solvent is clearly due to twisted intramolecular CT fluorescence, small secondary fluorescence in acetonitrile may also emanate from CT fluorescence during the DMABN twisting process. This conclusion is supported by an experimental interpretation on polarization spectroscopy. It was also found that the optimized DMABN geometries have certain wagging angles for the CT state and no wagging angle for the LE state. This may support an early experimental hypothesis that the dual fluorescence of DMABN is induced by the wagging mode due to vibronic coupling between LE and CT states. Consequently, the authors propose a fluorescence mechanism of DMABN in gas phase and in acetonitrile solvent: the main absorption proceeds to the CT state in both situations. In gas phase, single fluorescence is chiefly emitted from the LE state through the internal conversion from CT to LE states. Dual fluorescence in acetonitrile solvent may only be emitted from the CT state.

Excited state geometry optimizations by analytical energy gradient of long-range corrected time-dependent density functional theory

An analytical excitation energy gradient of long-range corrected time-dependent density functional theory (LC-TDDFT) is presented. This is based on a previous analytical TDDFT gradient formalism, which avoids solving the coupled-perturbed Kohn-Sham equation for each nuclear degree of freedom. In LC-TDDFT, exchange interactions are evaluated by combining the short-range part of a DFT exchange functional with the long-range part of the Hartree-Fock exchange integral. This LC-TDDFT gradient was first examined by calculating the excited state geometries and adiabatic excitation energies of small typical molecules and a small protonated Schiff base. As a result, we found that long-range interactions play a significant role even in valence excited states of small systems. This analytical LC-TDDFT gradient was also applied to the investigations of small twisted intramolecular charge transfer (TICT) systems. By comparing with calculated ab initio multireference perturbation theory and experimental results, we found that LC-TDDFT gave much more accurate absorption and fluorescence energies of these systems than those of conventional TDDFTs using pure and hybrid functionals. For optimized excited state geometries, LC-TDDFT provided fairly different twisting and wagging angles of these small TICT systems in comparison with conventional TDDFT results.