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

Nonadiabatic Derivative Couplings through Multiple Franck-Condon Modes Dictate the Energy Gap Law for Near and Short-Wave Infrared Dye Molecules

Near infrared (NIR, 700-1000 nm) and short-wave infrared (SWIR, 1000-2000 nm) dye molecules exhibit significant nonradiative decay rates from the first singlet excited state to the ground state. While these trends can be empirically explained by a simple energy gap law, detailed mechanisms of nearly universal behavior have remained unsettled for many cases. Theoretical and experimental results for two representative NIR/SWIR dye molecules reported here clarify the key mechanism for the observed energy gap law behavior. It is shown that the first derivative nonadiabatic coupling terms serve as major coupling pathways for nonadiabatic decay processes from the first excited singlet state to the ground state for these NIR and SWIR dye molecules and that vibrational modes other than the highest frequency modes also make significant contributions to the rate. This assessment is corroborated by further theoretical comparison with possible alternative mechanisms of intersystem crossing to triplet states and also by comparison with experimental data for deuterated molecules.

Enhancing Fluorescence in Both Solution and Solid States Induced by Imine Cage Formation

Developing luminescent materials that exhibit strong emissions in both solution and solid phases is highly desirable and challenging. Herein, we report imine-bond directed formation of a rigid organic cage (TPE-cage) that was synthesized by [2+4] imine condensation of a TPE-cored tetra-aldehyde (TPE-TA) with a clip-like diamine (XA) to illustrate confinement-induced fluorescence enhancement. Compared to the non-emissive TPE-TA (ϕF =0.26 %) in the dichloromethane (DCM) solution, the TPE-cage achieved a remarkable (~520-fold) emission enhancement (ϕF =70.38 %). In contrast, a monomeric tetra-imine model compound (TPE-model) showed only a minor enhancement (ϕF =0.56 %) in emission compared to the parent tetra-aldehyde TPE-TA. The emission of TPE-cage was further enhanced by ~1.5-fold (ϕF =80.96 %) in the aggregated state owing to aggregation-induced emission enhancement (AIEE). This approach establishes the potential for synthesizing luminescent materials with high emission in both solution and solid-state by employing a single-step imine condensation reaction.

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.

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.

Conical Intersection in Chemiluminescence of Cyclic Peroxides

Chemiluminescence (CL) utilizing chemiexcitation for energy transformation is one of the most highly sensitive and useful analytical techniques. The chemiexcitation is a chemical process of a ground-state reactant producing an excited-state product, in which a nonadiabatic event is facilitated by conical intersections (CIs), the specific molecular geometries where electronic states are degenerated. Cyclic peroxides, especially 1,2-dioxetane/dioxetanone derivatives, are the iconic chemiluminescent substances. In this Perspective, we concentrated on the CIs in the CL of cyclic peroxides. We first present a computational overview on the role of CIs between the ground (S₀) state and the lowest singlet excited (S₁) state in the thermolysis of cyclic peroxides. Subsequently, we discuss the role of the S₀/S₁ CI in the CL efficiency and point out misunderstandings in some theoretical studies on the singlet chemiexcitations of cyclic peroxides. Finally, we address the challenges and future prospects in theoretically calculating S₀/S₁ CIs and simulating the dynamics and chemiexcitation efficiency in the CL of cyclic peroxides.

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.

Through-Space Interaction of Tetraphenylethylene: What, Where, and How

Electronic conjugation through covalent bonds is generally considered as the basis for the electronic transition of organic luminescent materials. Tetraphenylethylene (TPE), an efficient fluorophore with aggregation-induced emission character, fluoresces blue emission in the aggregate state, and such photoluminescence is always ascribed to the through-bond conjugation (TBC) among the four phenyl rings and the central C═C bond. However, in this work, systematic spectroscopic studies and DFT theoretical simulation reveal that the intramolecular through-space interaction (TSI) between two vicinal phenyl rings generates the bright blue emission in TPE but not the TBC effect. Furthermore, the evaluation of excited-state decay dynamics suggests the significance of photoinduced isomerization in the nonradiative decay of TPE in the solution state. More importantly, different from the traditional qualitative description for TSI, the quantitative elucidation of the TSI is realized through the atoms-in-molecules analysis; meanwhile, a theoretical solid-state model for TPE and other multirotor systems for studying the electronic configuration is preliminarily established. The mechanistic model of TSI delineated in this work provides a new strategy to design luminescent materials beyond the traditional theory of TBC and expands the quantum understanding of molecular behavior to the aggregate level.

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

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