Evaluating the anharmonicity contributions to the molecular excited state internal conversion rates with finite temperature TD-DMRG

Quasi-intrinsic thiobase derivatives as potential targeted photosensitizers in two-photon photodynamic therapy

In this study, a set of potential quasi-intrinsic photosensitizers for two-photon photodynamic therapy (PDT) are proposed based on the unnatural 2-amino-8-(1'-β-ᴅ-2'-deoxyribofuranosyl)-imidazo[1,2-ɑ]-1,3,5-triazin-4(8H)-one (P), which is paired with the 6-amino-5-nitro-3-(1'-β-ᴅ-2'-deoxyribofuranosyl)-2(1H)-pyridone (Z) and can specifically recognize breast and liver cancer cells. Herein, the effects of sulfur substitution and electron-donating/electron-withdrawing groups on the photophysical properties in aqueous solution are systematically investigated. The one- and two-photon absorption spectra evidence that the modifications could result in red-shifted absorption wavelength and large two-photon absorption cross-section, which contributes to selective excitation and provides effective PDT for deep-seated tissues. To ensure the efficient triplet state population, the singlet-triplet energy gaps and spin-orbit coupling constants were examined, which is responsible for a rapid intersystem crossing rate. Furthermore, these thiobase derivatives are characterized by the long-lived T1 state and the large energy gap for radiationless transition to ensure the generation of cytotoxic singlet oxygen.

Encoding a Many-Body Potential Energy Surface into a Grid-Based Matrix Product Operator

An efficient algorithm for compressing a given many-body potential energy surface (PES) of molecular systems into a grid-based matrix product operator (MPO) is proposed. The PES is once represented by a full-dimensional or truncated many-body expansion form, which is obtained by ab initio calculations at each grid mesh point, and then all terms in the expansion are compressed and merged into a single MPO while maintaining the bond dimension of the MPO as small as possible. It was shown that the ab initio PES of the H2CO was compressed by more than 2 orders of magnitude in the size of the site operators without loss of accuracy. By the use of grid basis, the tensor rank of the site operators of the MPO is reduced from four to three due to the diagonal nature of the position-dependent operators on grid basis, which significantly reduces the computational cost of the tensor contractions required in the real and imaginary time evolution of the matrix product state (MPS) wave functions with the grid-based MPO (Grid-MPO) Hamiltonian. Similar to other grid-based methods, Grid-MPO is easily applicable to any kinds of potentials of molecular systems, such as analytical empirical model potentials expressed by position operators and ab initio potentials, if the values at the grid points are available. Using the Grid-MPO combined with the MPS, we calculated the time correlation function of the Eigen cation H 3 O + ( H 2 O ) 3 to predict the infrared spectrum and compared with the experimental and the previous theoretical studies. The actual scaling with the size of systems was examined for the multidimensional Henon-Heiles Hamiltonian. It was shown that the method is considerably accelerated by the graphic processing unit (GPU) because the sizes of site operators were kept small and all tensors were able to be stored on the VRAM of a GPU.

Finite-temperature vibronic spectra from the split-operator coherence thermofield dynamics

We present a numerically exact approach for evaluating vibrationally resolved electronic spectra at finite temperatures using the coherence thermofield dynamics. In this method, which avoids implementing an algorithm for solving the von Neumann equation for coherence, the thermal vibrational ensemble is first mapped to a pure-state wavepacket in an augmented space, and this wavepacket is then propagated by solving the standard, zero-temperature Schrödinger equation with the split-operator Fourier method. We show that the finite-temperature spectra obtained with the coherence thermofield dynamics in a Morse potential agree exactly with those computed by Boltzmann-averaging the spectra of individual vibrational levels. Because the split-operator thermofield dynamics on a full tensor-product grid is restricted to low-dimensional systems, we briefly discuss how the accessible dimensionality can be increased by various techniques developed for the zero-temperature split-operator Fourier method.

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.

Modeling the Fluorescence Quantum Yields of Aromatic Compounds: Benchmarking the Machinery to Compute Intersystem Crossing Rates

The from-first-principles calculation of fluorescence quantum yields (FQYs) and lifetimes of organic dyes remains very challenging. In this article, we extensively test the machinery to calculate FQYs. Specifically, we perform an extensive analysis on the parameters influencing the intersystem crossing (ISC), internal conversion (IC), and fluorescence rate constants calculations. The impact of (i) the electronic structure (chosen exchange-correlation functional and spin-orbit Hamiltonian), (ii) the vibronic parameters (coordinate system, broadening function, and dipole expansion), and (iii) the excited-state kinetic models are systematically assessed for a series of seven rigid aromatic molecules. Our studies provide more insights into the choice of parameters and the expected accuracy for the computational protocols aiming to deliver FQY values. Some challenges are highlighted, such as, on the one hand, the difficulty to benchmark against the experimental nonradiative rate constants, for which the separation between the IC and ISC contributions is often not provided in the literature and, on the other hand, the need to go beyond the harmonic approximation for the calculation of the IC rates.

Prediction of fluorescence quantum yields using the extended thawed Gaussian approximation

Spontaneous emission and internal conversion rates are calculated within harmonic approximations and compared to the results obtained within the semi-classical extended thawed Gaussian approximation (ETGA). This is the first application of the ETGA in the calculation of internal conversion and emission rates for real molecular systems, namely, formaldehyde, fluorobenzene, azulene, and a dicyano-squaraine dye. The viability of the models as black-box tools for prediction of spontaneous emission and internal conversion rates is assessed. All calculations were done using a consistent protocol in order to investigate how different methods perform without previous experimental knowledge using density functional theory (DFT) and time-dependent DFT (TD-DFT) with B3LYP, PBE0, ωB97XD, and CAM-B3LYP functionals. Contrasting the results with experimental data shows that there are further improvements required before theoretical predictions of emission and internal conversion rates can be used as reliable indicators for the photo-luminescence properties of molecules. We find that the ETGA performs rather similar to the vertical harmonical model. Including anharmonicities in the calculation of internal conversion rates has a moderate effect on the quantitative results in the studied systems. The emission rates are fairly stable with respect to computational parameters, but the internal conversion rate reveals itself to be highly dependent on the choice of the spectral line shape function, particularly the width of the Lorentzian function, associated with homogeneous broadening.

First-Principles Calculations of Excited-State Decay Rate Constants in Organic Fluorophores

In this Perspective, we discuss recent advances made to evaluate from first-principles the excited-state decay rate constants of organic fluorophores, focusing on the so-called static strategy. In this strategy, one essentially takes advantage of Fermi's golden rule (FGR) to evaluate rate constants at key points of the potential energy surfaces, a procedure that can be refined in a variety of ways. In this way, the radiative rate constant can be straightforwardly obtained by integrating the fluorescence line shape, itself determined from vibronic calculations. Likewise, FGR allows for a consistent calculation of the internal conversion (related to the non-adiabatic couplings) in the weak-coupling regime and intersystem crossing rates, therefore giving access to estimates of the emission yields when no complex photophysical phenomenon is at play. Beyond outlining the underlying theories, we summarize here the results of benchmarks performed for various types of rates, highlighting that both the quality of the vibronic calculations and the accuracy of the relative energies are crucial to reaching semiquantitative estimates. Finally, we illustrate the successes and challenges in determining the fluorescence quantum yields using a series of organic fluorophores.

Minimizing non-radiative decay in molecular aggregates through control of excitonic coupling

The widely known "Energy Gap Law" (EGL) predicts a monotonically exponential increase in the non-radiative decay rate (knr) as the energy gap narrows, which hinders the development of near-infrared (NIR) emissive molecular materials. Recently, several experiments proposed that the exciton delocalization in molecular aggregates could counteract EGL to facilitate NIR emission. In this work, the nearly exact time-dependent density matrix renormalization group (TD-DMRG) method is developed to evaluate the non-radiative decay rate for exciton-phonon coupled molecular aggregates. Systematical numerical simulations show, by increasing the excitonic coupling, knr will first decrease, then reach a minimum, and finally start to increase to follow EGL, which is an overall result of two opposite effects of a smaller energy gap and a smaller effective electron-phonon coupling. This anomalous non-monotonic behavior is found robust in a number of models, including dimer, one-dimensional chain, and two-dimensional square lattice. The optimal excitonic coupling strength that gives the minimum knr is about half of the monomer reorganization energy and is also influenced by system size, dimensionality, and temperature.

Overcoming the Limitation of Spin Statistics in Organic Light Emitting Diodes (OLEDs): Hot Exciton Mechanism and Its Characterization

Triplet harvesting processes are essential for enhancing efficiencies of fluorescent organic light-emitting diodes. Besides more conventional thermally activated delayed fluorescence and triplet-triplet annihilation, the hot exciton mechanism has been recently noticed because it helps reduce the efficiency roll-off and improve device stability. Hot exciton materials enable the conversion of triplet excitons to singlet ones via reverse inter-system crossing from high-lying triplet states and thereby the depopulation of long-lived triplet excitons that are prone to chemical and/or efficiency degradation. Although their anti-Kasha characteristics have not been clearly explained, numerous molecules with behaviors assigned to the hot exciton mechanism have been reported. Indeed, the related developments appear to have just passed the stage of infancy now, and there will likely be more roles that computational elucidations can play. With this perspective in mind, we review some selected experimental studies on the mechanism and the related designs and then on computational studies. On the computational side, we examine what has been found and what is still missing with regard to properly understanding this interesting mechanism. We further discuss potential future points of computational interests toward aiming for eventually presenting in silico design guides.

Theoretical characterization of two-photon fluorescent probes for nitric oxide detection: sensing mechanism, photophysical properties and protonation effects

Nitric oxide (NO) is an important signal molecule in biological systems and is correlated with many physiological processes and pathological diseases. To date, numerous fluorescent probes based on o-diamino aromatics have been designed and synthesized for NO detection utilizing the principle of photoinduced electron transfer (PET). However, the underlying PET mechanism has rarely been validated, and a systematic computational study on the photophysical properties is urgently desired. In this study, we used a theoretical protocol to comparatively investigate the sensing mechanism, photophysical properties and protonation effects of two emblematic probes NINO and PYSNO in aqueous solution, which combines a polarizable continuum model (PCM), time-dependent density functional theory (TD-DFT) and thermal vibration correlation function formalism (TVCF). Our findings reveal that the weak emission of NINO is due to activated PET with negative driving energy and blocked fluorescence with significant charge separation. In contrast, the poor luminescence of PYSNO is caused by the facilitated non-radiative dissipation, even though the fluorescence emission remains unobstructed. Although NINO has been successfully used in two-photon microscopy for detecting NO, we suggest that PYSNO possesses a superior two-photon absorption (TPA) cross section in the near-infrared region. The protonation effects suggest that both probes can function effectively in practical acidic lysosomal environments. Our study opens a new avenue for understanding the mechanism and predicting the properties of two-photon fluorescent probes for NO detection, thus aiding the rational design of efficient fluorescent sensors.

Excited-State THz Vibrations in Aggregates of PtII Complexes Contribute to the Enhancement of Near-Infrared Emission Efficiencies

The exploration of deactivation mechanisms for near-infrared(NIR)-emissive organic molecules has been a key issue in chemistry, materials science and molecular biology. In this study, based on transient absorption spectroscopy and transient grating photoluminescence spectroscopy, we demonstrate that the aggregated PtII complex 4H (efficient NIR emitter) exhibits collective out-of-plane motions with a frequency of 32 cm-1 (0.96 THz) in the excited states. Importantly, similar THz characteristics were also observed in analogous PtII complexes with prominent NIR emission efficiency. The conservation of THz motions enables excited-state deactivation to proceed along low-frequency vibrational coordinates, contributing to the suppression of nonradiative decay and remarkable NIR emission. These novel results highlight the significance of excited-state vibrations in nonradiative processes, which serve as a benchmark for improving device performance.

Photophysics of uracil: an explicit time-dependent generating function-based method combining both nonadiabatic and spin-orbit coupling effects

We present a composite framework for calculating the rates of non-radiative deactivation processes, namely internal conversion (IC) and intersystem crossing (ISC), on an equal footing by explicitly computing the non-adiabatic coupling (NAC) and spin-orbit coupling (SOC) constants, respectively. The stationary-state approach uses a time-dependent generating function based on Fermi's golden rule. We validate the applicability of the framework by computing the rate of IC for azulene, obtaining comparable rates to experimental and previous theoretical results. Next, we investigate the photophysics associated with the complex photodynamics of the uracil molecule. Interestingly, our simulated rates corroborate experimental observations. Detailed analyses using Duschinsky rotation matrices, displacement vectors and NAC matrix elements are presented to interpret the findings alongside testing the suitability of the approach for such molecular systems. The suitability of the Fermi's golden rule based method is explained qualitatively in terms of single-mode potential energy surfaces.

Internal conversion rates from the extended thawed Gaussian approximation: Theory and validation

The theoretical prediction of the rates of nonradiative processes in molecules is fundamental in assessing their emissive properties. In this context, global harmonic models have been widely used to simulate vibronic spectra as well as internal conversion rates and to predict photoluminescence quantum yields. However, these simplified models suffer from the limitations that are inherent to the harmonic approximation and can have a severe effect on the calculated internal conversion rates. Therefore, the development of more accurate semiclassical methods is highly desirable. Here, we introduce a procedure for the calculation of nonradiative rates in the framework of the time-dependent semi-classical Extended Thawed Gaussian Approximation (ETGA). We systematically investigate the performance of the ETGA method by comparing it to the adiabatic and vertical harmonic methods, which belong to the class of widely used global harmonic models. Its performance is tested in potentials that cannot be treated adequately by global harmonic models, beginning with Morse potentials of varying anharmonicity followed by a double well potential. The calculated radiative and nonradiative internal conversion rates are compared to reference values based on exact quantum dynamics. We find that the ETGA has the capability to predict internal conversion rates in anharmonic systems with an appreciable energy gap, whereas the global harmonic models prove to be insufficient.

Hybrid Quantum-Classical Boson Sampling Algorithm for Molecular Vibrationally Resolved Electronic Spectroscopy with Duschinsky Rotation and Anharmonicity

Using a photonic quantum computer for boson sampling has demonstrated a tremendous advantage over classical supercomputers. It is highly desirable to develop boson sampling algorithms for realistic scientific problems. In this work, we propose a hybrid quantum-classical sampling (HQCS) algorithm to calculate the optical spectrum for complex molecules considering Duschinsky rotation effects and anharmonicity. The classical sum-over-states method for this problem has a computational complexity that exponentially increases with system size. The HQCS algorithm creates an intermediate harmonic potential energy surface (PES) to bridge the initial and final PESs. The magnitude and sign of the overlap between the initial and the intermediate state are estimated by boson sampling and classical algorithms, respectively. The overlap between the intermediate and the final state is efficiently evaluated by classical algorithms. The feasibility of HQCS is demonstrated in calculations of the emission spectrum of a Morse model as well as the pyridine molecule.

Matrix Product State Formulation of the MCTDH Theory in Local Mode Representations for Anharmonic Potentials

The matrix product state formulation of the multiconfiguration time-dependent Hartree theory, MPS-MCTDH, reported previously [Kurashige, J. Chem. Phys. 2018, 19, 194114] is extended to realistic anharmonic potentials with n-mode representations beyond the linear vibronic coupling model. For realistic vibrational potentials, the local mode representation should give a more compact representation of the potentials, i.e., lowering the dimensionality of the entanglements, than the normal coordinates, and the MPS-MCTDH formulation should work more efficiently and maintain the accuracy with a small bond dimension of the MPS ansatz. In fact, it was confirmed that the use of the local coordinates made the interaction matrices diagonal dominant and the number of terms in the n-body expansion of the potentials was significantly reduced. The method was applied to the IR spectrum of the CH₂O molecule, the zero-point energies, and the vibrational energy redistribution dynamics of polyenes C_2nH_2n+2. The results showed that the efficiency of the MPS-MCTDH method is significantly accelerated by the use of local coordinates even if the long-range interactions are included in the potential.

Theoretical insights into the central “acceptor” bridge function on the whole visible light and near-infrared emission in tetraphenylpyrazine-based luminogens

The whole visible light and near-infrared emission can be realized via modification of the central bridges in TPP-based luminogens.