Internal Conversion Rate Research Articles

Interacting Emission Species among Donor and Acceptor Moieties in a Donor-Grafted Polymer Host/TADF-Guest System and Their Effects on Photoluminescence and Electroluminescence.

Thermally activated delayed fluorescence (TADF)-based electroluminescence (EL) devices adopting a host/guest strategy in their emitting layer (EML) are capable of realizing high efficiency. However, TADF emitters composed of donor and acceptor moieties as guests dispersed in organic host materials containing a donor and/or an acceptor are subject to donor-acceptor (D-A) interactions. In addition, electron delocalization between neighboring emitter molecules could form different species of aggregates. Here, we investigate the effects of intermolecular interacting emission species on the optoelectronic properties of sky-blue/green/red (sB/G/R) TADF emitters as guests using poly(biphenyl-Si/Ge) grafted with various donor moieties as hosts. We found the presence of guest/guest exciplex (Dg/Ag)*, host/guest exciplexes (Dh/Ag)*, and aggregates through the exploration of interactions between neighboring TADF guest molecules and between host and TADF-guest molecules. The nonradiative 3(Dh/Ag)* (ΔEST ≈ 0.5 eV) could increase the internal conversion rate (kIC) and reduce delayed luminescence, and both of them could cause a decrease in PLQY. The luminescence of 3(Dh/Ag)* may have a positive or negative effect on PLQY depending on its triplet energy. As the singlet and triplet energies of (aggregate)* are lower than those of (ICT)*, energy transfer from (ICT)* to (aggregate)* could occur. The low PLQY nature of (aggregate)* means that it is more likely to cause quenching in device emission. The emissions from (Dh/Ag)* and (aggregate)* are found to have increased full width at half-maximum and lead to lower emission color purity. Such intermolecular interactions should also occur in host/guest (TADF) systems and nondoped TADF emitter systems and thus are important factors for the molecular design of the TADF emitter and/or its accompanying host for high device efficiency and emission color purity.

Effect of N Atom Substitution on Electronic Resonances: A 2D Photoelectron Spectroscopic and Computational Study of Anthracene, Acridine, and Phenazine Anions.

The accommodation of an excess electron by polycyclic aromatic hydrocarbons (PAHs) has important chemical and technological implications ranging from molecular electronics to charge balance in interstellar molecular clouds. Here, we use two-dimensional photoelectron spectroscopy and equation-of-motion coupled-cluster calculations of the radical anions of acridine (C13H9N-) and phenazine (C12H8N2-) and compare our results for these species to those for the anthracene anion (C14H10-). The calculations predict the observed resonances and additionally find low-energy two-particle-one-hole states, which are not immediately apparent in the spectra, and offer a slightly revised interpretation of the resonances in anthracene. The study of acridine and phenazine allows us to understand how N atom substitution affects electron accommodation. While the electron affinity associated with the ground state anion undergoes a sizable increase with the successive substitution of N atoms, the two lowest energy excited anion states are not affected significantly by the substitution. The net result is that there is an increase in the energy gap between the two lowest energy resonances and the bound ground electronic state of the radical anion from anthracene to acridine to phenazine. Based on an energy gap law for the rate of internal conversion, this increased gap makes ground state formation progressively less likely, as evidenced by the photoelectron spectra.

Synthesis, Photophysical and Electronic Properties of a D-π-A Julolidine-Like Pyrenyl-o-Carborane.

We synthesized 2-(1-1,2-dicarbadodecaboranyl(12))-6,6,12,12-tetramethyl-7,8,11,12-tetrahydro-6H,10H-phenaleno[1,9-fg]pyrido[3,2,1-ij]quinoline (4), a julolidine-like pyrenyl-o-carborane, with pyrene substituted at the 2,7-positions on the HOMO/LUMO nodal plane. Using solid state molecular structures, photophysical data, cyclic voltammetry, DFT and LR-TDDFT calculations, we compare o-carborane and B(Mes)2 (Mes=2,4,6-Me3C6H2) as acceptor groups. Whereas the π-acceptor strength of B(Mes)2 is sufficient to drop the pyrene LUMO+1 below the LUMO, the carborane does not do this. We confirm the π-donor strength of the julolidine-like moiety, however, which raises the pyrene HOMO-1 above the HOMO. In contrast to the analogous pyrene-2-yl-o-carborane, 2-(1-1,2-dicarbadodecaboranyl(12))-pyrene VI, which exhibits dual fluorescence, because the rate of internal conversion between locally-excited (LE) and charge transfer (CT) (from the pyrene to the carborane) states is faster than the radiative decay rate, leading to a thermodynamic equilibrium between the 2 states, 4 shows only single fluorescence, as the CT state involving the carborane as the acceptor moiety in not kinetically accessible, so a more localized CT emission involving the julolidine-like pyrene moiety is observed.

The rates of non-adiabatic processes in large molecular systems: Toward an effective full-dimensional quantum mechanical approach.

Two computational approaches for computing the rates of internal conversions in molecular systems where a large set of nuclear degrees of freedom plays a role are discussed and compared. One approach is based on the numerical solution of the time-dependent Schrödinger equation and allows us to include almost the whole set of vibrational coordinates, thanks to the employment of effective procedures for selecting those elements of the Hilbert space which play a significant role in dynamics. The other approach, based on the time-dependent perturbation theory and limited to the use of the harmonic approximation, allows us to include the whole Hilbert space spanned by the vibrational states of the system. The two approaches are applied to the photophysics of azulene, whose anti-Kasha behavior caused by anomalous internal conversion rates is well assessed. The calculated rates for the decays of the first two excited singlet states are in very good agreement with experimental data, indicating the reliability of both methodologies.

Fast calculation of internal conversion rate constant using the time-dependent formalism

A new method for calculating the internal conversion rate constant, which takes into account all possible vibrational transitions between two adiabatic electronic states, is proposed. The simple analytical form of the correlation function obtained in the harmonic and anharmonic approximations and taking into account the Franck-Condon term makes it possible to perform fast calculations. In addition, the method takes into account temperature effects within harmonic kind, which extends its area of application to explain experimental processes. The approach has been applied to the study of molecules important for organic electronics, such as tetraoxa[8]circulene, free-base porphyrin and poly[n]fluorenes. The method provides valuable information on IC processes and facilitates the design of efficient molecular systems.

Efficient near-infrared emission benefits from slowing down the internal conversion process.

Organic deep-red (DR) and near-infrared (NIR) emitters with high photoluminescence quantum yield (PLQY) are rare due to the strong non-radiative (knr) decay. Here, we report two DR/NIR emitters with high PLQY, TPANZPyPI and TPANZ3PI. Interestingly, the TPANZPyPI film exhibits 46.5% PLQY at 699 nm. Theoretical calculations indicate that TPANZPyPI can achieve this high PLQY in the near-infrared emission region due to its small S1 to S0 internal conversion (IC) rate. Meanwhile, research has found that, compared to TPANZ3PI, TPANZPyPI with a more rigid structure can effectively suppress the T2 to T1 IC process, which is conducive to higher exciton utilization efficiency (EUE). TPANZPyPI's non-doped OLED shows NIR emission with 4.6% @ 684 nm maximum external quantum efficiency (EQEmax). Its doped OLEDs radiate DR with an EQEmax of 6.9% @ 666 nm. These EQEs are among the highest values for hybridized local charge transfer state materials emitting more than 640 nm. This work demonstrates for the first time, based on a combination of theory and experiment, that increasing the molecular rigidity can inhibit the excited state IC process in addition to the S1 to S0 IC, realizing efficient electroluminescence.

Insight into magnetically induced ring currents and photophysics of six-porphyrin nanorings.

The series of nanorings based on Zn-porphyrins and tetraoxa-isophlorins in different oxidation states (Q = 0, 2+, 4+, 6+) have been studied studied computationally at density functional theory level (DFT) using BHandHLYP functional combined with def2-SVP basis sets. Magnetically induced ring currents of nanorings have been calculated using the GIMIC method and the Ampère-Maxwell integration scheme. Ring current calculations show that neutral nanorings sustain equal diatropic and paratropic currents of 8 nA T-1, resulting in zero net ring current strengths. The charged nanorings sustain strong ring currents with tropicity depending on the oxidation state Q. Among the considered nanorings, the nanoring composed of 6 isophlorins c-Iso66+ is the most aromatic with a ring current of IGIMIC = 81.6 nA T-1. The structure c-P62+ with a ring current of IGIMIC = 54.9 nA T-1 can be considered as the most aromatic among the synthesized porphyrin nanorings. Spin-orbit coupling matrix elements, oscillator strengths, and excitation energies calculated at the CAM-B3LYP/def2-SVP level of theory were used to estimate rate constants for radiative and nonradiative processes. The algorithm based on X-H approximation were used to calculate the internal conversion rates (kIC). The main channel for the deactivation of the excitation energy in the studied nanorings is the process of internal conversion. The deactivation of excited energy occurs due to the vibrations of certain groups of C-H bonds in the nanorings. The nanoring c-Iso6 has magnetically allowed low-lying transitions that contributes significantly to the paratropic ring current, resulting in strong local antiaromaticity in the tetraoxa-isophlorin units.

Pressure effects on both fluorescent emission and charge transport properties of organic semiconductors: a computational study.

External pressure can regulate the photophysical property and charge transport performance of organic semiconductors, however, the underlying mechanism at the microscopic level is still elusive. Using thermal vibrational correlation function coupled quantum mechanics/molecular mechanics and full quantum charge transfer rate theory, we systematically explore the influence of pressure on fluorescence emission and charge transport behaviours of representative cyclooctatetrathiophene (COTh). It is found that, upon pressurization, the intramolecular configurations of COTh became more twisted, leading to the blue-shifted emission. The fluorescence quantum efficiency (FQE) of COTh crystals decreases monotonically in a wide pressure range of 0-4.38 GPa, because the increase of intermolecular electronic energy transfer rate constant (keet) is larger than the decrease of internal conversion rate constant (kic), and the variation of keet is dominant. The decrease in kic is attributed to the decreasing reorganization energy, reflecting the suppression of the low-frequency flipping vibrations of four thiophene rings and the high-frequency stretching vibrations of central cyclooctatetraene, while the keet increase is due to the simultaneous increase in exciton coupling and spectra overlap. Moreover, we predicted that the hole mobility of COTh increases monotonically by nearly an order of magnitude from 0.39 to 3.00 cm2 V-1 s-1 upon compression, because of the increase in transfer integral and the decrease of charged reorganization energy. Furthermore, its hole mobility exhibits obvious anisotropy. Our work systematically builds the external pressure, molecular packing, luminescence and transport properties relationships of organic semiconductors and provides theoretical guidance for the rational design of pressure responsive organic semiconductors with excellent photoelectric performance.

Deciphering the doublet luminescence mechanism in neutral organic radicals: spin-exchange coupling, reversed-quartet mechanism, excited-state dynamics.

Neutral organic radical molecules have recently attracted considerable attention as promising luminescent and quantum-information materials. However, the presence of a radical often shortens their excited-state lifetime and results in fluorescence quenching due to enhanced intersystem crossing (EISC). Recently, an experimental report introduced an efficient luminescent radical molecule, tris(2,4,6-trichlorophenyl)methyl-carbazole-anthracene (TTM-1Cz-An). In this study, we systematically performed quantum theoretical calculations combined with the path integral approach to quantitatively calculate the excited-state dynamics processes and spectral characteristics. Our theoretical findings suggest that the sing-doublet D1 state, originating from the anthracene excited singlet state, is quickly converted to the doublet (trip-doublet) state via EISC, facilitated by a significant nonequivalence exchange interaction, with ΔJ ST = 0.174 cm-1. The formation of the quartet state (Q1, trip-quartet) was predominantly dependent on the exchange coupling 3/2J TR = 0.086 cm-1 between the triplet spin electrons of anthracene and the TTM-1Cz radical. Direct spin-orbit coupling ISC to the Q1 state was minimal due to the nearly identical spatial wavefunctions of the and Q1 levels. The effective occurrence of reverse intersystem crossing (RISC) from the Q1 to D1 state is a critical step in controlling the luminescence of TTM-1Cz-An. The calculated RISC rate k RISC, including the Herzberg-Teller effect, was 3.64 × 105 s-1 at 298 K, significantly exceeding the phosphorescence and nonradiative rates of the Q1 state, thus enabling the D1 repopulation. Subsequently, a strong electronic coupling of 37.4 meV was observed between the D1 and D2 states, along with a dense manifold of doublet states near the D1 state energy, resulting in a larger reverse internal conversion rate k RIC of 9.26 × 1010 s-1. Distributed to the D2 state, the obtained emission rate of k f = 2.98-3.18 × 107 s-1 was in quite good agreement with the experimental value of 1.28 × 107 s-1, and its temperature effect was not remarkable. Our study not only provides strong support for the experimental findings but also offers valuable insights for the molecular design of high-efficiency radical emitters.

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.

Enhancing near-infrared II photodynamic therapy with nitric oxide for eradicating multidrug-resistant biofilms in deep tissues

Nitric oxide (NO) enhanced photodynamic therapy (PDT) is a promising approach to overcome drug tolerance and resistance to biofilm but is limited by its short excitation wavelengths and low yield of reactive oxygen species (ROS). Herein, we develop a compelling degradable polymer-based near-infrared II (NIR-II, 1000–1700 nm) photosensitizer (PNIR-II), which can maintain 50 % PDT efficacy even under a 2.6 cm tissue barrier. Remarkably, PNIR-II is synthesized by alternately connecting the electron donor thiophene to the electron acceptors diketopyrrolopyrrole (DPP) and boron dipyrromethene (BODIPY), where the intramolecular charge transfer properties can be tuned to increase the intersystem crossover rate and decrease the internal conversion rate, thereby stabilizing the NIR-II photodynamic rather than photothermal effect. For exerting a combination therapy to eradicate multidrug-resistant biofilms, PNIR-II is further assembled into nanoparticles (NPs) with a synthetic glutathione-triggered NO donor polymer. Under 1064 nm laser radiation, NPs precisely release ROS and NO that triggered by over-expressed GSH in the biofilm microenvironment, thereby forming more bactericidal reactive nitrogen species (RNS) in vitro and in vivo in the mice model that orderly destroy biofilm of multidrug-resistant Staphylococcus aureus cultures from clinical patients. It thus provides a new outlook for destroy the biofilm of deep tissues.

When do tripdoublet states fluoresce? A theoretical study of copper(II) porphyrin.

Open-shell molecules rarely fluoresce, due to their typically faster non-radiative relaxation rates compared to closed-shell ones. Even rarer is the fluorescence from states that have two more unpaired electrons than the open-shell ground state, since they involve excitations from closed-shell orbitals to vacant-shell orbitals, which are typically higher in energy compared to excitations from or out of open-shell orbitals. States that are dominated by the former type of excitations are known as tripdoublet states when they can be described as a triplet excitation antiferromagnetically coupled to a doublet state, and their description by unrestricted single-reference methods (e.g., U-TDDFT) is notoriously inaccurate due to large spin contamination. In this work, we applied our spin-adapted TDDFT method, X-TDDFT, and the efficient and accurate static-dynamic-static second order perturbation theory (SDSPT2), to the study of the excited states as well as their relaxation pathways of copper(II) porphyrin; previous experimental works suggested that the photoluminescence of some substituted copper(II) porphyrins originate from a tripdoublet state, formed by a triplet ligand π → π* excitation antiferromagnetically coupled with the unpaired d electron. Our results demonstrated favorable agreement between the X-TDDFT, SDSPT2 and experimental excitation energies, and revealed noticeable improvements of X-TDDFT compared to U-TDDFT, not only for vertical excitation energies but also for adiabatic energy differences. These suggest that X-TDDFT is a reliable tool for the study of tripdoublet state fluorescence. Intriguingly, we showed that the aforementioned tripdoublet state is only slightly above the lowest doublet excited state and lies only slightly higher than the lowest quartet state, which suggests that the tripdoublet of copper(II) porphyrin is long-lived enough to fluoresce due to a lack of efficient non-radiative relaxation pathways; an explanation for this unusual state ordering is given. Indeed, thermal vibration correlation function (TVCF)-based calculations of internal conversion, intersystem crossing, and radiative transition rates confirm that copper(II) porphyrin emits thermally activated delayed fluorescence (TADF) and a small amount of phosphorescence at low temperature (83K), in accordance with experiment. The present contribution is concluded by a few possible approaches of designing new molecules that fluoresce from tripdoublet states.

Effect of choosing coordinate systems on computationally predicting nonradiative transition rates of flexible thermally activated delayed fluorescence molecules

AbstractUnderstanding nonradiative transition mechanisms is important in various situations. However, compared with radiative processes where temporal profiles of photon emission can be monitored in a straightforward manner, experimentally accessing the rate information may not be an easy task with nonradiative transitions. Hence, applying theoretical tools toward predicting the rates can be a useful tactic. Such predictions become very useful in designing optoelectronic materials as in the molecules adopted for constructing organic light‐emitting diodes (OLEDs). The correlation function formalism is a method that can fulfill the purpose of designing OLED materials. The formalism requires information regarding the vibrational normal modes of the two electronic states before and after the transition. Because the method is also based on harmonic oscillator approximation, it can actually fail to provide high reliability when there is a large geometric distortion between the initial and the final states. In fact, the harmonic normal mode picture is more prone to lose reliability in the Cartesian coordinates than in the internal ones even at a small distortion, and hence adopting internal coordinates may be more preferable for practical calculations. This is because normal mode mixing becomes less severe when molecular coordinates are described with internal degrees of freedom such as bond stretching, bending, and torsion. In this regard, how much more reliable the nonradiative rate predictions in OLED materials become with the use of internal coordinate system deserves a close inspection. In this account, we review on the derivation of the correlation function formalism and provide how it can be adapted toward the use of the internal coordinates. As a demonstration, we evaluate the intersystem crossing and the internal conversion rates of a series of thermally activated delayed fluorescence (TADF) molecules with both Cartesian and internal coordinate systems. Overall, handling transitions involving substantial structural changes is improved indeed with the internal coordinates. However, limitations are still apparent for the TADF systems with a flexible donor–acceptor type construct especially when the inevitable inter‐domain twisting takes place with the electronic transition. Future prospect for handling the issue is commented as a concluding remark.

Dynamic Role of the Intramolecular Hydrogen Bonding in the S1 State Relaxation Dynamics Revealed by the Direct Measurement of the Mode-Dependent Internal Conversion Rate of 2-Chlorophenol and 2-Chlorothiophenol.

The dynamic role of the intramolecular hydrogen bond in the S1 relaxation of cis-2-chlorophenol (2-CP) or cis-2-chlorothiophenol (2-CTP) has been investigated in a state-specific manner. Whereas ultrafast internal conversion is dominant for 2-CP, the H-tunneling competes with internal conversion for 2-CTP even at the S1 origin. The S0-S1 internal conversion rate of 2-CTP could be directly measured from the S1 lifetimes of 2-CTP-d1 (Cl-C6H4-SD) as the D-tunneling is kinetically blocked, allowing distinct estimations of tunneling and internal conversion rates with increasing the energy. The internal conversion rate of 2-CTP increases by two times at the out-of-plane torsional mode excitation, suggesting that the internal conversion is facilitated at the nonplanar geometry. It then sharply increases at ∼600 cm-1, indicating that the S1/S0 conical intersection is readily accessible at the extended C-Cl bond length. The strength of the intramolecular hydrogen bond should be responsible for the distinct dynamic behaviors of 2-CP and 2-CTP.

Fluorescent Mechanism of a Highly Selective Probe for Copper(II) Detection: A Theoretical Study.

A highly selective probe for copper(II) detection based on the dansyl group was theoretically studied by means of (time-dependent) density functional theory. The calculated results indicated that the oscillator strength of the fluorescent process for the probe molecule is considerably large, but the counterpart of its copper(II) complex is nearly zero; therefore, the predicted radiative rate kr of the probe is several orders of magnitude larger than that of its complex; however, the predicted internal conversion rate kic of both the probe and its complex is of the same order of magnitude. In addition, the simulated intersystem crossing rate kisc of the complex is much greater than that of the probe due to the effect of heavy atom from the copper atom in the complex. Based on the above information, the calculated fluorescence quantum yield of the probe is 0.16% and that of the complex becomes 10-6%, which implies that the first excited state of the probe is bright state and that of the complex is dark state. For the complex, the hole-electron pair analysis indicates that the process of S0 → S1 belongs to metal-to-ligand charge transfer; its density-of-state diagram visually illustrates that the highest occupied molecular orbital (HOMO) contains the ingredient of the s orbital from the copper atom, which decreases the frontier orbital energy level and the overlap integral of HOMO and LUMO.

Calculation of Excited State Internal Conversion Rate Constant Using the One-Effective Mode Marcus-Jortner-Levich Theory.

In this article, the one-effective mode Marcus-Jortner-Levich (MJL) theory and the classical Marcus theory for electron transfer were applied to estimate the internal conversion rate constant, kIC, of organic molecules and a Ru-based complex, all belonging to the Marcus inverted region. For this, the reorganization energy was calculated using the minimum energy conical intersection point to account for more vibrational levels, correcting the density of states. The results showed good agreement with experimental and theoretically determined kIC, with a small overestimation by the Marcus theory. Also, molecules less dependent on the solvent effects, like benzophenone, presented better results than molecules with an expressive dependence, like 1-aminonaphthalene. Moreover, the results suggest that each molecule possesses unique normal modes leading to the excited state deactivation that does not necessarily match the X-H bond stretching, as previously suggested.

Study of the Modal Evolution of the Causal Relationship between Crude Oil, Gold, and Dollar Price Series

The rise and fall of crude oil prices, gold prices, and US dollar exchange rates is of great significance to investors. It is necessary to explore the evolution characteristics of the causal relationship between crude oil, gold, and US dollar, so as to provide reference for investors. We selected the ICE Brent crude oil continuous futures, the ICE WTI crude oil continuous futures, the NYMEX light crude oil continuous futures, the COMEX gold continuous futures, and the US dollar index as the research objects. Based on the theory of pattern causality, the causal relationship between crude oil, gold, and US dollar is divided into positive causal relationship (T), negative causal relationship (F), and disordered causal relationship (D). The causal modal evolution network of crude oil and gold prices against the US dollar index (BWCGG-U) and the causal relationship modal evolution network of the US dollar index on the price of crude oil and gold (U-BWCGG) were constructed. Complex network and sliding window are used to study the evolution characteristics of short-term causality between crude oil and gold and US dollar in 60 days. The results show that (1) the modes of causality between crude oil, gold, and the US dollar index are constantly changing, with a few key modes. The key modes are often transmitted to themselves. (2) The most critical modes of two networks are all FFFF, and the negative causality between gold and the US dollar index is more stable. Investors based on the gold (dollar index) price to judge the dollar index (gold futures) investment program are more reliable. (3) When crude oil and gold show causal modes of FFFF and DDDF, respectively, the emergence and transformation of the modes can be maintained for a period of time to provide a certain guarantee for investors’ investment. However, its internal conversion rate is high, which needs to be judged in combination with the actual situation to improve the forecasting ability.

A simplified Bixon–Jortner–Plotnikov method for fast calculation of radiationless transfer rates in symmetric molecules

A simplified form of the Bixon–Jortner–Plotnikov (BJP) method is derived for calculation of internal conversion (IC) rate in a symmetrical molecule. The rate is a sum of contributions from individual transitions between vibronic states. For each transition, vibrational modes are divided into two groups, the promoting (one or two modes per electronic transition) and the surrounding ones. In the case of the non-totally symmetric transition in a symmetric molecule, the overwhelming majority of transitions do not contribute to the overall rate. Moreover, the promoting and surrounding modes belong to different symmetry representations and can be separated. It is proposed to deal with the promoting modes directly, while approximating the effect of the surrounding modes by a Pekarian function. The method was tested on polyacenes and it was shown that the calculated IC rates are in agreement with the experimental ones. The simplified method can be applied for calculating the rates of non-totally symmetric transition in a symmetric molecule, if its point symmetry group does not change after transition.

Analytical derivative couplings within the framework of time-dependent density functional theory coupled with conductor-like polarizable continuum model: Formalism, implementation, and applications.

The nonadiabatic phenomena, which are characterized by a strong coupling between electronic and nuclear motions, are ubiquitous. The nonadiabatic effect of the studied system can be significantly affected by the surrounding environment, such as solvents, in which such nonadiabatic process takes place. It is essential to develop the theoretical models to simulate these processes while accurately modeling the solvent environment. The time-dependent density functional theory (TDDFT) is currently the most efficient approach to describe the electronic structures and dynamics of complex systems, while the polarizable continuum model (PCM) represents one of the most successful examples among continuum solvation models. Here, we formulate the first-order derivative couplings (DCs) between the ground and excited states as well as between two excited states by utilizing time-independent equation of motion formalism within the framework of both linear response and spin flip formulations of TDDFT/CPCM (the conductor-like PCM), and implement the analytical DCs into the Q-CHEM electronic structure software package. The analytic implementation is validated by the comparison of the analytical and finite-difference results, and reproducing geometric phase effect in the protonated formaldimine test case. Taking 4-(N,N-dimethylamino)benzonitrile and uracil in the gas phase and solution as an example, we demonstrate that the solvent effect is essential not only for the excitation energies of the low-lying excited-states but also for the DCs between these states. Finally, we calculate the internal conversion rate of benzophenone in a solvent with DC being used. The current implementation of analytical DCs together with the existing analytical gradient and Hessian of TDDFT/PCM excited states allows one to study the nonadiabatic effects of relatively large systems in solutions with low computational cost.

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.