Theory and Calculation of the Phosphorescence Phenomenon

Photooxidation-Driven Purely Organic Room-Temperature Phosphorescent Lysosome-Targeted Imaging

The construction of host-guest-binding-induced phosphorescent supramolecular assemblies has become one of increasingly significant topics in biomaterial research. Herein, we demonstrate that the cucurbit[8]uril host can induce the anthracene-conjugated bromophenylpyridinium guest to form a linear supramolecular assembly, thus facilitating the enhancement of red fluorescence emission by the host-stabilized charge-transfer interactions. When the anthryl group is photo-oxidized to anthraquinone, the obtained linear nanoconstructs can be readily converted into the homoternary inclusion complex, accompanied by the emergence of strong green phosphorescence in aqueous solution. More intriguingly, dual organelle-targeted imaging abilities have been also distinctively achieved in nuclei and lysosomes after undergoing photochemical reaction upon UV irradiation. This photooxidation-driven purely organic room-temperature phosphorescence provides a convenient and feasible strategy for supramolecular organelle identification to track specific biospecies and physiological events in the living cells.

Quantum Dots Based Fluorescent Probe for the Selective Detection of Heavy Metal Ions

Heavy metal ions are one of the primary causes of environmental pollution. A marshal effect of heavy metal ions is a paramount ultimatum to humans, aquatic animals and other organisms present in nature. Multitude arrays of materials have been proclaimed for sensing of heavy metal ions and also many methodologies are applied for heavy metal ion sensing. Due to their toxicity and non-biodegradability, it is required to be perceived immediately prior to its manifestation of harmful effects. Quantum Dots (QDs) are zero-dimensional nanomaterial particles and owing to their distinctive optical and electronic properties, they are utilized as nanosensors. QDs have enriched fluorescence properties which includes broad excitation spectrum, narrow emission spectrum and photostability. QDs offer eclectic and sensitive detection of heavy metal ions due to presence of discrete capping agents and different functional groups present on the surface of the QDs. These capping layers and functional groups attune the sensing capability of the QDs, which leverages the interactions of QDs with various analytes by different mechanisms. This review, comprising of papers from 2011 to 2020,focuses on heavy metal ions sensing potential of various quantum dots and its applicability as a nanosensor for on field heavy metal ions detection in water. Quantum Dots (QDs) based Heavy Metal Detection.

Machine Learning for Electronically Excited States of Molecules

Electronically excited states of molecules are at the heart of photochemistry, photophysics, as well as photobiology and also play a role in material science. Their theoretical description requires highly accurate quantum chemical calculations, which are computationally expensive. In this review, we focus on not only how machine learning is employed to speed up such excited-state simulations but also how this branch of artificial intelligence can be used to advance this exciting research field in all its aspects. Discussed applications of machine learning for excited states include excited-state dynamics simulations, static calculations of absorption spectra, as well as many others. In order to put these studies into context, we discuss the promises and pitfalls of the involved machine learning techniques. Since the latter are mostly based on quantum chemistry calculations, we also provide a short introduction into excited-state electronic structure methods and approaches for nonadiabatic dynamics simulations and describe tricks and problems when using them in machine learning for excited states of molecules.

Machine Learning for Electronically Excited States of Molecules

Electronically excited states of molecules are at the heart of photochemistry, photophysics, as well as photobiology and also play a role in material science. Their theoretical description requires highly accurate quantum chemical calculations, which are computationally expensive. In this review, we focus on not only how machine learning is employed to speed up such excited-state simulations but also how this branch of artificial intelligence can be used to advance this exciting research field in all its aspects. Discussed applications of machine learning for excited states include excited-state dynamics simulations, static calculations of absorption spectra, as well as many others. In order to put these studies into context, we discuss the promises and pitfalls of the involved machine learning techniques. Since the latter are mostly based on quantum chemistry calculations, we also provide a short introduction into excited-state electronic structure methods and approaches for nonadiabatic dynamics simulations and describe tricks and problems when using them in machine learning for excited states of molecules.

The Quest to Simulate Excited-State Dynamics of Transition Metal Complexes

This Perspective describes current computational efforts in the field of simulating photodynamics of transition metal complexes. We present the typical workflows and feature the strengths and limitations of the different contemporary approaches. From electronic structure methods suitable to describe transition metal complexes to approaches able to simulate their nuclear dynamics under the effect of light, we give particular attention to build a bridge between theory and experiment by critically discussing the different models commonly adopted in the interpretation of spectroscopic experiments and the simulation of particular observables. Thereby, we review all the studies of excited-state dynamics on transition metal complexes, both in gas phase and in solution from reduced to full dimensionality.

Delineating Conformation Control in the Photophysical Behaviour of a Molecular Donor-Acceptor-Donor Triad

Mechanochromic luminescent materials, exhibiting a change in luminescence behavior under external stimuli have emerged as one of the promising candidates for upcoming efficient OLEDs. Recently mechanochromic luminescence was reported in a donor-acceptor-donor (D-A-D) triad featuring two phenothiazine units separated by a dibenzo[a,j]phenazine motif. The triad follows different emissive routes ranging from phosphorescence to TADF based on the conformational switching of the D units. In this article, we investigate such conformation-dependent photophysical behavior of this triad through theoretical calculations. By analyzing the nature of ground state, excited state and factors determining the reverse ISC crossing rates associated with the relative orientation of the D and A units, we delineate the effect of the conformational changes on their photophysical properties. Our findings reveal that axial orientation of both the donor groups enhances the overlap between HOMO and LUMO leading to a large singlet-triplet gap ( Δ E S T ) which drives phosphorescence emission. On the contrary, the equatorial orientation of the donor groups minimizes Δ E S T to facilitate rISC making the conformers TADF active. The role of several geometric factors affecting the photophysical properties of the conformers is also highlighted. Finally, we show how to regulate the population difference among the conformers by functionalizing the triad to harvest the maximum TADF efficiency.

Reliable TDDFT Protocol Based on a Local Hybrid Functional for the Prediction of Vibronic Phosphorescence Spectra Applied to Tris(2,2'-bipyridine)-Metal Complexes

An efficient computational protocol for the prediction of vibrationally resolved phosphorescence spectra is developed and validated for five tris(2,2'-bipyridine)-metal complexes ([M(bpy)₃]ⁿ⁺, where M = Zn, Ru, Rh, Os, Ir). The outstanding feature of this protocol is the use of full linear-response time-dependent density functional theory (TDDFT) for the excited-state triplet calculation, i.e., the commonly seen strategies employing the Tamm-Dancoff approximation (TDA) or unrestricted density functional theory (DFT) calculations for the T₁ state are not needed. This is achieved by the use of a local hybrid functional (LH12ct-SsirPW92) that features a real-space dependent admixture of exact exchange governed by a local mixing function. The excellent performance of this LH for triplet excitation energies known from previous studies transfers to a remarkable mean absolute error of 0.06 eV for the phosphorescence 0-0 energies investigated herein, while the popular B3PW91 functional gives an error of 0.27 eV in TDDFT and 0.09 eV in unrestricted DFT calculations, respectively. The advantages of the local hybrid are particularly apparent for excited states with a mixed-valence character. The influence of spin-orbit coupling was found to be significant for [Os(bpy)₃]²⁺ red-shifting the 0-0 energy for phosphorescence by 0.17 eV, while the effect is negligible for the other complexes (<0.03 eV). The influence of the basis-set and integration-grid sizes is evaluated, and a computationally lighter protocol is validated that leads to drastic savings in computation time with negligible loss in accuracy.

Electron spin dynamics in excited state photochemistry: recent development in the study of intersystem crossing and charge transfer in organic compounds

Electron spin dynamics are crucial to photochemical and photophysical processes. However, to a large extent, they are neglected in routine photochemistry studies. Herein, we summarized the recent developments of electron spin dynamics in organic molecular systems. The electron-spin selective intersystem crossing (ISC) as well as charge separation (CS) and charge recombination (CR) of the organic molecular system are discussed, including ISC of the compounds with twisted π-conjugation frameworks and CR-induced ISC in compact orthogonal electron donor-acceptor dyads. We found that the electron spin polarization (ESP) of the triplet state formed in these systems is highly dependent on the molecular structure and geometry. The zero-field-splitting (ZFS) D and E parameters of the triplet state of series chromophores determined with time-resolved electron paramagnetic resonance (TREPR) spectroscopy are presented. Some unanswered questions in related areas are raised, which may inspire further theoretical investigations. The examples demonstrate that the study of electron spin dynamics is not only important in fundamental photochemistry to attain in-depth understanding of the ISC and the charge transfer processes, but is also useful for designing new efficient organic molecular materials for applications including photodynamic therapy, organic light-emitting diodes, and photon upconversion.

Electron spin resonance resolves intermediate triplet states in delayed fluorescence

Molecular organic fluorophores are currently used in organic light-emitting diodes, though non-emissive triplet excitons generated in devices incorporating conventional fluorophores limit the efficiency. This limit can be overcome in materials that have intramolecular charge-transfer excitonic states and associated small singlet-triplet energy separations; triplets can then be converted to emissive singlet excitons resulting in efficient delayed fluorescence. However, the mechanistic details of the spin interconversion have not yet been fully resolved. We report transient electron spin resonance studies that allow direct probing of the spin conversion in a series of delayed fluorescence fluorophores with varying energy gaps between local excitation and charge-transfer triplet states. The observation of distinct triplet signals, unusual in transient electron spin resonance, suggests that multiple triplet states mediate the photophysics for efficient light emission in delayed fluorescence emitters. We reveal that as the energy separation between local excitation and charge-transfer triplet states decreases, spin interconversion changes from a direct, singlet-triplet mechanism to an indirect mechanism involving intermediate states.

Exploring the Concept of Dimerization-Induced Intersystem Crossing: At the Origins of Spin-Orbit Coupling Selection Rules

Singlet-triplet interconversions (intersystem crossing, ISC) in organic molecules are at the basis of many important processes in cutting-edge photonic applications (organic light-emitting devices, photodynamic therapy, etc.). Selection rules for these transitions are mainly governed by the spin-orbit coupling (SOC) phenomenon. Although the SOC relies on complex relativistic phenomena, theoreticians have, with time, developed increasingly sophisticated and efficient approaches to gain access to a satisfactory evaluation of its magnitude. However, recent works have highlighted the remarkable and somehow unexpected efficiency of dimers of small conjugated molecules in terms of ISC quantum yields, whose origin has not been completely investigated. In this work, we bring a coupled experimental and theoretical analysis of the origin of the unusually large ISC efficiency on a series of such dimers that differ by their nature (covalent or supramolecular). We show that considering the dynamical nature of the SOC, and especially its dependence on angular orientations between the dimer subunits sometimes overlooked in the literature, it is necessary to rationalize some counterintuitive experimental observations. This combined experimental and theoretical work paves the way for new molecular engineering rules for SOC control.

A Versatile Multichannel Instrument for Measurement of Ratiometric Fluorescence Intensity and Phosphorescence Lifetime

Optical biosensing is being actively investigated for minimally-invasive monitoring of key biomarkers both in vitro and in vivo. However, typical benchtop instruments are not portable and are not well suited to high-throughput, real-time analysis. This paper presents a versatile multichannel instrument for measurement of emission intensity and lifetime values arising from luminescent biosensor materials. A detailed design description of the opto-electronic hardware as well as the control software is provided, elaborating a flexible, user-configurable system that may be customized or duplicated for a wide range of applications. This article presents experimental measurements that prove the in vitro and in vivo functionality of the system. Such tools may be adopted for many research and development purposes, including evaluation of new biosensor materials, and may also serve as prototypes for future miniaturized handheld or wearable devices.

Spectra and nature of the electronic states of [1]Benzothieno[3,2-b][1]benzothiophene (BTBT): Single crystal and the aggregates

Absorption, fluorescence, and phosphorescence spectra of single crystals of [1]benzothieno[3,2-b][1]benzothiophene (BTBT) and BTBT dispersed in frozen n-nonane, n-hexadecane, and dichloromethane matrices were studied at 5 K. Observation of a new absorption band and related changes in the fluorescence to phosphorescence intensity ratio, when the concentration of BTBT in the matrix increased above 10^-4M, indicated the presence of BTBT aggregates. Quantum-chemistry calculations performed for the simplest aggregate, isolated dimer, showed that its structure is similar to the "herringbone" element in the BTBT crystal unit cell and the lowest electronic excited singlet state of the dimer has the intermolecular charge-transfer character. A qualitatively different nature of this state in dimers and in crystals, when compared with the situation in BTBT monomer [locally excited (LE) state], is associated with a decrease in the intersystem crossing yield. The structured vibronic structure of phosphorescence spectra in the studied systems indicated LE character of the triplet states.

Room-Temperature Phosphorescence and Thermally Activated Delayed Fluorescence in the Pd Complex: Mechanism and Dual Upconversion Channels

The Pd complex PdN3N exhibits an unusual dual emission of room-temperature phosphorescence (RTP) and thermally activated delayed fluorescence (TADF), but the mechanism is elusive. Herein, we employed both density functional theory (DFT) and time-dependent DFT (TD-DFT) methods to explore excited-state properties of this Pd complex, which shows that the S₀, S₁, T₁, and T₂ states are involved in the luminescence. Both the S₁ → T₁ and S₁ → T₂ intersystem crossing (ISC) processes are more efficient than the S₁ fluorescence and insensitive to temperature. However, the direct T₁ → S₁ and T₂-mediated T₁ → T₂ → S₁ reverse ISC (rISC) processes change remarkably with temperature. At 300 K, these two processes are more efficient than the T₁ phosphorescence and therefore enable TADF. Importantly, the T₁ → S₁ rISC and T₁ phosphorescence rates are comparable at 300 K, which leads to dual emissions of TADF and RTP, whereas these two channels become blocked at 100 K so that only the T₁ phosphorescence is recorded experimentally.

An Organic Host-Guest System Producing Room-Temperature Phosphorescence at the Parts-Per-Billion Level

Manipulation of long-lived triplet excitons in organic molecules is key to applications including next-generation optoelectronics, background-free bioimaging, information encryption, and photodynamic therapy. However, for organic room-temperature phosphorescence (RTP), which stems from triplet excitons, it is still difficult to simultaneously achieve efficiency and lifetime enhancement on account of weak spin-orbit coupling and rapid nonradiative transitions, especially in the red and near-infrared region. Herein, we report that a series of fluorescent naphthalimides-which did not originally show observable phosphorescence in solution, as aggregates, in polymer films, or in any other tested host material, including heavy-atom matrices at cryogenic temperatures-can now efficiently produce ultralong RTP (ϕ=0.17, τ=243 ms) in phthalimide hosts. Notably, red RTP (λ_RTP =628 nm) is realized at a molar ratio of less than 10 parts per billion, demonstrating an unprecedentedly low guest-to-host ratio where efficient RTP can take place in molecular solids.

Tuning the emission color of a quantum emitter by using photonic local density of states

Quantum emitters characterized by their emission colors constitute important elements in the design of modern nano-optics. Although we can change the emission colors of a quantum emitter by tailoring its chemical component, once selected, the color usually cannot be changed. It will be tempting to find out whether the emission color of an emitter could be tuned without touching its chemical component. In this Letter, we theoretically propose a strategy to externally tune the emission color of a model emitter by changing its electromagnetic environment. We found that the photonic local density of states (PLDOS) strongly affect the competition between various internal radiative and nonradiative channels, thus enabling a selective electronic state to dominate the emission spectrum. Indeed, quantitative calculations show that the emission color of a model emitter could be tuned from red to green and blue as the PLDOS increases. Moreover, due to direct correspondence between the emission color and PLDOS, the emitter can be potentially used as a sensor to characterize the local electromagnetic environment by its emission color at the nanoscale. This simple strategy may prove to be useful in the future design of various nano-optical devices.

Molecular excited states through a machine learning lens

Theoretical simulations of electronic excitations and associated processes in molecules are indispensable for fundamental research and technological innovations. However, such simulations are notoriously challenging to perform with quantum mechanical methods. Advances in machine learning open many new avenues for assisting molecular excited-state simulations. In this Review, we track such progress, assess the current state of the art and highlight the critical issues to solve in the future. We overview a broad range of machine learning applications in excited-state research, which include the prediction of molecular properties, improvements of quantum mechanical methods for the calculations of excited-state properties and the search for new materials. Machine learning approaches can help us understand hidden factors that influence photo-processes, leading to a better control of such processes and new rules for the design of materials for optoelectronic applications.

The development of phosphorescent probes for in vitro and in vivo bioimaging

Phosphorescence is a process that slowly releases the photoexcitation energy after the removal of the excitation source. Although transition metal complexes and purely organic room-temperature phosphorescence (RTP) materials show excellent phosphorescence property, their applications in in vitro and in vivo bioimaging are limited due to their poor solubility in water. To overcome this issue, phosphorescent materials are modified with amphiphilic or hydrophilic polymers to endow them with biocompatibility. This review focuses on recent advances in the development of phosphorescent probes for in vitro and in vivo bioimaging. The photophysical mechanism and the design principles of transition metal complexes and purely organic RTP materials for the stabilization of the triplet excited state for enhanced phosphorescence are first discussed. Then, the applications in in vitro and in vivo bioimaging using transition metal complexes including iridium(iii) complexes, platinum(ii) complexes, rhodium(i) complexes, and purely organic RTP materials are summarized. Finally, the current challenges and perspectives for these emerging materials in bioimaging are discussed.

Bright luminescent lithium and magnesium carbene complexes

We report on the convenient synthesis of a CNC pincer ligand composed of carbazole and two mesoionic carbenes, as well as the corresponding lithium- and magnesium complexes. Mono-deprotonation affords a rare "naked" amide anion. In contrast to the proligand and its mono-deprotonated form, tri-deprotonated s-block complexes show bright luminescence, and their photophysical properties were therefore investigated by absorption- and luminescence spectroscopy. They reveal a quantum yield of 16% in solution at ambient temperature. Detailed quantum-chemical calculations assist in rationalizing the emissive properties based on an Intra-Ligand-Charge-Transfer (ILCT) between the carbazolido- and mesoionic carbene ligands. (Earth-)alkali metals prevent the distortion of the ligand following excitation and, thus, by avoiding non-radiative deactivation support bright luminescence.

Twisted BODIPY derivative: intersystem crossing, electron spin polarization and application as a novel photodynamic therapy reagent

The photophysical properties of a heavy atom-free BODIPY derivative with a twisted π-conjugated framework were studied. Efficient intersystem crossing (ISC quantum yield: 56%) and an exceptionally long-lived triplet state were observed (4.5 ms in solid polymer film matrix and 197.5 μs in solution). Time-resolved electron paramagnetic resonance (TREPR) spectroscopy and DFT computations confirmed the delocalization of the triplet state on the whole twisted π-conjugated framework and the zero-field-splitting (ZFS) D parameter of D = -69.5 mT, which is smaller than that of 2,6-diiodoBODIPY (D = -104.6 mT). The electron spin polarization (ESP) phase pattern of the triplet state TREPR spectrum of the twisted BODIPY is (a, a, e, a, e, e), which is different from that of 2,6-diiodo BODIPY (e, e, e, a, a, a), indicating that the electron spin selectivity of the ISC of the twisted structure is different from that of the spin orbital coupling effect. According to the computed spin-orbit coupling matrix elements (0.154-1.964 cm^-1), together with the matched energy of the S₁/T_n states, ISC was proposed to occur via S₁→T₂/T₃. The computational results were consistent with TREPR results on the electron spin selectivity (the overpopulation of the T_Y sublevel of the T₁ state). The advantage of the long-lived triplet state of the twisted BODIPY was demonstrated by its efficient singlet oxygen (¹O₂) photosensitizing (Φ_Δ = 50.0%) even under a severe hypoxia atmosphere (pO₂ = 0.2%, v/v). A high light toxicity (EC₅₀ = 1.0 μM) and low dark toxicity (EC₅₀ = 78.5 μM) were observed for the twisted BODIPY, and thus the cellular studies demonstrate its potential as a novel potent heavy atom-free photodynamic therapy (PDT) agent.

The study of intramolecular decay and intermolecular energy transfer for phosphorescent organic light-emitting devices

Due to the huge potential of organic light-emitting diodes (OLEDs) in optical display devices, the exciton utilization of devices should be elucidated comprehensively to achieve a high external quantum efficiency (EQE). In this study, theoretical calculations of intramolecular excited state decay and intermolecular excitation energy transfer (EET) were conducted to investigate the differences in EQE between the two studied systems. Compared to the PtOO7-based system (using PtOO7 as the guest and 26mCPy as the host), the greater EQE of the PtON7-based system (using PtON7 as the guest and 26mCPy as the host) was mainly governed by the stronger energy transfer efficiency, with a secondary role being played by the higher photoluminescence quantum yield of the emitter. We confirmed that the different triplet EET (TEET) rates mainly contribute to the difference in the energy transfer efficiency between two studied systems, where the higher TEET rate from 26mCPy to PtON7 can be attributed to the restrained structural deformation of PtON7 and the desirable energy gap in the energy transfer process. Our calculations indicated that the electronic structure can evidently affect the intramolecular excited state decay and intermolecular excitation energy transfer. In addition, considering the environmental effects on the emission spectra of the emitters, the simulated spectra were consistent with the experimental measurements, which indicated that our descriptions of electronic structures are accurate; furthermore, an effective description of the molecular environment should be obtained. Our computational protocol successfully explored the relationship between the electronic structures, intramolecular excited state decay, and intermolecular excitation energy transfer, which can provide a deep understanding for the design and development of high-quality OLEDs from a molecular perspective.

Generalization of Intrinsic Orbitals to Kramers-Paired Quaternion Spinors, Molecular Fragments, and Valence Virtual Spinors

Localization of molecular orbitals finds its importance in the representation of chemical bonding (and antibonding) and in the local correlation treatments beyond mean-field approximation. In this paper, we generalize the intrinsic atomic and bonding orbitals [G. Knizia, J. Chem. Theory Comput. 2013, 9, 11, 4834-4843] to relativistic applications using complex and quaternion spinors, as well as to molecular fragments instead of atomic fragments only. By performing a singular value decomposition, we show how localized valence virtual orbitals can be expressed on this intrinsic minimal basis. We demonstrate our method on systems of increasing complexity, starting from simple cases such as benzene, acrylic acid, and ferrocene molecules, and then demonstrate the use of molecular fragments and inclusion of relativistic effects for complexes containing heavy elements such as tellurium, iridium, and astatine. The aforementioned scheme is implemented into a standalone program interfaced with several different quantum chemistry packages.

Efficient metal-free organic room temperature phosphors

An innovative transformation of organic luminescent materials in recent years has realised the exciting research area of ultralong room-temperature phosphorescence. Here the credit for the advancements goes to the rational design of new organic phosphors. The continuous effort in the area has yielded wide varieties of metal-free organic systems capable of extending the lifetime to several seconds under ambient conditions with high quantum yield and attractive afterglow properties. The various strategies adopted in the past decade to manipulate the fate of triplet excitons suggest a bright future for this class of materials. To analyze the underlying processes in detail, we have chosen high performing organic triplet emitters that utilized the best possible ways to achieve a lifetime above one second along with impressive quantum yield and afterglow properties. Such a case study describing different classes of metal-free organic phosphors and strategies adopted for the efficient management of triplet excitons will stimulate the development of better candidates for futuristic applications. This Perspective discusses the phosphorescence features of single- and multi-component crystalline assemblies, host-guest assemblies, polymers, and polymer-based systems under various classes of molecules. The various applications of the organic phosphors, along with future perspectives, are also highlighted.

Solvent effects on the electronic and optical properties of Ni(II), Zn(II), and Fe(II) complexes of a Schiff base derived from 5-bromo-2-hydroxybenzaldehyde

In this article, the electronic, optical, and charge transfer properties of a Schiff base ligand prepared using 5-bromo-2-hydroxybenzaldehyde and ethyl 6-acetyl-2-amino-4,5,6,7-tetrahydrothieno[2,3- c]pyridine-3-carboxylate (C19H19BrN2O4S) and its Fe(II) (C19H30BrN2O10SClFe), Ni(II) (C19H28BrN2O9SClNi), and Zn(II) (C19H28BrN2O9SClZn) complexes are described based on different solvents environments and supported by theoretical calculations. Theoretical calculations are carried out using density functional theory (DFT/UB3LYP/LANL2DZ). The optical densities, optical band gaps, and refractive indices of the ligand and its Fe(II), Ni(II), and Zn(II) complexes in different solvent environments are obtained. The reorganization energies are calculated to determine the charge transfer rate of the studied compounds using both experimental and theoretical data. These experimental and theoretical results show that the ligand and its metal complexes can be used for optoelectronic applications and charge transfer materials in organic light-emitting diode applications.

Aggregation-induced phosphorescence of an anthraquinone based emitter

Room temperature phosphorescence (RTP) of metal-free organic molecules is a hot topic of current research interest. RTP can be enhanced through aggregation, crystallization, and the support of polymers and host-guest assemblies. The characteristics of highly phosphorescent aggregates formed from conventional chromophores make them ideal candidates for many potential applications. In this direction, we focused on the aggregation-induced phosphorescence of an anthraquinone derivative AqC6 in solution and in crystal state. The weakly emissive dilute solution exhibits a tunable emission with enhanced intensity and room temperature phosphorescence by increasing the concentration and solvent-antisolvent combination. The enhanced phosphorescence of crystals has been recreated in the solution by making use of aggregation. Interestingly, the support of PMMA enabled AqC6 to achieve enhanced processability, phosphorescence lifetime (174 ms) and quantum yield (5%).

Effect of π···π Interactions of Donor Rings on Persistent Room-Temperature Phosphorescence in D4-A Conjugates and Data Security Application

Organic room-temperature phosphorescence (RTP) materials with persistent RTP (PRTP) have attracted huge interest in inks, bioimaging, and photodynamic therapy. However, the design principle to increase the lifetime of organic molecules is underdeveloped. Herein, we show donor(D₄)-acceptor(A) molecules (TOEPh, TOCPh, TOMPh, TOF and TOPh) with similar orientation of donor rings in aggregates that cause a large number of noncovalent interactions. We observed that TOEPh, TOCPh, TOMPh and TOF showed PRTP, whereas TOPh showed only phosphorescence emission (Φ_P = ∼11%) with no PRTP property at ambient conditions. The spectroscopic and single-crystal X-ray analyses confirm the molecular assembly via J-aggregation with a face-to-face orientation of the donor rings. The crystal structure analysis (TOEPh, TOCPh, TOMPh, TOF) reveals that moderate π···π interactions (3.706 to 4.065 Å) between the donor rings cause the enhancement of the phosphorescence lifetime (26 to 245 ms), whereas the short phosphorescence lifetime (12 ms) of TOPh was observed because of the absence of π···π interactions. We found that TOEPh shows a long lifetime (245 ms) as compared to other derivatives because of the presence of ethoxy (-OEt) groups that enables spin-orbit coupling caused by strong lone pair (O)···π interactions present in the molecule. Utilizing the PRTP feature of TOEPh and the fluorescence emission of TOPh, we have shown data security applications in poly(methyl methacrylate).

Manipulating the Dynamics of Dark Excited States in Organic Materials for Phototheranostics

Manipulating the dynamics of dark excited states (DESs), such as higher excited singlet or excited triplet states with no or small radiative decay, are of both fundamental and practical interests, an important application being photoactivated diagnosis and therapy (phototheranostics), which include photoacoustic (PA) imaging, photodynamic therapy (PDT), and photothermal therapy (PTT). However, the current understanding of DESs in organic structures is rather limited, thus making any rational manipulation of DES in organic materials very challenging.A DES decays primarily by radiationless transition through two pathways: (i) singlet-to-triplet intersystem crossing (ISC) and (ii) internal conversion (IC) relaxation. The deactivation of a DES via ISC can generate cytotoxic reactive oxygen species (ROS) for PDT, while IC could convert photons into heat for PA imaging and PTT. In this Account, we highlight our research on developing a fundamental understanding of structure-property relationships for manipulation of DESs in organic materials in relation to phototheranostic applications. We describe the application of femtosecond transient absorption (fs-TA) spectroscopy for obtaining valuable insights into the DES dynamics. Afterward, we present our work on DESs in nonrigid molecules that revealed greatly enhanced ISC through geometry twisting, which leads to an innovative pathway to develop organic materials exhibiting external stimuli-responsive reversible switching of ISC. We introduce the concept of smart PDT where highly efficient ISC imparted by geometry twisting in the acidic environment specific to tumors leads to very efficient and highly localized PDT, thus leaving surrounding healthy tissues at a different pH unaffected. This insightful understanding of ISC can lead to the development of more advanced photosensitizers for PDT. Two other emergent concepts from our work presented here are (1) significantly enhanced IC producing strong local heating by combining two-photon absorption with excited state absorption for cumulative multiphoton absorption, thus greatly increasing the strength of the PA signal for nonlinear PA imaging, and (2) shown by an example of an organic molecule, BODIPY, nanoscale charge-transfer state mediated strong IC in aggregate nanoparticles resulting in exceptionally high photothermal conversion efficiency of 61% for both PA and PTT. Some in vivo results of the phototheranostic studies using BODIPY are presented, providing an elegant example of nanoscale manipulation of the excited state dynamics.This Account concludes with a summary and discussion of future perspectives. We hope this Account will deepen the understanding of molecular and nanoscale control of excited state dynamics in organic materials, hopefully enticing a broad range of scientists within different disciplinary areas.

Ultrafast processes: coordination chemistry and quantum theory

Coordination compounds, characterized by fascinating and tunable electronic properties, are capable of binding easily to proteins, polymers, wires and DNA. Upon irradiation, these molecular systems develop functions finding applications in solar cells, photocatalysis, luminescent and conformational probes, electron transfer triggers and diagnostic or therapeutic tools. The control of these functions is activated by the light wavelength, the metal/ligand cooperation and the environment within the first picoseconds (ps). After a brief summary of the theoretical background, this perspective reviews case studies, from 1st row to 3rd row transition metal complexes, that illustrate how spin-orbit, vibronic coupling and quantum effects drive the photophysics of this class of molecules at the early stage of the photoinduced elementary processes within the fs-ps time scale range.

Halide-Enhanced Spin-Orbit Coupling and the Phosphorescence Rate in Ir(III) Complexes

The spin-forbidden nature of phosphorescence in Ir(III) complexes is relaxed by the metal-induced effect of spin-orbit coupling (SOC). A further increase of the phosphorescence rate could potentially be achieved by introducing additional centers capable of further enhancing the SOC effect, such as metal-coordinated halides. Herein, we present a dinuclear Ir(III) complex Ir₂I₂ that contains two Ir(III)-iodide moieties. The complex shows intense phosphorescence with a quantum yield of Φ_PL(300 K) = 90% and a submicrosecond decay time of only τ(300 K) = 0.34 μs, as measured under ambient temperature for the degassed toluene solution. These values correspond to a top value T₁ → S₀ phosphorescence rate of k_r = 2.65 × 10⁶ s^-1. Investigations at cryogenic temperatures allowed us to determine the zero-field splitting (ZFS) of the emitting state T₁ ZFS(III-I) = 170 cm^-1 and unusually short individual decay times of T₁ substates: τ(I) = 6.4 μs, τ(II) = 7.6 μs, and τ(III) = 0.05 μs. This indicates a strong SOC of state T₁ with singlet states. Theoretical investigations suggest that the SOC of state T₁ with singlets is also contributed by halides. Strongly contributing to the higher occupied molecular orbitals of the complex (e.g., HOMO, HOMO - 1, and so forth), iodides work as important SOC centers that operate in tandem with metals. The examples of Ir₂I₂ and of earlier reported analogous complex Ir₂Cl₂ reveal that the metal-coordinated halides can enhance the SOC of state T₁ with singlets and, consequently, the phosphorescence rate. A comparative study of Ir₂I₂ and Ir₂Cl₂ shows that the share of halides in total contribution (halides plus metals) to the SOC of state T₁ with singlets increases strongly upon exchange of chlorides for iodides. The exchange also led to the decrease in values of ZFS of the T₁ state from ZFS(III-I) = 205 cm^-1 for Ir₂Cl₂ to T₁ ZFS(III-I) = 170 cm^-1 for Ir₂I₂. This results in a more efficient thermal population of the fastest emitting T₁ substate III, thus further enhancing the room-temperature phosphorescence rate.

Behind the scenes of spin-forbidden decay pathways in transition metal complexes

The interpretation of the ultrafast photophysics of transition metal complexes following photo-absorption is quite involved as the heavy metal center leads to a complicated and entangled singlet-triplet manifold. This opens up multiple pathways for deactivation, often with competitive rates. As a result, intersystem crossing (ISC) and phosphorescence are commonly observed in transition metal complexes. A detailed understanding of such an excited-state structure and dynamics calls for state-of-the-art experimental and theoretical methodologies. In this review, we delve into the inability of non-relativistic quantum theory to describe spin-forbidden transitions, which can be overcome by taking into account spin-orbit coupling, whose importance grows with increasing atomic number. We present the quantum chemical theory of phosphorescence and ISC together with illustrative examples. Finally, a few applications are highlighted, bridging the gap between theoretical studies and experimental applications, such as photofunctional materials.

Luminescence properties of [Ir(C^N)2(N^N)]+ complexes: relations between DFT computation results and emission band-shape analysis data

Luminescence properties of two series of [Ir(C^N)₂(N^N)]⁺ complexes bearing deprotonated 1-phenyl-1H-pyrazole or 1-(2,4-difluorophenyl)-1H-pyrazole as cyclometalating C^N ligands and different α-diimines (2,2′-bipyridine, 1,10-phenanthroline and their derivatives) as ancillary N^N ligands have been studied in acetonitrile solutions at room temperature and in 77 K methanol/ethanol (1 : 1) matrices. Ligand and temperature induced changes in the nature of the emissive ³*[Ir(C^N)₂(N^N)]⁺ species result in well-pronounced changes in their emission properties like emission wavelength, emission quantum yields and emission lifetimes. Depending on the nature of the coordinated C^N and N^N ligands and/or the measurement temperature, the investigated luminophores exhibit emissions arising from the intraligand transitions localized within the N^N ligand or from the metal-to-ligand charge-transfer transitions involving the Ir(C^N)₂⁺ and N^N moieties as confirmed by means of the DFT computations. The computed DFT energies of the excited ³*[Ir(C^N)₂(N^N)]⁺ states and outer/inner reorganization energies associated with the S₀ ← ³*[Ir(C^N)₂(N^N)]⁺ transitions remain in nice agreement with those available from the performed emission band-shape analyses. The observed agreement implies ordinary DFT computations at the B3LYP/LANL2DZ/6-31G(d,p) level of theory, even performed neglecting the spin–orbit phenomena, as enough accurate in the quantitative prediction of the most important parameters characterizing the investigated [Ir(C^N)₂(N^N)]⁺ luminophores.

For two series of [Ir(C^N)₂(N^N)]⁺ luminophores, the computed DFT quantities remain in nice agreement with those available from the emission band-shape analyses.

Ultrabright Au@Cu14 nanoclusters: 71.3% phosphorescence quantum yield in non-degassed solution at room temperature

The photoluminescence of metal nanoclusters is typically low, and phosphorescence emission is rare due to ultrafast free-electron dynamics and quenching by phonons. Here, we report an electronic engineering approach to achieving very high phosphorescence (quantum yield 71.3%) from a [Au@Cu₁₄(SPh ^t Bu)₁₂(PPh(C₂H₄CN)₂)₆]⁺ nanocluster (abbreviated Au@Cu ₁₄ ) in non-degassed solution at room temperature. The structure of Au@Cu ₁₄ has a single-Au-atom kernel, which is encapsulated by a rigid Cu(I) complex cage. This core-shell structure leads to highly efficient singlet-to-triplet intersystem crossing and suppression of nonradiative energy loss. Unlike the phosphorescent organic materials and organometallic complexes-which require de-aerated conditions due to severe quenching by air (i.e., O₂)-the phosphorescence from Au@Cu ₁₄ is much less sensitive to air, which is important for lighting and biomedical applications.

Insight into the drastically different triplet lifetimes of BODIPY obtained by optical/magnetic spectroscopy and theoretical computations

The triplet state lifetimes of organic chromophores are crucial for fundamental photochemistry studies as well as applications as photosensitizers in photocatalysis, photovoltaics, photodynamic therapy and photon upconversion. It is noteworthy that the triplet state lifetime of a chromophore can vary significantly for its analogues, while the exact reason was rarely studied. Herein with a few exemplars of typical BODIPY derivatives, which show triplet lifetimes varying up to 110-fold (1.4-160 μs), we found that for these derivatives with short triplet state lifetimes (ca. 1-3 μs), the electron spin polarization (ESP) pattern of the time-resolved electron paramagnetic resonance (TREPR) spectra of the triplet state is inverted at a longer delay time after laser pulse excitation, as a consequence of a strong anisotropy in the decay rates of the zero-field state sublevel of the triplet state. For the derivatives showing longer triplet state lifetimes (>50 μs), no such ESP inversion was observed. The observed fast decay of one sublevel is responsible for the short triplet state lifetime; theoretical computations indicate that it is due to a strong coupling between the T z sublevel and the ground state mediated by the spin-orbit interaction. Another finding is that the heavy atom effect on the shortening of the triplet state lifetime is more significant for the T1 states with lower energy. To the best of our knowledge, this is the first systematic study to rationalize the short triplet state lifetime of visible-light-harvesting organic chromophores. Our results are useful for fundamental photochemistry and the design of photosensitizers showing long-lived triplet states.

Deciphering the unusual fluorescence in weakly coupled bis-nitro-pyrrolo[3,2-b]pyrroles

Electron-deficient π-conjugated functional dyes lie at the heart of organic optoelectronics. Adding nitro groups to aromatic compounds usually quenches their fluorescence via inter-system crossing (ISC) or internal conversion (IC). While strong electronic coupling of the nitro groups with the dyes ensures the benefits from these electron-withdrawing substituents, it also leads to fluorescence quenching. Here, we demonstrate how such electronic coupling affects the photophysics of acceptor-donor-acceptor fluorescent dyes, with nitrophenyl acceptors and a pyrrolo[3,2-b]pyrrole donor. The position of the nitro groups and the donor-acceptor distance strongly affect the fluorescence properties of the bis-nitrotetraphenylpyrrolopyrroles. Concurrently, increasing solvent polarity quenches the emission that recovers upon solidifying the media. Intramolecular charge transfer (CT) and molecular dynamics, therefore, govern the fluorescence of these nitro-aromatics. While balanced donor-acceptor coupling ensures fast radiative deactivation and slow ISC essential for large fluorescence quantum yields, vibronic borrowing accounts for medium dependent IC via back CT. These mechanistic paradigms set important design principles for molecular photonics and electronics.

DpgC-Catalyzed Peroxidation of 3,5-Dihydroxyphenylacetyl-CoA (DPA-CoA): Insights into the Spin-Forbidden Transition and Charge Transfer Mechanisms*

Despite being a very strong oxidizing agent, most organic molecules are not oxidized in the presence of O₂ at room temperature because O₂ is a diradical whereas most organic molecules are closed-shell. Oxidation then requires a change in the spin state of the system, which is forbidden according to non-relativistic quantum theory. To overcome this limitation, oxygenases usually rely on metal or redox cofactors to catalyze the incorporation of, at least, one oxygen atom into an organic substrate. However, some oxygenases do not require any cofactor, and the detailed mechanism followed by these enzymes remains elusive. To fill this gap, here the mechanism for the enzymatic cofactor-independent oxidation of 3,5-dihydroxyphenylacetyl-CoA (DPA-CoA) is studied by combining multireference calculations on a model system with QM/MM calculations. Our results reveal that intersystem crossing takes place without requiring the previous protonation of molecular oxygen. The characterization of the electronic states reveals that electron transfer is concomitant with the triplet-singlet transition. The enzyme plays a passive role in promoting the intersystem crossing, although spontaneous reorganization of the water wire connecting the active site with the bulk presets the substrate for subsequent chemical transformations. The results show that the stabilization of the singlet radical-pair between dioxygen and enolate is enough to promote spin-forbidden reaction without the need for neither metal cofactors nor basic residues in the active site.

3,5-Anthryl-Bodipy dyad/triad: Preparation, effect of F-B-F induced conformation restriction on the photophysical properties, and application in triplet-triplet-annihilation upconversion

We prepared a series of compact Bodipy-anthryl electron donor/acceptor triads and dyads by attaching anthryl moieties at the 3-,5-positions of the Bodipy core, with a novel conformation restriction approach, to study the spin-orbit charge transfer intersystem crossing (SOCT-ISC). The conformation restrictions are imposed by the BF₂ unit of Bodipy without invoking the previously reported method with 1,7-dimethyl or 1,3-dimethyl groups. Our new approach shows a few advantages, including the stronger electron accepting ability of the methyl-free Bodipy core (reduction potential anodically shifted by +0.3 V vs the methylated Bodipy), red-shifted absorption (by 21 nm), and longer triplet state lifetime (372 µs vs 126 µs). The effects of the different mutual orientations of the electron donor and acceptor on ultraviolet-visible absorption, fluorescence, triplet state quantum yields, and lifetimes were studied. Triads with orthogonal geometries show higher singlet oxygen quantum yields (Φ_Δ = 37%) than those with more coplanar geometries. Since the non-radiative decay for the S₁ state is significant in the parent Bodipy chromophore (Φ_F = 6.0%), we propose that in dyads/triads, the charge separation and recombination-induced ISC outcompete the non-radiative decay to the ground state, which is new in the study of SOCT-ISC. Density functional theory computation indicated a shallow torsion potential energy curve as compared to the meso-anthryl-Bodipy dyad analog, which may contribute a low triplet state quantum yield of the new dyads/triads. Triplet-triplet annihilation upconversion was performed with the electron donor/acceptor dyads as the triplet photosensitizer, with an upconversion quantum yield of 12.3%.

Near-Infrared Phosphorescence Emission of Binuclear Mn(II) Based Metal-Organic Framework for Efficient Photoelectric Conversion

The development of metal-organic framework (MOF) based room-temperature phosphorescence (RTP) materials has raised extensive concern owing to their widespread applications in the field of anti-counterfeiting, photovoltaics, photocatalytic reactions, and bio-imaging. Herein, one new binuclear Mn(II) based 3D MOF [Mn₂(L)(BMIB)·(H₂O)] (1) (H₅L = 3,5-bis(3,5-dicarboxylphenxoy) benzoic acid, BMIB = tran-4-bis(2-methylimidazolyl)butylene) has been synthesized by a facile hydrothermal process. In 1, the protonated BMIB cations show infinite π-stacking arrangement, residing in the channels of the 3D network extended by L ligand and binuclear Mn(II) units. The orderly and uniform host-guest system at molecular level emits intense white light fluorescence and long-lived near infrared phosphorescence under ambient conditions. These photophysical processes were well-studied by density functional theory (DFT) calculations. Photoelectron measurements reveal high photoelectron response behavior and incident photon-to-current efficiency (IPCE).

Direct Observation of the S0 → T2 Transition in Phosphorescent Platinum(II) Octaethylporphyrin, Evidenced by Magnetic Circular Dichroism

In recent years, the importance of analyzing excited triplet states has increased dramatically because of their relevance in the design and development of photofunctional molecules. Since the second lowest excited triplet (T₂) state plays an important role in enhancing the nonradiative intersystem crossing (ISC) process from the lowest excited singlet (S₁) state to the lowest excited triplet (T₁) state, it is strongly desired to develop direct observation methods for the nonluminescent, short-lived T₂ state. In this study, the excited triplet states of platinum(II) octaethylporphyrin (PtOEP), which was used as the first phosphorescent organic light emitting diode and oxygen sensor, are investigated using UV-vis absorption, magnetic circular dichroism, and phosphorescence spectroscopies. At low temperature, in highly concentrated solutions, we observe a distinct Faraday A term for the S₀ → T₁ transition, as well as for the S₀ → T₂ transition. The novel spectroscopic methodology applied allows resolution of the excited-state properties of a wide variety of molecular systems.

Conformation-Dependent Phosphorescence of Galactose-Decorated Phosphors and Assembling-Induced Phosphorescence Enhancement

Amorphous organic room-temperature phosphorescent (RTP) materials are promising for their facile preparation and processability, while the conformation effects of phosphors at amorphous state are lack of study in comparison with the rigid effects due to the commonly irregular assembling and dispersal of phosphors in rigid systems. Herein, we report a series of phosphorescent molecules modified by polyhydroxy galactose, whose RTP emission at the amorphous state can be regulated by controlling the conformational distortion of the phosphorescent segments. Further, a strong RTP emission is facilely obtained by the co-assembling between polyhydroxy phosphors and polyhydroxy matrices (α-CD, β-CD, and chitosan). Owing to the rigid effect of the enhanced hydrogen bonding cross-linking, the highest RTP quantum yield reaches 19.4%; whereas, the RTP emissions of assemblies become conformation insensitive. The conflicting relationship between the conformation effect and rigid effect is attributed to the differences between aggregated single-component systems and dispersed assembling systems. Besides, the unique and different moisture responsiveness of the co-assembling samples is discovered and further applied in data encryption. The research expands the scope for designing amorphous pure organic RTP materials with supramolecular strategies and shows a modularized approach for assembling-enhanced phosphorescence.

The influence of spin-orbit coupling, Duschinsky rotation and displacement vector on the rate of intersystem crossing of benzophenone and its fused analog fluorenone: a time dependent correlation function based approach

To understand the effect of structural rigidity or flexibility on the intersystem crossing rate, herein we have adopted a time dependent correlation function based approach, an appropriate method for a harmonic oscillator under Condon approximation. Following this technique, we have developed generalized codes for calculating the rate of intersystem crossing (ISC) both at 0 K and at finite temperature. Since the rate of ISC is a measurable quantity, we have separated the real and imaginary parts of the complex correlation function carefully and eliminated the imaginary part by exploiting the odd nature of this function. Using this simplified method, we have calculated the ISC rate constant (kISC) of two molecules, namely, benzophenone and its fused analog, fluorenone. The calculations clearly elucidate that kISC of benzophenone is 103 times larger compared to that of fluorenone. Interestingly, our analyses reveal that the combined effect of spin-orbit coupling and the number of normal modes could increase the rate of ISC of benzophenone by three orders in comparison to that of fluorenone. Furthermore, the Duschinsky rotation matrix (J) and displacement vectors (D) could influence the rate of ISC by one order each, indicating that the overall rate of ISC of benzophenone could have been 105 times higher than that of fluorenone if the latter two factors, namely, J and D have practically no impact on the rate of ISC of fluorenone. However, it has been found that albeit J can't alter the rate of ISC of fluorenone, D indeed can change the rate by two orders, thereby keeping the overall ratio of the rate of ISC of benzophenone and fluorenone as 103. The present study elucidates that none of the above mentioned factors alone can explain the relative rate of ISC of the studied systems; rather a complex interplay between all these factors makes the rate of ISC of benzophenone 103 times higher than that of fluorenone.

Evaluation of strontium aluminate phosphorescent effect on blood as potential light source for phototherapy

Phototherapy has shown its effect on cell stimulation and inhibition based on Arndt-Schulz model. Even though this therapeutic method has apparent effect, but it has limitations for epithelial application due to limitations on light penetration. Hence, with the ideology of fully overcoming this limitation, phosphorescent powder (strontium aluminate) is proposed as the potential light source that emitting photon from inside the body for phototherapy purposes. The strontium aluminate powder used in the experiment has the highest peak absorption at wavelength around 650 nm and lowest at around 350 nm. According to FESEM images, the powder has the particle size varies from 10 to 50 μm at cubic phase. The assessment is done by studying the effect on erythrocyte after blood plasma is irradiated by strontium aluminate powder’s photon. The powder luminesces with a maximum at 491.5 nm when pumped with 473 nm laser at 100 mW in fixed amount of 0.005±0.001 g. Later, it is mixed with  centrifuged blood plasma for a predetermined time period (5, 10, 15, and 20 minutes). From this study, it shows that 5 minutes irradiation is the optimum  period for erythrocyte in term of morphology enhancement and increase of UV-visible absorption spectrum with at least 21% in comparing  with control blood. While the significant increment located at wavelengths 340 nm and 414 nm with both increased by 54% and 41%, respectively. However, for 10 minutes and beyond, the irradiation leads to morphology deterioration while the UV-visible spectrum decrement starts at 15 minutes and beyond. In conjunction, a comparison between blood plasma that either interacted with powder emitting photon or powder with no emission shows that photon emission plays a role in the phototherapy effect.

First-principles calculations of anharmonic and deuteration effects on the photophysical properties of polyacenes and porphyrinoids

A new method for calculating internal conversion rate constants (k[combining low line]IC), including anharmonic effects and using the Lagrangian multiplier technique, is proposed. The deuteration effect on k[combining low line]IC is investigated for naphthalene, anthracene, free-base porphyrin (H2P) and tetraphenylporphyrin (H2TPP). The results show that anharmonic effects are important when calculating k[combining low line]IC for transitions between electronic states that are energetically separated (ΔE) by more than 20 000-25 000 cm-1. Anharmonic effects are also important when ΔE < 20 000-25 000 cm-1 and when the accepting modes are X-H stretching vibrations with a frequency larger than 2000 cm-1. The calculations show that there is mixing between the S1 and S2 states of naphthalene induced by non-adiabatic interactions. The non-adiabatic interaction matrix element between the S1 and S2 states is 250 cm-1 and 50 cm-1 for the normal and fully deuterated naphthalene structure and this difference significantly affects the estimated fluorescence quantum yield. Besides aromatic hydrocarbons H2P and H2TPP, the k[combining low line]IC rate constant is also calculated for pyrometene (PM567) and tetraoxa[8]circulene (4B) with a detailed analysis of the effect of the vibrational anharmonicity.