Nonradiative Decay Mechanism Research Articles

Concentration-Dependent Nonradiative Decay Mechanisms in Fluorescence Self-Quenching: Insights from Azulene and 1,3-Dichloroazulene

A series of steady-state and time-resolved spectroscopies were performed on azulene (Az) and its 1,3-dihalogenated analogue, 1,3-dichloroazulene (DCAz). Understanding the intra/inter-molecular interactions in these types of systems is the key to unlocking the potential of these molecules and enabling their application in a range of future devices. Therefore, the concentration dependence of their self-quenched fluorescence intensities and of the reduced lifetimes of their second-excited singlet states were examined. A Stern-Volmer analysis was implemented based on these experiments, which resulted in DCAz exhibiting a higher bimolecular quenching constant, compared to Az, due to its shorter excited-state lifetime. The highly efficient self-quenching at room temperature was a result of a short-range energy transfer mechanism.

(Invited) Electrical, Optical, and Mechanical Properties of Two-Dimensional Materials

Atomically thin two-dimensional materials are direct bandgap semiconductors with a rich interplay of the valley and spin degrees of freedom, which offer the potential for electronics and optoelectronics. A strong Coulomb interaction leads to tightly bound electron-hole pairs or excitons and two-electron one-hole quasiparticles or trions. We solve the two-particle and three-particle problems for the wavefunctions for excitons and trions in the basis set of the model- Hamiltonian for single particles. The calculated linear absorptions, photoluminescence spectra, and polariton spectra as a function of doping and temperature explain the experimental data in 2D monolayers and predict novel spectroscopic features due to the many-body Coulomb interactions. Exciton lifetime plays a crucial role in optoelectronic applications. I will also discuss the phonon-assisted Auger non-radiative decay mechanism of excitons in doped 2D materials. Finally, I will discuss the strain engineering in monolayer 2D materials transferred on 1D and 2D patterned substrates. This material is based upon work supported by the Air Force Office of Scientific Research under award number FA9550-22-1-0312.

Spectral Heterogeneity of Phenol Blue in Protic Solvents Revealed by Ultrafast Nonradiative Decay Dynamics

AbstractPhenol blue (PhB) is a dye that exhibits positive solvatochromism which is also nonfluorescent due to its ultrashort excited state lifetime. We have conducted femtosecond time‐resolved transient absorption (TA) spectroscopic measurements of a PhB solution using two distinct excitation wavelengths, at shorter and longer wavelength sides of the visible absorption band. The results revealed that a long‐lived heterogeneity exists in protic solvents whereas, in aprotic solvents, the system rapidly returns to the original thermal equilibrium on the ultrafast timescale. Interestingly, the lifetime of the heterogeneity is longer for methanol (MeOH) compared to ethanol (EtOH) solution suggesting stronger interaction between PhB and MeOH. Additionally, since the excited state lifetime of PhB was still in the sub‐picosecond domain even in a polymer matrix, we suggest a nonradiative decay mechanism through high‐frequency vibrational modes without involving large structural reconfiguration such as twisting of the benzoquinone (BzQ) moiety.

Design Strategies for Luminescent Titanocenes: Improving the Photoluminescence and Photostability of Arylethynyltitanocenes.

Complexes that undergo ligand-to-metal charge transfer (LMCT) to d0 metals are of interest as possible photocatalysts. Cp2Ti(C2Ph)2 (where C2Ph = phenylethynyl) was reported to be weakly emissive in room-temperature (RT) fluid solution from its phenylethynyl-to-Ti 3LMCT state but readily photodecomposes. Coordination of CuX between the alkyne ligands to give Cp2Ti(C2Ph)2CuX (X = Cl, Br) has been shown to significantly increase the photostability, but such complexes are not emissive in RT solution. Herein, we investigate whether inhibition of alkyne-Ti-alkyne bond compression might be responsible for the increased photostability of the CuX complexes by investigating the decomposition of a structurally constrained analogue, Cp2Ti(OBET) (OBET = o-bis(ethynyl)tolane). To investigate the mechanism of nonradiative decay from the 3LMCT states in Cp2Ti(C2Ph)2CuX, the photophysical properties were investigated both upon deuteration and upon rigidifying in a poly(methyl methacrylate) film. These investigations suggested that inhibition of structural rearrangement may play a dominant role in increasing emission lifetimes and quantum yields. The bulkier Cp*2Ti(C2Ph)2CuBr was prepared and is emissive at 693 nm in RT THF solution with a photoluminescent quantum yield of 1.3 × 10-3 (τ = 0.18 μs). Time-dependent density functional theory (TDDFT) calculations suggest that emission occurs from a 3LMCT state dominated by Cp*-to-Ti charge transfer.

Synthesis, Characterization, Fluorescence Properties, and DFT Modeling of Difluoroboron Biindolediketonates.

We report a simple and efficient strategy to enhance the fluorescence of biocompatible biindole diketonates (bdks) in the visible spectrum through difluoroboronation (BF2bdks complexes). Emission spectroscopy testifies an increase in the fluorescence quantum yields from a few percent to as much as >0.7. This massive increment is essentially independent of substitutions at the indole (-H, -Cl, and -OCH3) and corresponds to a significant stabilization of the excited state with respect to non-radiative decay mechanisms: the non-radiative decay rates are reduced by as much as an order of magnitude, from 109 s-1 to 108 s-1, upon difluoroboronation. The stabilization of the excited state is large enough to enable sizeable 1O2 photosensitized production. Different time-dependent (TD) density functional theory (DFT) methods were assessed in their ability to model the electronic properties of the compounds, with TD-B3LYP-D3 providing the most accurate excitation energies. The calculations associate the first active optical transition in both the bdks and BF2bdks electronic spectra to the S0 → S1 transition, corresponding to a shift in the electronic density from the indoles to the oxygens or the O-BF2-O unit, respectively.

Exploring the Effects of Mutagenesis on FusionRed by Using Excited-State QM/MM Dynamics and Classical Force Field Simulations.

Fluorescent proteins (FPs) are a powerful tool for examining tissues, cells, and subcellular components in vivo and in vitro. FusionRed is a particular FP variant mutated from mKate2 that, in addition to lower cytotoxicity and aggregation rates, has shown potential for acting as a tunable photoswitch. This was posited to stem partially from the presence of a bulky side chain at position 158 and a further stabilizing residue at position 157. In this work, we apply computational techniques including classical molecular dynamics (MD) and combined quantum mechanics/molecular mechanics simulations (QM/MM) to explore the effect of mutagenesis at these locations in FusionRed on the chromophore structure, the excited-state surface, and relative positional stability of the chromophore in the protein pocket. We find specific connections between the statistical sampling of the underlying protein structure and the nonradiative decay mechanisms from excited-state dynamics. A single mutation (C158I) that restricts the motion of the chromophore through a favorable hydrophobic interaction corresponds to an increase in fluorescence quantum yield (FQY), while a second rescue mutation (C158I-A157N) partially restores the flexibility of the chromophore and photoswitchability with favorable water interactions on the surface of the protein that counteracts the original interaction. We suggest that applying this understanding of structural features that inhibit or favor rotation on the excited state can be applied for rational design of new, tunable and red photoswitches.

Comparative excited state dynamics of metallo meso-(4-fluoro-2,6-dimethyl-phenyl) porphyrins

• Metalloporphyrin synthesis and structural characterization. • Ultrafast excited state dynamics. • Nonradiative decay kinetics and mechanisms. The Mn(III)Cl and Pd(II) meso-(4-fluoro-2,6-dimethyl-phenyl) porphyrins have been synthesized and structurally characterized by x-ray crystallography. Together with its Zn(II) congener, this homologous series of porphyrins show the manifestation of d–d states and spin-orbit coupling on the excited state dynamics of metalloporphyrins.

Effect of Protonation and Deprotonation on Electron Transfer Mediated Decay and Interatomic Coulombic Decay.

Electronically excited atoms or molecules in an environment are often subject to interatomic/intermolecular Coulombic decay (ICD) and/or electron transfer mediated decay (ETMD) mechanisms. A few of the numerous variables that can impact these non-radiative decay mechanisms include bond distance, the number of nearby atoms or molecules, and the polarisation effect. In this paper, we have studied the effect of protonation and deprotonation on the ionization potential (IP), double ionization potential (DIP), and lifetime (or decay width) of the temporary bound state in these non-radiative decay processes. We have chosen LiH-NH3 and LiH-H2 O as test systems. The equation of motion coupled cluster singles and doubles method augmented by complex absorbing potential (CAP-EOM-CCSD) has been used in calculating the energetic position of the decaying state and the system's decay rate. Deprotonation of LiH-NH3 /LiH-H2 O either from the metal center (LiH) or from ammonia/water lowers the IP and DIP compared to the neutral systems. In contrast, protonation increases these quantities compared to neutral systems. The protonation closes the inner valence state relaxation channels for ICD/ETMD. For example, the decay of the O-2s/N-2s state stops in protonated systems (LiH2 + -H2 O, LiH2 + -NH3 , and LiH-NH4 + ). Our study also shows that the efficiency, i. e., the rate of ICD/ETMD, can be altered by protonation and deprotonation. It is expected to have implications for chemical and biological systems.

Excitation dynamics in polyacene molecules on rare-gas clusters.

Laser-induced fluorescence spectra and excitation lifetimes of anthracene, tetracene, and pentacene molecules attached to the surface of solid argon clusters have been measured with respect to cluster size, density of molecules, and excitation density. Results are compared to previous studies on the same sample molecules attached to neon clusters. A contrasting lifetime behavior of anthracene on neon and argon clusters is discussed, and mechanisms are suggested to interpret the results. Although both neon and argon clusters are considered to be weakly interacting environments, we find that the excitation decay dynamics of the studied acenes depends significantly on the cluster material. Moreover, we find even qualitative differences regarding the dependence on the dopant density. Based on these observations, previous assignments of collective radiative and non-radiative decay mechanisms are discussed in the context of the new experimental findings.

Time-Resolved Pair-Correlated Imaging of the Photodissociation of Acetaldehyde at 267 nm: Pathway Partitioning.

Photodissociation of acetaldehyde (CH3CHO) by UV excitation involves interwoven multiple reaction pathways, including nonradiative decay, isomerization, transition-state pathway, roaming, and other dissociation mechanisms. Recently, we employed picosecond time-resolved, pair-correlated product imaging in a study of acetaldehyde photodissociation at 267 nm to disentangle those competing mechanisms and to elucidate the possible roaming pathways (Yang, C. H.; Chem. Sci. 2020, 11, 6423-6430). Here, we complement the pair-correlated product speed distribution of CO(v = 0) at the high-j side of the CO rotational state distribution in the CO + CH4 channel and detail the two-dimensional data analysis of the time-resolved images. As a result, extensive comparisons with other studies can be made and the branching fractions of the previously assigned TScc(S0), non-TScc(S0), and CI(S1/S0) pathways for the CO(v = 0) + CH4 molecular channel are evaluated to be 0.74 ± 0.08, 0.15 ± 0.02, and 0.11 ± 0.02, respectively. Together with the macroscopic branching ratio between the molecular (CO + CH4) and radical (CH3 + HCO) channels at 267 nm from the literature, a global view of the microscopic pathways can then be delineated, which provides invaluable insights and should pave the way for further studies of this interesting system.

Spectroscopic and Photophysical Investigation of Model Dipyrroles Common to Bilins: Exploring Natural Design for Steering Torsion to Divergent Functions.

Biliproteins are a unique class of photosynthetic proteins in their diverse, and at times, divergent biophysical function. The two contexts of photosynthetic light harvesting and photoreception demonstrate characteristically opposite criteria for success, with light harvesting demanding structurally-rigid chromophores which minimize excitation quenching, and photoreception requiring structural flexibility to enable conformational isomerization. The functional plasticity borne out in these two biological contexts is a consequence of the structural plasticity of the pigments utilized by biliproteins―linear tetrapyrroles, or bilins. In this work, the intrinsic flexibility of the bilin framework is investigated in a bottom-up fashion by reducing the active nuclear degrees of freedom through model dipyrrole subunits of the bilin core and terminus free of external protein interactions. Steady-state spectroscopy was carried out on the dipyrrole (DPY) and dipyrrinone (DPN) subunits free in solution to characterize their intrinsic spectroscopic properties including absorption strengths and nonradiative activity. Transient absorption (TA) spectroscopy was utilized to determine the mechanism and kinetics of nonradiative decay of the dipyrrole subunits, revealing dynamics dominated by rapid internal conversion with some Z→E isomerization observable in DPY. Computational analysis of the ground state conformational landscapes indicates enhanced complexity in the asymmetric terminal subunit, and the prediction was confirmed by heterogeneity of species and kinetics observed in TA. Taken together, the large oscillator strengths (f ∼ 0.6) of the dipyrrolic derivatives and chemically-efficient spectral tunability seen through the ∼100 nm difference in absorption spectra, validate Nature's "selection" of multi-pyrrole pigments for light capture applications. However, the rapid deactivation of the excited state via their natural torsional activity when free in solution would limit their effective biological function. Comparison with phytochrome and phycocyanin 645 crystal structures reveals binding motifs within the in vivo bilin environment that help to facilitate or inhibit specific inter-pyrrole twisting vital for protein operation.

Role of Conical Intersections on the Efficiency of Fluorescent Organic Molecular Crystals.

Organic molecular crystals are attractive materials for luminescent applications because of their promised tunability. However, the link between the chemical structure and emissive behavior is poorly understood because of the numerous interconnected factors which are at play in determining radiative and nonradiative behaviors at the solid-state level. In particular, the decay through conical intersection dominates the nonadiabatic regions of the potential energy surface, and thus, their accessibility is a telling indicator of the luminosity of the material. In this study, we investigate the radiative mechanism for five organic molecular crystals which display a solid-state emission, with a focus on the role of conical intersections in their photomechanisms. The objective is to situate the importance of the accessibility of conical intersections with regards to emissive behavior, taking into account other nonradiative decay channels, namely, vibrational decay, and exciton hopping. We begin by giving a brief overview of the structural patterns of the five systems within a larger pool of 13 crystals for a richer comparison. We observe that because of the prevalence of sheet like and herringbone packing in organic molecular crystals, the conformational diversity of crystal dimers is limited. Additionally, similarly spaced dimers have exciton coupling values of a similar order within a 50 meV interval. Next, we focus on three exemplary cases, where we disentangle the role of nonradiative decay mechanisms and show how rotational minimum energy conical intersections in vacuum lead to puckered ones in the crystal, increasing their instability upon crystallization in typical packing motifs. In contrast, molecules with puckered conical intersections in vacuum tend to conserve this trait upon crystallization, and therefore, their quantum yield of fluorescence is determined predominantly by other nonradiative decay mechanisms.

Excited state dynamics of protonated keto uracil: intersystem crossing pathways in competition

The relaxation dynamics of protonated keto uracil has been investigated through cryogenic UV photodissociation spectroscopy. Steady-state spectroscopy and time-resolved photochemistry, including pump-probe photodissociation and kinetics of appearance of photofragments, are monitored over 10 orders of magnitude as a function of excess energy imparted in the bright $$^{\mathrm {1}}\uppi \uppi $$ * state. Although photofragments are produced in the ground electronic state after internal conversion, the non-radiative decay mechanism abruptly changes with a slight increase of excess energy in the $$^{\mathrm {1}}\uppi \uppi $$ * state. At the band origin, a three-step decay involving electronic couplings to the charge transfer $$^{\mathrm {1}}\hbox {n}_{\text {o}}\uppi $$ * state and the triplet $$^{\mathrm {3}}\uppi \uppi $$ * state with lifetimes in the range of $$10\,{\upmu }\hbox {s}$$ and 2 ms, respectively, is proposed. However, the pathway through the charge transfer state closes a few hundreds of wavenumbers above the band origin. From this excess energy, the excited state population is transferred through a low energy barrier towards a region of the $$^{\mathrm {1}}\uppi \uppi $$ * potential energy surface where a triple crossing with the $$^{\mathrm {3}}\uppi \uppi $$ * state and the ground state is located. The experimental results are assigned with the help of ab initio calculations at the spin-component scaled coupled-cluster level.

Ancillary ligand increases the efficiency of heteroleptic Ir-based triplet emitters in OLED devices

The excellent contrast ratio, visibility, and advantages in producing thin and light displays let organic light emitting diodes change the paradigm of the display industry. To improve future display technologies, higher electroluminescence efficiency is needed. Herein, the detailed study of the non-radiative decay mechanism employing density functional theory calculations is carried out and a simple, general strategy for the design of the ancillary ligand is formulated. It is shown that steric bulk properly directed towards the phenylisoquinoline ligands can significantly reduce the non-radiative decay rate.

Electronic State and Photophysics of 2-Ethylhexyl-4-methoxycinnamate as UV-B Sunscreen under Jet-Cooled Condition.

The title compound, 2-ethylhexyl-4-methoxycinnamate (2EH4MC), is known as a typical ingredient of sunscreen cosmetics that effectively converts the absorbed UV-B light to thermal energy. This energy conversion process includes the nonradiative decay (NRD): trans-cis isomerization and finally going back to the original structure with a release of thermal energy. In this study, we performed UV spectroscopy for jet-cooled 2EH4MC to investigate the electronic/geometrical structures as well as the NRD mechanism. Laser-induced-fluorescence (LIF) spectroscopy gave the well-resolved vibronic structure of the S1-S0 transition; UV-UV hole-burning (HB) spectroscopy and density functional theory (DFT) calculations revealed the presence of syn and anti isomers, where the methoxy (-OCH3) groups orient in opposite directions to each other. Picosecond UV-UV pump-probe spectroscopy revealed the NRD process from the excited singlet (S1 (1ππ*)) state occurs at a rate constant of ∼1010-1011 s-1, attributed to internal conversion (IC) to the 1nπ* state. Nanosecond UV-deep UV (DUV) pump-probe spectroscopy identified a transient triplet (T1 (3ππ*)) state, whose energy (from S0) and lifetime are 18 400 cm-1 and 20 ns, respectively. These results demonstrate that the photoisomerization of 2EH4MC includes multistep internal conversions and intersystem crossings, described as "S1 (trans, 1ππ*) → 1nπ* → T1 (3ππ*) → S0 (cis)".

Synergistic Approach of Ultrafast Spectroscopy and Molecular Simulations in the Characterization of Intramolecular Charge Transfer in Push-Pull Molecules.

The comprehensive characterization of Intramolecular Charge Transfer (ICT) stemming in push-pull molecules with a delocalized π-system of electrons is noteworthy for a bespoke design of organic materials, spanning widespread applications from photovoltaics to nanomedicine imaging devices. Photo-induced ICT is characterized by structural reorganizations, which allows the molecule to adapt to the new electronic density distribution. Herein, we discuss recent photophysical advances combined with recent progresses in the computational chemistry of photoactive molecular ensembles. We focus the discussion on femtosecond Transient Absorption Spectroscopy (TAS) enabling us to follow the transition from a Locally Excited (LE) state to the ICT and to understand how the environment polarity influences radiative and non-radiative decay mechanisms. In many cases, the charge transfer transition is accompanied by structural rearrangements, such as the twisting or molecule planarization. The possibility of an accurate prediction of the charge-transfer occurring in complex molecules and molecular materials represents an enormous advantage in guiding new molecular and materials design. We briefly report on recent advances in ultrafast multidimensional spectroscopy, in particular, Two-Dimensional Electronic Spectroscopy (2DES), in unraveling the ICT nature of push-pull molecular systems. A theoretical description at the atomistic level of photo-induced molecular transitions can predict with reasonable accuracy the properties of photoactive molecules. In this framework, the review includes a discussion on the advances from simulation and modeling, which have provided, over the years, significant information on photoexcitation, emission, charge-transport, and decay pathways. Density Functional Theory (DFT) coupled with the Time-Dependent (TD) framework can describe electronic properties and dynamics for a limited system size. More recently, Machine Learning (ML) or deep learning approaches, as well as free-energy simulations containing excited state potentials, can speed up the calculations with transferable accuracy to more complex molecules with extended system size. A perspective on combining ultrafast spectroscopy with molecular simulations is foreseen for optimizing the design of photoactive compounds with tunable properties.

A Study of Temperature‐Dependent Photoluminescence from As‐Deposited and Heavy‐Ion‐Irradiated Plasma‐Enhanced Chemical Vapor Deposition‐Grown Si‐Rich a‐SiNx:H Thin Films

Temperature‐dependent photoluminescence (PL) measurements in the range of 10–300 K are carried out on silicon‐rich hydrogenated silicon nitride films deposited by plasma‐enhanced chemical vapor deposition. The in situ formation of Si quantum dots (QDs) with an average size of 3.5 nm is observed. The composition of thin films is estimated by Rutherford backscattering and ellipsometry. Broad PL spectra from thin films are decomposed into contributions from Si QDs, N dangling bonds (DBs), and Si DBs (K‐centers). At a low temperature, a strong PL can be observed, its quenching with increase in temperature is explained by the thermal activation of nonradiative decay mechanisms. Further, temperature‐dependent PL for swift heavy‐ion‐irradiated films shows similar quenching with increase in temperature. However, the effect of irradiation on the luminescence mechanisms of a‐SiNx:H is revealed at low temperatures (<120 K) only, whereby a relatively narrow peak around 2.0 eV emerges. These results clearly show the role of radiative defects in the luminescence from Si‐rich silicon nitride.

Modifying the Nonradiative Decay Dynamics through Conical Intersections via Collective Coupling to a Cavity Mode.

The coupling of a molecular ensemble to the confined electromagnetic modes of a microcavity can strongly modify the photophysics and photochemistry of the molecules upon photoexcitation. We investigate here how collective coupling effects lead to modifications of the mechanisms and rates of photochemical processes, in particular, photodissociation and nonradiative decay in NaI and pyrazine, respectively. We show that, after direct excitation into the lower polaritonic states, the lower-energy light-matter hybrid states, the dynamics of the molecular ensemble coupled to light is very similar to the dynamics of the corresponding isolated molecules. Conversely, excitation into the upper polaritonic states results in more complex dynamics that involve as a first step the population transfer toward the manifold of intermediate dark states. These dynamics differ substantially from those of the isolated molecules and may result in measurable time delays for nonradiative decay or excited-state reaction mechanisms. Similarly, we describe how addition of a buffer of nonreactive molecules coupled to the cavity mode can be used to delay the onset of the photochemical processes of the reactive part of the ensemble, where the buffer medium is more effective in inhibiting the reactive process than only reactive molecules in the cavity.

Understanding Aggregation Induced Emission in a Propeller‐Shaped Blue Emitter

AbstractOrganic fluorophores with an enhanced emission in the condensed phase have great potential for the design of optoelectronic materials. Several propeller‐shaped molecules show aggregation‐induced emission (AIE), in particular, silole derivatives have attracted wide attention because of their significant quantum yields in the solid state. In this contribution, we investigate the mechanism of AIE of a propeller‐shaped blue emitter: 1,2,3,4‐tetraphenyl‐1,3‐cyclopentadiene (TPC). We explore the excited state mechanism in the light of models most commonly used to explain it: restriction of intramolecular motions (RIM) and restricted access to the conical intersection (RACI). Our interpretation is supported by excited state dynamics simulations and the analysis of Huang‐Rhys factors and reorganisation energies. We quantify the effects of intermolecular interactions and exciton couplings. The mechanism for TPC is compared with previous investigations of analogue silole compounds. Our systematic investigation highlights the role of conical intersections on the nonradiative decay mechanisms and complementary descriptions provided by the RIM and RACI models.

Renner-Teller and pseudo-Renner-Teller interactions in the electronic ground and excited states of the dicyanoacetylene radical cation: Assignment of vibronic spectrum and elucidation of nonradiative and radiative decay mechanisms

Vibronic interactions in the first five energetically lowest electronic states (X̃2Πu-Ã2Σg+-B̃2Σu+-C̃2Πg-D̃2Πu) of dicyanoacetylene radical cation (C4N2·+) and their effect on the nuclear dynamics are examined in this article. The spectroscopy of C4N2·+ is a subject of outstanding complexity and addressed by the [see, the recent article, J. Chem. Phys. 139, 184304 (2013)]. The energetic ordering of electronic states and the emission mechanism of the states seem to have ambiguity. Here we have undertaken a detailed theoretical study in an attempt to resolve it. A vibronic coupling Hamiltonian of the five electronic states mentioned above is constructed in a diabatic electronic basis and with the aid of ab initio quantum chemistry calculations. Quantum nuclear dynamics studies are carried out by both time-independent and time-dependent quantum mechanical methods. The vibronic spectrum is calculated and the progressions are identified in terms of vibrational modes and compared with experimental slow photoelectron spectroscopy results. Renner-Teller (RT) coupling within the degenerate electronic states (X̃, C̃ and D̃) and the pseudo-Renner-Teller (PRT) coupling among states are examined in detail to elucidate their impact on the vibronic structure of the state and its decay mechanism to the ground (X̃) electronic state. While the dynamics of the X̃ and D̃ states is somewhat simple, the same of the Ã, B̃ and C̃ states is outstandingly complex due to strong RT and PRT interactions.