Molecular phosphorescence enhancement by the plasmon field of metal nanoparticles.

A theoretical model is proposed that allows the estimation of the quantum yield of phosphorescence of dye molecules in the vicinity of plasmonic nanoparticles. For this purpose, the rate constants of the radiative and nonradiative intramolecular transitions for rhodamine 123 (Rh123) and brominated rhodamine (Rh123-2Br) dyes have been calculated. The plasmon effect of Ag nanoparticles on various types of luminescence processes has been studied both theoretically and experimentally. We show that in the presence of a plasmonic nanoparticle, the efficiency of the immediate and delayed fluorescence increases significantly. The phosphorescence rate of the rhodamine dyes also increases near plasmonic nanoparticles. The long-lived luminescence i.e., delayed fluorescence and phosphorescence is more enhanced for Rh123-2Br than for Rh123. The largest phosphorescence quantum yield is obtained when the dye molecule is at a distance of 4-6 nm from the nanoparticle surface. Our results can be used in the design of plasmon-enhancing nanostructures for light-emitting media, organic light-emitting diodes, photovoltaic devices, and catalysts for activation of molecular oxygen.

Experimental and computational studies of the optical properties of 2,5,8-tris(phenylthiolato)heptazine with an inverted singlet-triplet gap.

Photophysical properties of the three-fold symmetric 2,5,8-tris(phenylthiolato)heptazine molecule (1) are studied from combined experimental and computational viewpoints. The intense blue photoemission of 1 in the solid state and in toluene solution is proposed to have a fluorescent origin on the basis of a relatively short emission lifetime and no detectable triplet decay. Calculations at correlated ab initio levels of theory also show that 1 has a large inverted singlet-triplet (IST) gap, a non-vanishing spin-orbit coupling matrix element between the first excited singlet and triplet states, and a fast intersystem crossing rate constant that leads to singlet population from the higher-lying triplet state. The IST gap implies that the first excited singlet state is the lowest excited one, agreeing with the measured fluorescent behaviour of 1. IST gaps are also obtained for the oxygen-containing (2) and selenium-containing (3) analogues of 1 at the ADC(2) level of theory, but not for the tellurium one (4). Calculations of the magnetically induced current density demonstrate that the heptazine core of 1 is globally non-aromatic due to the alternation of carbon and nitrogen atoms along its external rim.

Engineering Tunable Ratiometric Dual Emission in Single Emitter-based Amorphous Systems.

Molecular emitters with multi-emissive properties are in high demand in numerous fields, while these properties basically depend on specific molecular conformation and packing. For amorphous systems, special molecular arrangement is unnecessary, but it remains challenging to achieve such luminescent behaviors. Herein, we present a general strategy that takes advantage of molecular rigidity and S1 -T1 energy gap balance for emitter design, which enables fluorescence-phosphorescence dual-emission properties in various solid forms, whether crystalline or amorphous. Subsequently, the amorphism of the emitters based polymethyl methacrylate films endowed an in situ regulation of the dual-emissive characteristics. With the ratiometric regulation of phosphorescence by external stimuli and stable fluorescence as internal reference, highly controllable luminescent color tuning (yellow to blue including white emission) was achieved. There properties together with a persistent luminous behavior is of benefit for an irreplaceable set of optical information combination, featuring an ultrahigh-security anti-counterfeiting ability. Our research introduces a concept of eliminating the crystal-form and molecular-conformational dependence of complex luminescent properties through emitter molecular design. This has profound implications for the development of functional materials.

Large Gas-Phase Source of Esters and Other Accretion Products in the Atmosphere.

Dimeric accretion products have been observed both in atmospheric aerosol particles and in the gas phase. With their low volatilities, they are key contributors to the formation of new aerosol particles, acting as seeds for more volatile organic vapors to partition onto. Many particle-phase accretion products have been identified as esters. Various gas- and particle-phase formation pathways have been suggested for them, yet evidence remains inconclusive. In contrast, peroxide accretion products have been shown to form via gas-phase peroxy radical (RO2) cross reactions. Here, we show that these reactions can also be a major source of esters and other types of accretion products. We studied α-pinene ozonolysis using state-of-the-art chemical ionization mass spectrometry together with different isotopic labeling approaches and quantum chemical calculations, finding strong evidence for fast radical isomerization before accretion. Specifically, this isomerization seems to happen within the intermediate complex of two alkoxy (RO) radicals, which generally determines the branching of all RO2-RO2 reactions. Accretion products are formed when the radicals in the complex recombine. We found that RO with suitable structures can undergo extremely rapid C-C ß scissions before recombination, often resulting in ester products. We also found evidence of this previously overlooked RO2-RO2 reaction pathway forming alkyl accretion products and speculate that some earlier peroxide identifications may in fact be hemiacetals or ethers. Our findings help answer several outstanding questions on the sources of accretion products in organic aerosol and bridge our knowledge of the gas phase formation and particle phase detection of accretion products. As esters are inherently more stable than peroxides, this also impacts their further reactivity in the aerosol.

Highly Efficient Room-Temperature Light-Induced Synthesis of Polymer Dots: A Programming Control Paradigm of Polymer Nanostructurization from Single-Component Precursor.

Polymer dots (PDs) have raised considerable research interest due to their advantages of designable nanostructures, high biocompatibility, versatile photoluminescent properties, and recyclability as nanophase. However, there remains a lack of in situ, real-time, and noncontact methods for synthesizing PDs. Here we report a rational strategy to synthesize PDs through a well-designed single-component precursor (an asymmetrical donor-acceptor-donor' molecular structure) by photoirradiation at ambient temperature. In contrast to thermal processes that normally lack atomic economy, our method is mild and successive, based on an aggregation-promoted sulfonimidization triggered by photoinduced delocalized intrinsic radical cations for polymerization, followed by photooxidation for termination with structural shaping to form PDs. This synthetic approach excludes any external additives, rendering a conversion rate of the precursor exceeding 99%. The prepared PDs, as a single entity, can realize the integration of nanocore luminescence and precursor-transferred luminescence, showing 41.5% of the total absolute luminescence quantum efficiency, which is higher than most reported PD cases. Based on these photoluminescent properties, together with the superior biocompatibility, a unique membrane microenvironmental biodetection could be exemplified. This strategy with programming control of the single precursor can serve as a significant step toward polymer nanomanufacturing with remote control, high-efficiency, precision, and real-time operability.

Incorporation of a Fluorine Atom in a Bridging Ligand of Half-Lantern PtII2 Complexes Provides up to 10-Fold Enhancement of Electroluminescence Brightness.

The binuclear half-lantern platinum(II) complexes [Pt(pbt)(µ-S∧N)]2 (pbtH = 2-phenylbenzothiazole, S∧N = benzo[d]thiazole-2-thiolate Pt1, 6-fluorobenzo[d]thiazole-2-thiolate Pt2, 6-chlorobenzo[d]thiazole-2-thiolate Pt3, 6-bromobenzo[d]thiazole-2-thiolate Pt4, and 6-iodobenzo[d]thiazole-2-thiolate Pt5) were synthesized by the treatment of the in situ formed [Pt(pbt)(NCMe)2]NO3 complex and appropriate benzo[d]thiazole-2-thiole in the presence of tBuOK; yield: 51-84%. Complexes Pt1-5 exhibit intense red photoluminescence originated from 3MMLCT state reaching 22% room temperature quantum yields in a CH2Cl2 solution. All complexes display excited-state decay kinetics both in solution and in the solid state; the kinetics was adequately modeled by single exponentials. The complexes display more than 10-fold higher electroluminescence brightness for the F-containing Pt2 (900 cd/m2) and 2-fold higher electroluminescence brightness for the Cl-containing Pt3 (143 cd/m2) compared to the H-substituted complex Pt1 (77 cd/m2). It is argued that this impressive device luminance growth, occurred on formal replacement of H-to-F, is associated with the intermolecular strong hydrogen bonding H···F relevant to the H-bond found in the structure of Pt2.

Influence of plasmons on the luminescence properties of solvatochromic merocyanine dyes with different solvatochromism.

The effect of localized surface plasmon resonance (LSPR) of a system consisting of a highly dipolar merocyanine dye and a silver nanoparticle (NP) was studied experimentally and theoretically. A theoretical model for estimating the fluorescence quantum yield (φfl) using quantum chemical calculations of intramolecular and intermolecular electronic transition rate constants was developed. Calculations show that the main deactivation channels of the lowest excited singlet state of the studied merocyanines are internal conversion (kIC(S1 → S0)) and fluorescence (kr(S1 → S0)). The intersystem-crossing transition has a low probability due to the large energy difference between the singlet and triplet levels. In the presence of plasmonic NPs, the fluorescence quantum yield is increased by a factor of two according to both experiment and computations. The calculated values of φfl, when considering changes in kr(S1 → S0) and the energy-transfer rate constant (ktransfer) from the dye to the NP was also twice as large at distances of 6-8 nm between the NP and the dye molecule. We also found that the LSPR effect can be increased or decreased depending on the value of the dielectric constant (εm) of the environment.

Computational Investigation of Substituent Effects on the Alcohol + Carbonyl Channel of Peroxy Radical Self- and Cross-Reactions.

Organic peroxy radicals (RO2) are key intermediates in atmospheric chemistry and can undergo a large variety of both uni- and bimolecular reactions. One of the least understood reaction classes of RO2 are their self- and cross-reactions: RO2 + R'O2. In our previous work, we have investigated how RO2 + R'O2 reactions can lead to the formation of ROOR' accretion products through intersystem crossings and subsequent recombination of a triplet intermediate complex 3(RO···OR'). Accretion products can potentially have very low saturation vapor pressures, and may therefore participate in the formation of aerosol particles. In this work, we investigate the competing H-shift channel, which leads to the formation of more volatile carbonyl and alcohol products. This is one of the main, and sometimes the dominant, RO2 + R'O2 reaction channels for small RO2. We investigate how substituents (R and R' groups) affect the H-shift barriers and rates for a set of 3(RO···OR') complexes. The variation in barrier heights and rates is found to be surprisingly small, and most computed H-shift rates are fast: around 108-109 s-1. We find that the barrier height is affected by three competing factors: (1) the weakening of the breaking C-H bond due to interactions with adjacent functional groups; (2) the overall binding energy of the 3(RO···OR'), which tends to increase the barrier height; and (3) the thermodynamic stability of the reaction products. We also calculated intersystem crossing rate coefficients (ISC) for the same systems and found that most of them were of the same order of magnitude as the H-shift rates. This suggests that both studied channels are competitive for small and medium-sized RO2. However, for complex enough R or R' groups, the binding energy effect may render the H-shift channel uncompetitive with intersystem crossings (and thus ROOR' formation), as the rate of the latter, while variable, seems to be largely independent of system size. This may help explain the experimental observation that accretion product formation becomes highly effective for large and multifunctional RO2.

Photo- and Electroluminescent Neutral Iridium(III) Complexes Bearing Imidoylamidinate Ligands.

Imidoylamidinate-based heteroleptic bis(2-phenylbenzothiazole)iridium(III) and -rhodium(III) complexes [(bt)2M(N∩N)] (bt = 2-phenylbenzothiazole, N∩N = N'-(benzo[d]thiazol-2-yl)acetimidamidyl (Ir1 and Rh1), N'-(6-fluorobenzo[d]thiazol-2-yl)acetimidamidyl (Ir2), N'-(benzo[d]oxazol-2-yl)acetimidamidyl (Ir3), N'-(1-methyl-1H-benzo[d]imidazol-2-yl)acetimidamidyl (Ir4); yields 70-84%) were obtained by the reaction of the in situ-generated solvento-complex [(bt)2M(NCMe)2]NO3 and benzo[d]thia/oxa/N-methylimidozol-2-amines in the presence of NaOMe. Complexes Ir1-4 exhibited intense orange photoluminescence, reaching 37% at room temperature quantum yields, being immobilized in a poly(methyl methacrylate) matrix. A photophysical study of these species in a CH2Cl2 solution, neat powder, and frozen (77 K) MeOC2H4OH-EtOH glass matrix─along with density-functional theory (DFT), ab initio methods, and spin-orbit coupling time-dependent DFT calculations─verified the effects of substitution in the imidoylamidinate ligands on the excited-state properties. Electrochemical (cyclic voltammetry and differential pulse voltammetry) and theoretical DFT studies demonstrated noninnocent behavior of the imidoylamidinate ligands in Ir1-4 and Rh1 complexes due to the significant contribution coming from these ligands in the HOMO of the complexes. The iridium(III) species exhibit a ligand (L, 2-phenylbenzothiazole)-centered (3LC), metal-to-ligand (L', imidoylamidinate) charge-transfer (3ML'CT,3MLCT) character of their emission. The imidoylamidinate-based iridium(III) species were proved to be effective as the emissive dopant in an organic light-emitting diode device, fabricated in the framework of this study.

Non-intersecting ring currents in [12]infinitene.

The aromaticity of the newly synthesized [12]infinitene is addressed via analysis of the magnetically induced current density and the induced magnetic field. Our calculations reveal that [12]infinitene responds to an external magnetic field by creating two current-density pathways that flow diatropically along the edges of the molecule. The current-density pathways do not intersect. The entire structure is completely shielded suggesting that the infinitene molecule is aromatic, contrary to what the Möbius rule for twisted annulene structures predicts. We also studied the dication of [12]infinitene, which sustains two paratropic ring currents flowing along the edges. The space between the stacked rings at the crossing point is shorter for the dication as compared to the neutral molecule. Hence, a strong through-space current density appears at the crossing point of π-π stacked rings.

On the origin of the inverted singlet-triplet gap of the 5th generation light-emitting molecules.

Excitation energies of the lowest singlet and triplet state of molecules whose first excited singlet state lies energetically below the first triplet state have been studied computationally at (time-dependent) density functional theory, coupled-cluster, and second-order multiconfiguration perturbation theory levels. The calculations at the ab initio levels show that the singlet-triplet gap is inverted as compared to the one expected from Hund's rule, whereas all density functionals yield the triplet state as the lowest excited state. Double excitations responsible for the inverted singlet-triplet gap have been identified. Employing the spin-flip and ΔSCF methods, singlet-triplet inversion was obtained at the density functional theory level for some of the studied molecules.

Integration of global ring currents using the Ampère-Maxwell law.

Magnetically induced ring currents are calculated from the magnetic shielding tensor by employing the Ampère-Maxwell law. The feasibility of the method is demonstrated by integrating the zz component of the shielding tensor along the symmetry axis of highly symmetric ring-shaped aromatic, antiaromatic and nonaromatic molecules. The calculated ring-current strengths agree perfectly with the ones obtained by integrating the current-density flux passing through a plane cutting half the molecular ring. The method can be used in combination with all electronic structure codes capable of calculating nuclear magnetic resonance (NMR) shielding tensors in general points in space. We also show that nucleus independent chemical shifts (NICS) along the symmetry axis are related to the spatial derivative of the strength of the global ring-current along the z axis.

Magnetically induced ring currents in metallocenothiaporphyrins.

The magnetically induced current-density susceptibility tensor (CDT) of the lowest singlet and triplet states of the metallocenothiaporphyrins, where the metal is V, Cr, Mn, Fe, Co, Ni, Mo, Tc, Ru, or Rh, have been studied with the gauge-including magnetically induced currents (GIMIC) method. The compounds containing V, Mn, Co, Tc or Rh were studied as cations because the neutral molecules have an odd number of electrons. The calculations show that the aromatic nature of most of the studied molecules follows the Hückel and Baird rules of aromaticity. CDT calculations on the high-spin states of the neutral metallocenothiaporphyrins with V, Mn, Co, Tc or Rh also shows that these molecules follow a unified extended Hückel and Baird aromaticity orbital-count rule stating that molecules with an odd number of occupied conjugated valence orbitals are aromatic, whereas molecules with an even number of occupied conjugated orbitals are antiaromatic.

Odd-Number Cyclo[n]Carbons Sustaining Alternating Aromaticity.

Cyclo[n]carbons (n = 5, 7, 9, ..., 29) composed from an odd number of carbon atoms are studied computationally at density functional theory (DFT) and ab initio complete active space self-consistent field (CASSCF) levels of theory to get insight into their electronic structure and aromaticity. DFT calculations predict a strongly delocalized carbene structure of the cyclo[n]carbons and an aromatic character for all of them. In contrast, calculations at the CASSCF level yield geometrically bent and electronically localized carbene structures leading to an alternating double aromaticity of the odd-number cyclo[n]carbons. CASSCF calculations yield a singlet electronic ground state for the studied cyclo[n]carbons except for C25, whereas at the DFT level the energy difference between the lowest singlet and triplet states depends on the employed functional. The BHandHLYP functional predicts a triplet ground state of the larger odd-number cyclo[n]carbons starting from n = 13. Current-density calculations at the BHandHLYP level using the CASSCF-optimized molecular structures show that there is a through-space delocalization in the cyclo[n]carbons. The current density avoids the carbene carbon atom, leading to an alternating double aromaticity of the odd-number cyclo[n]carbons satisfying the antiaromatic [4k+1] and aromatic [4k+3] rules. C11, C15, and C19 are aromatic and can be prioritized in future synthesis. We predict a bond-shift phenomenon for the triplet state of the cyclo[n]carbons leading to resonance structures that have different reactivity toward dimerization.

Dianthracenylazatrioxa[8]circulene: Synthesis, Characterization and Application in OLEDs.

A soluble, green-blue fluorescent, π-extended azatrioxa[8]circulene was synthesized by oxidative condensation of a 3,6-dihydroxycarbazole and 1,4-anthraquinone by using benzofuran scaffolding. This is the first circulene to incorporate anthracene within its carbon framework. Solvent-dependent fluorescence and bright green electroluminescence accompanied by excimer emission are the key optical properties of this material. The presence of sliding π-stacked columns in the single crystal of dianthracenylazatrioxa[8]circulene is found to cause a very high electron-hopping rate, thus making this material a promising n-type organic semiconductor with an electron mobility predicted to be around 2.26 cm2 V-1 s-1 . The best organic light-emitting diode (OLED) device based on the dianthracenylazatrioxa[8]circulene fluorescent emitter has a brightness of around 16 000 Cd m-2 and an external quantum efficiency of 3.3 %. Quantum dot-based OLEDs were fabricated by using dianthracenylazatrioxa[8]circulene as a host matrix material.

Computational Investigation of the Formation of Peroxide (ROOR) Accretion Products in the OH- and NO3-Initiated Oxidation of α-Pinene.

The formation of accretion products ("dimers") from recombination reactions of peroxyl radicals (RO2) is a key step in the gas-phase generation of low-volatility vapors, leading to atmospheric aerosol particles. We have recently demonstrated that this recombination reaction very likely proceeds via an intermediate complex of two alkoxy radicals (RO···OR') and that the accretion product pathway involves an intersystem crossing (ISC) of this complex from the triplet to the singlet surface. However, ISC rates have hitherto not been computed for large and chemically complex RO···OR' systems actually relevant to atmospheric aerosol formation. Here, we carry out systematic conformational sampling and ISC rate calculations on 3(RO···OR') clusters formed in the recombination reactions of different diastereomers of the first-generation peroxyl radicals originating in both OH- and NO3-initiated reactions of α-pinene, a key biogenic hydrocarbon for atmospheric aerosol formation. While we find large differences between the ISC rates of different diastereomer pairs, all systems have ISC rates of at least 106 s-1, and many have rates exceeding 1010 s-1. Especially the latter value demonstrates that accretion product formation via the suggested pathway is a competitive process also for α-pinene-derived RO2 and likely explains the experimentally observed gas-phase formation of C20 compounds in α-pinene oxidation.

Perhalophenyl Three-Coordinate Gold(I) Complexes as TADF Emitters: A Photophysical Study from Experimental and Computational Viewpoints.

We report the synthesis of novel perhalophenyl three-coordinated gold(I) complexes using 1,2-bis(diphenylphosphino)benzene (dppBz) as the chelating ligand and [AuR(tht)] (R = C6F5, C6Cl2F3, C6Cl5) as the perhalophenyl-gold(I) source, leading to [AuR(dppBz)] (R = C6F5 (1), C6Cl2F3 (2), C6Cl5 (3)) complexes. The solid-state structures of compounds 2 and 3 consist of discrete three-coordinated Au(I) complexes, which show a distorted trigonal planar geometry for the gold center with dissimilar Au-P distances. The distorted structural arrangement is closely related to its photophysical properties. The studied complexes display very intense emissions at room temperature (RT) and at 77 K in the solid state. Studies of the emissive properties of the complexes at different temperatures suggest that the emissions are phosphorescent at 77 K and exhibit thermally activated delayed fluorescence (TADF) at RT. First-principle calculations of the photophysical processes yielded rate constants for intersystem crossing and reverse intersystem crossing that are in excellent agreement with experimental data.

Photophysical properties of the triangular [Au(HN[double bond, length as m-dash]COH)]3 complex and its dimer.

Rate constants for radiative and non-radiative transitions of the [Au(HN[double bond, length as m-dash]COH)]3 complex and its dimer were calculated within the Herzberg-Teller approximation based on quantum mechanical principles. A high triplet quantum yield was estimated for the monomer. Internal conversion (IC) was found to be the major competing process to the intersystem crossing (ISC) from the lowest excited singlet state (S1) to the lowest triplet state (T1). ISC and IC from the spin-mixed T[combining tilde]1 state also dominate the triplet relaxation process resulting in a negligible phosphorescence quantum yield for the monomer. The IC and ISC rate constants of the dimer are considerably smaller due to much lower Franck-Condon factors. For the dimer a triplet quantum yield of 0.71 was estimated using the extended multi-configuration quasi-degenerate second-order perturbation theory (XMCQDPT2) method to calculate the transition energies. Fluorescence is the major competing process to the ISC relaxation of the S1 state of the dimer. The ISC and IC processes are insignificant for the relaxation of the T1 state, resulting in unity phosphorescence quantum yield. The high triplet and phosphorescence quantum yields of the [Au(HN[double bond, length as m-dash]COH)]3 dimer make it and its higher oligomers potential candidates as dopants for phosphorescent organic light emitting diodes and as down-converters in solid-state lighting systems.

Comparing Reaction Routes for 3(RO···OR') Intermediates Formed in Peroxy Radical Self- and Cross-Reactions.

Organic peroxy radicals (RO2) are key intermediates in the chemistry of the atmosphere. One of the main sink reactions of RO2 is the recombination reaction RO2 + R'O2, which has three main channels (all with O2 as a coproduct): (1) R-H═O + R'OH, (2) RO + R'O, and (3) ROOR'. The RO + R'O "alkoxy" channel promotes radical and oxidant recycling, while the ROOR' "dimer" channel leads to low-volatility products relevant to aerosol processes. The ROOR' channel has only recently been discovered to play a role in the gas phase. Recent computational studies indicate that all of these channels first go through an intermediate complex 1(RO···3O2···OR'). Here, 3O2 is very weakly bound and will likely evaporate from the system, giving a triplet cluster of two alkoxy radicals: 3(RO···OR'). In this study, we systematically investigate the three reaction channels for an atmospherically representative set of RO + R'O radicals formed in the corresponding RO2 + R'O2 reaction. First, we systematically sample the possible conformations of the RO···OR' clusters on the triplet potential energy surface. Next, we compute energetic parameters and attempt to estimate reaction rate coefficients for the three channels: evaporation/dissociation to RO + R'O, a hydrogen shift leading to the formation of R'-H═O + ROH, and "spin-flip" (intersystem crossing) leading to, or at least allowing, the formation of ROOR' dimers. While large uncertainties in the computed energetics prevent a quantitative comparison of reaction rates, all three channels were found to be very fast (with typical rates greater than 106 s-1). This qualitatively demonstrates that the computationally proposed novel RO2 + R'O2 reaction mechanism is compatible with experimental data showing non-negligible branching ratios for all three channels, at least for sufficiently complex RO2.

Aromaticity of Even-Number Cyclo[n]carbons (n = 6-100).

The recently synthesized cyclo[18]carbon molecule has been characterized in a number of studies by calculating electronic, spectroscopic, and mechanical properties. However, cyclo[18]carbon is only one member of the class of cyclo[n]carbons-standalone carbon allotrope representatives. Many of the larger members of this class of molecules have not been thoroughly investigated. In this work, we calculate the magnetically induced current density of cyclo[n]carbons in order to elucidate how electron delocalization and aromatic properties change with the size of the molecular ring (n), where n is an even number between 6 and 100. We find that the Hückel rules for aromaticity (4k + 2) and antiaromaticity (4k) become degenerate for large Cn rings (n > 50), which can be understood as a transition from a delocalized electronic structure to a nonaromatic structure with localized current density fluxes in the triple bonds. Actually, the calculations suggest that cyclo[n]carbons with n > 50 are nonaromatic cyclic polyalkynes. The influence of the amount of nonlocal exchange and the asymptotic behavior of the exchange-correlation potential of the employed density functionals on the strength of the magnetically induced ring current and the aromatic character of the large cyclo[n]carbons is also discussed.